%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU731^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n024.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 : Wed Feb 25 09:36:44 AM UTC 2026
% Result : Theorem 29.32s 5.17s
% Output : Refutation 29.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 53 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 4210 (1153 equ; 0 cnn)
% Maximal formula atoms : 249 ( 79 avg)
% Number of connectives : 2372 ( 78 ~; 61 |; 775 &; 443 @)
% ( 7 <=>;1008 =>; 0 <=; 0 <~>)
% Maximal formula depth : 254 ( 37 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 446 ( 443 usr; 257 con; 0-4 aty)
% Number of variables : 100 ( 0 ^; 76 !; 24 ?; 100 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_184,type,
atmost1p: $i > $o ).
thf(func_def_185,type,
atleast2p: $i > $o ).
thf(func_def_186,type,
atmost2p: $i > $o ).
thf(func_def_187,type,
upairsetp: $i > $o ).
thf(func_def_191,type,
kfst: $i > $i ).
thf(func_def_203,type,
ksnd: $i > $i ).
thf(func_def_213,type,
breln: $i > $i > $i > $o ).
thf(func_def_214,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_222,type,
func: $i > $i > $i > $o ).
thf(func_def_223,type,
funcSet: $i > $i > $i ).
thf(func_def_226,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_232,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_259,type,
if: $i > $o > $i > $i > $i ).
thf(func_def_299,type,
sP0: $i > $i > $i > $o ).
thf(func_def_300,type,
sP1: $i > $i > $i > $i > $o ).
thf(func_def_303,type,
sP4: $i > $o > $i > $i > $o ).
thf(func_def_305,type,
sP6: $i > $i > $o ).
thf(func_def_306,type,
sP7: $i > $o ).
thf(func_def_307,type,
sP8: $i > $i > $o ).
thf(func_def_308,type,
sP9: $i > $i > $o ).
thf(func_def_311,type,
sK12: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_312,type,
sK13: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_313,type,
sK14: $i > $o ).
thf(func_def_314,type,
sK15: $i > $o ).
thf(func_def_315,type,
sK16: $i > $o ).
thf(func_def_317,type,
sK18: $i > $i > $i > $i ).
thf(func_def_321,type,
sK22: $i > $i > $i > $i ).
thf(func_def_323,type,
sK24: $i > $o ).
thf(func_def_328,type,
sK29: $i > $o ).
thf(func_def_335,type,
sK36: $i > $i > $i > $i > $i ).
thf(func_def_350,type,
sK51: $i > $i > $i > $i > $i ).
thf(func_def_351,type,
sK52: $i > $i > $i > $i > $i ).
thf(func_def_352,type,
sK53: $i > $i > $i > $i > $i ).
thf(func_def_353,type,
sK54: $i > $i > $i > $i > $i ).
thf(func_def_363,type,
sK64: $i > $i > $i > $i ).
thf(func_def_365,type,
sK66: $i > $o ).
thf(func_def_373,type,
sK74: $i > $o ).
thf(func_def_375,type,
sK76: ( $i > $o ) > $i ).
thf(func_def_376,type,
sK77: ( $i > $o ) > $i ).
thf(func_def_377,type,
sK78: $i > $o ).
thf(func_def_387,type,
sK88: $i > $i > $o ).
thf(func_def_392,type,
sK93: $i > $o ).
thf(func_def_393,type,
sK94: ( $i > $o ) > $i ).
thf(func_def_394,type,
sK95: $i > $i > $o ).
thf(func_def_396,type,
sK97: $i > $i ).
thf(func_def_397,type,
sK98: $i > $i ).
thf(func_def_398,type,
sK99: $i > ( $i > $i > $o ) > $i ).
thf(func_def_399,type,
sK100: $i > ( $i > $i > $o ) > $i ).
thf(func_def_400,type,
sK101: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_405,type,
sK106: $i > $i > $o ).
thf(func_def_409,type,
sK110: $i > $o ).
thf(func_def_413,type,
sK114: $i > $i > $o ).
thf(func_def_434,type,
sK135: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_435,type,
sK136: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_439,type,
sK140: $i > $o ).
thf(func_def_449,type,
sK150: ( $i > $i ) > $i > $i > $i ).
thf(func_def_452,type,
sK153: $i > $i ).
thf(func_def_490,type,
sK191: $i > $i > $o ).
thf(func_def_491,type,
sK192: $i > $i ).
thf(func_def_508,type,
sK209: $i > $i > $i > $i ).
thf(func_def_533,type,
sK234: $i > $i > $i > $i > $i ).
thf(func_def_534,type,
sK235: ( $i > $o ) > $i > $i ).
thf(func_def_536,type,
sK237: $i > $o ).
thf(func_def_543,type,
sK244: $i > $i > $i ).
thf(func_def_554,type,
sK255: $i > $o ).
thf(func_def_558,type,
sK259: $i > $i > $i ).
thf(func_def_560,type,
sK261: $i > $o ).
thf(func_def_579,type,
sK280: $i > $i ).
thf(func_def_593,type,
sK294: $i > $i > $o ).
thf(func_def_598,type,
sK299: $i > ( $i > $o ) > $i ).
thf(func_def_599,type,
sK300: $i > $o ).
thf(func_def_604,type,
sK305: $i > $i > $i ).
thf(func_def_618,type,
sK319: $i > $i ).
thf(func_def_630,type,
sK331: $i > $i > $i ).
thf(func_def_631,type,
sK332: $i > $i > $i ).
thf(func_def_632,type,
sK333: $i > $i > $i ).
thf(func_def_633,type,
sK334: $i > $i > $i ).
thf(func_def_634,type,
sK335: $i > $i > $i > $i ).
thf(func_def_635,type,
sK336: $i > $i ).
thf(func_def_636,type,
sK337: $i > $i ).
thf(func_def_637,type,
sK338: $i > $i ).
thf(func_def_638,type,
sK339: $i > $i ).
thf(func_def_639,type,
sK340: $i > $i > $i ).
thf(func_def_640,type,
sK341: $i > $i > $i > $i ).
thf(func_def_641,type,
sK342: $i > $i > $i > $i ).
thf(func_def_642,type,
sK343: $i > $i > $i ).
thf(func_def_643,type,
sK344: $i > $i > $i ).
thf(func_def_645,type,
sK346: $i > $i ).
thf(func_def_646,type,
sK347: $i > $i ).
thf(func_def_647,type,
sK348: $i > $i ).
thf(func_def_648,type,
sK349: $i > $i > $i ).
thf(func_def_654,type,
sK355: ( $i > $o ) > $i ).
thf(func_def_655,type,
sK356: $i > $o ).
thf(func_def_656,type,
sK357: $i > $i ).
thf(func_def_660,type,
sK361: $i > $i > $o ).
thf(func_def_686,type,
sK387: $i > $i > $i ).
thf(func_def_699,type,
sK400: $i > $o ).
thf(func_def_701,type,
sK402: ( $i > $o ) > $i > $i ).
thf(func_def_729,type,
sK430: $i > $o ).
thf(func_def_731,type,
sK432: ( $i > $o ) > $i > $i ).
thf(func_def_732,type,
sK433: ( $i > $o ) > $i > $i ).
thf(func_def_733,type,
sK434: $i > ( $i > $o ) > $i ).
thf(func_def_734,type,
sK435: $i > $o ).
thf(func_def_737,type,
sK438: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_738,type,
sK439: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_742,type,
sK443: $i > $o ).
thf(func_def_746,type,
sK447: $i > ( $i > $o ) > $i ).
thf(func_def_747,type,
sK448: $i > $o ).
thf(func_def_760,type,
sK461: $i > $i ).
thf(func_def_762,type,
sK463: $i > $i ).
thf(func_def_766,type,
sK467: $i > $i ).
thf(func_def_768,type,
sK469: ( $i > $i ) > $i > $i > $i ).
thf(func_def_777,type,
sK478: $i > $i > $i > $i > $i ).
thf(func_def_778,type,
sK479: $i > $i > $i > $i > $i ).
thf(func_def_779,type,
sK480: $i > $i > $i ).
thf(func_def_782,type,
sK483: $i > $o ).
thf(func_def_791,type,
sK492: $i > $i > $i ).
thf(func_def_808,type,
sK509: $i > $o ).
thf(func_def_811,type,
sK512: $i > ( $i > $o ) > $i ).
thf(func_def_830,type,
sK531: $i > $o ).
thf(func_def_845,type,
sK546: $i > $i > $i > $i > $i ).
thf(func_def_870,type,
sK571: $i > $i > $o ).
thf(func_def_876,type,
sK577: $i > $i > $i ).
thf(func_def_877,type,
sK578: $i > $i > $i ).
thf(func_def_881,type,
sK582: $i > $o ).
thf(func_def_886,type,
sK587: $i > $o ).
thf(func_def_887,type,
sK588: $i > $o ).
thf(func_def_888,type,
sK589: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_889,type,
sK590: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_902,type,
sK603: $i > $i > $i > $i ).
thf(func_def_903,type,
sK604: $i > $i > $i > $i ).
thf(func_def_906,type,
sK607: $i > $o ).
thf(func_def_912,type,
sK613: $i > $o ).
thf(func_def_918,type,
sK619: $i > $i ).
thf(func_def_920,type,
sK621: $i > ( $i > $i ) > $i > $i ).
thf(func_def_923,type,
sK624: $i > $i ).
thf(func_def_928,type,
sK629: $i > $o ).
thf(func_def_930,type,
sK631: $i > ( $i > $o ) > $i ).
thf(func_def_931,type,
sK632: ( $i > $o ) > $i > $i ).
thf(func_def_933,type,
sK634: $i > $o ).
thf(func_def_945,type,
sK646: $i > $i ).
thf(func_def_947,type,
sK648: ( $i > $i ) > $i > $i > $i ).
thf(func_def_950,type,
sK651: $i > $i ).
thf(func_def_951,type,
sK652: $i > ( $i > $o ) > $i > $i ).
thf(func_def_953,type,
sK654: $i > $o ).
thf(func_def_957,type,
sK658: $i > $i ).
thf(func_def_960,type,
sK661: $i > $i > ( $i > $i ) > $i ).
thf(func_def_979,type,
sK680: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_980,type,
sK681: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_983,type,
sK684: $i > $o ).
thf(func_def_984,type,
sK685: $i > $o ).
thf(func_def_991,type,
sK692: ( $i > $o ) > $i ).
thf(func_def_992,type,
sK693: $i > $o ).
thf(func_def_993,type,
sK694: $i > $i ).
thf(func_def_1010,type,
sK711: $i > $i > $i ).
thf(func_def_1027,type,
sK728: $i > $o ).
thf(func_def_1029,type,
sK730: $i > ( $i > $o ) > $i ).
thf(func_def_1037,type,
sK738: $i > $i ).
thf(func_def_1039,type,
sK740: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1040,type,
sK741: $i > $i > $i ).
thf(func_def_1056,type,
sK757: $i > $o ).
thf(func_def_1058,type,
sK759: ( $i > $o ) > $i > $i ).
thf(func_def_1059,type,
sK760: ( $i > $o ) > $i > $i ).
thf(func_def_1071,type,
sK772: $o > $i > $i > $i ).
thf(func_def_1080,type,
ph781:
!>[X0: $tType] : X0 ).
thf(f15015,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f15014,f2428]) ).
thf(f2428,plain,
( ( in @ sK71 @ ( powerset @ sK70 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f1204]) ).
thf(f1204,plain,
( ( binunionLsub = $true )
& ( powersetTI1 = $true )
& ( doubleComplementE1 = $true )
& ( dpsetconstrI = $true )
& ( setminusER = $true )
& ( doubleComplementSub2 = $true )
& ( ap2apEq1 = $true )
& ( cartprodsndpairEq = $true )
& ( noeltsimpempty = $true )
& ( setukpairinjR2 = $true )
& ( prop2set2propI = $true )
& ( setukpairIL = $true )
& ( infuncsetfunc = $true )
& ( ifp = $true )
& ( funcImageSingleton = $true )
& ( setunion__Cong = $true )
& ( binintersectSubset4 = $true )
& ( upairsetE = $true )
& ( binintersectEL = $true )
& ( emptyinunitempty = $true )
& ( binintersectTELcontra = $true )
& ( subsetI2 = $true )
& ( kpairp = $true )
& ( dsetconstrEL = $true )
& ( emptyE1 = $true )
& ( setukpairinjL2 = $true )
& ( exu__Cong = $true )
& ( ex1I = $true )
& ( binunionRsub = $true )
& ( ex1E1 = $true )
& ( exuE1 = $true )
& ( setukpairinjL1 = $true )
& ( nonemptyI1 = $true )
& ( subsetTrans = $true )
& ( lam2p = $true )
& ( eqimpsubset1 = $true )
& ( exuI3 = $true )
& ( dpsetconstrER = $true )
& ( secondinupair = $true )
& ( iftrueProp2 = $true )
& ( singletoninpowerset = $true )
& ( setukpairinjR12 = $true )
& ( setminusI = $true )
& ( quantDeMorgan2 = $true )
& ( powerset__Cong = $true )
& ( upairsetIR = $true )
& ( notsubsetI = $true )
& ( emptyinPowerset = $true )
& ( funcGraphProp2 = $true )
& ( exuI2 = $true )
& ( emptyset__Cong = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( cartprodpairin = $true )
& ( funcext2 = $true )
& ( cartprodmempair1 = $true )
& ( theprop = $true )
& ( funcGraphProp1 = $true )
& ( emptyInPowerset = $true )
& ( ksndsingleton = $true )
& ( iffalseProp2 = $true )
& ( setadjoinOr = $true )
& ( bs114d = $true )
& ( setukpairinjR = $true )
& ( doubleComplementI1 = $true )
& ( ifSingleton = $true )
& ( exuE3e = $true )
& ( replAx = $true )
& ( subsetemptysetimpeq = $true )
& ( wellorderingAx = $true )
& ( binintersectSubset1 = $true )
& ( cartprodmempaircEq = $true )
& ( setunionsingleton1 = $true )
& ( setukpairinjR11 = $true )
& ( dsetconstr__Cong = $true )
& ( setminusERneg = $true )
& ( disjointsetsI1 = $true )
& ( nonemptyI = $true )
& ( cartprodpairmemER = $true )
& ( powersetTE1 = $true )
& ( kfstsingleton = $true )
& ( iffalseProp1 = $true )
& ( setunionsingleton2 = $true )
& ( setminusSubset1 = $true )
& ( setminusELneg = $true )
& ( subsetTI = $true )
& ( ubforcartprodlem2 = $true )
& ( powersetE = $true )
& ( ap2p = $true )
& ( eta1 = $true )
& ( binintersectT_lem = $true )
& ( funcGraphProp3 = $true )
& ( binintersectSubset3 = $true )
& ( setadjoinIL = $true )
& ( setukpairinjL = $true )
& ( setadjoinSub = $true )
& ( nonemptyImpWitness = $true )
& ( sepInPowerset = $true )
& ( upairequniteq = $true )
& ( setminusIRneg = $true )
& ( kpairiskpair = $true )
& ( notinemptyset = $true )
& ( subsetI1 = $true )
& ( binintersectRsub = $true )
& ( exuI1 = $true )
& ( upairset2IR = $true )
& ( cartprodmempair = $true )
& ( setextsub = $true )
& ( binunionIR = $true )
& ( binintersectER = $true )
& ( subbreln = $true )
& ( ap2apEq2 = $true )
& ( binunionE = $true )
& ( beta2 = $true )
& ( symdiffI1 = $true )
& ( powersetT_lem = $true )
& ( descrp = $true )
& ( setukpairinjR1 = $true )
& ( contrasubsetT2 = $true )
& ( omegaIndAx = $true )
& ( setunionI = $true )
& ( cartprodpairmemEL = $true )
& ( descr__Cong = $true )
& ( prop2setE = $true )
& ( dpsetconstrERa = $true )
& ( complementT_lem = $true )
& ( binintersectSubset2 = $true )
& ( emptysetAx = $true )
& ( symdiffE = $true )
& ( binunionT_lem = $true )
& ( setadjoinE = $true )
& ( powersetI1 = $true )
& ( cartprodfstpairEq = $true )
& ( theeq = $true )
& ( powersetI = $true )
& ( dpsetconstrEL1 = $true )
& ( quantDeMorgan4 = $true )
& ( notequalI2 = $true )
& ( binintersectTERcontra = $true )
& ( lam2lamEq = $true )
& ( setunionE = $true )
& ( eqinunit = $true )
& ( setminusILneg = $true )
& ( setext = $true )
& ( ubforcartprodlem1 = $true )
& ( dsetconstrI = $true )
& ( kpairsurjEq = $true )
& ( binunionEcases = $true )
& ( setOfPairsIsBReln = $true )
& ( apProp = $true )
& ( setminusSubset2 = $true )
& ( contrasubsetT = $true )
& ( funcGraphProp4 = $true )
& ( omegaSAx = $true )
& ( eqbreln = $true )
& ( emptysetimpfalse = $true )
& ( symdiffI2 = $true )
& ( setminusT_lem = $true )
& ( upairsubunion = $true )
& ( quantDeMorgan1 = $true )
& ( notdexE = $true )
& ( eqimpsubset2 = $true )
& ( ubforcartprodlem3 = $true )
& ( omega0Ax = $true )
& ( emptysetsubset = $true )
& ( sepSubset = $true )
& ( setadjoinSub2 = $true )
& ( iftrueProp1 = $true )
& ( setadjoinAx = $true )
& ( setextAx = $true )
& ( lamProp = $true )
& ( setunionAx = $true )
& ( setbeta = $true )
& ( contrasubsetT1 = $true )
& ( subset2powerset = $true )
& ( subsetE2 = $true )
& ( in__Cong = $true )
& ( symdiffIneg2 = $true )
& ( singletonsswitch = $true )
& ( setadjoinIR = $true )
& ( notdallE = $true )
& ( setoftrueEq = $true )
& ( singletonsubset = $true )
& ( exuE2 = $true )
& ( binunionIL = $true )
& ( dsetconstrER = $true )
& ( iftrueorfalse = $true )
& ( emptysetE = $true )
& ( omega__Cong = $true )
& ( doubleComplementSub1 = $true )
& ( powersetAx = $true )
& ( funcinfuncset = $true )
& ( symdiffIneg1 = $true )
& ( notequalI1 = $true )
& ( ex1E2 = $true )
& ( upairsetIL = $true )
& ( uniqinunit = $true )
& ( prop2setI = $true )
& ( ( setminus @ sK70 @ ( setminus @ sK70 @ sK71 ) )
!= sK71 )
& ( ( in @ sK71 @ ( powerset @ sK70 ) )
= $true )
& ( app = $true )
& ( dpsetconstrSub = $true )
& ( emptyI = $true )
& ( subPowSU = $true )
& ( brelnall1 = $true )
& ( exuEu = $true )
& ( complementTE1 = $true )
& ( ex1I2 = $true )
& ( lamp = $true )
& ( iftrue = $true )
& ( singletonprop = $true )
& ( dpsetconstrEL2 = $true )
& ( eta2 = $true )
& ( ksndpairEq = $true )
& ( setunionE2 = $true )
& ( subsetRefl = $true )
& ( setminusEL = $true )
& ( funcextLem = $true )
& ( setadjoin__Cong = $true )
& ( setukpairIR = $true )
& ( cartprodsndin = $true )
& ( cartprodpairsurjEq = $true )
& ( singletoninpowunion = $true )
& ( binintersectI = $true )
& ( binintersectLsub = $true )
& ( contrasubsetT3 = $true )
& ( inCongP = $true )
& ( setextT = $true )
& ( complementTI1 = $true )
& ( binintersectSubset5 = $true )
& ( setminusLsub = $true )
& ( upairinpowunion = $true )
& ( upairset2E = $true )
& ( beta1 = $true )
& ( cartprodfstin = $true )
& ( iffalse = $true )
& ( notinsingleton = $true )
& ( quantDeMorgan3 = $true )
& ( subsetE = $true )
& ( singletonsuniq = $true )
& ( exuE3u = $true )
& ( vacuousDall = $true )
& ( foundationAx = $true )
& ( brelnall2 = $true )
& ( setunionsingleton = $true )
& ( powersetE1 = $true )
& ( funcext = $true )
& ( kfstpairEq = $true )
& ( nonemptyE1 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK70,sK71])],[f1020,f1203]) ).
thf(f1203,plain,
( ? [X0: $i,X1: $i] :
( ( ( setminus @ X0 @ ( setminus @ X0 @ X1 ) )
!= X1 )
& ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) ) )
=> ( ( ( setminus @ sK70 @ ( setminus @ sK70 @ sK71 ) )
!= sK71 )
& ( ( in @ sK71 @ ( powerset @ sK70 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1020,plain,
( ( binunionLsub = $true )
& ( powersetTI1 = $true )
& ( doubleComplementE1 = $true )
& ( dpsetconstrI = $true )
& ( setminusER = $true )
& ( doubleComplementSub2 = $true )
& ( ap2apEq1 = $true )
& ( cartprodsndpairEq = $true )
& ( noeltsimpempty = $true )
& ( setukpairinjR2 = $true )
& ( prop2set2propI = $true )
& ( setukpairIL = $true )
& ( infuncsetfunc = $true )
& ( ifp = $true )
& ( funcImageSingleton = $true )
& ( setunion__Cong = $true )
& ( binintersectSubset4 = $true )
& ( upairsetE = $true )
& ( binintersectEL = $true )
& ( emptyinunitempty = $true )
& ( binintersectTELcontra = $true )
& ( subsetI2 = $true )
& ( kpairp = $true )
& ( dsetconstrEL = $true )
& ( emptyE1 = $true )
& ( setukpairinjL2 = $true )
& ( exu__Cong = $true )
& ( ex1I = $true )
& ( binunionRsub = $true )
& ( ex1E1 = $true )
& ( exuE1 = $true )
& ( setukpairinjL1 = $true )
& ( nonemptyI1 = $true )
& ( subsetTrans = $true )
& ( lam2p = $true )
& ( eqimpsubset1 = $true )
& ( exuI3 = $true )
& ( dpsetconstrER = $true )
& ( secondinupair = $true )
& ( iftrueProp2 = $true )
& ( singletoninpowerset = $true )
& ( setukpairinjR12 = $true )
& ( setminusI = $true )
& ( quantDeMorgan2 = $true )
& ( powerset__Cong = $true )
& ( upairsetIR = $true )
& ( notsubsetI = $true )
& ( emptyinPowerset = $true )
& ( funcGraphProp2 = $true )
& ( exuI2 = $true )
& ( emptyset__Cong = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( cartprodpairin = $true )
& ( funcext2 = $true )
& ( cartprodmempair1 = $true )
& ( theprop = $true )
& ( funcGraphProp1 = $true )
& ( emptyInPowerset = $true )
& ( ksndsingleton = $true )
& ( iffalseProp2 = $true )
& ( setadjoinOr = $true )
& ( bs114d = $true )
& ( setukpairinjR = $true )
& ( doubleComplementI1 = $true )
& ( ifSingleton = $true )
& ( exuE3e = $true )
& ( replAx = $true )
& ( subsetemptysetimpeq = $true )
& ( wellorderingAx = $true )
& ( binintersectSubset1 = $true )
& ( cartprodmempaircEq = $true )
& ( setunionsingleton1 = $true )
& ( setukpairinjR11 = $true )
& ( dsetconstr__Cong = $true )
& ( setminusERneg = $true )
& ( disjointsetsI1 = $true )
& ( nonemptyI = $true )
& ( cartprodpairmemER = $true )
& ( powersetTE1 = $true )
& ( kfstsingleton = $true )
& ( iffalseProp1 = $true )
& ( setunionsingleton2 = $true )
& ( setminusSubset1 = $true )
& ( setminusELneg = $true )
& ( subsetTI = $true )
& ( ubforcartprodlem2 = $true )
& ( powersetE = $true )
& ( ap2p = $true )
& ( eta1 = $true )
& ( binintersectT_lem = $true )
& ( funcGraphProp3 = $true )
& ( binintersectSubset3 = $true )
& ( setadjoinIL = $true )
& ( setukpairinjL = $true )
& ( setadjoinSub = $true )
& ( nonemptyImpWitness = $true )
& ( sepInPowerset = $true )
& ( upairequniteq = $true )
& ( setminusIRneg = $true )
& ( kpairiskpair = $true )
& ( notinemptyset = $true )
& ( subsetI1 = $true )
& ( binintersectRsub = $true )
& ( exuI1 = $true )
& ( upairset2IR = $true )
& ( cartprodmempair = $true )
& ( setextsub = $true )
& ( binunionIR = $true )
& ( binintersectER = $true )
& ( subbreln = $true )
& ( ap2apEq2 = $true )
& ( binunionE = $true )
& ( beta2 = $true )
& ( symdiffI1 = $true )
& ( powersetT_lem = $true )
& ( descrp = $true )
& ( setukpairinjR1 = $true )
& ( contrasubsetT2 = $true )
& ( omegaIndAx = $true )
& ( setunionI = $true )
& ( cartprodpairmemEL = $true )
& ( descr__Cong = $true )
& ( prop2setE = $true )
& ( dpsetconstrERa = $true )
& ( complementT_lem = $true )
& ( binintersectSubset2 = $true )
& ( emptysetAx = $true )
& ( symdiffE = $true )
& ( binunionT_lem = $true )
& ( setadjoinE = $true )
& ( powersetI1 = $true )
& ( cartprodfstpairEq = $true )
& ( theeq = $true )
& ( powersetI = $true )
& ( dpsetconstrEL1 = $true )
& ( quantDeMorgan4 = $true )
& ( notequalI2 = $true )
& ( binintersectTERcontra = $true )
& ( lam2lamEq = $true )
& ( setunionE = $true )
& ( eqinunit = $true )
& ( setminusILneg = $true )
& ( setext = $true )
& ( ubforcartprodlem1 = $true )
& ( dsetconstrI = $true )
& ( kpairsurjEq = $true )
& ( binunionEcases = $true )
& ( setOfPairsIsBReln = $true )
& ( apProp = $true )
& ( setminusSubset2 = $true )
& ( contrasubsetT = $true )
& ( funcGraphProp4 = $true )
& ( omegaSAx = $true )
& ( eqbreln = $true )
& ( emptysetimpfalse = $true )
& ( symdiffI2 = $true )
& ( setminusT_lem = $true )
& ( upairsubunion = $true )
& ( quantDeMorgan1 = $true )
& ( notdexE = $true )
& ( eqimpsubset2 = $true )
& ( ubforcartprodlem3 = $true )
& ( omega0Ax = $true )
& ( emptysetsubset = $true )
& ( sepSubset = $true )
& ( setadjoinSub2 = $true )
& ( iftrueProp1 = $true )
& ( setadjoinAx = $true )
& ( setextAx = $true )
& ( lamProp = $true )
& ( setunionAx = $true )
& ( setbeta = $true )
& ( contrasubsetT1 = $true )
& ( subset2powerset = $true )
& ( subsetE2 = $true )
& ( in__Cong = $true )
& ( symdiffIneg2 = $true )
& ( singletonsswitch = $true )
& ( setadjoinIR = $true )
& ( notdallE = $true )
& ( setoftrueEq = $true )
& ( singletonsubset = $true )
& ( exuE2 = $true )
& ( binunionIL = $true )
& ( dsetconstrER = $true )
& ( iftrueorfalse = $true )
& ( emptysetE = $true )
& ( omega__Cong = $true )
& ( doubleComplementSub1 = $true )
& ( powersetAx = $true )
& ( funcinfuncset = $true )
& ( symdiffIneg1 = $true )
& ( notequalI1 = $true )
& ( ex1E2 = $true )
& ( upairsetIL = $true )
& ( uniqinunit = $true )
& ( prop2setI = $true )
& ? [X0: $i,X1: $i] :
( ( ( setminus @ X0 @ ( setminus @ X0 @ X1 ) )
!= X1 )
& ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) ) )
& ( app = $true )
& ( dpsetconstrSub = $true )
& ( emptyI = $true )
& ( subPowSU = $true )
& ( brelnall1 = $true )
& ( exuEu = $true )
& ( complementTE1 = $true )
& ( ex1I2 = $true )
& ( lamp = $true )
& ( iftrue = $true )
& ( singletonprop = $true )
& ( dpsetconstrEL2 = $true )
& ( eta2 = $true )
& ( ksndpairEq = $true )
& ( setunionE2 = $true )
& ( subsetRefl = $true )
& ( setminusEL = $true )
& ( funcextLem = $true )
& ( setadjoin__Cong = $true )
& ( setukpairIR = $true )
& ( cartprodsndin = $true )
& ( cartprodpairsurjEq = $true )
& ( singletoninpowunion = $true )
& ( binintersectI = $true )
& ( binintersectLsub = $true )
& ( contrasubsetT3 = $true )
& ( inCongP = $true )
& ( setextT = $true )
& ( complementTI1 = $true )
& ( binintersectSubset5 = $true )
& ( setminusLsub = $true )
& ( upairinpowunion = $true )
& ( upairset2E = $true )
& ( beta1 = $true )
& ( cartprodfstin = $true )
& ( iffalse = $true )
& ( notinsingleton = $true )
& ( quantDeMorgan3 = $true )
& ( subsetE = $true )
& ( singletonsuniq = $true )
& ( exuE3u = $true )
& ( vacuousDall = $true )
& ( foundationAx = $true )
& ( brelnall2 = $true )
& ( setunionsingleton = $true )
& ( powersetE1 = $true )
& ( funcext = $true )
& ( kfstpairEq = $true )
& ( nonemptyE1 = $true ) ),
inference(flattening,[status(thm)],[f1019]) ).
thf(f1019,plain,
( ? [X0: $i,X1: $i] :
( ( ( setminus @ X0 @ ( setminus @ X0 @ X1 ) )
!= X1 )
& ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) ) )
& ( doubleComplementSub2 = $true )
& ( doubleComplementSub1 = $true )
& ( doubleComplementE1 = $true )
& ( doubleComplementI1 = $true )
& ( contrasubsetT3 = $true )
& ( contrasubsetT2 = $true )
& ( contrasubsetT1 = $true )
& ( contrasubsetT = $true )
& ( binintersectTERcontra = $true )
& ( binintersectTELcontra = $true )
& ( complementTE1 = $true )
& ( complementTI1 = $true )
& ( powersetTE1 = $true )
& ( powersetTI1 = $true )
& ( subsetTI = $true )
& ( setextT = $true )
& ( complementT_lem = $true )
& ( setminusT_lem = $true )
& ( powersetT_lem = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true )
& ( iftrueorfalse = $true )
& ( iffalse = $true )
& ( iftrue = $true )
& ( theeq = $true )
& ( ifp = $true )
& ( ifSingleton = $true )
& ( iftrueProp2 = $true )
& ( iftrueProp1 = $true )
& ( iffalseProp2 = $true )
& ( iffalseProp1 = $true )
& ( eta2 = $true )
& ( beta2 = $true )
& ( lam2lamEq = $true )
& ( eta1 = $true )
& ( beta1 = $true )
& ( ap2apEq2 = $true )
& ( ap2apEq1 = $true )
& ( funcext2 = $true )
& ( funcext = $true )
& ( eqbreln = $true )
& ( subbreln = $true )
& ( funcGraphProp4 = $true )
& ( funcextLem = $true )
& ( funcGraphProp2 = $true )
& ( funcGraphProp3 = $true )
& ( funcGraphProp1 = $true )
& ( ex1E2 = $true )
& ( brelnall2 = $true )
& ( brelnall1 = $true )
& ( lam2p = $true )
& ( lamp = $true )
& ( lamProp = $true )
& ( funcinfuncset = $true )
& ( ap2p = $true )
& ( infuncsetfunc = $true )
& ( app = $true )
& ( apProp = $true )
& ( funcImageSingleton = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrEL2 = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrERa = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrI = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodsndin = $true )
& ( kpairsurjEq = $true )
& ( ksndpairEq = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( setukpairinjR2 = $true )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f401]) ).
thf(f401,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ( ( ap2p = $true )
=> ( ( funcinfuncset = $true )
=> ( ( lamProp = $true )
=> ( ( lamp = $true )
=> ( ( lam2p = $true )
=> ( ( brelnall1 = $true )
=> ( ( brelnall2 = $true )
=> ( ( ex1E2 = $true )
=> ( ( funcGraphProp1 = $true )
=> ( ( funcGraphProp3 = $true )
=> ( ( funcGraphProp2 = $true )
=> ( ( funcextLem = $true )
=> ( ( funcGraphProp4 = $true )
=> ( ( subbreln = $true )
=> ( ( eqbreln = $true )
=> ( ( funcext = $true )
=> ( ( funcext2 = $true )
=> ( ( ap2apEq1 = $true )
=> ( ( ap2apEq2 = $true )
=> ( ( beta1 = $true )
=> ( ( eta1 = $true )
=> ( ( lam2lamEq = $true )
=> ( ( beta2 = $true )
=> ( ( eta2 = $true )
=> ( ( iffalseProp1 = $true )
=> ( ( iffalseProp2 = $true )
=> ( ( iftrueProp1 = $true )
=> ( ( iftrueProp2 = $true )
=> ( ( ifSingleton = $true )
=> ( ( ifp = $true )
=> ( ( theeq = $true )
=> ( ( iftrue = $true )
=> ( ( iffalse = $true )
=> ( ( iftrueorfalse = $true )
=> ( ( binintersectT_lem = $true )
=> ( ( binunionT_lem = $true )
=> ( ( powersetT_lem = $true )
=> ( ( setminusT_lem = $true )
=> ( ( complementT_lem = $true )
=> ( ( setextT = $true )
=> ( ( subsetTI = $true )
=> ( ( powersetTI1 = $true )
=> ( ( powersetTE1 = $true )
=> ( ( complementTI1 = $true )
=> ( ( complementTE1 = $true )
=> ( ( binintersectTELcontra = $true )
=> ( ( binintersectTERcontra = $true )
=> ( ( contrasubsetT = $true )
=> ( ( contrasubsetT1 = $true )
=> ( ( contrasubsetT2 = $true )
=> ( ( contrasubsetT3 = $true )
=> ( ( doubleComplementI1 = $true )
=> ( ( doubleComplementE1 = $true )
=> ( ( doubleComplementSub1 = $true )
=> ( ( doubleComplementSub2 = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
=> ( ( setminus @ X0 @ ( setminus @ X0 @ X1 ) )
= X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f400]) ).
thf(f400,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( ( setminus @ X0 @ ( setminus @ X0 @ X1 ) )
= X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f253]) ).
thf(f253,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ! [X3: $i,X11: $i] :
( ( in @ X11 @ ( powerset @ X3 ) )
=> ( ( setminus @ X3 @ ( setminus @ X3 @ X11 ) )
= X11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f252]) ).
thf(f252,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ! [X3: $i,X11: $i] :
( ( in @ X11 @ ( powerset @ X3 ) )
=> ( ( setminus @ X3 @ ( setminus @ X3 @ X11 ) )
= X11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.dOeEUbrAIn/DTF2THF_3484.p',doubleComplementEq) ).
thf(f15014,plain,
( ( in @ sK71 @ ( powerset @ sK70 ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f15001]) ).
thf(f15001,plain,
( ( sK71 != sK71 )
| ( ( in @ sK71 @ ( powerset @ sK70 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f2429,f11161]) ).
thf(f11161,plain,
! [X0: $i,X1: $i] :
( ( ( setminus @ X1 @ ( setminus @ X1 @ X0 ) )
= X0 )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f11160,f4837]) ).
thf(f4837,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) @ X1 )
= $true )
| ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f3953]) ).
thf(f3953,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) @ X1 )
= $true )
| ( $true != $true )
| ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f2974,f2622]) ).
thf(f2622,plain,
doubleComplementSub2 = $true,
inference(cnf_transformation,[status(thm)],[f1204]) ).
thf(f2974,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) )
| ( ( subset @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) @ X1 )
= $true )
| ( doubleComplementSub2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f1613]) ).
thf(f1613,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) )
| ( ( subset @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) @ X1 )
= $true ) )
| ( doubleComplementSub2 != $true ) )
& ( ( doubleComplementSub2 = $true )
| ( ( $true
= ( in @ sK330 @ ( powerset @ sK329 ) ) )
& ( ( subset @ ( setminus @ sK329 @ ( setminus @ sK329 @ sK330 ) ) @ sK330 )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK329,sK330])],[f1611,f1612]) ).
thf(f1612,plain,
( ? [X2: $i,X3: $i] :
( ( $true
= ( in @ X3 @ ( powerset @ X2 ) ) )
& ( ( subset @ ( setminus @ X2 @ ( setminus @ X2 @ X3 ) ) @ X3 )
!= $true ) )
=> ( ( $true
= ( in @ sK330 @ ( powerset @ sK329 ) ) )
& ( ( subset @ ( setminus @ sK329 @ ( setminus @ sK329 @ sK330 ) ) @ sK330 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1611,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) )
| ( ( subset @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) @ X1 )
= $true ) )
| ( doubleComplementSub2 != $true ) )
& ( ( doubleComplementSub2 = $true )
| ? [X2: $i,X3: $i] :
( ( $true
= ( in @ X3 @ ( powerset @ X2 ) ) )
& ( ( subset @ ( setminus @ X2 @ ( setminus @ X2 @ X3 ) ) @ X3 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f1610]) ).
thf(f1610,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) )
| ( ( subset @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) @ X1 )
= $true ) )
| ( doubleComplementSub2 != $true ) )
& ( ( doubleComplementSub2 = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
& ( ( subset @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) @ X1 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f814]) ).
thf(f814,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) )
| ( ( subset @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) @ X1 )
= $true ) )
<=> ( doubleComplementSub2 = $true ) ),
inference(ennf_transformation,[status(thm)],[f493]) ).
thf(f493,plain,
( ( doubleComplementSub2 = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
=> ( ( subset @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f492]) ).
thf(f492,plain,
( doubleComplementSub2
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f251]) ).
thf(f251,axiom,
( doubleComplementSub2
= ( ! [X3: $i,X11: $i] :
( ( in @ X11 @ ( powerset @ X3 ) )
=> ( subset @ ( setminus @ X3 @ ( setminus @ X3 @ X11 ) ) @ X11 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.dOeEUbrAIn/DTF2THF_3484.p',doubleComplementSub2) ).
thf(f11160,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( setminus @ X1 @ ( setminus @ X1 @ X0 ) )
= X0 )
| ( $true
!= ( subset @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f11159]) ).
thf(f11159,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( subset @ ( setminus @ X1 @ ( setminus @ X1 @ X0 ) ) @ X0 ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( setminus @ X1 @ ( setminus @ X1 @ X0 ) )
= X0 ) ),
inference(superposition,[status(thm)],[f4684,f4628]) ).
thf(f4628,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) )
= $true )
| ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f4398]) ).
thf(f4398,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) )
= $true )
| ( $true != $true )
| ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f3458,f2438]) ).
thf(f2438,plain,
doubleComplementSub1 = $true,
inference(cnf_transformation,[status(thm)],[f1204]) ).
thf(f3458,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) )
| ( ( subset @ X1 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) )
= $true )
| ( doubleComplementSub1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f2174]) ).
thf(f2174,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) )
| ( ( subset @ X1 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) )
= $true ) )
| ( doubleComplementSub1 != $true ) )
& ( ( doubleComplementSub1 = $true )
| ( ( ( in @ sK710 @ ( powerset @ sK709 ) )
= $true )
& ( $true
!= ( subset @ sK710 @ ( setminus @ sK709 @ ( setminus @ sK709 @ sK710 ) ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK709,sK710])],[f2172,f2173]) ).
thf(f2173,plain,
( ? [X2: $i,X3: $i] :
( ( $true
= ( in @ X3 @ ( powerset @ X2 ) ) )
& ( $true
!= ( subset @ X3 @ ( setminus @ X2 @ ( setminus @ X2 @ X3 ) ) ) ) )
=> ( ( ( in @ sK710 @ ( powerset @ sK709 ) )
= $true )
& ( $true
!= ( subset @ sK710 @ ( setminus @ sK709 @ ( setminus @ sK709 @ sK710 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2172,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) )
| ( ( subset @ X1 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) )
= $true ) )
| ( doubleComplementSub1 != $true ) )
& ( ( doubleComplementSub1 = $true )
| ? [X2: $i,X3: $i] :
( ( $true
= ( in @ X3 @ ( powerset @ X2 ) ) )
& ( $true
!= ( subset @ X3 @ ( setminus @ X2 @ ( setminus @ X2 @ X3 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2171]) ).
thf(f2171,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) )
| ( ( subset @ X1 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) )
= $true ) )
| ( doubleComplementSub1 != $true ) )
& ( ( doubleComplementSub1 = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
& ( ( subset @ X1 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f831]) ).
thf(f831,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) )
| ( ( subset @ X1 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) )
= $true ) )
<=> ( doubleComplementSub1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f549]) ).
thf(f549,plain,
( ( doubleComplementSub1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
=> ( ( subset @ X1 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f548]) ).
thf(f548,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ X1 @ ( setminus @ X0 @ ( setminus @ X0 @ X1 ) ) ) )
= doubleComplementSub1 ),
inference(rectify,[status(thm)],[f250]) ).
thf(f250,axiom,
! [X3: $i,X11: $i] :
( ( ( in @ X11 @ ( powerset @ X3 ) )
=> ( subset @ X11 @ ( setminus @ X3 @ ( setminus @ X3 @ X11 ) ) ) )
= doubleComplementSub1 ),
file('/export/starexec/sandbox/tmp/tmp.dOeEUbrAIn/DTF2THF_3484.p',doubleComplementSub1) ).
thf(f4684,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ X0 ) )
| ( $true
!= ( subset @ X0 @ X1 ) )
| ( X0 = X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f4093]) ).
thf(f4093,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( subset @ X1 @ X0 ) )
| ( $true
!= ( subset @ X0 @ X1 ) )
| ( X0 = X1 ) ),
inference(definition_unfolding,[status(thm)],[f3154,f2520]) ).
thf(f2520,plain,
setextsub = $true,
inference(cnf_transformation,[status(thm)],[f1204]) ).
thf(f3154,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X0 @ X1 ) )
| ( $true
!= ( subset @ X1 @ X0 ) )
| ( X0 = X1 )
| ( setextsub != $true ) ),
inference(cnf_transformation,[status(thm)],[f1808]) ).
thf(f1808,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X0 @ X1 ) )
| ( $true
!= ( subset @ X1 @ X0 ) )
| ( X0 = X1 ) )
| ( setextsub != $true ) )
& ( ( setextsub = $true )
| ( ( ( subset @ sK459 @ sK460 )
= $true )
& ( $true
= ( subset @ sK460 @ sK459 ) )
& ( sK460 != sK459 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK459,sK460])],[f1806,f1807]) ).
thf(f1807,plain,
( ? [X2: $i,X3: $i] :
( ( ( subset @ X2 @ X3 )
= $true )
& ( ( subset @ X3 @ X2 )
= $true )
& ( X2 != X3 ) )
=> ( ( ( subset @ sK459 @ sK460 )
= $true )
& ( $true
= ( subset @ sK460 @ sK459 ) )
& ( sK460 != sK459 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1806,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X0 @ X1 ) )
| ( $true
!= ( subset @ X1 @ X0 ) )
| ( X0 = X1 ) )
| ( setextsub != $true ) )
& ( ( setextsub = $true )
| ? [X2: $i,X3: $i] :
( ( ( subset @ X2 @ X3 )
= $true )
& ( ( subset @ X3 @ X2 )
= $true )
& ( X2 != X3 ) ) ) ),
inference(rectify,[status(thm)],[f1805]) ).
thf(f1805,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X0 @ X1 ) )
| ( $true
!= ( subset @ X1 @ X0 ) )
| ( X0 = X1 ) )
| ( setextsub != $true ) )
& ( ( setextsub = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( subset @ X0 @ X1 ) )
& ( $true
= ( subset @ X1 @ X0 ) )
& ( X0 != X1 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f936]) ).
thf(f936,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X0 @ X1 ) )
| ( $true
!= ( subset @ X1 @ X0 ) )
| ( X0 = X1 ) )
<=> ( setextsub = $true ) ),
inference(flattening,[status(thm)],[f935]) ).
thf(f935,plain,
( ( setextsub = $true )
<=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( $true
!= ( subset @ X1 @ X0 ) )
| ( $true
!= ( subset @ X0 @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f640]) ).
thf(f640,plain,
( ( setextsub = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X0 @ X1 ) )
=> ( ( $true
= ( subset @ X1 @ X0 ) )
=> ( X0 = X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f639]) ).
thf(f639,plain,
( setextsub
= ( ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f93]) ).
thf(f93,axiom,
( setextsub
= ( ! [X3: $i,X4: $i] :
( ( subset @ X3 @ X4 )
=> ( ( subset @ X4 @ X3 )
=> ( X3 = X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.dOeEUbrAIn/DTF2THF_3484.p',setextsub) ).
thf(f2429,plain,
( ( setminus @ sK70 @ ( setminus @ sK70 @ sK71 ) )
!= sK71 ),
inference(cnf_transformation,[status(thm)],[f1204]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU731^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.25 % Computer : n024.cluster.edu
% 0.08/0.25 % Model : x86_64 x86_64
% 0.08/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.25 % Memory : 8042.1875MB
% 0.08/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.25 % CPULimit : 300
% 0.08/0.25 % WCLimit : 300
% 0.08/0.25 % DateTime : Tue Feb 24 07:32:10 EST 2026
% 0.08/0.25 % CPUTime :
% 0.08/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.32 ---- Original DTF file ---
% 0.08/0.32 thf(spec,logic,$$dhol).
% 0.08/0.32 %------------------------------------------------------------------------------
% 0.08/0.32 % File : SEU731^1 : TPTP v9.2.1. Released v3.7.0.
% 0.08/0.32 % Domain : Set Theory
% 0.08/0.32 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.08/0.32 % Version : Especial.
% 0.08/0.32 % English : (! A:i.! X:i.in X (powerset A) -> X = setminus A (setminus A X))
% 0.08/0.32
% 0.08/0.32 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.08/0.32 % Source : [Bro08]
% 0.08/0.32 % Names : ZFC233g [Bro08]
% 0.08/0.32
% 0.08/0.32 % Status : Theorem
% 0.08/0.32 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0, 0.29 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0, 1.00 v3.7.0
% 0.08/0.32 % Syntax : Number of formulae : 537 ( 251 unt; 285 typ; 251 def)
% 0.08/0.32 % Number of atoms : 1439 ( 377 equ; 0 cnn)
% 0.08/0.32 % Maximal formula atoms : 249 ( 5 avg)
% 0.08/0.32 % Number of connectives : 2850 ( 64 ~; 12 |; 44 &;2021 @)
% 0.08/0.32 % ( 14 <=>; 695 =>; 0 <=; 0 <~>)
% 0.08/0.32 % Maximal formula depth : 253 ( 2 avg)
% 0.08/0.32 % Number of types : 2 ( 0 usr)
% 0.08/0.32 % Number of type conns : 132 ( 132 >; 0 *; 0 +; 0 <<)
% 0.08/0.32 % Number of symbols : 288 ( 285 usr; 251 con; 0-4 aty)
% 0.08/0.32 % Number of variables : 842 ( 74 ^; 733 !; 35 ?; 842 :)
% 0.08/0.32 % SPC : TH0_THM_EQU_NAR
% 0.08/0.32
% 0.08/0.32 % Comments : http://mathgate.info/detsetitem.php?id=291
% 0.08/0.32 %------------------------------------------------------------------------------
% 0.08/0.32 thf(in_type,type,
% 0.08/0.32 in: $i > $i > $o ).
% 0.08/0.32
% 0.08/0.32 thf(exu_type,type,
% 0.08/0.32 exu: ( $i > $o ) > $o ).
% 0.08/0.32
% 0.08/0.32 thf(exu,definition,
% 0.08/0.32 ( exu
% 0.08/0.32 = ( ^ [Xphi: $i > $o] :
% 0.08/0.32 ? [Xx: $i] :
% 0.08/0.32 ( ( Xphi @ Xx )
% 0.08/0.32 & ! [Xy: $i] :
% 0.08/0.32 ( ( Xphi @ Xy )
% 0.08/0.32 => ( Xx = Xy ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setextAx_type,type,
% 0.08/0.32 setextAx: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setextAx,definition,
% 0.08/0.32 ( setextAx
% 0.08/0.32 = ( ! [A: $i,B: $i] :
% 0.08/0.32 ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 <=> ( in @ Xx @ B ) )
% 0.08/0.32 => ( A = B ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(emptyset_type,type,
% 0.08/0.32 emptyset: $i ).
% 0.08/0.32
% 0.08/0.32 thf(emptysetAx_type,type,
% 0.08/0.32 emptysetAx: $o ).
% 0.08/0.32
% 0.08/0.32 thf(emptysetAx,definition,
% 0.08/0.32 ( emptysetAx
% 0.08/0.32 = ( ! [Xx: $i] :
% 0.08/0.32 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setadjoin_type,type,
% 0.08/0.32 setadjoin: $i > $i > $i ).
% 0.08/0.32
% 0.08/0.32 thf(setadjoinAx_type,type,
% 0.08/0.32 setadjoinAx: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setadjoinAx,definition,
% 0.08/0.32 ( setadjoinAx
% 0.08/0.32 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.08/0.32 <=> ( ( Xy = Xx )
% 0.08/0.32 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(powerset_type,type,
% 0.08/0.32 powerset: $i > $i ).
% 0.08/0.32
% 0.08/0.32 thf(powersetAx_type,type,
% 0.08/0.32 powersetAx: $o ).
% 0.08/0.32
% 0.08/0.32 thf(powersetAx,definition,
% 0.08/0.32 ( powersetAx
% 0.08/0.32 = ( ! [A: $i,B: $i] :
% 0.08/0.32 ( ( in @ B @ ( powerset @ A ) )
% 0.08/0.32 <=> ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ B )
% 0.08/0.32 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setunion_type,type,
% 0.08/0.32 setunion: $i > $i ).
% 0.08/0.32
% 0.08/0.32 thf(setunionAx_type,type,
% 0.08/0.32 setunionAx: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setunionAx,definition,
% 0.08/0.32 ( setunionAx
% 0.08/0.32 = ( ! [A: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ ( setunion @ A ) )
% 0.08/0.32 <=> ? [B: $i] :
% 0.08/0.32 ( ( in @ Xx @ B )
% 0.08/0.32 & ( in @ B @ A ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(omega_type,type,
% 0.08/0.32 omega: $i ).
% 0.08/0.32
% 0.08/0.32 thf(omega0Ax_type,type,
% 0.08/0.32 omega0Ax: $o ).
% 0.08/0.32
% 0.08/0.32 thf(omega0Ax,definition,
% 0.08/0.32 ( omega0Ax
% 0.08/0.32 = ( in @ emptyset @ omega ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(omegaSAx_type,type,
% 0.08/0.32 omegaSAx: $o ).
% 0.08/0.32
% 0.08/0.32 thf(omegaSAx,definition,
% 0.08/0.32 ( omegaSAx
% 0.08/0.32 = ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ omega )
% 0.08/0.32 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(omegaIndAx_type,type,
% 0.08/0.32 omegaIndAx: $o ).
% 0.08/0.32
% 0.08/0.32 thf(omegaIndAx,definition,
% 0.08/0.32 ( omegaIndAx
% 0.08/0.32 = ( ! [A: $i] :
% 0.08/0.32 ( ( ( in @ emptyset @ A )
% 0.08/0.32 & ! [Xx: $i] :
% 0.08/0.32 ( ( ( in @ Xx @ omega )
% 0.08/0.32 & ( in @ Xx @ A ) )
% 0.08/0.32 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.08/0.32 => ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ omega )
% 0.08/0.32 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(replAx_type,type,
% 0.08/0.32 replAx: $o ).
% 0.08/0.32
% 0.08/0.32 thf(replAx,definition,
% 0.08/0.32 ( replAx
% 0.08/0.32 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.08/0.32 ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( exu
% 0.08/0.32 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.08/0.32 => ? [B: $i] :
% 0.08/0.32 ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ B )
% 0.08/0.32 <=> ? [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ A )
% 0.08/0.32 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(foundationAx_type,type,
% 0.08/0.32 foundationAx: $o ).
% 0.08/0.32
% 0.08/0.32 thf(foundationAx,definition,
% 0.08/0.32 ( foundationAx
% 0.08/0.32 = ( ! [A: $i] :
% 0.08/0.32 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.08/0.32 => ? [B: $i] :
% 0.08/0.32 ( ( in @ B @ A )
% 0.08/0.32 & ~ ? [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ B )
% 0.08/0.32 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(wellorderingAx_type,type,
% 0.08/0.32 wellorderingAx: $o ).
% 0.08/0.32
% 0.08/0.32 thf(wellorderingAx,definition,
% 0.08/0.32 ( wellorderingAx
% 0.08/0.32 = ( ! [A: $i] :
% 0.08/0.32 ? [B: $i] :
% 0.08/0.32 ( ! [C: $i] :
% 0.08/0.32 ( ( in @ C @ B )
% 0.08/0.32 => ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ C )
% 0.08/0.32 => ( in @ Xx @ A ) ) )
% 0.08/0.32 & ! [Xx: $i,Xy: $i] :
% 0.08/0.32 ( ( ( in @ Xx @ A )
% 0.08/0.32 & ( in @ Xy @ A ) )
% 0.08/0.32 => ( ! [C: $i] :
% 0.08/0.32 ( ( in @ C @ B )
% 0.08/0.32 => ( ( in @ Xx @ C )
% 0.08/0.32 <=> ( in @ Xy @ C ) ) )
% 0.08/0.32 => ( Xx = Xy ) ) )
% 0.08/0.32 & ! [C: $i,D: $i] :
% 0.08/0.32 ( ( ( in @ C @ B )
% 0.08/0.32 & ( in @ D @ B ) )
% 0.08/0.32 => ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ C )
% 0.08/0.32 => ( in @ Xx @ D ) )
% 0.08/0.32 | ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ D )
% 0.08/0.32 => ( in @ Xx @ C ) ) ) )
% 0.08/0.32 & ! [C: $i] :
% 0.08/0.32 ( ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ C )
% 0.08/0.32 => ( in @ Xx @ A ) )
% 0.08/0.32 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.08/0.32 => ? [D: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ D @ B )
% 0.08/0.32 & ( in @ Xx @ C )
% 0.08/0.32 & ~ ? [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ D )
% 0.08/0.32 & ( in @ Xy @ C ) )
% 0.08/0.32 & ! [E: $i] :
% 0.08/0.32 ( ( in @ E @ B )
% 0.08/0.32 => ( ! [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ E )
% 0.08/0.32 => ( in @ Xy @ D ) )
% 0.08/0.32 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(descr_type,type,
% 0.08/0.32 descr: ( $i > $o ) > $i ).
% 0.08/0.32
% 0.08/0.32 thf(descrp_type,type,
% 0.08/0.32 descrp: $o ).
% 0.08/0.32
% 0.08/0.32 thf(descrp,definition,
% 0.08/0.32 ( descrp
% 0.08/0.32 = ( ! [Xphi: $i > $o] :
% 0.08/0.32 ( ( exu
% 0.08/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.08/0.32 => ( Xphi
% 0.08/0.32 @ ( descr
% 0.08/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(dsetconstr_type,type,
% 0.08/0.32 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.08/0.32
% 0.08/0.32 thf(dsetconstrI_type,type,
% 0.08/0.32 dsetconstrI: $o ).
