%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU764^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.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 09:37:00 AM UTC 2026
% Result : Theorem 9.49s 2.72s
% Output : Refutation 9.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of formulae : 78 ( 19 unt; 0 typ; 2 def)
% Number of atoms : 5300 (1380 equ; 0 cnn)
% Maximal formula atoms : 285 ( 67 avg)
% Number of connectives : 3727 ( 131 ~; 94 |; 917 &;1413 @)
% ( 8 <=>;1164 =>; 0 <=; 0 <~>)
% Maximal formula depth : 293 ( 30 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 487 ( 484 usr; 298 con; 0-4 aty)
% Number of variables : 152 ( 0 ^; 92 !; 60 ?; 152 :)
% 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_334,type,
sP2: $i > $i > $i > $o ).
thf(func_def_335,type,
sP3: $i > $i > $i > $i > $o ).
thf(func_def_338,type,
sP6: $i > $i > $o ).
thf(func_def_339,type,
sP7: $i > $o ).
thf(func_def_340,type,
sP8: $i > $i > $o ).
thf(func_def_341,type,
sP9: $i > $i > $o ).
thf(func_def_343,type,
sP11: $i > $i > $i > $o > $o ).
thf(func_def_345,type,
sK13: $i > $i > $i ).
thf(func_def_362,type,
sK30: $i > $i > $i > $i ).
thf(func_def_363,type,
sK31: $i > $i > $i > $i ).
thf(func_def_378,type,
sK46: $i > $o ).
thf(func_def_393,type,
sK61: $i > ( $i > $i ) > $i > $i ).
thf(func_def_395,type,
sK63: $i > $i ).
thf(func_def_406,type,
sK74: $i > $o ).
thf(func_def_427,type,
sK95: $i > $i ).
thf(func_def_429,type,
sK97: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_430,type,
sK98: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_434,type,
sK102: $i > $o ).
thf(func_def_449,type,
sK117: $i > $i > $i > $i > $i ).
thf(func_def_454,type,
sK122: ( $i > $o ) > $i > $i ).
thf(func_def_456,type,
sK124: $i > $o ).
thf(func_def_459,type,
sK127: $i > $i ).
thf(func_def_482,type,
sK150: $i > $o ).
thf(func_def_489,type,
sK157: $i > ( $i > $o ) > $i ).
thf(func_def_490,type,
sK158: $i > $o ).
thf(func_def_497,type,
sK165: $i > $i > $o ).
thf(func_def_506,type,
sK174: $i > $i > $i ).
thf(func_def_511,type,
sK179: $i > $i ).
thf(func_def_515,type,
sK183: $i > $i > $i ).
thf(func_def_531,type,
sK199: $i > $i > $i ).
thf(func_def_557,type,
sK225: $i > $i ).
thf(func_def_558,type,
sK226: $i > $i ).
thf(func_def_573,type,
sK241: $i > $o ).
thf(func_def_574,type,
sK242: $i > $o ).
thf(func_def_575,type,
sK243: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_576,type,
sK244: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_584,type,
sK252: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_585,type,
sK253: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_586,type,
sK254: $i > $o ).
thf(func_def_587,type,
sK255: $i > $o ).
thf(func_def_589,type,
sK257: $i > $i ).
thf(func_def_591,type,
sK259: $i > ( $i > $i ) > $i > $i ).
thf(func_def_600,type,
sK268: $i > $o ).
thf(func_def_610,type,
sK278: $i > $o ).
thf(func_def_613,type,
sK281: $i > $i > ( $i > $o ) > $i ).
thf(func_def_614,type,
sK282: $i > $o ).
thf(func_def_618,type,
sK286: ( $i > $o ) > $i ).
thf(func_def_619,type,
sK287: $i > $o ).
thf(func_def_620,type,
sK288: $i > $i ).
thf(func_def_623,type,
sK291: $i > $i > $i ).
thf(func_def_624,type,
sK292: $i > $i > $i ).
thf(func_def_645,type,
sK313: $i > $i > $i > $i > $i ).
thf(func_def_674,type,
sK342: $i > $i > $i > $i > $i ).
thf(func_def_675,type,
sK343: $i > $i > $i > $i > $i ).
thf(func_def_683,type,
sK351: $i > $i > $i > $i ).
thf(func_def_687,type,
sK355: $i > $i > $i > $i ).
thf(func_def_698,type,
sK366: $i > $o ).
thf(func_def_699,type,
sK367: $i > $o ).
thf(func_def_700,type,
sK368: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_701,type,
sK369: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_712,type,
sK380: $i > $o ).
thf(func_def_714,type,
sK382: ( $i > $o ) > $i > $i ).
thf(func_def_723,type,
sK391: $i > $o ).
thf(func_def_725,type,
sK393: ( $i > $o ) > $i ).
thf(func_def_726,type,
sK394: ( $i > $o ) > $i ).
thf(func_def_741,type,
sK409: $i > $i > ( $i > $i ) > $i ).
thf(func_def_742,type,
sK410: $i > $i ).
thf(func_def_751,type,
sK419: $i > $o ).
thf(func_def_762,type,
sK430: $i > $i ).
thf(func_def_781,type,
sK449: ( $i > $o ) > $i > $i ).
thf(func_def_783,type,
sK451: $i > $o ).
thf(func_def_806,type,
sK474: $i > $i > $i ).
thf(func_def_835,type,
sK503: $i > $o ).
thf(func_def_839,type,
sK507: $i > $i > $o ).
thf(func_def_853,type,
sK521: ( $i > $o ) > $i > $i ).
thf(func_def_855,type,
sK523: $i > $o ).
thf(func_def_860,type,
sK528: $i > $o ).
thf(func_def_862,type,
sK530: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_863,type,
sK531: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_864,type,
sK532: $i > $o ).
thf(func_def_867,type,
sK535: $i > $o ).
thf(func_def_869,type,
sK537: ( $i > $o ) > $i > $i ).
thf(func_def_871,type,
sK539: $i > $o ).
thf(func_def_874,type,
sK542: $i > ( $i > $o ) > $i ).
thf(func_def_915,type,
sK583: $i > $o ).
thf(func_def_917,type,
sK585: $i > ( $i > $o ) > $i ).
thf(func_def_922,type,
sK590: $i > $i > $i > $i > $i ).
thf(func_def_923,type,
sK591: $i > $i > $i > $i > $i ).
thf(func_def_924,type,
sK592: $i > $i > $i > $i > $i ).
thf(func_def_925,type,
sK593: $i > $i > $i > $i > $i ).
thf(func_def_927,type,
sK595: $i > $o ).
thf(func_def_929,type,
sK597: ( $i > $o ) > $i > $i ).
thf(func_def_930,type,
sK598: ( $i > $o ) > $i > $i ).
thf(func_def_931,type,
sK599: $i > ( $i > $o ) > $i ).
thf(func_def_932,type,
sK600: $i > $o ).
thf(func_def_937,type,
sK605: ( $i > $o ) > $i ).
thf(func_def_938,type,
sK606: $i > $o ).
thf(func_def_940,type,
sK608: $i > $i > $o ).
thf(func_def_948,type,
sK616: $o > $i > $i > $i ).
thf(func_def_970,type,
sK638: $i > $o ).
thf(func_def_987,type,
sK655: $i > $i > $i ).
thf(func_def_988,type,
sK656: $i > $i > $i ).
thf(func_def_989,type,
sK657: $i > $i > $i ).
thf(func_def_990,type,
sK658: $i > $i > $i ).
thf(func_def_991,type,
sK659: $i > $i > $i > $i ).
thf(func_def_992,type,
sK660: $i > $i ).
thf(func_def_993,type,
sK661: $i > $i ).
thf(func_def_994,type,
sK662: $i > $i ).
thf(func_def_995,type,
sK663: $i > $i ).
thf(func_def_996,type,
sK664: $i > $i > $i > $i ).
thf(func_def_997,type,
sK665: $i > $i > $i > $i ).
thf(func_def_998,type,
sK666: $i > $i > $i ).
thf(func_def_999,type,
sK667: $i > $i > $i ).
thf(func_def_1000,type,
sK668: $i > $i > $i ).
thf(func_def_1002,type,
sK670: $i > $i ).
thf(func_def_1003,type,
sK671: $i > $i ).
thf(func_def_1004,type,
sK672: $i > $i ).
thf(func_def_1005,type,
sK673: $i > $i > $i ).
thf(func_def_1013,type,
sK681: $i > $i > $i > $i ).
thf(func_def_1019,type,
sK687: $i > $o ).
thf(func_def_1021,type,
sK689: ( $i > $o ) > $i > $i ).
thf(func_def_1022,type,
sK690: ( $i > $o ) > $i > $i ).
thf(func_def_1032,type,
sK700: $i > $i > $o ).
thf(func_def_1039,type,
sK707: $i > $i > $i ).
thf(func_def_1040,type,
sK708: $i > $i > $i ).
thf(func_def_1047,type,
sK715: $i > $i ).
thf(func_def_1048,type,
sK716: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1057,type,
sK725: $i > $o ).
thf(func_def_1063,type,
sK731: $i > $i > $o ).
thf(func_def_1075,type,
sK743: $i > $i > $i > $i ).
thf(func_def_1084,type,
sK752: $i > $i ).
thf(func_def_1098,type,
sK766: $i > $o ).
thf(func_def_1129,type,
sK797: $i > $i > $o ).
thf(func_def_1130,type,
sK798: $i > $i ).
thf(func_def_1131,type,
sK799: $i > $i ).
thf(func_def_1132,type,
sK800: ( $i > $i > $o ) > $i > $i ).
thf(func_def_1133,type,
sK801: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_1134,type,
sK802: ( $i > $i > $o ) > $i > $i ).
thf(func_def_1149,type,
sK817: $i > $i > $o ).
thf(func_def_1152,type,
sK820: $i > $i > $i ).
thf(func_def_1162,type,
sK830: $i > $o ).
thf(func_def_1182,type,
sK850: $i > $o ).
thf(func_def_1183,type,
sK851: $i > $i ).
thf(func_def_1184,type,
sK852: ( $i > $o ) > $i ).
thf(func_def_1185,type,
sK853: $i > $o ).
thf(func_def_1192,type,
sK860: $i > $i > $i > $i > $i ).
thf(func_def_1219,type,
sK887: $i > $i ).
thf(func_def_1221,type,
sK889: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1231,type,
sK899: $i > $i > $o ).
thf(func_def_1234,type,
sK902: $i > $i ).
thf(func_def_1237,type,
sK905: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1246,type,
ph914:
!>[X0: $tType] : X0 ).
thf(f4460,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f4408,f4430,f4457]) ).
thf(f4457,plain,
spl913_8,
inference(avatar_contradiction_clause,[status(thm)],[f4456]) ).
thf(f4456,plain,
( $false
| spl913_8 ),
inference(subsumption_resolution,[status(thm)],[f4455,f2798]) ).
thf(f2798,plain,
( ( in @ sK27 @ ( powerset @ sK26 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f1287]) ).
thf(f1287,plain,
( ( doubleComplementEq = $true )
& ( dpsetconstrEL1 = $true )
& ( demorgan2 = $true )
& ( theeq = $true )
& ( binintersectT_lem = $true )
& ( setminusILneg = $true )
& ( singletonprop = $true )
& ( contraSubsetComplement = $true )
& ( setukpairinjR12 = $true )
& ( setadjoinIR = $true )
& ( ifSingleton = $true )
& ( iffalse = $true )
& ( setoftrueEq = $true )
& ( ap2apEq2 = $true )
& ( subsetI1 = $true )
& ( cartprodpairsurjEq = $true )
& ( descr__Cong = $true )
& ( emptyinPowerset = $true )
& ( powersetE = $true )
& ( eqinunit = $true )
& ( powersetTE1 = $true )
& ( eta2 = $true )
& ( quantDeMorgan4 = $true )
& ( exuE3e = $true )
& ( eqimpsubset1 = $true )
& ( nonemptyI1 = $true )
& ( woz13rule2 = $true )
& ( ubforcartprodlem2 = $true )
& ( nonemptyE1 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( woz13rule0 = $true )
& ( setminusEL = $true )
& ( quantDeMorgan1 = $true )
& ( binintersectSubset4 = $true )
& ( setadjoinE = $true )
& ( nonemptyImpWitness = $true )
& ( cartprodmempaircEq = $true )
& ( prop2set2propI = $true )
& ( subsetI2 = $true )
& ( kpairsurjEq = $true )
& ( funcinfuncset = $true )
& ( setminusERneg = $true )
& ( singletoninpowerset = $true )
& ( powersetI1 = $true )
& ( powersetTI1 = $true )
& ( dpsetconstrSub = $true )
& ( prop2setE = $true )
& ( setminusELneg = $true )
& ( singletonsswitch = $true )
& ( emptyE1 = $true )
& ( quantDeMorgan3 = $true )
& ( app = $true )
& ( setukpairinjR = $true )
& ( demorgan2b = $true )
& ( woz13rule1 = $true )
& ( symdiffI1 = $true )
& ( setukpairIL = $true )
& ( binunionTIRcontra = $true )
& ( cartprodsndin = $true )
& ( ap2p = $true )
& ( setunionE = $true )
& ( funcImageSingleton = $true )
& ( setminusT_lem = $true )
& ( setunionsingleton = $true )
& ( subsetTrans = $true )
& ( emptyinunitempty = $true )
& ( dsetconstrER = $true )
& ( upairsetIR = $true )
& ( complementTcontraSubset = $true )
& ( demorgan1 = $true )
& ( setadjoinAx = $true )
& ( binunionRsub = $true )
& ( setadjoinIL = $true )
& ( setminusSubset2 = $true )
& ( binunionE = $true )
& ( noeltsimpempty = $true )
& ( beta2 = $true )
& ( iftrue = $true )
& ( inPowerset = $true )
& ( notdallE = $true )
& ( sepInPowerset = $true )
& ( notequalI1 = $true )
& ( uniqinunit = $true )
& ( powersetT_lem = $true )
& ( setminusLsub = $true )
& ( demorgan2a2 = $true )
& ( binintersectSubset5 = $true )
& ( dpsetconstrI = $true )
& ( cartprodfstin = $true )
& ( binintersectSubset2 = $true )
& ( cartprodmempair = $true )
& ( complementTnotintersectT = $true )
& ( symdiffIneg2 = $true )
& ( replAx = $true )
& ( setminusER = $true )
& ( notdexE = $true )
& ( subsetemptysetimpeq = $true )
& ( setukpairIR = $true )
& ( setbeta = $true )
& ( woz13rule4 = $true )
& ( binunionT_lem = $true )
& ( setextT = $true )
& ( setOfPairsIsBReln = $true )
& ( subsetRefl = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( setukpairinjL1 = $true )
& ( symdiffI2 = $true )
& ( subPowSU = $true )
& ( exuE3u = $true )
& ( binintersectRsub = $true )
& ( emptyI = $true )
& ( subsetE2 = $true )
& ( bs114d = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( binintersectLsub = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( dpsetconstrEL2 = $true )
& ( prop2setI = $true )
& ( lam2p = $true )
& ( setukpairinjL2 = $true )
& ( complementTE1 = $true )
& ( singletonsuniq = $true )
& ( contrasubsetT1 = $true )
& ( notinemptyset = $true )
& ( emptyset__Cong = $true )
& ( powersetI = $true )
& ( setminusI = $true )
& ( setextAx = $true )
& ( demorgan2b2 = $true )
& ( singletonsubset = $true )
& ( setunionI = $true )
& ( funcGraphProp2 = $true )
& ( nonemptyI = $true )
& ( funcext2 = $true )
& ( exu__Cong = $true )
& ( binunionLsub = $true )
& ( inIntersectImpInUnion2 = $true )
& ( ubforcartprodlem3 = $true )
& ( upairsetIL = $true )
& ( binintersectTERcontra = $true )
& ( eqbreln = $true )
& ( subset2powerset = $true )
& ( funcGraphProp3 = $true )
& ( powersetAx = $true )
& ( binintersectSubset1 = $true )
& ( lam2lamEq = $true )
& ( subbreln = $true )
& ( ( in @ sK29 @ ( powerset @ sK26 ) )
= $true )
& ( ( setminus @ sK26 @ ( binintersect @ ( binunion @ sK25 @ sK27 ) @ ( binunion @ sK28 @ sK29 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK26 @ sK25 ) @ ( setminus @ sK26 @ sK27 ) ) @ ( binintersect @ ( setminus @ sK26 @ sK28 ) @ ( setminus @ sK26 @ sK29 ) ) ) )
& ( ( in @ sK28 @ ( powerset @ sK26 ) )
= $true )
& ( ( in @ sK27 @ ( powerset @ sK26 ) )
= $true )
& ( ( in @ sK25 @ ( powerset @ sK26 ) )
= $true )
& ( binunionIL = $true )
& ( theprop = $true )
& ( notequalI2 = $true )
& ( disjointsetsI1 = $true )
& ( iffalseProp2 = $true )
& ( iftrueProp1 = $true )
& ( kpairp = $true )
& ( kfstsingleton = $true )
& ( demorgan1a = $true )
& ( upairequniteq = $true )
& ( brelnall2 = $true )
& ( dsetconstr__Cong = $true )
& ( upairsetE = $true )
& ( quantDeMorgan2 = $true )
& ( setadjoin__Cong = $true )
& ( subsetE = $true )
& ( ap2apEq1 = $true )
& ( ksndpairEq = $true )
& ( setextsub = $true )
& ( exuI1 = $true )
& ( dsetconstrEL = $true )
& ( binintersectER = $true )
& ( complementImpComplementIntersect = $true )
& ( eta1 = $true )
& ( ex1E1 = $true )
& ( wellorderingAx = $true )
& ( cartprodpairin = $true )
& ( iffalseProp1 = $true )
& ( omega__Cong = $true )
& ( doubleComplementI1 = $true )
& ( doubleComplementSub2 = $true )
& ( setunion__Cong = $true )
& ( emptysetAx = $true )
& ( ifp = $true )
& ( omegaSAx = $true )
& ( setunionsingleton2 = $true )
& ( secondinupair = $true )
& ( setadjoinSub2 = $true )
& ( beta1 = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairmemER = $true )
& ( exuE1 = $true )
& ( cartprodpairmemEL = $true )
& ( in__Cong = $true )
& ( descrp = $true )
& ( setukpairinjR1 = $true )
& ( complementT_lem = $true )
& ( ksndsingleton = $true )
& ( powersetE1 = $true )
& ( setext = $true )
& ( lamProp = $true )
& ( inIntersectImpInUnion = $true )
& ( emptyInPowerset = $true )
& ( setunionAx = $true )
& ( notsubsetI = $true )
& ( woz13rule3 = $true )
& ( demorgan2a = $true )
& ( exuI2 = $true )
& ( apProp = $true )
& ( exuI3 = $true )
& ( setunionE2 = $true )
& ( foundationAx = $true )
& ( symdiffIneg1 = $true )
& ( brelnall1 = $true )
& ( setunionsingleton1 = $true )
& ( powersetsubset = $true )
& ( powerset__Cong = $true )
& ( binintersectI = $true )
& ( cartprodfstpairEq = $true )
& ( setukpairinjR2 = $true )
& ( doubleComplementE1 = $true )
& ( omegaIndAx = $true )
& ( binunionIR = $true )
& ( emptysetsubset = $true )
& ( singletoninpowunion = $true )
& ( contrasubsetT = $true )
& ( binunionTILcontra = $true )
& ( funcGraphProp1 = $true )
& ( binunionEcases = $true )
& ( setadjoinOr = $true )
& ( cartprodsndpairEq = $true )
& ( setukpairinjR11 = $true )
& ( doubleComplementSub1 = $true )
& ( binintersectEL = $true )
& ( symdiffE = $true )
& ( setukpairinjL = $true )
& ( exuE2 = $true )
& ( funcGraphProp4 = $true )
& ( binunionTEcontra = $true )
& ( demorgan1b = $true )
& ( infuncsetfunc = $true )
& ( dsetconstrI = $true )
& ( notinsingleton = $true )
& ( upairsubunion = $true )
& ( sepSubset = $true )
& ( ex1I2 = $true )
& ( iftrueProp2 = $true )
& ( binunionTE = $true )
& ( upairinpowunion = $true )
& ( complementTI1 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( contrasubsetT2 = $true )
& ( demorgan2a1 = $true )
& ( lamp = $true )
& ( iftrueorfalse = $true )
& ( vacuousDall = $true )
& ( ubforcartprodlem1 = $true )
& ( funcextLem = $true )
& ( subsetTI = $true )
& ( dpsetconstrERa = $true )
& ( upairset2E = $true )
& ( setadjoinSub = $true )
& ( omega0Ax = $true )
& ( exuEu = $true )
& ( dpsetconstrER = $true )
& ( contrasubsetT3 = $true )
& ( complementSubsetComplementIntersect = $true )
& ( funcext = $true )
& ( kfstpairEq = $true )
& ( setminusIRneg = $true )
& ( eqimpsubset2 = $true )
& ( kpairiskpair = $true )
& ( setminusSubset1 = $true )
& ( ex1I = $true )
& ( emptysetimpfalse = $true )
& ( binintersectTELcontra = $true )
& ( emptysetE = $true )
& ( binintersectSubset3 = $true )
& ( upairset2IR = $true )
& ( woz1_1 = $true )
& ( ex1E2 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( inCongP = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26,sK27,sK28,sK29])],[f1200,f1286,f1285,f1284,f1283]) ).
thf(f1283,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ ( powerset @ X1 ) )
= $true )
& ( ( setminus @ X1 @ ( binintersect @ ( binunion @ X0 @ X2 ) @ ( binunion @ X3 @ X4 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) @ ( binintersect @ ( setminus @ X1 @ X3 ) @ ( setminus @ X1 @ X4 ) ) ) ) )
& ( ( in @ X3 @ ( powerset @ X1 ) )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
=> ( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ ( powerset @ sK26 ) )
= $true )
& ( ( setminus @ sK26 @ ( binintersect @ ( binunion @ sK25 @ X2 ) @ ( binunion @ X3 @ X4 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK26 @ sK25 ) @ ( setminus @ sK26 @ X2 ) ) @ ( binintersect @ ( setminus @ sK26 @ X3 ) @ ( setminus @ sK26 @ X4 ) ) ) ) )
& ( ( in @ X3 @ ( powerset @ sK26 ) )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK26 ) ) ) )
& ( ( in @ sK25 @ ( powerset @ sK26 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1284,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ ( powerset @ sK26 ) )
= $true )
& ( ( setminus @ sK26 @ ( binintersect @ ( binunion @ sK25 @ X2 ) @ ( binunion @ X3 @ X4 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK26 @ sK25 ) @ ( setminus @ sK26 @ X2 ) ) @ ( binintersect @ ( setminus @ sK26 @ X3 ) @ ( setminus @ sK26 @ X4 ) ) ) ) )
& ( ( in @ X3 @ ( powerset @ sK26 ) )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK26 ) ) ) )
=> ( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ ( powerset @ sK26 ) )
= $true )
& ( ( binunion @ ( binintersect @ ( setminus @ sK26 @ sK25 ) @ ( setminus @ sK26 @ sK27 ) ) @ ( binintersect @ ( setminus @ sK26 @ X3 ) @ ( setminus @ sK26 @ X4 ) ) )
!= ( setminus @ sK26 @ ( binintersect @ ( binunion @ sK25 @ sK27 ) @ ( binunion @ X3 @ X4 ) ) ) ) )
& ( ( in @ X3 @ ( powerset @ sK26 ) )
= $true ) )
& ( ( in @ sK27 @ ( powerset @ sK26 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1285,plain,
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ ( powerset @ sK26 ) )
= $true )
& ( ( binunion @ ( binintersect @ ( setminus @ sK26 @ sK25 ) @ ( setminus @ sK26 @ sK27 ) ) @ ( binintersect @ ( setminus @ sK26 @ X3 ) @ ( setminus @ sK26 @ X4 ) ) )
!= ( setminus @ sK26 @ ( binintersect @ ( binunion @ sK25 @ sK27 ) @ ( binunion @ X3 @ X4 ) ) ) ) )
& ( ( in @ X3 @ ( powerset @ sK26 ) )
= $true ) )
=> ( ? [X4: $i] :
( ( ( in @ X4 @ ( powerset @ sK26 ) )
= $true )
& ( ( binunion @ ( binintersect @ ( setminus @ sK26 @ sK25 ) @ ( setminus @ sK26 @ sK27 ) ) @ ( binintersect @ ( setminus @ sK26 @ sK28 ) @ ( setminus @ sK26 @ X4 ) ) )
!= ( setminus @ sK26 @ ( binintersect @ ( binunion @ sK25 @ sK27 ) @ ( binunion @ sK28 @ X4 ) ) ) ) )
& ( ( in @ sK28 @ ( powerset @ sK26 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1286,plain,
( ? [X4: $i] :
( ( ( in @ X4 @ ( powerset @ sK26 ) )
= $true )
& ( ( binunion @ ( binintersect @ ( setminus @ sK26 @ sK25 ) @ ( setminus @ sK26 @ sK27 ) ) @ ( binintersect @ ( setminus @ sK26 @ sK28 ) @ ( setminus @ sK26 @ X4 ) ) )
!= ( setminus @ sK26 @ ( binintersect @ ( binunion @ sK25 @ sK27 ) @ ( binunion @ sK28 @ X4 ) ) ) ) )
=> ( ( ( in @ sK29 @ ( powerset @ sK26 ) )
= $true )
& ( ( setminus @ sK26 @ ( binintersect @ ( binunion @ sK25 @ sK27 ) @ ( binunion @ sK28 @ sK29 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK26 @ sK25 ) @ ( setminus @ sK26 @ sK27 ) ) @ ( binintersect @ ( setminus @ sK26 @ sK28 ) @ ( setminus @ sK26 @ sK29 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1200,plain,
( ( doubleComplementEq = $true )
& ( dpsetconstrEL1 = $true )
& ( demorgan2 = $true )
& ( theeq = $true )
& ( binintersectT_lem = $true )
& ( setminusILneg = $true )
& ( singletonprop = $true )
& ( contraSubsetComplement = $true )
& ( setukpairinjR12 = $true )
& ( setadjoinIR = $true )
& ( ifSingleton = $true )
& ( iffalse = $true )
& ( setoftrueEq = $true )
& ( ap2apEq2 = $true )
& ( subsetI1 = $true )
& ( cartprodpairsurjEq = $true )
& ( descr__Cong = $true )
& ( emptyinPowerset = $true )
& ( powersetE = $true )
& ( eqinunit = $true )
& ( powersetTE1 = $true )
& ( eta2 = $true )
& ( quantDeMorgan4 = $true )
& ( exuE3e = $true )
& ( eqimpsubset1 = $true )
& ( nonemptyI1 = $true )
& ( woz13rule2 = $true )
& ( ubforcartprodlem2 = $true )
& ( nonemptyE1 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( woz13rule0 = $true )
& ( setminusEL = $true )
& ( quantDeMorgan1 = $true )
& ( binintersectSubset4 = $true )
& ( setadjoinE = $true )
& ( nonemptyImpWitness = $true )
& ( cartprodmempaircEq = $true )
& ( prop2set2propI = $true )
& ( subsetI2 = $true )
& ( kpairsurjEq = $true )
& ( funcinfuncset = $true )
& ( setminusERneg = $true )
& ( singletoninpowerset = $true )
& ( powersetI1 = $true )
& ( powersetTI1 = $true )
& ( dpsetconstrSub = $true )
& ( prop2setE = $true )
& ( setminusELneg = $true )
& ( singletonsswitch = $true )
& ( emptyE1 = $true )
& ( quantDeMorgan3 = $true )
& ( app = $true )
& ( setukpairinjR = $true )
& ( demorgan2b = $true )
& ( woz13rule1 = $true )
& ( symdiffI1 = $true )
& ( setukpairIL = $true )
& ( binunionTIRcontra = $true )
& ( cartprodsndin = $true )
& ( ap2p = $true )
& ( setunionE = $true )
& ( funcImageSingleton = $true )
& ( setminusT_lem = $true )
& ( setunionsingleton = $true )
& ( subsetTrans = $true )
& ( emptyinunitempty = $true )
& ( dsetconstrER = $true )
& ( upairsetIR = $true )
& ( complementTcontraSubset = $true )
& ( demorgan1 = $true )
& ( setadjoinAx = $true )
& ( binunionRsub = $true )
& ( setadjoinIL = $true )
& ( setminusSubset2 = $true )
& ( binunionE = $true )
& ( noeltsimpempty = $true )
& ( beta2 = $true )
& ( iftrue = $true )
& ( inPowerset = $true )
& ( notdallE = $true )
& ( sepInPowerset = $true )
& ( notequalI1 = $true )
& ( uniqinunit = $true )
& ( powersetT_lem = $true )
& ( setminusLsub = $true )
& ( demorgan2a2 = $true )
& ( binintersectSubset5 = $true )
& ( dpsetconstrI = $true )
& ( cartprodfstin = $true )
& ( binintersectSubset2 = $true )
& ( cartprodmempair = $true )
& ( complementTnotintersectT = $true )
& ( symdiffIneg2 = $true )
& ( replAx = $true )
& ( setminusER = $true )
& ( notdexE = $true )
& ( subsetemptysetimpeq = $true )
& ( setukpairIR = $true )
& ( setbeta = $true )
& ( woz13rule4 = $true )
& ( binunionT_lem = $true )
& ( setextT = $true )
& ( setOfPairsIsBReln = $true )
& ( subsetRefl = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( setukpairinjL1 = $true )
& ( symdiffI2 = $true )
& ( subPowSU = $true )
& ( exuE3u = $true )
& ( binintersectRsub = $true )
& ( emptyI = $true )
& ( subsetE2 = $true )
& ( bs114d = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( binintersectLsub = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( dpsetconstrEL2 = $true )
& ( prop2setI = $true )
& ( lam2p = $true )
& ( setukpairinjL2 = $true )
& ( complementTE1 = $true )
& ( singletonsuniq = $true )
& ( contrasubsetT1 = $true )
& ( notinemptyset = $true )
& ( emptyset__Cong = $true )
& ( powersetI = $true )
& ( setminusI = $true )
& ( setextAx = $true )
& ( demorgan2b2 = $true )
& ( singletonsubset = $true )
& ( setunionI = $true )
& ( funcGraphProp2 = $true )
& ( nonemptyI = $true )
& ( funcext2 = $true )
& ( exu__Cong = $true )
& ( binunionLsub = $true )
& ( inIntersectImpInUnion2 = $true )
& ( ubforcartprodlem3 = $true )
& ( upairsetIL = $true )
& ( binintersectTERcontra = $true )
& ( eqbreln = $true )
& ( subset2powerset = $true )
& ( funcGraphProp3 = $true )
& ( powersetAx = $true )
& ( binintersectSubset1 = $true )
& ( lam2lamEq = $true )
& ( subbreln = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ ( powerset @ X1 ) )
= $true )
& ( ( setminus @ X1 @ ( binintersect @ ( binunion @ X0 @ X2 ) @ ( binunion @ X3 @ X4 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) @ ( binintersect @ ( setminus @ X1 @ X3 ) @ ( setminus @ X1 @ X4 ) ) ) ) )
& ( ( in @ X3 @ ( powerset @ X1 ) )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( binunionIL = $true )
& ( theprop = $true )
& ( notequalI2 = $true )
& ( disjointsetsI1 = $true )
& ( iffalseProp2 = $true )
& ( iftrueProp1 = $true )
& ( kpairp = $true )
& ( kfstsingleton = $true )
& ( demorgan1a = $true )
& ( upairequniteq = $true )
& ( brelnall2 = $true )
& ( dsetconstr__Cong = $true )
& ( upairsetE = $true )
& ( quantDeMorgan2 = $true )
& ( setadjoin__Cong = $true )
& ( subsetE = $true )
& ( ap2apEq1 = $true )
& ( ksndpairEq = $true )
& ( setextsub = $true )
& ( exuI1 = $true )
& ( dsetconstrEL = $true )
& ( binintersectER = $true )
& ( complementImpComplementIntersect = $true )
& ( eta1 = $true )
& ( ex1E1 = $true )
& ( wellorderingAx = $true )
& ( cartprodpairin = $true )
& ( iffalseProp1 = $true )
& ( omega__Cong = $true )
& ( doubleComplementI1 = $true )
& ( doubleComplementSub2 = $true )
& ( setunion__Cong = $true )
& ( emptysetAx = $true )
& ( ifp = $true )
& ( omegaSAx = $true )
& ( setunionsingleton2 = $true )
& ( secondinupair = $true )
& ( setadjoinSub2 = $true )
& ( beta1 = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairmemER = $true )
& ( exuE1 = $true )
& ( cartprodpairmemEL = $true )
& ( in__Cong = $true )
& ( descrp = $true )
& ( setukpairinjR1 = $true )
& ( complementT_lem = $true )
& ( ksndsingleton = $true )
& ( powersetE1 = $true )
& ( setext = $true )
& ( lamProp = $true )
& ( inIntersectImpInUnion = $true )
& ( emptyInPowerset = $true )
& ( setunionAx = $true )
& ( notsubsetI = $true )
& ( woz13rule3 = $true )
& ( demorgan2a = $true )
& ( exuI2 = $true )
& ( apProp = $true )
& ( exuI3 = $true )
& ( setunionE2 = $true )
& ( foundationAx = $true )
& ( symdiffIneg1 = $true )
& ( brelnall1 = $true )
& ( setunionsingleton1 = $true )
& ( powersetsubset = $true )
& ( powerset__Cong = $true )
& ( binintersectI = $true )
& ( cartprodfstpairEq = $true )
& ( setukpairinjR2 = $true )
& ( doubleComplementE1 = $true )
& ( omegaIndAx = $true )
& ( binunionIR = $true )
& ( emptysetsubset = $true )
& ( singletoninpowunion = $true )
& ( contrasubsetT = $true )
& ( binunionTILcontra = $true )
& ( funcGraphProp1 = $true )
& ( binunionEcases = $true )
& ( setadjoinOr = $true )
& ( cartprodsndpairEq = $true )
& ( setukpairinjR11 = $true )
& ( doubleComplementSub1 = $true )
& ( binintersectEL = $true )
& ( symdiffE = $true )
& ( setukpairinjL = $true )
& ( exuE2 = $true )
& ( funcGraphProp4 = $true )
& ( binunionTEcontra = $true )
& ( demorgan1b = $true )
& ( infuncsetfunc = $true )
& ( dsetconstrI = $true )
& ( notinsingleton = $true )
& ( upairsubunion = $true )
& ( sepSubset = $true )
& ( ex1I2 = $true )
& ( iftrueProp2 = $true )
& ( binunionTE = $true )
& ( upairinpowunion = $true )
& ( complementTI1 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( contrasubsetT2 = $true )
& ( demorgan2a1 = $true )
& ( lamp = $true )
& ( iftrueorfalse = $true )
& ( vacuousDall = $true )
& ( ubforcartprodlem1 = $true )
& ( funcextLem = $true )
& ( subsetTI = $true )
& ( dpsetconstrERa = $true )
& ( upairset2E = $true )
& ( setadjoinSub = $true )
& ( omega0Ax = $true )
& ( exuEu = $true )
& ( dpsetconstrER = $true )
& ( contrasubsetT3 = $true )
& ( complementSubsetComplementIntersect = $true )
& ( funcext = $true )
& ( kfstpairEq = $true )
& ( setminusIRneg = $true )
& ( eqimpsubset2 = $true )
& ( kpairiskpair = $true )
& ( setminusSubset1 = $true )
& ( ex1I = $true )
& ( emptysetimpfalse = $true )
& ( binintersectTELcontra = $true )
& ( emptysetE = $true )
& ( binintersectSubset3 = $true )
& ( upairset2IR = $true )
& ( woz1_1 = $true )
& ( ex1E2 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( inCongP = $true ) ),
inference(flattening,[status(thm)],[f1199]) ).
thf(f1199,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ ( powerset @ X1 ) )
= $true )
& ( ( setminus @ X1 @ ( binintersect @ ( binunion @ X0 @ X2 ) @ ( binunion @ X3 @ X4 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) @ ( binintersect @ ( setminus @ X1 @ X3 ) @ ( setminus @ X1 @ X4 ) ) ) ) )
& ( ( in @ X3 @ ( powerset @ X1 ) )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( woz1_1 = $true )
& ( woz13rule4 = $true )
& ( woz13rule3 = $true )
& ( woz13rule2 = $true )
& ( woz13rule1 = $true )
& ( woz13rule0 = $true )
& ( demorgan2 = $true )
& ( demorgan2b = $true )
& ( demorgan2b2 = $true )
& ( demorgan2a = $true )
& ( demorgan1 = $true )
& ( demorgan1b = $true )
& ( demorgan1a = $true )
& ( demorgan2a2 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( demorgan2a1 = $true )
& ( binunionTEcontra = $true )
& ( binunionTE = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( inIntersectImpInUnion2 = $true )
& ( inIntersectImpInUnion = $true )
& ( binunionTIRcontra = $true )
& ( binunionTILcontra = $true )
& ( complementTcontraSubset = $true )
& ( contraSubsetComplement = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( complementSubsetComplementIntersect = $true )
& ( complementImpComplementIntersect = $true )
& ( complementTnotintersectT = $true )
& ( doubleComplementEq = $true )
& ( 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)],[f614]) ).
thf(f614,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 )
=> ( ( doubleComplementEq = $true )
=> ( ( complementTnotintersectT = $true )
=> ( ( complementImpComplementIntersect = $true )
=> ( ( complementSubsetComplementIntersect = $true )
=> ( ( complementInPowersetComplementIntersect = $true )
=> ( ( contraSubsetComplement = $true )
=> ( ( complementTcontraSubset = $true )
=> ( ( binunionTILcontra = $true )
=> ( ( binunionTIRcontra = $true )
=> ( ( inIntersectImpInUnion = $true )
=> ( ( inIntersectImpInUnion2 = $true )
=> ( ( inIntersectImpInIntersectUnions = $true )
=> ( ( intersectInPowersetIntersectUnions = $true )
=> ( ( inComplementUnionImpNotIn1 = $true )
=> ( ( inComplementUnionImpInComplement1 = $true )
=> ( ( binunionTE = $true )
=> ( ( binunionTEcontra = $true )
=> ( ( demorgan2a1 = $true )
=> ( ( complementUnionInPowersetComplement = $true )
=> ( ( demorgan2a2 = $true )
=> ( ( demorgan1a = $true )
=> ( ( demorgan1b = $true )
=> ( ( demorgan1 = $true )
=> ( ( demorgan2a = $true )
=> ( ( demorgan2b2 = $true )
=> ( ( demorgan2b = $true )
=> ( ( demorgan2 = $true )
=> ( ( woz13rule0 = $true )
=> ( ( woz13rule1 = $true )
=> ( ( woz13rule2 = $true )
=> ( ( woz13rule3 = $true )
=> ( ( woz13rule4 = $true )
=> ( ( woz1_1 = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X1 ) )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ ( powerset @ X1 ) )
= $true )
=> ( ( setminus @ X1 @ ( binintersect @ ( binunion @ X0 @ X2 ) @ ( binunion @ X3 @ X4 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) @ ( binintersect @ ( setminus @ X1 @ X3 ) @ ( setminus @ X1 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f613]) ).
thf(f613,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
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ( setminus @ X1 @ ( binintersect @ ( binunion @ X0 @ X2 ) @ ( binunion @ X3 @ X4 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) ) @ ( binintersect @ ( setminus @ X1 @ X3 ) @ ( setminus @ X1 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f286]) ).
thf(f286,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
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ! [X11: $i,X3: $i] :
( ( in @ X11 @ ( powerset @ X3 ) )
=> ! [X16: $i] :
( ( in @ X16 @ ( powerset @ X3 ) )
=> ! [X17: $i] :
( ( in @ X17 @ ( powerset @ X3 ) )
=> ! [X18: $i] :
( ( in @ X18 @ ( powerset @ X3 ) )
=> ( ( setminus @ X3 @ ( binintersect @ ( binunion @ X11 @ X16 ) @ ( binunion @ X17 @ X18 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ X3 @ X11 ) @ ( setminus @ X3 @ X16 ) ) @ ( binintersect @ ( setminus @ X3 @ X17 ) @ ( setminus @ X3 @ X18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f285]) ).
thf(f285,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ! [X11: $i,X3: $i] :
( ( in @ X11 @ ( powerset @ X3 ) )
=> ! [X16: $i] :
( ( in @ X16 @ ( powerset @ X3 ) )
=> ! [X17: $i] :
( ( in @ X17 @ ( powerset @ X3 ) )
=> ! [X18: $i] :
( ( in @ X18 @ ( powerset @ X3 ) )
=> ( ( setminus @ X3 @ ( binintersect @ ( binunion @ X11 @ X16 ) @ ( binunion @ X17 @ X18 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ X3 @ X11 ) @ ( setminus @ X3 @ X16 ) ) @ ( binintersect @ ( setminus @ X3 @ X17 ) @ ( setminus @ X3 @ X18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.AAoQ5tR61a/DTF2THF_10139.p',woz1_2) ).
thf(f4455,plain,
( ( ( in @ sK27 @ ( powerset @ sK26 ) )
!= $true )
| spl913_8 ),
inference(subsumption_resolution,[status(thm)],[f4454,f2848]) ).
thf(f2848,plain,
binunionT_lem = $true,
inference(cnf_transformation,[status(thm)],[f1287]) ).
thf(f4454,plain,
( ( binunionT_lem != $true )
| ( ( in @ sK27 @ ( powerset @ sK26 ) )
!= $true )
| spl913_8 ),
inference(subsumption_resolution,[status(thm)],[f4445,f2797]) ).
thf(f2797,plain,
( ( in @ sK25 @ ( powerset @ sK26 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f1287]) ).
thf(f4445,plain,
( ( ( in @ sK25 @ ( powerset @ sK26 ) )
!= $true )
| ( ( in @ sK27 @ ( powerset @ sK26 ) )
!= $true )
| ( binunionT_lem != $true )
| spl913_8 ),
inference(trivial_inequality_removal,[status(thm)],[f4435]) ).
thf(f4435,plain,
( ( binunionT_lem != $true )
| ( ( in @ sK25 @ ( powerset @ sK26 ) )
!= $true )
| ( $true != $true )
| ( ( in @ sK27 @ ( powerset @ sK26 ) )
!= $true )
| spl913_8 ),
inference(superposition,[status(thm)],[f4407,f4052]) ).
thf(f4052,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true )
| ( binunionT_lem != $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f2523]) ).