% 0.08/0.32
% 0.08/0.32 thf(dsetconstrI,definition,
% 0.08/0.32 ( dsetconstrI
% 0.08/0.32 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( ( Xphi @ Xx )
% 0.08/0.32 => ( in @ Xx
% 0.08/0.32 @ ( dsetconstr @ A
% 0.08/0.32 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(dsetconstrEL_type,type,
% 0.08/0.32 dsetconstrEL: $o ).
% 0.08/0.32
% 0.08/0.32 thf(dsetconstrEL,definition,
% 0.08/0.32 ( dsetconstrEL
% 0.08/0.32 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx
% 0.08/0.32 @ ( dsetconstr @ A
% 0.08/0.32 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.08/0.32 => ( in @ Xx @ A ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(dsetconstrER_type,type,
% 0.08/0.32 dsetconstrER: $o ).
% 0.08/0.32
% 0.08/0.32 thf(dsetconstrER,definition,
% 0.08/0.32 ( dsetconstrER
% 0.08/0.32 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx
% 0.08/0.32 @ ( dsetconstr @ A
% 0.08/0.32 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.08/0.32 => ( Xphi @ Xx ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(exuE1_type,type,
% 0.08/0.32 exuE1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(exuE1,definition,
% 0.08/0.32 ( exuE1
% 0.08/0.32 = ( ! [Xphi: $i > $o] :
% 0.08/0.32 ( ( exu
% 0.08/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.08/0.32 => ? [Xx: $i] :
% 0.08/0.32 ( ( Xphi @ Xx )
% 0.08/0.32 & ! [Xy: $i] :
% 0.08/0.32 ( ( Xphi @ Xy )
% 0.08/0.32 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(prop2set_type,type,
% 0.08/0.32 prop2set: $o > $i ).
% 0.08/0.32
% 0.08/0.32 thf(prop2setE_type,type,
% 0.08/0.32 prop2setE: $o ).
% 0.08/0.32
% 0.08/0.32 thf(prop2setE,definition,
% 0.08/0.32 ( prop2setE
% 0.08/0.32 = ( ! [Xphi: $o,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.08/0.32 => Xphi ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(emptysetE_type,type,
% 0.08/0.32 emptysetE: $o ).
% 0.08/0.32
% 0.08/0.32 thf(emptysetE,definition,
% 0.08/0.32 ( emptysetE
% 0.08/0.32 = ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ emptyset )
% 0.08/0.32 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(emptysetimpfalse_type,type,
% 0.08/0.32 emptysetimpfalse: $o ).
% 0.08/0.32
% 0.08/0.32 thf(emptysetimpfalse,definition,
% 0.08/0.32 ( emptysetimpfalse
% 0.08/0.32 = ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ emptyset )
% 0.08/0.32 => $false ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(notinemptyset_type,type,
% 0.08/0.32 notinemptyset: $o ).
% 0.08/0.32
% 0.08/0.32 thf(notinemptyset,definition,
% 0.08/0.32 ( notinemptyset
% 0.08/0.32 = ( ! [Xx: $i] :
% 0.08/0.32 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(exuE3e_type,type,
% 0.08/0.32 exuE3e: $o ).
% 0.08/0.32
% 0.08/0.32 thf(exuE3e,definition,
% 0.08/0.32 ( exuE3e
% 0.08/0.32 = ( ! [Xphi: $i > $o] :
% 0.08/0.32 ( ( exu
% 0.08/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.08/0.32 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setext_type,type,
% 0.08/0.32 setext: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setext,definition,
% 0.08/0.32 ( setext
% 0.08/0.32 = ( ! [A: $i,B: $i] :
% 0.08/0.32 ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( in @ Xx @ B ) )
% 0.08/0.32 => ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ B )
% 0.08/0.32 => ( in @ Xx @ A ) )
% 0.08/0.32 => ( A = B ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(emptyI_type,type,
% 0.08/0.32 emptyI: $o ).
% 0.08/0.32
% 0.08/0.32 thf(emptyI,definition,
% 0.08/0.32 ( emptyI
% 0.08/0.32 = ( ! [A: $i] :
% 0.08/0.32 ( ! [Xx: $i] :
% 0.08/0.32 ~ ( in @ Xx @ A )
% 0.08/0.32 => ( A = emptyset ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(noeltsimpempty_type,type,
% 0.08/0.32 noeltsimpempty: $o ).
% 0.08/0.32
% 0.08/0.32 thf(noeltsimpempty,definition,
% 0.08/0.32 ( noeltsimpempty
% 0.08/0.32 = ( ! [A: $i] :
% 0.08/0.32 ( ! [Xx: $i] :
% 0.08/0.32 ~ ( in @ Xx @ A )
% 0.08/0.32 => ( A = emptyset ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setbeta_type,type,
% 0.08/0.32 setbeta: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setbeta,definition,
% 0.08/0.32 ( setbeta
% 0.08/0.32 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( ( in @ Xx
% 0.08/0.32 @ ( dsetconstr @ A
% 0.08/0.32 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.08/0.32 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(nonempty_type,type,
% 0.08/0.32 nonempty: $i > $o ).
% 0.08/0.32
% 0.08/0.32 thf(nonempty,definition,
% 0.08/0.32 ( nonempty
% 0.08/0.32 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(nonemptyE1_type,type,
% 0.08/0.32 nonemptyE1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(nonemptyE1,definition,
% 0.08/0.32 ( nonemptyE1
% 0.08/0.32 = ( ! [A: $i] :
% 0.08/0.32 ( ( nonempty @ A )
% 0.08/0.32 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(nonemptyI_type,type,
% 0.08/0.32 nonemptyI: $o ).
% 0.08/0.32
% 0.08/0.32 thf(nonemptyI,definition,
% 0.08/0.32 ( nonemptyI
% 0.08/0.32 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( ( Xphi @ Xx )
% 0.08/0.32 => ( nonempty
% 0.08/0.32 @ ( dsetconstr @ A
% 0.08/0.32 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(nonemptyI1_type,type,
% 0.08/0.32 nonemptyI1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(nonemptyI1,definition,
% 0.08/0.32 ( nonemptyI1
% 0.08/0.32 = ( ! [A: $i] :
% 0.08/0.32 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.08/0.32 => ( nonempty @ A ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setadjoinIL_type,type,
% 0.08/0.32 setadjoinIL: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setadjoinIL,definition,
% 0.08/0.32 ( setadjoinIL
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(emptyinunitempty_type,type,
% 0.08/0.32 emptyinunitempty: $o ).
% 0.08/0.32
% 0.08/0.32 thf(emptyinunitempty,definition,
% 0.08/0.32 ( emptyinunitempty
% 0.08/0.32 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setadjoinIR_type,type,
% 0.08/0.32 setadjoinIR: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setadjoinIR,definition,
% 0.08/0.32 ( setadjoinIR
% 0.08/0.32 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ A )
% 0.08/0.32 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setadjoinE_type,type,
% 0.08/0.32 setadjoinE: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setadjoinE,definition,
% 0.08/0.32 ( setadjoinE
% 0.08/0.32 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.08/0.32 => ! [Xphi: $o] :
% 0.08/0.32 ( ( ( Xy = Xx )
% 0.08/0.32 => Xphi )
% 0.08/0.32 => ( ( ( in @ Xy @ A )
% 0.08/0.32 => Xphi )
% 0.08/0.32 => Xphi ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setadjoinOr_type,type,
% 0.08/0.32 setadjoinOr: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setadjoinOr,definition,
% 0.08/0.32 ( setadjoinOr
% 0.08/0.32 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.08/0.32 => ( ( Xy = Xx )
% 0.08/0.32 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setoftrueEq_type,type,
% 0.08/0.32 setoftrueEq: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setoftrueEq,definition,
% 0.08/0.32 ( setoftrueEq
% 0.08/0.32 = ( ! [A: $i] :
% 0.08/0.32 ( ( dsetconstr @ A
% 0.08/0.32 @ ^ [Xx: $i] : $true )
% 0.08/0.32 = A ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(powersetI_type,type,
% 0.08/0.32 powersetI: $o ).
% 0.08/0.32
% 0.08/0.32 thf(powersetI,definition,
% 0.08/0.32 ( powersetI
% 0.08/0.32 = ( ! [A: $i,B: $i] :
% 0.08/0.32 ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ B )
% 0.08/0.32 => ( in @ Xx @ A ) )
% 0.08/0.32 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(emptyinPowerset_type,type,
% 0.08/0.32 emptyinPowerset: $o ).
% 0.08/0.32
% 0.08/0.32 thf(emptyinPowerset,definition,
% 0.08/0.32 ( emptyinPowerset
% 0.08/0.32 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(emptyInPowerset_type,type,
% 0.08/0.32 emptyInPowerset: $o ).
% 0.08/0.32
% 0.08/0.32 thf(emptyInPowerset,definition,
% 0.08/0.32 ( emptyInPowerset
% 0.08/0.32 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(powersetE_type,type,
% 0.08/0.32 powersetE: $o ).
% 0.08/0.32
% 0.08/0.32 thf(powersetE,definition,
% 0.08/0.32 ( powersetE
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ B @ ( powerset @ A ) )
% 0.08/0.32 => ( ( in @ Xx @ B )
% 0.08/0.32 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setunionI_type,type,
% 0.08/0.32 setunionI: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setunionI,definition,
% 0.08/0.32 ( setunionI
% 0.08/0.32 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.08/0.32 ( ( in @ Xx @ B )
% 0.08/0.32 => ( ( in @ B @ A )
% 0.08/0.32 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setunionE_type,type,
% 0.08/0.32 setunionE: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setunionE,definition,
% 0.08/0.32 ( setunionE
% 0.08/0.32 = ( ! [A: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ ( setunion @ A ) )
% 0.08/0.32 => ! [Xphi: $o] :
% 0.08/0.32 ( ! [B: $i] :
% 0.08/0.32 ( ( in @ Xx @ B )
% 0.08/0.32 => ( ( in @ B @ A )
% 0.08/0.32 => Xphi ) )
% 0.08/0.32 => Xphi ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(subPowSU_type,type,
% 0.08/0.32 subPowSU: $o ).
% 0.08/0.32
% 0.08/0.32 thf(subPowSU,definition,
% 0.08/0.32 ( subPowSU
% 0.08/0.32 = ( ! [A: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(exuE2_type,type,
% 0.08/0.32 exuE2: $o ).
% 0.08/0.32
% 0.08/0.32 thf(exuE2,definition,
% 0.08/0.32 ( exuE2
% 0.08/0.32 = ( ! [Xphi: $i > $o] :
% 0.08/0.32 ( ( exu
% 0.08/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.08/0.32 => ? [Xx: $i] :
% 0.08/0.32 ! [Xy: $i] :
% 0.08/0.32 ( ( Xphi @ Xy )
% 0.08/0.32 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(nonemptyImpWitness_type,type,
% 0.08/0.32 nonemptyImpWitness: $o ).
% 0.08/0.32
% 0.08/0.32 thf(nonemptyImpWitness,definition,
% 0.08/0.32 ( nonemptyImpWitness
% 0.08/0.32 = ( ! [A: $i] :
% 0.08/0.32 ( ( nonempty @ A )
% 0.08/0.32 => ? [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 & $true ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(uniqinunit_type,type,
% 0.08/0.32 uniqinunit: $o ).
% 0.08/0.32
% 0.08/0.32 thf(uniqinunit,definition,
% 0.08/0.32 ( uniqinunit
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i] :
% 0.08/0.32 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.08/0.32 => ( Xx = Xy ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(notinsingleton_type,type,
% 0.08/0.32 notinsingleton: $o ).
% 0.08/0.32
% 0.08/0.32 thf(notinsingleton,definition,
% 0.08/0.32 ( notinsingleton
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i] :
% 0.08/0.32 ( ( Xx != Xy )
% 0.08/0.32 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(eqinunit_type,type,
% 0.08/0.32 eqinunit: $o ).
% 0.08/0.32
% 0.08/0.32 thf(eqinunit,definition,
% 0.08/0.32 ( eqinunit
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i] :
% 0.08/0.32 ( ( Xx = Xy )
% 0.08/0.32 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(singletonsswitch_type,type,
% 0.08/0.32 singletonsswitch: $o ).
% 0.08/0.32
% 0.08/0.32 thf(singletonsswitch,definition,
% 0.08/0.32 ( singletonsswitch
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i] :
% 0.08/0.32 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.08/0.32 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(upairsetE_type,type,
% 0.08/0.32 upairsetE: $o ).
% 0.08/0.32
% 0.08/0.32 thf(upairsetE,definition,
% 0.08/0.32 ( upairsetE
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.08/0.32 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.08/0.32 => ( ( Xz = Xx )
% 0.08/0.32 | ( Xz = Xy ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(upairsetIL_type,type,
% 0.08/0.32 upairsetIL: $o ).
% 0.08/0.32
% 0.08/0.32 thf(upairsetIL,definition,
% 0.08/0.32 ( upairsetIL
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(upairsetIR_type,type,
% 0.08/0.32 upairsetIR: $o ).
% 0.08/0.32
% 0.08/0.32 thf(upairsetIR,definition,
% 0.08/0.32 ( upairsetIR
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(emptyE1_type,type,
% 0.08/0.32 emptyE1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(emptyE1,definition,
% 0.08/0.32 ( emptyE1
% 0.08/0.32 = ( ! [A: $i,Xphi: $i > $o] :
% 0.08/0.32 ( ? [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 & ( Xphi @ Xx ) )
% 0.08/0.32 => ( ( ( dsetconstr @ A
% 0.08/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.08/0.32 = emptyset )
% 0.08/0.32 => $false ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(vacuousDall_type,type,
% 0.08/0.32 vacuousDall: $o ).
% 0.08/0.32
% 0.08/0.32 thf(vacuousDall,definition,
% 0.08/0.32 ( vacuousDall
% 0.08/0.32 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ emptyset )
% 0.08/0.32 => ( Xphi @ Xx ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(quantDeMorgan1_type,type,
% 0.08/0.32 quantDeMorgan1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(quantDeMorgan1,definition,
% 0.08/0.32 ( quantDeMorgan1
% 0.08/0.32 = ( ! [A: $i,Xphi: $i > $o] :
% 0.08/0.32 ( ~ ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( Xphi @ Xx ) )
% 0.08/0.32 => ? [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(quantDeMorgan2_type,type,
% 0.08/0.32 quantDeMorgan2: $o ).
% 0.08/0.32
% 0.08/0.32 thf(quantDeMorgan2,definition,
% 0.08/0.32 ( quantDeMorgan2
% 0.08/0.32 = ( ! [A: $i,Xphi: $i > $o] :
% 0.08/0.32 ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ~ ( Xphi @ Xx ) )
% 0.08/0.32 => ~ ? [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(quantDeMorgan3_type,type,
% 0.08/0.32 quantDeMorgan3: $o ).
% 0.08/0.32
% 0.08/0.32 thf(quantDeMorgan3,definition,
% 0.08/0.32 ( quantDeMorgan3
% 0.08/0.32 = ( ! [A: $i,Xphi: $i > $o] :
% 0.08/0.32 ( ~ ? [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 & ( Xphi @ Xx ) )
% 0.08/0.32 => ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(quantDeMorgan4_type,type,
% 0.08/0.32 quantDeMorgan4: $o ).
% 0.08/0.32
% 0.08/0.32 thf(quantDeMorgan4,definition,
% 0.08/0.32 ( quantDeMorgan4
% 0.08/0.32 = ( ! [A: $i,Xphi: $i > $o] :
% 0.08/0.32 ( ? [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 & ~ ( Xphi @ Xx ) )
% 0.08/0.32 => ~ ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(prop2setI_type,type,
% 0.08/0.32 prop2setI: $o ).
% 0.08/0.32
% 0.08/0.32 thf(prop2setI,definition,
% 0.08/0.32 ( prop2setI
% 0.08/0.32 = ( ! [Xphi: $o] :
% 0.08/0.32 ( Xphi
% 0.08/0.32 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(set2prop_type,type,
% 0.08/0.32 set2prop: $i > $o ).
% 0.08/0.32
% 0.08/0.32 thf(prop2set2propI_type,type,
% 0.08/0.32 prop2set2propI: $o ).
% 0.08/0.32
% 0.08/0.32 thf(prop2set2propI,definition,
% 0.08/0.32 ( prop2set2propI
% 0.08/0.32 = ( ! [Xphi: $o] :
% 0.08/0.32 ( Xphi
% 0.08/0.32 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(notdexE_type,type,
% 0.08/0.32 notdexE: $o ).
% 0.08/0.32
% 0.08/0.32 thf(notdexE,definition,
% 0.08/0.32 ( notdexE
% 0.08/0.32 = ( ! [A: $i,Xphi: $i > $o] :
% 0.08/0.32 ( ~ ? [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 & ( Xphi @ Xx ) )
% 0.08/0.32 => ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(notdallE_type,type,
% 0.08/0.32 notdallE: $o ).
% 0.08/0.32
% 0.08/0.32 thf(notdallE,definition,
% 0.08/0.32 ( notdallE
% 0.08/0.32 = ( ! [A: $i,Xphi: $i > $o] :
% 0.08/0.32 ( ~ ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( Xphi @ Xx ) )
% 0.08/0.32 => ? [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(exuI1_type,type,
% 0.08/0.32 exuI1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(exuI1,definition,
% 0.08/0.32 ( exuI1
% 0.08/0.32 = ( ! [Xphi: $i > $o] :
% 0.08/0.32 ( ? [Xx: $i] :
% 0.08/0.32 ( ( Xphi @ Xx )
% 0.08/0.32 & ! [Xy: $i] :
% 0.08/0.32 ( ( Xphi @ Xy )
% 0.08/0.32 => ( Xx = Xy ) ) )
% 0.08/0.32 => ( exu
% 0.08/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(exuI3_type,type,
% 0.08/0.32 exuI3: $o ).
% 0.08/0.32
% 0.08/0.32 thf(exuI3,definition,
% 0.08/0.32 ( exuI3
% 0.08/0.32 = ( ! [Xphi: $i > $o] :
% 0.08/0.32 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.08/0.32 => ( ! [Xx: $i,Xy: $i] :
% 0.08/0.32 ( ( Xphi @ Xx )
% 0.08/0.32 => ( ( Xphi @ Xy )
% 0.08/0.32 => ( Xx = Xy ) ) )
% 0.08/0.32 => ( exu
% 0.08/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(exuI2_type,type,
% 0.08/0.32 exuI2: $o ).
% 0.08/0.32
% 0.08/0.32 thf(exuI2,definition,
% 0.08/0.32 ( exuI2
% 0.08/0.32 = ( ! [Xphi: $i > $o] :
% 0.08/0.32 ( ? [Xx: $i] :
% 0.08/0.32 ! [Xy: $i] :
% 0.08/0.32 ( ( Xphi @ Xy )
% 0.08/0.32 <=> ( Xy = Xx ) )
% 0.08/0.32 => ( exu
% 0.08/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(inCongP_type,type,
% 0.08/0.32 inCongP: $o ).
% 0.08/0.32
% 0.08/0.32 thf(inCongP,definition,
% 0.08/0.32 ( inCongP
% 0.08/0.32 = ( ! [A: $i,B: $i] :
% 0.08/0.32 ( ( A = B )
% 0.08/0.32 => ! [Xx: $i,Xy: $i] :
% 0.08/0.32 ( ( Xx = Xy )
% 0.08/0.32 => ( ( in @ Xx @ A )
% 0.08/0.32 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(in__Cong_type,type,
% 0.08/0.32 in__Cong: $o ).
% 0.08/0.32
% 0.08/0.32 thf(in__Cong,definition,
% 0.08/0.32 ( in__Cong
% 0.08/0.32 = ( ! [A: $i,B: $i] :
% 0.08/0.32 ( ( A = B )
% 0.08/0.32 => ! [Xx: $i,Xy: $i] :
% 0.08/0.32 ( ( Xx = Xy )
% 0.08/0.32 => ( ( in @ Xx @ A )
% 0.08/0.32 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(exuE3u_type,type,
% 0.08/0.32 exuE3u: $o ).
% 0.08/0.32
% 0.08/0.32 thf(exuE3u,definition,
% 0.08/0.32 ( exuE3u
% 0.08/0.32 = ( ! [Xphi: $i > $o] :
% 0.08/0.32 ( ( exu
% 0.08/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.08/0.32 => ! [Xx: $i,Xy: $i] :
% 0.08/0.32 ( ( Xphi @ Xx )
% 0.08/0.32 => ( ( Xphi @ Xy )
% 0.08/0.32 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(exu__Cong_type,type,
% 0.08/0.32 exu__Cong: $o ).
% 0.08/0.32
% 0.08/0.32 thf(exu__Cong,definition,
% 0.08/0.32 ( exu__Cong
% 0.08/0.32 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.08/0.32 ( ! [Xx: $i,Xy: $i] :
% 0.08/0.32 ( ( Xx = Xy )
% 0.08/0.32 => ( ( Xphi @ Xx )
% 0.08/0.32 <=> ( Xpsi @ Xy ) ) )
% 0.08/0.32 => ( ( exu
% 0.08/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.08/0.32 <=> ( exu
% 0.08/0.32 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(emptyset__Cong_type,type,
% 0.08/0.32 emptyset__Cong: $o ).
% 0.08/0.32
% 0.08/0.32 thf(emptyset__Cong,definition,
% 0.08/0.32 ( emptyset__Cong
% 0.08/0.32 = ( emptyset = emptyset ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setadjoin__Cong_type,type,
% 0.08/0.32 setadjoin__Cong: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setadjoin__Cong,definition,
% 0.08/0.32 ( setadjoin__Cong
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i] :
% 0.08/0.32 ( ( Xx = Xy )
% 0.08/0.32 => ! [Xz: $i,Xu: $i] :
% 0.08/0.32 ( ( Xz = Xu )
% 0.08/0.32 => ( ( setadjoin @ Xx @ Xz )
% 0.08/0.32 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(powerset__Cong_type,type,
% 0.08/0.32 powerset__Cong: $o ).
% 0.08/0.32
% 0.08/0.32 thf(powerset__Cong,definition,
% 0.08/0.32 ( powerset__Cong
% 0.08/0.32 = ( ! [A: $i,B: $i] :
% 0.08/0.32 ( ( A = B )
% 0.08/0.32 => ( ( powerset @ A )
% 0.08/0.32 = ( powerset @ B ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setunion__Cong_type,type,
% 0.08/0.32 setunion__Cong: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setunion__Cong,definition,
% 0.08/0.32 ( setunion__Cong
% 0.08/0.32 = ( ! [A: $i,B: $i] :
% 0.08/0.32 ( ( A = B )
% 0.08/0.32 => ( ( setunion @ A )
% 0.08/0.32 = ( setunion @ B ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(omega__Cong_type,type,
% 0.08/0.32 omega__Cong: $o ).
% 0.08/0.32
% 0.08/0.32 thf(omega__Cong,definition,
% 0.08/0.32 ( omega__Cong
% 0.08/0.32 = ( omega = omega ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(exuEu_type,type,
% 0.08/0.32 exuEu: $o ).
% 0.08/0.32
% 0.08/0.32 thf(exuEu,definition,
% 0.08/0.32 ( exuEu
% 0.08/0.32 = ( ! [Xphi: $i > $o] :
% 0.08/0.32 ( ( exu
% 0.08/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.08/0.32 => ! [Xx: $i,Xy: $i] :
% 0.08/0.32 ( ( Xphi @ Xx )
% 0.08/0.32 => ( ( Xphi @ Xy )
% 0.08/0.32 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(descr__Cong_type,type,
% 0.08/0.32 descr__Cong: $o ).
% 0.08/0.32
% 0.08/0.32 thf(descr__Cong,definition,
% 0.08/0.32 ( descr__Cong
% 0.08/0.32 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.08/0.32 ( ! [Xx: $i,Xy: $i] :
% 0.08/0.32 ( ( Xx = Xy )
% 0.08/0.32 => ( ( Xphi @ Xx )
% 0.08/0.32 <=> ( Xpsi @ Xy ) ) )
% 0.08/0.32 => ( ( exu
% 0.08/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.08/0.32 => ( ( exu
% 0.08/0.32 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.08/0.32 => ( ( descr
% 0.08/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.08/0.32 = ( descr
% 0.08/0.32 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(dsetconstr__Cong_type,type,
% 0.08/0.32 dsetconstr__Cong: $o ).
% 0.08/0.32
% 0.08/0.32 thf(dsetconstr__Cong,definition,
% 0.08/0.32 ( dsetconstr__Cong
% 0.08/0.32 = ( ! [A: $i,B: $i] :
% 0.08/0.32 ( ( A = B )
% 0.08/0.32 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.08/0.32 ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ! [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ B )
% 0.08/0.32 => ( ( Xx = Xy )
% 0.08/0.32 => ( ( Xphi @ Xx )
% 0.08/0.32 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.08/0.32 => ( ( dsetconstr @ A
% 0.08/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.08/0.32 = ( dsetconstr @ B
% 0.08/0.32 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(subset_type,type,
% 0.08/0.32 subset: $i > $i > $o ).
% 0.08/0.32
% 0.08/0.32 thf(disjoint_type,type,
% 0.08/0.32 disjoint: $i > $i > $o ).
% 0.08/0.32
% 0.08/0.32 thf(setsmeet_type,type,
% 0.08/0.32 setsmeet: $i > $i > $o ).
% 0.08/0.32
% 0.08/0.32 thf(subsetI1_type,type,
% 0.08/0.32 subsetI1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(subsetI1,definition,
% 0.08/0.32 ( subsetI1
% 0.08/0.32 = ( ! [A: $i,B: $i] :
% 0.08/0.32 ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( in @ Xx @ B ) )
% 0.08/0.32 => ( subset @ A @ B ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(eqimpsubset2_type,type,
% 0.08/0.32 eqimpsubset2: $o ).
% 0.08/0.32
% 0.08/0.32 thf(eqimpsubset2,definition,
% 0.08/0.32 ( eqimpsubset2
% 0.08/0.32 = ( ! [A: $i,B: $i] :
% 0.08/0.32 ( ( A = B )
% 0.08/0.32 => ( subset @ B @ A ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(eqimpsubset1_type,type,
% 0.08/0.32 eqimpsubset1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(eqimpsubset1,definition,
% 0.08/0.32 ( eqimpsubset1
% 0.08/0.32 = ( ! [A: $i,B: $i] :
% 0.08/0.32 ( ( A = B )
% 0.08/0.32 => ( subset @ A @ B ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(subsetI2_type,type,
% 0.08/0.32 subsetI2: $o ).
% 0.08/0.32
% 0.08/0.32 thf(subsetI2,definition,
% 0.08/0.32 ( subsetI2
% 0.08/0.32 = ( ! [A: $i,B: $i] :
% 0.08/0.32 ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( in @ Xx @ B ) )
% 0.08/0.32 => ( subset @ A @ B ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(emptysetsubset_type,type,
% 0.08/0.32 emptysetsubset: $o ).
% 0.08/0.32
% 0.08/0.32 thf(emptysetsubset,definition,
% 0.08/0.32 ( emptysetsubset
% 0.08/0.32 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(subsetE_type,type,
% 0.08/0.32 subsetE: $o ).
% 0.08/0.32
% 0.08/0.32 thf(subsetE,definition,
% 0.08/0.32 ( subsetE
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ( subset @ A @ B )
% 0.08/0.32 => ( ( in @ Xx @ A )
% 0.08/0.32 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(subsetE2_type,type,
% 0.08/0.32 subsetE2: $o ).
% 0.08/0.32
% 0.08/0.32 thf(subsetE2,definition,
% 0.08/0.32 ( subsetE2
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ( subset @ A @ B )
% 0.08/0.32 => ( ~ ( in @ Xx @ B )
% 0.08/0.32 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(notsubsetI_type,type,
% 0.08/0.32 notsubsetI: $o ).
% 0.08/0.32
% 0.08/0.32 thf(notsubsetI,definition,
% 0.08/0.32 ( notsubsetI
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( ~ ( in @ Xx @ B )
% 0.08/0.32 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(notequalI1_type,type,
% 0.08/0.32 notequalI1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(notequalI1,definition,
% 0.08/0.32 ( notequalI1
% 0.08/0.32 = ( ! [A: $i,B: $i] :
% 0.08/0.32 ( ~ ( subset @ A @ B )
% 0.08/0.32 => ( A != B ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(notequalI2_type,type,
% 0.08/0.32 notequalI2: $o ).
% 0.08/0.32
% 0.08/0.32 thf(notequalI2,definition,
% 0.08/0.32 ( notequalI2
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( ~ ( in @ Xx @ B )
% 0.08/0.32 => ( A != B ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(subsetRefl_type,type,
% 0.08/0.32 subsetRefl: $o ).
% 0.08/0.32
% 0.08/0.32 thf(subsetRefl,definition,
% 0.08/0.32 ( subsetRefl
% 0.08/0.32 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(subsetTrans_type,type,
% 0.08/0.32 subsetTrans: $o ).
% 0.08/0.32
% 0.08/0.32 thf(subsetTrans,definition,
% 0.08/0.32 ( subsetTrans
% 0.08/0.32 = ( ! [A: $i,B: $i,C: $i] :
% 0.08/0.32 ( ( subset @ A @ B )
% 0.08/0.32 => ( ( subset @ B @ C )
% 0.08/0.32 => ( subset @ A @ C ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setadjoinSub_type,type,
% 0.08/0.32 setadjoinSub: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setadjoinSub,definition,
% 0.08/0.32 ( setadjoinSub
% 0.08/0.32 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setadjoinSub2_type,type,
% 0.08/0.32 setadjoinSub2: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setadjoinSub2,definition,
% 0.08/0.32 ( setadjoinSub2
% 0.08/0.32 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.08/0.32 ( ( subset @ A @ B )
% 0.08/0.32 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(subset2powerset_type,type,
% 0.08/0.32 subset2powerset: $o ).
% 0.08/0.32
% 0.08/0.32 thf(subset2powerset,definition,
% 0.08/0.32 ( subset2powerset
% 0.08/0.32 = ( ! [A: $i,B: $i] :
% 0.08/0.32 ( ( subset @ A @ B )
% 0.08/0.32 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setextsub_type,type,
% 0.08/0.32 setextsub: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setextsub,definition,
% 0.08/0.32 ( setextsub
% 0.08/0.32 = ( ! [A: $i,B: $i] :
% 0.08/0.32 ( ( subset @ A @ B )
% 0.08/0.32 => ( ( subset @ B @ A )
% 0.08/0.32 => ( A = B ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(subsetemptysetimpeq_type,type,
% 0.08/0.32 subsetemptysetimpeq: $o ).
% 0.08/0.32
% 0.08/0.32 thf(subsetemptysetimpeq,definition,
% 0.08/0.32 ( subsetemptysetimpeq
% 0.08/0.32 = ( ! [A: $i] :
% 0.08/0.32 ( ( subset @ A @ emptyset )
% 0.08/0.32 => ( A = emptyset ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(powersetI1_type,type,
% 0.08/0.32 powersetI1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(powersetI1,definition,
% 0.08/0.32 ( powersetI1
% 0.08/0.32 = ( ! [A: $i,B: $i] :
% 0.08/0.32 ( ( subset @ B @ A )
% 0.08/0.32 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(powersetE1_type,type,
% 0.08/0.32 powersetE1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(powersetE1,definition,
% 0.08/0.32 ( powersetE1
% 0.08/0.32 = ( ! [A: $i,B: $i] :
% 0.08/0.32 ( ( in @ B @ ( powerset @ A ) )
% 0.08/0.32 => ( subset @ B @ A ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(inPowerset_type,type,
% 0.08/0.32 inPowerset: $o ).
% 0.08/0.32
% 0.08/0.32 thf(inPowerset,definition,
% 0.08/0.32 ( inPowerset
% 0.08/0.32 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(powersetsubset_type,type,
% 0.08/0.32 powersetsubset: $o ).
% 0.08/0.32
% 0.08/0.32 thf(powersetsubset,definition,
% 0.08/0.32 ( powersetsubset
% 0.08/0.32 = ( ! [A: $i,B: $i] :
% 0.08/0.32 ( ( subset @ A @ B )
% 0.08/0.32 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(sepInPowerset_type,type,
% 0.08/0.32 sepInPowerset: $o ).
% 0.08/0.32
% 0.08/0.32 thf(sepInPowerset,definition,
% 0.08/0.32 ( sepInPowerset
% 0.08/0.32 = ( ! [A: $i,Xphi: $i > $o] :
% 0.08/0.32 ( in
% 0.08/0.32 @ ( dsetconstr @ A
% 0.08/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.08/0.32 @ ( powerset @ A ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(sepSubset_type,type,
% 0.08/0.32 sepSubset: $o ).
% 0.08/0.32
% 0.08/0.32 thf(sepSubset,definition,
% 0.08/0.32 ( sepSubset
% 0.08/0.32 = ( ! [A: $i,Xphi: $i > $o] :
% 0.08/0.32 ( subset
% 0.08/0.32 @ ( dsetconstr @ A
% 0.08/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.08/0.32 @ A ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(binunion_type,type,
% 0.08/0.32 binunion: $i > $i > $i ).
% 0.08/0.32
% 0.08/0.32 thf(binunionIL_type,type,
% 0.08/0.32 binunionIL: $o ).
% 0.08/0.32
% 0.08/0.32 thf(binunionIL,definition,
% 0.08/0.32 ( binunionIL
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(upairset2IR_type,type,
% 0.08/0.32 upairset2IR: $o ).
% 0.08/0.32
% 0.08/0.32 thf(upairset2IR,definition,
% 0.08/0.32 ( upairset2IR
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(binunionIR_type,type,
% 0.08/0.32 binunionIR: $o ).
% 0.08/0.32
% 0.08/0.32 thf(binunionIR,definition,
% 0.08/0.32 ( binunionIR
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ B )
% 0.08/0.32 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(binunionEcases_type,type,
% 0.08/0.32 binunionEcases: $o ).
% 0.08/0.32
% 0.08/0.32 thf(binunionEcases,definition,
% 0.08/0.32 ( binunionEcases
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.08/0.32 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.08/0.32 => ( ( ( in @ Xx @ A )
% 0.08/0.32 => Xphi )
% 0.08/0.32 => ( ( ( in @ Xx @ B )
% 0.08/0.32 => Xphi )
% 0.08/0.32 => Xphi ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(binunionE_type,type,
% 0.08/0.32 binunionE: $o ).
% 0.08/0.32
% 0.08/0.32 thf(binunionE,definition,
% 0.08/0.32 ( binunionE
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.08/0.32 => ( ( in @ Xx @ A )
% 0.08/0.32 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(binunionLsub_type,type,
% 0.08/0.32 binunionLsub: $o ).
% 0.08/0.32
% 0.08/0.32 thf(binunionLsub,definition,
% 0.08/0.32 ( binunionLsub
% 0.08/0.32 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(binunionRsub_type,type,
% 0.08/0.32 binunionRsub: $o ).
% 0.08/0.32
% 0.08/0.32 thf(binunionRsub,definition,
% 0.08/0.32 ( binunionRsub
% 0.08/0.32 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(binintersect_type,type,
% 0.08/0.32 binintersect: $i > $i > $i ).
% 0.08/0.32
% 0.08/0.32 thf(binintersectI_type,type,
% 0.08/0.32 binintersectI: $o ).
% 0.08/0.32
% 0.08/0.32 thf(binintersectI,definition,
% 0.08/0.32 ( binintersectI
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( ( in @ Xx @ B )
% 0.08/0.32 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(binintersectSubset5_type,type,
% 0.08/0.32 binintersectSubset5: $o ).
% 0.08/0.32
% 0.08/0.32 thf(binintersectSubset5,definition,
% 0.08/0.32 ( binintersectSubset5
% 0.08/0.32 = ( ! [A: $i,B: $i,C: $i] :
% 0.08/0.32 ( ( subset @ C @ A )
% 0.08/0.32 => ( ( subset @ C @ B )
% 0.08/0.32 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(binintersectEL_type,type,
% 0.08/0.32 binintersectEL: $o ).
% 0.08/0.32
% 0.08/0.32 thf(binintersectEL,definition,
% 0.08/0.32 ( binintersectEL
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.08/0.32 => ( in @ Xx @ A ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(binintersectLsub_type,type,
% 0.08/0.32 binintersectLsub: $o ).
% 0.08/0.32
% 0.08/0.32 thf(binintersectLsub,definition,
% 0.08/0.32 ( binintersectLsub
% 0.08/0.32 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(binintersectSubset2_type,type,
% 0.08/0.32 binintersectSubset2: $o ).
% 0.08/0.32
% 0.08/0.32 thf(binintersectSubset2,definition,
% 0.08/0.32 ( binintersectSubset2
% 0.08/0.32 = ( ! [A: $i,B: $i] :
% 0.08/0.32 ( ( subset @ A @ B )
% 0.08/0.32 => ( ( binintersect @ A @ B )
% 0.08/0.32 = A ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(binintersectSubset3_type,type,
% 0.08/0.32 binintersectSubset3: $o ).
% 0.08/0.32
% 0.08/0.32 thf(binintersectSubset3,definition,
% 0.08/0.32 ( binintersectSubset3
% 0.08/0.32 = ( ! [A: $i,B: $i] :
% 0.08/0.32 ( ( ( binintersect @ A @ B )
% 0.08/0.32 = B )
% 0.08/0.32 => ( subset @ B @ A ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(binintersectER_type,type,
% 0.08/0.32 binintersectER: $o ).
% 0.08/0.32
% 0.08/0.32 thf(binintersectER,definition,
% 0.08/0.32 ( binintersectER
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.08/0.32 => ( in @ Xx @ B ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(disjointsetsI1_type,type,
% 0.08/0.32 disjointsetsI1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(disjointsetsI1,definition,
% 0.08/0.32 ( disjointsetsI1
% 0.08/0.32 = ( ! [A: $i,B: $i] :
% 0.08/0.32 ( ~ ? [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 & ( in @ Xx @ B ) )
% 0.08/0.32 => ( ( binintersect @ A @ B )
% 0.08/0.32 = emptyset ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(binintersectRsub_type,type,
% 0.08/0.32 binintersectRsub: $o ).
% 0.08/0.32
% 0.08/0.32 thf(binintersectRsub,definition,
% 0.08/0.32 ( binintersectRsub
% 0.08/0.32 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(binintersectSubset4_type,type,
% 0.08/0.32 binintersectSubset4: $o ).
% 0.08/0.32
% 0.08/0.32 thf(binintersectSubset4,definition,
% 0.08/0.32 ( binintersectSubset4
% 0.08/0.32 = ( ! [A: $i,B: $i] :
% 0.08/0.32 ( ( subset @ B @ A )
% 0.08/0.32 => ( ( binintersect @ A @ B )
% 0.08/0.32 = B ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(binintersectSubset1_type,type,
% 0.08/0.32 binintersectSubset1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(binintersectSubset1,definition,
% 0.08/0.32 ( binintersectSubset1
% 0.08/0.32 = ( ! [A: $i,B: $i] :
% 0.08/0.32 ( ( ( binintersect @ A @ B )
% 0.08/0.32 = A )
% 0.08/0.32 => ( subset @ A @ B ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(bs114d_type,type,
% 0.08/0.32 bs114d: $o ).
% 0.08/0.32
% 0.08/0.32 thf(bs114d,definition,
% 0.08/0.32 ( bs114d
% 0.08/0.32 = ( ! [A: $i,B: $i,C: $i] :
% 0.08/0.32 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.08/0.32 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(regular_type,type,
% 0.08/0.32 regular: $i > $o ).
% 0.08/0.32
% 0.08/0.32 thf(setminus_type,type,
% 0.08/0.32 setminus: $i > $i > $i ).
% 0.08/0.32
% 0.08/0.32 thf(setminusI_type,type,
% 0.08/0.32 setminusI: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setminusI,definition,
% 0.08/0.32 ( setminusI
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( ~ ( in @ Xx @ B )
% 0.08/0.32 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setminusEL_type,type,
% 0.08/0.32 setminusEL: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setminusEL,definition,
% 0.08/0.32 ( setminusEL
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.08/0.32 => ( in @ Xx @ A ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setminusER_type,type,
% 0.08/0.32 setminusER: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setminusER,definition,
% 0.08/0.32 ( setminusER
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.08/0.32 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setminusSubset2_type,type,
% 0.08/0.32 setminusSubset2: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setminusSubset2,definition,
% 0.08/0.32 ( setminusSubset2
% 0.08/0.32 = ( ! [A: $i,B: $i] :
% 0.08/0.32 ( ( subset @ A @ B )
% 0.08/0.32 => ( ( setminus @ A @ B )
% 0.08/0.32 = emptyset ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setminusERneg_type,type,
% 0.08/0.32 setminusERneg: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setminusERneg,definition,
% 0.08/0.32 ( setminusERneg
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.08/0.32 => ( ( in @ Xx @ A )
% 0.08/0.32 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setminusELneg_type,type,
% 0.08/0.32 setminusELneg: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setminusELneg,definition,
% 0.08/0.32 ( setminusELneg
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.08/0.32 => ( ~ ( in @ Xx @ B )
% 0.08/0.32 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setminusILneg_type,type,
% 0.08/0.32 setminusILneg: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setminusILneg,definition,
% 0.08/0.32 ( setminusILneg
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ~ ( in @ Xx @ A )
% 0.08/0.32 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setminusIRneg_type,type,
% 0.08/0.32 setminusIRneg: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setminusIRneg,definition,
% 0.08/0.32 ( setminusIRneg
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ B )
% 0.08/0.32 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setminusLsub_type,type,
% 0.08/0.32 setminusLsub: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setminusLsub,definition,
% 0.08/0.32 ( setminusLsub
% 0.08/0.32 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setminusSubset1_type,type,
% 0.08/0.32 setminusSubset1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setminusSubset1,definition,
% 0.08/0.32 ( setminusSubset1
% 0.08/0.32 = ( ! [A: $i,B: $i] :
% 0.08/0.32 ( ( ( setminus @ A @ B )
% 0.08/0.32 = emptyset )
% 0.08/0.32 => ( subset @ A @ B ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(symdiff_type,type,
% 0.08/0.32 symdiff: $i > $i > $i ).
% 0.08/0.32
% 0.08/0.32 thf(symdiffE_type,type,
% 0.08/0.32 symdiffE: $o ).
% 0.08/0.32
% 0.08/0.32 thf(symdiffE,definition,
% 0.08/0.32 ( symdiffE
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.08/0.32 => ! [Xphi: $o] :
% 0.08/0.32 ( ( ( in @ Xx @ A )
% 0.08/0.32 => ( ~ ( in @ Xx @ B )
% 0.08/0.32 => Xphi ) )
% 0.08/0.32 => ( ( ~ ( in @ Xx @ A )
% 0.08/0.32 => ( ( in @ Xx @ B )
% 0.08/0.32 => Xphi ) )
% 0.08/0.32 => Xphi ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(symdiffI1_type,type,
% 0.08/0.32 symdiffI1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(symdiffI1,definition,
% 0.08/0.32 ( symdiffI1
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( ~ ( in @ Xx @ B )
% 0.08/0.32 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(symdiffI2_type,type,
% 0.08/0.32 symdiffI2: $o ).
% 0.08/0.32
% 0.08/0.32 thf(symdiffI2,definition,
% 0.08/0.32 ( symdiffI2
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ~ ( in @ Xx @ A )
% 0.08/0.32 => ( ( in @ Xx @ B )
% 0.08/0.32 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(symdiffIneg1_type,type,
% 0.08/0.32 symdiffIneg1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(symdiffIneg1,definition,
% 0.08/0.32 ( symdiffIneg1
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( ( in @ Xx @ B )
% 0.08/0.32 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(symdiffIneg2_type,type,
% 0.08/0.32 symdiffIneg2: $o ).
% 0.08/0.32
% 0.08/0.32 thf(symdiffIneg2,definition,
% 0.08/0.32 ( symdiffIneg2
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ~ ( in @ Xx @ A )
% 0.08/0.32 => ( ~ ( in @ Xx @ B )
% 0.08/0.32 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(iskpair_type,type,
% 0.08/0.32 iskpair: $i > $o ).
% 0.08/0.32
% 0.08/0.32 thf(secondinupair_type,type,
% 0.08/0.32 secondinupair: $o ).
% 0.08/0.32
% 0.08/0.32 thf(secondinupair,definition,
% 0.08/0.32 ( secondinupair
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setukpairIL_type,type,
% 0.08/0.32 setukpairIL: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setukpairIL,definition,
% 0.08/0.32 ( setukpairIL
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setukpairIR_type,type,
% 0.08/0.32 setukpairIR: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setukpairIR,definition,
% 0.08/0.32 ( setukpairIR
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(kpairiskpair_type,type,
% 0.08/0.32 kpairiskpair: $o ).
% 0.08/0.32
% 0.08/0.32 thf(kpairiskpair,definition,
% 0.08/0.32 ( kpairiskpair
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(kpair_type,type,
% 0.08/0.32 kpair: $i > $i > $i ).
% 0.08/0.32
% 0.08/0.32 thf(kpairp_type,type,
% 0.08/0.32 kpairp: $o ).
% 0.08/0.32
% 0.08/0.32 thf(kpairp,definition,
% 0.08/0.32 ( kpairp
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(cartprod_type,type,
% 0.08/0.32 cartprod: $i > $i > $i ).
% 0.08/0.32
% 0.08/0.32 thf(singletonsubset_type,type,
% 0.08/0.32 singletonsubset: $o ).
% 0.08/0.32
% 0.08/0.32 thf(singletonsubset,definition,
% 0.08/0.32 ( singletonsubset
% 0.08/0.32 = ( ! [A: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(singletoninpowerset_type,type,
% 0.08/0.32 singletoninpowerset: $o ).
% 0.08/0.32
% 0.08/0.32 thf(singletoninpowerset,definition,
% 0.08/0.32 ( singletoninpowerset
% 0.08/0.32 = ( ! [A: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(singletoninpowunion_type,type,
% 0.08/0.32 singletoninpowunion: $o ).
% 0.08/0.32
% 0.08/0.32 thf(singletoninpowunion,definition,
% 0.08/0.32 ( singletoninpowunion
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(upairset2E_type,type,
% 0.08/0.32 upairset2E: $o ).
% 0.08/0.32
% 0.08/0.32 thf(upairset2E,definition,
% 0.08/0.32 ( upairset2E
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.08/0.32 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.08/0.32 => ( ( Xz = Xx )
% 0.08/0.32 | ( Xz = Xy ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(upairsubunion_type,type,
% 0.08/0.32 upairsubunion: $o ).
% 0.08/0.32
% 0.08/0.32 thf(upairsubunion,definition,
% 0.08/0.32 ( upairsubunion
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ! [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ B )
% 0.08/0.32 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(upairinpowunion_type,type,
% 0.08/0.32 upairinpowunion: $o ).
% 0.08/0.32
% 0.08/0.32 thf(upairinpowunion,definition,
% 0.08/0.32 ( upairinpowunion
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ! [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ B )
% 0.08/0.32 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(ubforcartprodlem1_type,type,
% 0.08/0.32 ubforcartprodlem1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(ubforcartprodlem1,definition,
% 0.08/0.32 ( ubforcartprodlem1
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ! [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ B )
% 0.08/0.32 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(ubforcartprodlem2_type,type,
% 0.08/0.32 ubforcartprodlem2: $o ).
% 0.08/0.32
% 0.08/0.32 thf(ubforcartprodlem2,definition,
% 0.08/0.32 ( ubforcartprodlem2
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ! [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ B )
% 0.08/0.32 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(ubforcartprodlem3_type,type,
% 0.08/0.32 ubforcartprodlem3: $o ).
% 0.08/0.32
% 0.08/0.32 thf(ubforcartprodlem3,definition,
% 0.08/0.32 ( ubforcartprodlem3
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ! [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ B )
% 0.08/0.32 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(cartprodpairin_type,type,
% 0.08/0.32 cartprodpairin: $o ).
% 0.08/0.32
% 0.08/0.32 thf(cartprodpairin,definition,
% 0.08/0.32 ( cartprodpairin
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ! [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ B )
% 0.08/0.32 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(cartprodmempair1_type,type,
% 0.08/0.32 cartprodmempair1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(cartprodmempair1,definition,
% 0.08/0.32 ( cartprodmempair1
% 0.08/0.32 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.08/0.32 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.08/0.32 => ? [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 & ? [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ B )
% 0.08/0.32 & ( Xu
% 0.08/0.32 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(cartprodmempair_type,type,
% 0.08/0.32 cartprodmempair: $o ).
% 0.08/0.32
% 0.08/0.32 thf(cartprodmempair,definition,
% 0.08/0.32 ( cartprodmempair
% 0.08/0.32 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.08/0.32 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.08/0.32 => ( iskpair @ Xu ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setunionE2_type,type,
% 0.08/0.32 setunionE2: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setunionE2,definition,
% 0.08/0.32 ( setunionE2
% 0.08/0.32 = ( ! [A: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ ( setunion @ A ) )
% 0.08/0.32 => ? [X: $i] :
% 0.08/0.32 ( ( in @ X @ A )
% 0.08/0.32 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setunionsingleton1_type,type,
% 0.08/0.32 setunionsingleton1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setunionsingleton1,definition,
% 0.08/0.32 ( setunionsingleton1
% 0.08/0.32 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setunionsingleton2_type,type,
% 0.08/0.32 setunionsingleton2: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setunionsingleton2,definition,
% 0.08/0.32 ( setunionsingleton2
% 0.08/0.32 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setunionsingleton_type,type,
% 0.08/0.32 setunionsingleton: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setunionsingleton,definition,
% 0.08/0.32 ( setunionsingleton
% 0.08/0.32 = ( ! [Xx: $i] :
% 0.08/0.32 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.08/0.32 = Xx ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(singleton_type,type,
% 0.08/0.32 singleton: $i > $o ).
% 0.08/0.32
% 0.08/0.32 thf(singletonprop_type,type,
% 0.08/0.32 singletonprop: $o ).
% 0.08/0.32
% 0.08/0.32 thf(singletonprop,definition,
% 0.08/0.32 ( singletonprop
% 0.08/0.32 = ( ! [A: $i,Xphi: $i > $o] :
% 0.08/0.32 ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ! [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ A )
% 0.08/0.32 => ( ( Xphi @ Xx )
% 0.08/0.32 => ( ( Xphi @ Xy )
% 0.08/0.32 => ( Xx = Xy ) ) ) ) )
% 0.08/0.32 => ( ? [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 & ( Xphi @ Xx ) )
% 0.08/0.32 => ( singleton
% 0.08/0.32 @ ( dsetconstr @ A
% 0.08/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(ex1_type,type,
% 0.08/0.32 ex1: $i > ( $i > $o ) > $o ).
% 0.08/0.32
% 0.08/0.32 thf(ex1,definition,
% 0.08/0.32 ( ex1
% 0.08/0.32 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.08/0.32 ( singleton
% 0.08/0.32 @ ( dsetconstr @ A
% 0.08/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(ex1E1_type,type,
% 0.08/0.32 ex1E1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(ex1E1,definition,
% 0.08/0.32 ( ex1E1
% 0.08/0.32 = ( ! [A: $i,Xphi: $i > $o] :
% 0.08/0.32 ( ( ex1 @ A
% 0.08/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.08/0.32 => ? [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(ex1I_type,type,
% 0.08/0.32 ex1I: $o ).
% 0.08/0.32
% 0.08/0.32 thf(ex1I,definition,
% 0.08/0.32 ( ex1I
% 0.08/0.32 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( ( Xphi @ Xx )
% 0.08/0.32 => ( ! [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ A )
% 0.08/0.32 => ( ( Xphi @ Xy )
% 0.08/0.32 => ( Xy = Xx ) ) )
% 0.08/0.32 => ( ex1 @ A
% 0.08/0.32 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(ex1I2_type,type,
% 0.08/0.32 ex1I2: $o ).
% 0.08/0.32
% 0.08/0.32 thf(ex1I2,definition,
% 0.08/0.32 ( ex1I2
% 0.08/0.32 = ( ! [A: $i,Xphi: $i > $o] :
% 0.08/0.32 ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ! [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ A )
% 0.08/0.32 => ( ( Xphi @ Xx )
% 0.08/0.32 => ( ( Xphi @ Xy )
% 0.08/0.32 => ( Xx = Xy ) ) ) ) )
% 0.08/0.32 => ( ? [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 & ( Xphi @ Xx ) )
% 0.08/0.32 => ( ex1 @ A
% 0.08/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(singletonsuniq_type,type,
% 0.08/0.32 singletonsuniq: $o ).
% 0.08/0.32
% 0.08/0.32 thf(singletonsuniq,definition,
% 0.08/0.32 ( singletonsuniq
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i] :
% 0.08/0.32 ( ( ( setadjoin @ Xx @ emptyset )
% 0.08/0.32 = ( setadjoin @ Xy @ emptyset ) )
% 0.08/0.32 => ( Xx = Xy ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(atmost1p_type,type,
% 0.08/0.32 atmost1p: $i > $o ).
% 0.08/0.32
% 0.08/0.32 thf(atleast2p_type,type,
% 0.08/0.32 atleast2p: $i > $o ).
% 0.08/0.32
% 0.08/0.32 thf(atmost2p_type,type,
% 0.08/0.32 atmost2p: $i > $o ).
% 0.08/0.32
% 0.08/0.32 thf(upairsetp_type,type,
% 0.08/0.32 upairsetp: $i > $o ).
% 0.08/0.32
% 0.08/0.32 thf(setukpairinjL1_type,type,
% 0.08/0.32 setukpairinjL1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setukpairinjL1,definition,
% 0.08/0.32 ( setukpairinjL1
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.08/0.32 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.08/0.32 => ( Xx = Xz ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(kfstsingleton_type,type,
% 0.08/0.32 kfstsingleton: $o ).
% 0.08/0.32
% 0.08/0.32 thf(kfstsingleton,definition,
% 0.08/0.32 ( kfstsingleton
% 0.08/0.32 = ( ! [Xu: $i] :
% 0.08/0.32 ( ( iskpair @ Xu )
% 0.08/0.32 => ( singleton
% 0.08/0.32 @ ( dsetconstr @ ( setunion @ Xu )
% 0.08/0.32 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(theprop_type,type,
% 0.08/0.32 theprop: $o ).
% 0.08/0.32
% 0.08/0.32 thf(theprop,definition,
% 0.08/0.32 ( theprop
% 0.08/0.32 = ( ! [X: $i] :
% 0.08/0.32 ( ( singleton @ X )
% 0.08/0.32 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(kfst_type,type,
% 0.08/0.32 kfst: $i > $i ).
% 0.08/0.32
% 0.08/0.32 thf(kfstpairEq_type,type,
% 0.08/0.32 kfstpairEq: $o ).
% 0.08/0.32
% 0.08/0.32 thf(kfstpairEq,definition,
% 0.08/0.32 ( kfstpairEq
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i] :
% 0.08/0.32 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.08/0.32 = Xx ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(cartprodfstin_type,type,
% 0.08/0.32 cartprodfstin: $o ).