thf(f2523,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( binunionT_lem != $true ) )
& ( ( binunionT_lem = $true )
| ( ( $true
!= ( in @ ( binunion @ sK828 @ sK829 ) @ ( powerset @ sK827 ) ) )
& ( ( in @ sK829 @ ( powerset @ sK827 ) )
= $true )
& ( ( in @ sK828 @ ( powerset @ sK827 ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK827,sK828,sK829])],[f2520,f2522,f2521]) ).
thf(f2521,plain,
( ? [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( $true
!= ( in @ ( binunion @ X4 @ X5 ) @ ( powerset @ X3 ) ) )
& ( ( in @ X5 @ ( powerset @ X3 ) )
= $true ) )
& ( ( in @ X4 @ ( powerset @ X3 ) )
= $true ) )
=> ( ? [X5: $i] :
( ( $true
!= ( in @ ( binunion @ sK828 @ X5 ) @ ( powerset @ sK827 ) ) )
& ( ( in @ X5 @ ( powerset @ sK827 ) )
= $true ) )
& ( ( in @ sK828 @ ( powerset @ sK827 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2522,plain,
( ? [X5: $i] :
( ( $true
!= ( in @ ( binunion @ sK828 @ X5 ) @ ( powerset @ sK827 ) ) )
& ( ( in @ X5 @ ( powerset @ sK827 ) )
= $true ) )
=> ( ( $true
!= ( in @ ( binunion @ sK828 @ sK829 ) @ ( powerset @ sK827 ) ) )
& ( ( in @ sK829 @ ( powerset @ sK827 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2520,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( binunionT_lem != $true ) )
& ( ( binunionT_lem = $true )
| ? [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( $true
!= ( in @ ( binunion @ X4 @ X5 ) @ ( powerset @ X3 ) ) )
& ( ( in @ X5 @ ( powerset @ X3 ) )
= $true ) )
& ( ( in @ X4 @ ( powerset @ X3 ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f2519]) ).
thf(f2519,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( binunionT_lem != $true ) )
& ( ( binunionT_lem = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
!= $true )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f1089]) ).
thf(f1089,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( binunionT_lem = $true ) ),
inference(ennf_transformation,[status(thm)],[f843]) ).
thf(f843,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ( ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) )
= $true ) ) )
<=> ( binunionT_lem = $true ) ),
inference(fool_elimination,[status(thm)],[f842]) ).
thf(f842,plain,
( binunionT_lem
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( in @ ( binunion @ X1 @ X2 ) @ ( powerset @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f232]) ).
thf(f232,axiom,
( binunionT_lem
= ( ! [X3: $i,X11: $i] :
( ( in @ X11 @ ( powerset @ X3 ) )
=> ! [X16: $i] :
( ( in @ X16 @ ( powerset @ X3 ) )
=> ( in @ ( binunion @ X11 @ X16 ) @ ( powerset @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.AAoQ5tR61a/DTF2THF_10139.p',binunionT_lem) ).
thf(f4407,plain,
( ( ( in @ ( binunion @ sK25 @ sK27 ) @ ( powerset @ sK26 ) )
!= $true )
| spl913_8 ),
inference(avatar_component_clause,[status(thm)],[f4405]) ).
thf(f4405,definition,
( spl913_8
<=> ( ( in @ ( binunion @ sK25 @ sK27 ) @ ( powerset @ sK26 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl913_8])],[avatar_definition]) ).
thf(f4430,plain,
spl913_7,
inference(avatar_contradiction_clause,[status(thm)],[f4429]) ).
thf(f4429,plain,
( $false
| spl913_7 ),
inference(subsumption_resolution,[status(thm)],[f4428,f2848]) ).
thf(f4428,plain,
( ( binunionT_lem != $true )
| spl913_7 ),
inference(subsumption_resolution,[status(thm)],[f4427,f2799]) ).
thf(f2799,plain,
( ( in @ sK28 @ ( powerset @ sK26 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f1287]) ).
thf(f4427,plain,
( ( ( in @ sK28 @ ( powerset @ sK26 ) )
!= $true )
| ( binunionT_lem != $true )
| spl913_7 ),
inference(subsumption_resolution,[status(thm)],[f4423,f2801]) ).
thf(f2801,plain,
( ( in @ sK29 @ ( powerset @ sK26 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f1287]) ).
thf(f4423,plain,
( ( ( in @ sK29 @ ( powerset @ sK26 ) )
!= $true )
| ( binunionT_lem != $true )
| ( ( in @ sK28 @ ( powerset @ sK26 ) )
!= $true )
| spl913_7 ),
inference(trivial_inequality_removal,[status(thm)],[f4410]) ).
thf(f4410,plain,
( ( ( in @ sK28 @ ( powerset @ sK26 ) )
!= $true )
| ( binunionT_lem != $true )
| ( ( in @ sK29 @ ( powerset @ sK26 ) )
!= $true )
| ( $true != $true )
| spl913_7 ),
inference(superposition,[status(thm)],[f4403,f4052]) ).
thf(f4403,plain,
( ( ( in @ ( binunion @ sK28 @ sK29 ) @ ( powerset @ sK26 ) )
!= $true )
| spl913_7 ),
inference(avatar_component_clause,[status(thm)],[f4401]) ).
thf(f4401,definition,
( spl913_7
<=> ( ( in @ ( binunion @ sK28 @ sK29 ) @ ( powerset @ sK26 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl913_7])],[avatar_definition]) ).
thf(f4408,plain,
( ~ spl913_7
| ~ spl913_8 ),
inference(avatar_split_clause,[status(thm)],[f4399,f4405,f4401]) ).
thf(f4399,plain,
( ( ( in @ ( binunion @ sK28 @ sK29 ) @ ( powerset @ sK26 ) )
!= $true )
| ( ( in @ ( binunion @ sK25 @ sK27 ) @ ( powerset @ sK26 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f4398,f2879]) ).
thf(f2879,plain,
demorgan1 = $true,
inference(cnf_transformation,[status(thm)],[f1287]) ).
thf(f4398,plain,
( ( ( in @ ( binunion @ sK25 @ sK27 ) @ ( powerset @ sK26 ) )
!= $true )
| ( ( in @ ( binunion @ sK28 @ sK29 ) @ ( powerset @ sK26 ) )
!= $true )
| ( demorgan1 != $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f4397]) ).
thf(f4397,plain,
( ( demorgan1 != $true )
| ( ( in @ ( binunion @ sK28 @ sK29 ) @ ( powerset @ sK26 ) )
!= $true )
| ( ( in @ ( binunion @ sK25 @ sK27 ) @ ( powerset @ sK26 ) )
!= $true )
| ( ( setminus @ sK26 @ ( binintersect @ ( binunion @ sK25 @ sK27 ) @ ( binunion @ sK28 @ sK29 ) ) )
!= ( setminus @ sK26 @ ( binintersect @ ( binunion @ sK25 @ sK27 ) @ ( binunion @ sK28 @ sK29 ) ) ) ) ),
inference(superposition,[status(thm)],[f4396,f3537]) ).
thf(f3537,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) )
= ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
| ( demorgan1 != $true )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1965]) ).
thf(f1965,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) )
= ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( demorgan1 != $true ) )
& ( ( demorgan1 = $true )
| ( ( ( in @ sK466 @ ( powerset @ sK464 ) )
= $true )
& ( ( binunion @ ( setminus @ sK464 @ sK465 ) @ ( setminus @ sK464 @ sK466 ) )
!= ( setminus @ sK464 @ ( binintersect @ sK465 @ sK466 ) ) )
& ( ( in @ sK465 @ ( powerset @ sK464 ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK464,sK465,sK466])],[f1962,f1964,f1963]) ).
thf(f1963,plain,
( ? [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( ( in @ X5 @ ( powerset @ X3 ) )
= $true )
& ( ( binunion @ ( setminus @ X3 @ X4 ) @ ( setminus @ X3 @ X5 ) )
!= ( setminus @ X3 @ ( binintersect @ X4 @ X5 ) ) ) )
& ( ( in @ X4 @ ( powerset @ X3 ) )
= $true ) )
=> ( ? [X5: $i] :
( ( ( in @ X5 @ ( powerset @ sK464 ) )
= $true )
& ( ( setminus @ sK464 @ ( binintersect @ sK465 @ X5 ) )
!= ( binunion @ ( setminus @ sK464 @ sK465 ) @ ( setminus @ sK464 @ X5 ) ) ) )
& ( ( in @ sK465 @ ( powerset @ sK464 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1964,plain,
( ? [X5: $i] :
( ( ( in @ X5 @ ( powerset @ sK464 ) )
= $true )
& ( ( setminus @ sK464 @ ( binintersect @ sK465 @ X5 ) )
!= ( binunion @ ( setminus @ sK464 @ sK465 ) @ ( setminus @ sK464 @ X5 ) ) ) )
=> ( ( ( in @ sK466 @ ( powerset @ sK464 ) )
= $true )
& ( ( binunion @ ( setminus @ sK464 @ sK465 ) @ ( setminus @ sK464 @ sK466 ) )
!= ( setminus @ sK464 @ ( binintersect @ sK465 @ sK466 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1962,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) )
= ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( demorgan1 != $true ) )
& ( ( demorgan1 = $true )
| ? [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( ( in @ X5 @ ( powerset @ X3 ) )
= $true )
& ( ( binunion @ ( setminus @ X3 @ X4 ) @ ( setminus @ X3 @ X5 ) )
!= ( setminus @ X3 @ ( binintersect @ X4 @ X5 ) ) ) )
& ( ( in @ X4 @ ( powerset @ X3 ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f1961]) ).
thf(f1961,plain,
( ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) )
= ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( demorgan1 != $true ) )
& ( ( demorgan1 = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ( ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) )
!= ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f1079]) ).
thf(f1079,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ( ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) )
= ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
<=> ( demorgan1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f742]) ).
thf(f742,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ( ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) )
= ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) ) )
<=> ( demorgan1 = $true ) ),
inference(fool_elimination,[status(thm)],[f741]) ).
thf(f741,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( binunion @ ( setminus @ X0 @ X1 ) @ ( setminus @ X0 @ X2 ) )
= ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) ) )
= demorgan1 ),
inference(rectify,[status(thm)],[f274]) ).
thf(f274,axiom,
! [X3: $i,X11: $i] :
( ( ( in @ X11 @ ( powerset @ X3 ) )
=> ! [X16: $i] :
( ( in @ X16 @ ( powerset @ X3 ) )
=> ( ( setminus @ X3 @ ( binintersect @ X11 @ X16 ) )
= ( binunion @ ( setminus @ X3 @ X11 ) @ ( setminus @ X3 @ X16 ) ) ) ) )
= demorgan1 ),
file('/export/starexec/sandbox2/tmp/tmp.AAoQ5tR61a/DTF2THF_10139.p',demorgan1) ).
thf(f4396,plain,
( ( setminus @ sK26 @ ( binintersect @ ( binunion @ sK25 @ sK27 ) @ ( binunion @ sK28 @ sK29 ) ) )
!= ( binunion @ ( setminus @ sK26 @ ( binunion @ sK25 @ sK27 ) ) @ ( setminus @ sK26 @ ( binunion @ sK28 @ sK29 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f4395,f2797]) ).
thf(f4395,plain,
( ( ( in @ sK25 @ ( powerset @ sK26 ) )
!= $true )
| ( ( setminus @ sK26 @ ( binintersect @ ( binunion @ sK25 @ sK27 ) @ ( binunion @ sK28 @ sK29 ) ) )
!= ( binunion @ ( setminus @ sK26 @ ( binunion @ sK25 @ sK27 ) ) @ ( setminus @ sK26 @ ( binunion @ sK28 @ sK29 ) ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f4394,f2946]) ).
thf(f2946,plain,
demorgan2 = $true,
inference(cnf_transformation,[status(thm)],[f1287]) ).
thf(f4394,plain,
( ( demorgan2 != $true )
| ( ( in @ sK25 @ ( powerset @ sK26 ) )
!= $true )
| ( ( setminus @ sK26 @ ( binintersect @ ( binunion @ sK25 @ sK27 ) @ ( binunion @ sK28 @ sK29 ) ) )
!= ( binunion @ ( setminus @ sK26 @ ( binunion @ sK25 @ sK27 ) ) @ ( setminus @ sK26 @ ( binunion @ sK28 @ sK29 ) ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f4393,f2798]) ).
thf(f4393,plain,
( ( ( in @ sK27 @ ( powerset @ sK26 ) )
!= $true )
| ( ( setminus @ sK26 @ ( binintersect @ ( binunion @ sK25 @ sK27 ) @ ( binunion @ sK28 @ sK29 ) ) )
!= ( binunion @ ( setminus @ sK26 @ ( binunion @ sK25 @ sK27 ) ) @ ( setminus @ sK26 @ ( binunion @ sK28 @ sK29 ) ) ) )
| ( demorgan2 != $true )
| ( ( in @ sK25 @ ( powerset @ sK26 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f4333,f3599]) ).
thf(f3599,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( setminus @ X4 @ ( binunion @ X3 @ X5 ) )
= ( binintersect @ ( setminus @ X4 @ X3 ) @ ( setminus @ X4 @ X5 ) ) )
| ( demorgan2 != $true )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true )
| ( ( in @ X3 @ ( powerset @ X4 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f2041]) ).
thf(f2041,plain,
( ( ( demorgan2 = $true )
| ( ( ( setminus @ sK516 @ ( binunion @ sK515 @ sK517 ) )
!= ( binintersect @ ( setminus @ sK516 @ sK515 ) @ ( setminus @ sK516 @ sK517 ) ) )
& ( $true
= ( in @ sK517 @ ( powerset @ sK516 ) ) )
& ( $true
= ( in @ sK515 @ ( powerset @ sK516 ) ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ! [X5: $i] :
( ( ( setminus @ X4 @ ( binunion @ X3 @ X5 ) )
= ( binintersect @ ( setminus @ X4 @ X3 ) @ ( setminus @ X4 @ X5 ) ) )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true ) )
| ( ( in @ X3 @ ( powerset @ X4 ) )
!= $true ) )
| ( demorgan2 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK515,sK516,sK517])],[f2038,f2040,f2039]) ).
thf(f2039,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) )
!= ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
=> ( ? [X2: $i] :
( ( ( binintersect @ ( setminus @ sK516 @ sK515 ) @ ( setminus @ sK516 @ X2 ) )
!= ( setminus @ sK516 @ ( binunion @ sK515 @ X2 ) ) )
& ( ( in @ X2 @ ( powerset @ sK516 ) )
= $true ) )
& ( $true
= ( in @ sK515 @ ( powerset @ sK516 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2040,plain,
( ? [X2: $i] :
( ( ( binintersect @ ( setminus @ sK516 @ sK515 ) @ ( setminus @ sK516 @ X2 ) )
!= ( setminus @ sK516 @ ( binunion @ sK515 @ X2 ) ) )
& ( ( in @ X2 @ ( powerset @ sK516 ) )
= $true ) )
=> ( ( ( setminus @ sK516 @ ( binunion @ sK515 @ sK517 ) )
!= ( binintersect @ ( setminus @ sK516 @ sK515 ) @ ( setminus @ sK516 @ sK517 ) ) )
& ( $true
= ( in @ sK517 @ ( powerset @ sK516 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2038,plain,
( ( ( demorgan2 = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) )
!= ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i] :
( ! [X5: $i] :
( ( ( setminus @ X4 @ ( binunion @ X3 @ X5 ) )
= ( binintersect @ ( setminus @ X4 @ X3 ) @ ( setminus @ X4 @ X5 ) ) )
| ( ( in @ X5 @ ( powerset @ X4 ) )
!= $true ) )
| ( ( in @ X3 @ ( powerset @ X4 ) )
!= $true ) )
| ( demorgan2 != $true ) ) ),
inference(rectify,[status(thm)],[f2037]) ).
thf(f2037,plain,
( ( ( demorgan2 = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) )
!= ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ) )
& ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) )
= ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) )
| ( demorgan2 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f1028]) ).
thf(f1028,plain,
( ( demorgan2 = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) )
= ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f395]) ).
thf(f395,plain,
( ( demorgan2 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ( ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) )
= ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f394]) ).
thf(f394,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ( binintersect @ ( setminus @ X1 @ X0 ) @ ( setminus @ X1 @ X2 ) )
= ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) ) ) )
= demorgan2 ),
inference(rectify,[status(thm)],[f278]) ).
thf(f278,axiom,
! [X11: $i,X3: $i] :
( ( ( in @ X11 @ ( powerset @ X3 ) )
=> ! [X16: $i] :
( ( in @ X16 @ ( powerset @ X3 ) )
=> ( ( setminus @ X3 @ ( binunion @ X11 @ X16 ) )
= ( binintersect @ ( setminus @ X3 @ X11 ) @ ( setminus @ X3 @ X16 ) ) ) ) )
= demorgan2 ),
file('/export/starexec/sandbox2/tmp/tmp.AAoQ5tR61a/DTF2THF_10139.p',demorgan2) ).
thf(f4333,plain,
( ( setminus @ sK26 @ ( binintersect @ ( binunion @ sK25 @ sK27 ) @ ( binunion @ sK28 @ sK29 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK26 @ sK25 ) @ ( setminus @ sK26 @ sK27 ) ) @ ( setminus @ sK26 @ ( binunion @ sK28 @ sK29 ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f4332,f2799]) ).
thf(f4332,plain,
( ( ( in @ sK28 @ ( powerset @ sK26 ) )
!= $true )
| ( ( setminus @ sK26 @ ( binintersect @ ( binunion @ sK25 @ sK27 ) @ ( binunion @ sK28 @ sK29 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK26 @ sK25 ) @ ( setminus @ sK26 @ sK27 ) ) @ ( setminus @ sK26 @ ( binunion @ sK28 @ sK29 ) ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f4331,f2801]) ).
thf(f4331,plain,
( ( ( setminus @ sK26 @ ( binintersect @ ( binunion @ sK25 @ sK27 ) @ ( binunion @ sK28 @ sK29 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK26 @ sK25 ) @ ( setminus @ sK26 @ sK27 ) ) @ ( setminus @ sK26 @ ( binunion @ sK28 @ sK29 ) ) ) )
| ( ( in @ sK29 @ ( powerset @ sK26 ) )
!= $true )
| ( ( in @ sK28 @ ( powerset @ sK26 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f4329,f2946]) ).
thf(f4329,plain,
( ( demorgan2 != $true )
| ( ( setminus @ sK26 @ ( binintersect @ ( binunion @ sK25 @ sK27 ) @ ( binunion @ sK28 @ sK29 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK26 @ sK25 ) @ ( setminus @ sK26 @ sK27 ) ) @ ( setminus @ sK26 @ ( binunion @ sK28 @ sK29 ) ) ) )
| ( ( in @ sK28 @ ( powerset @ sK26 ) )
!= $true )
| ( ( in @ sK29 @ ( powerset @ sK26 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f2800,f3599]) ).
thf(f2800,plain,
( ( setminus @ sK26 @ ( binintersect @ ( binunion @ sK25 @ sK27 ) @ ( binunion @ sK28 @ sK29 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ sK26 @ sK25 ) @ ( setminus @ sK26 @ sK27 ) ) @ ( binintersect @ ( setminus @ sK26 @ sK28 ) @ ( setminus @ sK26 @ sK29 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f1287]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU764^1 : TPTP v9.2.1. Released v3.7.0.
% 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n013.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:33:08 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.47 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : SEU764^1 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.47 % Domain : Set Theory
% 0.28/0.47 % Problem : Typed Set Theory - First Wizard of Oz Examples - WoZ1 Problems
% 0.28/0.47 % Version : Especial.
% 0.28/0.47 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.28/0.47 % (! Z:i.in Z (powerset A) -> (! W:i.in W (powerset A) ->
% 0.28/0.47 % setminus A (binintersect (binunion X Y) (binunion Z W)) =
% 0.28/0.47 % binunion (binintersect (setminus A X) (setminus A Y))
% 0.28/0.47 % (binintersect (setminus A Z) (setminus A W))))))
% 0.28/0.47
% 0.28/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.28/0.47 % Source : [Bro08]
% 0.28/0.47 % Names : ZFC266g [Bro08]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.50 v8.2.0, 0.69 v8.1.0, 0.55 v7.5.0, 0.71 v7.4.0, 0.56 v7.3.0, 0.67 v7.2.0, 0.62 v7.1.0, 0.75 v7.0.0, 1.00 v6.2.0, 0.57 v5.5.0, 0.67 v5.4.0, 1.00 v3.7.0
% 0.28/0.47 % Syntax : Number of formulae : 603 ( 284 unt; 318 typ; 284 def)
% 0.28/0.47 % Number of atoms : 1698 ( 413 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 285 ( 5 avg)
% 0.28/0.47 % Number of connectives : 3615 ( 73 ~; 12 |; 44 &;2614 @)
% 0.28/0.47 % ( 14 <=>; 858 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 292 ( 2 avg)
% 0.28/0.47 % Number of types : 2 ( 0 usr)
% 0.28/0.47 % Number of type conns : 132 ( 132 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 321 ( 318 usr; 284 con; 0-4 aty)
% 0.28/0.47 % Number of variables : 973 ( 74 ^; 864 !; 35 ?; 973 :)
% 0.28/0.47 % SPC : TH0_THM_EQU_NAR
% 0.28/0.47
% 0.28/0.47 % Comments : http://mathgate.info/detsetitem.php?id=325
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 thf(in_type,type,
% 0.28/0.47 in: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(exu_type,type,
% 0.28/0.47 exu: ( $i > $o ) > $o ).
% 0.28/0.47
% 0.28/0.47 thf(exu,definition,
% 0.28/0.47 ( exu
% 0.28/0.47 = ( ^ [Xphi: $i > $o] :
% 0.28/0.47 ? [Xx: $i] :
% 0.28/0.47 ( ( Xphi @ Xx )
% 0.28/0.47 & ! [Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setextAx_type,type,
% 0.28/0.47 setextAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setextAx,definition,
% 0.28/0.47 ( setextAx
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 <=> ( in @ Xx @ B ) )
% 0.28/0.47 => ( A = B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyset_type,type,
% 0.28/0.47 emptyset: $i ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetAx_type,type,
% 0.28/0.47 emptysetAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetAx,definition,
% 0.28/0.47 ( emptysetAx
% 0.28/0.47 = ( ! [Xx: $i] :
% 0.28/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoin_type,type,
% 0.28/0.47 setadjoin: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinAx_type,type,
% 0.28/0.47 setadjoinAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinAx,definition,
% 0.28/0.47 ( setadjoinAx
% 0.28/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.47 <=> ( ( Xy = Xx )
% 0.28/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powerset_type,type,
% 0.28/0.47 powerset: $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(powersetAx_type,type,
% 0.28/0.47 powersetAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetAx,definition,
% 0.28/0.47 ( powersetAx
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.47 <=> ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunion_type,type,
% 0.28/0.47 setunion: $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(setunionAx_type,type,
% 0.28/0.47 setunionAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionAx,definition,
% 0.28/0.47 ( setunionAx
% 0.28/0.47 = ( ! [A: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.47 <=> ? [B: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 & ( in @ B @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(omega_type,type,
% 0.28/0.47 omega: $i ).
% 0.28/0.47
% 0.28/0.47 thf(omega0Ax_type,type,
% 0.28/0.47 omega0Ax: $o ).
% 0.28/0.47
% 0.28/0.47 thf(omega0Ax,definition,
% 0.28/0.47 ( omega0Ax
% 0.28/0.47 = ( in @ emptyset @ omega ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(omegaSAx_type,type,
% 0.28/0.47 omegaSAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(omegaSAx,definition,
% 0.28/0.47 ( omegaSAx
% 0.28/0.47 = ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ omega )
% 0.28/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(omegaIndAx_type,type,
% 0.28/0.47 omegaIndAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(omegaIndAx,definition,
% 0.28/0.47 ( omegaIndAx
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ( ( in @ emptyset @ A )
% 0.28/0.47 & ! [Xx: $i] :
% 0.28/0.47 ( ( ( in @ Xx @ omega )
% 0.28/0.47 & ( in @ Xx @ A ) )
% 0.28/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ omega )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(replAx_type,type,
% 0.28/0.47 replAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(replAx,definition,
% 0.28/0.47 ( replAx
% 0.28/0.47 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( exu
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.28/0.47 => ? [B: $i] :
% 0.28/0.47 ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 <=> ? [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(foundationAx_type,type,
% 0.28/0.47 foundationAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(foundationAx,definition,
% 0.28/0.47 ( foundationAx
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.28/0.47 => ? [B: $i] :
% 0.28/0.47 ( ( in @ B @ A )
% 0.28/0.47 & ~ ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(wellorderingAx_type,type,
% 0.28/0.47 wellorderingAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(wellorderingAx,definition,
% 0.28/0.47 ( wellorderingAx
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ? [B: $i] :
% 0.28/0.47 ( ! [C: $i] :
% 0.28/0.47 ( ( in @ C @ B )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ C )
% 0.28/0.47 => ( in @ Xx @ A ) ) )
% 0.28/0.47 & ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( ( in @ Xx @ A )
% 0.28/0.47 & ( in @ Xy @ A ) )
% 0.28/0.47 => ( ! [C: $i] :
% 0.28/0.47 ( ( in @ C @ B )
% 0.28/0.47 => ( ( in @ Xx @ C )
% 0.28/0.47 <=> ( in @ Xy @ C ) ) )
% 0.28/0.47 => ( Xx = Xy ) ) )
% 0.28/0.47 & ! [C: $i,D: $i] :
% 0.28/0.47 ( ( ( in @ C @ B )
% 0.28/0.47 & ( in @ D @ B ) )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ C )
% 0.28/0.47 => ( in @ Xx @ D ) )
% 0.28/0.47 | ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ D )
% 0.28/0.47 => ( in @ Xx @ C ) ) ) )
% 0.28/0.47 & ! [C: $i] :
% 0.28/0.47 ( ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ C )
% 0.28/0.47 => ( in @ Xx @ A ) )
% 0.28/0.47 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.28/0.47 => ? [D: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ D @ B )
% 0.28/0.47 & ( in @ Xx @ C )
% 0.28/0.47 & ~ ? [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ D )
% 0.28/0.47 & ( in @ Xy @ C ) )
% 0.28/0.47 & ! [E: $i] :
% 0.28/0.47 ( ( in @ E @ B )
% 0.28/0.47 => ( ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ E )
% 0.28/0.47 => ( in @ Xy @ D ) )
% 0.28/0.47 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(descr_type,type,
% 0.28/0.47 descr: ( $i > $o ) > $i ).
% 0.28/0.47
% 0.28/0.47 thf(descrp_type,type,
% 0.28/0.47 descrp: $o ).
% 0.28/0.47
% 0.28/0.47 thf(descrp,definition,
% 0.28/0.47 ( descrp
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ( Xphi
% 0.28/0.47 @ ( descr
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstr_type,type,
% 0.28/0.47 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstrI_type,type,
% 0.28/0.47 dsetconstrI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstrI,definition,
% 0.28/0.47 ( dsetconstrI
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 => ( in @ Xx
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstrEL_type,type,
% 0.28/0.47 dsetconstrEL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstrEL,definition,
% 0.28/0.47 ( dsetconstrEL
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstrER_type,type,
% 0.28/0.47 dsetconstrER: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstrER,definition,
% 0.28/0.47 ( dsetconstrER
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuE1_type,type,
% 0.28/0.47 exuE1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuE1,definition,
% 0.28/0.47 ( exuE1
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ( ( Xphi @ Xx )
% 0.28/0.47 & ! [Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(prop2set_type,type,
% 0.28/0.47 prop2set: $o > $i ).
% 0.28/0.47
% 0.28/0.47 thf(prop2setE_type,type,
% 0.28/0.47 prop2setE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(prop2setE,definition,
% 0.28/0.47 ( prop2setE
% 0.28/0.47 = ( ! [Xphi: $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.28/0.47 => Xphi ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetE_type,type,
% 0.28/0.47 emptysetE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetE,definition,
% 0.28/0.47 ( emptysetE
% 0.28/0.47 = ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ emptyset )
% 0.28/0.47 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetimpfalse_type,type,
% 0.28/0.47 emptysetimpfalse: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetimpfalse,definition,
% 0.28/0.47 ( emptysetimpfalse
% 0.28/0.47 = ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ emptyset )
% 0.28/0.47 => $false ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notinemptyset_type,type,
% 0.28/0.47 notinemptyset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notinemptyset,definition,
% 0.28/0.47 ( notinemptyset
% 0.28/0.47 = ( ! [Xx: $i] :
% 0.28/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuE3e_type,type,
% 0.28/0.47 exuE3e: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuE3e,definition,
% 0.28/0.47 ( exuE3e
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setext_type,type,
% 0.28/0.47 setext: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setext,definition,
% 0.28/0.47 ( setext
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ B ) )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ A ) )
% 0.28/0.47 => ( A = B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyI_type,type,
% 0.28/0.47 emptyI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyI,definition,
% 0.28/0.47 ( emptyI
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ~ ( in @ Xx @ A )
% 0.28/0.47 => ( A = emptyset ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(noeltsimpempty_type,type,
% 0.28/0.47 noeltsimpempty: $o ).
% 0.28/0.47
% 0.28/0.47 thf(noeltsimpempty,definition,
% 0.28/0.47 ( noeltsimpempty
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ~ ( in @ Xx @ A )
% 0.28/0.47 => ( A = emptyset ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setbeta_type,type,
% 0.28/0.47 setbeta: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setbeta,definition,
% 0.28/0.47 ( setbeta
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.47 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(nonempty_type,type,
% 0.28/0.47 nonempty: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(nonempty,definition,
% 0.28/0.47 ( nonempty
% 0.28/0.47 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyE1_type,type,
% 0.28/0.47 nonemptyE1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyE1,definition,
% 0.28/0.47 ( nonemptyE1
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ( nonempty @ A )
% 0.28/0.47 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyI_type,type,
% 0.28/0.47 nonemptyI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyI,definition,
% 0.28/0.47 ( nonemptyI
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 => ( nonempty
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyI1_type,type,
% 0.28/0.47 nonemptyI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyI1,definition,
% 0.28/0.47 ( nonemptyI1
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.28/0.47 => ( nonempty @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinIL_type,type,
% 0.28/0.47 setadjoinIL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinIL,definition,
% 0.28/0.47 ( setadjoinIL
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyinunitempty_type,type,
% 0.28/0.47 emptyinunitempty: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyinunitempty,definition,
% 0.28/0.47 ( emptyinunitempty
% 0.28/0.47 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinIR_type,type,
% 0.28/0.47 setadjoinIR: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinIR,definition,
% 0.28/0.47 ( setadjoinIR
% 0.28/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinE_type,type,
% 0.28/0.47 setadjoinE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinE,definition,
% 0.28/0.47 ( setadjoinE
% 0.28/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.47 => ! [Xphi: $o] :
% 0.28/0.47 ( ( ( Xy = Xx )
% 0.28/0.47 => Xphi )
% 0.28/0.47 => ( ( ( in @ Xy @ A )
% 0.28/0.47 => Xphi )
% 0.28/0.47 => Xphi ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinOr_type,type,
% 0.28/0.47 setadjoinOr: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinOr,definition,
% 0.28/0.47 ( setadjoinOr
% 0.28/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.47 => ( ( Xy = Xx )
% 0.28/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setoftrueEq_type,type,
% 0.28/0.47 setoftrueEq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setoftrueEq,definition,
% 0.28/0.47 ( setoftrueEq
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xx: $i] : $true )
% 0.28/0.47 = A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powersetI_type,type,
% 0.28/0.47 powersetI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetI,definition,
% 0.28/0.47 ( powersetI
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ A ) )
% 0.28/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyinPowerset_type,type,
% 0.28/0.47 emptyinPowerset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyinPowerset,definition,
% 0.28/0.47 ( emptyinPowerset
% 0.28/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyInPowerset_type,type,
% 0.28/0.47 emptyInPowerset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyInPowerset,definition,
% 0.28/0.47 ( emptyInPowerset
% 0.28/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powersetE_type,type,
% 0.28/0.47 powersetE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetE,definition,
% 0.28/0.47 ( powersetE
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.47 => ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunionI_type,type,
% 0.28/0.47 setunionI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionI,definition,
% 0.28/0.47 ( setunionI
% 0.28/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( ( in @ B @ A )
% 0.28/0.47 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunionE_type,type,
% 0.28/0.47 setunionE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionE,definition,
% 0.28/0.47 ( setunionE
% 0.28/0.47 = ( ! [A: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.47 => ! [Xphi: $o] :
% 0.28/0.47 ( ! [B: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( ( in @ B @ A )
% 0.28/0.47 => Xphi ) )
% 0.28/0.47 => Xphi ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subPowSU_type,type,
% 0.28/0.47 subPowSU: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subPowSU,definition,
% 0.28/0.47 ( subPowSU
% 0.28/0.47 = ( ! [A: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuE2_type,type,
% 0.28/0.47 exuE2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuE2,definition,
% 0.28/0.47 ( exuE2
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ! [Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xy )
% 0.28/0.47 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyImpWitness_type,type,
% 0.28/0.47 nonemptyImpWitness: $o ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyImpWitness,definition,
% 0.28/0.47 ( nonemptyImpWitness
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ( nonempty @ A )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & $true ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(uniqinunit_type,type,
% 0.28/0.47 uniqinunit: $o ).
% 0.28/0.47
% 0.28/0.47 thf(uniqinunit,definition,
% 0.28/0.47 ( uniqinunit
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notinsingleton_type,type,
% 0.28/0.47 notinsingleton: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notinsingleton,definition,
% 0.28/0.47 ( notinsingleton
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx != Xy )
% 0.28/0.47 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(eqinunit_type,type,
% 0.28/0.47 eqinunit: $o ).
% 0.28/0.47
% 0.28/0.47 thf(eqinunit,definition,
% 0.28/0.47 ( eqinunit
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(singletonsswitch_type,type,
% 0.28/0.47 singletonsswitch: $o ).
% 0.28/0.47
% 0.28/0.47 thf(singletonsswitch,definition,
% 0.28/0.47 ( singletonsswitch
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairsetE_type,type,
% 0.28/0.47 upairsetE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairsetE,definition,
% 0.28/0.47 ( upairsetE
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.28/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.28/0.47 => ( ( Xz = Xx )
% 0.28/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairsetIL_type,type,
% 0.28/0.47 upairsetIL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairsetIL,definition,
% 0.28/0.47 ( upairsetIL
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairsetIR_type,type,
% 0.28/0.47 upairsetIR: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairsetIR,definition,
% 0.28/0.47 ( upairsetIR
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyE1_type,type,
% 0.28/0.47 emptyE1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyE1,definition,
% 0.28/0.47 ( emptyE1
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( Xphi @ Xx ) )
% 0.28/0.47 => ( ( ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 = emptyset )
% 0.28/0.47 => $false ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(vacuousDall_type,type,
% 0.28/0.47 vacuousDall: $o ).
% 0.28/0.47
% 0.28/0.47 thf(vacuousDall,definition,
% 0.28/0.47 ( vacuousDall
% 0.28/0.47 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ emptyset )
% 0.28/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan1_type,type,
% 0.28/0.47 quantDeMorgan1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan1,definition,
% 0.28/0.47 ( quantDeMorgan1
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ~ ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( Xphi @ Xx ) )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan2_type,type,
% 0.28/0.47 quantDeMorgan2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan2,definition,
% 0.28/0.47 ( quantDeMorgan2
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ~ ( Xphi @ Xx ) )
% 0.28/0.47 => ~ ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan3_type,type,
% 0.28/0.47 quantDeMorgan3: $o ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan3,definition,
% 0.28/0.47 ( quantDeMorgan3
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ~ ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( Xphi @ Xx ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan4_type,type,
% 0.28/0.47 quantDeMorgan4: $o ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan4,definition,
% 0.28/0.47 ( quantDeMorgan4
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ~ ( Xphi @ Xx ) )
% 0.28/0.47 => ~ ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(prop2setI_type,type,
% 0.28/0.47 prop2setI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(prop2setI,definition,
% 0.28/0.47 ( prop2setI
% 0.28/0.47 = ( ! [Xphi: $o] :
% 0.28/0.47 ( Xphi
% 0.28/0.47 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(set2prop_type,type,
% 0.28/0.47 set2prop: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(prop2set2propI_type,type,
% 0.28/0.47 prop2set2propI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(prop2set2propI,definition,
% 0.28/0.47 ( prop2set2propI
% 0.28/0.47 = ( ! [Xphi: $o] :
% 0.28/0.47 ( Xphi
% 0.28/0.47 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notdexE_type,type,
% 0.28/0.47 notdexE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notdexE,definition,
% 0.28/0.47 ( notdexE
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ~ ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( Xphi @ Xx ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notdallE_type,type,
% 0.28/0.47 notdallE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notdallE,definition,
% 0.28/0.47 ( notdallE
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ~ ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( Xphi @ Xx ) )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuI1_type,type,
% 0.28/0.47 exuI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuI1,definition,
% 0.28/0.47 ( exuI1
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ? [Xx: $i] :
% 0.28/0.47 ( ( Xphi @ Xx )
% 0.28/0.47 & ! [Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) )
% 0.28/0.47 => ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuI3_type,type,
% 0.28/0.47 exuI3: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuI3,definition,
% 0.28/0.47 ( exuI3
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.28/0.47 => ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xx )
% 0.28/0.47 => ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) )
% 0.28/0.47 => ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuI2_type,type,
% 0.28/0.47 exuI2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuI2,definition,
% 0.28/0.47 ( exuI2
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ? [Xx: $i] :
% 0.28/0.47 ! [Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xy )
% 0.28/0.47 <=> ( Xy = Xx ) )
% 0.28/0.47 => ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(inCongP_type,type,
% 0.28/0.47 inCongP: $o ).
% 0.28/0.47
% 0.28/0.47 thf(inCongP,definition,
% 0.28/0.47 ( inCongP
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(in__Cong_type,type,
% 0.28/0.47 in__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(in__Cong,definition,
% 0.28/0.47 ( in__Cong
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( ( in @ Xx @ A )
% 0.28/0.47 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuE3u_type,type,
% 0.28/0.47 exuE3u: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuE3u,definition,
% 0.28/0.47 ( exuE3u
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xx )
% 0.28/0.47 => ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exu__Cong_type,type,
% 0.28/0.47 exu__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exu__Cong,definition,
% 0.28/0.47 ( exu__Cong
% 0.28/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.28/0.47 => ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 <=> ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyset__Cong_type,type,
% 0.28/0.47 emptyset__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyset__Cong,definition,
% 0.28/0.47 ( emptyset__Cong
% 0.28/0.48 = ( emptyset = emptyset ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setadjoin__Cong_type,type,
% 0.28/0.48 setadjoin__Cong: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setadjoin__Cong,definition,
% 0.28/0.48 ( setadjoin__Cong
% 0.28/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.48 ( ( Xx = Xy )
% 0.28/0.48 => ! [Xz: $i,Xu: $i] :
% 0.28/0.48 ( ( Xz = Xu )
% 0.28/0.48 => ( ( setadjoin @ Xx @ Xz )
% 0.28/0.48 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(powerset__Cong_type,type,
% 0.28/0.48 powerset__Cong: $o ).
% 0.28/0.48
% 0.28/0.48 thf(powerset__Cong,definition,
% 0.28/0.48 ( powerset__Cong
% 0.28/0.48 = ( ! [A: $i,B: $i] :
% 0.28/0.48 ( ( A = B )
% 0.28/0.48 => ( ( powerset @ A )
% 0.28/0.48 = ( powerset @ B ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setunion__Cong_type,type,
% 0.28/0.48 setunion__Cong: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setunion__Cong,definition,
% 0.28/0.48 ( setunion__Cong
% 0.28/0.48 = ( ! [A: $i,B: $i] :
% 0.28/0.48 ( ( A = B )
% 0.28/0.48 => ( ( setunion @ A )
% 0.28/0.48 = ( setunion @ B ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(omega__Cong_type,type,
% 0.28/0.48 omega__Cong: $o ).
% 0.28/0.48
% 0.28/0.48 thf(omega__Cong,definition,
% 0.28/0.48 ( omega__Cong
% 0.28/0.48 = ( omega = omega ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(exuEu_type,type,
% 0.28/0.48 exuEu: $o ).
% 0.28/0.48
% 0.28/0.48 thf(exuEu,definition,
% 0.28/0.48 ( exuEu
% 0.28/0.48 = ( ! [Xphi: $i > $o] :
% 0.28/0.48 ( ( exu
% 0.28/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.48 => ! [Xx: $i,Xy: $i] :
% 0.28/0.48 ( ( Xphi @ Xx )
% 0.28/0.48 => ( ( Xphi @ Xy )
% 0.28/0.48 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(descr__Cong_type,type,
% 0.28/0.48 descr__Cong: $o ).
% 0.28/0.48
% 0.28/0.48 thf(descr__Cong,definition,
% 0.28/0.48 ( descr__Cong
% 0.28/0.48 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.48 ( ! [Xx: $i,Xy: $i] :
% 0.28/0.48 ( ( Xx = Xy )
% 0.28/0.48 => ( ( Xphi @ Xx )
% 0.28/0.48 <=> ( Xpsi @ Xy ) ) )
% 0.28/0.48 => ( ( exu
% 0.28/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.48 => ( ( exu
% 0.28/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.28/0.48 => ( ( descr
% 0.28/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.48 = ( descr
% 0.28/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(dsetconstr__Cong_type,type,
% 0.28/0.48 dsetconstr__Cong: $o ).
% 0.28/0.48
% 0.28/0.48 thf(dsetconstr__Cong,definition,
% 0.28/0.48 ( dsetconstr__Cong
% 0.28/0.48 = ( ! [A: $i,B: $i] :
% 0.28/0.48 ( ( A = B )
% 0.28/0.48 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.48 ( ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ B )
% 0.28/0.48 => ( ( Xx = Xy )
% 0.28/0.48 => ( ( Xphi @ Xx )
% 0.28/0.48 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.28/0.48 => ( ( dsetconstr @ A
% 0.28/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.48 = ( dsetconstr @ B
% 0.28/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(subset_type,type,
% 0.28/0.48 subset: $i > $i > $o ).
% 0.28/0.48
% 0.28/0.48 thf(disjoint_type,type,
% 0.28/0.48 disjoint: $i > $i > $o ).
% 0.28/0.48
% 0.28/0.48 thf(setsmeet_type,type,
% 0.28/0.48 setsmeet: $i > $i > $o ).