% 0.08/0.32
% 0.08/0.32 thf(cartprodfstin,definition,
% 0.08/0.32 ( cartprodfstin
% 0.08/0.32 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.08/0.32 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.08/0.32 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setukpairinjL2_type,type,
% 0.08/0.32 setukpairinjL2: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setukpairinjL2,definition,
% 0.08/0.32 ( setukpairinjL2
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.08/0.32 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.08/0.32 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.08/0.32 => ( Xx = Xz ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setukpairinjL_type,type,
% 0.08/0.32 setukpairinjL: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setukpairinjL,definition,
% 0.08/0.32 ( setukpairinjL
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.08/0.32 ( ( ( kpair @ Xx @ Xy )
% 0.08/0.32 = ( kpair @ Xz @ Xu ) )
% 0.08/0.32 => ( Xx = Xz ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setukpairinjR11_type,type,
% 0.08/0.32 setukpairinjR11: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setukpairinjR11,definition,
% 0.08/0.32 ( setukpairinjR11
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i] :
% 0.08/0.32 ( ( Xx = Xy )
% 0.08/0.32 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.08/0.32 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setukpairinjR12_type,type,
% 0.08/0.32 setukpairinjR12: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setukpairinjR12,definition,
% 0.08/0.32 ( setukpairinjR12
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i] :
% 0.08/0.32 ( ( Xx = Xy )
% 0.08/0.32 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.08/0.32 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setukpairinjR1_type,type,
% 0.08/0.32 setukpairinjR1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setukpairinjR1,definition,
% 0.08/0.32 ( setukpairinjR1
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.08/0.32 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.08/0.32 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.08/0.32 => ( ( Xz = Xu )
% 0.08/0.32 => ( Xy = Xu ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(upairequniteq_type,type,
% 0.08/0.32 upairequniteq: $o ).
% 0.08/0.32
% 0.08/0.32 thf(upairequniteq,definition,
% 0.08/0.32 ( upairequniteq
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.08/0.32 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.08/0.32 = ( setadjoin @ Xz @ emptyset ) )
% 0.08/0.32 => ( Xx = Xy ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setukpairinjR2_type,type,
% 0.08/0.32 setukpairinjR2: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setukpairinjR2,definition,
% 0.08/0.32 ( setukpairinjR2
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.08/0.32 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.08/0.32 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.08/0.32 => ( Xy = Xu ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setukpairinjR_type,type,
% 0.08/0.32 setukpairinjR: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setukpairinjR,definition,
% 0.08/0.32 ( setukpairinjR
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.08/0.32 ( ( ( kpair @ Xx @ Xy )
% 0.08/0.32 = ( kpair @ Xz @ Xu ) )
% 0.08/0.32 => ( Xy = Xu ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(ksndsingleton_type,type,
% 0.08/0.32 ksndsingleton: $o ).
% 0.08/0.32
% 0.08/0.32 thf(ksndsingleton,definition,
% 0.08/0.32 ( ksndsingleton
% 0.08/0.32 = ( ! [Xu: $i] :
% 0.08/0.32 ( ( iskpair @ Xu )
% 0.08/0.32 => ( singleton
% 0.08/0.32 @ ( dsetconstr @ ( setunion @ Xu )
% 0.08/0.32 @ ^ [Xx: $i] :
% 0.08/0.32 ( Xu
% 0.08/0.32 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(ksnd_type,type,
% 0.08/0.32 ksnd: $i > $i ).
% 0.08/0.32
% 0.08/0.32 thf(ksndpairEq_type,type,
% 0.08/0.32 ksndpairEq: $o ).
% 0.08/0.32
% 0.08/0.32 thf(ksndpairEq,definition,
% 0.08/0.32 ( ksndpairEq
% 0.08/0.32 = ( ! [Xx: $i,Xy: $i] :
% 0.08/0.32 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.08/0.32 = Xy ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(kpairsurjEq_type,type,
% 0.08/0.32 kpairsurjEq: $o ).
% 0.08/0.32
% 0.08/0.32 thf(kpairsurjEq,definition,
% 0.08/0.32 ( kpairsurjEq
% 0.08/0.32 = ( ! [Xu: $i] :
% 0.08/0.32 ( ( iskpair @ Xu )
% 0.08/0.32 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.08/0.32 = Xu ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(cartprodsndin_type,type,
% 0.08/0.32 cartprodsndin: $o ).
% 0.08/0.32
% 0.08/0.32 thf(cartprodsndin,definition,
% 0.08/0.32 ( cartprodsndin
% 0.08/0.32 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.08/0.32 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.08/0.32 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(cartprodpairmemEL_type,type,
% 0.08/0.32 cartprodpairmemEL: $o ).
% 0.08/0.32
% 0.08/0.32 thf(cartprodpairmemEL,definition,
% 0.08/0.32 ( cartprodpairmemEL
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.08/0.32 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.08/0.32 => ( in @ Xx @ A ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(cartprodpairmemER_type,type,
% 0.08/0.32 cartprodpairmemER: $o ).
% 0.08/0.32
% 0.08/0.32 thf(cartprodpairmemER,definition,
% 0.08/0.32 ( cartprodpairmemER
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.08/0.32 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.08/0.32 => ( in @ Xy @ B ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(cartprodmempaircEq_type,type,
% 0.08/0.32 cartprodmempaircEq: $o ).
% 0.08/0.32
% 0.08/0.32 thf(cartprodmempaircEq,definition,
% 0.08/0.32 ( cartprodmempaircEq
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ! [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ B )
% 0.08/0.32 => ( ( kpair @ Xx @ Xy )
% 0.08/0.32 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(cartprodfstpairEq_type,type,
% 0.08/0.32 cartprodfstpairEq: $o ).
% 0.08/0.32
% 0.08/0.32 thf(cartprodfstpairEq,definition,
% 0.08/0.32 ( cartprodfstpairEq
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ! [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ B )
% 0.08/0.32 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.08/0.32 = Xx ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(cartprodsndpairEq_type,type,
% 0.08/0.32 cartprodsndpairEq: $o ).
% 0.08/0.32
% 0.08/0.32 thf(cartprodsndpairEq,definition,
% 0.08/0.32 ( cartprodsndpairEq
% 0.08/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ! [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ B )
% 0.08/0.32 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.08/0.32 = Xy ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(cartprodpairsurjEq_type,type,
% 0.08/0.32 cartprodpairsurjEq: $o ).
% 0.08/0.32
% 0.08/0.32 thf(cartprodpairsurjEq,definition,
% 0.08/0.32 ( cartprodpairsurjEq
% 0.08/0.32 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.08/0.32 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.08/0.32 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.08/0.32 = Xu ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(breln_type,type,
% 0.08/0.32 breln: $i > $i > $i > $o ).
% 0.08/0.32
% 0.08/0.32 thf(breln,definition,
% 0.08/0.32 ( breln
% 0.08/0.32 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(dpsetconstr_type,type,
% 0.08/0.32 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.08/0.32
% 0.08/0.32 thf(dpsetconstrI_type,type,
% 0.08/0.32 dpsetconstrI: $o ).
% 0.08/0.32
% 0.08/0.32 thf(dpsetconstrI,definition,
% 0.08/0.32 ( dpsetconstrI
% 0.08/0.32 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ! [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ B )
% 0.08/0.32 => ( ( Xphi @ Xx @ Xy )
% 0.08/0.32 => ( in @ ( kpair @ Xx @ Xy )
% 0.08/0.32 @ ( dpsetconstr @ A @ B
% 0.08/0.32 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(dpsetconstrSub_type,type,
% 0.08/0.32 dpsetconstrSub: $o ).
% 0.08/0.32
% 0.08/0.32 thf(dpsetconstrSub,definition,
% 0.08/0.32 ( dpsetconstrSub
% 0.08/0.32 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.08/0.32 ( subset
% 0.08/0.32 @ ( dpsetconstr @ A @ B
% 0.08/0.32 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.08/0.32 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(setOfPairsIsBReln_type,type,
% 0.08/0.32 setOfPairsIsBReln: $o ).
% 0.08/0.32
% 0.08/0.32 thf(setOfPairsIsBReln,definition,
% 0.08/0.32 ( setOfPairsIsBReln
% 0.08/0.32 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.08/0.32 ( breln @ A @ B
% 0.08/0.32 @ ( dpsetconstr @ A @ B
% 0.08/0.32 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(dpsetconstrERa_type,type,
% 0.08/0.32 dpsetconstrERa: $o ).
% 0.08/0.32
% 0.08/0.32 thf(dpsetconstrERa,definition,
% 0.08/0.32 ( dpsetconstrERa
% 0.08/0.32 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ! [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ B )
% 0.08/0.32 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.08/0.32 @ ( dpsetconstr @ A @ B
% 0.08/0.32 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.08/0.32 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(dpsetconstrEL1_type,type,
% 0.08/0.32 dpsetconstrEL1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(dpsetconstrEL1,definition,
% 0.08/0.32 ( dpsetconstrEL1
% 0.08/0.32 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.08/0.32 ( ( in @ ( kpair @ Xx @ Xy )
% 0.08/0.32 @ ( dpsetconstr @ A @ B
% 0.08/0.32 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.08/0.32 => ( in @ Xx @ A ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(dpsetconstrEL2_type,type,
% 0.08/0.32 dpsetconstrEL2: $o ).
% 0.08/0.32
% 0.08/0.32 thf(dpsetconstrEL2,definition,
% 0.08/0.32 ( dpsetconstrEL2
% 0.08/0.32 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.08/0.32 ( ( in @ ( kpair @ Xx @ Xy )
% 0.08/0.32 @ ( dpsetconstr @ A @ B
% 0.08/0.32 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.08/0.32 => ( in @ Xy @ B ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(dpsetconstrER_type,type,
% 0.08/0.32 dpsetconstrER: $o ).
% 0.08/0.32
% 0.08/0.32 thf(dpsetconstrER,definition,
% 0.08/0.32 ( dpsetconstrER
% 0.08/0.32 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.08/0.32 ( ( in @ ( kpair @ Xx @ Xy )
% 0.08/0.32 @ ( dpsetconstr @ A @ B
% 0.08/0.32 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.08/0.32 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(func_type,type,
% 0.08/0.32 func: $i > $i > $i > $o ).
% 0.08/0.32
% 0.08/0.32 thf(funcSet_type,type,
% 0.08/0.32 funcSet: $i > $i > $i ).
% 0.08/0.32
% 0.08/0.32 thf(funcImageSingleton_type,type,
% 0.08/0.32 funcImageSingleton: $o ).
% 0.08/0.32
% 0.08/0.32 thf(funcImageSingleton,definition,
% 0.08/0.32 ( funcImageSingleton
% 0.08/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.08/0.32 ( ( func @ A @ B @ Xf )
% 0.08/0.32 => ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( singleton
% 0.08/0.32 @ ( dsetconstr @ B
% 0.08/0.32 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(apProp_type,type,
% 0.08/0.32 apProp: $o ).
% 0.08/0.32
% 0.08/0.32 thf(apProp,definition,
% 0.08/0.32 ( apProp
% 0.08/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.08/0.32 ( ( func @ A @ B @ Xf )
% 0.08/0.32 => ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( in
% 0.08/0.32 @ ( setunion
% 0.08/0.32 @ ( dsetconstr @ B
% 0.08/0.32 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.08/0.32 @ B ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(ap_type,type,
% 0.08/0.32 ap: $i > $i > $i > $i > $i ).
% 0.08/0.32
% 0.08/0.32 thf(app_type,type,
% 0.08/0.32 app: $o ).
% 0.08/0.32
% 0.08/0.32 thf(app,definition,
% 0.08/0.32 ( app
% 0.08/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.08/0.32 ( ( func @ A @ B @ Xf )
% 0.08/0.32 => ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(infuncsetfunc_type,type,
% 0.08/0.32 infuncsetfunc: $o ).
% 0.08/0.32
% 0.08/0.32 thf(infuncsetfunc,definition,
% 0.08/0.32 ( infuncsetfunc
% 0.08/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.08/0.32 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.08/0.32 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(ap2p_type,type,
% 0.08/0.32 ap2p: $o ).
% 0.08/0.32
% 0.08/0.32 thf(ap2p,definition,
% 0.08/0.32 ( ap2p
% 0.08/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.08/0.32 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.08/0.32 => ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(funcinfuncset_type,type,
% 0.08/0.32 funcinfuncset: $o ).
% 0.08/0.32
% 0.08/0.32 thf(funcinfuncset,definition,
% 0.08/0.32 ( funcinfuncset
% 0.08/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.08/0.32 ( ( func @ A @ B @ Xf )
% 0.08/0.32 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(lamProp_type,type,
% 0.08/0.32 lamProp: $o ).
% 0.08/0.32
% 0.08/0.32 thf(lamProp,definition,
% 0.08/0.32 ( lamProp
% 0.08/0.32 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.08/0.32 ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.08/0.32 => ( func @ A @ B
% 0.08/0.32 @ ( dpsetconstr @ A @ B
% 0.08/0.32 @ ^ [Xx: $i,Xy: $i] :
% 0.08/0.32 ( ( Xf @ Xx )
% 0.08/0.32 = Xy ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(lam_type,type,
% 0.08/0.32 lam: $i > $i > ( $i > $i ) > $i ).
% 0.08/0.32
% 0.08/0.32 thf(lamp_type,type,
% 0.08/0.32 lamp: $o ).
% 0.08/0.32
% 0.08/0.32 thf(lamp,definition,
% 0.08/0.32 ( lamp
% 0.08/0.32 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.08/0.32 ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.08/0.32 => ( func @ A @ B
% 0.08/0.32 @ ( lam @ A @ B
% 0.08/0.32 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(lam2p_type,type,
% 0.08/0.32 lam2p: $o ).
% 0.08/0.32
% 0.08/0.32 thf(lam2p,definition,
% 0.08/0.32 ( lam2p
% 0.08/0.32 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.08/0.32 ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.08/0.32 => ( in
% 0.08/0.32 @ ( lam @ A @ B
% 0.08/0.32 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.08/0.32 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(brelnall1_type,type,
% 0.08/0.32 brelnall1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(brelnall1,definition,
% 0.08/0.32 ( brelnall1
% 0.08/0.32 = ( ! [A: $i,B: $i,R: $i] :
% 0.08/0.32 ( ( breln @ A @ B @ R )
% 0.08/0.32 => ! [Xphi: $i > $o] :
% 0.08/0.32 ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ! [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ B )
% 0.08/0.32 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.08/0.32 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.08/0.32 => ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ R )
% 0.08/0.32 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(brelnall2_type,type,
% 0.08/0.32 brelnall2: $o ).
% 0.08/0.32
% 0.08/0.32 thf(brelnall2,definition,
% 0.08/0.32 ( brelnall2
% 0.08/0.32 = ( ! [A: $i,B: $i,R: $i] :
% 0.08/0.32 ( ( breln @ A @ B @ R )
% 0.08/0.32 => ! [Xphi: $i > $o] :
% 0.08/0.32 ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ! [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ B )
% 0.08/0.32 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.08/0.32 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.08/0.32 => ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ R )
% 0.08/0.32 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(ex1E2_type,type,
% 0.08/0.32 ex1E2: $o ).
% 0.08/0.32
% 0.08/0.32 thf(ex1E2,definition,
% 0.08/0.32 ( ex1E2
% 0.08/0.32 = ( ! [A: $i,Xphi: $i > $o] :
% 0.08/0.32 ( ( ex1 @ A
% 0.08/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.08/0.32 => ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ! [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ A )
% 0.08/0.32 => ( ( Xphi @ Xx )
% 0.08/0.32 => ( ( Xphi @ Xy )
% 0.08/0.32 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(funcGraphProp1_type,type,
% 0.08/0.32 funcGraphProp1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(funcGraphProp1,definition,
% 0.08/0.32 ( funcGraphProp1
% 0.08/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.08/0.32 ( ( func @ A @ B @ Xf )
% 0.08/0.32 => ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(funcGraphProp3_type,type,
% 0.08/0.32 funcGraphProp3: $o ).
% 0.08/0.32
% 0.08/0.32 thf(funcGraphProp3,definition,
% 0.08/0.32 ( funcGraphProp3
% 0.08/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.08/0.32 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.08/0.32 => ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(funcGraphProp2_type,type,
% 0.08/0.32 funcGraphProp2: $o ).
% 0.08/0.32
% 0.08/0.32 thf(funcGraphProp2,definition,
% 0.08/0.32 ( funcGraphProp2
% 0.08/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.08/0.32 ( ( func @ A @ B @ Xf )
% 0.08/0.32 => ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ! [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ B )
% 0.08/0.32 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.08/0.32 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.08/0.32 = Xy ) ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(funcextLem_type,type,
% 0.08/0.32 funcextLem: $o ).
% 0.08/0.32
% 0.08/0.32 thf(funcextLem,definition,
% 0.08/0.32 ( funcextLem
% 0.08/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.08/0.32 ( ( func @ A @ B @ Xf )
% 0.08/0.32 => ! [Xg: $i] :
% 0.08/0.32 ( ( func @ A @ B @ Xg )
% 0.08/0.32 => ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.08/0.32 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.08/0.32 => ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ! [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ B )
% 0.08/0.32 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 0.08/0.32 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(funcGraphProp4_type,type,
% 0.08/0.32 funcGraphProp4: $o ).
% 0.08/0.32
% 0.08/0.32 thf(funcGraphProp4,definition,
% 0.08/0.32 ( funcGraphProp4
% 0.08/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.08/0.32 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.08/0.32 => ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ! [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ B )
% 0.08/0.32 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.08/0.32 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.08/0.32 = Xy ) ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(subbreln_type,type,
% 0.08/0.32 subbreln: $o ).
% 0.08/0.32
% 0.08/0.32 thf(subbreln,definition,
% 0.08/0.32 ( subbreln
% 0.08/0.32 = ( ! [A: $i,B: $i,R: $i] :
% 0.08/0.32 ( ( breln @ A @ B @ R )
% 0.08/0.32 => ! [S: $i] :
% 0.08/0.32 ( ( breln @ A @ B @ S )
% 0.08/0.32 => ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ! [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ B )
% 0.08/0.32 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.08/0.32 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.08/0.32 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(eqbreln_type,type,
% 0.08/0.32 eqbreln: $o ).
% 0.08/0.32
% 0.08/0.32 thf(eqbreln,definition,
% 0.08/0.32 ( eqbreln
% 0.08/0.32 = ( ! [A: $i,B: $i,R: $i] :
% 0.08/0.32 ( ( breln @ A @ B @ R )
% 0.08/0.32 => ! [S: $i] :
% 0.08/0.32 ( ( breln @ A @ B @ S )
% 0.08/0.32 => ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ! [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ B )
% 0.08/0.32 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.08/0.32 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.08/0.32 => ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ! [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ B )
% 0.08/0.32 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.08/0.32 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.08/0.32 => ( R = S ) ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(funcext_type,type,
% 0.08/0.32 funcext: $o ).
% 0.08/0.32
% 0.08/0.32 thf(funcext,definition,
% 0.08/0.32 ( funcext
% 0.08/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.08/0.32 ( ( func @ A @ B @ Xf )
% 0.08/0.32 => ! [Xg: $i] :
% 0.08/0.32 ( ( func @ A @ B @ Xg )
% 0.08/0.32 => ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.08/0.32 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.08/0.32 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(funcext2_type,type,
% 0.08/0.32 funcext2: $o ).
% 0.08/0.32
% 0.08/0.32 thf(funcext2,definition,
% 0.08/0.32 ( funcext2
% 0.08/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.08/0.32 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.08/0.32 => ! [Xg: $i] :
% 0.08/0.32 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 0.08/0.32 => ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.08/0.32 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.08/0.32 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(ap2apEq1_type,type,
% 0.08/0.32 ap2apEq1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(ap2apEq1,definition,
% 0.08/0.32 ( ap2apEq1
% 0.08/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.08/0.32 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.08/0.32 => ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.08/0.32 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(ap2apEq2_type,type,
% 0.08/0.32 ap2apEq2: $o ).
% 0.08/0.32
% 0.08/0.32 thf(ap2apEq2,definition,
% 0.08/0.32 ( ap2apEq2
% 0.08/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.08/0.32 ( ( func @ A @ B @ Xf )
% 0.08/0.32 => ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.08/0.32 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(beta1_type,type,
% 0.08/0.32 beta1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(beta1,definition,
% 0.08/0.32 ( beta1
% 0.08/0.32 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.08/0.32 ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.08/0.32 => ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( ( ap @ A @ B
% 0.08/0.32 @ ( lam @ A @ B
% 0.08/0.32 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.08/0.32 @ Xx )
% 0.08/0.32 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(eta1_type,type,
% 0.08/0.32 eta1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(eta1,definition,
% 0.08/0.32 ( eta1
% 0.08/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.08/0.32 ( ( func @ A @ B @ Xf )
% 0.08/0.32 => ( ( lam @ A @ B
% 0.08/0.32 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.08/0.32 = Xf ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(lam2lamEq_type,type,
% 0.08/0.32 lam2lamEq: $o ).
% 0.08/0.32
% 0.08/0.32 thf(lam2lamEq,definition,
% 0.08/0.32 ( lam2lamEq
% 0.08/0.32 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.08/0.32 ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.08/0.32 => ( ( lam @ A @ B
% 0.08/0.32 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.08/0.32 = ( lam @ A @ B
% 0.08/0.32 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(beta2_type,type,
% 0.08/0.32 beta2: $o ).
% 0.08/0.32
% 0.08/0.32 thf(beta2,definition,
% 0.08/0.32 ( beta2
% 0.08/0.32 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.08/0.32 ( ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.08/0.32 => ! [Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ( ( ap @ A @ B
% 0.08/0.32 @ ( lam @ A @ B
% 0.08/0.32 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.08/0.32 @ Xx )
% 0.08/0.32 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(eta2_type,type,
% 0.08/0.32 eta2: $o ).
% 0.08/0.32
% 0.08/0.32 thf(eta2,definition,
% 0.08/0.32 ( eta2
% 0.08/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.08/0.32 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.08/0.32 => ( ( lam @ A @ B
% 0.08/0.32 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.08/0.32 = Xf ) ) ) ) ).
% 0.08/0.32
% 0.08/0.32 thf(iffalseProp1_type,type,
% 0.08/0.32 iffalseProp1: $o ).
% 0.08/0.32
% 0.08/0.32 thf(iffalseProp1,definition,
% 0.08/0.32 ( iffalseProp1
% 0.08/0.32 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.08/0.32 ( ( in @ Xx @ A )
% 0.08/0.32 => ! [Xy: $i] :
% 0.08/0.32 ( ( in @ Xy @ A )
% 0.08/0.32 => ( ~ Xphi
% 0.08/0.32 => ( in @ Xy
% 0.08/0.32 @ ( dsetconstr @ A
% 0.08/0.33 @ ^ [Xz: $i] :
% 0.08/0.33 ( ( Xphi
% 0.08/0.33 & ( Xz = Xx ) )
% 0.08/0.33 | ( ~ Xphi
% 0.08/0.33 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(iffalseProp2_type,type,
% 0.08/0.33 iffalseProp2: $o ).
% 0.08/0.33
% 0.08/0.33 thf(iffalseProp2,definition,
% 0.08/0.33 ( iffalseProp2
% 0.08/0.33 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.08/0.33 ( ( in @ Xx @ A )
% 0.08/0.33 => ! [Xy: $i] :
% 0.08/0.33 ( ( in @ Xy @ A )
% 0.08/0.33 => ( ~ Xphi
% 0.08/0.33 => ( ( dsetconstr @ A
% 0.08/0.33 @ ^ [Xz: $i] :
% 0.08/0.33 ( ( Xphi
% 0.08/0.33 & ( Xz = Xx ) )
% 0.08/0.33 | ( ~ Xphi
% 0.08/0.33 & ( Xz = Xy ) ) ) )
% 0.08/0.33 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(iftrueProp1_type,type,
% 0.08/0.33 iftrueProp1: $o ).
% 0.08/0.33
% 0.08/0.33 thf(iftrueProp1,definition,
% 0.08/0.33 ( iftrueProp1
% 0.08/0.33 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.08/0.33 ( ( in @ Xx @ A )
% 0.08/0.33 => ! [Xy: $i] :
% 0.08/0.33 ( ( in @ Xy @ A )
% 0.08/0.33 => ( Xphi
% 0.08/0.33 => ( in @ Xx
% 0.08/0.33 @ ( dsetconstr @ A
% 0.08/0.33 @ ^ [Xz: $i] :
% 0.08/0.33 ( ( Xphi
% 0.08/0.33 & ( Xz = Xx ) )
% 0.08/0.33 | ( ~ Xphi
% 0.08/0.33 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(iftrueProp2_type,type,
% 0.08/0.33 iftrueProp2: $o ).
% 0.08/0.33
% 0.08/0.33 thf(iftrueProp2,definition,
% 0.08/0.33 ( iftrueProp2
% 0.08/0.33 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.08/0.33 ( ( in @ Xx @ A )
% 0.08/0.33 => ! [Xy: $i] :
% 0.08/0.33 ( ( in @ Xy @ A )
% 0.08/0.33 => ( Xphi
% 0.08/0.33 => ( ( dsetconstr @ A
% 0.08/0.33 @ ^ [Xz: $i] :
% 0.08/0.33 ( ( Xphi
% 0.08/0.33 & ( Xz = Xx ) )
% 0.08/0.33 | ( ~ Xphi
% 0.08/0.33 & ( Xz = Xy ) ) ) )
% 0.08/0.33 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(ifSingleton_type,type,
% 0.08/0.33 ifSingleton: $o ).
% 0.08/0.33
% 0.08/0.33 thf(ifSingleton,definition,
% 0.08/0.33 ( ifSingleton
% 0.08/0.33 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.08/0.33 ( ( in @ Xx @ A )
% 0.08/0.33 => ! [Xy: $i] :
% 0.08/0.33 ( ( in @ Xy @ A )
% 0.08/0.33 => ( singleton
% 0.08/0.33 @ ( dsetconstr @ A
% 0.08/0.33 @ ^ [Xz: $i] :
% 0.08/0.33 ( ( Xphi
% 0.08/0.33 & ( Xz = Xx ) )
% 0.08/0.33 | ( ~ Xphi
% 0.08/0.33 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(if_type,type,
% 0.08/0.33 if: $i > $o > $i > $i > $i ).
% 0.08/0.33
% 0.08/0.33 thf(ifp_type,type,
% 0.08/0.33 ifp: $o ).
% 0.08/0.33
% 0.08/0.33 thf(ifp,definition,
% 0.08/0.33 ( ifp
% 0.08/0.33 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.08/0.33 ( ( in @ Xx @ A )
% 0.08/0.33 => ! [Xy: $i] :
% 0.08/0.33 ( ( in @ Xy @ A )
% 0.08/0.33 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(theeq_type,type,
% 0.08/0.33 theeq: $o ).
% 0.08/0.33
% 0.08/0.33 thf(theeq,definition,
% 0.08/0.33 ( theeq
% 0.08/0.33 = ( ! [X: $i] :
% 0.08/0.33 ( ( singleton @ X )
% 0.08/0.33 => ! [Xx: $i] :
% 0.08/0.33 ( ( in @ Xx @ X )
% 0.08/0.33 => ( ( setunion @ X )
% 0.08/0.33 = Xx ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(iftrue_type,type,
% 0.08/0.33 iftrue: $o ).
% 0.08/0.33
% 0.08/0.33 thf(iftrue,definition,
% 0.08/0.33 ( iftrue
% 0.08/0.33 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.08/0.33 ( ( in @ Xx @ A )
% 0.08/0.33 => ! [Xy: $i] :
% 0.08/0.33 ( ( in @ Xy @ A )
% 0.08/0.33 => ( Xphi
% 0.08/0.33 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.08/0.33 = Xx ) ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(iffalse_type,type,
% 0.08/0.33 iffalse: $o ).
% 0.08/0.33
% 0.08/0.33 thf(iffalse,definition,
% 0.08/0.33 ( iffalse
% 0.08/0.33 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.08/0.33 ( ( in @ Xx @ A )
% 0.08/0.33 => ! [Xy: $i] :
% 0.08/0.33 ( ( in @ Xy @ A )
% 0.08/0.33 => ( ~ Xphi
% 0.08/0.33 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.08/0.33 = Xy ) ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(iftrueorfalse_type,type,
% 0.08/0.33 iftrueorfalse: $o ).
% 0.08/0.33
% 0.08/0.33 thf(iftrueorfalse,definition,
% 0.08/0.33 ( iftrueorfalse
% 0.08/0.33 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.08/0.33 ( ( in @ Xx @ A )
% 0.08/0.33 => ! [Xy: $i] :
% 0.08/0.33 ( ( in @ Xy @ A )
% 0.08/0.33 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(binintersectT_lem_type,type,
% 0.08/0.33 binintersectT_lem: $o ).
% 0.08/0.33
% 0.08/0.33 thf(binintersectT_lem,definition,
% 0.08/0.33 ( binintersectT_lem
% 0.08/0.33 = ( ! [A: $i,X: $i] :
% 0.08/0.33 ( ( in @ X @ ( powerset @ A ) )
% 0.08/0.33 => ! [Y: $i] :
% 0.08/0.33 ( ( in @ Y @ ( powerset @ A ) )
% 0.08/0.33 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(binunionT_lem_type,type,
% 0.08/0.33 binunionT_lem: $o ).
% 0.08/0.33
% 0.08/0.33 thf(binunionT_lem,definition,
% 0.08/0.33 ( binunionT_lem
% 0.08/0.33 = ( ! [A: $i,X: $i] :
% 0.08/0.33 ( ( in @ X @ ( powerset @ A ) )
% 0.08/0.33 => ! [Y: $i] :
% 0.08/0.33 ( ( in @ Y @ ( powerset @ A ) )
% 0.08/0.33 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(powersetT_lem_type,type,
% 0.08/0.33 powersetT_lem: $o ).
% 0.08/0.33
% 0.08/0.33 thf(powersetT_lem,definition,
% 0.08/0.33 ( powersetT_lem
% 0.08/0.33 = ( ! [A: $i,X: $i] :
% 0.08/0.33 ( ( in @ X @ ( powerset @ A ) )
% 0.08/0.33 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(setminusT_lem_type,type,
% 0.08/0.33 setminusT_lem: $o ).
% 0.08/0.33
% 0.08/0.33 thf(setminusT_lem,definition,
% 0.08/0.33 ( setminusT_lem
% 0.08/0.33 = ( ! [A: $i,X: $i] :
% 0.08/0.33 ( ( in @ X @ ( powerset @ A ) )
% 0.08/0.33 => ! [Y: $i] :
% 0.08/0.33 ( ( in @ Y @ ( powerset @ A ) )
% 0.08/0.33 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(complementT_lem_type,type,
% 0.08/0.33 complementT_lem: $o ).
% 0.08/0.33
% 0.08/0.33 thf(complementT_lem,definition,
% 0.08/0.33 ( complementT_lem
% 0.08/0.33 = ( ! [A: $i,X: $i] :
% 0.08/0.33 ( ( in @ X @ ( powerset @ A ) )
% 0.08/0.33 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(setextT_type,type,
% 0.08/0.33 setextT: $o ).
% 0.08/0.33
% 0.08/0.33 thf(setextT,definition,
% 0.08/0.33 ( setextT
% 0.08/0.33 = ( ! [A: $i,X: $i] :
% 0.08/0.33 ( ( in @ X @ ( powerset @ A ) )
% 0.08/0.33 => ! [Y: $i] :
% 0.08/0.33 ( ( in @ Y @ ( powerset @ A ) )
% 0.08/0.33 => ( ! [Xx: $i] :
% 0.08/0.33 ( ( in @ Xx @ A )
% 0.08/0.33 => ( ( in @ Xx @ X )
% 0.08/0.33 => ( in @ Xx @ Y ) ) )
% 0.08/0.33 => ( ! [Xx: $i] :
% 0.08/0.33 ( ( in @ Xx @ A )
% 0.08/0.33 => ( ( in @ Xx @ Y )
% 0.08/0.33 => ( in @ Xx @ X ) ) )
% 0.08/0.33 => ( X = Y ) ) ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(subsetTI_type,type,
% 0.08/0.33 subsetTI: $o ).
% 0.08/0.33
% 0.08/0.33 thf(subsetTI,definition,
% 0.08/0.33 ( subsetTI
% 0.08/0.33 = ( ! [A: $i,X: $i] :
% 0.08/0.33 ( ( in @ X @ ( powerset @ A ) )
% 0.08/0.33 => ! [Y: $i] :
% 0.08/0.33 ( ( in @ Y @ ( powerset @ A ) )
% 0.08/0.33 => ( ! [Xx: $i] :
% 0.08/0.33 ( ( in @ Xx @ A )
% 0.08/0.33 => ( ( in @ Xx @ X )
% 0.08/0.33 => ( in @ Xx @ Y ) ) )
% 0.08/0.33 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(powersetTI1_type,type,
% 0.08/0.33 powersetTI1: $o ).
% 0.08/0.33
% 0.08/0.33 thf(powersetTI1,definition,
% 0.08/0.33 ( powersetTI1
% 0.08/0.33 = ( ! [A: $i,X: $i] :
% 0.08/0.33 ( ( in @ X @ ( powerset @ A ) )
% 0.08/0.33 => ! [Y: $i] :
% 0.08/0.33 ( ( in @ Y @ ( powerset @ A ) )
% 0.08/0.33 => ( ! [Xx: $i] :
% 0.08/0.33 ( ( in @ Xx @ A )
% 0.08/0.33 => ( ( in @ Xx @ X )
% 0.08/0.33 => ( in @ Xx @ Y ) ) )
% 0.08/0.33 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(powersetTE1_type,type,
% 0.08/0.33 powersetTE1: $o ).
% 0.08/0.33
% 0.08/0.33 thf(powersetTE1,definition,
% 0.08/0.33 ( powersetTE1
% 0.08/0.33 = ( ! [A: $i,X: $i] :
% 0.08/0.33 ( ( in @ X @ ( powerset @ A ) )
% 0.08/0.33 => ! [Y: $i] :
% 0.08/0.33 ( ( in @ Y @ ( powerset @ A ) )
% 0.08/0.33 => ! [Xx: $i] :
% 0.08/0.33 ( ( in @ Xx @ A )
% 0.08/0.33 => ( ( in @ X @ ( powerset @ Y ) )
% 0.08/0.33 => ( ( in @ Xx @ X )
% 0.08/0.33 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(complementTI1_type,type,
% 0.08/0.33 complementTI1: $o ).
% 0.08/0.33
% 0.08/0.33 thf(complementTI1,definition,
% 0.08/0.33 ( complementTI1
% 0.08/0.33 = ( ! [A: $i,X: $i] :
% 0.08/0.33 ( ( in @ X @ ( powerset @ A ) )
% 0.08/0.33 => ! [Xx: $i] :
% 0.08/0.33 ( ( in @ Xx @ A )
% 0.08/0.33 => ( ( in @ Xx @ X )
% 0.08/0.33 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(complementTE1_type,type,
% 0.08/0.33 complementTE1: $o ).
% 0.08/0.33
% 0.08/0.33 thf(complementTE1,definition,
% 0.08/0.33 ( complementTE1
% 0.08/0.33 = ( ! [A: $i,X: $i] :
% 0.08/0.33 ( ( in @ X @ ( powerset @ A ) )
% 0.08/0.33 => ! [Xx: $i] :
% 0.08/0.33 ( ( in @ Xx @ A )
% 0.08/0.33 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 0.08/0.33 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(binintersectTELcontra_type,type,
% 0.08/0.33 binintersectTELcontra: $o ).
% 0.08/0.33
% 0.08/0.33 thf(binintersectTELcontra,definition,
% 0.08/0.33 ( binintersectTELcontra
% 0.08/0.33 = ( ! [A: $i,X: $i] :
% 0.08/0.33 ( ( in @ X @ ( powerset @ A ) )
% 0.08/0.33 => ! [Y: $i] :
% 0.08/0.33 ( ( in @ Y @ ( powerset @ A ) )
% 0.08/0.33 => ! [Xx: $i] :
% 0.08/0.33 ( ( in @ Xx @ A )
% 0.08/0.33 => ( ~ ( in @ Xx @ X )
% 0.08/0.33 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(binintersectTERcontra_type,type,
% 0.08/0.33 binintersectTERcontra: $o ).
% 0.08/0.33
% 0.08/0.33 thf(binintersectTERcontra,definition,
% 0.08/0.33 ( binintersectTERcontra
% 0.08/0.33 = ( ! [A: $i,X: $i] :
% 0.08/0.33 ( ( in @ X @ ( powerset @ A ) )
% 0.08/0.33 => ! [Y: $i] :
% 0.08/0.33 ( ( in @ Y @ ( powerset @ A ) )
% 0.08/0.33 => ! [Xx: $i] :
% 0.08/0.33 ( ( in @ Xx @ A )
% 0.08/0.33 => ( ~ ( in @ Xx @ Y )
% 0.08/0.33 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(contrasubsetT_type,type,
% 0.08/0.33 contrasubsetT: $o ).
% 0.08/0.33
% 0.08/0.33 thf(contrasubsetT,definition,
% 0.08/0.33 ( contrasubsetT
% 0.08/0.33 = ( ! [A: $i,X: $i] :
% 0.08/0.33 ( ( in @ X @ ( powerset @ A ) )
% 0.08/0.33 => ! [Y: $i] :
% 0.08/0.33 ( ( in @ Y @ ( powerset @ A ) )
% 0.08/0.33 => ! [Xx: $i] :
% 0.08/0.33 ( ( in @ Xx @ A )
% 0.08/0.33 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.08/0.33 => ( ( in @ Xx @ Y )
% 0.08/0.33 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(contrasubsetT1_type,type,
% 0.08/0.33 contrasubsetT1: $o ).
% 0.08/0.33
% 0.08/0.33 thf(contrasubsetT1,definition,
% 0.08/0.33 ( contrasubsetT1
% 0.08/0.33 = ( ! [A: $i,X: $i] :
% 0.08/0.33 ( ( in @ X @ ( powerset @ A ) )
% 0.08/0.33 => ! [Y: $i] :
% 0.08/0.33 ( ( in @ Y @ ( powerset @ A ) )
% 0.08/0.33 => ! [Xx: $i] :
% 0.08/0.33 ( ( in @ Xx @ A )
% 0.08/0.33 => ( ( subset @ X @ Y )
% 0.08/0.33 => ( ~ ( in @ Xx @ Y )
% 0.08/0.33 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(contrasubsetT2_type,type,
% 0.08/0.33 contrasubsetT2: $o ).
% 0.08/0.33
% 0.08/0.33 thf(contrasubsetT2,definition,
% 0.08/0.33 ( contrasubsetT2
% 0.08/0.33 = ( ! [A: $i,X: $i] :
% 0.08/0.33 ( ( in @ X @ ( powerset @ A ) )
% 0.08/0.33 => ! [Y: $i] :
% 0.08/0.33 ( ( in @ Y @ ( powerset @ A ) )
% 0.08/0.33 => ( ( subset @ X @ Y )
% 0.08/0.33 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(contrasubsetT3_type,type,
% 0.08/0.33 contrasubsetT3: $o ).
% 0.08/0.33
% 0.08/0.33 thf(contrasubsetT3,definition,
% 0.08/0.33 ( contrasubsetT3
% 0.08/0.33 = ( ! [A: $i,X: $i] :
% 0.08/0.33 ( ( in @ X @ ( powerset @ A ) )
% 0.08/0.33 => ! [Y: $i] :
% 0.08/0.33 ( ( in @ Y @ ( powerset @ A ) )
% 0.08/0.33 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 0.08/0.33 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(doubleComplementI1_type,type,
% 0.08/0.33 doubleComplementI1: $o ).
% 0.08/0.33
% 0.08/0.33 thf(doubleComplementI1,definition,
% 0.08/0.33 ( doubleComplementI1
% 0.08/0.33 = ( ! [A: $i,X: $i] :
% 0.08/0.33 ( ( in @ X @ ( powerset @ A ) )
% 0.08/0.33 => ! [Xx: $i] :
% 0.08/0.33 ( ( in @ Xx @ A )
% 0.08/0.33 => ( ( in @ Xx @ X )
% 0.08/0.33 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(doubleComplementE1_type,type,
% 0.08/0.33 doubleComplementE1: $o ).
% 0.08/0.33
% 0.08/0.33 thf(doubleComplementE1,definition,
% 0.08/0.33 ( doubleComplementE1
% 0.08/0.33 = ( ! [A: $i,X: $i] :
% 0.08/0.33 ( ( in @ X @ ( powerset @ A ) )
% 0.08/0.33 => ! [Xx: $i] :
% 0.08/0.33 ( ( in @ Xx @ A )
% 0.08/0.33 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 0.08/0.33 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(doubleComplementSub1_type,type,
% 0.08/0.33 doubleComplementSub1: $o ).
% 0.08/0.33
% 0.08/0.33 thf(doubleComplementSub1,definition,
% 0.08/0.33 ( doubleComplementSub1
% 0.08/0.33 = ( ! [A: $i,X: $i] :
% 0.08/0.33 ( ( in @ X @ ( powerset @ A ) )
% 0.08/0.33 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(doubleComplementSub2_type,type,
% 0.08/0.33 doubleComplementSub2: $o ).
% 0.08/0.33
% 0.08/0.33 thf(doubleComplementSub2,definition,
% 0.08/0.33 ( doubleComplementSub2
% 0.08/0.33 = ( ! [A: $i,X: $i] :
% 0.08/0.33 ( ( in @ X @ ( powerset @ A ) )
% 0.08/0.33 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 thf(doubleComplementEq,conjecture,
% 0.08/0.33 ( setextAx
% 0.08/0.33 => ( emptysetAx
% 0.08/0.33 => ( setadjoinAx
% 0.08/0.33 => ( powersetAx
% 0.08/0.33 => ( setunionAx
% 0.08/0.33 => ( omega0Ax
% 0.08/0.33 => ( omegaSAx
% 0.08/0.33 => ( omegaIndAx
% 0.08/0.33 => ( replAx
% 0.08/0.33 => ( foundationAx
% 0.08/0.33 => ( wellorderingAx
% 0.08/0.33 => ( descrp
% 0.08/0.33 => ( dsetconstrI
% 0.08/0.33 => ( dsetconstrEL
% 0.08/0.33 => ( dsetconstrER
% 0.08/0.33 => ( exuE1
% 0.08/0.33 => ( prop2setE
% 0.08/0.33 => ( emptysetE
% 0.08/0.33 => ( emptysetimpfalse
% 0.08/0.33 => ( notinemptyset
% 0.08/0.33 => ( exuE3e
% 0.08/0.33 => ( setext
% 0.08/0.33 => ( emptyI
% 0.08/0.33 => ( noeltsimpempty
% 0.08/0.33 => ( setbeta
% 0.08/0.33 => ( nonemptyE1
% 0.08/0.33 => ( nonemptyI
% 0.08/0.33 => ( nonemptyI1
% 0.08/0.33 => ( setadjoinIL
% 0.08/0.33 => ( emptyinunitempty
% 0.08/0.33 => ( setadjoinIR
% 0.08/0.33 => ( setadjoinE
% 0.08/0.33 => ( setadjoinOr
% 0.08/0.33 => ( setoftrueEq
% 0.08/0.33 => ( powersetI
% 0.08/0.33 => ( emptyinPowerset
% 0.08/0.33 => ( emptyInPowerset
% 0.08/0.33 => ( powersetE
% 0.08/0.33 => ( setunionI
% 0.08/0.33 => ( setunionE
% 0.08/0.33 => ( subPowSU
% 0.08/0.33 => ( exuE2
% 0.08/0.33 => ( nonemptyImpWitness
% 0.08/0.33 => ( uniqinunit
% 0.08/0.33 => ( notinsingleton
% 0.08/0.33 => ( eqinunit
% 0.08/0.33 => ( singletonsswitch
% 0.08/0.33 => ( upairsetE
% 0.08/0.33 => ( upairsetIL
% 0.08/0.33 => ( upairsetIR
% 0.08/0.33 => ( emptyE1
% 0.08/0.33 => ( vacuousDall
% 0.08/0.33 => ( quantDeMorgan1
% 0.08/0.33 => ( quantDeMorgan2
% 0.08/0.33 => ( quantDeMorgan3
% 0.08/0.33 => ( quantDeMorgan4
% 0.08/0.33 => ( prop2setI
% 0.08/0.33 => ( prop2set2propI
% 0.08/0.33 => ( notdexE
% 0.08/0.33 => ( notdallE
% 0.08/0.33 => ( exuI1
% 0.08/0.33 => ( exuI3
% 0.08/0.33 => ( exuI2
% 0.08/0.33 => ( inCongP
% 0.08/0.33 => ( in__Cong
% 0.08/0.33 => ( exuE3u
% 0.08/0.33 => ( exu__Cong
% 0.08/0.33 => ( emptyset__Cong
% 0.08/0.33 => ( setadjoin__Cong
% 0.08/0.33 => ( powerset__Cong
% 0.08/0.33 => ( setunion__Cong
% 0.08/0.33 => ( omega__Cong
% 0.08/0.33 => ( exuEu
% 0.08/0.33 => ( descr__Cong
% 0.08/0.33 => ( dsetconstr__Cong
% 0.08/0.33 => ( subsetI1
% 0.08/0.33 => ( eqimpsubset2
% 0.08/0.33 => ( eqimpsubset1
% 0.08/0.33 => ( subsetI2
% 0.08/0.33 => ( emptysetsubset
% 0.08/0.33 => ( subsetE
% 0.08/0.33 => ( subsetE2
% 0.08/0.33 => ( notsubsetI
% 0.08/0.33 => ( notequalI1
% 0.08/0.33 => ( notequalI2
% 0.08/0.33 => ( subsetRefl
% 0.08/0.33 => ( subsetTrans
% 0.08/0.33 => ( setadjoinSub
% 0.08/0.33 => ( setadjoinSub2
% 0.08/0.33 => ( subset2powerset
% 0.08/0.33 => ( setextsub
% 0.08/0.33 => ( subsetemptysetimpeq
% 0.08/0.33 => ( powersetI1
% 0.08/0.33 => ( powersetE1
% 0.08/0.33 => ( inPowerset
% 0.08/0.33 => ( powersetsubset
% 0.08/0.33 => ( sepInPowerset
% 0.08/0.33 => ( sepSubset
% 0.08/0.33 => ( binunionIL
% 0.08/0.33 => ( upairset2IR
% 0.08/0.33 => ( binunionIR
% 0.08/0.33 => ( binunionEcases
% 0.08/0.33 => ( binunionE
% 0.08/0.33 => ( binunionLsub
% 0.08/0.33 => ( binunionRsub
% 0.08/0.33 => ( binintersectI
% 0.08/0.33 => ( binintersectSubset5
% 0.08/0.33 => ( binintersectEL
% 0.08/0.33 => ( binintersectLsub
% 0.08/0.33 => ( binintersectSubset2
% 0.08/0.33 => ( binintersectSubset3
% 0.08/0.33 => ( binintersectER
% 0.08/0.33 => ( disjointsetsI1
% 0.08/0.33 => ( binintersectRsub
% 0.08/0.33 => ( binintersectSubset4
% 0.08/0.33 => ( binintersectSubset1
% 0.08/0.33 => ( bs114d
% 0.08/0.33 => ( setminusI
% 0.08/0.33 => ( setminusEL
% 0.08/0.33 => ( setminusER
% 0.08/0.33 => ( setminusSubset2
% 0.08/0.33 => ( setminusERneg
% 0.08/0.33 => ( setminusELneg
% 0.08/0.33 => ( setminusILneg
% 0.08/0.33 => ( setminusIRneg
% 0.08/0.33 => ( setminusLsub
% 0.08/0.33 => ( setminusSubset1
% 0.08/0.33 => ( symdiffE
% 0.08/0.33 => ( symdiffI1
% 0.08/0.33 => ( symdiffI2
% 0.08/0.33 => ( symdiffIneg1
% 0.08/0.33 => ( symdiffIneg2
% 0.08/0.33 => ( secondinupair
% 0.08/0.33 => ( setukpairIL
% 0.08/0.33 => ( setukpairIR
% 0.08/0.33 => ( kpairiskpair
% 0.08/0.33 => ( kpairp
% 0.08/0.33 => ( singletonsubset
% 0.08/0.33 => ( singletoninpowerset
% 0.08/0.33 => ( singletoninpowunion
% 0.08/0.33 => ( upairset2E
% 0.08/0.33 => ( upairsubunion
% 0.08/0.33 => ( upairinpowunion
% 0.08/0.33 => ( ubforcartprodlem1
% 0.08/0.33 => ( ubforcartprodlem2
% 0.08/0.33 => ( ubforcartprodlem3
% 0.08/0.33 => ( cartprodpairin
% 0.08/0.33 => ( cartprodmempair1
% 0.08/0.33 => ( cartprodmempair
% 0.08/0.33 => ( setunionE2
% 0.08/0.33 => ( setunionsingleton1
% 0.08/0.33 => ( setunionsingleton2
% 0.08/0.33 => ( setunionsingleton
% 0.08/0.33 => ( singletonprop
% 0.08/0.33 => ( ex1E1
% 0.08/0.33 => ( ex1I
% 0.08/0.33 => ( ex1I2
% 0.08/0.33 => ( singletonsuniq
% 0.08/0.33 => ( setukpairinjL1
% 0.08/0.33 => ( kfstsingleton
% 0.08/0.33 => ( theprop
% 0.08/0.33 => ( kfstpairEq
% 0.08/0.33 => ( cartprodfstin
% 0.08/0.33 => ( setukpairinjL2
% 0.08/0.33 => ( setukpairinjL
% 0.08/0.33 => ( setukpairinjR11
% 0.08/0.33 => ( setukpairinjR12
% 0.08/0.33 => ( setukpairinjR1
% 0.08/0.33 => ( upairequniteq
% 0.08/0.33 => ( setukpairinjR2
% 0.08/0.33 => ( setukpairinjR
% 0.08/0.33 => ( ksndsingleton
% 0.08/0.33 => ( ksndpairEq
% 0.08/0.33 => ( kpairsurjEq
% 0.08/0.33 => ( cartprodsndin
% 0.08/0.33 => ( cartprodpairmemEL
% 0.08/0.33 => ( cartprodpairmemER
% 0.08/0.33 => ( cartprodmempaircEq
% 0.08/0.33 => ( cartprodfstpairEq
% 0.08/0.33 => ( cartprodsndpairEq
% 0.08/0.33 => ( cartprodpairsurjEq
% 0.08/0.33 => ( dpsetconstrI
% 0.08/0.33 => ( dpsetconstrSub
% 0.08/0.33 => ( setOfPairsIsBReln
% 0.08/0.33 => ( dpsetconstrERa
% 0.08/0.33 => ( dpsetconstrEL1
% 0.08/0.33 => ( dpsetconstrEL2
% 0.08/0.33 => ( dpsetconstrER
% 0.08/0.33 => ( funcImageSingleton
% 0.08/0.33 => ( apProp
% 0.08/0.33 => ( app
% 0.08/0.33 => ( infuncsetfunc
% 0.08/0.33 => ( ap2p
% 0.08/0.33 => ( funcinfuncset
% 0.08/0.33 => ( lamProp
% 0.08/0.33 => ( lamp
% 0.08/0.33 => ( lam2p
% 0.08/0.33 => ( brelnall1
% 0.08/0.33 => ( brelnall2
% 0.08/0.33 => ( ex1E2
% 0.08/0.33 => ( funcGraphProp1
% 0.08/0.33 => ( funcGraphProp3
% 0.08/0.33 => ( funcGraphProp2
% 0.08/0.33 => ( funcextLem
% 0.08/0.33 => ( funcGraphProp4
% 0.08/0.33 => ( subbreln
% 0.08/0.33 => ( eqbreln
% 0.08/0.33 => ( funcext
% 0.08/0.33 => ( funcext2
% 0.08/0.33 => ( ap2apEq1
% 0.08/0.33 => ( ap2apEq2
% 0.08/0.33 => ( beta1
% 0.08/0.33 => ( eta1
% 0.08/0.33 => ( lam2lamEq
% 0.08/0.33 => ( beta2
% 0.08/0.33 => ( eta2
% 0.08/0.33 => ( iffalseProp1
% 0.08/0.33 => ( iffalseProp2
% 0.08/0.33 => ( iftrueProp1
% 0.08/0.33 => ( iftrueProp2
% 0.08/0.33 => ( ifSingleton
% 0.08/0.33 => ( ifp
% 0.08/0.33 => ( theeq
% 0.08/0.33 => ( iftrue
% 0.08/0.33 => ( iffalse
% 0.08/0.33 => ( iftrueorfalse
% 0.08/0.33 => ( binintersectT_lem
% 0.08/0.33 => ( binunionT_lem
% 0.08/0.33 => ( powersetT_lem
% 0.08/0.33 => ( setminusT_lem
% 0.08/0.33 => ( complementT_lem
% 0.08/0.33 => ( setextT
% 0.08/0.33 => ( subsetTI
% 0.08/0.33 => ( powersetTI1
% 0.08/0.33 => ( powersetTE1
% 0.08/0.33 => ( complementTI1
% 0.08/0.33 => ( complementTE1
% 0.08/0.33 => ( binintersectTELcontra
% 0.08/0.33 => ( binintersectTERcontra
% 0.08/0.33 => ( contrasubsetT
% 0.08/0.33 => ( contrasubsetT1
% 0.08/0.33 => ( contrasubsetT2
% 0.08/0.33 => ( contrasubsetT3
% 0.08/0.33 => ( doubleComplementI1
% 0.08/0.33 => ( doubleComplementE1
% 0.08/0.33 => ( doubleComplementSub1
% 0.08/0.33 => ( doubleComplementSub2
% 0.08/0.33 => ! [A: $i,X: $i] :
% 0.08/0.33 ( ( in @ X @ ( powerset @ A ) )
% 0.08/0.33 => ( X
% 0.08/0.33 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.08/0.33
% 0.08/0.33 %------------------------------------------------------------------------------
% 0.08/0.33 ------------------------
% 2.16/1.18 ---- Embedded in THF ---
% 2.16/1.18 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.16/1.18 %%% Generated on Tue Feb 24 07:32:11 EST 2026
% 2.16/1.18 %%% using '$$dhol' embedding, version 1.3.0.
% 2.16/1.18 %%% Logic specification used:
% 2.16/1.18 %%% thf(spec, logic, $$dhol).
% 2.16/1.18
% 2.16/1.18 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.dOeEUbrAIn/DTF2DTF3484.p
% See solution above
% 2.16/1.18 ------------------------
% 2.33/1.21 ---- Cleaned THF ---
% 2.33/1.21 thf(in_type,type,
% 2.33/1.21 in: $i > $i > $o ).
% 2.33/1.21
% 2.33/1.21 thf(exu_type,type,
% 2.33/1.21 exu: ( $i > $o ) > $o ).
% 2.33/1.21
% 2.33/1.21 thf(exu,definition,
% 2.33/1.21 ( exu
% 2.33/1.21 = ( ^ [Xphi: $i > $o] :
% 2.33/1.21 ? [Xx: $i] :
% 2.33/1.21 ( ( Xphi @ Xx )
% 2.33/1.21 & ! [Xy: $i] :
% 2.33/1.21 ( ( Xphi @ Xy )
% 2.33/1.21 => ( Xx = Xy ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setextAx_type,type,
% 2.33/1.21 setextAx: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setextAx,definition,
% 2.33/1.21 ( setextAx
% 2.33/1.21 = ( ! [A: $i,B: $i] :
% 2.33/1.21 ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 <=> ( in @ Xx @ B ) )
% 2.33/1.21 => ( A = B ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(emptyset_type,type,
% 2.33/1.21 emptyset: $i ).
% 2.33/1.21
% 2.33/1.21 thf(emptysetAx_type,type,
% 2.33/1.21 emptysetAx: $o ).
% 2.33/1.21
% 2.33/1.21 thf(emptysetAx,definition,
% 2.33/1.21 ( emptysetAx
% 2.33/1.21 = ( ! [Xx: $i] :
% 2.33/1.21 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setadjoin_type,type,
% 2.33/1.21 setadjoin: $i > $i > $i ).
% 2.33/1.21
% 2.33/1.21 thf(setadjoinAx_type,type,
% 2.33/1.21 setadjoinAx: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setadjoinAx,definition,
% 2.33/1.21 ( setadjoinAx
% 2.33/1.21 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.33/1.21 <=> ( ( Xy = Xx )
% 2.33/1.21 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(powerset_type,type,
% 2.33/1.21 powerset: $i > $i ).
% 2.33/1.21
% 2.33/1.21 thf(powersetAx_type,type,
% 2.33/1.21 powersetAx: $o ).
% 2.33/1.21
% 2.33/1.21 thf(powersetAx,definition,
% 2.33/1.21 ( powersetAx
% 2.33/1.21 = ( ! [A: $i,B: $i] :
% 2.33/1.21 ( ( in @ B @ ( powerset @ A ) )
% 2.33/1.21 <=> ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ B )
% 2.33/1.21 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setunion_type,type,
% 2.33/1.21 setunion: $i > $i ).
% 2.33/1.21
% 2.33/1.21 thf(setunionAx_type,type,
% 2.33/1.21 setunionAx: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setunionAx,definition,
% 2.33/1.21 ( setunionAx
% 2.33/1.21 = ( ! [A: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ ( setunion @ A ) )
% 2.33/1.21 <=> ? [B: $i] :
% 2.33/1.21 ( ( in @ Xx @ B )
% 2.33/1.21 & ( in @ B @ A ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(omega_type,type,
% 2.33/1.21 omega: $i ).
% 2.33/1.21
% 2.33/1.21 thf(omega0Ax_type,type,
% 2.33/1.21 omega0Ax: $o ).
% 2.33/1.21
% 2.33/1.21 thf(omega0Ax,definition,
% 2.33/1.21 ( omega0Ax
% 2.33/1.21 = ( in @ emptyset @ omega ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(omegaSAx_type,type,
% 2.33/1.21 omegaSAx: $o ).
% 2.33/1.21
% 2.33/1.21 thf(omegaSAx,definition,
% 2.33/1.21 ( omegaSAx
% 2.33/1.21 = ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ omega )
% 2.33/1.21 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(omegaIndAx_type,type,
% 2.33/1.21 omegaIndAx: $o ).
% 2.33/1.21
% 2.33/1.21 thf(omegaIndAx,definition,
% 2.33/1.21 ( omegaIndAx
% 2.33/1.21 = ( ! [A: $i] :
% 2.33/1.21 ( ( ( in @ emptyset @ A )
% 2.33/1.21 & ! [Xx: $i] :
% 2.33/1.21 ( ( ( in @ Xx @ omega )
% 2.33/1.21 & ( in @ Xx @ A ) )
% 2.33/1.21 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ omega )
% 2.33/1.21 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(replAx_type,type,
% 2.33/1.21 replAx: $o ).
% 2.33/1.21
% 2.33/1.21 thf(replAx,definition,
% 2.33/1.21 ( replAx
% 2.33/1.21 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.33/1.21 ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( exu
% 2.33/1.21 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.33/1.21 => ? [B: $i] :
% 2.33/1.21 ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ B )
% 2.33/1.21 <=> ? [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ A )
% 2.33/1.21 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(foundationAx_type,type,
% 2.33/1.21 foundationAx: $o ).
% 2.33/1.21
% 2.33/1.21 thf(foundationAx,definition,
% 2.33/1.21 ( foundationAx
% 2.33/1.21 = ( ! [A: $i] :
% 2.33/1.21 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.33/1.21 => ? [B: $i] :
% 2.33/1.21 ( ( in @ B @ A )
% 2.33/1.21 & ~ ? [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ B )
% 2.33/1.21 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(wellorderingAx_type,type,
% 2.33/1.21 wellorderingAx: $o ).
% 2.33/1.21
% 2.33/1.21 thf(wellorderingAx,definition,
% 2.33/1.21 ( wellorderingAx
% 2.33/1.21 = ( ! [A: $i] :
% 2.33/1.21 ? [B: $i] :
% 2.33/1.21 ( ! [C: $i] :
% 2.33/1.21 ( ( in @ C @ B )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ C )
% 2.33/1.21 => ( in @ Xx @ A ) ) )
% 2.33/1.21 & ! [Xx: $i,Xy: $i] :
% 2.33/1.21 ( ( ( in @ Xx @ A )
% 2.33/1.21 & ( in @ Xy @ A ) )
% 2.33/1.21 => ( ! [C: $i] :
% 2.33/1.21 ( ( in @ C @ B )
% 2.33/1.21 => ( ( in @ Xx @ C )
% 2.33/1.21 <=> ( in @ Xy @ C ) ) )
% 2.33/1.21 => ( Xx = Xy ) ) )
% 2.33/1.21 & ! [C: $i,D: $i] :
% 2.33/1.21 ( ( ( in @ C @ B )
% 2.33/1.21 & ( in @ D @ B ) )
% 2.33/1.21 => ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ C )
% 2.33/1.21 => ( in @ Xx @ D ) )
% 2.33/1.21 | ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ D )
% 2.33/1.21 => ( in @ Xx @ C ) ) ) )
% 2.33/1.21 & ! [C: $i] :
% 2.33/1.21 ( ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ C )
% 2.33/1.21 => ( in @ Xx @ A ) )
% 2.33/1.21 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.33/1.21 => ? [D: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ D @ B )
% 2.33/1.21 & ( in @ Xx @ C )
% 2.33/1.21 & ~ ? [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ D )
% 2.33/1.21 & ( in @ Xy @ C ) )
% 2.33/1.21 & ! [E: $i] :
% 2.33/1.21 ( ( in @ E @ B )
% 2.33/1.21 => ( ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ E )
% 2.33/1.21 => ( in @ Xy @ D ) )
% 2.33/1.21 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(descr_type,type,
% 2.33/1.21 descr: ( $i > $o ) > $i ).
% 2.33/1.21
% 2.33/1.21 thf(descrp_type,type,
% 2.33/1.21 descrp: $o ).
% 2.33/1.21
% 2.33/1.21 thf(descrp,definition,
% 2.33/1.21 ( descrp
% 2.33/1.21 = ( ! [Xphi: $i > $o] :
% 2.33/1.21 ( ( exu
% 2.33/1.21 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.33/1.21 => ( Xphi
% 2.33/1.21 @ ( descr
% 2.33/1.21 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(dsetconstr_type,type,
% 2.33/1.21 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.33/1.21
% 2.33/1.21 thf(dsetconstrI_type,type,
% 2.33/1.21 dsetconstrI: $o ).
% 2.33/1.21
% 2.33/1.21 thf(dsetconstrI,definition,
% 2.33/1.21 ( dsetconstrI
% 2.33/1.21 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ( Xphi @ Xx )
% 2.33/1.21 => ( in @ Xx
% 2.33/1.21 @ ( dsetconstr @ A
% 2.33/1.21 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(dsetconstrEL_type,type,
% 2.33/1.21 dsetconstrEL: $o ).
% 2.33/1.21
% 2.33/1.21 thf(dsetconstrEL,definition,
% 2.33/1.21 ( dsetconstrEL
% 2.33/1.21 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx
% 2.33/1.21 @ ( dsetconstr @ A
% 2.33/1.21 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.33/1.21 => ( in @ Xx @ A ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(dsetconstrER_type,type,
% 2.33/1.21 dsetconstrER: $o ).
% 2.33/1.21
% 2.33/1.21 thf(dsetconstrER,definition,
% 2.33/1.21 ( dsetconstrER
% 2.33/1.21 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx
% 2.33/1.21 @ ( dsetconstr @ A
% 2.33/1.21 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.33/1.21 => ( Xphi @ Xx ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(exuE1_type,type,
% 2.33/1.21 exuE1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(exuE1,definition,
% 2.33/1.21 ( exuE1
% 2.33/1.21 = ( ! [Xphi: $i > $o] :
% 2.33/1.21 ( ( exu
% 2.33/1.21 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.33/1.21 => ? [Xx: $i] :
% 2.33/1.21 ( ( Xphi @ Xx )
% 2.33/1.21 & ! [Xy: $i] :
% 2.33/1.21 ( ( Xphi @ Xy )
% 2.33/1.21 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(prop2set_type,type,
% 2.33/1.21 prop2set: $o > $i ).
% 2.33/1.21
% 2.33/1.21 thf(prop2setE_type,type,
% 2.33/1.21 prop2setE: $o ).
% 2.33/1.21
% 2.33/1.21 thf(prop2setE,definition,
% 2.33/1.21 ( prop2setE
% 2.33/1.21 = ( ! [Xphi: $o,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.33/1.21 => Xphi ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(emptysetE_type,type,
% 2.33/1.21 emptysetE: $o ).
% 2.33/1.21
% 2.33/1.21 thf(emptysetE,definition,
% 2.33/1.21 ( emptysetE
% 2.33/1.21 = ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ emptyset )
% 2.33/1.21 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(emptysetimpfalse_type,type,
% 2.33/1.21 emptysetimpfalse: $o ).
% 2.33/1.21
% 2.33/1.21 thf(emptysetimpfalse,definition,
% 2.33/1.21 ( emptysetimpfalse
% 2.33/1.21 = ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ emptyset )
% 2.33/1.21 => $false ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(notinemptyset_type,type,
% 2.33/1.21 notinemptyset: $o ).
% 2.33/1.21
% 2.33/1.21 thf(notinemptyset,definition,
% 2.33/1.21 ( notinemptyset
% 2.33/1.21 = ( ! [Xx: $i] :
% 2.33/1.21 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(exuE3e_type,type,
% 2.33/1.21 exuE3e: $o ).
% 2.33/1.21
% 2.33/1.21 thf(exuE3e,definition,
% 2.33/1.21 ( exuE3e
% 2.33/1.21 = ( ! [Xphi: $i > $o] :
% 2.33/1.21 ( ( exu
% 2.33/1.21 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.33/1.21 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setext_type,type,
% 2.33/1.21 setext: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setext,definition,
% 2.33/1.21 ( setext
% 2.33/1.21 = ( ! [A: $i,B: $i] :
% 2.33/1.21 ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( in @ Xx @ B ) )
% 2.33/1.21 => ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ B )
% 2.33/1.21 => ( in @ Xx @ A ) )
% 2.33/1.21 => ( A = B ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(emptyI_type,type,
% 2.33/1.21 emptyI: $o ).
% 2.33/1.21
% 2.33/1.21 thf(emptyI,definition,
% 2.33/1.21 ( emptyI
% 2.33/1.21 = ( ! [A: $i] :
% 2.33/1.21 ( ! [Xx: $i] :
% 2.33/1.21 ~ ( in @ Xx @ A )
% 2.33/1.21 => ( A = emptyset ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(noeltsimpempty_type,type,
% 2.33/1.21 noeltsimpempty: $o ).
% 2.33/1.21
% 2.33/1.21 thf(noeltsimpempty,definition,
% 2.33/1.21 ( noeltsimpempty
% 2.33/1.21 = ( ! [A: $i] :
% 2.33/1.21 ( ! [Xx: $i] :
% 2.33/1.21 ~ ( in @ Xx @ A )
% 2.33/1.21 => ( A = emptyset ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setbeta_type,type,
% 2.33/1.21 setbeta: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setbeta,definition,
% 2.33/1.21 ( setbeta
% 2.33/1.21 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ( in @ Xx
% 2.33/1.21 @ ( dsetconstr @ A
% 2.33/1.21 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.33/1.21 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(nonempty_type,type,
% 2.33/1.21 nonempty: $i > $o ).
% 2.33/1.21
% 2.33/1.21 thf(nonempty,definition,
% 2.33/1.21 ( nonempty
% 2.33/1.21 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(nonemptyE1_type,type,
% 2.33/1.21 nonemptyE1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(nonemptyE1,definition,
% 2.33/1.21 ( nonemptyE1
% 2.33/1.21 = ( ! [A: $i] :
% 2.33/1.21 ( ( nonempty @ A )
% 2.33/1.21 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(nonemptyI_type,type,
% 2.33/1.21 nonemptyI: $o ).
% 2.33/1.21
% 2.33/1.21 thf(nonemptyI,definition,
% 2.33/1.21 ( nonemptyI
% 2.33/1.21 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ( Xphi @ Xx )
% 2.33/1.21 => ( nonempty
% 2.33/1.21 @ ( dsetconstr @ A
% 2.33/1.21 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(nonemptyI1_type,type,
% 2.33/1.21 nonemptyI1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(nonemptyI1,definition,
% 2.33/1.21 ( nonemptyI1
% 2.33/1.21 = ( ! [A: $i] :
% 2.33/1.21 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.33/1.21 => ( nonempty @ A ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setadjoinIL_type,type,
% 2.33/1.21 setadjoinIL: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setadjoinIL,definition,
% 2.33/1.21 ( setadjoinIL
% 2.33/1.21 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(emptyinunitempty_type,type,
% 2.33/1.21 emptyinunitempty: $o ).
% 2.33/1.21
% 2.33/1.21 thf(emptyinunitempty,definition,
% 2.33/1.21 ( emptyinunitempty
% 2.33/1.21 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setadjoinIR_type,type,
% 2.33/1.21 setadjoinIR: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setadjoinIR,definition,
% 2.33/1.21 ( setadjoinIR
% 2.33/1.21 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ A )
% 2.33/1.21 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setadjoinE_type,type,
% 2.33/1.21 setadjoinE: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setadjoinE,definition,
% 2.33/1.21 ( setadjoinE
% 2.33/1.21 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.33/1.21 => ! [Xphi: $o] :
% 2.33/1.21 ( ( ( Xy = Xx )
% 2.33/1.21 => Xphi )
% 2.33/1.21 => ( ( ( in @ Xy @ A )
% 2.33/1.21 => Xphi )
% 2.33/1.21 => Xphi ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setadjoinOr_type,type,
% 2.33/1.21 setadjoinOr: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setadjoinOr,definition,
% 2.33/1.21 ( setadjoinOr
% 2.33/1.21 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.33/1.21 => ( ( Xy = Xx )
% 2.33/1.21 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setoftrueEq_type,type,
% 2.33/1.21 setoftrueEq: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setoftrueEq,definition,
% 2.33/1.21 ( setoftrueEq
% 2.33/1.21 = ( ! [A: $i] :
% 2.33/1.21 ( ( dsetconstr @ A
% 2.33/1.21 @ ^ [Xx: $i] : $true )
% 2.33/1.21 = A ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(powersetI_type,type,
% 2.33/1.21 powersetI: $o ).
% 2.33/1.21
% 2.33/1.21 thf(powersetI,definition,
% 2.33/1.21 ( powersetI
% 2.33/1.21 = ( ! [A: $i,B: $i] :
% 2.33/1.21 ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ B )
% 2.33/1.21 => ( in @ Xx @ A ) )
% 2.33/1.21 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(emptyinPowerset_type,type,
% 2.33/1.21 emptyinPowerset: $o ).
% 2.33/1.21
% 2.33/1.21 thf(emptyinPowerset,definition,
% 2.33/1.21 ( emptyinPowerset
% 2.33/1.21 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(emptyInPowerset_type,type,
% 2.33/1.21 emptyInPowerset: $o ).
% 2.33/1.21
% 2.33/1.21 thf(emptyInPowerset,definition,
% 2.33/1.21 ( emptyInPowerset
% 2.33/1.21 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(powersetE_type,type,
% 2.33/1.21 powersetE: $o ).
% 2.33/1.21
% 2.33/1.21 thf(powersetE,definition,
% 2.33/1.21 ( powersetE
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ B @ ( powerset @ A ) )
% 2.33/1.21 => ( ( in @ Xx @ B )
% 2.33/1.21 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setunionI_type,type,
% 2.33/1.21 setunionI: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setunionI,definition,
% 2.33/1.21 ( setunionI
% 2.33/1.21 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.33/1.21 ( ( in @ Xx @ B )
% 2.33/1.21 => ( ( in @ B @ A )
% 2.33/1.21 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setunionE_type,type,
% 2.33/1.21 setunionE: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setunionE,definition,
% 2.33/1.21 ( setunionE
% 2.33/1.21 = ( ! [A: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ ( setunion @ A ) )
% 2.33/1.21 => ! [Xphi: $o] :
% 2.33/1.21 ( ! [B: $i] :
% 2.33/1.21 ( ( in @ Xx @ B )
% 2.33/1.21 => ( ( in @ B @ A )
% 2.33/1.21 => Xphi ) )
% 2.33/1.21 => Xphi ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(subPowSU_type,type,
% 2.33/1.21 subPowSU: $o ).
% 2.33/1.21
% 2.33/1.21 thf(subPowSU,definition,
% 2.33/1.21 ( subPowSU
% 2.33/1.21 = ( ! [A: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(exuE2_type,type,
% 2.33/1.21 exuE2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(exuE2,definition,
% 2.33/1.21 ( exuE2
% 2.33/1.21 = ( ! [Xphi: $i > $o] :
% 2.33/1.21 ( ( exu
% 2.33/1.21 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.33/1.21 => ? [Xx: $i] :
% 2.33/1.21 ! [Xy: $i] :
% 2.33/1.21 ( ( Xphi @ Xy )
% 2.33/1.21 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(nonemptyImpWitness_type,type,
% 2.33/1.21 nonemptyImpWitness: $o ).
% 2.33/1.21
% 2.33/1.21 thf(nonemptyImpWitness,definition,
% 2.33/1.21 ( nonemptyImpWitness
% 2.33/1.21 = ( ! [A: $i] :
% 2.33/1.21 ( ( nonempty @ A )
% 2.33/1.21 => ? [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 & $true ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(uniqinunit_type,type,
% 2.33/1.21 uniqinunit: $o ).
% 2.33/1.21
% 2.33/1.21 thf(uniqinunit,definition,
% 2.33/1.21 ( uniqinunit
% 2.33/1.21 = ( ! [Xx: $i,Xy: $i] :
% 2.33/1.21 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.33/1.21 => ( Xx = Xy ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(notinsingleton_type,type,
% 2.33/1.21 notinsingleton: $o ).
% 2.33/1.21
% 2.33/1.21 thf(notinsingleton,definition,
% 2.33/1.21 ( notinsingleton
% 2.33/1.21 = ( ! [Xx: $i,Xy: $i] :
% 2.33/1.21 ( ( Xx != Xy )
% 2.33/1.21 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(eqinunit_type,type,
% 2.33/1.21 eqinunit: $o ).
% 2.33/1.21
% 2.33/1.21 thf(eqinunit,definition,
% 2.33/1.21 ( eqinunit
% 2.33/1.21 = ( ! [Xx: $i,Xy: $i] :
% 2.33/1.21 ( ( Xx = Xy )
% 2.33/1.21 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(singletonsswitch_type,type,
% 2.33/1.21 singletonsswitch: $o ).
% 2.33/1.21
% 2.33/1.21 thf(singletonsswitch,definition,
% 2.33/1.21 ( singletonsswitch
% 2.33/1.21 = ( ! [Xx: $i,Xy: $i] :
% 2.33/1.21 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.33/1.21 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(upairsetE_type,type,
% 2.33/1.21 upairsetE: $o ).
% 2.33/1.21
% 2.33/1.21 thf(upairsetE,definition,
% 2.33/1.21 ( upairsetE
% 2.33/1.21 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.33/1.21 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.33/1.21 => ( ( Xz = Xx )
% 2.33/1.21 | ( Xz = Xy ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(upairsetIL_type,type,
% 2.33/1.21 upairsetIL: $o ).
% 2.33/1.21
% 2.33/1.21 thf(upairsetIL,definition,
% 2.33/1.21 ( upairsetIL
% 2.33/1.21 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(upairsetIR_type,type,
% 2.33/1.21 upairsetIR: $o ).
% 2.33/1.21
% 2.33/1.21 thf(upairsetIR,definition,
% 2.33/1.21 ( upairsetIR
% 2.33/1.21 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(emptyE1_type,type,
% 2.33/1.21 emptyE1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(emptyE1,definition,
% 2.33/1.21 ( emptyE1
% 2.33/1.21 = ( ! [A: $i,Xphi: $i > $o] :
% 2.33/1.21 ( ? [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 & ( Xphi @ Xx ) )
% 2.33/1.21 => ( ( ( dsetconstr @ A
% 2.33/1.21 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.33/1.21 = emptyset )
% 2.33/1.21 => $false ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(vacuousDall_type,type,
% 2.33/1.21 vacuousDall: $o ).
% 2.33/1.21
% 2.33/1.21 thf(vacuousDall,definition,
% 2.33/1.21 ( vacuousDall
% 2.33/1.21 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ emptyset )
% 2.33/1.21 => ( Xphi @ Xx ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(quantDeMorgan1_type,type,
% 2.33/1.21 quantDeMorgan1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(quantDeMorgan1,definition,
% 2.33/1.21 ( quantDeMorgan1
% 2.33/1.21 = ( ! [A: $i,Xphi: $i > $o] :
% 2.33/1.21 ( ~ ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( Xphi @ Xx ) )
% 2.33/1.21 => ? [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(quantDeMorgan2_type,type,
% 2.33/1.21 quantDeMorgan2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(quantDeMorgan2,definition,
% 2.33/1.21 ( quantDeMorgan2
% 2.33/1.21 = ( ! [A: $i,Xphi: $i > $o] :
% 2.33/1.21 ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ~ ( Xphi @ Xx ) )
% 2.33/1.21 => ~ ? [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(quantDeMorgan3_type,type,
% 2.33/1.21 quantDeMorgan3: $o ).
% 2.33/1.21
% 2.33/1.21 thf(quantDeMorgan3,definition,
% 2.33/1.21 ( quantDeMorgan3
% 2.33/1.21 = ( ! [A: $i,Xphi: $i > $o] :
% 2.33/1.21 ( ~ ? [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 & ( Xphi @ Xx ) )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(quantDeMorgan4_type,type,
% 2.33/1.21 quantDeMorgan4: $o ).
% 2.33/1.21
% 2.33/1.21 thf(quantDeMorgan4,definition,
% 2.33/1.21 ( quantDeMorgan4
% 2.33/1.21 = ( ! [A: $i,Xphi: $i > $o] :
% 2.33/1.21 ( ? [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 & ~ ( Xphi @ Xx ) )
% 2.33/1.21 => ~ ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(prop2setI_type,type,
% 2.33/1.21 prop2setI: $o ).
% 2.33/1.21
% 2.33/1.21 thf(prop2setI,definition,
% 2.33/1.21 ( prop2setI
% 2.33/1.21 = ( ! [Xphi: $o] :
% 2.33/1.21 ( Xphi
% 2.33/1.21 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(set2prop_type,type,
% 2.33/1.21 set2prop: $i > $o ).
% 2.33/1.21
% 2.33/1.21 thf(prop2set2propI_type,type,
% 2.33/1.21 prop2set2propI: $o ).
% 2.33/1.21
% 2.33/1.21 thf(prop2set2propI,definition,
% 2.33/1.21 ( prop2set2propI
% 2.33/1.21 = ( ! [Xphi: $o] :
% 2.33/1.21 ( Xphi
% 2.33/1.21 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(notdexE_type,type,
% 2.33/1.21 notdexE: $o ).
% 2.33/1.21
% 2.33/1.21 thf(notdexE,definition,
% 2.33/1.21 ( notdexE
% 2.33/1.21 = ( ! [A: $i,Xphi: $i > $o] :
% 2.33/1.21 ( ~ ? [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 & ( Xphi @ Xx ) )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(notdallE_type,type,
% 2.33/1.21 notdallE: $o ).
% 2.33/1.21
% 2.33/1.21 thf(notdallE,definition,
% 2.33/1.21 ( notdallE
% 2.33/1.21 = ( ! [A: $i,Xphi: $i > $o] :
% 2.33/1.21 ( ~ ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( Xphi @ Xx ) )
% 2.33/1.21 => ? [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(exuI1_type,type,
% 2.33/1.21 exuI1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(exuI1,definition,
% 2.33/1.21 ( exuI1
% 2.33/1.21 = ( ! [Xphi: $i > $o] :
% 2.33/1.21 ( ? [Xx: $i] :
% 2.33/1.21 ( ( Xphi @ Xx )
% 2.33/1.21 & ! [Xy: $i] :
% 2.33/1.21 ( ( Xphi @ Xy )
% 2.33/1.21 => ( Xx = Xy ) ) )
% 2.33/1.21 => ( exu
% 2.33/1.21 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(exuI3_type,type,
% 2.33/1.21 exuI3: $o ).
% 2.33/1.21
% 2.33/1.21 thf(exuI3,definition,
% 2.33/1.21 ( exuI3
% 2.33/1.21 = ( ! [Xphi: $i > $o] :
% 2.33/1.21 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.33/1.21 => ( ! [Xx: $i,Xy: $i] :
% 2.33/1.21 ( ( Xphi @ Xx )
% 2.33/1.21 => ( ( Xphi @ Xy )
% 2.33/1.21 => ( Xx = Xy ) ) )
% 2.33/1.21 => ( exu
% 2.33/1.21 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(exuI2_type,type,
% 2.33/1.21 exuI2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(exuI2,definition,
% 2.33/1.21 ( exuI2
% 2.33/1.21 = ( ! [Xphi: $i > $o] :
% 2.33/1.21 ( ? [Xx: $i] :
% 2.33/1.21 ! [Xy: $i] :
% 2.33/1.21 ( ( Xphi @ Xy )
% 2.33/1.21 <=> ( Xy = Xx ) )
% 2.33/1.21 => ( exu
% 2.33/1.21 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(inCongP_type,type,
% 2.33/1.21 inCongP: $o ).
% 2.33/1.21
% 2.33/1.21 thf(inCongP,definition,
% 2.33/1.21 ( inCongP
% 2.33/1.21 = ( ! [A: $i,B: $i] :
% 2.33/1.21 ( ( A = B )
% 2.33/1.21 => ! [Xx: $i,Xy: $i] :
% 2.33/1.21 ( ( Xx = Xy )
% 2.33/1.21 => ( ( in @ Xx @ A )
% 2.33/1.21 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(in__Cong_type,type,
% 2.33/1.21 in__Cong: $o ).
% 2.33/1.21
% 2.33/1.21 thf(in__Cong,definition,
% 2.33/1.21 ( in__Cong
% 2.33/1.21 = ( ! [A: $i,B: $i] :
% 2.33/1.21 ( ( A = B )
% 2.33/1.21 => ! [Xx: $i,Xy: $i] :
% 2.33/1.21 ( ( Xx = Xy )
% 2.33/1.21 => ( ( in @ Xx @ A )
% 2.33/1.21 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(exuE3u_type,type,
% 2.33/1.21 exuE3u: $o ).
% 2.33/1.21
% 2.33/1.21 thf(exuE3u,definition,
% 2.33/1.21 ( exuE3u
% 2.33/1.21 = ( ! [Xphi: $i > $o] :
% 2.33/1.21 ( ( exu
% 2.33/1.21 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.33/1.21 => ! [Xx: $i,Xy: $i] :
% 2.33/1.21 ( ( Xphi @ Xx )
% 2.33/1.21 => ( ( Xphi @ Xy )
% 2.33/1.21 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(exu__Cong_type,type,
% 2.33/1.21 exu__Cong: $o ).
% 2.33/1.21
% 2.33/1.21 thf(exu__Cong,definition,
% 2.33/1.21 ( exu__Cong
% 2.33/1.21 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.33/1.21 ( ! [Xx: $i,Xy: $i] :
% 2.33/1.21 ( ( Xx = Xy )
% 2.33/1.21 => ( ( Xphi @ Xx )
% 2.33/1.21 <=> ( Xpsi @ Xy ) ) )
% 2.33/1.21 => ( ( exu
% 2.33/1.21 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.33/1.21 <=> ( exu
% 2.33/1.21 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(emptyset__Cong_type,type,
% 2.33/1.21 emptyset__Cong: $o ).
% 2.33/1.21
% 2.33/1.21 thf(emptyset__Cong,definition,
% 2.33/1.21 ( emptyset__Cong
% 2.33/1.21 = ( emptyset = emptyset ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setadjoin__Cong_type,type,
% 2.33/1.21 setadjoin__Cong: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setadjoin__Cong,definition,
% 2.33/1.21 ( setadjoin__Cong
% 2.33/1.21 = ( ! [Xx: $i,Xy: $i] :
% 2.33/1.21 ( ( Xx = Xy )
% 2.33/1.21 => ! [Xz: $i,Xu: $i] :
% 2.33/1.21 ( ( Xz = Xu )
% 2.33/1.21 => ( ( setadjoin @ Xx @ Xz )
% 2.33/1.21 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(powerset__Cong_type,type,
% 2.33/1.21 powerset__Cong: $o ).
% 2.33/1.21
% 2.33/1.21 thf(powerset__Cong,definition,
% 2.33/1.21 ( powerset__Cong
% 2.33/1.21 = ( ! [A: $i,B: $i] :
% 2.33/1.21 ( ( A = B )
% 2.33/1.21 => ( ( powerset @ A )
% 2.33/1.21 = ( powerset @ B ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setunion__Cong_type,type,
% 2.33/1.21 setunion__Cong: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setunion__Cong,definition,
% 2.33/1.21 ( setunion__Cong
% 2.33/1.21 = ( ! [A: $i,B: $i] :
% 2.33/1.21 ( ( A = B )
% 2.33/1.21 => ( ( setunion @ A )
% 2.33/1.21 = ( setunion @ B ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(omega__Cong_type,type,
% 2.33/1.21 omega__Cong: $o ).
% 2.33/1.21
% 2.33/1.21 thf(omega__Cong,definition,
% 2.33/1.21 ( omega__Cong
% 2.33/1.21 = ( omega = omega ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(exuEu_type,type,
% 2.33/1.21 exuEu: $o ).
% 2.33/1.21
% 2.33/1.21 thf(exuEu,definition,
% 2.33/1.21 ( exuEu
% 2.33/1.21 = ( ! [Xphi: $i > $o] :
% 2.33/1.21 ( ( exu
% 2.33/1.21 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.33/1.21 => ! [Xx: $i,Xy: $i] :
% 2.33/1.21 ( ( Xphi @ Xx )
% 2.33/1.21 => ( ( Xphi @ Xy )
% 2.33/1.21 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(descr__Cong_type,type,
% 2.33/1.21 descr__Cong: $o ).
% 2.33/1.21
% 2.33/1.21 thf(descr__Cong,definition,
% 2.33/1.21 ( descr__Cong
% 2.33/1.21 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.33/1.21 ( ! [Xx: $i,Xy: $i] :
% 2.33/1.21 ( ( Xx = Xy )
% 2.33/1.21 => ( ( Xphi @ Xx )
% 2.33/1.21 <=> ( Xpsi @ Xy ) ) )
% 2.33/1.21 => ( ( exu
% 2.33/1.21 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.33/1.21 => ( ( exu
% 2.33/1.21 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.33/1.21 => ( ( descr
% 2.33/1.21 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.33/1.21 = ( descr
% 2.33/1.21 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(dsetconstr__Cong_type,type,
% 2.33/1.21 dsetconstr__Cong: $o ).
% 2.33/1.21
% 2.33/1.21 thf(dsetconstr__Cong,definition,
% 2.33/1.21 ( dsetconstr__Cong
% 2.33/1.21 = ( ! [A: $i,B: $i] :
% 2.33/1.21 ( ( A = B )
% 2.33/1.21 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.33/1.21 ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ B )
% 2.33/1.21 => ( ( Xx = Xy )
% 2.33/1.21 => ( ( Xphi @ Xx )
% 2.33/1.21 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.33/1.21 => ( ( dsetconstr @ A
% 2.33/1.21 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.33/1.21 = ( dsetconstr @ B
% 2.33/1.21 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(subset_type,type,
% 2.33/1.21 subset: $i > $i > $o ).
% 2.33/1.21
% 2.33/1.21 thf(disjoint_type,type,
% 2.33/1.21 disjoint: $i > $i > $o ).
% 2.33/1.21
% 2.33/1.21 thf(setsmeet_type,type,
% 2.33/1.21 setsmeet: $i > $i > $o ).
% 2.33/1.21
% 2.33/1.21 thf(subsetI1_type,type,
% 2.33/1.21 subsetI1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(subsetI1,definition,
% 2.33/1.21 ( subsetI1
% 2.33/1.21 = ( ! [A: $i,B: $i] :
% 2.33/1.21 ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( in @ Xx @ B ) )
% 2.33/1.21 => ( subset @ A @ B ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(eqimpsubset2_type,type,
% 2.33/1.21 eqimpsubset2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(eqimpsubset2,definition,
% 2.33/1.21 ( eqimpsubset2
% 2.33/1.21 = ( ! [A: $i,B: $i] :
% 2.33/1.21 ( ( A = B )
% 2.33/1.21 => ( subset @ B @ A ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(eqimpsubset1_type,type,
% 2.33/1.21 eqimpsubset1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(eqimpsubset1,definition,
% 2.33/1.21 ( eqimpsubset1
% 2.33/1.21 = ( ! [A: $i,B: $i] :
% 2.33/1.21 ( ( A = B )
% 2.33/1.21 => ( subset @ A @ B ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(subsetI2_type,type,
% 2.33/1.21 subsetI2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(subsetI2,definition,
% 2.33/1.21 ( subsetI2
% 2.33/1.21 = ( ! [A: $i,B: $i] :
% 2.33/1.21 ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( in @ Xx @ B ) )
% 2.33/1.21 => ( subset @ A @ B ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(emptysetsubset_type,type,
% 2.33/1.21 emptysetsubset: $o ).
% 2.33/1.21
% 2.33/1.21 thf(emptysetsubset,definition,
% 2.33/1.21 ( emptysetsubset
% 2.33/1.21 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(subsetE_type,type,
% 2.33/1.21 subsetE: $o ).
% 2.33/1.21
% 2.33/1.21 thf(subsetE,definition,
% 2.33/1.21 ( subsetE
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ( subset @ A @ B )
% 2.33/1.21 => ( ( in @ Xx @ A )
% 2.33/1.21 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(subsetE2_type,type,
% 2.33/1.21 subsetE2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(subsetE2,definition,
% 2.33/1.21 ( subsetE2
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ( subset @ A @ B )
% 2.33/1.21 => ( ~ ( in @ Xx @ B )
% 2.33/1.21 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(notsubsetI_type,type,
% 2.33/1.21 notsubsetI: $o ).
% 2.33/1.21
% 2.33/1.21 thf(notsubsetI,definition,
% 2.33/1.21 ( notsubsetI
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ~ ( in @ Xx @ B )
% 2.33/1.21 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(notequalI1_type,type,
% 2.33/1.21 notequalI1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(notequalI1,definition,
% 2.33/1.21 ( notequalI1
% 2.33/1.21 = ( ! [A: $i,B: $i] :
% 2.33/1.21 ( ~ ( subset @ A @ B )
% 2.33/1.21 => ( A != B ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(notequalI2_type,type,
% 2.33/1.21 notequalI2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(notequalI2,definition,
% 2.33/1.21 ( notequalI2
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ~ ( in @ Xx @ B )
% 2.33/1.21 => ( A != B ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(subsetRefl_type,type,
% 2.33/1.21 subsetRefl: $o ).
% 2.33/1.21
% 2.33/1.21 thf(subsetRefl,definition,
% 2.33/1.21 ( subsetRefl
% 2.33/1.21 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(subsetTrans_type,type,
% 2.33/1.21 subsetTrans: $o ).
% 2.33/1.21
% 2.33/1.21 thf(subsetTrans,definition,
% 2.33/1.21 ( subsetTrans
% 2.33/1.21 = ( ! [A: $i,B: $i,C: $i] :
% 2.33/1.21 ( ( subset @ A @ B )
% 2.33/1.21 => ( ( subset @ B @ C )
% 2.33/1.21 => ( subset @ A @ C ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setadjoinSub_type,type,
% 2.33/1.21 setadjoinSub: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setadjoinSub,definition,
% 2.33/1.21 ( setadjoinSub
% 2.33/1.21 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setadjoinSub2_type,type,
% 2.33/1.21 setadjoinSub2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setadjoinSub2,definition,
% 2.33/1.21 ( setadjoinSub2
% 2.33/1.21 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.33/1.21 ( ( subset @ A @ B )
% 2.33/1.21 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(subset2powerset_type,type,
% 2.33/1.21 subset2powerset: $o ).
% 2.33/1.21
% 2.33/1.21 thf(subset2powerset,definition,
% 2.33/1.21 ( subset2powerset
% 2.33/1.21 = ( ! [A: $i,B: $i] :
% 2.33/1.21 ( ( subset @ A @ B )
% 2.33/1.21 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setextsub_type,type,
% 2.33/1.21 setextsub: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setextsub,definition,
% 2.33/1.21 ( setextsub
% 2.33/1.21 = ( ! [A: $i,B: $i] :
% 2.33/1.21 ( ( subset @ A @ B )
% 2.33/1.21 => ( ( subset @ B @ A )
% 2.33/1.21 => ( A = B ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(subsetemptysetimpeq_type,type,
% 2.33/1.21 subsetemptysetimpeq: $o ).
% 2.33/1.21
% 2.33/1.21 thf(subsetemptysetimpeq,definition,
% 2.33/1.21 ( subsetemptysetimpeq
% 2.33/1.21 = ( ! [A: $i] :
% 2.33/1.21 ( ( subset @ A @ emptyset )
% 2.33/1.21 => ( A = emptyset ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(powersetI1_type,type,
% 2.33/1.21 powersetI1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(powersetI1,definition,
% 2.33/1.21 ( powersetI1
% 2.33/1.21 = ( ! [A: $i,B: $i] :
% 2.33/1.21 ( ( subset @ B @ A )
% 2.33/1.21 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(powersetE1_type,type,
% 2.33/1.21 powersetE1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(powersetE1,definition,
% 2.33/1.21 ( powersetE1
% 2.33/1.21 = ( ! [A: $i,B: $i] :
% 2.33/1.21 ( ( in @ B @ ( powerset @ A ) )
% 2.33/1.21 => ( subset @ B @ A ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(inPowerset_type,type,
% 2.33/1.21 inPowerset: $o ).
% 2.33/1.21
% 2.33/1.21 thf(inPowerset,definition,
% 2.33/1.21 ( inPowerset
% 2.33/1.21 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(powersetsubset_type,type,
% 2.33/1.21 powersetsubset: $o ).
% 2.33/1.21
% 2.33/1.21 thf(powersetsubset,definition,
% 2.33/1.21 ( powersetsubset
% 2.33/1.21 = ( ! [A: $i,B: $i] :
% 2.33/1.21 ( ( subset @ A @ B )
% 2.33/1.21 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(sepInPowerset_type,type,
% 2.33/1.21 sepInPowerset: $o ).
% 2.33/1.21
% 2.33/1.21 thf(sepInPowerset,definition,
% 2.33/1.21 ( sepInPowerset
% 2.33/1.21 = ( ! [A: $i,Xphi: $i > $o] :
% 2.33/1.21 ( in
% 2.33/1.21 @ ( dsetconstr @ A
% 2.33/1.21 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.33/1.21 @ ( powerset @ A ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(sepSubset_type,type,
% 2.33/1.21 sepSubset: $o ).
% 2.33/1.21
% 2.33/1.21 thf(sepSubset,definition,
% 2.33/1.21 ( sepSubset
% 2.33/1.21 = ( ! [A: $i,Xphi: $i > $o] :
% 2.33/1.21 ( subset
% 2.33/1.21 @ ( dsetconstr @ A
% 2.33/1.21 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.33/1.21 @ A ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(binunion_type,type,
% 2.33/1.21 binunion: $i > $i > $i ).
% 2.33/1.21
% 2.33/1.21 thf(binunionIL_type,type,
% 2.33/1.21 binunionIL: $o ).
% 2.33/1.21
% 2.33/1.21 thf(binunionIL,definition,
% 2.33/1.21 ( binunionIL
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(upairset2IR_type,type,
% 2.33/1.21 upairset2IR: $o ).
% 2.33/1.21
% 2.33/1.21 thf(upairset2IR,definition,
% 2.33/1.21 ( upairset2IR
% 2.33/1.21 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(binunionIR_type,type,
% 2.33/1.21 binunionIR: $o ).
% 2.33/1.21
% 2.33/1.21 thf(binunionIR,definition,
% 2.33/1.21 ( binunionIR
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ B )
% 2.33/1.21 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(binunionEcases_type,type,
% 2.33/1.21 binunionEcases: $o ).
% 2.33/1.21
% 2.33/1.21 thf(binunionEcases,definition,
% 2.33/1.21 ( binunionEcases
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.33/1.21 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.33/1.21 => ( ( ( in @ Xx @ A )
% 2.33/1.21 => Xphi )
% 2.33/1.21 => ( ( ( in @ Xx @ B )
% 2.33/1.21 => Xphi )
% 2.33/1.21 => Xphi ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(binunionE_type,type,
% 2.33/1.21 binunionE: $o ).
% 2.33/1.21
% 2.33/1.21 thf(binunionE,definition,
% 2.33/1.21 ( binunionE
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.33/1.21 => ( ( in @ Xx @ A )
% 2.33/1.21 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(binunionLsub_type,type,
% 2.33/1.21 binunionLsub: $o ).
% 2.33/1.21
% 2.33/1.21 thf(binunionLsub,definition,
% 2.33/1.21 ( binunionLsub
% 2.33/1.21 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(binunionRsub_type,type,
% 2.33/1.21 binunionRsub: $o ).
% 2.33/1.21
% 2.33/1.21 thf(binunionRsub,definition,
% 2.33/1.21 ( binunionRsub
% 2.33/1.21 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(binintersect_type,type,
% 2.33/1.21 binintersect: $i > $i > $i ).
% 2.33/1.21
% 2.33/1.21 thf(binintersectI_type,type,
% 2.33/1.21 binintersectI: $o ).
% 2.33/1.21
% 2.33/1.21 thf(binintersectI,definition,
% 2.33/1.21 ( binintersectI
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ( in @ Xx @ B )
% 2.33/1.21 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(binintersectSubset5_type,type,
% 2.33/1.21 binintersectSubset5: $o ).
% 2.33/1.21
% 2.33/1.21 thf(binintersectSubset5,definition,
% 2.33/1.21 ( binintersectSubset5
% 2.33/1.21 = ( ! [A: $i,B: $i,C: $i] :
% 2.33/1.21 ( ( subset @ C @ A )
% 2.33/1.21 => ( ( subset @ C @ B )
% 2.33/1.21 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(binintersectEL_type,type,
% 2.33/1.21 binintersectEL: $o ).
% 2.33/1.21
% 2.33/1.21 thf(binintersectEL,definition,
% 2.33/1.21 ( binintersectEL
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.33/1.21 => ( in @ Xx @ A ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(binintersectLsub_type,type,
% 2.33/1.21 binintersectLsub: $o ).
% 2.33/1.21
% 2.33/1.21 thf(binintersectLsub,definition,
% 2.33/1.21 ( binintersectLsub
% 2.33/1.21 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(binintersectSubset2_type,type,
% 2.33/1.21 binintersectSubset2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(binintersectSubset2,definition,
% 2.33/1.21 ( binintersectSubset2
% 2.33/1.21 = ( ! [A: $i,B: $i] :
% 2.33/1.21 ( ( subset @ A @ B )
% 2.33/1.21 => ( ( binintersect @ A @ B )
% 2.33/1.21 = A ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(binintersectSubset3_type,type,
% 2.33/1.21 binintersectSubset3: $o ).
% 2.33/1.21
% 2.33/1.21 thf(binintersectSubset3,definition,
% 2.33/1.21 ( binintersectSubset3
% 2.33/1.21 = ( ! [A: $i,B: $i] :
% 2.33/1.21 ( ( ( binintersect @ A @ B )
% 2.33/1.21 = B )
% 2.33/1.21 => ( subset @ B @ A ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(binintersectER_type,type,
% 2.33/1.21 binintersectER: $o ).
% 2.33/1.21
% 2.33/1.21 thf(binintersectER,definition,
% 2.33/1.21 ( binintersectER
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.33/1.21 => ( in @ Xx @ B ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(disjointsetsI1_type,type,
% 2.33/1.21 disjointsetsI1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(disjointsetsI1,definition,
% 2.33/1.21 ( disjointsetsI1
% 2.33/1.21 = ( ! [A: $i,B: $i] :
% 2.33/1.21 ( ~ ? [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 & ( in @ Xx @ B ) )
% 2.33/1.21 => ( ( binintersect @ A @ B )
% 2.33/1.21 = emptyset ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(binintersectRsub_type,type,
% 2.33/1.21 binintersectRsub: $o ).
% 2.33/1.21
% 2.33/1.21 thf(binintersectRsub,definition,
% 2.33/1.21 ( binintersectRsub
% 2.33/1.21 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(binintersectSubset4_type,type,
% 2.33/1.21 binintersectSubset4: $o ).
% 2.33/1.21
% 2.33/1.21 thf(binintersectSubset4,definition,
% 2.33/1.21 ( binintersectSubset4
% 2.33/1.21 = ( ! [A: $i,B: $i] :
% 2.33/1.21 ( ( subset @ B @ A )
% 2.33/1.21 => ( ( binintersect @ A @ B )
% 2.33/1.21 = B ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(binintersectSubset1_type,type,
% 2.33/1.21 binintersectSubset1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(binintersectSubset1,definition,
% 2.33/1.21 ( binintersectSubset1
% 2.33/1.21 = ( ! [A: $i,B: $i] :
% 2.33/1.21 ( ( ( binintersect @ A @ B )
% 2.33/1.21 = A )
% 2.33/1.21 => ( subset @ A @ B ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(bs114d_type,type,
% 2.33/1.21 bs114d: $o ).
% 2.33/1.21
% 2.33/1.21 thf(bs114d,definition,
% 2.33/1.21 ( bs114d
% 2.33/1.21 = ( ! [A: $i,B: $i,C: $i] :
% 2.33/1.21 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.33/1.21 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(regular_type,type,
% 2.33/1.21 regular: $i > $o ).
% 2.33/1.21
% 2.33/1.21 thf(setminus_type,type,
% 2.33/1.21 setminus: $i > $i > $i ).
% 2.33/1.21
% 2.33/1.21 thf(setminusI_type,type,
% 2.33/1.21 setminusI: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setminusI,definition,
% 2.33/1.21 ( setminusI
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ~ ( in @ Xx @ B )
% 2.33/1.21 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setminusEL_type,type,
% 2.33/1.21 setminusEL: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setminusEL,definition,
% 2.33/1.21 ( setminusEL
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.33/1.21 => ( in @ Xx @ A ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setminusER_type,type,
% 2.33/1.21 setminusER: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setminusER,definition,
% 2.33/1.21 ( setminusER
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.33/1.21 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setminusSubset2_type,type,
% 2.33/1.21 setminusSubset2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setminusSubset2,definition,
% 2.33/1.21 ( setminusSubset2
% 2.33/1.21 = ( ! [A: $i,B: $i] :
% 2.33/1.21 ( ( subset @ A @ B )
% 2.33/1.21 => ( ( setminus @ A @ B )
% 2.33/1.21 = emptyset ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setminusERneg_type,type,
% 2.33/1.21 setminusERneg: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setminusERneg,definition,
% 2.33/1.21 ( setminusERneg
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.33/1.21 => ( ( in @ Xx @ A )
% 2.33/1.21 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setminusELneg_type,type,
% 2.33/1.21 setminusELneg: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setminusELneg,definition,
% 2.33/1.21 ( setminusELneg
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.33/1.21 => ( ~ ( in @ Xx @ B )
% 2.33/1.21 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setminusILneg_type,type,
% 2.33/1.21 setminusILneg: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setminusILneg,definition,
% 2.33/1.21 ( setminusILneg
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ~ ( in @ Xx @ A )
% 2.33/1.21 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setminusIRneg_type,type,
% 2.33/1.21 setminusIRneg: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setminusIRneg,definition,
% 2.33/1.21 ( setminusIRneg
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ B )
% 2.33/1.21 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setminusLsub_type,type,
% 2.33/1.21 setminusLsub: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setminusLsub,definition,
% 2.33/1.21 ( setminusLsub
% 2.33/1.21 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setminusSubset1_type,type,
% 2.33/1.21 setminusSubset1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setminusSubset1,definition,
% 2.33/1.21 ( setminusSubset1
% 2.33/1.21 = ( ! [A: $i,B: $i] :
% 2.33/1.21 ( ( ( setminus @ A @ B )
% 2.33/1.21 = emptyset )
% 2.33/1.21 => ( subset @ A @ B ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(symdiff_type,type,
% 2.33/1.21 symdiff: $i > $i > $i ).
% 2.33/1.21
% 2.33/1.21 thf(symdiffE_type,type,
% 2.33/1.21 symdiffE: $o ).
% 2.33/1.21
% 2.33/1.21 thf(symdiffE,definition,
% 2.33/1.21 ( symdiffE
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.33/1.21 => ! [Xphi: $o] :
% 2.33/1.21 ( ( ( in @ Xx @ A )
% 2.33/1.21 => ( ~ ( in @ Xx @ B )
% 2.33/1.21 => Xphi ) )
% 2.33/1.21 => ( ( ~ ( in @ Xx @ A )
% 2.33/1.21 => ( ( in @ Xx @ B )
% 2.33/1.21 => Xphi ) )
% 2.33/1.21 => Xphi ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(symdiffI1_type,type,
% 2.33/1.21 symdiffI1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(symdiffI1,definition,
% 2.33/1.21 ( symdiffI1
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ~ ( in @ Xx @ B )
% 2.33/1.21 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(symdiffI2_type,type,
% 2.33/1.21 symdiffI2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(symdiffI2,definition,
% 2.33/1.21 ( symdiffI2
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ~ ( in @ Xx @ A )
% 2.33/1.21 => ( ( in @ Xx @ B )
% 2.33/1.21 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(symdiffIneg1_type,type,
% 2.33/1.21 symdiffIneg1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(symdiffIneg1,definition,
% 2.33/1.21 ( symdiffIneg1
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ( in @ Xx @ B )
% 2.33/1.21 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(symdiffIneg2_type,type,
% 2.33/1.21 symdiffIneg2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(symdiffIneg2,definition,
% 2.33/1.21 ( symdiffIneg2
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ~ ( in @ Xx @ A )
% 2.33/1.21 => ( ~ ( in @ Xx @ B )
% 2.33/1.21 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(iskpair_type,type,
% 2.33/1.21 iskpair: $i > $o ).
% 2.33/1.21
% 2.33/1.21 thf(secondinupair_type,type,
% 2.33/1.21 secondinupair: $o ).
% 2.33/1.21
% 2.33/1.21 thf(secondinupair,definition,
% 2.33/1.21 ( secondinupair
% 2.33/1.21 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setukpairIL_type,type,
% 2.33/1.21 setukpairIL: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setukpairIL,definition,
% 2.33/1.21 ( setukpairIL
% 2.33/1.21 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setukpairIR_type,type,
% 2.33/1.21 setukpairIR: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setukpairIR,definition,
% 2.33/1.21 ( setukpairIR
% 2.33/1.21 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(kpairiskpair_type,type,
% 2.33/1.21 kpairiskpair: $o ).
% 2.33/1.21
% 2.33/1.21 thf(kpairiskpair,definition,
% 2.33/1.21 ( kpairiskpair
% 2.33/1.21 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(kpair_type,type,
% 2.33/1.21 kpair: $i > $i > $i ).
% 2.33/1.21
% 2.33/1.21 thf(kpairp_type,type,
% 2.33/1.21 kpairp: $o ).
% 2.33/1.21
% 2.33/1.21 thf(kpairp,definition,
% 2.33/1.21 ( kpairp
% 2.33/1.21 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(cartprod_type,type,
% 2.33/1.21 cartprod: $i > $i > $i ).
% 2.33/1.21
% 2.33/1.21 thf(singletonsubset_type,type,
% 2.33/1.21 singletonsubset: $o ).
% 2.33/1.21
% 2.33/1.21 thf(singletonsubset,definition,
% 2.33/1.21 ( singletonsubset
% 2.33/1.21 = ( ! [A: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(singletoninpowerset_type,type,
% 2.33/1.21 singletoninpowerset: $o ).
% 2.33/1.21
% 2.33/1.21 thf(singletoninpowerset,definition,
% 2.33/1.21 ( singletoninpowerset
% 2.33/1.21 = ( ! [A: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(singletoninpowunion_type,type,
% 2.33/1.21 singletoninpowunion: $o ).
% 2.33/1.21
% 2.33/1.21 thf(singletoninpowunion,definition,
% 2.33/1.21 ( singletoninpowunion
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(upairset2E_type,type,
% 2.33/1.21 upairset2E: $o ).
% 2.33/1.21
% 2.33/1.21 thf(upairset2E,definition,
% 2.33/1.21 ( upairset2E
% 2.33/1.21 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.33/1.21 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.33/1.21 => ( ( Xz = Xx )
% 2.33/1.21 | ( Xz = Xy ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(upairsubunion_type,type,
% 2.33/1.21 upairsubunion: $o ).
% 2.33/1.21
% 2.33/1.21 thf(upairsubunion,definition,
% 2.33/1.21 ( upairsubunion
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ B )
% 2.33/1.21 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(upairinpowunion_type,type,
% 2.33/1.21 upairinpowunion: $o ).
% 2.33/1.21
% 2.33/1.21 thf(upairinpowunion,definition,
% 2.33/1.21 ( upairinpowunion
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ B )
% 2.33/1.21 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(ubforcartprodlem1_type,type,
% 2.33/1.21 ubforcartprodlem1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(ubforcartprodlem1,definition,
% 2.33/1.21 ( ubforcartprodlem1
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ B )
% 2.33/1.21 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(ubforcartprodlem2_type,type,
% 2.33/1.21 ubforcartprodlem2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(ubforcartprodlem2,definition,
% 2.33/1.21 ( ubforcartprodlem2
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ B )
% 2.33/1.21 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(ubforcartprodlem3_type,type,
% 2.33/1.21 ubforcartprodlem3: $o ).
% 2.33/1.21
% 2.33/1.21 thf(ubforcartprodlem3,definition,
% 2.33/1.21 ( ubforcartprodlem3
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ B )
% 2.33/1.21 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(cartprodpairin_type,type,
% 2.33/1.21 cartprodpairin: $o ).
% 2.33/1.21
% 2.33/1.21 thf(cartprodpairin,definition,
% 2.33/1.21 ( cartprodpairin
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ B )
% 2.33/1.21 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(cartprodmempair1_type,type,
% 2.33/1.21 cartprodmempair1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(cartprodmempair1,definition,
% 2.33/1.21 ( cartprodmempair1
% 2.33/1.21 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.33/1.21 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.33/1.21 => ? [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 & ? [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ B )
% 2.33/1.21 & ( Xu
% 2.33/1.21 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(cartprodmempair_type,type,
% 2.33/1.21 cartprodmempair: $o ).