% 0.28/0.48
% 0.28/0.48 thf(subsetI1_type,type,
% 0.28/0.48 subsetI1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(subsetI1,definition,
% 0.28/0.48 ( subsetI1
% 0.28/0.48 = ( ! [A: $i,B: $i] :
% 0.28/0.48 ( ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( in @ Xx @ B ) )
% 0.28/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(eqimpsubset2_type,type,
% 0.28/0.48 eqimpsubset2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(eqimpsubset2,definition,
% 0.28/0.48 ( eqimpsubset2
% 0.28/0.48 = ( ! [A: $i,B: $i] :
% 0.28/0.48 ( ( A = B )
% 0.28/0.48 => ( subset @ B @ A ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(eqimpsubset1_type,type,
% 0.28/0.48 eqimpsubset1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(eqimpsubset1,definition,
% 0.28/0.48 ( eqimpsubset1
% 0.28/0.48 = ( ! [A: $i,B: $i] :
% 0.28/0.48 ( ( A = B )
% 0.28/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(subsetI2_type,type,
% 0.28/0.48 subsetI2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(subsetI2,definition,
% 0.28/0.48 ( subsetI2
% 0.28/0.48 = ( ! [A: $i,B: $i] :
% 0.28/0.48 ( ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( in @ Xx @ B ) )
% 0.28/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(emptysetsubset_type,type,
% 0.28/0.48 emptysetsubset: $o ).
% 0.28/0.48
% 0.28/0.48 thf(emptysetsubset,definition,
% 0.28/0.48 ( emptysetsubset
% 0.28/0.48 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(subsetE_type,type,
% 0.28/0.48 subsetE: $o ).
% 0.28/0.48
% 0.28/0.48 thf(subsetE,definition,
% 0.28/0.48 ( subsetE
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ( subset @ A @ B )
% 0.28/0.48 => ( ( in @ Xx @ A )
% 0.28/0.48 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(subsetE2_type,type,
% 0.28/0.48 subsetE2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(subsetE2,definition,
% 0.28/0.48 ( subsetE2
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ( subset @ A @ B )
% 0.28/0.48 => ( ~ ( in @ Xx @ B )
% 0.28/0.48 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(notsubsetI_type,type,
% 0.28/0.48 notsubsetI: $o ).
% 0.28/0.48
% 0.28/0.48 thf(notsubsetI,definition,
% 0.28/0.48 ( notsubsetI
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ~ ( in @ Xx @ B )
% 0.28/0.48 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(notequalI1_type,type,
% 0.28/0.48 notequalI1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(notequalI1,definition,
% 0.28/0.48 ( notequalI1
% 0.28/0.48 = ( ! [A: $i,B: $i] :
% 0.28/0.48 ( ~ ( subset @ A @ B )
% 0.28/0.48 => ( A != B ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(notequalI2_type,type,
% 0.28/0.48 notequalI2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(notequalI2,definition,
% 0.28/0.48 ( notequalI2
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ~ ( in @ Xx @ B )
% 0.28/0.48 => ( A != B ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(subsetRefl_type,type,
% 0.28/0.48 subsetRefl: $o ).
% 0.28/0.48
% 0.28/0.48 thf(subsetRefl,definition,
% 0.28/0.48 ( subsetRefl
% 0.28/0.48 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(subsetTrans_type,type,
% 0.28/0.48 subsetTrans: $o ).
% 0.28/0.48
% 0.28/0.48 thf(subsetTrans,definition,
% 0.28/0.48 ( subsetTrans
% 0.28/0.48 = ( ! [A: $i,B: $i,C: $i] :
% 0.28/0.48 ( ( subset @ A @ B )
% 0.28/0.48 => ( ( subset @ B @ C )
% 0.28/0.48 => ( subset @ A @ C ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setadjoinSub_type,type,
% 0.28/0.48 setadjoinSub: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setadjoinSub,definition,
% 0.28/0.48 ( setadjoinSub
% 0.28/0.48 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setadjoinSub2_type,type,
% 0.28/0.48 setadjoinSub2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setadjoinSub2,definition,
% 0.28/0.48 ( setadjoinSub2
% 0.28/0.48 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.28/0.48 ( ( subset @ A @ B )
% 0.28/0.48 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(subset2powerset_type,type,
% 0.28/0.48 subset2powerset: $o ).
% 0.28/0.48
% 0.28/0.48 thf(subset2powerset,definition,
% 0.28/0.48 ( subset2powerset
% 0.28/0.48 = ( ! [A: $i,B: $i] :
% 0.28/0.48 ( ( subset @ A @ B )
% 0.28/0.48 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setextsub_type,type,
% 0.28/0.48 setextsub: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setextsub,definition,
% 0.28/0.48 ( setextsub
% 0.28/0.48 = ( ! [A: $i,B: $i] :
% 0.28/0.48 ( ( subset @ A @ B )
% 0.28/0.48 => ( ( subset @ B @ A )
% 0.28/0.48 => ( A = B ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(subsetemptysetimpeq_type,type,
% 0.28/0.48 subsetemptysetimpeq: $o ).
% 0.28/0.48
% 0.28/0.48 thf(subsetemptysetimpeq,definition,
% 0.28/0.48 ( subsetemptysetimpeq
% 0.28/0.48 = ( ! [A: $i] :
% 0.28/0.48 ( ( subset @ A @ emptyset )
% 0.28/0.48 => ( A = emptyset ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(powersetI1_type,type,
% 0.28/0.48 powersetI1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(powersetI1,definition,
% 0.28/0.48 ( powersetI1
% 0.28/0.48 = ( ! [A: $i,B: $i] :
% 0.28/0.48 ( ( subset @ B @ A )
% 0.28/0.48 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(powersetE1_type,type,
% 0.28/0.48 powersetE1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(powersetE1,definition,
% 0.28/0.48 ( powersetE1
% 0.28/0.48 = ( ! [A: $i,B: $i] :
% 0.28/0.48 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.48 => ( subset @ B @ A ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(inPowerset_type,type,
% 0.28/0.48 inPowerset: $o ).
% 0.28/0.48
% 0.28/0.48 thf(inPowerset,definition,
% 0.28/0.48 ( inPowerset
% 0.28/0.48 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(powersetsubset_type,type,
% 0.28/0.48 powersetsubset: $o ).
% 0.28/0.48
% 0.28/0.48 thf(powersetsubset,definition,
% 0.28/0.48 ( powersetsubset
% 0.28/0.48 = ( ! [A: $i,B: $i] :
% 0.28/0.48 ( ( subset @ A @ B )
% 0.28/0.48 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(sepInPowerset_type,type,
% 0.28/0.48 sepInPowerset: $o ).
% 0.28/0.48
% 0.28/0.48 thf(sepInPowerset,definition,
% 0.28/0.48 ( sepInPowerset
% 0.28/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.48 ( in
% 0.28/0.48 @ ( dsetconstr @ A
% 0.28/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.48 @ ( powerset @ A ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(sepSubset_type,type,
% 0.28/0.48 sepSubset: $o ).
% 0.28/0.48
% 0.28/0.48 thf(sepSubset,definition,
% 0.28/0.48 ( sepSubset
% 0.28/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.48 ( subset
% 0.28/0.48 @ ( dsetconstr @ A
% 0.28/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.48 @ A ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(binunion_type,type,
% 0.28/0.48 binunion: $i > $i > $i ).
% 0.28/0.48
% 0.28/0.48 thf(binunionIL_type,type,
% 0.28/0.48 binunionIL: $o ).
% 0.28/0.48
% 0.28/0.48 thf(binunionIL,definition,
% 0.28/0.48 ( binunionIL
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(upairset2IR_type,type,
% 0.28/0.48 upairset2IR: $o ).
% 0.28/0.48
% 0.28/0.48 thf(upairset2IR,definition,
% 0.28/0.48 ( upairset2IR
% 0.28/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(binunionIR_type,type,
% 0.28/0.48 binunionIR: $o ).
% 0.28/0.48
% 0.28/0.48 thf(binunionIR,definition,
% 0.28/0.48 ( binunionIR
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ B )
% 0.28/0.48 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(binunionEcases_type,type,
% 0.28/0.48 binunionEcases: $o ).
% 0.28/0.48
% 0.28/0.48 thf(binunionEcases,definition,
% 0.28/0.48 ( binunionEcases
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.28/0.48 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.28/0.48 => ( ( ( in @ Xx @ A )
% 0.28/0.48 => Xphi )
% 0.28/0.48 => ( ( ( in @ Xx @ B )
% 0.28/0.48 => Xphi )
% 0.28/0.48 => Xphi ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(binunionE_type,type,
% 0.28/0.48 binunionE: $o ).
% 0.28/0.48
% 0.28/0.48 thf(binunionE,definition,
% 0.28/0.48 ( binunionE
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.28/0.48 => ( ( in @ Xx @ A )
% 0.28/0.48 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(binunionLsub_type,type,
% 0.28/0.48 binunionLsub: $o ).
% 0.28/0.48
% 0.28/0.48 thf(binunionLsub,definition,
% 0.28/0.48 ( binunionLsub
% 0.28/0.48 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(binunionRsub_type,type,
% 0.28/0.48 binunionRsub: $o ).
% 0.28/0.48
% 0.28/0.48 thf(binunionRsub,definition,
% 0.28/0.48 ( binunionRsub
% 0.28/0.48 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(binintersect_type,type,
% 0.28/0.48 binintersect: $i > $i > $i ).
% 0.28/0.48
% 0.28/0.48 thf(binintersectI_type,type,
% 0.28/0.48 binintersectI: $o ).
% 0.28/0.48
% 0.28/0.48 thf(binintersectI,definition,
% 0.28/0.48 ( binintersectI
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( in @ Xx @ B )
% 0.28/0.48 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(binintersectSubset5_type,type,
% 0.28/0.48 binintersectSubset5: $o ).
% 0.28/0.48
% 0.28/0.48 thf(binintersectSubset5,definition,
% 0.28/0.48 ( binintersectSubset5
% 0.28/0.48 = ( ! [A: $i,B: $i,C: $i] :
% 0.28/0.48 ( ( subset @ C @ A )
% 0.28/0.48 => ( ( subset @ C @ B )
% 0.28/0.48 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(binintersectEL_type,type,
% 0.28/0.48 binintersectEL: $o ).
% 0.28/0.48
% 0.28/0.48 thf(binintersectEL,definition,
% 0.28/0.48 ( binintersectEL
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.28/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(binintersectLsub_type,type,
% 0.28/0.48 binintersectLsub: $o ).
% 0.28/0.48
% 0.28/0.48 thf(binintersectLsub,definition,
% 0.28/0.48 ( binintersectLsub
% 0.28/0.48 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(binintersectSubset2_type,type,
% 0.28/0.48 binintersectSubset2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(binintersectSubset2,definition,
% 0.28/0.48 ( binintersectSubset2
% 0.28/0.48 = ( ! [A: $i,B: $i] :
% 0.28/0.48 ( ( subset @ A @ B )
% 0.28/0.48 => ( ( binintersect @ A @ B )
% 0.28/0.48 = A ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(binintersectSubset3_type,type,
% 0.28/0.48 binintersectSubset3: $o ).
% 0.28/0.48
% 0.28/0.48 thf(binintersectSubset3,definition,
% 0.28/0.48 ( binintersectSubset3
% 0.28/0.48 = ( ! [A: $i,B: $i] :
% 0.28/0.48 ( ( ( binintersect @ A @ B )
% 0.28/0.48 = B )
% 0.28/0.48 => ( subset @ B @ A ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(binintersectER_type,type,
% 0.28/0.48 binintersectER: $o ).
% 0.28/0.48
% 0.28/0.48 thf(binintersectER,definition,
% 0.28/0.48 ( binintersectER
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.28/0.48 => ( in @ Xx @ B ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(disjointsetsI1_type,type,
% 0.28/0.48 disjointsetsI1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(disjointsetsI1,definition,
% 0.28/0.48 ( disjointsetsI1
% 0.28/0.48 = ( ! [A: $i,B: $i] :
% 0.28/0.48 ( ~ ? [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 & ( in @ Xx @ B ) )
% 0.28/0.48 => ( ( binintersect @ A @ B )
% 0.28/0.48 = emptyset ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(binintersectRsub_type,type,
% 0.28/0.48 binintersectRsub: $o ).
% 0.28/0.48
% 0.28/0.48 thf(binintersectRsub,definition,
% 0.28/0.48 ( binintersectRsub
% 0.28/0.48 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(binintersectSubset4_type,type,
% 0.28/0.48 binintersectSubset4: $o ).
% 0.28/0.48
% 0.28/0.48 thf(binintersectSubset4,definition,
% 0.28/0.48 ( binintersectSubset4
% 0.28/0.48 = ( ! [A: $i,B: $i] :
% 0.28/0.48 ( ( subset @ B @ A )
% 0.28/0.48 => ( ( binintersect @ A @ B )
% 0.28/0.48 = B ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(binintersectSubset1_type,type,
% 0.28/0.48 binintersectSubset1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(binintersectSubset1,definition,
% 0.28/0.48 ( binintersectSubset1
% 0.28/0.48 = ( ! [A: $i,B: $i] :
% 0.28/0.48 ( ( ( binintersect @ A @ B )
% 0.28/0.48 = A )
% 0.28/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(bs114d_type,type,
% 0.28/0.48 bs114d: $o ).
% 0.28/0.48
% 0.28/0.48 thf(bs114d,definition,
% 0.28/0.48 ( bs114d
% 0.28/0.48 = ( ! [A: $i,B: $i,C: $i] :
% 0.28/0.48 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.28/0.48 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(regular_type,type,
% 0.28/0.48 regular: $i > $o ).
% 0.28/0.48
% 0.28/0.48 thf(setminus_type,type,
% 0.28/0.48 setminus: $i > $i > $i ).
% 0.28/0.48
% 0.28/0.48 thf(setminusI_type,type,
% 0.28/0.48 setminusI: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setminusI,definition,
% 0.28/0.48 ( setminusI
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ~ ( in @ Xx @ B )
% 0.28/0.48 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setminusEL_type,type,
% 0.28/0.48 setminusEL: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setminusEL,definition,
% 0.28/0.48 ( setminusEL
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.28/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setminusER_type,type,
% 0.28/0.48 setminusER: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setminusER,definition,
% 0.28/0.48 ( setminusER
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.28/0.48 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setminusSubset2_type,type,
% 0.28/0.48 setminusSubset2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setminusSubset2,definition,
% 0.28/0.48 ( setminusSubset2
% 0.28/0.48 = ( ! [A: $i,B: $i] :
% 0.28/0.48 ( ( subset @ A @ B )
% 0.28/0.48 => ( ( setminus @ A @ B )
% 0.28/0.48 = emptyset ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setminusERneg_type,type,
% 0.28/0.48 setminusERneg: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setminusERneg,definition,
% 0.28/0.48 ( setminusERneg
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.28/0.48 => ( ( in @ Xx @ A )
% 0.28/0.48 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setminusELneg_type,type,
% 0.28/0.48 setminusELneg: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setminusELneg,definition,
% 0.28/0.48 ( setminusELneg
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.28/0.48 => ( ~ ( in @ Xx @ B )
% 0.28/0.48 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setminusILneg_type,type,
% 0.28/0.48 setminusILneg: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setminusILneg,definition,
% 0.28/0.48 ( setminusILneg
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ~ ( in @ Xx @ A )
% 0.28/0.48 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setminusIRneg_type,type,
% 0.28/0.48 setminusIRneg: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setminusIRneg,definition,
% 0.28/0.48 ( setminusIRneg
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ B )
% 0.28/0.48 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setminusLsub_type,type,
% 0.28/0.48 setminusLsub: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setminusLsub,definition,
% 0.28/0.48 ( setminusLsub
% 0.28/0.48 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setminusSubset1_type,type,
% 0.28/0.48 setminusSubset1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setminusSubset1,definition,
% 0.28/0.48 ( setminusSubset1
% 0.28/0.48 = ( ! [A: $i,B: $i] :
% 0.28/0.48 ( ( ( setminus @ A @ B )
% 0.28/0.48 = emptyset )
% 0.28/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(symdiff_type,type,
% 0.28/0.48 symdiff: $i > $i > $i ).
% 0.28/0.48
% 0.28/0.48 thf(symdiffE_type,type,
% 0.28/0.48 symdiffE: $o ).
% 0.28/0.48
% 0.28/0.48 thf(symdiffE,definition,
% 0.28/0.48 ( symdiffE
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.28/0.48 => ! [Xphi: $o] :
% 0.28/0.48 ( ( ( in @ Xx @ A )
% 0.28/0.48 => ( ~ ( in @ Xx @ B )
% 0.28/0.48 => Xphi ) )
% 0.28/0.48 => ( ( ~ ( in @ Xx @ A )
% 0.28/0.48 => ( ( in @ Xx @ B )
% 0.28/0.48 => Xphi ) )
% 0.28/0.48 => Xphi ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(symdiffI1_type,type,
% 0.28/0.48 symdiffI1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(symdiffI1,definition,
% 0.28/0.48 ( symdiffI1
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ~ ( in @ Xx @ B )
% 0.28/0.48 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(symdiffI2_type,type,
% 0.28/0.48 symdiffI2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(symdiffI2,definition,
% 0.28/0.48 ( symdiffI2
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ~ ( in @ Xx @ A )
% 0.28/0.48 => ( ( in @ Xx @ B )
% 0.28/0.48 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(symdiffIneg1_type,type,
% 0.28/0.48 symdiffIneg1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(symdiffIneg1,definition,
% 0.28/0.48 ( symdiffIneg1
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( in @ Xx @ B )
% 0.28/0.48 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(symdiffIneg2_type,type,
% 0.28/0.48 symdiffIneg2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(symdiffIneg2,definition,
% 0.28/0.48 ( symdiffIneg2
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ~ ( in @ Xx @ A )
% 0.28/0.48 => ( ~ ( in @ Xx @ B )
% 0.28/0.48 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(iskpair_type,type,
% 0.28/0.48 iskpair: $i > $o ).
% 0.28/0.48
% 0.28/0.48 thf(secondinupair_type,type,
% 0.28/0.48 secondinupair: $o ).
% 0.28/0.48
% 0.28/0.48 thf(secondinupair,definition,
% 0.28/0.48 ( secondinupair
% 0.28/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setukpairIL_type,type,
% 0.28/0.48 setukpairIL: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setukpairIL,definition,
% 0.28/0.48 ( setukpairIL
% 0.28/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setukpairIR_type,type,
% 0.28/0.48 setukpairIR: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setukpairIR,definition,
% 0.28/0.48 ( setukpairIR
% 0.28/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(kpairiskpair_type,type,
% 0.28/0.48 kpairiskpair: $o ).
% 0.28/0.48
% 0.28/0.48 thf(kpairiskpair,definition,
% 0.28/0.48 ( kpairiskpair
% 0.28/0.48 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(kpair_type,type,
% 0.28/0.48 kpair: $i > $i > $i ).
% 0.28/0.48
% 0.28/0.48 thf(kpairp_type,type,
% 0.28/0.48 kpairp: $o ).
% 0.28/0.48
% 0.28/0.48 thf(kpairp,definition,
% 0.28/0.48 ( kpairp
% 0.28/0.48 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(cartprod_type,type,
% 0.28/0.48 cartprod: $i > $i > $i ).
% 0.28/0.48
% 0.28/0.48 thf(singletonsubset_type,type,
% 0.28/0.48 singletonsubset: $o ).
% 0.28/0.48
% 0.28/0.48 thf(singletonsubset,definition,
% 0.28/0.48 ( singletonsubset
% 0.28/0.48 = ( ! [A: $i,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(singletoninpowerset_type,type,
% 0.28/0.48 singletoninpowerset: $o ).
% 0.28/0.48
% 0.28/0.48 thf(singletoninpowerset,definition,
% 0.28/0.48 ( singletoninpowerset
% 0.28/0.48 = ( ! [A: $i,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(singletoninpowunion_type,type,
% 0.28/0.48 singletoninpowunion: $o ).
% 0.28/0.48
% 0.28/0.48 thf(singletoninpowunion,definition,
% 0.28/0.48 ( singletoninpowunion
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(upairset2E_type,type,
% 0.28/0.48 upairset2E: $o ).
% 0.28/0.48
% 0.28/0.48 thf(upairset2E,definition,
% 0.28/0.48 ( upairset2E
% 0.28/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.28/0.48 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.28/0.48 => ( ( Xz = Xx )
% 0.28/0.48 | ( Xz = Xy ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(upairsubunion_type,type,
% 0.28/0.48 upairsubunion: $o ).
% 0.28/0.48
% 0.28/0.48 thf(upairsubunion,definition,
% 0.28/0.48 ( upairsubunion
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ B )
% 0.28/0.48 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(upairinpowunion_type,type,
% 0.28/0.48 upairinpowunion: $o ).
% 0.28/0.48
% 0.28/0.48 thf(upairinpowunion,definition,
% 0.28/0.48 ( upairinpowunion
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ B )
% 0.28/0.48 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(ubforcartprodlem1_type,type,
% 0.28/0.48 ubforcartprodlem1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(ubforcartprodlem1,definition,
% 0.28/0.48 ( ubforcartprodlem1
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ B )
% 0.28/0.48 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(ubforcartprodlem2_type,type,
% 0.28/0.48 ubforcartprodlem2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(ubforcartprodlem2,definition,
% 0.28/0.48 ( ubforcartprodlem2
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ B )
% 0.28/0.48 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(ubforcartprodlem3_type,type,
% 0.28/0.48 ubforcartprodlem3: $o ).
% 0.28/0.48
% 0.28/0.48 thf(ubforcartprodlem3,definition,
% 0.28/0.48 ( ubforcartprodlem3
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ B )
% 0.28/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(cartprodpairin_type,type,
% 0.28/0.48 cartprodpairin: $o ).