% 2.33/1.21
% 2.33/1.21 thf(cartprodmempair,definition,
% 2.33/1.21 ( cartprodmempair
% 2.33/1.21 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.33/1.21 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.33/1.21 => ( iskpair @ Xu ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setunionE2_type,type,
% 2.33/1.21 setunionE2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setunionE2,definition,
% 2.33/1.21 ( setunionE2
% 2.33/1.21 = ( ! [A: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ ( setunion @ A ) )
% 2.33/1.21 => ? [X: $i] :
% 2.33/1.21 ( ( in @ X @ A )
% 2.33/1.21 & ( in @ Xx @ X ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setunionsingleton1_type,type,
% 2.33/1.21 setunionsingleton1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setunionsingleton1,definition,
% 2.33/1.21 ( setunionsingleton1
% 2.33/1.21 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setunionsingleton2_type,type,
% 2.33/1.21 setunionsingleton2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setunionsingleton2,definition,
% 2.33/1.21 ( setunionsingleton2
% 2.33/1.21 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setunionsingleton_type,type,
% 2.33/1.21 setunionsingleton: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setunionsingleton,definition,
% 2.33/1.21 ( setunionsingleton
% 2.33/1.21 = ( ! [Xx: $i] :
% 2.33/1.21 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 2.33/1.21 = Xx ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(singleton_type,type,
% 2.33/1.21 singleton: $i > $o ).
% 2.33/1.21
% 2.33/1.21 thf(singletonprop_type,type,
% 2.33/1.21 singletonprop: $o ).
% 2.33/1.21
% 2.33/1.21 thf(singletonprop,definition,
% 2.33/1.21 ( singletonprop
% 2.33/1.21 = ( ! [A: $i,Xphi: $i > $o] :
% 2.33/1.21 ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ A )
% 2.33/1.21 => ( ( Xphi @ Xx )
% 2.33/1.21 => ( ( Xphi @ Xy )
% 2.33/1.21 => ( Xx = Xy ) ) ) ) )
% 2.33/1.21 => ( ? [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 & ( Xphi @ Xx ) )
% 2.33/1.21 => ( singleton
% 2.33/1.21 @ ( dsetconstr @ A
% 2.33/1.21 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(ex1_type,type,
% 2.33/1.21 ex1: $i > ( $i > $o ) > $o ).
% 2.33/1.21
% 2.33/1.21 thf(ex1,definition,
% 2.33/1.21 ( ex1
% 2.33/1.21 = ( ^ [A: $i,Xphi: $i > $o] :
% 2.33/1.21 ( singleton
% 2.33/1.21 @ ( dsetconstr @ A
% 2.33/1.21 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(ex1E1_type,type,
% 2.33/1.21 ex1E1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(ex1E1,definition,
% 2.33/1.21 ( ex1E1
% 2.33/1.21 = ( ! [A: $i,Xphi: $i > $o] :
% 2.33/1.21 ( ( ex1 @ A
% 2.33/1.21 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.33/1.21 => ? [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(ex1I_type,type,
% 2.33/1.21 ex1I: $o ).
% 2.33/1.21
% 2.33/1.21 thf(ex1I,definition,
% 2.33/1.21 ( ex1I
% 2.33/1.21 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ( Xphi @ Xx )
% 2.33/1.21 => ( ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ A )
% 2.33/1.21 => ( ( Xphi @ Xy )
% 2.33/1.21 => ( Xy = Xx ) ) )
% 2.33/1.21 => ( ex1 @ A
% 2.33/1.21 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(ex1I2_type,type,
% 2.33/1.21 ex1I2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(ex1I2,definition,
% 2.33/1.21 ( ex1I2
% 2.33/1.21 = ( ! [A: $i,Xphi: $i > $o] :
% 2.33/1.21 ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ A )
% 2.33/1.21 => ( ( Xphi @ Xx )
% 2.33/1.21 => ( ( Xphi @ Xy )
% 2.33/1.21 => ( Xx = Xy ) ) ) ) )
% 2.33/1.21 => ( ? [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 & ( Xphi @ Xx ) )
% 2.33/1.21 => ( ex1 @ A
% 2.33/1.21 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(singletonsuniq_type,type,
% 2.33/1.21 singletonsuniq: $o ).
% 2.33/1.21
% 2.33/1.21 thf(singletonsuniq,definition,
% 2.33/1.21 ( singletonsuniq
% 2.33/1.21 = ( ! [Xx: $i,Xy: $i] :
% 2.33/1.21 ( ( ( setadjoin @ Xx @ emptyset )
% 2.33/1.21 = ( setadjoin @ Xy @ emptyset ) )
% 2.33/1.21 => ( Xx = Xy ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(atmost1p_type,type,
% 2.33/1.21 atmost1p: $i > $o ).
% 2.33/1.21
% 2.33/1.21 thf(atleast2p_type,type,
% 2.33/1.21 atleast2p: $i > $o ).
% 2.33/1.21
% 2.33/1.21 thf(atmost2p_type,type,
% 2.33/1.21 atmost2p: $i > $o ).
% 2.33/1.21
% 2.33/1.21 thf(upairsetp_type,type,
% 2.33/1.21 upairsetp: $i > $o ).
% 2.33/1.21
% 2.33/1.21 thf(setukpairinjL1_type,type,
% 2.33/1.21 setukpairinjL1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setukpairinjL1,definition,
% 2.33/1.21 ( setukpairinjL1
% 2.33/1.21 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.33/1.21 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 2.33/1.21 => ( Xx = Xz ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(kfstsingleton_type,type,
% 2.33/1.21 kfstsingleton: $o ).
% 2.33/1.21
% 2.33/1.21 thf(kfstsingleton,definition,
% 2.33/1.21 ( kfstsingleton
% 2.33/1.21 = ( ! [Xu: $i] :
% 2.33/1.21 ( ( iskpair @ Xu )
% 2.33/1.21 => ( singleton
% 2.33/1.21 @ ( dsetconstr @ ( setunion @ Xu )
% 2.33/1.21 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(theprop_type,type,
% 2.33/1.21 theprop: $o ).
% 2.33/1.21
% 2.33/1.21 thf(theprop,definition,
% 2.33/1.21 ( theprop
% 2.33/1.21 = ( ! [X: $i] :
% 2.33/1.21 ( ( singleton @ X )
% 2.33/1.21 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(kfst_type,type,
% 2.33/1.21 kfst: $i > $i ).
% 2.33/1.21
% 2.33/1.21 thf(kfstpairEq_type,type,
% 2.33/1.21 kfstpairEq: $o ).
% 2.33/1.21
% 2.33/1.21 thf(kfstpairEq,definition,
% 2.33/1.21 ( kfstpairEq
% 2.33/1.21 = ( ! [Xx: $i,Xy: $i] :
% 2.33/1.21 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.33/1.21 = Xx ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(cartprodfstin_type,type,
% 2.33/1.21 cartprodfstin: $o ).
% 2.33/1.21
% 2.33/1.21 thf(cartprodfstin,definition,
% 2.33/1.21 ( cartprodfstin
% 2.33/1.21 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.33/1.21 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.33/1.21 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setukpairinjL2_type,type,
% 2.33/1.21 setukpairinjL2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setukpairinjL2,definition,
% 2.33/1.21 ( setukpairinjL2
% 2.33/1.21 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.33/1.21 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.33/1.21 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.33/1.21 => ( Xx = Xz ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setukpairinjL_type,type,
% 2.33/1.21 setukpairinjL: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setukpairinjL,definition,
% 2.33/1.21 ( setukpairinjL
% 2.33/1.21 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.33/1.21 ( ( ( kpair @ Xx @ Xy )
% 2.33/1.21 = ( kpair @ Xz @ Xu ) )
% 2.33/1.21 => ( Xx = Xz ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setukpairinjR11_type,type,
% 2.33/1.21 setukpairinjR11: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setukpairinjR11,definition,
% 2.33/1.21 ( setukpairinjR11
% 2.33/1.21 = ( ! [Xx: $i,Xy: $i] :
% 2.33/1.21 ( ( Xx = Xy )
% 2.33/1.21 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.33/1.21 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setukpairinjR12_type,type,
% 2.33/1.21 setukpairinjR12: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setukpairinjR12,definition,
% 2.33/1.21 ( setukpairinjR12
% 2.33/1.21 = ( ! [Xx: $i,Xy: $i] :
% 2.33/1.21 ( ( Xx = Xy )
% 2.33/1.21 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.33/1.21 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setukpairinjR1_type,type,
% 2.33/1.21 setukpairinjR1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setukpairinjR1,definition,
% 2.33/1.21 ( setukpairinjR1
% 2.33/1.21 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.33/1.21 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.33/1.21 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.33/1.21 => ( ( Xz = Xu )
% 2.33/1.21 => ( Xy = Xu ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(upairequniteq_type,type,
% 2.33/1.21 upairequniteq: $o ).
% 2.33/1.21
% 2.33/1.21 thf(upairequniteq,definition,
% 2.33/1.21 ( upairequniteq
% 2.33/1.21 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.33/1.21 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.33/1.21 = ( setadjoin @ Xz @ emptyset ) )
% 2.33/1.21 => ( Xx = Xy ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setukpairinjR2_type,type,
% 2.33/1.21 setukpairinjR2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setukpairinjR2,definition,
% 2.33/1.21 ( setukpairinjR2
% 2.33/1.21 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.33/1.21 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.33/1.21 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.33/1.21 => ( Xy = Xu ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setukpairinjR_type,type,
% 2.33/1.21 setukpairinjR: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setukpairinjR,definition,
% 2.33/1.21 ( setukpairinjR
% 2.33/1.21 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.33/1.21 ( ( ( kpair @ Xx @ Xy )
% 2.33/1.21 = ( kpair @ Xz @ Xu ) )
% 2.33/1.21 => ( Xy = Xu ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(ksndsingleton_type,type,
% 2.33/1.21 ksndsingleton: $o ).
% 2.33/1.21
% 2.33/1.21 thf(ksndsingleton,definition,
% 2.33/1.21 ( ksndsingleton
% 2.33/1.21 = ( ! [Xu: $i] :
% 2.33/1.21 ( ( iskpair @ Xu )
% 2.33/1.21 => ( singleton
% 2.33/1.21 @ ( dsetconstr @ ( setunion @ Xu )
% 2.33/1.21 @ ^ [Xx: $i] :
% 2.33/1.21 ( Xu
% 2.33/1.21 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(ksnd_type,type,
% 2.33/1.21 ksnd: $i > $i ).
% 2.33/1.21
% 2.33/1.21 thf(ksndpairEq_type,type,
% 2.33/1.21 ksndpairEq: $o ).
% 2.33/1.21
% 2.33/1.21 thf(ksndpairEq,definition,
% 2.33/1.21 ( ksndpairEq
% 2.33/1.21 = ( ! [Xx: $i,Xy: $i] :
% 2.33/1.21 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.33/1.21 = Xy ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(kpairsurjEq_type,type,
% 2.33/1.21 kpairsurjEq: $o ).
% 2.33/1.21
% 2.33/1.21 thf(kpairsurjEq,definition,
% 2.33/1.21 ( kpairsurjEq
% 2.33/1.21 = ( ! [Xu: $i] :
% 2.33/1.21 ( ( iskpair @ Xu )
% 2.33/1.21 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.33/1.21 = Xu ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(cartprodsndin_type,type,
% 2.33/1.21 cartprodsndin: $o ).
% 2.33/1.21
% 2.33/1.21 thf(cartprodsndin,definition,
% 2.33/1.21 ( cartprodsndin
% 2.33/1.21 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.33/1.21 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.33/1.21 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(cartprodpairmemEL_type,type,
% 2.33/1.21 cartprodpairmemEL: $o ).
% 2.33/1.21
% 2.33/1.21 thf(cartprodpairmemEL,definition,
% 2.33/1.21 ( cartprodpairmemEL
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.33/1.21 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.33/1.21 => ( in @ Xx @ A ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(cartprodpairmemER_type,type,
% 2.33/1.21 cartprodpairmemER: $o ).
% 2.33/1.21
% 2.33/1.21 thf(cartprodpairmemER,definition,
% 2.33/1.21 ( cartprodpairmemER
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.33/1.21 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.33/1.21 => ( in @ Xy @ B ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(cartprodmempaircEq_type,type,
% 2.33/1.21 cartprodmempaircEq: $o ).
% 2.33/1.21
% 2.33/1.21 thf(cartprodmempaircEq,definition,
% 2.33/1.21 ( cartprodmempaircEq
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ B )
% 2.33/1.21 => ( ( kpair @ Xx @ Xy )
% 2.33/1.21 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(cartprodfstpairEq_type,type,
% 2.33/1.21 cartprodfstpairEq: $o ).
% 2.33/1.21
% 2.33/1.21 thf(cartprodfstpairEq,definition,
% 2.33/1.21 ( cartprodfstpairEq
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ B )
% 2.33/1.21 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.33/1.21 = Xx ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(cartprodsndpairEq_type,type,
% 2.33/1.21 cartprodsndpairEq: $o ).
% 2.33/1.21
% 2.33/1.21 thf(cartprodsndpairEq,definition,
% 2.33/1.21 ( cartprodsndpairEq
% 2.33/1.21 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ B )
% 2.33/1.21 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.33/1.21 = Xy ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(cartprodpairsurjEq_type,type,
% 2.33/1.21 cartprodpairsurjEq: $o ).
% 2.33/1.21
% 2.33/1.21 thf(cartprodpairsurjEq,definition,
% 2.33/1.21 ( cartprodpairsurjEq
% 2.33/1.21 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.33/1.21 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.33/1.21 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.33/1.21 = Xu ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(breln_type,type,
% 2.33/1.21 breln: $i > $i > $i > $o ).
% 2.33/1.21
% 2.33/1.21 thf(breln,definition,
% 2.33/1.21 ( breln
% 2.33/1.21 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(dpsetconstr_type,type,
% 2.33/1.21 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 2.33/1.21
% 2.33/1.21 thf(dpsetconstrI_type,type,
% 2.33/1.21 dpsetconstrI: $o ).
% 2.33/1.21
% 2.33/1.21 thf(dpsetconstrI,definition,
% 2.33/1.21 ( dpsetconstrI
% 2.33/1.21 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ B )
% 2.33/1.21 => ( ( Xphi @ Xx @ Xy )
% 2.33/1.21 => ( in @ ( kpair @ Xx @ Xy )
% 2.33/1.21 @ ( dpsetconstr @ A @ B
% 2.33/1.21 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(dpsetconstrSub_type,type,
% 2.33/1.21 dpsetconstrSub: $o ).
% 2.33/1.21
% 2.33/1.21 thf(dpsetconstrSub,definition,
% 2.33/1.21 ( dpsetconstrSub
% 2.33/1.21 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.33/1.21 ( subset
% 2.33/1.21 @ ( dpsetconstr @ A @ B
% 2.33/1.21 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 2.33/1.21 @ ( cartprod @ A @ B ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setOfPairsIsBReln_type,type,
% 2.33/1.21 setOfPairsIsBReln: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setOfPairsIsBReln,definition,
% 2.33/1.21 ( setOfPairsIsBReln
% 2.33/1.21 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.33/1.21 ( breln @ A @ B
% 2.33/1.21 @ ( dpsetconstr @ A @ B
% 2.33/1.21 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(dpsetconstrERa_type,type,
% 2.33/1.21 dpsetconstrERa: $o ).
% 2.33/1.21
% 2.33/1.21 thf(dpsetconstrERa,definition,
% 2.33/1.21 ( dpsetconstrERa
% 2.33/1.21 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ B )
% 2.33/1.21 => ( ( in @ ( kpair @ Xx @ Xy )
% 2.33/1.21 @ ( dpsetconstr @ A @ B
% 2.33/1.21 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.33/1.21 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(dpsetconstrEL1_type,type,
% 2.33/1.21 dpsetconstrEL1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(dpsetconstrEL1,definition,
% 2.33/1.21 ( dpsetconstrEL1
% 2.33/1.21 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.33/1.21 ( ( in @ ( kpair @ Xx @ Xy )
% 2.33/1.21 @ ( dpsetconstr @ A @ B
% 2.33/1.21 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.33/1.21 => ( in @ Xx @ A ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(dpsetconstrEL2_type,type,
% 2.33/1.21 dpsetconstrEL2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(dpsetconstrEL2,definition,
% 2.33/1.21 ( dpsetconstrEL2
% 2.33/1.21 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.33/1.21 ( ( in @ ( kpair @ Xx @ Xy )
% 2.33/1.21 @ ( dpsetconstr @ A @ B
% 2.33/1.21 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.33/1.21 => ( in @ Xy @ B ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(dpsetconstrER_type,type,
% 2.33/1.21 dpsetconstrER: $o ).
% 2.33/1.21
% 2.33/1.21 thf(dpsetconstrER,definition,
% 2.33/1.21 ( dpsetconstrER
% 2.33/1.21 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.33/1.21 ( ( in @ ( kpair @ Xx @ Xy )
% 2.33/1.21 @ ( dpsetconstr @ A @ B
% 2.33/1.21 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.33/1.21 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(func_type,type,
% 2.33/1.21 func: $i > $i > $i > $o ).
% 2.33/1.21
% 2.33/1.21 thf(funcSet_type,type,
% 2.33/1.21 funcSet: $i > $i > $i ).
% 2.33/1.21
% 2.33/1.21 thf(funcImageSingleton_type,type,
% 2.33/1.21 funcImageSingleton: $o ).
% 2.33/1.21
% 2.33/1.21 thf(funcImageSingleton,definition,
% 2.33/1.21 ( funcImageSingleton
% 2.33/1.21 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.33/1.21 ( ( func @ A @ B @ Xf )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( singleton
% 2.33/1.21 @ ( dsetconstr @ B
% 2.33/1.21 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(apProp_type,type,
% 2.33/1.21 apProp: $o ).
% 2.33/1.21
% 2.33/1.21 thf(apProp,definition,
% 2.33/1.21 ( apProp
% 2.33/1.21 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.33/1.21 ( ( func @ A @ B @ Xf )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( in
% 2.33/1.21 @ ( setunion
% 2.33/1.21 @ ( dsetconstr @ B
% 2.33/1.21 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 2.33/1.21 @ B ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(ap_type,type,
% 2.33/1.21 ap: $i > $i > $i > $i > $i ).
% 2.33/1.21
% 2.33/1.21 thf(app_type,type,
% 2.33/1.21 app: $o ).
% 2.33/1.21
% 2.33/1.21 thf(app,definition,
% 2.33/1.21 ( app
% 2.33/1.21 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.33/1.21 ( ( func @ A @ B @ Xf )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(infuncsetfunc_type,type,
% 2.33/1.21 infuncsetfunc: $o ).
% 2.33/1.21
% 2.33/1.21 thf(infuncsetfunc,definition,
% 2.33/1.21 ( infuncsetfunc
% 2.33/1.21 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.33/1.21 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.33/1.21 => ( func @ A @ B @ Xf ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(ap2p_type,type,
% 2.33/1.21 ap2p: $o ).
% 2.33/1.21
% 2.33/1.21 thf(ap2p,definition,
% 2.33/1.21 ( ap2p
% 2.33/1.21 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.33/1.21 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(funcinfuncset_type,type,
% 2.33/1.21 funcinfuncset: $o ).
% 2.33/1.21
% 2.33/1.21 thf(funcinfuncset,definition,
% 2.33/1.21 ( funcinfuncset
% 2.33/1.21 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.33/1.21 ( ( func @ A @ B @ Xf )
% 2.33/1.21 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(lamProp_type,type,
% 2.33/1.21 lamProp: $o ).
% 2.33/1.21
% 2.33/1.21 thf(lamProp,definition,
% 2.33/1.21 ( lamProp
% 2.33/1.21 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.33/1.21 ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.33/1.21 => ( func @ A @ B
% 2.33/1.21 @ ( dpsetconstr @ A @ B
% 2.33/1.21 @ ^ [Xx: $i,Xy: $i] :
% 2.33/1.21 ( ( Xf @ Xx )
% 2.33/1.21 = Xy ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(lam_type,type,
% 2.33/1.21 lam: $i > $i > ( $i > $i ) > $i ).
% 2.33/1.21
% 2.33/1.21 thf(lamp_type,type,
% 2.33/1.21 lamp: $o ).
% 2.33/1.21
% 2.33/1.21 thf(lamp,definition,
% 2.33/1.21 ( lamp
% 2.33/1.21 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.33/1.21 ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.33/1.21 => ( func @ A @ B
% 2.33/1.21 @ ( lam @ A @ B
% 2.33/1.21 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(lam2p_type,type,
% 2.33/1.21 lam2p: $o ).
% 2.33/1.21
% 2.33/1.21 thf(lam2p,definition,
% 2.33/1.21 ( lam2p
% 2.33/1.21 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.33/1.21 ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.33/1.21 => ( in
% 2.33/1.21 @ ( lam @ A @ B
% 2.33/1.21 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 2.33/1.21 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(brelnall1_type,type,
% 2.33/1.21 brelnall1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(brelnall1,definition,
% 2.33/1.21 ( brelnall1
% 2.33/1.21 = ( ! [A: $i,B: $i,R: $i] :
% 2.33/1.21 ( ( breln @ A @ B @ R )
% 2.33/1.21 => ! [Xphi: $i > $o] :
% 2.33/1.21 ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ B )
% 2.33/1.21 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.33/1.21 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ R )
% 2.33/1.21 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(brelnall2_type,type,
% 2.33/1.21 brelnall2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(brelnall2,definition,
% 2.33/1.21 ( brelnall2
% 2.33/1.21 = ( ! [A: $i,B: $i,R: $i] :
% 2.33/1.21 ( ( breln @ A @ B @ R )
% 2.33/1.21 => ! [Xphi: $i > $o] :
% 2.33/1.21 ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ B )
% 2.33/1.21 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.33/1.21 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ R )
% 2.33/1.21 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(ex1E2_type,type,
% 2.33/1.21 ex1E2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(ex1E2,definition,
% 2.33/1.21 ( ex1E2
% 2.33/1.21 = ( ! [A: $i,Xphi: $i > $o] :
% 2.33/1.21 ( ( ex1 @ A
% 2.33/1.21 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ A )
% 2.33/1.21 => ( ( Xphi @ Xx )
% 2.33/1.21 => ( ( Xphi @ Xy )
% 2.33/1.21 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(funcGraphProp1_type,type,
% 2.33/1.21 funcGraphProp1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(funcGraphProp1,definition,
% 2.33/1.21 ( funcGraphProp1
% 2.33/1.21 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.33/1.21 ( ( func @ A @ B @ Xf )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(funcGraphProp3_type,type,
% 2.33/1.21 funcGraphProp3: $o ).
% 2.33/1.21
% 2.33/1.21 thf(funcGraphProp3,definition,
% 2.33/1.21 ( funcGraphProp3
% 2.33/1.21 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.33/1.21 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(funcGraphProp2_type,type,
% 2.33/1.21 funcGraphProp2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(funcGraphProp2,definition,
% 2.33/1.21 ( funcGraphProp2
% 2.33/1.21 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.33/1.21 ( ( func @ A @ B @ Xf )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ B )
% 2.33/1.21 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 2.33/1.21 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.33/1.21 = Xy ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(funcextLem_type,type,
% 2.33/1.21 funcextLem: $o ).
% 2.33/1.21
% 2.33/1.21 thf(funcextLem,definition,
% 2.33/1.21 ( funcextLem
% 2.33/1.21 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.33/1.21 ( ( func @ A @ B @ Xf )
% 2.33/1.21 => ! [Xg: $i] :
% 2.33/1.21 ( ( func @ A @ B @ Xg )
% 2.33/1.21 => ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.33/1.21 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ B )
% 2.33/1.21 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 2.33/1.21 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(funcGraphProp4_type,type,
% 2.33/1.21 funcGraphProp4: $o ).
% 2.33/1.21
% 2.33/1.21 thf(funcGraphProp4,definition,
% 2.33/1.21 ( funcGraphProp4
% 2.33/1.21 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.33/1.21 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ B )
% 2.33/1.21 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 2.33/1.21 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.33/1.21 = Xy ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(subbreln_type,type,
% 2.33/1.21 subbreln: $o ).
% 2.33/1.21
% 2.33/1.21 thf(subbreln,definition,
% 2.33/1.21 ( subbreln
% 2.33/1.21 = ( ! [A: $i,B: $i,R: $i] :
% 2.33/1.21 ( ( breln @ A @ B @ R )
% 2.33/1.21 => ! [S: $i] :
% 2.33/1.21 ( ( breln @ A @ B @ S )
% 2.33/1.21 => ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ B )
% 2.33/1.21 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.33/1.21 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.33/1.21 => ( subset @ R @ S ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(eqbreln_type,type,
% 2.33/1.21 eqbreln: $o ).
% 2.33/1.21
% 2.33/1.21 thf(eqbreln,definition,
% 2.33/1.21 ( eqbreln
% 2.33/1.21 = ( ! [A: $i,B: $i,R: $i] :
% 2.33/1.21 ( ( breln @ A @ B @ R )
% 2.33/1.21 => ! [S: $i] :
% 2.33/1.21 ( ( breln @ A @ B @ S )
% 2.33/1.21 => ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ B )
% 2.33/1.21 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.33/1.21 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.33/1.21 => ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ B )
% 2.33/1.21 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 2.33/1.21 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 2.33/1.21 => ( R = S ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(funcext_type,type,
% 2.33/1.21 funcext: $o ).
% 2.33/1.21
% 2.33/1.21 thf(funcext,definition,
% 2.33/1.21 ( funcext
% 2.33/1.21 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.33/1.21 ( ( func @ A @ B @ Xf )
% 2.33/1.21 => ! [Xg: $i] :
% 2.33/1.21 ( ( func @ A @ B @ Xg )
% 2.33/1.21 => ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.33/1.21 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.33/1.21 => ( Xf = Xg ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(funcext2_type,type,
% 2.33/1.21 funcext2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(funcext2,definition,
% 2.33/1.21 ( funcext2
% 2.33/1.21 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.33/1.21 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.33/1.21 => ! [Xg: $i] :
% 2.33/1.21 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 2.33/1.21 => ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.33/1.21 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.33/1.21 => ( Xf = Xg ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(ap2apEq1_type,type,
% 2.33/1.21 ap2apEq1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(ap2apEq1,definition,
% 2.33/1.21 ( ap2apEq1
% 2.33/1.21 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.33/1.21 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.33/1.21 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(ap2apEq2_type,type,
% 2.33/1.21 ap2apEq2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(ap2apEq2,definition,
% 2.33/1.21 ( ap2apEq2
% 2.33/1.21 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.33/1.21 ( ( func @ A @ B @ Xf )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.33/1.21 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(beta1_type,type,
% 2.33/1.21 beta1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(beta1,definition,
% 2.33/1.21 ( beta1
% 2.33/1.21 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.33/1.21 ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ( ap @ A @ B
% 2.33/1.21 @ ( lam @ A @ B
% 2.33/1.21 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 2.33/1.21 @ Xx )
% 2.33/1.21 = ( Xf @ Xx ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(eta1_type,type,
% 2.33/1.21 eta1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(eta1,definition,
% 2.33/1.21 ( eta1
% 2.33/1.21 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.33/1.21 ( ( func @ A @ B @ Xf )
% 2.33/1.21 => ( ( lam @ A @ B
% 2.33/1.21 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 2.33/1.21 = Xf ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(lam2lamEq_type,type,
% 2.33/1.21 lam2lamEq: $o ).
% 2.33/1.21
% 2.33/1.21 thf(lam2lamEq,definition,
% 2.33/1.21 ( lam2lamEq
% 2.33/1.21 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.33/1.21 ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.33/1.21 => ( ( lam @ A @ B
% 2.33/1.21 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 2.33/1.21 = ( lam @ A @ B
% 2.33/1.21 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(beta2_type,type,
% 2.33/1.21 beta2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(beta2,definition,
% 2.33/1.21 ( beta2
% 2.33/1.21 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.33/1.21 ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ( ap @ A @ B
% 2.33/1.21 @ ( lam @ A @ B
% 2.33/1.21 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 2.33/1.21 @ Xx )
% 2.33/1.21 = ( Xf @ Xx ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(eta2_type,type,
% 2.33/1.21 eta2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(eta2,definition,
% 2.33/1.21 ( eta2
% 2.33/1.21 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.33/1.21 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.33/1.21 => ( ( lam @ A @ B
% 2.33/1.21 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 2.33/1.21 = Xf ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(iffalseProp1_type,type,
% 2.33/1.21 iffalseProp1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(iffalseProp1,definition,
% 2.33/1.21 ( iffalseProp1
% 2.33/1.21 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ A )
% 2.33/1.21 => ( ~ Xphi
% 2.33/1.21 => ( in @ Xy
% 2.33/1.21 @ ( dsetconstr @ A
% 2.33/1.21 @ ^ [Xz: $i] :
% 2.33/1.21 ( ( Xphi
% 2.33/1.21 & ( Xz = Xx ) )
% 2.33/1.21 | ( ~ Xphi
% 2.33/1.21 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(iffalseProp2_type,type,
% 2.33/1.21 iffalseProp2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(iffalseProp2,definition,
% 2.33/1.21 ( iffalseProp2
% 2.33/1.21 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ A )
% 2.33/1.21 => ( ~ Xphi
% 2.33/1.21 => ( ( dsetconstr @ A
% 2.33/1.21 @ ^ [Xz: $i] :
% 2.33/1.21 ( ( Xphi
% 2.33/1.21 & ( Xz = Xx ) )
% 2.33/1.21 | ( ~ Xphi
% 2.33/1.21 & ( Xz = Xy ) ) ) )
% 2.33/1.21 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(iftrueProp1_type,type,
% 2.33/1.21 iftrueProp1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(iftrueProp1,definition,
% 2.33/1.21 ( iftrueProp1
% 2.33/1.21 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ A )
% 2.33/1.21 => ( Xphi
% 2.33/1.21 => ( in @ Xx
% 2.33/1.21 @ ( dsetconstr @ A
% 2.33/1.21 @ ^ [Xz: $i] :
% 2.33/1.21 ( ( Xphi
% 2.33/1.21 & ( Xz = Xx ) )
% 2.33/1.21 | ( ~ Xphi
% 2.33/1.21 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(iftrueProp2_type,type,
% 2.33/1.21 iftrueProp2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(iftrueProp2,definition,
% 2.33/1.21 ( iftrueProp2
% 2.33/1.21 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ A )
% 2.33/1.21 => ( Xphi
% 2.33/1.21 => ( ( dsetconstr @ A
% 2.33/1.21 @ ^ [Xz: $i] :
% 2.33/1.21 ( ( Xphi
% 2.33/1.21 & ( Xz = Xx ) )
% 2.33/1.21 | ( ~ Xphi
% 2.33/1.21 & ( Xz = Xy ) ) ) )
% 2.33/1.21 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(ifSingleton_type,type,
% 2.33/1.21 ifSingleton: $o ).
% 2.33/1.21
% 2.33/1.21 thf(ifSingleton,definition,
% 2.33/1.21 ( ifSingleton
% 2.33/1.21 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ A )
% 2.33/1.21 => ( singleton
% 2.33/1.21 @ ( dsetconstr @ A
% 2.33/1.21 @ ^ [Xz: $i] :
% 2.33/1.21 ( ( Xphi
% 2.33/1.21 & ( Xz = Xx ) )
% 2.33/1.21 | ( ~ Xphi
% 2.33/1.21 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(if_type,type,
% 2.33/1.21 if: $i > $o > $i > $i > $i ).
% 2.33/1.21
% 2.33/1.21 thf(ifp_type,type,
% 2.33/1.21 ifp: $o ).
% 2.33/1.21
% 2.33/1.21 thf(ifp,definition,
% 2.33/1.21 ( ifp
% 2.33/1.21 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ A )
% 2.33/1.21 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(theeq_type,type,
% 2.33/1.21 theeq: $o ).
% 2.33/1.21
% 2.33/1.21 thf(theeq,definition,
% 2.33/1.21 ( theeq
% 2.33/1.21 = ( ! [X: $i] :
% 2.33/1.21 ( ( singleton @ X )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ X )
% 2.33/1.21 => ( ( setunion @ X )
% 2.33/1.21 = Xx ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(iftrue_type,type,
% 2.33/1.21 iftrue: $o ).
% 2.33/1.21
% 2.33/1.21 thf(iftrue,definition,
% 2.33/1.21 ( iftrue
% 2.33/1.21 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ A )
% 2.33/1.21 => ( Xphi
% 2.33/1.21 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 2.33/1.21 = Xx ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(iffalse_type,type,
% 2.33/1.21 iffalse: $o ).
% 2.33/1.21
% 2.33/1.21 thf(iffalse,definition,
% 2.33/1.21 ( iffalse
% 2.33/1.21 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ A )
% 2.33/1.21 => ( ~ Xphi
% 2.33/1.21 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 2.33/1.21 = Xy ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(iftrueorfalse_type,type,
% 2.33/1.21 iftrueorfalse: $o ).
% 2.33/1.21
% 2.33/1.21 thf(iftrueorfalse,definition,
% 2.33/1.21 ( iftrueorfalse
% 2.33/1.21 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ! [Xy: $i] :
% 2.33/1.21 ( ( in @ Xy @ A )
% 2.33/1.21 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(binintersectT_lem_type,type,
% 2.33/1.21 binintersectT_lem: $o ).
% 2.33/1.21
% 2.33/1.21 thf(binintersectT_lem,definition,
% 2.33/1.21 ( binintersectT_lem
% 2.33/1.21 = ( ! [A: $i,X: $i] :
% 2.33/1.21 ( ( in @ X @ ( powerset @ A ) )
% 2.33/1.21 => ! [Y: $i] :
% 2.33/1.21 ( ( in @ Y @ ( powerset @ A ) )
% 2.33/1.21 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(binunionT_lem_type,type,
% 2.33/1.21 binunionT_lem: $o ).
% 2.33/1.21
% 2.33/1.21 thf(binunionT_lem,definition,
% 2.33/1.21 ( binunionT_lem
% 2.33/1.21 = ( ! [A: $i,X: $i] :
% 2.33/1.21 ( ( in @ X @ ( powerset @ A ) )
% 2.33/1.21 => ! [Y: $i] :
% 2.33/1.21 ( ( in @ Y @ ( powerset @ A ) )
% 2.33/1.21 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(powersetT_lem_type,type,
% 2.33/1.21 powersetT_lem: $o ).
% 2.33/1.21
% 2.33/1.21 thf(powersetT_lem,definition,
% 2.33/1.21 ( powersetT_lem
% 2.33/1.21 = ( ! [A: $i,X: $i] :
% 2.33/1.21 ( ( in @ X @ ( powerset @ A ) )
% 2.33/1.21 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setminusT_lem_type,type,
% 2.33/1.21 setminusT_lem: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setminusT_lem,definition,
% 2.33/1.21 ( setminusT_lem
% 2.33/1.21 = ( ! [A: $i,X: $i] :
% 2.33/1.21 ( ( in @ X @ ( powerset @ A ) )
% 2.33/1.21 => ! [Y: $i] :
% 2.33/1.21 ( ( in @ Y @ ( powerset @ A ) )
% 2.33/1.21 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(complementT_lem_type,type,
% 2.33/1.21 complementT_lem: $o ).
% 2.33/1.21
% 2.33/1.21 thf(complementT_lem,definition,
% 2.33/1.21 ( complementT_lem
% 2.33/1.21 = ( ! [A: $i,X: $i] :
% 2.33/1.21 ( ( in @ X @ ( powerset @ A ) )
% 2.33/1.21 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(setextT_type,type,
% 2.33/1.21 setextT: $o ).
% 2.33/1.21
% 2.33/1.21 thf(setextT,definition,
% 2.33/1.21 ( setextT
% 2.33/1.21 = ( ! [A: $i,X: $i] :
% 2.33/1.21 ( ( in @ X @ ( powerset @ A ) )
% 2.33/1.21 => ! [Y: $i] :
% 2.33/1.21 ( ( in @ Y @ ( powerset @ A ) )
% 2.33/1.21 => ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ( in @ Xx @ X )
% 2.33/1.21 => ( in @ Xx @ Y ) ) )
% 2.33/1.21 => ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ( in @ Xx @ Y )
% 2.33/1.21 => ( in @ Xx @ X ) ) )
% 2.33/1.21 => ( X = Y ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(subsetTI_type,type,
% 2.33/1.21 subsetTI: $o ).
% 2.33/1.21
% 2.33/1.21 thf(subsetTI,definition,
% 2.33/1.21 ( subsetTI
% 2.33/1.21 = ( ! [A: $i,X: $i] :
% 2.33/1.21 ( ( in @ X @ ( powerset @ A ) )
% 2.33/1.21 => ! [Y: $i] :
% 2.33/1.21 ( ( in @ Y @ ( powerset @ A ) )
% 2.33/1.21 => ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ( in @ Xx @ X )
% 2.33/1.21 => ( in @ Xx @ Y ) ) )
% 2.33/1.21 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(powersetTI1_type,type,
% 2.33/1.21 powersetTI1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(powersetTI1,definition,
% 2.33/1.21 ( powersetTI1
% 2.33/1.21 = ( ! [A: $i,X: $i] :
% 2.33/1.21 ( ( in @ X @ ( powerset @ A ) )
% 2.33/1.21 => ! [Y: $i] :
% 2.33/1.21 ( ( in @ Y @ ( powerset @ A ) )
% 2.33/1.21 => ( ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ( in @ Xx @ X )
% 2.33/1.21 => ( in @ Xx @ Y ) ) )
% 2.33/1.21 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(powersetTE1_type,type,
% 2.33/1.21 powersetTE1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(powersetTE1,definition,
% 2.33/1.21 ( powersetTE1
% 2.33/1.21 = ( ! [A: $i,X: $i] :
% 2.33/1.21 ( ( in @ X @ ( powerset @ A ) )
% 2.33/1.21 => ! [Y: $i] :
% 2.33/1.21 ( ( in @ Y @ ( powerset @ A ) )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ( in @ X @ ( powerset @ Y ) )
% 2.33/1.21 => ( ( in @ Xx @ X )
% 2.33/1.21 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(complementTI1_type,type,
% 2.33/1.21 complementTI1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(complementTI1,definition,
% 2.33/1.21 ( complementTI1
% 2.33/1.21 = ( ! [A: $i,X: $i] :
% 2.33/1.21 ( ( in @ X @ ( powerset @ A ) )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ( in @ Xx @ X )
% 2.33/1.21 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(complementTE1_type,type,
% 2.33/1.21 complementTE1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(complementTE1,definition,
% 2.33/1.21 ( complementTE1
% 2.33/1.21 = ( ! [A: $i,X: $i] :
% 2.33/1.21 ( ( in @ X @ ( powerset @ A ) )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 2.33/1.21 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(binintersectTELcontra_type,type,
% 2.33/1.21 binintersectTELcontra: $o ).
% 2.33/1.21
% 2.33/1.21 thf(binintersectTELcontra,definition,
% 2.33/1.21 ( binintersectTELcontra
% 2.33/1.21 = ( ! [A: $i,X: $i] :
% 2.33/1.21 ( ( in @ X @ ( powerset @ A ) )
% 2.33/1.21 => ! [Y: $i] :
% 2.33/1.21 ( ( in @ Y @ ( powerset @ A ) )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ~ ( in @ Xx @ X )
% 2.33/1.21 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(binintersectTERcontra_type,type,
% 2.33/1.21 binintersectTERcontra: $o ).
% 2.33/1.21
% 2.33/1.21 thf(binintersectTERcontra,definition,
% 2.33/1.21 ( binintersectTERcontra
% 2.33/1.21 = ( ! [A: $i,X: $i] :
% 2.33/1.21 ( ( in @ X @ ( powerset @ A ) )
% 2.33/1.21 => ! [Y: $i] :
% 2.33/1.21 ( ( in @ Y @ ( powerset @ A ) )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ~ ( in @ Xx @ Y )
% 2.33/1.21 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(contrasubsetT_type,type,
% 2.33/1.21 contrasubsetT: $o ).
% 2.33/1.21
% 2.33/1.21 thf(contrasubsetT,definition,
% 2.33/1.21 ( contrasubsetT
% 2.33/1.21 = ( ! [A: $i,X: $i] :
% 2.33/1.21 ( ( in @ X @ ( powerset @ A ) )
% 2.33/1.21 => ! [Y: $i] :
% 2.33/1.21 ( ( in @ Y @ ( powerset @ A ) )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.33/1.21 => ( ( in @ Xx @ Y )
% 2.33/1.21 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(contrasubsetT1_type,type,
% 2.33/1.21 contrasubsetT1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(contrasubsetT1,definition,
% 2.33/1.21 ( contrasubsetT1
% 2.33/1.21 = ( ! [A: $i,X: $i] :
% 2.33/1.21 ( ( in @ X @ ( powerset @ A ) )
% 2.33/1.21 => ! [Y: $i] :
% 2.33/1.21 ( ( in @ Y @ ( powerset @ A ) )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ( subset @ X @ Y )
% 2.33/1.21 => ( ~ ( in @ Xx @ Y )
% 2.33/1.21 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(contrasubsetT2_type,type,
% 2.33/1.21 contrasubsetT2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(contrasubsetT2,definition,
% 2.33/1.21 ( contrasubsetT2
% 2.33/1.21 = ( ! [A: $i,X: $i] :
% 2.33/1.21 ( ( in @ X @ ( powerset @ A ) )
% 2.33/1.21 => ! [Y: $i] :
% 2.33/1.21 ( ( in @ Y @ ( powerset @ A ) )
% 2.33/1.21 => ( ( subset @ X @ Y )
% 2.33/1.21 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(contrasubsetT3_type,type,
% 2.33/1.21 contrasubsetT3: $o ).
% 2.33/1.21
% 2.33/1.21 thf(contrasubsetT3,definition,
% 2.33/1.21 ( contrasubsetT3
% 2.33/1.21 = ( ! [A: $i,X: $i] :
% 2.33/1.21 ( ( in @ X @ ( powerset @ A ) )
% 2.33/1.21 => ! [Y: $i] :
% 2.33/1.21 ( ( in @ Y @ ( powerset @ A ) )
% 2.33/1.21 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 2.33/1.21 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(doubleComplementI1_type,type,
% 2.33/1.21 doubleComplementI1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(doubleComplementI1,definition,
% 2.33/1.21 ( doubleComplementI1
% 2.33/1.21 = ( ! [A: $i,X: $i] :
% 2.33/1.21 ( ( in @ X @ ( powerset @ A ) )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ( in @ Xx @ X )
% 2.33/1.21 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(doubleComplementE1_type,type,
% 2.33/1.21 doubleComplementE1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(doubleComplementE1,definition,
% 2.33/1.21 ( doubleComplementE1
% 2.33/1.21 = ( ! [A: $i,X: $i] :
% 2.33/1.21 ( ( in @ X @ ( powerset @ A ) )
% 2.33/1.21 => ! [Xx: $i] :
% 2.33/1.21 ( ( in @ Xx @ A )
% 2.33/1.21 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 2.33/1.21 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(doubleComplementSub1_type,type,
% 2.33/1.21 doubleComplementSub1: $o ).
% 2.33/1.21
% 2.33/1.21 thf(doubleComplementSub1,definition,
% 2.33/1.21 ( doubleComplementSub1
% 2.33/1.21 = ( ! [A: $i,X: $i] :
% 2.33/1.21 ( ( in @ X @ ( powerset @ A ) )
% 2.33/1.21 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(doubleComplementSub2_type,type,
% 2.33/1.21 doubleComplementSub2: $o ).
% 2.33/1.21
% 2.33/1.21 thf(doubleComplementSub2,definition,
% 2.33/1.21 ( doubleComplementSub2
% 2.33/1.21 = ( ! [A: $i,X: $i] :
% 2.33/1.21 ( ( in @ X @ ( powerset @ A ) )
% 2.33/1.21 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 2.33/1.21
% 2.33/1.21 thf(doubleComplementEq,conjecture,
% 2.33/1.21 ( setextAx
% 2.33/1.21 => ( emptysetAx
% 2.33/1.21 => ( setadjoinAx
% 2.33/1.21 => ( powersetAx
% 2.33/1.21 => ( setunionAx
% 2.33/1.21 => ( omega0Ax
% 2.33/1.21 => ( omegaSAx
% 2.33/1.21 => ( omegaIndAx
% 2.33/1.21 => ( replAx
% 2.33/1.21 => ( foundationAx
% 2.33/1.21 => ( wellorderingAx
% 2.33/1.21 => ( descrp
% 2.33/1.21 => ( dsetconstrI
% 2.33/1.21 => ( dsetconstrEL
% 2.33/1.21 => ( dsetconstrER
% 2.33/1.21 => ( exuE1
% 2.33/1.21 => ( prop2setE
% 2.33/1.21 => ( emptysetE
% 2.33/1.21 => ( emptysetimpfalse
% 2.33/1.21 => ( notinemptyset
% 2.33/1.21 => ( exuE3e
% 2.33/1.21 => ( setext
% 2.33/1.21 => ( emptyI
% 2.33/1.21 => ( noeltsimpempty
% 2.33/1.21 => ( setbeta
% 2.33/1.21 => ( nonemptyE1
% 2.33/1.21 => ( nonemptyI
% 2.33/1.21 => ( nonemptyI1
% 2.33/1.21 => ( setadjoinIL
% 2.33/1.21 => ( emptyinunitempty
% 2.33/1.21 => ( setadjoinIR
% 2.33/1.21 => ( setadjoinE
% 2.33/1.21 => ( setadjoinOr
% 2.33/1.21 => ( setoftrueEq
% 2.33/1.21 => ( powersetI
% 2.33/1.21 => ( emptyinPowerset
% 2.33/1.21 => ( emptyInPowerset
% 2.33/1.21 => ( powersetE
% 2.33/1.21 => ( setunionI
% 2.33/1.21 => ( setunionE
% 2.33/1.21 => ( subPowSU
% 2.33/1.21 => ( exuE2
% 2.33/1.21 => ( nonemptyImpWitness
% 2.33/1.21 => ( uniqinunit
% 2.33/1.21 => ( notinsingleton
% 2.33/1.21 => ( eqinunit
% 2.33/1.21 => ( singletonsswitch
% 2.33/1.21 => ( upairsetE
% 2.33/1.21 => ( upairsetIL
% 2.33/1.21 => ( upairsetIR
% 2.33/1.21 => ( emptyE1
% 2.33/1.21 => ( vacuousDall
% 2.33/1.21 => ( quantDeMorgan1
% 2.33/1.21 => ( quantDeMorgan2
% 2.33/1.21 => ( quantDeMorgan3
% 2.33/1.21 => ( quantDeMorgan4
% 2.33/1.21 => ( prop2setI
% 2.33/1.21 => ( prop2set2propI
% 2.33/1.21 => ( notdexE
% 2.33/1.21 => ( notdallE
% 2.33/1.21 => ( exuI1
% 2.33/1.21 => ( exuI3
% 2.33/1.21 => ( exuI2
% 2.33/1.21 => ( inCongP
% 2.33/1.21 => ( in__Cong
% 2.33/1.21 => ( exuE3u
% 2.33/1.21 => ( exu__Cong
% 2.33/1.21 => ( emptyset__Cong
% 2.33/1.21 => ( setadjoin__Cong
% 2.33/1.21 => ( powerset__Cong
% 2.33/1.21 => ( setunion__Cong
% 2.33/1.21 => ( omega__Cong
% 2.33/1.21 => ( exuEu
% 2.33/1.21 => ( descr__Cong
% 2.33/1.21 => ( dsetconstr__Cong
% 2.33/1.21 => ( subsetI1
% 2.33/1.21 => ( eqimpsubset2
% 2.33/1.21 => ( eqimpsubset1
% 2.33/1.21 => ( subsetI2
% 2.33/1.21 => ( emptysetsubset
% 2.33/1.21 => ( subsetE
% 2.33/1.21 => ( subsetE2
% 2.33/1.21 => ( notsubsetI
% 2.33/1.21 => ( notequalI1
% 2.33/1.21 => ( notequalI2
% 2.33/1.21 => ( subsetRefl
% 2.33/1.21 => ( subsetTrans
% 2.33/1.21 => ( setadjoinSub
% 2.33/1.21 => ( setadjoinSub2
% 2.33/1.21 => ( subset2powerset
% 2.33/1.21 => ( setextsub
% 2.33/1.21 => ( subsetemptysetimpeq
% 2.33/1.21 => ( powersetI1
% 2.33/1.21 => ( powersetE1
% 2.33/1.21 => ( inPowerset
% 2.33/1.21 => ( powersetsubset
% 2.33/1.21 => ( sepInPowerset
% 2.33/1.21 => ( sepSubset
% 2.33/1.21 => ( binunionIL
% 2.33/1.21 => ( upairset2IR
% 2.33/1.21 => ( binunionIR
% 2.33/1.21 => ( binunionEcases
% 2.33/1.21 => ( binunionE
% 2.33/1.21 => ( binunionLsub
% 2.33/1.21 => ( binunionRsub
% 2.33/1.21 => ( binintersectI
% 2.33/1.21 => ( binintersectSubset5
% 2.33/1.21 => ( binintersectEL
% 2.33/1.21 => ( binintersectLsub
% 2.33/1.21 => ( binintersectSubset2
% 2.33/1.21 => ( binintersectSubset3
% 2.33/1.21 => ( binintersectER
% 2.33/1.21 => ( disjointsetsI1
% 2.33/1.21 => ( binintersectRsub
% 2.33/1.21 => ( binintersectSubset4
% 2.33/1.21 => ( binintersectSubset1
% 2.33/1.21 => ( bs114d
% 2.33/1.21 => ( setminusI
% 2.33/1.21 => ( setminusEL
% 2.33/1.21 => ( setminusER
% 2.33/1.21 => ( setminusSubset2
% 2.33/1.21 => ( setminusERneg
% 2.33/1.21 => ( setminusELneg
% 2.33/1.21 => ( setminusILneg
% 2.33/1.21 => ( setminusIRneg
% 2.33/1.21 => ( setminusLsub
% 2.33/1.21 => ( setminusSubset1
% 2.33/1.21 => ( symdiffE
% 2.33/1.21 => ( symdiffI1
% 2.33/1.21 => ( symdiffI2
% 2.33/1.21 => ( symdiffIneg1
% 2.33/1.21 => ( symdiffIneg2
% 2.33/1.21 => ( secondinupair
% 2.33/1.21 => ( setukpairIL
% 2.33/1.21 => ( setukpairIR
% 2.33/1.21 => ( kpairiskpair
% 2.33/1.21 => ( kpairp
% 2.33/1.21 => ( singletonsubset
% 2.33/1.21 => ( singletoninpowerset
% 2.33/1.21 => ( singletoninpowunion
% 2.33/1.21 => ( upairset2E
% 2.33/1.21 => ( upairsubunion
% 2.33/1.21 => ( upairinpowunion
% 2.33/1.21 => ( ubforcartprodlem1
% 2.33/1.21 => ( ubforcartprodlem2
% 2.33/1.21 => ( ubforcartprodlem3
% 2.33/1.21 => ( cartprodpairin
% 2.33/1.21 => ( cartprodmempair1
% 2.33/1.21 => ( cartprodmempair
% 2.33/1.21 => ( setunionE2
% 2.33/1.21 => ( setunionsingleton1
% 2.33/1.21 => ( setunionsingleton2
% 2.33/1.21 => ( setunionsingleton
% 2.33/1.21 => ( singletonprop
% 2.33/1.21 => ( ex1E1
% 2.33/1.21 => ( ex1I
% 2.33/1.21 => ( ex1I2
% 2.33/1.21 => ( singletonsuniq
% 2.33/1.21 => ( setukpairinjL1
% 2.33/1.21 => ( kfstsingleton
% 2.33/1.21 => ( theprop
% 2.33/1.21 => ( kfstpairEq
% 2.33/1.21 => ( cartprodfstin
% 2.33/1.21 => ( setukpairinjL2
% 2.33/1.21 => ( setukpairinjL
% 2.33/1.21 => ( setukpairinjR11
% 2.33/1.21 => ( setukpairinjR12
% 2.33/1.21 => ( setukpairinjR1
% 2.33/1.21 => ( upairequniteq
% 2.33/1.21 => ( setukpairinjR2
% 2.33/1.21 => ( setukpairinjR
% 2.33/1.21 => ( ksndsingleton
% 2.33/1.21 => ( ksndpairEq
% 2.33/1.21 => ( kpairsurjEq
% 2.33/1.21 => ( cartprodsndin
% 2.33/1.21 => ( cartprodpairmemEL
% 2.33/1.21 => ( cartprodpairmemER
% 2.33/1.21 => ( cartprodmempaircEq
% 2.33/1.21 => ( cartprodfstpairEq
% 2.33/1.21 => ( cartprodsndpairEq
% 2.33/1.21 => ( cartprodpairsurjEq
% 2.33/1.21 => ( dpsetconstrI
% 2.33/1.21 => ( dpsetconstrSub
% 2.33/1.21 => ( setOfPairsIsBReln
% 2.33/1.21 => ( dpsetconstrERa
% 2.33/1.21 => ( dpsetconstrEL1
% 2.33/1.21 => ( dpsetconstrEL2
% 2.33/1.21 => ( dpsetconstrER
% 2.33/1.21 => ( funcImageSingleton
% 2.33/1.21 => ( apProp
% 2.33/1.21 => ( app
% 2.33/1.21 => ( infuncsetfunc
% 2.33/1.21 => ( ap2p
% 2.33/1.21 => ( funcinfuncset
% 2.33/1.21 => ( lamProp
% 2.33/1.21 => ( lamp
% 2.33/1.21 => ( lam2p
% 2.33/1.21 => ( brelnall1
% 2.33/1.21 => ( brelnall2
% 2.33/1.21 => ( ex1E2
% 2.33/1.21 => ( funcGraphProp1
% 2.33/1.21 => ( funcGraphProp3
% 2.33/1.21 => ( funcGraphProp2
% 2.33/1.21 => ( funcextLem
% 2.33/1.21 => ( funcGraphProp4
% 2.33/1.21 => ( subbreln
% 2.33/1.21 => ( eqbreln
% 2.33/1.21 => ( funcext
% 2.33/1.21 => ( funcext2
% 2.33/1.21 => ( ap2apEq1
% 2.33/1.21 => ( ap2apEq2
% 2.33/1.21 => ( beta1
% 2.33/1.21 => ( eta1
% 2.33/1.21 => ( lam2lamEq
% 2.33/1.21 => ( beta2
% 2.33/1.21 => ( eta2
% 2.33/1.21 => ( iffalseProp1
% 2.33/1.21 => ( iffalseProp2
% 2.33/1.21 => ( iftrueProp1
% 2.33/1.21 => ( iftrueProp2
% 2.33/1.21 => ( ifSingleton
% 2.33/1.21 => ( ifp
% 2.33/1.21 => ( theeq
% 2.33/1.21 => ( iftrue
% 2.33/1.21 => ( iffalse
% 2.33/1.21 => ( iftrueorfalse
% 2.33/1.21 => ( binintersectT_lem
% 2.33/1.21 => ( binunionT_lem
% 2.33/1.21 => ( powersetT_lem
% 2.33/1.21 => ( setminusT_lem
% 2.33/1.21 => ( complementT_lem
% 2.33/1.21 => ( setextT
% 2.33/1.21 => ( subsetTI
% 2.33/1.21 => ( powersetTI1
% 2.33/1.21 => ( powersetTE1
% 2.33/1.21 => ( complementTI1
% 2.33/1.21 => ( complementTE1
% 2.33/1.21 => ( binintersectTELcontra
% 2.33/1.21 => ( binintersectTERcontra
% 2.33/1.21 => ( contrasubsetT
% 2.33/1.21 => ( contrasubsetT1
% 2.33/1.21 => ( contrasubsetT2
% 2.33/1.21 => ( contrasubsetT3
% 2.33/1.21 => ( doubleComplementI1
% 2.33/1.21 => ( doubleComplementE1
% 2.33/1.21 => ( doubleComplementSub1
% 2.33/1.21 => ( doubleComplementSub2
% 2.33/1.21 => ! [A: $i,X: $i] :
% 2.33/1.21 ( ( in @ X @ ( powerset @ A ) )
% 2.33/1.21 => ( X
% 2.33/1.21 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.33/1.21 ------------------------
% 2.33/1.24 % (3685)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_3484 for (2999ds/27Mi)
% 2.33/1.24 % (3683)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3484 for (2999ds/183Mi)
% 2.33/1.24 % (3684)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_3484 for (2999ds/4Mi)
% 2.33/1.24 % (3688)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_3484 for (2999ds/275Mi)
% 2.33/1.24 % (3687)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_3484 for (2999ds/2Mi)
% 2.33/1.24 % (3686)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3484 for (2999ds/2Mi)
% 2.33/1.24 % (3689)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3484 for (2999ds/18Mi)
% 2.33/1.24 % (3686)Instruction limit reached!