% 0.28/0.48
% 0.28/0.48 thf(cartprodpairin,definition,
% 0.28/0.48 ( cartprodpairin
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ B )
% 0.28/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(cartprodmempair1_type,type,
% 0.28/0.48 cartprodmempair1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(cartprodmempair1,definition,
% 0.28/0.48 ( cartprodmempair1
% 0.28/0.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.28/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.28/0.48 => ? [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 & ? [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ B )
% 0.28/0.48 & ( Xu
% 0.28/0.48 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(cartprodmempair_type,type,
% 0.28/0.48 cartprodmempair: $o ).
% 0.28/0.48
% 0.28/0.48 thf(cartprodmempair,definition,
% 0.28/0.48 ( cartprodmempair
% 0.28/0.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.28/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.28/0.48 => ( iskpair @ Xu ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setunionE2_type,type,
% 0.28/0.48 setunionE2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setunionE2,definition,
% 0.28/0.48 ( setunionE2
% 0.28/0.48 = ( ! [A: $i,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.48 => ? [X: $i] :
% 0.28/0.48 ( ( in @ X @ A )
% 0.28/0.48 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setunionsingleton1_type,type,
% 0.28/0.48 setunionsingleton1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setunionsingleton1,definition,
% 0.28/0.48 ( setunionsingleton1
% 0.28/0.48 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setunionsingleton2_type,type,
% 0.28/0.48 setunionsingleton2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setunionsingleton2,definition,
% 0.28/0.48 ( setunionsingleton2
% 0.28/0.48 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setunionsingleton_type,type,
% 0.28/0.48 setunionsingleton: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setunionsingleton,definition,
% 0.28/0.48 ( setunionsingleton
% 0.28/0.48 = ( ! [Xx: $i] :
% 0.28/0.48 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.28/0.48 = Xx ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(singleton_type,type,
% 0.28/0.48 singleton: $i > $o ).
% 0.28/0.48
% 0.28/0.48 thf(singletonprop_type,type,
% 0.28/0.48 singletonprop: $o ).
% 0.28/0.48
% 0.28/0.48 thf(singletonprop,definition,
% 0.28/0.48 ( singletonprop
% 0.28/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.48 ( ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ A )
% 0.28/0.48 => ( ( Xphi @ Xx )
% 0.28/0.48 => ( ( Xphi @ Xy )
% 0.28/0.48 => ( Xx = Xy ) ) ) ) )
% 0.28/0.48 => ( ? [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 & ( Xphi @ Xx ) )
% 0.28/0.48 => ( singleton
% 0.28/0.48 @ ( dsetconstr @ A
% 0.28/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(ex1_type,type,
% 0.28/0.48 ex1: $i > ( $i > $o ) > $o ).
% 0.28/0.48
% 0.28/0.48 thf(ex1,definition,
% 0.28/0.48 ( ex1
% 0.28/0.48 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.28/0.48 ( singleton
% 0.28/0.48 @ ( dsetconstr @ A
% 0.28/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(ex1E1_type,type,
% 0.28/0.48 ex1E1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(ex1E1,definition,
% 0.28/0.48 ( ex1E1
% 0.28/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.48 ( ( ex1 @ A
% 0.28/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.48 => ? [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(ex1I_type,type,
% 0.28/0.48 ex1I: $o ).
% 0.28/0.48
% 0.28/0.48 thf(ex1I,definition,
% 0.28/0.48 ( ex1I
% 0.28/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( Xphi @ Xx )
% 0.28/0.48 => ( ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ A )
% 0.28/0.48 => ( ( Xphi @ Xy )
% 0.28/0.48 => ( Xy = Xx ) ) )
% 0.28/0.48 => ( ex1 @ A
% 0.28/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(ex1I2_type,type,
% 0.28/0.48 ex1I2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(ex1I2,definition,
% 0.28/0.48 ( ex1I2
% 0.28/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.48 ( ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ A )
% 0.28/0.48 => ( ( Xphi @ Xx )
% 0.28/0.48 => ( ( Xphi @ Xy )
% 0.28/0.48 => ( Xx = Xy ) ) ) ) )
% 0.28/0.48 => ( ? [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 & ( Xphi @ Xx ) )
% 0.28/0.48 => ( ex1 @ A
% 0.28/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(singletonsuniq_type,type,
% 0.28/0.48 singletonsuniq: $o ).
% 0.28/0.48
% 0.28/0.48 thf(singletonsuniq,definition,
% 0.28/0.48 ( singletonsuniq
% 0.28/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.48 ( ( ( setadjoin @ Xx @ emptyset )
% 0.28/0.48 = ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.48 => ( Xx = Xy ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(atmost1p_type,type,
% 0.28/0.48 atmost1p: $i > $o ).
% 0.28/0.48
% 0.28/0.48 thf(atleast2p_type,type,
% 0.28/0.48 atleast2p: $i > $o ).
% 0.28/0.48
% 0.28/0.48 thf(atmost2p_type,type,
% 0.28/0.48 atmost2p: $i > $o ).
% 0.28/0.48
% 0.28/0.48 thf(upairsetp_type,type,
% 0.28/0.48 upairsetp: $i > $o ).
% 0.28/0.48
% 0.28/0.48 thf(setukpairinjL1_type,type,
% 0.28/0.48 setukpairinjL1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setukpairinjL1,definition,
% 0.28/0.48 ( setukpairinjL1
% 0.28/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.28/0.48 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.28/0.48 => ( Xx = Xz ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(kfstsingleton_type,type,
% 0.28/0.48 kfstsingleton: $o ).
% 0.28/0.48
% 0.28/0.48 thf(kfstsingleton,definition,
% 0.28/0.48 ( kfstsingleton
% 0.28/0.48 = ( ! [Xu: $i] :
% 0.28/0.48 ( ( iskpair @ Xu )
% 0.28/0.48 => ( singleton
% 0.28/0.48 @ ( dsetconstr @ ( setunion @ Xu )
% 0.28/0.48 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(theprop_type,type,
% 0.28/0.48 theprop: $o ).
% 0.28/0.48
% 0.28/0.48 thf(theprop,definition,
% 0.28/0.48 ( theprop
% 0.28/0.48 = ( ! [X: $i] :
% 0.28/0.48 ( ( singleton @ X )
% 0.28/0.48 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(kfst_type,type,
% 0.28/0.48 kfst: $i > $i ).
% 0.28/0.48
% 0.28/0.48 thf(kfstpairEq_type,type,
% 0.28/0.48 kfstpairEq: $o ).
% 0.28/0.48
% 0.28/0.48 thf(kfstpairEq,definition,
% 0.28/0.48 ( kfstpairEq
% 0.28/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.48 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.28/0.48 = Xx ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(cartprodfstin_type,type,
% 0.28/0.48 cartprodfstin: $o ).
% 0.28/0.48
% 0.28/0.48 thf(cartprodfstin,definition,
% 0.28/0.48 ( cartprodfstin
% 0.28/0.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.28/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.28/0.48 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setukpairinjL2_type,type,
% 0.28/0.48 setukpairinjL2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setukpairinjL2,definition,
% 0.28/0.48 ( setukpairinjL2
% 0.28/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.28/0.48 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.28/0.48 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.28/0.48 => ( Xx = Xz ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setukpairinjL_type,type,
% 0.28/0.48 setukpairinjL: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setukpairinjL,definition,
% 0.28/0.48 ( setukpairinjL
% 0.28/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.28/0.48 ( ( ( kpair @ Xx @ Xy )
% 0.28/0.48 = ( kpair @ Xz @ Xu ) )
% 0.28/0.48 => ( Xx = Xz ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setukpairinjR11_type,type,
% 0.28/0.48 setukpairinjR11: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setukpairinjR11,definition,
% 0.28/0.48 ( setukpairinjR11
% 0.28/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.48 ( ( Xx = Xy )
% 0.28/0.48 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.48 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setukpairinjR12_type,type,
% 0.28/0.48 setukpairinjR12: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setukpairinjR12,definition,
% 0.28/0.48 ( setukpairinjR12
% 0.28/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.48 ( ( Xx = Xy )
% 0.28/0.48 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.28/0.48 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setukpairinjR1_type,type,
% 0.28/0.48 setukpairinjR1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setukpairinjR1,definition,
% 0.28/0.48 ( setukpairinjR1
% 0.28/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.28/0.48 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.28/0.48 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.28/0.48 => ( ( Xz = Xu )
% 0.28/0.48 => ( Xy = Xu ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(upairequniteq_type,type,
% 0.28/0.48 upairequniteq: $o ).
% 0.28/0.48
% 0.28/0.48 thf(upairequniteq,definition,
% 0.28/0.48 ( upairequniteq
% 0.28/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.28/0.48 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.48 = ( setadjoin @ Xz @ emptyset ) )
% 0.28/0.48 => ( Xx = Xy ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setukpairinjR2_type,type,
% 0.28/0.48 setukpairinjR2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setukpairinjR2,definition,
% 0.28/0.48 ( setukpairinjR2
% 0.28/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.28/0.48 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.28/0.48 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.28/0.48 => ( Xy = Xu ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setukpairinjR_type,type,
% 0.28/0.48 setukpairinjR: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setukpairinjR,definition,
% 0.28/0.48 ( setukpairinjR
% 0.28/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.28/0.48 ( ( ( kpair @ Xx @ Xy )
% 0.28/0.48 = ( kpair @ Xz @ Xu ) )
% 0.28/0.48 => ( Xy = Xu ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(ksndsingleton_type,type,
% 0.28/0.48 ksndsingleton: $o ).
% 0.28/0.48
% 0.28/0.48 thf(ksndsingleton,definition,
% 0.28/0.48 ( ksndsingleton
% 0.28/0.48 = ( ! [Xu: $i] :
% 0.28/0.48 ( ( iskpair @ Xu )
% 0.28/0.48 => ( singleton
% 0.28/0.48 @ ( dsetconstr @ ( setunion @ Xu )
% 0.28/0.48 @ ^ [Xx: $i] :
% 0.28/0.48 ( Xu
% 0.28/0.48 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(ksnd_type,type,
% 0.28/0.48 ksnd: $i > $i ).
% 0.28/0.48
% 0.28/0.48 thf(ksndpairEq_type,type,
% 0.28/0.48 ksndpairEq: $o ).
% 0.28/0.48
% 0.28/0.48 thf(ksndpairEq,definition,
% 0.28/0.48 ( ksndpairEq
% 0.28/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.48 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.28/0.48 = Xy ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(kpairsurjEq_type,type,
% 0.28/0.48 kpairsurjEq: $o ).
% 0.28/0.48
% 0.28/0.48 thf(kpairsurjEq,definition,
% 0.28/0.48 ( kpairsurjEq
% 0.28/0.48 = ( ! [Xu: $i] :
% 0.28/0.48 ( ( iskpair @ Xu )
% 0.28/0.48 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.28/0.48 = Xu ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(cartprodsndin_type,type,
% 0.28/0.48 cartprodsndin: $o ).
% 0.28/0.48
% 0.28/0.48 thf(cartprodsndin,definition,
% 0.28/0.48 ( cartprodsndin
% 0.28/0.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.28/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.28/0.48 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(cartprodpairmemEL_type,type,
% 0.28/0.48 cartprodpairmemEL: $o ).
% 0.28/0.48
% 0.28/0.48 thf(cartprodpairmemEL,definition,
% 0.28/0.48 ( cartprodpairmemEL
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.28/0.48 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.28/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(cartprodpairmemER_type,type,
% 0.28/0.48 cartprodpairmemER: $o ).
% 0.28/0.48
% 0.28/0.48 thf(cartprodpairmemER,definition,
% 0.28/0.48 ( cartprodpairmemER
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.28/0.48 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.28/0.48 => ( in @ Xy @ B ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(cartprodmempaircEq_type,type,
% 0.28/0.48 cartprodmempaircEq: $o ).
% 0.28/0.48
% 0.28/0.48 thf(cartprodmempaircEq,definition,
% 0.28/0.48 ( cartprodmempaircEq
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ B )
% 0.28/0.48 => ( ( kpair @ Xx @ Xy )
% 0.28/0.48 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(cartprodfstpairEq_type,type,
% 0.28/0.48 cartprodfstpairEq: $o ).
% 0.28/0.48
% 0.28/0.48 thf(cartprodfstpairEq,definition,
% 0.28/0.48 ( cartprodfstpairEq
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ B )
% 0.28/0.48 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.28/0.48 = Xx ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(cartprodsndpairEq_type,type,
% 0.28/0.48 cartprodsndpairEq: $o ).
% 0.28/0.48
% 0.28/0.48 thf(cartprodsndpairEq,definition,
% 0.28/0.48 ( cartprodsndpairEq
% 0.28/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ B )
% 0.28/0.48 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.28/0.48 = Xy ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(cartprodpairsurjEq_type,type,
% 0.28/0.48 cartprodpairsurjEq: $o ).
% 0.28/0.48
% 0.28/0.48 thf(cartprodpairsurjEq,definition,
% 0.28/0.48 ( cartprodpairsurjEq
% 0.28/0.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.28/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.28/0.48 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.28/0.48 = Xu ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(breln_type,type,
% 0.28/0.48 breln: $i > $i > $i > $o ).
% 0.28/0.48
% 0.28/0.48 thf(breln,definition,
% 0.28/0.48 ( breln
% 0.28/0.48 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(dpsetconstr_type,type,
% 0.28/0.48 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.28/0.48
% 0.28/0.48 thf(dpsetconstrI_type,type,
% 0.28/0.48 dpsetconstrI: $o ).
% 0.28/0.48
% 0.28/0.48 thf(dpsetconstrI,definition,
% 0.28/0.48 ( dpsetconstrI
% 0.28/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ B )
% 0.28/0.48 => ( ( Xphi @ Xx @ Xy )
% 0.28/0.48 => ( in @ ( kpair @ Xx @ Xy )
% 0.28/0.48 @ ( dpsetconstr @ A @ B
% 0.28/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(dpsetconstrSub_type,type,
% 0.28/0.48 dpsetconstrSub: $o ).
% 0.28/0.48
% 0.28/0.48 thf(dpsetconstrSub,definition,
% 0.28/0.48 ( dpsetconstrSub
% 0.28/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.28/0.48 ( subset
% 0.28/0.48 @ ( dpsetconstr @ A @ B
% 0.28/0.48 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.28/0.48 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setOfPairsIsBReln_type,type,
% 0.28/0.48 setOfPairsIsBReln: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setOfPairsIsBReln,definition,
% 0.28/0.48 ( setOfPairsIsBReln
% 0.28/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.28/0.48 ( breln @ A @ B
% 0.28/0.48 @ ( dpsetconstr @ A @ B
% 0.28/0.48 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(dpsetconstrERa_type,type,
% 0.28/0.48 dpsetconstrERa: $o ).
% 0.28/0.48
% 0.28/0.48 thf(dpsetconstrERa,definition,
% 0.28/0.48 ( dpsetconstrERa
% 0.28/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ B )
% 0.28/0.48 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.28/0.48 @ ( dpsetconstr @ A @ B
% 0.28/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.28/0.48 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(dpsetconstrEL1_type,type,
% 0.28/0.48 dpsetconstrEL1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(dpsetconstrEL1,definition,
% 0.28/0.48 ( dpsetconstrEL1
% 0.28/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.28/0.48 ( ( in @ ( kpair @ Xx @ Xy )
% 0.28/0.48 @ ( dpsetconstr @ A @ B
% 0.28/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.28/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(dpsetconstrEL2_type,type,
% 0.28/0.48 dpsetconstrEL2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(dpsetconstrEL2,definition,
% 0.28/0.48 ( dpsetconstrEL2
% 0.28/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.28/0.48 ( ( in @ ( kpair @ Xx @ Xy )
% 0.28/0.48 @ ( dpsetconstr @ A @ B
% 0.28/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.28/0.48 => ( in @ Xy @ B ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(dpsetconstrER_type,type,
% 0.28/0.48 dpsetconstrER: $o ).
% 0.28/0.48
% 0.28/0.48 thf(dpsetconstrER,definition,
% 0.28/0.48 ( dpsetconstrER
% 0.28/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.28/0.48 ( ( in @ ( kpair @ Xx @ Xy )
% 0.28/0.48 @ ( dpsetconstr @ A @ B
% 0.28/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.28/0.48 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(func_type,type,
% 0.28/0.48 func: $i > $i > $i > $o ).
% 0.28/0.48
% 0.28/0.48 thf(funcSet_type,type,
% 0.28/0.48 funcSet: $i > $i > $i ).
% 0.28/0.48
% 0.28/0.48 thf(funcImageSingleton_type,type,
% 0.28/0.48 funcImageSingleton: $o ).
% 0.28/0.48
% 0.28/0.48 thf(funcImageSingleton,definition,
% 0.28/0.48 ( funcImageSingleton
% 0.28/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.48 ( ( func @ A @ B @ Xf )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( singleton
% 0.28/0.48 @ ( dsetconstr @ B
% 0.28/0.48 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(apProp_type,type,
% 0.28/0.48 apProp: $o ).
% 0.28/0.48
% 0.28/0.48 thf(apProp,definition,
% 0.28/0.48 ( apProp
% 0.28/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.48 ( ( func @ A @ B @ Xf )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( in
% 0.28/0.48 @ ( setunion
% 0.28/0.48 @ ( dsetconstr @ B
% 0.28/0.48 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.28/0.48 @ B ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(ap_type,type,
% 0.28/0.48 ap: $i > $i > $i > $i > $i ).
% 0.28/0.48
% 0.28/0.48 thf(app_type,type,
% 0.28/0.48 app: $o ).
% 0.28/0.48
% 0.28/0.48 thf(app,definition,
% 0.28/0.48 ( app
% 0.28/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.48 ( ( func @ A @ B @ Xf )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(infuncsetfunc_type,type,
% 0.28/0.48 infuncsetfunc: $o ).
% 0.28/0.48
% 0.28/0.48 thf(infuncsetfunc,definition,
% 0.28/0.48 ( infuncsetfunc
% 0.28/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.28/0.48 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(ap2p_type,type,
% 0.28/0.48 ap2p: $o ).
% 0.28/0.48
% 0.28/0.48 thf(ap2p,definition,
% 0.28/0.48 ( ap2p
% 0.28/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(funcinfuncset_type,type,
% 0.28/0.48 funcinfuncset: $o ).
% 0.28/0.48
% 0.28/0.48 thf(funcinfuncset,definition,
% 0.28/0.48 ( funcinfuncset
% 0.28/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.48 ( ( func @ A @ B @ Xf )
% 0.28/0.48 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(lamProp_type,type,
% 0.28/0.48 lamProp: $o ).
% 0.28/0.48
% 0.28/0.48 thf(lamProp,definition,
% 0.28/0.48 ( lamProp
% 0.28/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.28/0.48 ( ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.28/0.48 => ( func @ A @ B
% 0.28/0.48 @ ( dpsetconstr @ A @ B
% 0.28/0.48 @ ^ [Xx: $i,Xy: $i] :
% 0.28/0.48 ( ( Xf @ Xx )
% 0.28/0.48 = Xy ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(lam_type,type,
% 0.28/0.48 lam: $i > $i > ( $i > $i ) > $i ).
% 0.28/0.48
% 0.28/0.48 thf(lamp_type,type,
% 0.28/0.48 lamp: $o ).
% 0.28/0.48
% 0.28/0.48 thf(lamp,definition,
% 0.28/0.48 ( lamp
% 0.28/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.28/0.48 ( ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.28/0.48 => ( func @ A @ B
% 0.28/0.48 @ ( lam @ A @ B
% 0.28/0.48 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(lam2p_type,type,
% 0.28/0.48 lam2p: $o ).
% 0.28/0.48
% 0.28/0.48 thf(lam2p,definition,
% 0.28/0.48 ( lam2p
% 0.28/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.28/0.48 ( ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.28/0.48 => ( in
% 0.28/0.48 @ ( lam @ A @ B
% 0.28/0.48 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.28/0.48 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(brelnall1_type,type,
% 0.28/0.48 brelnall1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(brelnall1,definition,
% 0.28/0.48 ( brelnall1
% 0.28/0.48 = ( ! [A: $i,B: $i,R: $i] :
% 0.28/0.48 ( ( breln @ A @ B @ R )
% 0.28/0.48 => ! [Xphi: $i > $o] :
% 0.28/0.48 ( ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ B )
% 0.28/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.28/0.48 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ R )
% 0.28/0.48 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(brelnall2_type,type,
% 0.28/0.48 brelnall2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(brelnall2,definition,
% 0.28/0.48 ( brelnall2
% 0.28/0.48 = ( ! [A: $i,B: $i,R: $i] :
% 0.28/0.48 ( ( breln @ A @ B @ R )
% 0.28/0.48 => ! [Xphi: $i > $o] :
% 0.28/0.48 ( ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ B )
% 0.28/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.28/0.48 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ R )
% 0.28/0.48 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(ex1E2_type,type,
% 0.28/0.48 ex1E2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(ex1E2,definition,
% 0.28/0.48 ( ex1E2
% 0.28/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.48 ( ( ex1 @ A
% 0.28/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ A )
% 0.28/0.48 => ( ( Xphi @ Xx )
% 0.28/0.48 => ( ( Xphi @ Xy )
% 0.28/0.48 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(funcGraphProp1_type,type,
% 0.28/0.48 funcGraphProp1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(funcGraphProp1,definition,
% 0.28/0.48 ( funcGraphProp1
% 0.28/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.48 ( ( func @ A @ B @ Xf )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(funcGraphProp3_type,type,
% 0.28/0.48 funcGraphProp3: $o ).