% 2.33/1.24 % (3686)------------------------------
% 2.33/1.24 % (3686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.33/1.24 % (3686)Termination reason: Unknown
% 2.33/1.24 % (3686)Termination phase: shuffling
% 2.33/1.24 % (3687)Instruction limit reached!
% 2.33/1.24 % (3687)------------------------------
% 2.33/1.24 % (3687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.33/1.24
% 2.33/1.24 % (3686)Memory used [KB]: 1407
% 2.33/1.24 % (3686)Time elapsed: 0.003 s
% 2.33/1.24 % (3686)Instructions burned: 3 (million)
% 2.33/1.24 % (3686)------------------------------
% 2.33/1.24 % (3686)------------------------------
% 2.33/1.24 % (3687)Termination reason: Unknown
% 2.33/1.24 % (3687)Termination phase: shuffling
% 2.33/1.24
% 2.33/1.24 % (3687)Memory used [KB]: 1407
% 2.33/1.24 % (3687)Time elapsed: 0.003 s
% 2.33/1.24 % (3687)Instructions burned: 3 (million)
% 2.33/1.24 % (3687)------------------------------
% 2.33/1.24 % (3687)------------------------------
% 2.33/1.24 % (3684)Instruction limit reached!
% 2.33/1.24 % (3684)------------------------------
% 2.33/1.24 % (3684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.33/1.24 % (3684)Termination reason: Unknown
% 2.33/1.24 % (3684)Termination phase: shuffling
% 2.33/1.24
% 2.33/1.24 % (3684)Memory used [KB]: 1535
% 2.33/1.24 % (3684)Time elapsed: 0.004 s
% 2.33/1.24 % (3684)Instructions burned: 5 (million)
% 2.33/1.24 % (3684)------------------------------
% 2.33/1.24 % (3684)------------------------------
% 2.33/1.24 % (3685)Instruction limit reached!
% 2.33/1.24 % (3685)------------------------------
% 2.33/1.24 % (3685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.33/1.24 % (3685)Termination reason: Unknown
% 2.33/1.24 % (3685)Termination phase: shuffling
% 2.33/1.24
% 2.33/1.24 % (3685)Memory used [KB]: 1918
% 2.33/1.24 % (3685)Time elapsed: 0.009 s
% 2.33/1.24 % (3685)Instructions burned: 27 (million)
% 2.33/1.24 % (3685)------------------------------
% 2.33/1.24 % (3685)------------------------------
% 2.33/1.25 % (3689)Instruction limit reached!
% 2.33/1.25 % (3689)------------------------------
% 2.33/1.25 % (3689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.33/1.25 % (3689)Termination reason: Unknown
% 2.33/1.25 % (3689)Termination phase: shuffling
% 2.33/1.25
% 2.33/1.25 % (3689)Memory used [KB]: 1791
% 2.33/1.25 % (3689)Time elapsed: 0.011 s
% 2.33/1.25 % (3689)Instructions burned: 19 (million)
% 2.33/1.25 % (3689)------------------------------
% 2.33/1.25 % (3689)------------------------------
% 2.33/1.25 % (3698)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_3484 for (2999ds/37Mi)
% 2.33/1.25 % (3697)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3484 for (2999ds/3Mi)
% 2.33/1.25 % (3699)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_3484 for (2999ds/15Mi)
% 2.33/1.26 % (3697)Instruction limit reached!
% 2.33/1.26 % (3697)------------------------------
% 2.33/1.26 % (3697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.33/1.26 % (3697)Termination reason: Unknown
% 2.33/1.26 % (3697)Termination phase: shuffling
% 2.33/1.26
% 2.33/1.26 % (3697)Memory used [KB]: 1407
% 2.33/1.26 % (3697)Time elapsed: 0.003 s
% 2.33/1.26 % (3697)Instructions burned: 3 (million)
% 2.33/1.26 % (3697)------------------------------
% 2.33/1.26 % (3697)------------------------------
% 2.33/1.26 % (3701)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_3484 for (2999ds/1041Mi)
% 2.33/1.26 % (3700)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3484 for (2999ds/3Mi)
% 2.33/1.26 % (3700)Instruction limit reached!
% 2.33/1.26 % (3700)------------------------------
% 2.33/1.26 % (3700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.33/1.26 % (3700)Termination reason: Unknown
% 2.33/1.26 % (3700)Termination phase: shuffling
% 2.33/1.26
% 2.33/1.26 % (3700)Memory used [KB]: 1407
% 2.33/1.26 % (3700)Time elapsed: 0.003 s
% 2.33/1.26 % (3700)Instructions burned: 3 (million)
% 2.33/1.26 % (3700)------------------------------
% 2.33/1.26 % (3700)------------------------------
% 2.33/1.26 % (3699)Instruction limit reached!
% 2.33/1.26 % (3699)------------------------------
% 2.33/1.26 % (3699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.33/1.26 % (3699)Termination reason: Unknown
% 2.33/1.26 % (3699)Termination phase: shuffling
% 2.33/1.26
% 2.33/1.26 % (3699)Memory used [KB]: 1791
% 2.33/1.26 % (3699)Time elapsed: 0.009 s
% 2.33/1.26 % (3699)Instructions burned: 15 (million)
% 2.33/1.26 % (3699)------------------------------
% 2.33/1.26 % (3699)------------------------------
% 2.33/1.27 % (3698)Instruction limit reached!
% 2.33/1.27 % (3698)------------------------------
% 2.33/1.27 % (3698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.33/1.27 % (3698)Termination reason: Unknown
% 2.33/1.27 % (3698)Termination phase: shuffling
% 2.33/1.27
% 2.33/1.27 % (3698)Memory used [KB]: 2302
% 2.33/1.27 % (3698)Time elapsed: 0.018 s
% 2.33/1.27 % (3698)Instructions burned: 38 (million)
% 2.33/1.27 % (3698)------------------------------
% 2.33/1.27 % (3698)------------------------------
% 2.33/1.28 % (3708)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3484 for (2999ds/16Mi)
% 2.33/1.28 % (3709)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_3484 for (2999ds/3Mi)
% 2.33/1.28 % (3709)Instruction limit reached!
% 2.33/1.28 % (3709)------------------------------
% 2.33/1.28 % (3709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.33/1.28 % (3709)Termination reason: Unknown
% 2.33/1.28 % (3709)Termination phase: shuffling
% 2.33/1.28
% 2.33/1.28 % (3709)Memory used [KB]: 1407
% 2.33/1.28 % (3709)Time elapsed: 0.003 s
% 2.33/1.28 % (3709)Instructions burned: 3 (million)
% 2.33/1.28 % (3709)------------------------------
% 2.33/1.28 % (3709)------------------------------
% 2.33/1.28 % (3706)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3484 for (2999ds/7Mi)
% 2.33/1.28 % (3706)Instruction limit reached!
% 2.33/1.28 % (3706)------------------------------
% 2.33/1.28 % (3706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.33/1.28 % (3706)Termination reason: Unknown
% 2.33/1.28 % (3706)Termination phase: shuffling
% 2.33/1.28
% 2.33/1.28 % (3706)Memory used [KB]: 1535
% 2.33/1.28 % (3706)Time elapsed: 0.005 s
% 2.33/1.28 % (3706)Instructions burned: 7 (million)
% 2.33/1.28 % (3706)------------------------------
% 2.33/1.28 % (3706)------------------------------
% 2.33/1.28 % (3708)Instruction limit reached!
% 2.33/1.28 % (3708)------------------------------
% 2.33/1.28 % (3708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.33/1.28 % (3708)Termination reason: Unknown
% 2.33/1.28 % (3708)Termination phase: shuffling
% 2.33/1.28
% 2.33/1.28 % (3708)Memory used [KB]: 1791
% 2.33/1.28 % (3708)Time elapsed: 0.009 s
% 2.33/1.28 % (3708)Instructions burned: 16 (million)
% 2.33/1.28 % (3708)------------------------------
% 2.33/1.28 % (3708)------------------------------
% 2.33/1.29 % (3715)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3484 for (2999ds/7Mi)
% 2.33/1.29 % (3715)Instruction limit reached!
% 2.33/1.29 % (3715)------------------------------
% 2.33/1.29 % (3715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.33/1.29 % (3715)Termination reason: Unknown
% 2.33/1.29 % (3715)Termination phase: shuffling
% 2.33/1.29
% 2.33/1.29 % (3715)Memory used [KB]: 1535
% 2.33/1.29 % (3715)Time elapsed: 0.004 s
% 2.33/1.29 % (3715)Instructions burned: 7 (million)
% 2.33/1.29 % (3715)------------------------------
% 2.33/1.29 % (3715)------------------------------
% 2.35/1.30 % (3717)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3484 for (2999ds/3Mi)
% 2.35/1.30 % (3717)Instruction limit reached!
% 2.35/1.30 % (3717)------------------------------
% 2.35/1.30 % (3717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.30 % (3711)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_3484 for (2999ds/3Mi)
% 2.35/1.30 % (3717)Termination reason: Unknown
% 2.35/1.30 % (3717)Termination phase: shuffling
% 2.35/1.30
% 2.35/1.30 % (3717)Memory used [KB]: 1535
% 2.35/1.30 % (3717)Time elapsed: 0.003 s
% 2.35/1.30 % (3717)Instructions burned: 5 (million)
% 2.35/1.30 % (3717)------------------------------
% 2.35/1.30 % (3717)------------------------------
% 2.35/1.30 % (3711)Instruction limit reached!
% 2.35/1.30 % (3711)------------------------------
% 2.35/1.30 % (3711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.30 % (3711)Termination reason: Unknown
% 2.35/1.30 % (3711)Termination phase: shuffling
% 2.35/1.30
% 2.35/1.30 % (3711)Memory used [KB]: 1407
% 2.35/1.30 % (3711)Time elapsed: 0.003 s
% 2.35/1.30 % (3711)Instructions burned: 3 (million)
% 2.35/1.30 % (3711)------------------------------
% 2.35/1.30 % (3711)------------------------------
% 2.35/1.31 % (3718)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_3484 for (2999ds/4Mi)
% 2.35/1.31 % (3718)Instruction limit reached!
% 2.35/1.31 % (3718)------------------------------
% 2.35/1.31 % (3718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.31 % (3718)Termination reason: Unknown
% 2.35/1.31 % (3718)Termination phase: shuffling
% 2.35/1.31
% 2.35/1.31 % (3718)Memory used [KB]: 1535
% 2.35/1.31 % (3718)Time elapsed: 0.004 s
% 2.35/1.31 % (3718)Instructions burned: 5 (million)
% 2.35/1.31 % (3718)------------------------------
% 2.35/1.31 % (3718)------------------------------
% 2.35/1.31 % (3724)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3484 for (2999ds/6Mi)
% 2.35/1.31 % (3724)Instruction limit reached!
% 2.35/1.31 % (3724)------------------------------
% 2.35/1.31 % (3724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.31 % (3724)Termination reason: Unknown
% 2.35/1.31 % (3724)Termination phase: shuffling
% 2.35/1.31
% 2.35/1.31 % (3724)Memory used [KB]: 1535
% 2.35/1.31 % (3724)Time elapsed: 0.003 s
% 2.35/1.31 % (3724)Instructions burned: 7 (million)
% 2.35/1.31 % (3724)------------------------------
% 2.35/1.31 % (3724)------------------------------
% 2.35/1.31 % (3721)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_3484 for (2999ds/18Mi)
% 2.35/1.31 % (3722)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_3484 for (2999ds/710Mi)
% 2.35/1.32 % (3721)Instruction limit reached!
% 2.35/1.32 % (3721)------------------------------
% 2.35/1.32 % (3721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.32 % (3721)Termination reason: Unknown
% 2.35/1.32 % (3721)Termination phase: shuffling
% 2.35/1.32
% 2.35/1.32 % (3721)Memory used [KB]: 1791
% 2.35/1.32 % (3721)Time elapsed: 0.007 s
% 2.35/1.32 % (3721)Instructions burned: 20 (million)
% 2.35/1.32 % (3721)------------------------------
% 2.35/1.32 % (3721)------------------------------
% 2.35/1.32 % (3683)Instruction limit reached!
% 2.35/1.32 % (3683)------------------------------
% 2.35/1.32 % (3683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.32 % (3683)Termination reason: Unknown
% 2.35/1.32 % (3683)Termination phase: Saturation
% 2.35/1.32
% 2.35/1.32 % (3683)Memory used [KB]: 7675
% 2.35/1.32 % (3683)Time elapsed: 0.083 s
% 2.35/1.32 % (3683)Instructions burned: 183 (million)
% 2.35/1.32 % (3683)------------------------------
% 2.35/1.32 % (3683)------------------------------
% 2.35/1.33 % (3728)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_3484 for (2998ds/21Mi)
% 2.35/1.33 % (3730)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_3484 for (2998ds/5Mi)
% 2.35/1.33 % (3726)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_3484 for (2999ds/902Mi)
% 2.35/1.33 % (3730)Instruction limit reached!
% 2.35/1.33 % (3730)------------------------------
% 2.35/1.33 % (3730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.33 % (3730)Termination reason: Unknown
% 2.35/1.33 % (3730)Termination phase: shuffling
% 2.35/1.33
% 2.35/1.33 % (3730)Memory used [KB]: 1535
% 2.35/1.33 % (3730)Time elapsed: 0.003 s
% 2.35/1.33 % (3730)Instructions burned: 7 (million)
% 2.35/1.33 % (3730)------------------------------
% 2.35/1.33 % (3730)------------------------------
% 2.35/1.33 % (3728)Instruction limit reached!
% 2.35/1.33 % (3728)------------------------------
% 2.35/1.33 % (3728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.33 % (3728)Termination reason: Unknown
% 2.35/1.33 % (3728)Termination phase: shuffling
% 2.35/1.33
% 2.35/1.33 % (3728)Memory used [KB]: 1918
% 2.35/1.33 % (3728)Time elapsed: 0.008 s
% 2.35/1.33 % (3728)Instructions burned: 22 (million)
% 2.35/1.33 % (3728)------------------------------
% 2.35/1.33 % (3728)------------------------------
% 2.35/1.34 % (3734)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_3484 for (2998ds/377Mi)
% 2.35/1.34 % (3731)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_3484 for (2998ds/6Mi)
% 2.35/1.35 % (3731)Instruction limit reached!
% 2.35/1.35 % (3731)------------------------------
% 2.35/1.35 % (3731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.35 % (3731)Termination reason: Unknown
% 2.35/1.35 % (3731)Termination phase: shuffling
% 2.35/1.35
% 2.35/1.35 % (3731)Memory used [KB]: 1535
% 2.35/1.35 % (3731)Time elapsed: 0.005 s
% 2.35/1.35 % (3731)Instructions burned: 7 (million)
% 2.35/1.35 % (3731)------------------------------
% 2.35/1.35 % (3731)------------------------------
% 2.35/1.35 % (3688)Instruction limit reached!
% 2.35/1.35 % (3688)------------------------------
% 2.35/1.35 % (3688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.35 % (3688)Termination reason: Unknown
% 2.35/1.35 % (3688)Termination phase: Saturation
% 2.35/1.35
% 2.35/1.35 % (3688)Memory used [KB]: 9594
% 2.35/1.35 % (3688)Time elapsed: 0.113 s
% 2.35/1.35 % (3688)Instructions burned: 275 (million)
% 2.35/1.35 % (3688)------------------------------
% 2.35/1.35 % (3688)------------------------------
% 2.35/1.35 % (3736)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_3484 for (2998ds/779Mi)
% 2.35/1.36 % (3739)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_3484 for (2998ds/879Mi)
% 2.35/1.37 % (3738)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_3484 for (2998ds/19Mi)
% 2.35/1.37 % (3738)Instruction limit reached!
% 2.35/1.37 % (3738)------------------------------
% 2.35/1.37 % (3738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.37 % (3738)Termination reason: Unknown
% 2.35/1.37 % (3738)Termination phase: shuffling
% 2.35/1.37
% 2.35/1.37 % (3738)Memory used [KB]: 1791
% 2.35/1.37 % (3738)Time elapsed: 0.011 s
% 2.35/1.37 % (3738)Instructions burned: 20 (million)
% 2.35/1.37 % (3738)------------------------------
% 2.35/1.37 % (3738)------------------------------
% 2.35/1.39 % (3743)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_3484 for (2998ds/17Mi)
% 2.35/1.40 % (3743)Instruction limit reached!
% 2.35/1.40 % (3743)------------------------------
% 2.35/1.40 % (3743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.40 % (3743)Termination reason: Unknown
% 2.35/1.40 % (3743)Termination phase: shuffling
% 2.35/1.40
% 2.35/1.40 % (3743)Memory used [KB]: 1791
% 2.35/1.40 % (3743)Time elapsed: 0.010 s
% 2.35/1.40 % (3743)Instructions burned: 18 (million)
% 2.35/1.40 % (3743)------------------------------
% 2.35/1.40 % (3743)------------------------------
% 2.35/1.42 % (3745)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_3484 for (2998ds/3Mi)
% 2.35/1.42 % (3745)Instruction limit reached!
% 2.35/1.42 % (3745)------------------------------
% 2.35/1.42 % (3745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.42 % (3745)Termination reason: Unknown
% 2.35/1.42 % (3745)Termination phase: shuffling
% 2.35/1.42
% 2.35/1.42 % (3745)Memory used [KB]: 1407
% 2.35/1.42 % (3745)Time elapsed: 0.003 s
% 2.35/1.42 % (3745)Instructions burned: 3 (million)
% 2.35/1.42 % (3745)------------------------------
% 2.35/1.42 % (3745)------------------------------
% 2.35/1.43 % (3747)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_3484 for (2997ds/30Mi)
% 2.35/1.45 % (3747)Instruction limit reached!
% 2.35/1.45 % (3747)------------------------------
% 2.35/1.45 % (3747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.45 % (3747)Termination reason: Unknown
% 2.35/1.45 % (3747)Termination phase: shuffling
% 2.35/1.45
% 2.35/1.45 % (3747)Memory used [KB]: 2046
% 2.35/1.45 % (3747)Time elapsed: 0.016 s
% 2.35/1.45 % (3747)Instructions burned: 31 (million)
% 2.35/1.45 % (3747)------------------------------
% 2.35/1.45 % (3747)------------------------------
% 2.35/1.46 % (3749)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_3484 for (2997ds/127Mi)
% 2.35/1.50 % (3734)Instruction limit reached!
% 2.35/1.50 % (3734)------------------------------
% 2.35/1.50 % (3734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.50 % (3734)Termination reason: Unknown
% 2.35/1.50 % (3734)Termination phase: Saturation
% 2.35/1.50
% 2.35/1.50 % (3734)Memory used [KB]: 9338
% 2.35/1.50 % (3734)Time elapsed: 0.160 s
% 2.35/1.50 % (3734)Instructions burned: 377 (million)
% 2.35/1.50 % (3734)------------------------------
% 2.35/1.50 % (3734)------------------------------
% 2.35/1.51 % (3751)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_3484 for (2997ds/100Mi)
% 2.35/1.51 % (3749)Instruction limit reached!
% 2.35/1.51 % (3749)------------------------------
% 2.35/1.51 % (3749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.51 % (3749)Termination reason: Unknown
% 2.35/1.51 % (3749)Termination phase: Property scanning
% 2.35/1.51
% 2.35/1.51 % (3749)Memory used [KB]: 2686
% 2.35/1.51 % (3749)Time elapsed: 0.053 s
% 2.35/1.51 % (3749)Instructions burned: 130 (million)
% 2.35/1.51 % (3749)------------------------------
% 2.35/1.51 % (3749)------------------------------
% 2.35/1.52 % (3753)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_3484 for (2997ds/3Mi)
% 2.35/1.53 % (3753)Instruction limit reached!
% 2.35/1.53 % (3753)------------------------------
% 2.35/1.53 % (3753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.53 % (3753)Termination reason: Unknown
% 2.35/1.53 % (3753)Termination phase: shuffling
% 2.35/1.53
% 2.35/1.53 % (3753)Memory used [KB]: 1535
% 2.35/1.53 % (3753)Time elapsed: 0.003 s
% 2.35/1.53 % (3753)Instructions burned: 6 (million)
% 2.35/1.53 % (3753)------------------------------
% 2.35/1.53 % (3753)------------------------------
% 2.35/1.54 % (3754)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_3484 for (2996ds/20Mi)
% 2.35/1.54 % (3751)Instruction limit reached!
% 2.35/1.54 % (3751)------------------------------
% 2.35/1.54 % (3751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.54 % (3751)Termination reason: Unknown
% 2.35/1.54 % (3751)Termination phase: Function definition elimination
% 2.35/1.54
% 2.35/1.54 % (3751)Memory used [KB]: 2558
% 2.35/1.54 % (3751)Time elapsed: 0.028 s
% 2.35/1.54 % (3751)Instructions burned: 103 (million)
% 2.35/1.54 % (3751)------------------------------
% 2.35/1.54 % (3751)------------------------------
% 2.35/1.54 % (3754)Instruction limit reached!
% 2.35/1.54 % (3754)------------------------------
% 2.35/1.54 % (3754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.54 % (3754)Termination reason: Unknown
% 2.35/1.54 % (3754)Termination phase: shuffling
% 2.35/1.54
% 2.35/1.54 % (3754)Memory used [KB]: 1791
% 2.35/1.54 % (3754)Time elapsed: 0.008 s
% 2.35/1.54 % (3754)Instructions burned: 21 (million)
% 2.35/1.54 % (3754)------------------------------
% 2.35/1.54 % (3754)------------------------------
% 2.35/1.55 % (3755)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_3484 for (2996ds/86Mi)
% 2.35/1.55 % (3756)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_3484 for (2996ds/107Mi)
% 2.35/1.57 % (3755)Instruction limit reached!
% 2.35/1.57 % (3755)------------------------------
% 2.35/1.57 % (3755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.57 % (3755)Termination reason: Unknown
% 2.35/1.57 % (3755)Termination phase: Property scanning
% 2.35/1.57
% 2.35/1.57 % (3755)Memory used [KB]: 2558
% 2.35/1.57 % (3755)Time elapsed: 0.023 s
% 2.35/1.57 % (3755)Instructions burned: 87 (million)
% 2.35/1.57 % (3755)------------------------------
% 2.35/1.57 % (3755)------------------------------
% 2.35/1.57 % (3722)Instruction limit reached!
% 2.35/1.57 % (3722)------------------------------
% 2.35/1.57 % (3722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.57 % (3722)Termination reason: Unknown
% 2.35/1.57 % (3722)Termination phase: Saturation
% 2.35/1.57
% 2.35/1.57 % (3722)Memory used [KB]: 10490
% 2.35/1.57 % (3722)Time elapsed: 0.286 s
% 2.35/1.57 % (3722)Instructions burned: 711 (million)
% 2.35/1.57 % (3722)------------------------------
% 2.35/1.57 % (3722)------------------------------
% 2.35/1.58 % (3756)Instruction limit reached!
% 2.35/1.58 % (3756)------------------------------
% 2.35/1.58 % (3756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.58 % (3756)Termination reason: Unknown
% 2.35/1.58 % (3756)Termination phase: Property scanning
% 2.35/1.58
% 2.35/1.58 % (3756)Memory used [KB]: 2558
% 2.35/1.58 % (3756)Time elapsed: 0.028 s
% 2.35/1.58 % (3756)Instructions burned: 109 (million)
% 2.35/1.58 % (3756)------------------------------
% 2.35/1.58 % (3756)------------------------------
% 2.35/1.58 % (3757)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_3484 for (2996ds/39Mi)
% 2.35/1.58 % (3758)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_3484 for (2996ds/448Mi)
% 2.35/1.59 % (3760)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_3484 for (2996ds/46Mi)
% 2.35/1.59 % (3757)Instruction limit reached!
% 2.35/1.59 % (3757)------------------------------
% 2.35/1.59 % (3757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.59 % (3757)Termination reason: Unknown
% 2.35/1.59 % (3757)Termination phase: shuffling
% 2.35/1.59
% 2.35/1.59 % (3757)Memory used [KB]: 2302
% 2.35/1.59 % (3757)Time elapsed: 0.012 s
% 2.35/1.59 % (3757)Instructions burned: 39 (million)
% 2.35/1.59 % (3757)------------------------------
% 2.35/1.59 % (3757)------------------------------
% 2.35/1.59 % (3701)Instruction limit reached!
% 2.35/1.59 % (3701)------------------------------
% 2.35/1.59 % (3701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.59 % (3701)Termination reason: Unknown
% 2.35/1.59 % (3701)Termination phase: Saturation
% 2.35/1.59
% 2.35/1.59 % (3701)Memory used [KB]: 14711
% 2.35/1.59 % (3701)Time elapsed: 0.337 s
% 2.35/1.59 % (3701)Instructions burned: 1041 (million)
% 2.35/1.59 % (3701)------------------------------
% 2.35/1.59 % (3701)------------------------------
% 2.35/1.60 % (3768)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_3484 for (2996ds/98Mi)
% 2.35/1.60 % (3760)Instruction limit reached!
% 2.35/1.60 % (3760)------------------------------
% 2.35/1.60 % (3760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.60 % (3760)Termination reason: Unknown
% 2.35/1.60 % (3760)Termination phase: Property scanning
% 2.35/1.60
% 2.35/1.60 % (3760)Memory used [KB]: 2430
% 2.35/1.60 % (3760)Time elapsed: 0.014 s
% 2.35/1.60 % (3760)Instructions burned: 46 (million)
% 2.35/1.60 % (3760)------------------------------
% 2.35/1.60 % (3760)------------------------------
% 2.35/1.60 % (3772)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_3484 for (2996ds/507Mi)
% 2.35/1.60 % (3736)Instruction limit reached!
% 2.35/1.60 % (3736)------------------------------
% 2.35/1.60 % (3736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.60 % (3736)Termination reason: Unknown
% 2.35/1.60 % (3736)Termination phase: Saturation
% 2.35/1.60
% 2.35/1.60 % (3736)Memory used [KB]: 7547
% 2.35/1.60 % (3736)Time elapsed: 0.258 s
% 2.35/1.60 % (3736)Instructions burned: 779 (million)
% 2.35/1.60 % (3736)------------------------------
% 2.35/1.60 % (3736)------------------------------
% 2.35/1.61 % (3779)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_3484 for (2996ds/149Mi)
% 2.35/1.61 % (3783)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_3484 for (2996ds/39Mi)
% 2.35/1.62 % (3768)Instruction limit reached!
% 2.35/1.62 % (3768)------------------------------
% 2.35/1.62 % (3768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.62 % (3768)Termination reason: Unknown
% 2.35/1.62 % (3768)Termination phase: Property scanning
% 2.35/1.62
% 2.35/1.62 % (3768)Memory used [KB]: 2430
% 2.35/1.62 % (3768)Time elapsed: 0.026 s
% 2.35/1.62 % (3768)Instructions burned: 98 (million)
% 2.35/1.62 % (3768)------------------------------
% 2.35/1.62 % (3768)------------------------------
% 2.35/1.63 % (3783)Instruction limit reached!
% 2.35/1.63 % (3783)------------------------------
% 2.35/1.63 % (3783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.63 % (3783)Termination reason: Unknown
% 2.35/1.63 % (3783)Termination phase: shuffling
% 2.35/1.63
% 2.35/1.63 % (3783)Memory used [KB]: 2302
% 2.35/1.63 % (3783)Time elapsed: 0.012 s
% 2.35/1.63 % (3783)Instructions burned: 40 (million)
% 2.35/1.63 % (3783)------------------------------
% 2.35/1.63 % (3783)------------------------------
% 2.35/1.63 % (3801)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_3484 for (2995ds/6Mi)
% 2.35/1.63 % (3803)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_3484 for (2995ds/1087Mi)
% 2.35/1.64 % (3801)Instruction limit reached!
% 2.35/1.64 % (3801)------------------------------
% 2.35/1.64 % (3801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.64 % (3801)Termination reason: Unknown
% 2.35/1.64 % (3801)Termination phase: shuffling
% 2.35/1.64
% 2.35/1.64 % (3801)Memory used [KB]: 1535
% 2.35/1.64 % (3801)Time elapsed: 0.003 s
% 2.35/1.64 % (3801)Instructions burned: 6 (million)
% 2.35/1.64 % (3801)------------------------------
% 2.35/1.64 % (3801)------------------------------
% 2.35/1.65 % (3808)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_3484 for (2995ds/47Mi)
% 2.35/1.65 % (3739)Refutation not found, non-redundant clauses discarded% (3739)------------------------------
% 2.35/1.65 % (3739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.65 % (3739)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.35/1.65
% 2.35/1.65 % (3739)Memory used [KB]: 9722
% 2.35/1.65 % (3739)Time elapsed: 0.291 s
% 2.35/1.65 % (3739)Instructions burned: 869 (million)
% 2.35/1.65 % (3739)------------------------------
% 2.35/1.65 % (3739)------------------------------
% 2.35/1.65 % (3779)Instruction limit reached!
% 2.35/1.65 % (3779)------------------------------
% 2.35/1.65 % (3779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.65 % (3779)Termination reason: Unknown
% 2.35/1.65 % (3779)Termination phase: Property scanning
% 2.35/1.65
% 2.35/1.65 % (3779)Memory used [KB]: 3326
% 2.35/1.65 % (3779)Time elapsed: 0.040 s
% 2.35/1.65 % (3779)Instructions burned: 150 (million)
% 2.35/1.65 % (3779)------------------------------
% 2.35/1.65 % (3779)------------------------------
% 2.35/1.66 % (3808)Instruction limit reached!
% 2.35/1.66 % (3808)------------------------------
% 2.35/1.66 % (3808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.66 % (3808)Termination reason: Unknown
% 2.35/1.66 % (3808)Termination phase: Property scanning
% 2.35/1.66
% 2.35/1.66 % (3808)Memory used [KB]: 2430
% 2.35/1.66 % (3808)Time elapsed: 0.014 s
% 2.35/1.66 % (3808)Instructions burned: 47 (million)
% 2.35/1.66 % (3808)------------------------------
% 2.35/1.66 % (3808)------------------------------
% 2.35/1.66 % (3818)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_3484 for (2995ds/44Mi)
% 2.35/1.66 % (3820)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_3484 for (2995ds/432Mi)
% 2.35/1.67 % (3826)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_3484 for (2995ds/62Mi)
% 2.35/1.67 % (3726)Instruction limit reached!
% 2.35/1.67 % (3726)------------------------------
% 2.35/1.67 % (3726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.67 % (3726)Termination reason: Unknown
% 2.35/1.67 % (3726)Termination phase: Saturation
% 2.35/1.67
% 2.35/1.67 % (3726)Memory used [KB]: 12153
% 2.35/1.67 % (3726)Time elapsed: 0.342 s
% 2.35/1.67 % (3726)Instructions burned: 904 (million)
% 2.35/1.67 % (3726)------------------------------
% 2.35/1.67 % (3726)------------------------------
% 2.35/1.67 % (3818)Instruction limit reached!
% 2.35/1.67 % (3818)------------------------------
% 2.35/1.67 % (3818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.67 % (3818)Termination reason: Unknown
% 2.35/1.67 % (3818)Termination phase: Property scanning
% 2.35/1.67
% 2.35/1.67 % (3818)Memory used [KB]: 2302
% 2.35/1.67 % (3818)Time elapsed: 0.014 s
% 2.35/1.67 % (3818)Instructions burned: 47 (million)
% 2.35/1.67 % (3818)------------------------------
% 2.35/1.67 % (3818)------------------------------
% 2.35/1.68 % (3836)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_3484 for (2995ds/31Mi)
% 2.35/1.68 % (3837)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_3484 for (2995ds/96Mi)
% 2.35/1.68 % (3826)Instruction limit reached!
% 2.35/1.68 % (3826)------------------------------
% 2.35/1.68 % (3826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.68 % (3826)Termination reason: Unknown
% 2.35/1.68 % (3826)Termination phase: Property scanning
% 2.35/1.68
% 2.35/1.68 % (3826)Memory used [KB]: 2430
% 2.35/1.68 % (3826)Time elapsed: 0.018 s
% 2.35/1.68 % (3826)Instructions burned: 64 (million)
% 2.35/1.68 % (3826)------------------------------
% 2.35/1.68 % (3826)------------------------------
% 2.35/1.69 % (3836)Instruction limit reached!
% 2.35/1.69 % (3836)------------------------------
% 2.35/1.69 % (3836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.69 % (3836)Termination reason: Unknown
% 2.35/1.69 % (3836)Termination phase: shuffling
% 2.35/1.69
% 2.35/1.69 % (3836)Memory used [KB]: 2046
% 2.35/1.69 % (3836)Time elapsed: 0.010 s
% 2.35/1.69 % (3836)Instructions burned: 33 (million)
% 2.35/1.69 % (3836)------------------------------
% 2.35/1.69 % (3836)------------------------------
% 2.35/1.69 % (3850)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_3484 for (2995ds/453Mi)
% 2.35/1.70 % (3853)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_3484 for (2995ds/71Mi)
% 2.35/1.70 % (3758)Instruction limit reached!
% 2.35/1.70 % (3758)------------------------------
% 2.35/1.70 % (3758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.70 % (3758)Termination reason: Unknown
% 2.35/1.70 % (3758)Termination phase: Saturation
% 2.35/1.70
% 2.35/1.70 % (3758)Memory used [KB]: 7419
% 2.35/1.70 % (3758)Time elapsed: 0.114 s
% 2.35/1.70 % (3758)Instructions burned: 451 (million)
% 2.35/1.70 % (3758)------------------------------
% 2.35/1.70 % (3758)------------------------------
% 2.35/1.71 % (3837)Instruction limit reached!
% 2.35/1.71 % (3837)------------------------------
% 2.35/1.71 % (3837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.71 % (3837)Termination reason: Unknown
% 2.35/1.71 % (3837)Termination phase: Property scanning
% 2.35/1.71
% 2.35/1.71 % (3837)Memory used [KB]: 2558
% 2.35/1.71 % (3837)Time elapsed: 0.026 s
% 2.35/1.71 % (3837)Instructions burned: 97 (million)
% 2.35/1.71 % (3837)------------------------------
% 2.35/1.71 % (3837)------------------------------
% 2.35/1.71 % (3860)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_3484 for (2995ds/83Mi)
% 2.35/1.72 % (3874)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_3484 for (2995ds/11Mi)
% 2.35/1.72 % (3853)Instruction limit reached!
% 2.35/1.72 % (3853)------------------------------
% 2.35/1.72 % (3853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.72 % (3853)Termination reason: Unknown
% 2.35/1.72 % (3853)Termination phase: Property scanning
% 2.35/1.72
% 2.35/1.72 % (3853)Memory used [KB]: 2558
% 2.35/1.72 % (3853)Time elapsed: 0.021 s
% 2.35/1.72 % (3853)Instructions burned: 74 (million)
% 2.35/1.72 % (3853)------------------------------
% 2.35/1.72 % (3853)------------------------------
% 2.35/1.72 % (3874)Instruction limit reached!
% 2.35/1.72 % (3874)------------------------------
% 2.35/1.72 % (3874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.72 % (3874)Termination reason: Unknown
% 2.35/1.72 % (3874)Termination phase: shuffling
% 2.35/1.72
% 2.35/1.72 % (3874)Memory used [KB]: 1663
% 2.35/1.72 % (3874)Time elapsed: 0.005 s
% 2.35/1.72 % (3874)Instructions burned: 13 (million)
% 2.35/1.72 % (3874)------------------------------
% 2.35/1.72 % (3874)------------------------------
% 2.35/1.73 % (3886)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_3484 for (2995ds/41Mi)
% 2.35/1.73 % (3860)Instruction limit reached!
% 2.35/1.73 % (3860)------------------------------
% 2.35/1.73 % (3860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.73 % (3860)Termination reason: Unknown
% 2.35/1.73 % (3860)Termination phase: SInE selection
% 2.35/1.73
% 2.35/1.73 % (3860)Memory used [KB]: 2430
% 2.35/1.73 % (3860)Time elapsed: 0.023 s
% 2.35/1.73 % (3860)Instructions burned: 84 (million)
% 2.35/1.73 % (3860)------------------------------
% 2.35/1.73 % (3860)------------------------------
% 2.35/1.73 % (3887)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3484 for (2995ds/6Mi)
% 2.35/1.73 % (3887)Instruction limit reached!
% 2.35/1.73 % (3887)------------------------------
% 2.35/1.73 % (3887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.73 % (3887)Termination reason: Unknown
% 2.35/1.73 % (3887)Termination phase: shuffling
% 2.35/1.73
% 2.35/1.73 % (3887)Memory used [KB]: 1535
% 2.35/1.73 % (3887)Time elapsed: 0.003 s
% 2.35/1.73 % (3887)Instructions burned: 7 (million)
% 2.35/1.73 % (3887)------------------------------
% 2.35/1.73 % (3887)------------------------------
% 2.35/1.74 % (3886)Instruction limit reached!
% 2.35/1.74 % (3886)------------------------------
% 2.35/1.74 % (3886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.74 % (3886)Termination reason: Unknown
% 2.35/1.74 % (3886)Termination phase: shuffling
% 2.35/1.74
% 2.35/1.74 % (3886)Memory used [KB]: 2302
% 2.35/1.74 % (3886)Time elapsed: 0.012 s
% 2.35/1.74 % (3886)Instructions burned: 42 (million)
% 2.35/1.74 % (3886)------------------------------
% 2.35/1.74 % (3886)------------------------------
% 2.35/1.74 % (3899)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_3484 for (2994ds/150Mi)
% 2.35/1.74 % (3903)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_3484 for (2994ds/343Mi)
% 2.35/1.75 % (3906)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_3484 for (2994ds/109Mi)
% 2.35/1.75 % (3772)Instruction limit reached!
% 2.35/1.75 % (3772)------------------------------
% 2.35/1.75 % (3772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.75 % (3772)Termination reason: Unknown
% 2.35/1.75 % (3772)Termination phase: Saturation
% 2.35/1.75
% 2.35/1.75 % (3772)Memory used [KB]: 8059
% 2.35/1.75 % (3772)Time elapsed: 0.148 s
% 2.35/1.75 % (3772)Instructions burned: 507 (million)
% 2.35/1.75 % (3772)------------------------------
% 2.35/1.75 % (3772)------------------------------
% 2.35/1.76 % (3920)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_3484 for (2994ds/253Mi)
% 2.35/1.77 % (3820)Instruction limit reached!
% 2.35/1.77 % (3820)------------------------------
% 2.35/1.77 % (3820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.77 % (3820)Termination reason: Unknown
% 2.35/1.77 % (3820)Termination phase: Saturation
% 2.35/1.77
% 2.35/1.77 % (3820)Memory used [KB]: 2942
% 2.35/1.77 % (3820)Time elapsed: 0.111 s
% 2.35/1.77 % (3820)Instructions burned: 435 (million)
% 2.35/1.77 % (3820)------------------------------
% 2.35/1.77 % (3820)------------------------------
% 2.35/1.77 % (3906)Instruction limit reached!
% 2.35/1.77 % (3906)------------------------------
% 2.35/1.77 % (3906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.77 % (3906)Termination reason: Unknown
% 2.35/1.77 % (3906)Termination phase: Property scanning
% 2.35/1.77
% 2.35/1.77 % (3906)Memory used [KB]: 2558
% 2.35/1.77 % (3906)Time elapsed: 0.029 s
% 2.35/1.77 % (3906)Instructions burned: 111 (million)
% 2.35/1.77 % (3906)------------------------------
% 2.35/1.77 % (3906)------------------------------
% 2.35/1.78 % (3930)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_3484 for (2994ds/140Mi)
% 2.35/1.78 % (3899)Instruction limit reached!
% 2.35/1.78 % (3899)------------------------------
% 2.35/1.78 % (3899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.78 % (3899)Termination reason: Unknown
% 2.35/1.78 % (3899)Termination phase: Property scanning
% 2.35/1.78
% 2.35/1.78 % (3899)Memory used [KB]: 4477
% 2.35/1.78 % (3899)Time elapsed: 0.045 s
% 2.35/1.78 % (3899)Instructions burned: 152 (million)
% 2.35/1.78 % (3899)------------------------------
% 2.35/1.78 % (3899)------------------------------
% 2.35/1.78 % (3932)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_3484 for (2994ds/614Mi)
% 2.35/1.79 % (3938)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_3484 for (2994ds/202Mi)
% 2.35/1.81 % (3850)Instruction limit reached!
% 2.35/1.81 % (3850)------------------------------
% 2.35/1.81 % (3850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.81 % (3850)Termination reason: Unknown
% 2.35/1.81 % (3850)Termination phase: Saturation
% 2.35/1.81
% 2.35/1.81 % (3850)Memory used [KB]: 7419
% 2.35/1.81 % (3850)Time elapsed: 0.115 s
% 2.35/1.81 % (3850)Instructions burned: 455 (million)
% 2.35/1.81 % (3850)------------------------------
% 2.35/1.81 % (3850)------------------------------
% 2.35/1.81 % (3930)Instruction limit reached!
% 2.35/1.81 % (3930)------------------------------
% 2.35/1.81 % (3930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.81 % (3930)Termination reason: Unknown
% 2.35/1.81 % (3930)Termination phase: Property scanning
% 2.35/1.81
% 2.35/1.81 % (3930)Memory used [KB]: 2558
% 2.35/1.81 % (3930)Time elapsed: 0.037 s
% 2.35/1.81 % (3930)Instructions burned: 140 (million)
% 2.35/1.81 % (3930)------------------------------
% 2.35/1.81 % (3930)------------------------------
% 2.35/1.82 % (3952)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_3484 for (2994ds/339Mi)
% 2.35/1.82 % (3956)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_3484 for (2993ds/283Mi)
% 2.35/1.83 % (3903)Instruction limit reached!
% 2.35/1.83 % (3903)------------------------------
% 2.35/1.83 % (3903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.83 % (3903)Termination reason: Unknown
% 2.35/1.83 % (3903)Termination phase: Saturation
% 2.35/1.83
% 2.35/1.83 % (3903)Memory used [KB]: 8571
% 2.35/1.83 % (3903)Time elapsed: 0.093 s
% 2.35/1.83 % (3903)Instructions burned: 345 (million)
% 2.35/1.83 % (3903)------------------------------
% 2.35/1.83 % (3903)------------------------------
% 2.35/1.84 % (3920)Instruction limit reached!
% 2.35/1.84 % (3920)------------------------------
% 2.35/1.84 % (3920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.84 % (3920)Termination reason: Unknown
% 2.35/1.84 % (3920)Termination phase: Saturation
% 2.35/1.84
% 2.35/1.84 % (3920)Memory used [KB]: 9594
% 2.35/1.84 % (3920)Time elapsed: 0.076 s
% 2.35/1.84 % (3920)Instructions burned: 255 (million)
% 2.35/1.84 % (3920)------------------------------
% 2.35/1.84 % (3920)------------------------------
% 2.35/1.84 % (3964)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_3484 for (2993ds/134Mi)
% 2.35/1.85 % (3967)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_3484 for (2993ds/298Mi)
% 2.35/1.85 % (3938)Instruction limit reached!
% 2.35/1.85 % (3938)------------------------------
% 2.35/1.85 % (3938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.85 % (3938)Termination reason: Unknown
% 2.35/1.85 % (3938)Termination phase: Saturation
% 2.35/1.85
% 2.35/1.85 % (3938)Memory used [KB]: 4605
% 2.35/1.85 % (3938)Time elapsed: 0.057 s
% 2.35/1.85 % (3938)Instructions burned: 202 (million)
% 2.35/1.85 % (3938)------------------------------
% 2.35/1.85 % (3938)------------------------------
% 2.35/1.86 % (3977)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_3484 for (2993ds/192Mi)
% 2.35/1.88 % (3964)Instruction limit reached!
% 2.35/1.88 % (3964)------------------------------
% 2.35/1.88 % (3964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.88 % (3964)Termination reason: Unknown
% 2.35/1.88 % (3964)Termination phase: Property scanning
% 2.35/1.88
% 2.35/1.88 % (3964)Memory used [KB]: 2558
% 2.35/1.88 % (3964)Time elapsed: 0.036 s
% 2.35/1.88 % (3964)Instructions burned: 134 (million)
% 2.35/1.88 % (3964)------------------------------
% 2.35/1.88 % (3964)------------------------------
% 2.35/1.89 % (3995)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_3484 for (2993ds/258Mi)
% 2.35/1.90 % (3956)Instruction limit reached!
% 2.35/1.90 % (3956)------------------------------
% 2.35/1.90 % (3956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.90 % (3956)Termination reason: Unknown
% 2.35/1.90 % (3956)Termination phase: Saturation
% 2.35/1.90
% 2.35/1.90 % (3956)Memory used [KB]: 7419
% 2.35/1.90 % (3956)Time elapsed: 0.073 s
% 2.35/1.90 % (3956)Instructions burned: 284 (million)
% 2.35/1.90 % (3956)------------------------------
% 2.35/1.90 % (3956)------------------------------
% 2.35/1.91 % (4016)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_3484 for (2993ds/90Mi)
% 2.35/1.91 % (3977)Instruction limit reached!
% 2.35/1.91 % (3977)------------------------------
% 2.35/1.91 % (3977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.91 % (3977)Termination reason: Unknown
% 2.35/1.91 % (3977)Termination phase: Saturation
% 2.35/1.91
% 2.35/1.91 % (3977)Memory used [KB]: 7675
% 2.35/1.91 % (3977)Time elapsed: 0.053 s
% 2.35/1.91 % (3977)Instructions burned: 194 (million)
% 2.35/1.91 % (3977)------------------------------
% 2.35/1.91 % (3977)------------------------------
% 2.35/1.91 % (3952)Instruction limit reached!
% 2.35/1.91 % (3952)------------------------------
% 2.35/1.91 % (3952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.91 % (3952)Termination reason: Unknown
% 2.35/1.91 % (3952)Termination phase: Saturation
% 2.35/1.91
% 2.35/1.91 % (3952)Memory used [KB]: 7803
% 2.35/1.91 % (3952)Time elapsed: 0.096 s
% 2.35/1.91 % (3952)Instructions burned: 341 (million)
% 2.35/1.91 % (3952)------------------------------
% 2.35/1.91 % (3952)------------------------------
% 2.35/1.92 % (4024)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_3484 for (2993ds/231Mi)
% 2.35/1.92 % (3967)Instruction limit reached!
% 2.35/1.92 % (3967)------------------------------
% 2.35/1.92 % (3967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.92 % (3967)Termination reason: Unknown
% 2.35/1.92 % (3967)Termination phase: Saturation
% 2.35/1.92
% 2.35/1.92 % (3967)Memory used [KB]: 7419
% 2.35/1.92 % (3967)Time elapsed: 0.078 s
% 2.35/1.92 % (3967)Instructions burned: 301 (million)
% 2.35/1.92 % (3967)------------------------------
% 2.35/1.92 % (3967)------------------------------
% 2.35/1.92 % (4025)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_3484 for (2993ds/458Mi)
% 2.35/1.93 % (4016)Instruction limit reached!
% 2.35/1.93 % (4016)------------------------------
% 2.35/1.93 % (4016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.93 % (4016)Termination reason: Unknown
% 2.35/1.93 % (4016)Termination phase: Property scanning
% 2.35/1.93
% 2.35/1.93 % (4016)Memory used [KB]: 2558
% 2.35/1.93 % (4016)Time elapsed: 0.025 s
% 2.35/1.93 % (4016)Instructions burned: 92 (million)
% 2.35/1.93 % (4016)------------------------------
% 2.35/1.93 % (4016)------------------------------
% 2.35/1.93 % (4026)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_3484 for (2992ds/31Mi)
% 2.35/1.94 % (4027)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_3484 for (2992ds/297Mi)
% 2.35/1.94 % (4026)Instruction limit reached!
% 2.35/1.94 % (4026)------------------------------
% 2.35/1.94 % (4026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.94 % (4026)Termination reason: Unknown
% 2.35/1.94 % (4026)Termination phase: shuffling
% 2.35/1.94
% 2.35/1.94 % (4026)Memory used [KB]: 2046
% 2.35/1.94 % (4026)Time elapsed: 0.010 s
% 2.35/1.94 % (4026)Instructions burned: 31 (million)
% 2.35/1.94 % (4026)------------------------------
% 2.35/1.94 % (4026)------------------------------
% 2.35/1.95 % (4028)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_3484 for (2992ds/987Mi)
% 2.35/1.95 % (3995)Instruction limit reached!
% 2.35/1.95 % (3995)------------------------------
% 2.35/1.95 % (3995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.95 % (3995)Termination reason: Unknown
% 2.35/1.95 % (3995)Termination phase: Saturation
% 2.35/1.95
% 2.35/1.95 % (3995)Memory used [KB]: 7931
% 2.35/1.95 % (3995)Time elapsed: 0.069 s
% 2.35/1.95 % (3995)Instructions burned: 259 (million)
% 2.35/1.95 % (3995)------------------------------
% 2.35/1.95 % (3995)------------------------------
% 2.35/1.96 % (4029)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_3484 for (2992ds/182Mi)
% 2.35/1.96 % (3932)Instruction limit reached!
% 2.35/1.96 % (3932)------------------------------
% 2.35/1.96 % (3932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.96 % (3932)Termination reason: Unknown
% 2.35/1.96 % (3932)Termination phase: Saturation
% 2.35/1.96
% 2.35/1.96 % (3932)Memory used [KB]: 9722
% 2.35/1.96 % (3932)Time elapsed: 0.182 s
% 2.35/1.96 % (3932)Instructions burned: 616 (million)
% 2.35/1.96 % (3932)------------------------------
% 2.35/1.96 % (3932)------------------------------
% 2.35/1.97 % (4030)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_3484 for (2992ds/182Mi)
% 2.35/1.98 % (3803)Instruction limit reached!
% 2.35/1.98 % (3803)------------------------------
% 2.35/1.98 % (3803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.98 % (3803)Termination reason: Unknown
% 2.35/1.98 % (3803)Termination phase: Saturation
% 2.35/1.98
% 2.35/1.98 % (3803)Memory used [KB]: 11513
% 2.35/1.98 % (3803)Time elapsed: 0.345 s
% 2.35/1.98 % (3803)Instructions burned: 1087 (million)
% 2.35/1.98 % (3803)------------------------------
% 2.35/1.98 % (3803)------------------------------
% 2.35/1.98 % (4024)Instruction limit reached!
% 2.35/1.98 % (4024)------------------------------
% 2.35/1.98 % (4024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/1.98 % (4024)Termination reason: Unknown
% 2.35/1.98 % (4024)Termination phase: Saturation
% 2.35/1.98
% 2.35/1.98 % (4024)Memory used [KB]: 8699
% 2.35/1.98 % (4024)Time elapsed: 0.061 s
% 2.35/1.98 % (4024)Instructions burned: 231 (million)
% 2.35/1.98 % (4024)------------------------------
% 2.35/1.98 % (4024)------------------------------
% 2.35/1.99 % (4031)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_3484 for (2992ds/154Mi)
% 2.35/1.99 % (4032)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_3484 for (2992ds/79Mi)
% 2.35/2.01 % (4032)Instruction limit reached!
% 2.35/2.01 % (4032)------------------------------
% 2.35/2.01 % (4032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/2.01 % (4032)Termination reason: Unknown
% 2.35/2.01 % (4032)Termination phase: Property scanning
% 2.35/2.01
% 2.35/2.01 % (4032)Memory used [KB]: 2558
% 2.35/2.01 % (4032)Time elapsed: 0.022 s
% 2.35/2.01 % (4032)Instructions burned: 82 (million)
% 2.35/2.01 % (4032)------------------------------
% 2.35/2.01 % (4032)------------------------------
% 2.35/2.01 % (4029)Instruction limit reached!
% 2.35/2.01 % (4029)------------------------------
% 2.35/2.01 % (4029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/2.01 % (4029)Termination reason: Unknown
% 2.35/2.01 % (4029)Termination phase: Saturation
% 2.35/2.01
% 2.35/2.01 % (4029)Memory used [KB]: 7675
% 2.35/2.01 % (4029)Time elapsed: 0.048 s
% 2.35/2.01 % (4029)Instructions burned: 184 (million)
% 2.35/2.01 % (4029)------------------------------
% 2.35/2.01 % (4029)------------------------------
% 2.35/2.01 % (4027)Instruction limit reached!
% 2.35/2.01 % (4027)------------------------------
% 2.35/2.01 % (4027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.35/2.01 % (4027)Termination reason: Unknown
% 2.35/2.01 % (4027)Termination phase: Saturation
% 2.35/2.01
% 2.35/2.01 % (4027)Memory used [KB]: 7419
% 2.35/2.01 % (4027)Time elapsed: 0.073 s
% 2.35/2.01 % (4027)Instructions burned: 297 (million)
% 2.35/2.01 % (4027)------------------------------
% 2.35/2.01 % (4027)------------------------------
% 7.73/2.02 % (4033)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_3484 for (2992ds/216Mi)
% 7.73/2.02 % (4034)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_3484 for (2992ds/114Mi)
% 7.73/2.02 % (4035)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_3484 for (2992ds/922Mi)
% 7.73/2.02 % (4030)Instruction limit reached!
% 7.73/2.02 % (4030)------------------------------
% 7.73/2.02 % (4030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.02 % (4030)Termination reason: Unknown
% 7.73/2.02 % (4030)Termination phase: Saturation
% 7.73/2.02
% 7.73/2.02 % (4030)Memory used [KB]: 8699
% 7.73/2.02 % (4030)Time elapsed: 0.050 s
% 7.73/2.02 % (4030)Instructions burned: 183 (million)
% 7.73/2.02 % (4030)------------------------------
% 7.73/2.02 % (4030)------------------------------
% 7.73/2.03 % (4031)Instruction limit reached!
% 7.73/2.03 % (4031)------------------------------
% 7.73/2.03 % (4031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.03 % (4031)Termination reason: Unknown
% 7.73/2.03 % (4031)Termination phase: Saturation
% 7.73/2.03
% 7.73/2.03 % (4031)Memory used [KB]: 7164
% 7.73/2.03 % (4031)Time elapsed: 0.039 s
% 7.73/2.03 % (4031)Instructions burned: 155 (million)
% 7.73/2.03 % (4031)------------------------------
% 7.73/2.03 % (4031)------------------------------
% 7.73/2.03 % (4036)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_3484 for (2991ds/182Mi)
% 7.73/2.04 % (4037)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_3484 for (2991ds/164Mi)
% 7.73/2.05 % (4025)Instruction limit reached!
% 7.73/2.05 % (4025)------------------------------
% 7.73/2.05 % (4025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.05 % (4025)Termination reason: Unknown
% 7.73/2.05 % (4025)Termination phase: Saturation
% 7.73/2.05
% 7.73/2.05 % (4025)Memory used [KB]: 9466
% 7.73/2.05 % (4025)Time elapsed: 0.128 s
% 7.73/2.05 % (4025)Instructions burned: 460 (million)
% 7.73/2.05 % (4025)------------------------------
% 7.73/2.05 % (4025)------------------------------
% 7.73/2.05 % (4034)Instruction limit reached!
% 7.73/2.05 % (4034)------------------------------
% 7.73/2.05 % (4034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.05 % (4034)Termination reason: Unknown
% 7.73/2.05 % (4034)Termination phase: Property scanning
% 7.73/2.05
% 7.73/2.05 % (4034)Memory used [KB]: 2686
% 7.73/2.05 % (4034)Time elapsed: 0.030 s
% 7.73/2.05 % (4034)Instructions burned: 114 (million)
% 7.73/2.05 % (4034)------------------------------
% 7.73/2.05 % (4034)------------------------------
% 7.73/2.06 % (4038)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_3484 for (2991ds/50Mi)
% 7.73/2.06 % (4039)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_3484 for (2991ds/368Mi)
% 7.73/2.07 % (4038)Instruction limit reached!
% 7.73/2.07 % (4038)------------------------------
% 7.73/2.07 % (4038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.07 % (4038)Termination reason: Unknown
% 7.73/2.07 % (4038)Termination phase: Property scanning
% 7.73/2.07
% 7.73/2.07 % (4038)Memory used [KB]: 2430
% 7.73/2.07 % (4038)Time elapsed: 0.014 s
% 7.73/2.07 % (4038)Instructions burned: 50 (million)
% 7.73/2.07 % (4038)------------------------------
% 7.73/2.07 % (4038)------------------------------
% 7.73/2.07 % (4033)Instruction limit reached!
% 7.73/2.07 % (4033)------------------------------
% 7.73/2.07 % (4033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.07 % (4033)Termination reason: Unknown
% 7.73/2.07 % (4033)Termination phase: Saturation
% 7.73/2.07
% 7.73/2.07 % (4033)Memory used [KB]: 7419
% 7.73/2.07 % (4033)Time elapsed: 0.054 s
% 7.73/2.07 % (4033)Instructions burned: 218 (million)
% 7.73/2.07 % (4033)------------------------------
% 7.73/2.07 % (4033)------------------------------
% 7.73/2.08 % (4037)Instruction limit reached!
% 7.73/2.08 % (4037)------------------------------
% 7.73/2.08 % (4037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.08 % (4037)Termination reason: Unknown
% 7.73/2.08 % (4037)Termination phase: Saturation
% 7.73/2.08
% 7.73/2.08 % (4037)Memory used [KB]: 2558
% 7.73/2.08 % (4037)Time elapsed: 0.041 s
% 7.73/2.08 % (4037)Instructions burned: 164 (million)
% 7.73/2.08 % (4037)------------------------------
% 7.73/2.08 % (4037)------------------------------
% 7.73/2.08 % (4036)Instruction limit reached!
% 7.73/2.08 % (4036)------------------------------
% 7.73/2.08 % (4036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.08 % (4036)Termination reason: Unknown
% 7.73/2.08 % (4036)Termination phase: Saturation
% 7.73/2.08
% 7.73/2.08 % (4036)Memory used [KB]: 7419
% 7.73/2.08 % (4036)Time elapsed: 0.046 s
% 7.73/2.08 % (4036)Instructions burned: 183 (million)
% 7.73/2.08 % (4036)------------------------------
% 7.73/2.08 % (4036)------------------------------
% 7.73/2.08 % (4040)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_3484 for (2991ds/1021Mi)
% 7.73/2.08 % (4041)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_3484 for (2991ds/267Mi)
% 7.73/2.09 % (4042)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_3484 for (2991ds/204Mi)
% 7.73/2.09 % (4043)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_3484 for (2991ds/26Mi)
% 7.73/2.09 % (4043)Instruction limit reached!
% 7.73/2.09 % (4043)------------------------------
% 7.73/2.09 % (4043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.09 % (4043)Termination reason: Unknown
% 7.73/2.09 % (4043)Termination phase: shuffling
% 7.73/2.09
% 7.73/2.09 % (4043)Memory used [KB]: 1918
% 7.73/2.09 % (4043)Time elapsed: 0.008 s
% 7.73/2.09 % (4043)Instructions burned: 27 (million)
% 7.73/2.09 % (4043)------------------------------
% 7.73/2.09 % (4043)------------------------------
% 7.73/2.10 % (4044)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_3484 for (2991ds/53Mi)
% 8.19/2.12 % (4044)Instruction limit reached!
% 8.19/2.12 % (4044)------------------------------
% 8.19/2.12 % (4044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.19/2.12 % (4044)Termination reason: Unknown
% 8.19/2.12 % (4044)Termination phase: Property scanning
% 8.19/2.12
% 8.19/2.12 % (4044)Memory used [KB]: 2430
% 8.19/2.12 % (4044)Time elapsed: 0.015 s
% 8.19/2.12 % (4044)Instructions burned: 54 (million)
% 8.19/2.12 % (4044)------------------------------
% 8.19/2.12 % (4044)------------------------------
% 8.19/2.13 % (4045)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_3484 for (2990ds/4436Mi)
% 8.19/2.14 % (4042)Instruction limit reached!
% 8.19/2.14 % (4042)------------------------------
% 8.19/2.14 % (4042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.19/2.14 % (4042)Termination reason: Unknown
% 8.19/2.14 % (4042)Termination phase: Saturation
% 8.19/2.14
% 8.19/2.14 % (4042)Memory used [KB]: 7419
% 8.19/2.14 % (4042)Time elapsed: 0.052 s
% 8.19/2.14 % (4042)Instructions burned: 206 (million)
% 8.19/2.14 % (4042)------------------------------
% 8.19/2.14 % (4042)------------------------------
% 8.19/2.15 % (4046)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_3484 for (2990ds/1539Mi)
% 8.19/2.15 % (4041)Instruction limit reached!
% 8.19/2.15 % (4041)------------------------------
% 8.19/2.15 % (4041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.19/2.15 % (4041)Termination reason: Unknown
% 8.19/2.15 % (4041)Termination phase: Saturation
% 8.19/2.15
% 8.19/2.15 % (4041)Memory used [KB]: 7419
% 8.19/2.15 % (4041)Time elapsed: 0.067 s
% 8.19/2.15 % (4041)Instructions burned: 269 (million)
% 8.19/2.15 % (4041)------------------------------
% 8.19/2.15 % (4041)------------------------------
% 8.19/2.16 % (4047)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_3484 for (2990ds/408Mi)
% 8.19/2.16 % (4039)Instruction limit reached!
% 8.19/2.16 % (4039)------------------------------
% 8.19/2.16 % (4039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.19/2.16 % (4039)Termination reason: Unknown
% 8.19/2.16 % (4039)Termination phase: Saturation
% 8.19/2.16
% 8.19/2.16 % (4039)Memory used [KB]: 8827
% 8.19/2.16 % (4039)Time elapsed: 0.102 s
% 8.19/2.16 % (4039)Instructions burned: 368 (million)
% 8.19/2.16 % (4039)------------------------------
% 8.19/2.16 % (4039)------------------------------
% 8.19/2.17 % (4048)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_3484 for (2990ds/5205Mi)
% 8.55/2.20 % (4028)Instruction limit reached!
% 8.55/2.20 % (4028)------------------------------
% 8.55/2.20 % (4028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.55/2.20 % (4028)Termination reason: Unknown
% 8.55/2.20 % (4028)Termination phase: Saturation
% 8.55/2.20
% 8.55/2.20 % (4028)Memory used [KB]: 14711
% 8.55/2.20 % (4028)Time elapsed: 0.252 s
% 8.55/2.20 % (4028)Instructions burned: 990 (million)
% 8.55/2.20 % (4028)------------------------------
% 8.55/2.20 % (4028)------------------------------
% 8.55/2.21 % (4049)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_3484 for (2990ds/1913Mi)
% 8.55/2.28 % (4047)Instruction limit reached!
% 8.55/2.28 % (4047)------------------------------
% 8.55/2.28 % (4047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.55/2.28 % (4047)Termination reason: Unknown
% 8.55/2.28 % (4047)Termination phase: Saturation
% 8.55/2.28
% 8.55/2.28 % (4047)Memory used [KB]: 10746
% 8.55/2.28 % (4047)Time elapsed: 0.125 s
% 8.55/2.28 % (4047)Instructions burned: 409 (million)
% 8.55/2.28 % (4047)------------------------------
% 8.55/2.28 % (4047)------------------------------
% 8.55/2.29 % (4050)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_3484 for (2989ds/4350Mi)
% 8.70/2.30 % (4035)Instruction limit reached!
% 8.70/2.30 % (4035)------------------------------
% 8.70/2.30 % (4035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/2.30 % (4035)Termination reason: Unknown
% 8.70/2.30 % (4035)Termination phase: Saturation
% 8.70/2.30
% 8.70/2.30 % (4035)Memory used [KB]: 10874
% 8.70/2.30 % (4035)Time elapsed: 0.283 s
% 8.70/2.30 % (4035)Instructions burned: 922 (million)
% 8.70/2.30 % (4035)------------------------------
% 8.70/2.30 % (4035)------------------------------
% 8.70/2.31 % (4051)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_3484 for (2989ds/68Mi)
% 8.70/2.33 % (4051)Instruction limit reached!
% 8.70/2.33 % (4051)------------------------------
% 8.70/2.33 % (4051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/2.33 % (4051)Termination reason: Unknown
% 8.70/2.33 % (4051)Termination phase: Property scanning
% 8.70/2.33
% 8.70/2.33 % (4051)Memory used [KB]: 2430
% 8.70/2.33 % (4051)Time elapsed: 0.019 s
% 8.70/2.33 % (4051)Instructions burned: 68 (million)
% 8.70/2.33 % (4051)------------------------------
% 8.70/2.33 % (4051)------------------------------
% 8.70/2.34 % (4052)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_3484 for (2988ds/358Mi)
% 9.02/2.40 % (4040)Instruction limit reached!
% 9.02/2.40 % (4040)------------------------------
% 9.02/2.40 % (4040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.02/2.40 % (4040)Termination reason: Unknown
% 9.02/2.40 % (4040)Termination phase: Saturation
% 9.02/2.40
% 9.02/2.40 % (4040)Memory used [KB]: 12153
% 9.02/2.40 % (4040)Time elapsed: 0.316 s
% 9.02/2.40 % (4040)Instructions burned: 1021 (million)
% 9.02/2.40 % (4040)------------------------------
% 9.02/2.40 % (4040)------------------------------
% 9.02/2.41 % (4053)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_3484 for (2988ds/31Mi)
% 9.02/2.42 % (4053)Instruction limit reached!
% 9.02/2.42 % (4053)------------------------------
% 9.02/2.42 % (4053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.02/2.42 % (4053)Termination reason: Unknown
% 9.02/2.42 % (4053)Termination phase: shuffling
% 9.02/2.42
% 9.02/2.42 % (4053)Memory used [KB]: 2046
% 9.02/2.42 % (4053)Time elapsed: 0.010 s
% 9.02/2.42 % (4053)Instructions burned: 33 (million)
% 9.02/2.42 % (4053)------------------------------
% 9.02/2.42 % (4053)------------------------------
% 9.02/2.42 % (4054)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_3484 for (2988ds/279Mi)
% 9.02/2.43 % (4052)Instruction limit reached!
% 9.02/2.43 % (4052)------------------------------
% 9.02/2.43 % (4052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.02/2.43 % (4052)Termination reason: Unknown
% 9.02/2.43 % (4052)Termination phase: Saturation
% 9.02/2.43
% 9.02/2.43 % (4052)Memory used [KB]: 8571
% 9.02/2.43 % (4052)Time elapsed: 0.095 s
% 9.02/2.43 % (4052)Instructions burned: 361 (million)
% 9.02/2.43 % (4052)------------------------------
% 9.02/2.43 % (4052)------------------------------
% 9.02/2.44 % (4055)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_3484 for (2987ds/258Mi)
% 9.02/2.49 % (4054)Instruction limit reached!
% 9.02/2.49 % (4054)------------------------------
% 9.02/2.49 % (4054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.02/2.49 % (4054)Termination reason: Unknown
% 9.02/2.49 % (4054)Termination phase: Saturation
% 9.02/2.49
% 9.02/2.49 % (4054)Memory used [KB]: 7419
% 9.02/2.49 % (4054)Time elapsed: 0.070 s
% 9.02/2.49 % (4054)Instructions burned: 282 (million)
% 9.02/2.49 % (4054)------------------------------
% 9.02/2.49 % (4054)------------------------------
% 9.54/2.50 % (4056)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_3484 for (2987ds/26Mi)
% 9.54/2.51 % (4056)Instruction limit reached!
% 9.54/2.51 % (4056)------------------------------
% 9.54/2.51 % (4056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.54/2.51 % (4056)Termination reason: Unknown
% 9.54/2.51 % (4056)Termination phase: shuffling
% 9.54/2.51
% 9.54/2.51 % (4056)Memory used [KB]: 1918
% 9.54/2.51 % (4056)Time elapsed: 0.008 s
% 9.54/2.51 % (4056)Instructions burned: 27 (million)
% 9.54/2.51 % (4056)------------------------------
% 9.54/2.51 % (4056)------------------------------
% 9.54/2.51 % (4055)Instruction limit reached!
% 9.54/2.51 % (4055)------------------------------
% 9.54/2.51 % (4055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.54/2.51 % (4055)Termination reason: Unknown
% 9.54/2.51 % (4055)Termination phase: Saturation
% 9.54/2.51
% 9.54/2.51 % (4055)Memory used [KB]: 8443
% 9.54/2.51 % (4055)Time elapsed: 0.068 s
% 9.54/2.51 % (4055)Instructions burned: 258 (million)
% 9.54/2.51 % (4055)------------------------------
% 9.54/2.51 % (4055)------------------------------
% 9.54/2.52 % (4057)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_3484 for (2987ds/995Mi)
% 9.54/2.52 % (4058)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_3484 for (2987ds/373Mi)
% 9.63/2.61 % (4046)Instruction limit reached!
% 9.63/2.61 % (4046)------------------------------
% 9.63/2.61 % (4046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.63/2.61 % (4046)Termination reason: Unknown
% 9.63/2.61 % (4046)Termination phase: Saturation
% 9.63/2.61
% 9.63/2.61 % (4046)Memory used [KB]: 10490
% 9.63/2.61 % (4046)Time elapsed: 0.469 s
% 9.63/2.61 % (4046)Instructions burned: 1539 (million)
% 9.63/2.61 % (4046)------------------------------
% 9.63/2.61 % (4046)------------------------------
% 9.63/2.62 % (4058)Instruction limit reached!
% 9.63/2.62 % (4058)------------------------------
% 9.63/2.62 % (4058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.63/2.62 % (4058)Termination reason: Unknown
% 9.63/2.62 % (4058)Termination phase: Saturation
% 9.63/2.62
% 9.63/2.62 % (4058)Memory used [KB]: 8699
% 9.63/2.62 % (4058)Time elapsed: 0.104 s
% 9.63/2.62 % (4058)Instructions burned: 375 (million)
% 9.63/2.62 % (4058)------------------------------
% 9.63/2.62 % (4058)------------------------------
% 9.63/2.62 % (4059)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_3484 for (2986ds/253Mi)
% 9.63/2.63 % (4060)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_3484 for (2986ds/832Mi)
% 9.63/2.69 % (4059)Instruction limit reached!
% 9.63/2.69 % (4059)------------------------------
% 9.63/2.69 % (4059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.63/2.69 % (4059)Termination reason: Unknown
% 9.63/2.69 % (4059)Termination phase: Saturation
% 9.63/2.69
% 9.63/2.69 % (4059)Memory used [KB]: 7419
% 9.63/2.69 % (4059)Time elapsed: 0.064 s
% 9.63/2.69 % (4059)Instructions burned: 255 (million)
% 9.63/2.69 % (4059)------------------------------
% 9.63/2.69 % (4059)------------------------------
% 10.31/2.70 % (4061)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_3484 for (2985ds/668Mi)
% 10.31/2.77 % (4057)Instruction limit reached!
% 10.31/2.77 % (4057)------------------------------
% 10.31/2.77 % (4057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.31/2.77 % (4057)Termination reason: Unknown
% 10.31/2.77 % (4057)Termination phase: Saturation
% 10.31/2.77
% 10.31/2.77 % (4057)Memory used [KB]: 13816
% 10.31/2.77 % (4057)Time elapsed: 0.250 s
% 10.31/2.77 % (4057)Instructions burned: 998 (million)
% 10.31/2.77 % (4057)------------------------------
% 10.31/2.77 % (4057)------------------------------
% 10.31/2.78 % (4062)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_3484 for (2984ds/40Mi)
% 10.31/2.79 % (4062)Instruction limit reached!
% 10.31/2.79 % (4062)------------------------------
% 10.31/2.79 % (4062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.31/2.79 % (4062)Termination reason: Unknown
% 10.31/2.79 % (4062)Termination phase: shuffling
% 10.31/2.79
% 10.31/2.79 % (4062)Memory used [KB]: 2302
% 10.31/2.79 % (4062)Time elapsed: 0.012 s
% 10.31/2.79 % (4062)Instructions burned: 41 (million)
% 10.31/2.79 % (4062)------------------------------
% 10.31/2.79 % (4062)------------------------------
% 10.31/2.79 % (4049)Instruction limit reached!
% 10.31/2.79 % (4049)------------------------------
% 10.31/2.79 % (4049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.31/2.79 % (4049)Termination reason: Unknown
% 10.31/2.79 % (4049)Termination phase: Saturation
% 10.31/2.79
% 10.31/2.79 % (4049)Memory used [KB]: 5884
% 10.31/2.79 % (4049)Time elapsed: 0.582 s
% 10.31/2.79 % (4049)Instructions burned: 1916 (million)
% 10.31/2.79 % (4049)------------------------------
% 10.31/2.79 % (4049)------------------------------
% 11.18/2.80 % (4063)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_3484 for (2984ds/294Mi)
% 11.18/2.80 % (4064)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_3484 for (2984ds/187Mi)
% 11.18/2.85 % (4064)Instruction limit reached!
% 11.18/2.85 % (4064)------------------------------
% 11.18/2.85 % (4064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.18/2.85 % (4064)Termination reason: Unknown
% 11.18/2.85 % (4064)Termination phase: Saturation
% 11.18/2.85
% 11.18/2.85 % (4064)Memory used [KB]: 7675
% 11.18/2.85 % (4064)Time elapsed: 0.049 s
% 11.18/2.85 % (4064)Instructions burned: 188 (million)
% 11.18/2.85 % (4064)------------------------------
% 11.18/2.85 % (4064)------------------------------
% 11.18/2.86 % (4065)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_3484 for (2983ds/371Mi)
% 11.18/2.86 % (4061)Instruction limit reached!
% 11.18/2.86 % (4061)------------------------------
% 11.18/2.86 % (4061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.18/2.86 % (4061)Termination reason: Unknown
% 11.18/2.86 % (4061)Termination phase: Saturation
% 11.18/2.86
% 11.18/2.86 % (4061)Memory used [KB]: 18421
% 11.18/2.86 % (4061)Time elapsed: 0.169 s
% 11.18/2.86 % (4061)Instructions burned: 669 (million)
% 11.18/2.86 % (4061)------------------------------
% 11.18/2.86 % (4061)------------------------------
% 11.18/2.87 % (4063)Instruction limit reached!
% 11.18/2.87 % (4063)------------------------------
% 11.18/2.87 % (4063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.18/2.87 % (4063)Termination reason: Unknown
% 11.18/2.87 % (4063)Termination phase: Saturation
% 11.18/2.87
% 11.18/2.87 % (4063)Memory used [KB]: 7419
% 11.18/2.87 % (4063)Time elapsed: 0.073 s
% 11.18/2.87 % (4063)Instructions burned: 294 (million)
% 11.18/2.87 % (4063)------------------------------
% 11.18/2.87 % (4063)------------------------------
% 11.18/2.87 % (4066)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_3484 for (2983ds/1827Mi)
% 11.18/2.88 % (4060)Instruction limit reached!
% 11.18/2.88 % (4060)------------------------------
% 11.18/2.88 % (4060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.18/2.88 % (4060)Termination reason: Unknown
% 11.18/2.88 % (4060)Termination phase: Saturation
% 11.18/2.88
% 11.18/2.88 % (4060)Memory used [KB]: 11001
% 11.18/2.88 % (4060)Time elapsed: 0.248 s
% 11.18/2.88 % (4060)Instructions burned: 834 (million)
% 11.18/2.88 % (4060)------------------------------
% 11.18/2.88 % (4060)------------------------------
% 11.18/2.88 % (4067)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_3484 for (2983ds/70Mi)
% 11.18/2.89 % (4068)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_3484 for (2983ds/316Mi)
% 11.76/2.90 % (4067)Instruction limit reached!
% 11.76/2.90 % (4067)------------------------------
% 11.76/2.90 % (4067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.76/2.90 % (4067)Termination reason: Unknown
% 11.76/2.90 % (4067)Termination phase: Property scanning
% 11.76/2.90
% 11.76/2.90 % (4067)Memory used [KB]: 2430
% 11.76/2.90 % (4067)Time elapsed: 0.019 s
% 11.76/2.90 % (4067)Instructions burned: 71 (million)
% 11.76/2.90 % (4067)------------------------------
% 11.76/2.90 % (4067)------------------------------
% 11.76/2.91 % (4069)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_3484 for (2983ds/932Mi)
% 11.76/2.96 % (4065)Instruction limit reached!
% 11.76/2.96 % (4065)------------------------------
% 11.76/2.96 % (4065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.76/2.96 % (4065)Termination reason: Unknown
% 11.76/2.96 % (4065)Termination phase: Saturation
% 11.76/2.96
% 11.76/2.96 % (4065)Memory used [KB]: 8699
% 11.76/2.96 % (4065)Time elapsed: 0.104 s
% 11.76/2.96 % (4065)Instructions burned: 373 (million)
% 11.76/2.96 % (4065)------------------------------
% 11.76/2.96 % (4065)------------------------------
% 11.76/2.97 % (4068)Instruction limit reached!
% 11.76/2.97 % (4068)------------------------------
% 11.76/2.97 % (4068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.76/2.97 % (4068)Termination reason: Unknown
% 11.76/2.97 % (4068)Termination phase: Saturation
% 11.76/2.97
% 11.76/2.97 % (4068)Memory used [KB]: 7419
% 11.76/2.97 % (4068)Time elapsed: 0.082 s
% 11.76/2.97 % (4068)Instructions burned: 317 (million)
% 11.76/2.97 % (4068)------------------------------
% 11.76/2.97 % (4068)------------------------------
% 11.76/2.97 % (4070)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_3484 for (2982ds/4714Mi)
% 11.76/2.98 % (4071)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_3484 for (2982ds/8250Mi)
% 15.42/3.14 % (4069)Instruction limit reached!
% 15.42/3.14 % (4069)------------------------------
% 15.42/3.14 % (4069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.42/3.14 % (4069)Termination reason: Unknown
% 15.42/3.14 % (4069)Termination phase: Saturation
% 15.42/3.14
% 15.42/3.14 % (4069)Memory used [KB]: 15351
% 15.42/3.14 % (4069)Time elapsed: 0.237 s
% 15.42/3.14 % (4069)Instructions burned: 934 (million)
% 15.42/3.14 % (4069)------------------------------
% 15.42/3.14 % (4069)------------------------------
% 15.42/3.15 % (4072)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_3484 for (2980ds/770Mi)
% 16.59/3.36 % (4072)Instruction limit reached!
% 16.59/3.36 % (4072)------------------------------
% 16.59/3.36 % (4072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.59/3.36 % (4072)Termination reason: Unknown
% 16.59/3.36 % (4072)Termination phase: Saturation
% 16.59/3.36
% 16.59/3.36 % (4072)Memory used [KB]: 7419
% 16.59/3.36 % (4072)Time elapsed: 0.209 s
% 16.59/3.36 % (4072)Instructions burned: 772 (million)
% 16.59/3.36 % (4072)------------------------------
% 16.59/3.36 % (4072)------------------------------
% 16.59/3.37 % (4073)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_3484 for (2978ds/794Mi)
% 16.59/3.39 % (4066)Instruction limit reached!
% 16.59/3.39 % (4066)------------------------------
% 16.59/3.39 % (4066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.59/3.39 % (4066)Termination reason: Unknown
% 16.59/3.39 % (4066)Termination phase: Saturation
% 16.59/3.39
% 16.59/3.39 % (4066)Memory used [KB]: 19957
% 16.59/3.39 % (4066)Time elapsed: 0.541 s
% 16.59/3.39 % (4066)Instructions burned: 1830 (million)
% 16.59/3.39 % (4066)------------------------------
% 16.59/3.39 % (4066)------------------------------
% 17.40/3.40 % (4074)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_3484 for (2978ds/464Mi)
% 17.40/3.45 % (4048)Instruction limit reached!
% 17.40/3.45 % (4048)------------------------------
% 17.40/3.45 % (4048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.40/3.45 % (4048)Termination reason: Unknown
% 17.40/3.45 % (4048)Termination phase: Saturation
% 17.40/3.45
% 17.40/3.45 % (4048)Memory used [KB]: 14967
% 17.40/3.45 % (4048)Time elapsed: 1.284 s
% 17.40/3.45 % (4048)Instructions burned: 5207 (million)
% 17.40/3.45 % (4048)------------------------------
% 17.40/3.45 % (4048)------------------------------
% 17.40/3.46 % (4075)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_3484 for (2977ds/1376Mi)
% 17.87/3.51 % (4045)Instruction limit reached!
% 17.87/3.51 % (4045)------------------------------
% 17.87/3.51 % (4045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.87/3.51 % (4045)Termination reason: Unknown
% 17.87/3.51 % (4045)Termination phase: Saturation
% 17.87/3.51
% 17.87/3.51 % (4045)Memory used [KB]: 17270
% 17.87/3.51 % (4045)Time elapsed: 1.387 s
% 17.87/3.51 % (4045)Instructions burned: 4436 (million)
% 17.87/3.51 % (4045)------------------------------
% 17.87/3.51 % (4045)------------------------------
% 17.87/3.52 % (4076)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_3484 for (2977ds/906Mi)
% 17.87/3.53 % (4074)Instruction limit reached!
% 17.87/3.53 % (4074)------------------------------
% 17.87/3.53 % (4074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.87/3.53 % (4074)Termination reason: Unknown
% 17.87/3.53 % (4074)Termination phase: Saturation
% 17.87/3.53
% 17.87/3.53 % (4074)Memory used [KB]: 9338
% 17.87/3.53 % (4074)Time elapsed: 0.132 s
% 17.87/3.53 % (4074)Instructions burned: 465 (million)
% 17.87/3.53 % (4074)------------------------------
% 17.87/3.53 % (4074)------------------------------
% 17.87/3.54 % (4077)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_3484 for (2976ds/434Mi)
% 18.34/3.61 % (4073)Instruction limit reached!
% 18.34/3.61 % (4073)------------------------------
% 18.34/3.61 % (4073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.34/3.61 % (4073)Termination reason: Unknown
% 18.34/3.61 % (4073)Termination phase: Saturation
% 18.34/3.61
% 18.34/3.61 % (4073)Memory used [KB]: 5628
% 18.34/3.61 % (4073)Time elapsed: 0.235 s
% 18.34/3.61 % (4073)Instructions burned: 795 (million)
% 18.34/3.61 % (4073)------------------------------
% 18.34/3.61 % (4073)------------------------------
% 18.34/3.62 % (4078)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_3484 for (2976ds/865Mi)
% 18.34/3.62 % (4050)Instruction limit reached!
% 18.34/3.62 % (4050)------------------------------
% 18.34/3.62 % (4050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.34/3.62 % (4050)Termination reason: Unknown
% 18.34/3.62 % (4050)Termination phase: Saturation
% 18.34/3.62
% 18.34/3.62 % (4050)Memory used [KB]: 13304
% 18.34/3.62 % (4050)Time elapsed: 1.325 s
% 18.34/3.62 % (4050)Instructions burned: 4351 (million)
% 18.34/3.62 % (4050)------------------------------
% 18.34/3.62 % (4050)------------------------------
% 18.34/3.63 % (4079)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_3484 for (2976ds/593Mi)
% 18.34/3.67 % (4077)Instruction limit reached!
% 18.34/3.67 % (4077)------------------------------
% 18.34/3.67 % (4077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.34/3.67 % (4077)Termination reason: Unknown
% 18.34/3.67 % (4077)Termination phase: Saturation
% 18.34/3.67
% 18.34/3.67 % (4077)Memory used [KB]: 10362
% 18.34/3.67 % (4077)Time elapsed: 0.126 s
% 18.34/3.67 % (4077)Instructions burned: 434 (million)
% 18.34/3.67 % (4077)------------------------------
% 18.34/3.67 % (4077)------------------------------
% 18.34/3.68 % (4080)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_3484 for (2975ds/443Mi)
% 18.96/3.77 % (4079)Instruction limit reached!
% 18.96/3.77 % (4079)------------------------------
% 18.96/3.77 % (4079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.96/3.77 % (4079)Termination reason: Unknown
% 18.96/3.77 % (4079)Termination phase: Saturation
% 18.96/3.77
% 18.96/3.77 % (4079)Memory used [KB]: 7547
% 18.96/3.77 % (4079)Time elapsed: 0.149 s
% 18.96/3.77 % (4079)Instructions burned: 597 (million)
% 18.96/3.77 % (4079)------------------------------
% 18.96/3.77 % (4079)------------------------------
% 18.96/3.78 % (4081)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_3484 for (2974ds/594Mi)
% 19.31/3.80 % (4076)Instruction limit reached!
% 19.31/3.80 % (4076)------------------------------
% 19.31/3.80 % (4076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.31/3.80 % (4076)Termination reason: Unknown
% 19.31/3.80 % (4076)Termination phase: Saturation
% 19.31/3.80
% 19.31/3.80 % (4076)Memory used [KB]: 10746
% 19.31/3.80 % (4076)Time elapsed: 0.281 s
% 19.31/3.80 % (4076)Instructions burned: 908 (million)
% 19.31/3.80 % (4076)------------------------------
% 19.31/3.80 % (4076)------------------------------
% 19.31/3.80 % (4080)Instruction limit reached!
% 19.31/3.80 % (4080)------------------------------
% 19.31/3.80 % (4080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.31/3.80 % (4080)Termination reason: Unknown
% 19.31/3.80 % (4080)Termination phase: Saturation
% 19.31/3.80
% 19.31/3.80 % (4080)Memory used [KB]: 8827
% 19.31/3.80 % (4080)Time elapsed: 0.148 s
% 19.31/3.80 % (4080)Instructions burned: 446 (million)
% 19.31/3.80 % (4080)------------------------------
% 19.31/3.80 % (4080)------------------------------
% 19.31/3.81 % (4075)Instruction limit reached!
% 19.31/3.81 % (4075)------------------------------
% 19.31/3.81 % (4075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.31/3.81 % (4075)Termination reason: Unknown
% 19.31/3.81 % (4075)Termination phase: Saturation
% 19.31/3.81
% 19.31/3.81 % (4075)Memory used [KB]: 9338
% 19.31/3.81 % (4075)Time elapsed: 0.349 s
% 19.31/3.81 % (4075)Instructions burned: 1379 (million)
% 19.31/3.81 % (4075)------------------------------
% 19.31/3.81 % (4075)------------------------------
% 19.31/3.81 % (4082)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_3484 for (2974ds/327Mi)
% 19.31/3.81 % (4083)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_3484 for (2974ds/5411Mi)
% 19.31/3.82 % (4084)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_3484 for (2974ds/1762Mi)
% 19.31/3.87 % (4078)Instruction limit reached!
% 19.31/3.87 % (4078)------------------------------
% 19.31/3.87 % (4078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.31/3.87 % (4078)Termination reason: Unknown
% 19.31/3.87 % (4078)Termination phase: Saturation
% 19.31/3.87
% 19.31/3.87 % (4078)Memory used [KB]: 10490
% 19.31/3.87 % (4078)Time elapsed: 0.258 s
% 19.31/3.87 % (4078)Instructions burned: 868 (million)
% 19.31/3.87 % (4078)------------------------------
% 19.31/3.87 % (4078)------------------------------
% 19.31/3.88 % (4085)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_3484 for (2973ds/96Mi)
% 20.57/3.91 % (4085)Instruction limit reached!
% 20.57/3.91 % (4085)------------------------------
% 20.57/3.91 % (4085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.57/3.91 % (4085)Termination reason: Unknown
% 20.57/3.91 % (4085)Termination phase: Property scanning
% 20.57/3.91
% 20.57/3.91 % (4085)Memory used [KB]: 2430
% 20.57/3.91 % (4085)Time elapsed: 0.025 s
% 20.57/3.91 % (4085)Instructions burned: 96 (million)
% 20.57/3.91 % (4085)------------------------------
% 20.57/3.91 % (4085)------------------------------
% 20.57/3.91 % (4082)Instruction limit reached!
% 20.57/3.91 % (4082)------------------------------
% 20.57/3.91 % (4082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.57/3.91 % (4082)Termination reason: Unknown
% 20.57/3.91 % (4082)Termination phase: Saturation
% 20.57/3.91
% 20.57/3.91 % (4082)Memory used [KB]: 11001
% 20.57/3.91 % (4082)Time elapsed: 0.098 s
% 20.57/3.91 % (4082)Instructions burned: 327 (million)
% 20.57/3.91 % (4082)------------------------------
% 20.57/3.91 % (4082)------------------------------
% 20.57/3.92 % (4086)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_3484 for (2973ds/503Mi)
% 20.57/3.92 % (4087)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_3484 for (2973ds/90Mi)
% 20.57/3.94 % (4087)Instruction limit reached!
% 20.57/3.94 % (4087)------------------------------
% 20.57/3.94 % (4087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.57/3.94 % (4087)Termination reason: Unknown
% 20.57/3.94 % (4087)Termination phase: Property scanning
% 20.57/3.94
% 20.57/3.94 % (4087)Memory used [KB]: 2558
% 20.57/3.94 % (4087)Time elapsed: 0.024 s
% 20.57/3.94 % (4087)Instructions burned: 90 (million)
% 20.57/3.94 % (4087)------------------------------
% 20.57/3.94 % (4087)------------------------------
% 20.57/3.95 % (4088)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_3484 for (2972ds/593Mi)
% 20.57/3.96 % (4081)Instruction limit reached!
% 20.57/3.96 % (4081)------------------------------
% 20.57/3.96 % (4081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.57/3.96 % (4081)Termination reason: Unknown
% 20.57/3.96 % (4081)Termination phase: Saturation
% 20.57/3.96
% 20.57/3.96 % (4081)Memory used [KB]: 9466
% 20.57/3.96 % (4081)Time elapsed: 0.195 s
% 20.57/3.96 % (4081)Instructions burned: 594 (million)
% 20.57/3.96 % (4081)------------------------------
% 20.57/3.96 % (4081)------------------------------
% 20.57/3.97 % (4089)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_3484 for (2972ds/1512Mi)
% 21.75/4.06 % (4086)Instruction limit reached!
% 21.75/4.06 % (4086)------------------------------
% 21.75/4.06 % (4086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.75/4.06 % (4086)Termination reason: Unknown
% 21.75/4.06 % (4086)Termination phase: Saturation
% 21.75/4.06
% 21.75/4.06 % (4086)Memory used [KB]: 9594
% 21.75/4.06 % (4086)Time elapsed: 0.143 s
% 21.75/4.06 % (4086)Instructions burned: 503 (million)
% 21.75/4.06 % (4086)------------------------------
% 21.75/4.06 % (4086)------------------------------
% 21.75/4.07 % (4090)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_3484 for (2971ds/569Mi)
% 22.41/4.13 % (4088)Instruction limit reached!
% 22.41/4.13 % (4088)------------------------------
% 22.41/4.13 % (4088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.41/4.13 % (4088)Termination reason: Unknown
% 22.41/4.13 % (4088)Termination phase: Saturation
% 22.41/4.13
% 22.41/4.13 % (4088)Memory used [KB]: 9850
% 22.41/4.13 % (4088)Time elapsed: 0.174 s
% 22.41/4.13 % (4088)Instructions burned: 593 (million)
% 22.41/4.13 % (4088)------------------------------
% 22.41/4.13 % (4088)------------------------------
% 22.41/4.13 % (4070)Instruction limit reached!
% 22.41/4.13 % (4070)------------------------------
% 22.41/4.13 % (4070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.41/4.13 % (4070)Termination reason: Unknown
% 22.41/4.13 % (4070)Termination phase: Saturation
% 22.41/4.13
% 22.41/4.13 % (4070)Memory used [KB]: 7547
% 22.41/4.13 % (4070)Time elapsed: 1.163 s
% 22.41/4.13 % (4070)Instructions burned: 4716 (million)
% 22.41/4.13 % (4070)------------------------------
% 22.41/4.13 % (4070)------------------------------
% 22.41/4.14 % (4091)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_3484 for (2970ds/501Mi)
% 22.41/4.14 % (4092)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_3484 for (2970ds/562Mi)
% 22.80/4.21 % (4090)Instruction limit reached!
% 22.80/4.21 % (4090)------------------------------
% 22.80/4.21 % (4090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.80/4.21 % (4090)Termination reason: Unknown
% 22.80/4.21 % (4090)Termination phase: Saturation
% 22.80/4.21
% 22.80/4.21 % (4090)Memory used [KB]: 12153
% 22.80/4.21 % (4090)Time elapsed: 0.144 s
% 22.80/4.21 % (4090)Instructions burned: 570 (million)
% 22.80/4.21 % (4090)------------------------------
% 22.80/4.21 % (4090)------------------------------
% 22.80/4.22 % (4093)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_3484 for (2970ds/406Mi)
% 22.80/4.25 % (4084)Instruction limit reached!
% 22.80/4.25 % (4084)------------------------------
% 22.80/4.25 % (4084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.80/4.25 % (4084)Termination reason: Unknown
% 22.80/4.25 % (4084)Termination phase: Saturation
% 22.80/4.25
% 22.80/4.25 % (4084)Memory used [KB]: 21875
% 22.80/4.25 % (4084)Time elapsed: 0.429 s
% 22.80/4.25 % (4084)Instructions burned: 1762 (million)
% 22.80/4.25 % (4084)------------------------------
% 22.80/4.25 % (4084)------------------------------
% 22.80/4.26 % (4094)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_3484 for (2969ds/582Mi)
% 22.80/4.28 % (4091)Instruction limit reached!
% 22.80/4.28 % (4091)------------------------------
% 22.80/4.28 % (4091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.80/4.28 % (4091)Termination reason: Unknown
% 22.80/4.28 % (4091)Termination phase: Saturation
% 22.80/4.28
% 22.80/4.28 % (4091)Memory used [KB]: 9978
% 22.80/4.28 % (4091)Time elapsed: 0.150 s
% 22.80/4.28 % (4091)Instructions burned: 503 (million)
% 22.80/4.28 % (4091)------------------------------
% 22.80/4.28 % (4091)------------------------------
% 22.80/4.29 % (4095)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_3484 for (2969ds/456Mi)
% 23.49/4.30 % (4092)Instruction limit reached!
% 23.49/4.30 % (4092)------------------------------
% 23.49/4.30 % (4092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.49/4.30 % (4092)Termination reason: Unknown
% 23.49/4.30 % (4092)Termination phase: Saturation
% 23.49/4.30
% 23.49/4.30 % (4092)Memory used [KB]: 8315
% 23.49/4.30 % (4092)Time elapsed: 0.159 s
% 23.49/4.30 % (4092)Instructions burned: 564 (million)
% 23.49/4.30 % (4092)------------------------------
% 23.49/4.30 % (4092)------------------------------
% 23.49/4.31 % (4096)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_3484 for (2969ds/393Mi)
% 23.49/4.33 % (4093)Instruction limit reached!
% 23.49/4.33 % (4093)------------------------------
% 23.49/4.33 % (4093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.49/4.33 % (4093)Termination reason: Unknown
% 23.49/4.33 % (4093)Termination phase: Saturation
% 23.49/4.33
% 23.49/4.33 % (4093)Memory used [KB]: 7675
% 23.49/4.33 % (4093)Time elapsed: 0.110 s
% 23.49/4.33 % (4093)Instructions burned: 406 (million)
% 23.49/4.33 % (4093)------------------------------
% 23.49/4.33 % (4093)------------------------------
% 23.49/4.34 % (4097)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_3484 for (2968ds/1335Mi)
% 24.06/4.42 % (4096)Instruction limit reached!
% 24.06/4.42 % (4096)------------------------------
% 24.06/4.42 % (4096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.06/4.42 % (4096)Termination reason: Unknown
% 24.06/4.42 % (4096)Termination phase: Saturation
% 24.06/4.42
% 24.06/4.42 % (4096)Memory used [KB]: 9338
% 24.06/4.42 % (4096)Time elapsed: 0.105 s
% 24.06/4.42 % (4096)Instructions burned: 394 (million)
% 24.06/4.42 % (4096)------------------------------
% 24.06/4.42 % (4096)------------------------------
% 24.06/4.42 % (4095)Instruction limit reached!
% 24.06/4.42 % (4095)------------------------------
% 24.06/4.42 % (4095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.06/4.42 % (4095)Termination reason: Unknown
% 24.06/4.42 % (4095)Termination phase: Saturation
% 24.06/4.42
% 24.06/4.42 % (4095)Memory used [KB]: 9466
% 24.06/4.42 % (4095)Time elapsed: 0.129 s
% 24.06/4.42 % (4095)Instructions burned: 458 (million)
% 24.06/4.42 % (4095)------------------------------
% 24.06/4.42 % (4095)------------------------------
% 24.06/4.43 % (4098)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_3484 for (2968ds/3373Mi)
% 24.06/4.43 % (4089)Instruction limit reached!
% 24.06/4.43 % (4089)------------------------------
% 24.06/4.43 % (4089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.06/4.43 % (4089)Termination reason: Unknown
% 24.06/4.43 % (4089)Termination phase: Saturation
% 24.06/4.43
% 24.06/4.43 % (4089)Memory used [KB]: 12281
% 24.06/4.43 % (4089)Time elapsed: 0.466 s
% 24.06/4.43 % (4089)Instructions burned: 1513 (million)
% 24.06/4.43 % (4089)------------------------------
% 24.06/4.43 % (4089)------------------------------
% 24.06/4.43 % (4099)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_3484 for (2968ds/474Mi)
% 24.06/4.44 % (4094)Instruction limit reached!
% 24.06/4.44 % (4094)------------------------------
% 24.06/4.44 % (4094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.06/4.44 % (4094)Termination reason: Unknown
% 24.06/4.44 % (4094)Termination phase: Saturation
% 24.06/4.44
% 24.06/4.44 % (4094)Memory used [KB]: 10234
% 24.06/4.44 % (4094)Time elapsed: 0.178 s
% 24.06/4.44 % (4094)Instructions burned: 582 (million)
% 24.06/4.44 % (4094)------------------------------
% 24.06/4.44 % (4094)------------------------------
% 24.06/4.44 % (4100)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_3484 for (2967ds/157Mi)
% 24.06/4.45 % (4101)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_3484 for (2967ds/590Mi)
% 24.06/4.48 % (4100)Instruction limit reached!
% 24.06/4.48 % (4100)------------------------------
% 24.06/4.48 % (4100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.06/4.48 % (4100)Termination reason: Unknown
% 24.06/4.48 % (4100)Termination phase: Saturation
% 24.06/4.48
% 24.06/4.48 % (4100)Memory used [KB]: 7164
% 24.06/4.48 % (4100)Time elapsed: 0.040 s
% 24.06/4.48 % (4100)Instructions burned: 160 (million)
% 24.06/4.48 % (4100)------------------------------
% 24.06/4.48 % (4100)------------------------------
% 24.06/4.49 % (4102)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_3484 for (2967ds/104Mi)
% 24.79/4.51 % (4102)Instruction limit reached!
% 24.79/4.51 % (4102)------------------------------
% 24.79/4.51 % (4102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.79/4.51 % (4102)Termination reason: Unknown
% 24.79/4.51 % (4102)Termination phase: Function definition elimination
% 24.79/4.51
% 24.79/4.51 % (4102)Memory used [KB]: 2558
% 24.79/4.51 % (4102)Time elapsed: 0.027 s
% 24.79/4.51 % (4102)Instructions burned: 104 (million)
% 24.79/4.51 % (4102)------------------------------
% 24.79/4.51 % (4102)------------------------------
% 24.79/4.52 % (4103)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_3484 for (2967ds/414Mi)
% 24.79/4.55 % (4099)Instruction limit reached!
% 24.79/4.55 % (4099)------------------------------
% 24.79/4.55 % (4099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.79/4.55 % (4099)Termination reason: Unknown
% 24.79/4.55 % (4099)Termination phase: Saturation
% 24.79/4.55
% 24.79/4.55 % (4099)Memory used [KB]: 7547
% 24.79/4.55 % (4099)Time elapsed: 0.118 s
% 24.79/4.55 % (4099)Instructions burned: 476 (million)
% 24.79/4.55 % (4099)------------------------------
% 24.79/4.55 % (4099)------------------------------
% 24.79/4.56 % (4104)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_3484 for (2966ds/715Mi)
% 25.15/4.61 % (4101)Instruction limit reached!
% 25.15/4.61 % (4101)------------------------------
% 25.15/4.61 % (4101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.15/4.61 % (4101)Termination reason: Unknown
% 25.15/4.61 % (4101)Termination phase: Saturation
% 25.15/4.61
% 25.15/4.61 % (4101)Memory used [KB]: 8315
% 25.15/4.61 % (4101)Time elapsed: 0.168 s
% 25.15/4.61 % (4101)Instructions burned: 593 (million)
% 25.15/4.61 % (4101)------------------------------
% 25.15/4.61 % (4101)------------------------------
% 25.15/4.62 % (4105)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_3484 for (2965ds/961Mi)
% 25.15/4.63 % (4103)Instruction limit reached!
% 25.15/4.63 % (4103)------------------------------
% 25.15/4.63 % (4103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.15/4.63 % (4103)Termination reason: Unknown
% 25.15/4.63 % (4103)Termination phase: Saturation
% 25.15/4.63
% 25.15/4.63 % (4103)Memory used [KB]: 7419
% 25.15/4.63 % (4103)Time elapsed: 0.103 s
% 25.15/4.63 % (4103)Instructions burned: 415 (million)
% 25.15/4.63 % (4103)------------------------------
% 25.15/4.63 % (4103)------------------------------
% 25.15/4.64 % (4106)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_3484 for (2965ds/1213Mi)
% 25.64/4.73 % (4097)Instruction limit reached!
% 25.64/4.73 % (4097)------------------------------
% 25.64/4.73 % (4097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.64/4.73 % (4097)Termination reason: Unknown
% 25.64/4.73 % (4097)Termination phase: Saturation
% 25.64/4.73
% 25.64/4.73 % (4097)Memory used [KB]: 9978
% 25.64/4.73 % (4097)Time elapsed: 0.397 s
% 25.64/4.73 % (4097)Instructions burned: 1337 (million)
% 25.64/4.73 % (4097)------------------------------
% 25.64/4.73 % (4097)------------------------------
% 25.64/4.74 % (4107)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_3484 for (2964ds/1979Mi)
% 25.64/4.77 % (4104)Instruction limit reached!
% 25.64/4.77 % (4104)------------------------------
% 25.64/4.77 % (4104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.64/4.77 % (4104)Termination reason: Unknown
% 25.64/4.77 % (4104)Termination phase: Saturation
% 25.64/4.77
% 25.64/4.77 % (4104)Memory used [KB]: 5117
% 25.64/4.77 % (4104)Time elapsed: 0.210 s
% 25.64/4.77 % (4104)Instructions burned: 717 (million)
% 25.64/4.77 % (4104)------------------------------
% 25.64/4.77 % (4104)------------------------------
% 25.64/4.78 % (4108)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_3484 for (2964ds/481Mi)
% 26.46/4.89 % (4108)Instruction limit reached!
% 26.46/4.89 % (4108)------------------------------
% 26.46/4.89 % (4108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.46/4.89 % (4108)Termination reason: Unknown
% 26.46/4.89 % (4108)Termination phase: Saturation
% 26.46/4.89
% 26.46/4.89 % (4108)Memory used [KB]: 7419
% 26.46/4.89 % (4108)Time elapsed: 0.119 s
% 26.46/4.89 % (4108)Instructions burned: 481 (million)
% 26.46/4.89 % (4108)------------------------------
% 26.46/4.89 % (4108)------------------------------
% 26.79/4.90 % (4109)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_3484 for (2963ds/783Mi)
% 26.79/4.91 % (4105)Instruction limit reached!
% 26.79/4.91 % (4105)------------------------------
% 26.79/4.91 % (4105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.79/4.91 % (4105)Termination reason: Unknown
% 26.79/4.91 % (4105)Termination phase: Saturation
% 26.79/4.91
% 26.79/4.91 % (4105)Memory used [KB]: 9850
% 26.79/4.91 % (4105)Time elapsed: 0.284 s
% 26.79/4.91 % (4105)Instructions burned: 962 (million)
% 26.79/4.91 % (4105)------------------------------
% 26.79/4.91 % (4105)------------------------------
% 26.79/4.92 % (4110)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_3484 for (2963ds/432Mi)
% 26.79/5.01 % (4106)Instruction limit reached!
% 26.79/5.01 % (4106)------------------------------
% 26.79/5.01 % (4106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.79/5.01 % (4106)Termination reason: Unknown
% 26.79/5.01 % (4106)Termination phase: Saturation
% 26.79/5.01
% 26.79/5.01 % (4106)Memory used [KB]: 13816
% 26.79/5.01 % (4106)Time elapsed: 0.371 s
% 26.79/5.01 % (4106)Instructions burned: 1215 (million)
% 26.79/5.01 % (4106)------------------------------
% 26.79/5.01 % (4106)------------------------------
% 28.73/5.02 % (4111)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_3484 for (2962ds/1670Mi)
% 28.73/5.04 % (4110)Instruction limit reached!
% 28.73/5.04 % (4110)------------------------------
% 28.73/5.04 % (4110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.73/5.04 % (4110)Termination reason: Unknown
% 28.73/5.04 % (4110)Termination phase: Saturation
% 28.73/5.04
% 28.73/5.04 % (4110)Memory used [KB]: 8827
% 28.73/5.04 % (4110)Time elapsed: 0.121 s
% 28.73/5.04 % (4110)Instructions burned: 433 (million)
% 28.73/5.04 % (4110)------------------------------
% 28.73/5.04 % (4110)------------------------------
% 28.73/5.04 % (4112)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_3484 for (2961ds/90Mi)
% 28.73/5.07 % (4112)Instruction limit reached!
% 28.73/5.07 % (4112)------------------------------
% 28.73/5.07 % (4112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.73/5.07 % (4112)Termination reason: Unknown
% 28.73/5.07 % (4112)Termination phase: Property scanning
% 28.73/5.07
% 28.73/5.07 % (4112)Memory used [KB]: 2558
% 28.73/5.07 % (4112)Time elapsed: 0.024 s
% 28.73/5.07 % (4112)Instructions burned: 91 (million)
% 28.73/5.07 % (4112)------------------------------
% 28.73/5.07 % (4112)------------------------------
% 28.73/5.08 % (4113)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_3484 for (2961ds/346Mi)
% 29.32/5.14 % (4109)Instruction limit reached!
% 29.32/5.14 % (4109)------------------------------
% 29.32/5.14 % (4109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.32/5.14 % (4109)Termination reason: Unknown
% 29.32/5.14 % (4109)Termination phase: Saturation
% 29.32/5.14
% 29.32/5.14 % (4109)Memory used [KB]: 11257
% 29.32/5.14 % (4109)Time elapsed: 0.240 s
% 29.32/5.14 % (4109)Instructions burned: 785 (million)
% 29.32/5.14 % (4109)------------------------------
% 29.32/5.14 % (4109)------------------------------
% 29.32/5.15 % (4114)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_3484 for (2960ds/401Mi)
% 29.32/5.16 % (4083)First to succeed.
% 29.32/5.16 % (4113)Instruction limit reached!
% 29.32/5.16 % (4113)------------------------------
% 29.32/5.16 % (4113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.32/5.16 % (4113)Termination reason: Unknown
% 29.32/5.16 % (4113)Termination phase: Saturation
% 29.32/5.16
% 29.32/5.16 % (4113)Memory used [KB]: 7419
% 29.32/5.16 % (4113)Time elapsed: 0.086 s
% 29.32/5.16 % (4113)Instructions burned: 348 (million)
% 29.32/5.16 % (4113)------------------------------
% 29.32/5.16 % (4113)------------------------------
% 29.32/5.17 % (4083)Refutation found. Thanks to Tanya!
% 29.32/5.17 % SZS status Theorem for DTF2THF_3484
% 29.32/5.17 % SZS output start Proof for DTF2THF_3484
% 29.32/5.17 thf(func_def_0, type, in: $i > $i > $o).
% 29.32/5.17 thf(func_def_1, type, exu: ($i > $o) > $o).
% 29.32/5.17 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 29.32/5.17 thf(func_def_8, type, powerset: $i > $i).
% 29.32/5.17 thf(func_def_10, type, setunion: $i > $i).
% 29.32/5.17 thf(func_def_19, type, descr: ($i > $o) > $i).
% 29.32/5.17 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 29.32/5.17 thf(func_def_26, type, prop2set: $o > $i).
% 29.32/5.17 thf(func_def_36, type, nonempty: $i > $o).
% 29.32/5.17 thf(func_def_69, type, set2prop: $i > $o).
% 29.32/5.17 thf(func_def_88, type, subset: $i > $i > $o).
% 29.32/5.17 thf(func_def_89, type, disjoint: $i > $i > $o).
% 29.32/5.17 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 29.32/5.17 thf(func_def_114, type, binunion: $i > $i > $i).
% 29.32/5.17 thf(func_def_122, type, binintersect: $i > $i > $i).
% 29.32/5.17 thf(func_def_135, type, regular: $i > $o).
% 29.32/5.17 thf(func_def_136, type, setminus: $i > $i > $i).
% 29.32/5.17 thf(func_def_147, type, symdiff: $i > $i > $i).
% 29.32/5.17 thf(func_def_153, type, iskpair: $i > $o).