% 0.28/0.48
% 0.28/0.48 thf(funcGraphProp3,definition,
% 0.28/0.48 ( funcGraphProp3
% 0.28/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(funcGraphProp2_type,type,
% 0.28/0.48 funcGraphProp2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(funcGraphProp2,definition,
% 0.28/0.48 ( funcGraphProp2
% 0.28/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.48 ( ( func @ A @ B @ Xf )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ B )
% 0.28/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.28/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.28/0.48 = Xy ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(funcextLem_type,type,
% 0.28/0.48 funcextLem: $o ).
% 0.28/0.48
% 0.28/0.48 thf(funcextLem,definition,
% 0.28/0.48 ( funcextLem
% 0.28/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.48 ( ( func @ A @ B @ Xf )
% 0.28/0.48 => ! [Xg: $i] :
% 0.28/0.48 ( ( func @ A @ B @ Xg )
% 0.28/0.48 => ( ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.28/0.48 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ B )
% 0.28/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 0.28/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(funcGraphProp4_type,type,
% 0.28/0.48 funcGraphProp4: $o ).
% 0.28/0.48
% 0.28/0.48 thf(funcGraphProp4,definition,
% 0.28/0.48 ( funcGraphProp4
% 0.28/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ B )
% 0.28/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.28/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.28/0.48 = Xy ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(subbreln_type,type,
% 0.28/0.48 subbreln: $o ).
% 0.28/0.48
% 0.28/0.48 thf(subbreln,definition,
% 0.28/0.48 ( subbreln
% 0.28/0.48 = ( ! [A: $i,B: $i,R: $i] :
% 0.28/0.48 ( ( breln @ A @ B @ R )
% 0.28/0.48 => ! [S: $i] :
% 0.28/0.48 ( ( breln @ A @ B @ S )
% 0.28/0.48 => ( ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ B )
% 0.28/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.28/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.28/0.48 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(eqbreln_type,type,
% 0.28/0.48 eqbreln: $o ).
% 0.28/0.48
% 0.28/0.48 thf(eqbreln,definition,
% 0.28/0.48 ( eqbreln
% 0.28/0.48 = ( ! [A: $i,B: $i,R: $i] :
% 0.28/0.48 ( ( breln @ A @ B @ R )
% 0.28/0.48 => ! [S: $i] :
% 0.28/0.48 ( ( breln @ A @ B @ S )
% 0.28/0.48 => ( ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ B )
% 0.28/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.28/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.28/0.48 => ( ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ B )
% 0.28/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.28/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.28/0.48 => ( R = S ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(funcext_type,type,
% 0.28/0.48 funcext: $o ).
% 0.28/0.48
% 0.28/0.48 thf(funcext,definition,
% 0.28/0.48 ( funcext
% 0.28/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.48 ( ( func @ A @ B @ Xf )
% 0.28/0.48 => ! [Xg: $i] :
% 0.28/0.48 ( ( func @ A @ B @ Xg )
% 0.28/0.48 => ( ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.28/0.48 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.28/0.48 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(funcext2_type,type,
% 0.28/0.48 funcext2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(funcext2,definition,
% 0.28/0.48 ( funcext2
% 0.28/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.28/0.48 => ! [Xg: $i] :
% 0.28/0.48 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 0.28/0.48 => ( ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.28/0.48 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.28/0.48 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(ap2apEq1_type,type,
% 0.28/0.48 ap2apEq1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(ap2apEq1,definition,
% 0.28/0.48 ( ap2apEq1
% 0.28/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.28/0.48 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(ap2apEq2_type,type,
% 0.28/0.48 ap2apEq2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(ap2apEq2,definition,
% 0.28/0.48 ( ap2apEq2
% 0.28/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.48 ( ( func @ A @ B @ Xf )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.28/0.48 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(beta1_type,type,
% 0.28/0.48 beta1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(beta1,definition,
% 0.28/0.48 ( beta1
% 0.28/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.28/0.48 ( ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( ap @ A @ B
% 0.28/0.48 @ ( lam @ A @ B
% 0.28/0.48 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.28/0.48 @ Xx )
% 0.28/0.48 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(eta1_type,type,
% 0.28/0.48 eta1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(eta1,definition,
% 0.28/0.48 ( eta1
% 0.28/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.48 ( ( func @ A @ B @ Xf )
% 0.28/0.48 => ( ( lam @ A @ B
% 0.28/0.48 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.28/0.48 = Xf ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(lam2lamEq_type,type,
% 0.28/0.48 lam2lamEq: $o ).
% 0.28/0.48
% 0.28/0.48 thf(lam2lamEq,definition,
% 0.28/0.48 ( lam2lamEq
% 0.28/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.28/0.48 ( ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.28/0.48 => ( ( lam @ A @ B
% 0.28/0.48 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.28/0.48 = ( lam @ A @ B
% 0.28/0.48 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(beta2_type,type,
% 0.28/0.48 beta2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(beta2,definition,
% 0.28/0.48 ( beta2
% 0.28/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.28/0.48 ( ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( ap @ A @ B
% 0.28/0.48 @ ( lam @ A @ B
% 0.28/0.48 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.28/0.48 @ Xx )
% 0.28/0.48 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(eta2_type,type,
% 0.28/0.48 eta2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(eta2,definition,
% 0.28/0.48 ( eta2
% 0.28/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.28/0.48 => ( ( lam @ A @ B
% 0.28/0.48 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.28/0.48 = Xf ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(iffalseProp1_type,type,
% 0.28/0.48 iffalseProp1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(iffalseProp1,definition,
% 0.28/0.48 ( iffalseProp1
% 0.28/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ A )
% 0.28/0.48 => ( ~ Xphi
% 0.28/0.48 => ( in @ Xy
% 0.28/0.48 @ ( dsetconstr @ A
% 0.28/0.48 @ ^ [Xz: $i] :
% 0.28/0.48 ( ( Xphi
% 0.28/0.48 & ( Xz = Xx ) )
% 0.28/0.48 | ( ~ Xphi
% 0.28/0.48 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(iffalseProp2_type,type,
% 0.28/0.48 iffalseProp2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(iffalseProp2,definition,
% 0.28/0.48 ( iffalseProp2
% 0.28/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ A )
% 0.28/0.48 => ( ~ Xphi
% 0.28/0.48 => ( ( dsetconstr @ A
% 0.28/0.48 @ ^ [Xz: $i] :
% 0.28/0.48 ( ( Xphi
% 0.28/0.48 & ( Xz = Xx ) )
% 0.28/0.48 | ( ~ Xphi
% 0.28/0.48 & ( Xz = Xy ) ) ) )
% 0.28/0.48 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(iftrueProp1_type,type,
% 0.28/0.48 iftrueProp1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(iftrueProp1,definition,
% 0.28/0.48 ( iftrueProp1
% 0.28/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ A )
% 0.28/0.48 => ( Xphi
% 0.28/0.48 => ( in @ Xx
% 0.28/0.48 @ ( dsetconstr @ A
% 0.28/0.48 @ ^ [Xz: $i] :
% 0.28/0.48 ( ( Xphi
% 0.28/0.48 & ( Xz = Xx ) )
% 0.28/0.48 | ( ~ Xphi
% 0.28/0.48 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(iftrueProp2_type,type,
% 0.28/0.48 iftrueProp2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(iftrueProp2,definition,
% 0.28/0.48 ( iftrueProp2
% 0.28/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ A )
% 0.28/0.48 => ( Xphi
% 0.28/0.48 => ( ( dsetconstr @ A
% 0.28/0.48 @ ^ [Xz: $i] :
% 0.28/0.48 ( ( Xphi
% 0.28/0.48 & ( Xz = Xx ) )
% 0.28/0.48 | ( ~ Xphi
% 0.28/0.48 & ( Xz = Xy ) ) ) )
% 0.28/0.48 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(ifSingleton_type,type,
% 0.28/0.48 ifSingleton: $o ).
% 0.28/0.48
% 0.28/0.48 thf(ifSingleton,definition,
% 0.28/0.48 ( ifSingleton
% 0.28/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ A )
% 0.28/0.48 => ( singleton
% 0.28/0.48 @ ( dsetconstr @ A
% 0.28/0.48 @ ^ [Xz: $i] :
% 0.28/0.48 ( ( Xphi
% 0.28/0.48 & ( Xz = Xx ) )
% 0.28/0.48 | ( ~ Xphi
% 0.28/0.48 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(if_type,type,
% 0.28/0.48 if: $i > $o > $i > $i > $i ).
% 0.28/0.48
% 0.28/0.48 thf(ifp_type,type,
% 0.28/0.48 ifp: $o ).
% 0.28/0.48
% 0.28/0.48 thf(ifp,definition,
% 0.28/0.48 ( ifp
% 0.28/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ A )
% 0.28/0.48 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(theeq_type,type,
% 0.28/0.48 theeq: $o ).
% 0.28/0.48
% 0.28/0.48 thf(theeq,definition,
% 0.28/0.48 ( theeq
% 0.28/0.48 = ( ! [X: $i] :
% 0.28/0.48 ( ( singleton @ X )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ X )
% 0.28/0.48 => ( ( setunion @ X )
% 0.28/0.48 = Xx ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(iftrue_type,type,
% 0.28/0.48 iftrue: $o ).
% 0.28/0.48
% 0.28/0.48 thf(iftrue,definition,
% 0.28/0.48 ( iftrue
% 0.28/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ A )
% 0.28/0.48 => ( Xphi
% 0.28/0.48 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.28/0.48 = Xx ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(iffalse_type,type,
% 0.28/0.48 iffalse: $o ).
% 0.28/0.48
% 0.28/0.48 thf(iffalse,definition,
% 0.28/0.48 ( iffalse
% 0.28/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ A )
% 0.28/0.48 => ( ~ Xphi
% 0.28/0.48 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.28/0.48 = Xy ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(iftrueorfalse_type,type,
% 0.28/0.48 iftrueorfalse: $o ).
% 0.28/0.48
% 0.28/0.48 thf(iftrueorfalse,definition,
% 0.28/0.48 ( iftrueorfalse
% 0.28/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ! [Xy: $i] :
% 0.28/0.48 ( ( in @ Xy @ A )
% 0.28/0.48 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(binintersectT_lem_type,type,
% 0.28/0.48 binintersectT_lem: $o ).
% 0.28/0.48
% 0.28/0.48 thf(binintersectT_lem,definition,
% 0.28/0.48 ( binintersectT_lem
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(binunionT_lem_type,type,
% 0.28/0.48 binunionT_lem: $o ).
% 0.28/0.48
% 0.28/0.48 thf(binunionT_lem,definition,
% 0.28/0.48 ( binunionT_lem
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(powersetT_lem_type,type,
% 0.28/0.48 powersetT_lem: $o ).
% 0.28/0.48
% 0.28/0.48 thf(powersetT_lem,definition,
% 0.28/0.48 ( powersetT_lem
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setminusT_lem_type,type,
% 0.28/0.48 setminusT_lem: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setminusT_lem,definition,
% 0.28/0.48 ( setminusT_lem
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(complementT_lem_type,type,
% 0.28/0.48 complementT_lem: $o ).
% 0.28/0.48
% 0.28/0.48 thf(complementT_lem,definition,
% 0.28/0.48 ( complementT_lem
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(setextT_type,type,
% 0.28/0.48 setextT: $o ).
% 0.28/0.48
% 0.28/0.48 thf(setextT,definition,
% 0.28/0.48 ( setextT
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ( ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( in @ Xx @ X )
% 0.28/0.48 => ( in @ Xx @ Y ) ) )
% 0.28/0.48 => ( ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( in @ Xx @ Y )
% 0.28/0.48 => ( in @ Xx @ X ) ) )
% 0.28/0.48 => ( X = Y ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(subsetTI_type,type,
% 0.28/0.48 subsetTI: $o ).
% 0.28/0.48
% 0.28/0.48 thf(subsetTI,definition,
% 0.28/0.48 ( subsetTI
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ( ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( in @ Xx @ X )
% 0.28/0.48 => ( in @ Xx @ Y ) ) )
% 0.28/0.48 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(powersetTI1_type,type,
% 0.28/0.48 powersetTI1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(powersetTI1,definition,
% 0.28/0.48 ( powersetTI1
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ( ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( in @ Xx @ X )
% 0.28/0.48 => ( in @ Xx @ Y ) ) )
% 0.28/0.48 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(powersetTE1_type,type,
% 0.28/0.48 powersetTE1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(powersetTE1,definition,
% 0.28/0.48 ( powersetTE1
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( in @ X @ ( powerset @ Y ) )
% 0.28/0.48 => ( ( in @ Xx @ X )
% 0.28/0.48 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(complementTI1_type,type,
% 0.28/0.48 complementTI1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(complementTI1,definition,
% 0.28/0.48 ( complementTI1
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( in @ Xx @ X )
% 0.28/0.48 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(complementTE1_type,type,
% 0.28/0.48 complementTE1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(complementTE1,definition,
% 0.28/0.48 ( complementTE1
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 0.28/0.48 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(binintersectTELcontra_type,type,
% 0.28/0.48 binintersectTELcontra: $o ).
% 0.28/0.48
% 0.28/0.48 thf(binintersectTELcontra,definition,
% 0.28/0.48 ( binintersectTELcontra
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ~ ( in @ Xx @ X )
% 0.28/0.48 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(binintersectTERcontra_type,type,
% 0.28/0.48 binintersectTERcontra: $o ).
% 0.28/0.48
% 0.28/0.48 thf(binintersectTERcontra,definition,
% 0.28/0.48 ( binintersectTERcontra
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ~ ( in @ Xx @ Y )
% 0.28/0.48 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(contrasubsetT_type,type,
% 0.28/0.48 contrasubsetT: $o ).
% 0.28/0.48
% 0.28/0.48 thf(contrasubsetT,definition,
% 0.28/0.48 ( contrasubsetT
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.28/0.48 => ( ( in @ Xx @ Y )
% 0.28/0.48 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(contrasubsetT1_type,type,
% 0.28/0.48 contrasubsetT1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(contrasubsetT1,definition,
% 0.28/0.48 ( contrasubsetT1
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( subset @ X @ Y )
% 0.28/0.48 => ( ~ ( in @ Xx @ Y )
% 0.28/0.48 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(contrasubsetT2_type,type,
% 0.28/0.48 contrasubsetT2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(contrasubsetT2,definition,
% 0.28/0.48 ( contrasubsetT2
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ( ( subset @ X @ Y )
% 0.28/0.48 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(contrasubsetT3_type,type,
% 0.28/0.48 contrasubsetT3: $o ).
% 0.28/0.48
% 0.28/0.48 thf(contrasubsetT3,definition,
% 0.28/0.48 ( contrasubsetT3
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 0.28/0.48 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(doubleComplementI1_type,type,
% 0.28/0.48 doubleComplementI1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(doubleComplementI1,definition,
% 0.28/0.48 ( doubleComplementI1
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( in @ Xx @ X )
% 0.28/0.48 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(doubleComplementE1_type,type,
% 0.28/0.48 doubleComplementE1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(doubleComplementE1,definition,
% 0.28/0.48 ( doubleComplementE1
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 0.28/0.48 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(doubleComplementSub1_type,type,
% 0.28/0.48 doubleComplementSub1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(doubleComplementSub1,definition,
% 0.28/0.48 ( doubleComplementSub1
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(doubleComplementSub2_type,type,
% 0.28/0.48 doubleComplementSub2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(doubleComplementSub2,definition,
% 0.28/0.48 ( doubleComplementSub2
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(doubleComplementEq_type,type,
% 0.28/0.48 doubleComplementEq: $o ).
% 0.28/0.48
% 0.28/0.48 thf(doubleComplementEq,definition,
% 0.28/0.48 ( doubleComplementEq
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ( X
% 0.28/0.48 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(complementTnotintersectT_type,type,
% 0.28/0.48 complementTnotintersectT: $o ).
% 0.28/0.48
% 0.28/0.48 thf(complementTnotintersectT,definition,
% 0.28/0.48 ( complementTnotintersectT
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.28/0.48 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(complementImpComplementIntersect_type,type,
% 0.28/0.48 complementImpComplementIntersect: $o ).
% 0.28/0.48
% 0.28/0.48 thf(complementImpComplementIntersect,definition,
% 0.28/0.48 ( complementImpComplementIntersect
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.28/0.48 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(complementSubsetComplementIntersect_type,type,
% 0.28/0.48 complementSubsetComplementIntersect: $o ).
% 0.28/0.48
% 0.28/0.48 thf(complementSubsetComplementIntersect,definition,
% 0.28/0.48 ( complementSubsetComplementIntersect
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(complementInPowersetComplementIntersect_type,type,
% 0.28/0.48 complementInPowersetComplementIntersect: $o ).
% 0.28/0.48
% 0.28/0.48 thf(complementInPowersetComplementIntersect,definition,
% 0.28/0.48 ( complementInPowersetComplementIntersect
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(contraSubsetComplement_type,type,
% 0.28/0.48 contraSubsetComplement: $o ).
% 0.28/0.48
% 0.28/0.48 thf(contraSubsetComplement,definition,
% 0.28/0.48 ( contraSubsetComplement
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( in @ Xx @ Y )
% 0.28/0.48 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(complementTcontraSubset_type,type,
% 0.28/0.48 complementTcontraSubset: $o ).
% 0.28/0.48
% 0.28/0.48 thf(complementTcontraSubset,definition,
% 0.28/0.48 ( complementTcontraSubset
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.28/0.48 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(binunionTILcontra_type,type,
% 0.28/0.48 binunionTILcontra: $o ).
% 0.28/0.48
% 0.28/0.48 thf(binunionTILcontra,definition,
% 0.28/0.48 ( binunionTILcontra
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.28/0.48 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(binunionTIRcontra_type,type,
% 0.28/0.48 binunionTIRcontra: $o ).
% 0.28/0.48
% 0.28/0.48 thf(binunionTIRcontra,definition,
% 0.28/0.48 ( binunionTIRcontra
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.28/0.48 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(inIntersectImpInUnion_type,type,
% 0.28/0.48 inIntersectImpInUnion: $o ).
% 0.28/0.48
% 0.28/0.48 thf(inIntersectImpInUnion,definition,
% 0.28/0.48 ( inIntersectImpInUnion
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Z: $i] :
% 0.28/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.28/0.48 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(inIntersectImpInUnion2_type,type,
% 0.28/0.48 inIntersectImpInUnion2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(inIntersectImpInUnion2,definition,
% 0.28/0.48 ( inIntersectImpInUnion2
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Z: $i] :
% 0.28/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.28/0.48 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(inIntersectImpInIntersectUnions_type,type,
% 0.28/0.48 inIntersectImpInIntersectUnions: $o ).
% 0.28/0.48
% 0.28/0.48 thf(inIntersectImpInIntersectUnions,definition,
% 0.28/0.48 ( inIntersectImpInIntersectUnions
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Z: $i] :
% 0.28/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.28/0.48 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(intersectInPowersetIntersectUnions_type,type,
% 0.28/0.48 intersectInPowersetIntersectUnions: $o ).
% 0.28/0.48
% 0.28/0.48 thf(intersectInPowersetIntersectUnions,definition,
% 0.28/0.48 ( intersectInPowersetIntersectUnions
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Z: $i] :
% 0.28/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.28/0.48 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(inComplementUnionImpNotIn1_type,type,
% 0.28/0.48 inComplementUnionImpNotIn1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(inComplementUnionImpNotIn1,definition,
% 0.28/0.48 ( inComplementUnionImpNotIn1
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.28/0.48 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(inComplementUnionImpInComplement1_type,type,
% 0.28/0.48 inComplementUnionImpInComplement1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(inComplementUnionImpInComplement1,definition,
% 0.28/0.48 ( inComplementUnionImpInComplement1
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.28/0.48 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(binunionTE_type,type,
% 0.28/0.48 binunionTE: $o ).
% 0.28/0.48
% 0.28/0.48 thf(binunionTE,definition,
% 0.28/0.48 ( binunionTE
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Xphi: $o,Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.28/0.48 => ( ( ( in @ Xx @ X )
% 0.28/0.48 => Xphi )
% 0.28/0.48 => ( ( ( in @ Xx @ Y )
% 0.28/0.48 => Xphi )
% 0.28/0.48 => Xphi ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(binunionTEcontra_type,type,
% 0.28/0.48 binunionTEcontra: $o ).
% 0.28/0.48
% 0.28/0.48 thf(binunionTEcontra,definition,
% 0.28/0.48 ( binunionTEcontra
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ~ ( in @ Xx @ X )
% 0.28/0.48 => ( ~ ( in @ Xx @ Y )
% 0.28/0.48 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(demorgan2a1_type,type,
% 0.28/0.48 demorgan2a1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(demorgan2a1,definition,
% 0.28/0.48 ( demorgan2a1
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.28/0.48 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(complementUnionInPowersetComplement_type,type,
% 0.28/0.48 complementUnionInPowersetComplement: $o ).
% 0.28/0.48
% 0.28/0.48 thf(complementUnionInPowersetComplement,definition,
% 0.28/0.48 ( complementUnionInPowersetComplement
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(demorgan2a2_type,type,
% 0.28/0.48 demorgan2a2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(demorgan2a2,definition,
% 0.28/0.48 ( demorgan2a2
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.28/0.48 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(demorgan1a_type,type,
% 0.28/0.48 demorgan1a: $o ).