% 29.32/5.17 thf(func_def_158, type, kpair: $i > $i > $i).
% 29.32/5.17 thf(func_def_160, type, cartprod: $i > $i > $i).
% 29.32/5.17 thf(func_def_177, type, singleton: $i > $o).
% 29.32/5.17 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 29.32/5.17 thf(func_def_184, type, atmost1p: $i > $o).
% 29.32/5.17 thf(func_def_185, type, atleast2p: $i > $o).
% 29.32/5.17 thf(func_def_186, type, atmost2p: $i > $o).
% 29.32/5.17 thf(func_def_187, type, upairsetp: $i > $o).
% 29.32/5.17 thf(func_def_191, type, kfst: $i > $i).
% 29.32/5.17 thf(func_def_203, type, ksnd: $i > $i).
% 29.32/5.17 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 29.32/5.17 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 29.32/5.17 thf(func_def_222, type, func: $i > $i > $i > $o).
% 29.32/5.17 thf(func_def_223, type, funcSet: $i > $i > $i).
% 29.32/5.17 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 29.32/5.17 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 29.32/5.17 thf(func_def_259, type, if: $i > $o > $i > $i > $i).
% 29.32/5.17 thf(func_def_299, type, sP0: $i > $i > $i > $o).
% 29.32/5.17 thf(func_def_300, type, sP1: $i > $i > $i > $i > $o).
% 29.32/5.17 thf(func_def_303, type, sP4: $i > $o > $i > $i > $o).
% 29.32/5.17 thf(func_def_305, type, sP6: $i > $i > $o).
% 29.32/5.17 thf(func_def_306, type, sP7: $i > $o).
% 29.32/5.17 thf(func_def_307, type, sP8: $i > $i > $o).
% 29.32/5.17 thf(func_def_308, type, sP9: $i > $i > $o).
% 29.32/5.17 thf(func_def_311, type, sK12: ($i > $o) > ($i > $o) > $i).
% 29.32/5.17 thf(func_def_312, type, sK13: ($i > $o) > ($i > $o) > $i).
% 29.32/5.17 thf(func_def_313, type, sK14: $i > $o).
% 29.32/5.17 thf(func_def_314, type, sK15: $i > $o).
% 29.32/5.17 thf(func_def_315, type, sK16: $i > $o).
% 29.32/5.17 thf(func_def_317, type, sK18: $i > $i > $i > $i).
% 29.32/5.17 thf(func_def_321, type, sK22: $i > $i > $i > $i).
% 29.32/5.17 thf(func_def_323, type, sK24: $i > $o).
% 29.32/5.17 thf(func_def_328, type, sK29: $i > $o).
% 29.32/5.17 thf(func_def_335, type, sK36: $i > $i > $i > $i > $i).
% 29.32/5.17 thf(func_def_350, type, sK51: $i > $i > $i > $i > $i).
% 29.32/5.17 thf(func_def_351, type, sK52: $i > $i > $i > $i > $i).
% 29.32/5.17 thf(func_def_352, type, sK53: $i > $i > $i > $i > $i).
% 29.32/5.17 thf(func_def_353, type, sK54: $i > $i > $i > $i > $i).
% 29.32/5.17 thf(func_def_363, type, sK64: $i > $i > $i > $i).
% 29.32/5.17 thf(func_def_365, type, sK66: $i > $o).
% 29.32/5.17 thf(func_def_373, type, sK74: $i > $o).
% 29.32/5.17 thf(func_def_375, type, sK76: ($i > $o) > $i).
% 29.32/5.17 thf(func_def_376, type, sK77: ($i > $o) > $i).
% 29.32/5.17 thf(func_def_377, type, sK78: $i > $o).
% 29.32/5.17 thf(func_def_387, type, sK88: $i > $i > $o).
% 29.32/5.17 thf(func_def_392, type, sK93: $i > $o).
% 29.32/5.17 thf(func_def_393, type, sK94: ($i > $o) > $i).
% 29.32/5.17 thf(func_def_394, type, sK95: $i > $i > $o).
% 29.32/5.17 thf(func_def_396, type, sK97: $i > $i).
% 29.32/5.17 thf(func_def_397, type, sK98: $i > $i).
% 29.32/5.17 thf(func_def_398, type, sK99: $i > ($i > $i > $o) > $i).
% 29.32/5.17 thf(func_def_399, type, sK100: $i > ($i > $i > $o) > $i).
% 29.32/5.17 thf(func_def_400, type, sK101: $i > $i > ($i > $i > $o) > $i).
% 29.32/5.17 thf(func_def_405, type, sK106: $i > $i > $o).
% 29.32/5.17 thf(func_def_409, type, sK110: $i > $o).
% 29.32/5.17 thf(func_def_413, type, sK114: $i > $i > $o).
% 29.32/5.17 thf(func_def_434, type, sK135: ($i > $o) > $i > $i > $i > $i).
% 29.32/5.17 thf(func_def_435, type, sK136: ($i > $o) > $i > $i > $i > $i).
% 29.32/5.17 thf(func_def_439, type, sK140: $i > $o).
% 29.32/5.17 thf(func_def_449, type, sK150: ($i > $i) > $i > $i > $i).
% 29.32/5.17 thf(func_def_452, type, sK153: $i > $i).
% 29.32/5.17 thf(func_def_490, type, sK191: $i > $i > $o).
% 29.32/5.17 thf(func_def_491, type, sK192: $i > $i).
% 29.32/5.17 thf(func_def_508, type, sK209: $i > $i > $i > $i).
% 29.32/5.17 thf(func_def_533, type, sK234: $i > $i > $i > $i > $i).
% 29.32/5.17 thf(func_def_534, type, sK235: ($i > $o) > $i > $i).
% 29.32/5.17 thf(func_def_536, type, sK237: $i > $o).
% 29.32/5.17 thf(func_def_543, type, sK244: $i > $i > $i).
% 29.32/5.17 thf(func_def_554, type, sK255: $i > $o).
% 29.32/5.17 thf(func_def_558, type, sK259: $i > $i > $i).
% 29.32/5.17 thf(func_def_560, type, sK261: $i > $o).
% 29.32/5.17 thf(func_def_579, type, sK280: $i > $i).
% 29.32/5.17 thf(func_def_593, type, sK294: $i > $i > $o).
% 29.32/5.17 thf(func_def_598, type, sK299: $i > ($i > $o) > $i).
% 29.32/5.17 thf(func_def_599, type, sK300: $i > $o).
% 29.32/5.17 thf(func_def_604, type, sK305: $i > $i > $i).
% 29.32/5.17 thf(func_def_618, type, sK319: $i > $i).
% 29.32/5.17 thf(func_def_630, type, sK331: $i > $i > $i).
% 29.32/5.17 thf(func_def_631, type, sK332: $i > $i > $i).
% 29.32/5.17 thf(func_def_632, type, sK333: $i > $i > $i).
% 29.32/5.17 thf(func_def_633, type, sK334: $i > $i > $i).
% 29.32/5.17 thf(func_def_634, type, sK335: $i > $i > $i > $i).
% 29.32/5.17 thf(func_def_635, type, sK336: $i > $i).
% 29.32/5.17 thf(func_def_636, type, sK337: $i > $i).
% 29.32/5.17 thf(func_def_637, type, sK338: $i > $i).
% 29.32/5.17 thf(func_def_638, type, sK339: $i > $i).
% 29.32/5.17 thf(func_def_639, type, sK340: $i > $i > $i).
% 29.32/5.17 thf(func_def_640, type, sK341: $i > $i > $i > $i).
% 29.32/5.17 thf(func_def_641, type, sK342: $i > $i > $i > $i).
% 29.32/5.17 thf(func_def_642, type, sK343: $i > $i > $i).
% 29.32/5.17 thf(func_def_643, type, sK344: $i > $i > $i).
% 29.32/5.17 thf(func_def_645, type, sK346: $i > $i).
% 29.32/5.17 thf(func_def_646, type, sK347: $i > $i).
% 29.32/5.17 thf(func_def_647, type, sK348: $i > $i).
% 29.32/5.17 thf(func_def_648, type, sK349: $i > $i > $i).
% 29.32/5.17 thf(func_def_654, type, sK355: ($i > $o) > $i).
% 29.32/5.17 thf(func_def_655, type, sK356: $i > $o).
% 29.32/5.17 thf(func_def_656, type, sK357: $i > $i).
% 29.32/5.17 thf(func_def_660, type, sK361: $i > $i > $o).
% 29.32/5.17 thf(func_def_686, type, sK387: $i > $i > $i).
% 29.32/5.17 thf(func_def_699, type, sK400: $i > $o).
% 29.32/5.17 thf(func_def_701, type, sK402: ($i > $o) > $i > $i).
% 29.32/5.17 thf(func_def_729, type, sK430: $i > $o).
% 29.32/5.17 thf(func_def_731, type, sK432: ($i > $o) > $i > $i).
% 29.32/5.17 thf(func_def_732, type, sK433: ($i > $o) > $i > $i).
% 29.32/5.17 thf(func_def_733, type, sK434: $i > ($i > $o) > $i).
% 29.32/5.17 thf(func_def_734, type, sK435: $i > $o).
% 29.32/5.17 thf(func_def_737, type, sK438: ($i > $o) > $i > $i > $i > $i).
% 29.32/5.17 thf(func_def_738, type, sK439: ($i > $o) > $i > $i > $i > $i).
% 29.32/5.17 thf(func_def_742, type, sK443: $i > $o).
% 29.32/5.17 thf(func_def_746, type, sK447: $i > ($i > $o) > $i).
% 29.32/5.17 thf(func_def_747, type, sK448: $i > $o).
% 29.32/5.17 thf(func_def_760, type, sK461: $i > $i).
% 29.32/5.17 thf(func_def_762, type, sK463: $i > $i).
% 29.32/5.17 thf(func_def_766, type, sK467: $i > $i).
% 29.32/5.17 thf(func_def_768, type, sK469: ($i > $i) > $i > $i > $i).
% 29.32/5.17 thf(func_def_777, type, sK478: $i > $i > $i > $i > $i).
% 29.32/5.17 thf(func_def_778, type, sK479: $i > $i > $i > $i > $i).
% 29.32/5.17 thf(func_def_779, type, sK480: $i > $i > $i).
% 29.32/5.17 thf(func_def_782, type, sK483: $i > $o).
% 29.32/5.17 thf(func_def_791, type, sK492: $i > $i > $i).
% 29.32/5.17 thf(func_def_808, type, sK509: $i > $o).
% 29.32/5.17 thf(func_def_811, type, sK512: $i > ($i > $o) > $i).
% 29.32/5.17 thf(func_def_830, type, sK531: $i > $o).
% 29.32/5.17 thf(func_def_845, type, sK546: $i > $i > $i > $i > $i).
% 29.32/5.17 thf(func_def_870, type, sK571: $i > $i > $o).
% 29.32/5.17 thf(func_def_876, type, sK577: $i > $i > $i).
% 29.32/5.17 thf(func_def_877, type, sK578: $i > $i > $i).
% 29.32/5.17 thf(func_def_881, type, sK582: $i > $o).
% 29.32/5.17 thf(func_def_886, type, sK587: $i > $o).
% 29.32/5.17 thf(func_def_887, type, sK588: $i > $o).
% 29.32/5.17 thf(func_def_888, type, sK589: ($i > $o) > ($i > $o) > $i).
% 29.32/5.17 thf(func_def_889, type, sK590: ($i > $o) > ($i > $o) > $i).
% 29.32/5.17 thf(func_def_902, type, sK603: $i > $i > $i > $i).
% 29.32/5.17 thf(func_def_903, type, sK604: $i > $i > $i > $i).
% 29.32/5.17 thf(func_def_906, type, sK607: $i > $o).
% 29.32/5.17 thf(func_def_912, type, sK613: $i > $o).
% 29.32/5.17 thf(func_def_918, type, sK619: $i > $i).
% 29.32/5.17 thf(func_def_920, type, sK621: $i > ($i > $i) > $i > $i).
% 29.32/5.17 thf(func_def_923, type, sK624: $i > $i).
% 29.32/5.17 thf(func_def_928, type, sK629: $i > $o).
% 29.32/5.17 thf(func_def_930, type, sK631: $i > ($i > $o) > $i).
% 29.32/5.17 thf(func_def_931, type, sK632: ($i > $o) > $i > $i).
% 29.32/5.17 thf(func_def_933, type, sK634: $i > $o).
% 29.32/5.17 thf(func_def_945, type, sK646: $i > $i).
% 29.32/5.17 thf(func_def_947, type, sK648: ($i > $i) > $i > $i > $i).
% 29.32/5.17 thf(func_def_950, type, sK651: $i > $i).
% 29.32/5.17 thf(func_def_951, type, sK652: $i > ($i > $o) > $i > $i).
% 29.32/5.17 thf(func_def_953, type, sK654: $i > $o).
% 29.32/5.17 thf(func_def_957, type, sK658: $i > $i).
% 29.32/5.17 thf(func_def_960, type, sK661: $i > $i > ($i > $i) > $i).
% 29.32/5.17 thf(func_def_979, type, sK680: ($i > $o) > ($i > $o) > $i > $i > $i).
% 29.32/5.17 thf(func_def_980, type, sK681: ($i > $o) > ($i > $o) > $i > $i > $i).
% 29.32/5.17 thf(func_def_983, type, sK684: $i > $o).
% 29.32/5.17 thf(func_def_984, type, sK685: $i > $o).
% 29.32/5.17 thf(func_def_991, type, sK692: ($i > $o) > $i).
% 29.32/5.17 thf(func_def_992, type, sK693: $i > $o).
% 29.32/5.17 thf(func_def_993, type, sK694: $i > $i).
% 29.32/5.17 thf(func_def_1010, type, sK711: $i > $i > $i).
% 29.32/5.17 thf(func_def_1027, type, sK728: $i > $o).
% 29.32/5.17 thf(func_def_1029, type, sK730: $i > ($i > $o) > $i).
% 29.32/5.17 thf(func_def_1037, type, sK738: $i > $i).
% 29.32/5.17 thf(func_def_1039, type, sK740: ($i > $i) > $i > $i > $i).
% 29.32/5.17 thf(func_def_1040, type, sK741: $i > $i > $i).
% 29.32/5.17 thf(func_def_1056, type, sK757: $i > $o).
% 29.32/5.17 thf(func_def_1058, type, sK759: ($i > $o) > $i > $i).
% 29.32/5.17 thf(func_def_1059, type, sK760: ($i > $o) > $i > $i).
% 29.32/5.17 thf(func_def_1071, type, sK772: $o > $i > $i > $i).
% 29.32/5.17 thf(func_def_1080, type, ph781: !>[X0: $tType]:(X0)).
% 29.32/5.17 thf(f15015,plain,(
% 29.32/5.17 $false),
% 29.32/5.17 inference(subsumption_resolution,[status(thm)],[f15014,f2428])).
% 29.32/5.17 thf(f2428,plain,(
% 29.32/5.17 ((in @ sK71 @ (powerset @ sK70)) = $true)),
% 29.32/5.17 inference(cnf_transformation,[status(thm)],[f1204])).
% 29.32/5.17 thf(f1204,plain,(
% 29.32/5.17 (binunionLsub = $true) & (powersetTI1 = $true) & (doubleComplementE1 = $true) & (dpsetconstrI = $true) & (setminusER = $true) & (doubleComplementSub2 = $true) & (ap2apEq1 = $true) & (cartprodsndpairEq = $true) & (noeltsimpempty = $true) & (setukpairinjR2 = $true) & (prop2set2propI = $true) & (setukpairIL = $true) & (infuncsetfunc = $true) & (ifp = $true) & (funcImageSingleton = $true) & (setunion__Cong = $true) & (binintersectSubset4 = $true) & (upairsetE = $true) & (binintersectEL = $true) & (emptyinunitempty = $true) & (binintersectTELcontra = $true) & (subsetI2 = $true) & (kpairp = $true) & (dsetconstrEL = $true) & (emptyE1 = $true) & (setukpairinjL2 = $true) & (exu__Cong = $true) & (ex1I = $true) & (binunionRsub = $true) & (ex1E1 = $true) & (exuE1 = $true) & (setukpairinjL1 = $true) & (nonemptyI1 = $true) & (subsetTrans = $true) & (lam2p = $true) & (eqimpsubset1 = $true) & (exuI3 = $true) & (dpsetconstrER = $true) & (secondinupair = $true) & (iftrueProp2 = $true) & (singletoninpowerset = $true) & (setukpairinjR12 = $true) & (setminusI = $true) & (quantDeMorgan2 = $true) & (powerset__Cong = $true) & (upairsetIR = $true) & (notsubsetI = $true) & (emptyinPowerset = $true) & (funcGraphProp2 = $true) & (exuI2 = $true) & (emptyset__Cong = $true) & (powersetsubset = $true) & (inPowerset = $true) & (cartprodpairin = $true) & (funcext2 = $true) & (cartprodmempair1 = $true) & (theprop = $true) & (funcGraphProp1 = $true) & (emptyInPowerset = $true) & (ksndsingleton = $true) & (iffalseProp2 = $true) & (setadjoinOr = $true) & (bs114d = $true) & (setukpairinjR = $true) & (doubleComplementI1 = $true) & (ifSingleton = $true) & (exuE3e = $true) & (replAx = $true) & (subsetemptysetimpeq = $true) & (wellorderingAx = $true) & (binintersectSubset1 = $true) & (cartprodmempaircEq = $true) & (setunionsingleton1 = $true) & (setukpairinjR11 = $true) & (dsetconstr__Cong = $true) & (setminusERneg = $true) & (disjointsetsI1 = $true) & (nonemptyI = $true) & (cartprodpairmemER = $true) & (powersetTE1 = $true) & (kfstsingleton = $true) & (iffalseProp1 = $true) & (setunionsingleton2 = $true) & (setminusSubset1 = $true) & (setminusELneg = $true) & (subsetTI = $true) & (ubforcartprodlem2 = $true) & (powersetE = $true) & (ap2p = $true) & (eta1 = $true) & (binintersectT_lem = $true) & (funcGraphProp3 = $true) & (binintersectSubset3 = $true) & (setadjoinIL = $true) & (setukpairinjL = $true) & (setadjoinSub = $true) & (nonemptyImpWitness = $true) & (sepInPowerset = $true) & (upairequniteq = $true) & (setminusIRneg = $true) & (kpairiskpair = $true) & (notinemptyset = $true) & (subsetI1 = $true) & (binintersectRsub = $true) & (exuI1 = $true) & (upairset2IR = $true) & (cartprodmempair = $true) & (setextsub = $true) & (binunionIR = $true) & (binintersectER = $true) & (subbreln = $true) & (ap2apEq2 = $true) & (binunionE = $true) & (beta2 = $true) & (symdiffI1 = $true) & (powersetT_lem = $true) & (descrp = $true) & (setukpairinjR1 = $true) & (contrasubsetT2 = $true) & (omegaIndAx = $true) & (setunionI = $true) & (cartprodpairmemEL = $true) & (descr__Cong = $true) & (prop2setE = $true) & (dpsetconstrERa = $true) & (complementT_lem = $true) & (binintersectSubset2 = $true) & (emptysetAx = $true) & (symdiffE = $true) & (binunionT_lem = $true) & (setadjoinE = $true) & (powersetI1 = $true) & (cartprodfstpairEq = $true) & (theeq = $true) & (powersetI = $true) & (dpsetconstrEL1 = $true) & (quantDeMorgan4 = $true) & (notequalI2 = $true) & (binintersectTERcontra = $true) & (lam2lamEq = $true) & (setunionE = $true) & (eqinunit = $true) & (setminusILneg = $true) & (setext = $true) & (ubforcartprodlem1 = $true) & (dsetconstrI = $true) & (kpairsurjEq = $true) & (binunionEcases = $true) & (setOfPairsIsBReln = $true) & (apProp = $true) & (setminusSubset2 = $true) & (contrasubsetT = $true) & (funcGraphProp4 = $true) & (omegaSAx = $true) & (eqbreln = $true) & (emptysetimpfalse = $true) & (symdiffI2 = $true) & (setminusT_lem = $true) & (upairsubunion = $true) & (quantDeMorgan1 = $true) & (notdexE = $true) & (eqimpsubset2 = $true) & (ubforcartprodlem3 = $true) & (omega0Ax = $true) & (emptysetsubset = $true) & (sepSubset = $true) & (setadjoinSub2 = $true) & (iftrueProp1 = $true) & (setadjoinAx = $true) & (setextAx = $true) & (lamProp = $true) & (setunionAx = $true) & (setbeta = $true) & (contrasubsetT1 = $true) & (subset2powerset = $true) & (subsetE2 = $true) & (in__Cong = $true) & (symdiffIneg2 = $true) & (singletonsswitch = $true) & (setadjoinIR = $true) & (notdallE = $true) & (setoftrueEq = $true) & (singletonsubset = $true) & (exuE2 = $true) & (binunionIL = $true) & (dsetconstrER = $true) & (iftrueorfalse = $true) & (emptysetE = $true) & (omega__Cong = $true) & (doubleComplementSub1 = $true) & (powersetAx = $true) & (funcinfuncset = $true) & (symdiffIneg1 = $true) & (notequalI1 = $true) & (ex1E2 = $true) & (upairsetIL = $true) & (uniqinunit = $true) & (prop2setI = $true) & (((setminus @ sK70 @ (setminus @ sK70 @ sK71)) != sK71) & ((in @ sK71 @ (powerset @ sK70)) = $true)) & (app = $true) & (dpsetconstrSub = $true) & (emptyI = $true) & (subPowSU = $true) & (brelnall1 = $true) & (exuEu = $true) & (complementTE1 = $true) & (ex1I2 = $true) & (lamp = $true) & (iftrue = $true) & (singletonprop = $true) & (dpsetconstrEL2 = $true) & (eta2 = $true) & (ksndpairEq = $true) & (setunionE2 = $true) & (subsetRefl = $true) & (setminusEL = $true) & (funcextLem = $true) & (setadjoin__Cong = $true) & (setukpairIR = $true) & (cartprodsndin = $true) & (cartprodpairsurjEq = $true) & (singletoninpowunion = $true) & (binintersectI = $true) & (binintersectLsub = $true) & (contrasubsetT3 = $true) & (inCongP = $true) & (setextT = $true) & (complementTI1 = $true) & (binintersectSubset5 = $true) & (setminusLsub = $true) & (upairinpowunion = $true) & (upairset2E = $true) & (beta1 = $true) & (cartprodfstin = $true) & (iffalse = $true) & (notinsingleton = $true) & (quantDeMorgan3 = $true) & (subsetE = $true) & (singletonsuniq = $true) & (exuE3u = $true) & (vacuousDall = $true) & (foundationAx = $true) & (brelnall2 = $true) & (setunionsingleton = $true) & (powersetE1 = $true) & (funcext = $true) & (kfstpairEq = $true) & (nonemptyE1 = $true)),
% 29.32/5.17 inference(skolemisation,[status(esa),new_symbols(skolem,[sK70,sK71])],[f1020,f1203])).
% 29.32/5.17 thf(f1203,plain,(
% 29.32/5.17 ? [X0 : $i,X1 : $i] : (((setminus @ X0 @ (setminus @ X0 @ X1)) != X1) & ($true = (in @ X1 @ (powerset @ X0)))) => (((setminus @ sK70 @ (setminus @ sK70 @ sK71)) != sK71) & ((in @ sK71 @ (powerset @ sK70)) = $true))),
% 29.32/5.17 introduced(definition,[],[choice_axiom])).
% 29.32/5.17 thf(f1020,plain,(
% 29.32/5.17 (binunionLsub = $true) & (powersetTI1 = $true) & (doubleComplementE1 = $true) & (dpsetconstrI = $true) & (setminusER = $true) & (doubleComplementSub2 = $true) & (ap2apEq1 = $true) & (cartprodsndpairEq = $true) & (noeltsimpempty = $true) & (setukpairinjR2 = $true) & (prop2set2propI = $true) & (setukpairIL = $true) & (infuncsetfunc = $true) & (ifp = $true) & (funcImageSingleton = $true) & (setunion__Cong = $true) & (binintersectSubset4 = $true) & (upairsetE = $true) & (binintersectEL = $true) & (emptyinunitempty = $true) & (binintersectTELcontra = $true) & (subsetI2 = $true) & (kpairp = $true) & (dsetconstrEL = $true) & (emptyE1 = $true) & (setukpairinjL2 = $true) & (exu__Cong = $true) & (ex1I = $true) & (binunionRsub = $true) & (ex1E1 = $true) & (exuE1 = $true) & (setukpairinjL1 = $true) & (nonemptyI1 = $true) & (subsetTrans = $true) & (lam2p = $true) & (eqimpsubset1 = $true) & (exuI3 = $true) & (dpsetconstrER = $true) & (secondinupair = $true) & (iftrueProp2 = $true) & (singletoninpowerset = $true) & (setukpairinjR12 = $true) & (setminusI = $true) & (quantDeMorgan2 = $true) & (powerset__Cong = $true) & (upairsetIR = $true) & (notsubsetI = $true) & (emptyinPowerset = $true) & (funcGraphProp2 = $true) & (exuI2 = $true) & (emptyset__Cong = $true) & (powersetsubset = $true) & (inPowerset = $true) & (cartprodpairin = $true) & (funcext2 = $true) & (cartprodmempair1 = $true) & (theprop = $true) & (funcGraphProp1 = $true) & (emptyInPowerset = $true) & (ksndsingleton = $true) & (iffalseProp2 = $true) & (setadjoinOr = $true) & (bs114d = $true) & (setukpairinjR = $true) & (doubleComplementI1 = $true) & (ifSingleton = $true) & (exuE3e = $true) & (replAx = $true) & (subsetemptysetimpeq = $true) & (wellorderingAx = $true) & (binintersectSubset1 = $true) & (cartprodmempaircEq = $true) & (setunionsingleton1 = $true) & (setukpairinjR11 = $true) & (dsetconstr__Cong = $true) & (setminusERneg = $true) & (disjointsetsI1 = $true) & (nonemptyI = $true) & (cartprodpairmemER = $true) & (powersetTE1 = $true) & (kfstsingleton = $true) & (iffalseProp1 = $true) & (setunionsingleton2 = $true) & (setminusSubset1 = $true) & (setminusELneg = $true) & (subsetTI = $true) & (ubforcartprodlem2 = $true) & (powersetE = $true) & (ap2p = $true) & (eta1 = $true) & (binintersectT_lem = $true) & (funcGraphProp3 = $true) & (binintersectSubset3 = $true) & (setadjoinIL = $true) & (setukpairinjL = $true) & (setadjoinSub = $true) & (nonemptyImpWitness = $true) & (sepInPowerset = $true) & (upairequniteq = $true) & (setminusIRneg = $true) & (kpairiskpair = $true) & (notinemptyset = $true) & (subsetI1 = $true) & (binintersectRsub = $true) & (exuI1 = $true) & (upairset2IR = $true) & (cartprodmempair = $true) & (setextsub = $true) & (binunionIR = $true) & (binintersectER = $true) & (subbreln = $true) & (ap2apEq2 = $true) & (binunionE = $true) & (beta2 = $true) & (symdiffI1 = $true) & (powersetT_lem = $true) & (descrp = $true) & (setukpairinjR1 = $true) & (contrasubsetT2 = $true) & (omegaIndAx = $true) & (setunionI = $true) & (cartprodpairmemEL = $true) & (descr__Cong = $true) & (prop2setE = $true) & (dpsetconstrERa = $true) & (complementT_lem = $true) & (binintersectSubset2 = $true) & (emptysetAx = $true) & (symdiffE = $true) & (binunionT_lem = $true) & (setadjoinE = $true) & (powersetI1 = $true) & (cartprodfstpairEq = $true) & (theeq = $true) & (powersetI = $true) & (dpsetconstrEL1 = $true) & (quantDeMorgan4 = $true) & (notequalI2 = $true) & (binintersectTERcontra = $true) & (lam2lamEq = $true) & (setunionE = $true) & (eqinunit = $true) & (setminusILneg = $true) & (setext = $true) & (ubforcartprodlem1 = $true) & (dsetconstrI = $true) & (kpairsurjEq = $true) & (binunionEcases = $true) & (setOfPairsIsBReln = $true) & (apProp = $true) & (setminusSubset2 = $true) & (contrasubsetT = $true) & (funcGraphProp4 = $true) & (omegaSAx = $true) & (eqbreln = $true) & (emptysetimpfalse = $true) & (symdiffI2 = $true) & (setminusT_lem = $true) & (upairsubunion = $true) & (quantDeMorgan1 = $true) & (notdexE = $true) & (eqimpsubset2 = $true) & (ubforcartprodlem3 = $true) & (omega0Ax = $true) & (emptysetsubset = $true) & (sepSubset = $true) & (setadjoinSub2 = $true) & (iftrueProp1 = $true) & (setadjoinAx = $true) & (setextAx = $true) & (lamProp = $true) & (setunionAx = $true) & (setbeta = $true) & (contrasubsetT1 = $true) & (subset2powerset = $true) & (subsetE2 = $true) & (in__Cong = $true) & (symdiffIneg2 = $true) & (singletonsswitch = $true) & (setadjoinIR = $true) & (notdallE = $true) & (setoftrueEq = $true) & (singletonsubset = $true) & (exuE2 = $true) & (binunionIL = $true) & (dsetconstrER = $true) & (iftrueorfalse = $true) & (emptysetE = $true) & (omega__Cong = $true) & (doubleComplementSub1 = $true) & (powersetAx = $true) & (funcinfuncset = $true) & (symdiffIneg1 = $true) & (notequalI1 = $true) & (ex1E2 = $true) & (upairsetIL = $true) & (uniqinunit = $true) & (prop2setI = $true) & ? [X0 : $i,X1 : $i] : (((setminus @ X0 @ (setminus @ X0 @ X1)) != X1) & ($true = (in @ X1 @ (powerset @ X0)))) & (app = $true) & (dpsetconstrSub = $true) & (emptyI = $true) & (subPowSU = $true) & (brelnall1 = $true) & (exuEu = $true) & (complementTE1 = $true) & (ex1I2 = $true) & (lamp = $true) & (iftrue = $true) & (singletonprop = $true) & (dpsetconstrEL2 = $true) & (eta2 = $true) & (ksndpairEq = $true) & (setunionE2 = $true) & (subsetRefl = $true) & (setminusEL = $true) & (funcextLem = $true) & (setadjoin__Cong = $true) & (setukpairIR = $true) & (cartprodsndin = $true) & (cartprodpairsurjEq = $true) & (singletoninpowunion = $true) & (binintersectI = $true) & (binintersectLsub = $true) & (contrasubsetT3 = $true) & (inCongP = $true) & (setextT = $true) & (complementTI1 = $true) & (binintersectSubset5 = $true) & (setminusLsub = $true) & (upairinpowunion = $true) & (upairset2E = $true) & (beta1 = $true) & (cartprodfstin = $true) & (iffalse = $true) & (notinsingleton = $true) & (quantDeMorgan3 = $true) & (subsetE = $true) & (singletonsuniq = $true) & (exuE3u = $true) & (vacuousDall = $true) & (foundationAx = $true) & (brelnall2 = $true) & (setunionsingleton = $true) & (powersetE1 = $true) & (funcext = $true) & (kfstpairEq = $true) & (nonemptyE1 = $true)),
% 29.32/5.17 inference(flattening,[status(thm)],[f1019])).
% 29.32/5.17 thf(f1019,plain,(
% 29.32/5.17 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (((setminus @ X0 @ (setminus @ X0 @ X1)) != X1) & ($true = (in @ X1 @ (powerset @ X0)))) & (doubleComplementSub2 = $true)) & (doubleComplementSub1 = $true)) & (doubleComplementE1 = $true)) & (doubleComplementI1 = $true)) & (contrasubsetT3 = $true)) & (contrasubsetT2 = $true)) & (contrasubsetT1 = $true)) & (contrasubsetT = $true)) & (binintersectTERcontra = $true)) & (binintersectTELcontra = $true)) & (complementTE1 = $true)) & (complementTI1 = $true)) & (powersetTE1 = $true)) & (powersetTI1 = $true)) & (subsetTI = $true)) & (setextT = $true)) & (complementT_lem = $true)) & (setminusT_lem = $true)) & (powersetT_lem = $true)) & (binunionT_lem = $true)) & (binintersectT_lem = $true)) & (iftrueorfalse = $true)) & (iffalse = $true)) & (iftrue = $true)) & (theeq = $true)) & (ifp = $true)) & (ifSingleton = $true)) & (iftrueProp2 = $true)) & (iftrueProp1 = $true)) & (iffalseProp2 = $true)) & (iffalseProp1 = $true)) & (eta2 = $true)) & (beta2 = $true)) & (lam2lamEq = $true)) & (eta1 = $true)) & (beta1 = $true)) & (ap2apEq2 = $true)) & (ap2apEq1 = $true)) & (funcext2 = $true)) & (funcext = $true)) & (eqbreln = $true)) & (subbreln = $true)) & (funcGraphProp4 = $true)) & (funcextLem = $true)) & (funcGraphProp2 = $true)) & (funcGraphProp3 = $true)) & (funcGraphProp1 = $true)) & (ex1E2 = $true)) & (brelnall2 = $true)) & (brelnall1 = $true)) & (lam2p = $true)) & (lamp = $true)) & (lamProp = $true)) & (funcinfuncset = $true)) & (ap2p = $true)) & (infuncsetfunc = $true)) & (app = $true)) & (apProp = $true)) & (funcImageSingleton = $true)) & (dpsetconstrER = $true)) & (dpsetconstrEL2 = $true)) & (dpsetconstrEL1 = $true)) & (dpsetconstrERa = $true)) & (setOfPairsIsBReln = $true)) & (dpsetconstrSub = $true)) & (dpsetconstrI = $true)) & (cartprodpairsurjEq = $true)) & (cartprodsndpairEq = $true)) & (cartprodfstpairEq = $true)) & (cartprodmempaircEq = $true)) & (cartprodpairmemER = $true)) & (cartprodpairmemEL = $true)) & (cartprodsndin = $true)) & (kpairsurjEq = $true)) & (ksndpairEq = $true)) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (setukpairinjR2 = $true)) & (upairequniteq = $true)) & (setukpairinjR1 = $true)) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 29.32/5.17 inference(ennf_transformation,[status(thm)],[f401])).
% 29.32/5.17 thf(f401,plain,(
% 29.32/5.17 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ((upairequniteq = $true) => ((setukpairinjR2 = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ((ksndpairEq = $true) => ((kpairsurjEq = $true) => ((cartprodsndin = $true) => ((cartprodpairmemEL = $true) => ((cartprodpairmemER = $true) => ((cartprodmempaircEq = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ((cartprodpairsurjEq = $true) => ((dpsetconstrI = $true) => ((dpsetconstrSub = $true) => ((setOfPairsIsBReln = $true) => ((dpsetconstrERa = $true) => ((dpsetconstrEL1 = $true) => ((dpsetconstrEL2 = $true) => ((dpsetconstrER = $true) => ((funcImageSingleton = $true) => ((apProp = $true) => ((app = $true) => ((infuncsetfunc = $true) => ((ap2p = $true) => ((funcinfuncset = $true) => ((lamProp = $true) => ((lamp = $true) => ((lam2p = $true) => ((brelnall1 = $true) => ((brelnall2 = $true) => ((ex1E2 = $true) => ((funcGraphProp1 = $true) => ((funcGraphProp3 = $true) => ((funcGraphProp2 = $true) => ((funcextLem = $true) => ((funcGraphProp4 = $true) => ((subbreln = $true) => ((eqbreln = $true) => ((funcext = $true) => ((funcext2 = $true) => ((ap2apEq1 = $true) => ((ap2apEq2 = $true) => ((beta1 = $true) => ((eta1 = $true) => ((lam2lamEq = $true) => ((beta2 = $true) => ((eta2 = $true) => ((iffalseProp1 = $true) => ((iffalseProp2 = $true) => ((iftrueProp1 = $true) => ((iftrueProp2 = $true) => ((ifSingleton = $true) => ((ifp = $true) => ((theeq = $true) => ((iftrue = $true) => ((iffalse = $true) => ((iftrueorfalse = $true) => ((binintersectT_lem = $true) => ((binunionT_lem = $true) => ((powersetT_lem = $true) => ((setminusT_lem = $true) => ((complementT_lem = $true) => ((setextT = $true) => ((subsetTI = $true) => ((powersetTI1 = $true) => ((powersetTE1 = $true) => ((complementTI1 = $true) => ((complementTE1 = $true) => ((binintersectTELcontra = $true) => ((binintersectTERcontra = $true) => ((contrasubsetT = $true) => ((contrasubsetT1 = $true) => ((contrasubsetT2 = $true) => ((contrasubsetT3 = $true) => ((doubleComplementI1 = $true) => ((doubleComplementE1 = $true) => ((doubleComplementSub1 = $true) => ((doubleComplementSub2 = $true) => ! [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (powerset @ X0))) => ((setminus @ X0 @ (setminus @ X0 @ X1)) = X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 29.32/5.17 inference(fool_elimination,[status(thm)],[f400])).
% 29.32/5.17 thf(f400,plain,(
% 29.32/5.17 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ((setminus @ X0 @ (setminus @ X0 @ X1)) = X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 29.32/5.17 inference(rectify,[status(thm)],[f253])).
% 29.32/5.17 thf(f253,negated_conjecture,(
% 29.32/5.17 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => ! [X3 : $i,X11 : $i] : ((in @ X11 @ (powerset @ X3)) => ((setminus @ X3 @ (setminus @ X3 @ X11)) = X11)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 29.32/5.17 inference(negated_conjecture,[status(cth)],[f252])).
% 29.32/5.17 thf(f252,conjecture,(
% 29.32/5.17 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => ! [X3 : $i,X11 : $i] : ((in @ X11 @ (powerset @ X3)) => ((setminus @ X3 @ (setminus @ X3 @ X11)) = X11))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 29.32/5.17 file('/export/starexec/sandbox/tmp/tmp.dOeEUbrAIn/DTF2THF_3484.p',doubleComplementEq)).
% 29.32/5.17 thf(f15014,plain,(
% 29.32/5.17 ((in @ sK71 @ (powerset @ sK70)) != $true)),
% 29.32/5.17 inference(trivial_inequality_removal,[status(thm)],[f15001])).
% 29.32/5.17 thf(f15001,plain,(
% 29.32/5.17 (sK71 != sK71) | ((in @ sK71 @ (powerset @ sK70)) != $true)),
% 29.32/5.17 inference(superposition,[status(thm)],[f2429,f11161])).
% 29.32/5.17 thf(f11161,plain,(
% 29.32/5.17 ( ! [X0 : $i,X1 : $i] : (((setminus @ X1 @ (setminus @ X1 @ X0)) = X0) | ((in @ X0 @ (powerset @ X1)) != $true)) )),
% 29.32/5.17 inference(subsumption_resolution,[status(thm)],[f11160,f4837])).
% 29.32/5.17 thf(f4837,plain,(
% 29.32/5.17 ( ! [X0 : $i,X1 : $i] : (((subset @ (setminus @ X0 @ (setminus @ X0 @ X1)) @ X1) = $true) | ($true != (in @ X1 @ (powerset @ X0)))) )),
% 29.32/5.17 inference(trivial_inequality_removal,[status(thm)],[f3953])).
% 29.32/5.17 thf(f3953,plain,(
% 29.32/5.17 ( ! [X0 : $i,X1 : $i] : (((subset @ (setminus @ X0 @ (setminus @ X0 @ X1)) @ X1) = $true) | ($true != $true) | ($true != (in @ X1 @ (powerset @ X0)))) )),
% 29.32/5.17 inference(definition_unfolding,[status(thm)],[f2974,f2622])).
% 29.32/5.17 thf(f2622,plain,(
% 29.32/5.17 (doubleComplementSub2 = $true)),
% 29.32/5.17 inference(cnf_transformation,[status(thm)],[f1204])).
% 29.32/5.17 thf(f2974,plain,(
% 29.32/5.17 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (powerset @ X0))) | ((subset @ (setminus @ X0 @ (setminus @ X0 @ X1)) @ X1) = $true) | (doubleComplementSub2 != $true)) )),
% 29.32/5.17 inference(cnf_transformation,[status(thm)],[f1613])).
% 29.32/5.17 thf(f1613,plain,(
% 29.32/5.17 (! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (powerset @ X0))) | ((subset @ (setminus @ X0 @ (setminus @ X0 @ X1)) @ X1) = $true)) | (doubleComplementSub2 != $true)) & ((doubleComplementSub2 = $true) | (($true = (in @ sK330 @ (powerset @ sK329))) & ((subset @ (setminus @ sK329 @ (setminus @ sK329 @ sK330)) @ sK330) != $true)))),
% 29.32/5.17 inference(skolemisation,[status(esa),new_symbols(skolem,[sK329,sK330])],[f1611,f1612])).
% 29.32/5.17 thf(f1612,plain,(
% 29.32/5.17 ? [X2 : $i,X3 : $i] : (($true = (in @ X3 @ (powerset @ X2))) & ((subset @ (setminus @ X2 @ (setminus @ X2 @ X3)) @ X3) != $true)) => (($true = (in @ sK330 @ (powerset @ sK329))) & ((subset @ (setminus @ sK329 @ (setminus @ sK329 @ sK330)) @ sK330) != $true))),
% 29.32/5.17 introduced(definition,[],[choice_axiom])).
% 29.32/5.17 thf(f1611,plain,(
% 29.32/5.17 (! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (powerset @ X0))) | ((subset @ (setminus @ X0 @ (setminus @ X0 @ X1)) @ X1) = $true)) | (doubleComplementSub2 != $true)) & ((doubleComplementSub2 = $true) | ? [X2 : $i,X3 : $i] : (($true = (in @ X3 @ (powerset @ X2))) & ((subset @ (setminus @ X2 @ (setminus @ X2 @ X3)) @ X3) != $true)))),
% 29.32/5.17 inference(rectify,[status(thm)],[f1610])).
% 29.32/5.17 thf(f1610,plain,(
% 29.32/5.17 (! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (powerset @ X0))) | ((subset @ (setminus @ X0 @ (setminus @ X0 @ X1)) @ X1) = $true)) | (doubleComplementSub2 != $true)) & ((doubleComplementSub2 = $true) | ? [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (powerset @ X0))) & ((subset @ (setminus @ X0 @ (setminus @ X0 @ X1)) @ X1) != $true)))),
% 29.32/5.17 inference(nnf_transformation,[status(thm)],[f814])).
% 29.32/5.17 thf(f814,plain,(
% 29.32/5.17 ! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (powerset @ X0))) | ((subset @ (setminus @ X0 @ (setminus @ X0 @ X1)) @ X1) = $true)) <=> (doubleComplementSub2 = $true)),
% 29.32/5.17 inference(ennf_transformation,[status(thm)],[f493])).
% 29.32/5.17 thf(f493,plain,(
% 29.32/5.17 (doubleComplementSub2 = $true) <=> ! [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (powerset @ X0))) => ((subset @ (setminus @ X0 @ (setminus @ X0 @ X1)) @ X1) = $true))),
% 29.32/5.17 inference(fool_elimination,[status(thm)],[f492])).
% 29.32/5.17 thf(f492,plain,(
% 29.32/5.17 (doubleComplementSub2 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ (setminus @ X0 @ (setminus @ X0 @ X1)) @ X1)))),
% 29.32/5.17 inference(rectify,[status(thm)],[f251])).
% 29.32/5.17 thf(f251,axiom,(
% 29.32/5.17 (doubleComplementSub2 = ! [X3 : $i,X11 : $i] : ((in @ X11 @ (powerset @ X3)) => (subset @ (setminus @ X3 @ (setminus @ X3 @ X11)) @ X11)))),
% 29.32/5.17 file('/export/starexec/sandbox/tmp/tmp.dOeEUbrAIn/DTF2THF_3484.p',doubleComplementSub2)).
% 29.32/5.17 thf(f11160,plain,(
% 29.32/5.17 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) != $true) | ((setminus @ X1 @ (setminus @ X1 @ X0)) = X0) | ($true != (subset @ (setminus @ X1 @ (setminus @ X1 @ X0)) @ X0))) )),
% 29.32/5.17 inference(trivial_inequality_removal,[status(thm)],[f11159])).
% 29.32/5.17 thf(f11159,plain,(
% 29.32/5.17 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true != (subset @ (setminus @ X1 @ (setminus @ X1 @ X0)) @ X0)) | ((in @ X0 @ (powerset @ X1)) != $true) | ((setminus @ X1 @ (setminus @ X1 @ X0)) = X0)) )),
% 29.32/5.17 inference(superposition,[status(thm)],[f4684,f4628])).
% 29.32/5.17 thf(f4628,plain,(
% 29.32/5.17 ( ! [X0 : $i,X1 : $i] : (((subset @ X1 @ (setminus @ X0 @ (setminus @ X0 @ X1))) = $true) | ($true != (in @ X1 @ (powerset @ X0)))) )),
% 29.32/5.17 inference(trivial_inequality_removal,[status(thm)],[f4398])).
% 29.32/5.17 thf(f4398,plain,(
% 29.32/5.17 ( ! [X0 : $i,X1 : $i] : (((subset @ X1 @ (setminus @ X0 @ (setminus @ X0 @ X1))) = $true) | ($true != $true) | ($true != (in @ X1 @ (powerset @ X0)))) )),
% 29.32/5.17 inference(definition_unfolding,[status(thm)],[f3458,f2438])).
% 29.32/5.17 thf(f2438,plain,(
% 29.32/5.17 (doubleComplementSub1 = $true)),
% 29.32/5.17 inference(cnf_transformation,[status(thm)],[f1204])).
% 29.32/5.17 thf(f3458,plain,(
% 29.32/5.17 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (powerset @ X0))) | ((subset @ X1 @ (setminus @ X0 @ (setminus @ X0 @ X1))) = $true) | (doubleComplementSub1 != $true)) )),
% 29.32/5.17 inference(cnf_transformation,[status(thm)],[f2174])).
% 29.32/5.17 thf(f2174,plain,(
% 29.32/5.17 (! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (powerset @ X0))) | ((subset @ X1 @ (setminus @ X0 @ (setminus @ X0 @ X1))) = $true)) | (doubleComplementSub1 != $true)) & ((doubleComplementSub1 = $true) | (((in @ sK710 @ (powerset @ sK709)) = $true) & ($true != (subset @ sK710 @ (setminus @ sK709 @ (setminus @ sK709 @ sK710))))))),
% 29.32/5.17 inference(skolemisation,[status(esa),new_symbols(skolem,[sK709,sK710])],[f2172,f2173])).
% 29.32/5.17 thf(f2173,plain,(
% 29.32/5.17 ? [X2 : $i,X3 : $i] : (($true = (in @ X3 @ (powerset @ X2))) & ($true != (subset @ X3 @ (setminus @ X2 @ (setminus @ X2 @ X3))))) => (((in @ sK710 @ (powerset @ sK709)) = $true) & ($true != (subset @ sK710 @ (setminus @ sK709 @ (setminus @ sK709 @ sK710)))))),
% 29.32/5.17 introduced(definition,[],[choice_axiom])).
% 29.32/5.17 thf(f2172,plain,(
% 29.32/5.17 (! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (powerset @ X0))) | ((subset @ X1 @ (setminus @ X0 @ (setminus @ X0 @ X1))) = $true)) | (doubleComplementSub1 != $true)) & ((doubleComplementSub1 = $true) | ? [X2 : $i,X3 : $i] : (($true = (in @ X3 @ (powerset @ X2))) & ($true != (subset @ X3 @ (setminus @ X2 @ (setminus @ X2 @ X3))))))),
% 29.32/5.17 inference(rectify,[status(thm)],[f2171])).
% 29.32/5.17 thf(f2171,plain,(
% 29.32/5.17 (! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (powerset @ X0))) | ((subset @ X1 @ (setminus @ X0 @ (setminus @ X0 @ X1))) = $true)) | (doubleComplementSub1 != $true)) & ((doubleComplementSub1 = $true) | ? [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (powerset @ X0))) & ((subset @ X1 @ (setminus @ X0 @ (setminus @ X0 @ X1))) != $true)))),
% 29.32/5.17 inference(nnf_transformation,[status(thm)],[f831])).
% 29.32/5.17 thf(f831,plain,(
% 29.32/5.17 ! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (powerset @ X0))) | ((subset @ X1 @ (setminus @ X0 @ (setminus @ X0 @ X1))) = $true)) <=> (doubleComplementSub1 = $true)),
% 29.32/5.17 inference(ennf_transformation,[status(thm)],[f549])).
% 29.32/5.17 thf(f549,plain,(
% 29.32/5.17 (doubleComplementSub1 = $true) <=> ! [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (powerset @ X0))) => ((subset @ X1 @ (setminus @ X0 @ (setminus @ X0 @ X1))) = $true))),
% 29.32/5.17 inference(fool_elimination,[status(thm)],[f548])).
% 29.32/5.17 thf(f548,plain,(
% 29.32/5.17 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ X1 @ (setminus @ X0 @ (setminus @ X0 @ X1)))) = doubleComplementSub1)),
% 29.32/5.17 inference(rectify,[status(thm)],[f250])).
% 29.32/5.17 thf(f250,axiom,(
% 29.32/5.17 (! [X3 : $i,X11 : $i] : ((in @ X11 @ (powerset @ X3)) => (subset @ X11 @ (setminus @ X3 @ (setminus @ X3 @ X11)))) = doubleComplementSub1)),
% 29.32/5.17 file('/export/starexec/sandbox/tmp/tmp.dOeEUbrAIn/DTF2THF_3484.p',doubleComplementSub1)).
% 29.32/5.17 thf(f4684,plain,(
% 29.32/5.17 ( ! [X0 : $i,X1 : $i] : (($true != (subset @ X1 @ X0)) | ($true != (subset @ X0 @ X1)) | (X0 = X1)) )),
% 29.32/5.17 inference(trivial_inequality_removal,[status(thm)],[f4093])).
% 29.32/5.17 thf(f4093,plain,(
% 29.32/5.17 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true != (subset @ X1 @ X0)) | ($true != (subset @ X0 @ X1)) | (X0 = X1)) )),
% 29.32/5.17 inference(definition_unfolding,[status(thm)],[f3154,f2520])).
% 29.32/5.17 thf(f2520,plain,(
% 29.32/5.17 (setextsub = $true)),
% 29.32/5.17 inference(cnf_transformation,[status(thm)],[f1204])).
% 29.32/5.17 thf(f3154,plain,(
% 29.32/5.17 ( ! [X0 : $i,X1 : $i] : (($true != (subset @ X0 @ X1)) | ($true != (subset @ X1 @ X0)) | (X0 = X1) | (setextsub != $true)) )),
% 29.32/5.17 inference(cnf_transformation,[status(thm)],[f1808])).
% 29.32/5.17 thf(f1808,plain,(
% 29.32/5.17 (! [X0 : $i,X1 : $i] : (($true != (subset @ X0 @ X1)) | ($true != (subset @ X1 @ X0)) | (X0 = X1)) | (setextsub != $true)) & ((setextsub = $true) | (((subset @ sK459 @ sK460) = $true) & ($true = (subset @ sK460 @ sK459)) & (sK460 != sK459)))),
% 29.32/5.17 inference(skolemisation,[status(esa),new_symbols(skolem,[sK459,sK460])],[f1806,f1807])).
% 29.32/5.17 thf(f1807,plain,(
% 29.32/5.17 ? [X2 : $i,X3 : $i] : (((subset @ X2 @ X3) = $true) & ((subset @ X3 @ X2) = $true) & (X2 != X3)) => (((subset @ sK459 @ sK460) = $true) & ($true = (subset @ sK460 @ sK459)) & (sK460 != sK459))),
% 29.32/5.17 introduced(definition,[],[choice_axiom])).
% 29.32/5.17 thf(f1806,plain,(
% 29.32/5.17 (! [X0 : $i,X1 : $i] : (($true != (subset @ X0 @ X1)) | ($true != (subset @ X1 @ X0)) | (X0 = X1)) | (setextsub != $true)) & ((setextsub = $true) | ? [X2 : $i,X3 : $i] : (((subset @ X2 @ X3) = $true) & ((subset @ X3 @ X2) = $true) & (X2 != X3)))),
% 29.32/5.17 inference(rectify,[status(thm)],[f1805])).
% 29.32/5.17 thf(f1805,plain,(
% 29.32/5.17 (! [X0 : $i,X1 : $i] : (($true != (subset @ X0 @ X1)) | ($true != (subset @ X1 @ X0)) | (X0 = X1)) | (setextsub != $true)) & ((setextsub = $true) | ? [X0 : $i,X1 : $i] : (($true = (subset @ X0 @ X1)) & ($true = (subset @ X1 @ X0)) & (X0 != X1)))),
% 29.32/5.17 inference(nnf_transformation,[status(thm)],[f936])).
% 29.32/5.17 thf(f936,plain,(
% 29.32/5.17 ! [X0 : $i,X1 : $i] : (($true != (subset @ X0 @ X1)) | ($true != (subset @ X1 @ X0)) | (X0 = X1)) <=> (setextsub = $true)),
% 29.32/5.17 inference(flattening,[status(thm)],[f935])).
% 29.32/5.17 thf(f935,plain,(
% 29.32/5.17 (setextsub = $true) <=> ! [X0 : $i,X1 : $i] : (((X0 = X1) | ($true != (subset @ X1 @ X0))) | ($true != (subset @ X0 @ X1)))),
% 29.32/5.17 inference(ennf_transformation,[status(thm)],[f640])).
% 29.32/5.17 thf(f640,plain,(
% 29.32/5.17 (setextsub = $true) <=> ! [X0 : $i,X1 : $i] : (($true = (subset @ X0 @ X1)) => (($true = (subset @ X1 @ X0)) => (X0 = X1)))),
% 29.32/5.17 inference(fool_elimination,[status(thm)],[f639])).
% 29.32/5.17 thf(f639,plain,(
% 29.32/5.17 (setextsub = ! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X0) => (X0 = X1))))),
% 29.32/5.17 inference(rectify,[status(thm)],[f93])).
% 29.32/5.17 thf(f93,axiom,(
% 29.32/5.17 (setextsub = ! [X3 : $i,X4 : $i] : ((subset @ X3 @ X4) => ((subset @ X4 @ X3) => (X3 = X4))))),
% 29.32/5.17 file('/export/starexec/sandbox/tmp/tmp.dOeEUbrAIn/DTF2THF_3484.p',setextsub)).
% 29.32/5.17 thf(f2429,plain,(
% 29.32/5.17 ((setminus @ sK70 @ (setminus @ sK70 @ sK71)) != sK71)),
% 29.32/5.17 inference(cnf_transformation,[status(thm)],[f1204])).
% 29.32/5.17 % SZS output end Proof for DTF2THF_3484
% 29.32/5.17 % (4083)------------------------------
% 29.32/5.17 % (4083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.32/5.17 % (4083)Termination reason: Refutation
% 29.32/5.17
% 29.32/5.17 % (4083)Memory used [KB]: 14200
% 29.32/5.17 % (4083)Time elapsed: 1.371 s
% 29.32/5.17 % (4083)Instructions burned: 4307 (million)
% 29.32/5.17 % (4083)------------------------------
% 29.32/5.17 % (4083)------------------------------
% 29.32/5.17 % (3680)Success in time 3.95 s
%------------------------------------------------------------------------------