% 0.28/0.48
% 0.28/0.48 thf(demorgan1a,definition,
% 0.28/0.48 ( demorgan1a
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 0.28/0.48 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(demorgan1b_type,type,
% 0.28/0.48 demorgan1b: $o ).
% 0.28/0.48
% 0.28/0.48 thf(demorgan1b,definition,
% 0.28/0.48 ( demorgan1b
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.28/0.48 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(demorgan1_type,type,
% 0.28/0.48 demorgan1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(demorgan1,definition,
% 0.28/0.48 ( demorgan1
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 0.28/0.48 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(demorgan2a_type,type,
% 0.28/0.48 demorgan2a: $o ).
% 0.28/0.48
% 0.28/0.48 thf(demorgan2a,definition,
% 0.28/0.48 ( demorgan2a
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.28/0.48 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(demorgan2b2_type,type,
% 0.28/0.48 demorgan2b2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(demorgan2b2,definition,
% 0.28/0.48 ( demorgan2b2
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.28/0.48 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 0.28/0.48 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(demorgan2b_type,type,
% 0.28/0.48 demorgan2b: $o ).
% 0.28/0.48
% 0.28/0.48 thf(demorgan2b,definition,
% 0.28/0.48 ( demorgan2b
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.28/0.48 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(demorgan2_type,type,
% 0.28/0.48 demorgan2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(demorgan2,definition,
% 0.28/0.48 ( demorgan2
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 0.28/0.48 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(woz13rule0_type,type,
% 0.28/0.48 woz13rule0: $o ).
% 0.28/0.48
% 0.28/0.48 thf(woz13rule0,definition,
% 0.28/0.48 ( woz13rule0
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.28/0.48 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(woz13rule1_type,type,
% 0.28/0.48 woz13rule1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(woz13rule1,definition,
% 0.28/0.48 ( woz13rule1
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Z: $i] :
% 0.28/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.28/0.48 => ( ( subset @ X @ Z )
% 0.28/0.48 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(woz13rule2_type,type,
% 0.28/0.48 woz13rule2: $o ).
% 0.28/0.48
% 0.28/0.48 thf(woz13rule2,definition,
% 0.28/0.48 ( woz13rule2
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Z: $i] :
% 0.28/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.28/0.48 => ( ( subset @ Y @ Z )
% 0.28/0.48 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(woz13rule3_type,type,
% 0.28/0.48 woz13rule3: $o ).
% 0.28/0.48
% 0.28/0.48 thf(woz13rule3,definition,
% 0.28/0.48 ( woz13rule3
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Z: $i] :
% 0.28/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.28/0.48 => ( ( subset @ X @ Y )
% 0.28/0.48 => ( ( subset @ X @ Z )
% 0.28/0.48 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(woz13rule4_type,type,
% 0.28/0.48 woz13rule4: $o ).
% 0.28/0.48
% 0.28/0.48 thf(woz13rule4,definition,
% 0.28/0.48 ( woz13rule4
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Z: $i] :
% 0.28/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.28/0.48 => ! [W: $i] :
% 0.28/0.48 ( ( in @ W @ ( powerset @ A ) )
% 0.28/0.48 => ( ( subset @ X @ Z )
% 0.28/0.48 => ( ( subset @ Y @ W )
% 0.28/0.48 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(woz1_1_type,type,
% 0.28/0.48 woz1_1: $o ).
% 0.28/0.48
% 0.28/0.48 thf(woz1_1,definition,
% 0.28/0.48 ( woz1_1
% 0.28/0.48 = ( ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(woz1_2,conjecture,
% 0.28/0.48 ( setextAx
% 0.28/0.48 => ( emptysetAx
% 0.28/0.48 => ( setadjoinAx
% 0.28/0.48 => ( powersetAx
% 0.28/0.48 => ( setunionAx
% 0.28/0.48 => ( omega0Ax
% 0.28/0.48 => ( omegaSAx
% 0.28/0.48 => ( omegaIndAx
% 0.28/0.48 => ( replAx
% 0.28/0.48 => ( foundationAx
% 0.28/0.48 => ( wellorderingAx
% 0.28/0.48 => ( descrp
% 0.28/0.48 => ( dsetconstrI
% 0.28/0.48 => ( dsetconstrEL
% 0.28/0.48 => ( dsetconstrER
% 0.28/0.48 => ( exuE1
% 0.28/0.48 => ( prop2setE
% 0.28/0.48 => ( emptysetE
% 0.28/0.48 => ( emptysetimpfalse
% 0.28/0.48 => ( notinemptyset
% 0.28/0.48 => ( exuE3e
% 0.28/0.48 => ( setext
% 0.28/0.48 => ( emptyI
% 0.28/0.48 => ( noeltsimpempty
% 0.28/0.48 => ( setbeta
% 0.28/0.48 => ( nonemptyE1
% 0.28/0.48 => ( nonemptyI
% 0.28/0.48 => ( nonemptyI1
% 0.28/0.48 => ( setadjoinIL
% 0.28/0.48 => ( emptyinunitempty
% 0.28/0.48 => ( setadjoinIR
% 0.28/0.48 => ( setadjoinE
% 0.28/0.48 => ( setadjoinOr
% 0.28/0.48 => ( setoftrueEq
% 0.28/0.48 => ( powersetI
% 0.28/0.48 => ( emptyinPowerset
% 0.28/0.48 => ( emptyInPowerset
% 0.28/0.48 => ( powersetE
% 0.28/0.48 => ( setunionI
% 0.28/0.48 => ( setunionE
% 0.28/0.48 => ( subPowSU
% 0.28/0.48 => ( exuE2
% 0.28/0.48 => ( nonemptyImpWitness
% 0.28/0.48 => ( uniqinunit
% 0.28/0.48 => ( notinsingleton
% 0.28/0.48 => ( eqinunit
% 0.28/0.48 => ( singletonsswitch
% 0.28/0.48 => ( upairsetE
% 0.28/0.48 => ( upairsetIL
% 0.28/0.48 => ( upairsetIR
% 0.28/0.48 => ( emptyE1
% 0.28/0.48 => ( vacuousDall
% 0.28/0.48 => ( quantDeMorgan1
% 0.28/0.48 => ( quantDeMorgan2
% 0.28/0.48 => ( quantDeMorgan3
% 0.28/0.48 => ( quantDeMorgan4
% 0.28/0.48 => ( prop2setI
% 0.28/0.48 => ( prop2set2propI
% 0.28/0.48 => ( notdexE
% 0.28/0.48 => ( notdallE
% 0.28/0.48 => ( exuI1
% 0.28/0.48 => ( exuI3
% 0.28/0.48 => ( exuI2
% 0.28/0.48 => ( inCongP
% 0.28/0.48 => ( in__Cong
% 0.28/0.48 => ( exuE3u
% 0.28/0.48 => ( exu__Cong
% 0.28/0.48 => ( emptyset__Cong
% 0.28/0.48 => ( setadjoin__Cong
% 0.28/0.48 => ( powerset__Cong
% 0.28/0.48 => ( setunion__Cong
% 0.28/0.48 => ( omega__Cong
% 0.28/0.48 => ( exuEu
% 0.28/0.48 => ( descr__Cong
% 0.28/0.48 => ( dsetconstr__Cong
% 0.28/0.48 => ( subsetI1
% 0.28/0.48 => ( eqimpsubset2
% 0.28/0.48 => ( eqimpsubset1
% 0.28/0.48 => ( subsetI2
% 0.28/0.48 => ( emptysetsubset
% 0.28/0.48 => ( subsetE
% 0.28/0.48 => ( subsetE2
% 0.28/0.48 => ( notsubsetI
% 0.28/0.48 => ( notequalI1
% 0.28/0.48 => ( notequalI2
% 0.28/0.48 => ( subsetRefl
% 0.28/0.48 => ( subsetTrans
% 0.28/0.48 => ( setadjoinSub
% 0.28/0.48 => ( setadjoinSub2
% 0.28/0.48 => ( subset2powerset
% 0.28/0.48 => ( setextsub
% 0.28/0.48 => ( subsetemptysetimpeq
% 0.28/0.48 => ( powersetI1
% 0.28/0.48 => ( powersetE1
% 0.28/0.48 => ( inPowerset
% 0.28/0.48 => ( powersetsubset
% 0.28/0.48 => ( sepInPowerset
% 0.28/0.48 => ( sepSubset
% 0.28/0.48 => ( binunionIL
% 0.28/0.48 => ( upairset2IR
% 0.28/0.48 => ( binunionIR
% 0.28/0.48 => ( binunionEcases
% 0.28/0.48 => ( binunionE
% 0.28/0.48 => ( binunionLsub
% 0.28/0.48 => ( binunionRsub
% 0.28/0.48 => ( binintersectI
% 0.28/0.48 => ( binintersectSubset5
% 0.28/0.48 => ( binintersectEL
% 0.28/0.48 => ( binintersectLsub
% 0.28/0.48 => ( binintersectSubset2
% 0.28/0.48 => ( binintersectSubset3
% 0.28/0.48 => ( binintersectER
% 0.28/0.48 => ( disjointsetsI1
% 0.28/0.48 => ( binintersectRsub
% 0.28/0.48 => ( binintersectSubset4
% 0.28/0.48 => ( binintersectSubset1
% 0.28/0.48 => ( bs114d
% 0.28/0.48 => ( setminusI
% 0.28/0.48 => ( setminusEL
% 0.28/0.48 => ( setminusER
% 0.28/0.48 => ( setminusSubset2
% 0.28/0.48 => ( setminusERneg
% 0.28/0.48 => ( setminusELneg
% 0.28/0.48 => ( setminusILneg
% 0.28/0.48 => ( setminusIRneg
% 0.28/0.48 => ( setminusLsub
% 0.28/0.48 => ( setminusSubset1
% 0.28/0.48 => ( symdiffE
% 0.28/0.48 => ( symdiffI1
% 0.28/0.48 => ( symdiffI2
% 0.28/0.48 => ( symdiffIneg1
% 0.28/0.48 => ( symdiffIneg2
% 0.28/0.48 => ( secondinupair
% 0.28/0.48 => ( setukpairIL
% 0.28/0.48 => ( setukpairIR
% 0.28/0.48 => ( kpairiskpair
% 0.28/0.48 => ( kpairp
% 0.28/0.48 => ( singletonsubset
% 0.28/0.48 => ( singletoninpowerset
% 0.28/0.48 => ( singletoninpowunion
% 0.28/0.48 => ( upairset2E
% 0.28/0.48 => ( upairsubunion
% 0.28/0.48 => ( upairinpowunion
% 0.28/0.48 => ( ubforcartprodlem1
% 0.28/0.48 => ( ubforcartprodlem2
% 0.28/0.48 => ( ubforcartprodlem3
% 0.28/0.48 => ( cartprodpairin
% 0.28/0.48 => ( cartprodmempair1
% 0.28/0.48 => ( cartprodmempair
% 0.28/0.48 => ( setunionE2
% 0.28/0.48 => ( setunionsingleton1
% 0.28/0.48 => ( setunionsingleton2
% 0.28/0.48 => ( setunionsingleton
% 0.28/0.48 => ( singletonprop
% 0.28/0.48 => ( ex1E1
% 0.28/0.48 => ( ex1I
% 0.28/0.48 => ( ex1I2
% 0.28/0.48 => ( singletonsuniq
% 0.28/0.48 => ( setukpairinjL1
% 0.28/0.48 => ( kfstsingleton
% 0.28/0.48 => ( theprop
% 0.28/0.48 => ( kfstpairEq
% 0.28/0.48 => ( cartprodfstin
% 0.28/0.48 => ( setukpairinjL2
% 0.28/0.48 => ( setukpairinjL
% 0.28/0.48 => ( setukpairinjR11
% 0.28/0.48 => ( setukpairinjR12
% 0.28/0.48 => ( setukpairinjR1
% 0.28/0.48 => ( upairequniteq
% 0.28/0.48 => ( setukpairinjR2
% 0.28/0.48 => ( setukpairinjR
% 0.28/0.48 => ( ksndsingleton
% 0.28/0.48 => ( ksndpairEq
% 0.28/0.48 => ( kpairsurjEq
% 0.28/0.48 => ( cartprodsndin
% 0.28/0.48 => ( cartprodpairmemEL
% 0.28/0.48 => ( cartprodpairmemER
% 0.28/0.48 => ( cartprodmempaircEq
% 0.28/0.48 => ( cartprodfstpairEq
% 0.28/0.48 => ( cartprodsndpairEq
% 0.28/0.48 => ( cartprodpairsurjEq
% 0.28/0.48 => ( dpsetconstrI
% 0.28/0.48 => ( dpsetconstrSub
% 0.28/0.48 => ( setOfPairsIsBReln
% 0.28/0.48 => ( dpsetconstrERa
% 0.28/0.48 => ( dpsetconstrEL1
% 0.28/0.48 => ( dpsetconstrEL2
% 0.28/0.48 => ( dpsetconstrER
% 0.28/0.48 => ( funcImageSingleton
% 0.28/0.48 => ( apProp
% 0.28/0.48 => ( app
% 0.28/0.48 => ( infuncsetfunc
% 0.28/0.48 => ( ap2p
% 0.28/0.48 => ( funcinfuncset
% 0.28/0.48 => ( lamProp
% 0.28/0.48 => ( lamp
% 0.28/0.48 => ( lam2p
% 0.28/0.48 => ( brelnall1
% 0.28/0.48 => ( brelnall2
% 0.28/0.48 => ( ex1E2
% 0.28/0.48 => ( funcGraphProp1
% 0.28/0.48 => ( funcGraphProp3
% 0.28/0.48 => ( funcGraphProp2
% 0.28/0.48 => ( funcextLem
% 0.28/0.48 => ( funcGraphProp4
% 0.28/0.48 => ( subbreln
% 0.28/0.48 => ( eqbreln
% 0.28/0.48 => ( funcext
% 0.28/0.48 => ( funcext2
% 0.28/0.48 => ( ap2apEq1
% 0.28/0.48 => ( ap2apEq2
% 0.28/0.48 => ( beta1
% 0.28/0.48 => ( eta1
% 0.28/0.48 => ( lam2lamEq
% 0.28/0.48 => ( beta2
% 0.28/0.48 => ( eta2
% 0.28/0.48 => ( iffalseProp1
% 0.28/0.48 => ( iffalseProp2
% 0.28/0.48 => ( iftrueProp1
% 0.28/0.48 => ( iftrueProp2
% 0.28/0.48 => ( ifSingleton
% 0.28/0.48 => ( ifp
% 0.28/0.48 => ( theeq
% 0.28/0.48 => ( iftrue
% 0.28/0.48 => ( iffalse
% 0.28/0.48 => ( iftrueorfalse
% 0.28/0.48 => ( binintersectT_lem
% 0.28/0.48 => ( binunionT_lem
% 0.28/0.48 => ( powersetT_lem
% 0.28/0.48 => ( setminusT_lem
% 0.28/0.48 => ( complementT_lem
% 0.28/0.48 => ( setextT
% 0.28/0.48 => ( subsetTI
% 0.28/0.48 => ( powersetTI1
% 0.28/0.48 => ( powersetTE1
% 0.28/0.48 => ( complementTI1
% 0.28/0.48 => ( complementTE1
% 0.28/0.48 => ( binintersectTELcontra
% 0.28/0.48 => ( binintersectTERcontra
% 0.28/0.48 => ( contrasubsetT
% 0.28/0.48 => ( contrasubsetT1
% 0.28/0.48 => ( contrasubsetT2
% 0.28/0.48 => ( contrasubsetT3
% 0.28/0.48 => ( doubleComplementI1
% 0.28/0.48 => ( doubleComplementE1
% 0.28/0.48 => ( doubleComplementSub1
% 0.28/0.48 => ( doubleComplementSub2
% 0.28/0.48 => ( doubleComplementEq
% 0.28/0.48 => ( complementTnotintersectT
% 0.28/0.48 => ( complementImpComplementIntersect
% 0.28/0.48 => ( complementSubsetComplementIntersect
% 0.28/0.48 => ( complementInPowersetComplementIntersect
% 0.28/0.48 => ( contraSubsetComplement
% 0.28/0.48 => ( complementTcontraSubset
% 0.28/0.48 => ( binunionTILcontra
% 0.28/0.48 => ( binunionTIRcontra
% 0.28/0.48 => ( inIntersectImpInUnion
% 0.28/0.48 => ( inIntersectImpInUnion2
% 0.28/0.48 => ( inIntersectImpInIntersectUnions
% 0.28/0.48 => ( intersectInPowersetIntersectUnions
% 0.28/0.48 => ( inComplementUnionImpNotIn1
% 0.28/0.48 => ( inComplementUnionImpInComplement1
% 0.28/0.48 => ( binunionTE
% 0.28/0.48 => ( binunionTEcontra
% 0.28/0.48 => ( demorgan2a1
% 0.28/0.48 => ( complementUnionInPowersetComplement
% 0.28/0.48 => ( demorgan2a2
% 0.28/0.48 => ( demorgan1a
% 0.28/0.48 => ( demorgan1b
% 0.28/0.48 => ( demorgan1
% 0.28/0.48 => ( demorgan2a
% 0.28/0.48 => ( demorgan2b2
% 0.28/0.48 => ( demorgan2b
% 0.28/0.48 => ( demorgan2
% 0.28/0.48 => ( woz13rule0
% 0.28/0.48 => ( woz13rule1
% 0.28/0.48 => ( woz13rule2
% 0.28/0.48 => ( woz13rule3
% 0.28/0.48 => ( woz13rule4
% 0.28/0.48 => ( woz1_1
% 0.28/0.48 => ! [A: $i,X: $i] :
% 0.28/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.48 => ! [Y: $i] :
% 0.28/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.48 => ! [Z: $i] :
% 0.28/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.28/0.48 => ! [W: $i] :
% 0.28/0.48 ( ( in @ W @ ( powerset @ A ) )
% 0.28/0.48 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 0.28/0.48 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 %------------------------------------------------------------------------------
% 0.28/0.48 ------------------------
% 0.33/1.60 ---- Embedded in THF ---
% 0.33/1.60 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.33/1.60 %%% Generated on Tue Feb 24 12:33:09 EST 2026
% 0.33/1.60 %%% using '$$dhol' embedding, version 1.3.0.
% 0.33/1.60 %%% Logic specification used:
% 0.33/1.60 %%% thf(spec, logic, $$dhol).
% 0.33/1.60
% 0.33/1.60 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.AAoQ5tR61a/DTF2DTF10139.p
% See solution above
% 0.33/1.61 ------------------------
% 0.33/1.64 ---- Cleaned THF ---
% 0.33/1.64 thf(in_type,type,
% 0.33/1.64 in: $i > $i > $o ).
% 0.33/1.64
% 0.33/1.64 thf(exu_type,type,
% 0.33/1.64 exu: ( $i > $o ) > $o ).
% 0.33/1.64
% 0.33/1.64 thf(exu,definition,
% 0.33/1.64 ( exu
% 0.33/1.64 = ( ^ [Xphi: $i > $o] :
% 0.33/1.64 ? [Xx: $i] :
% 0.33/1.64 ( ( Xphi @ Xx )
% 0.33/1.64 & ! [Xy: $i] :
% 0.33/1.64 ( ( Xphi @ Xy )
% 0.33/1.64 => ( Xx = Xy ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setextAx_type,type,
% 0.33/1.64 setextAx: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setextAx,definition,
% 0.33/1.64 ( setextAx
% 0.33/1.64 = ( ! [A: $i,B: $i] :
% 0.33/1.64 ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 <=> ( in @ Xx @ B ) )
% 0.33/1.64 => ( A = B ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(emptyset_type,type,
% 0.33/1.64 emptyset: $i ).
% 0.33/1.64
% 0.33/1.64 thf(emptysetAx_type,type,
% 0.33/1.64 emptysetAx: $o ).
% 0.33/1.64
% 0.33/1.64 thf(emptysetAx,definition,
% 0.33/1.64 ( emptysetAx
% 0.33/1.64 = ( ! [Xx: $i] :
% 0.33/1.64 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setadjoin_type,type,
% 0.33/1.64 setadjoin: $i > $i > $i ).
% 0.33/1.64
% 0.33/1.64 thf(setadjoinAx_type,type,
% 0.33/1.64 setadjoinAx: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setadjoinAx,definition,
% 0.33/1.64 ( setadjoinAx
% 0.33/1.64 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.33/1.64 <=> ( ( Xy = Xx )
% 0.33/1.64 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(powerset_type,type,
% 0.33/1.64 powerset: $i > $i ).
% 0.33/1.64
% 0.33/1.64 thf(powersetAx_type,type,
% 0.33/1.64 powersetAx: $o ).
% 0.33/1.64
% 0.33/1.64 thf(powersetAx,definition,
% 0.33/1.64 ( powersetAx
% 0.33/1.64 = ( ! [A: $i,B: $i] :
% 0.33/1.64 ( ( in @ B @ ( powerset @ A ) )
% 0.33/1.64 <=> ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ B )
% 0.33/1.64 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setunion_type,type,
% 0.33/1.64 setunion: $i > $i ).
% 0.33/1.64
% 0.33/1.64 thf(setunionAx_type,type,
% 0.33/1.64 setunionAx: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setunionAx,definition,
% 0.33/1.64 ( setunionAx
% 0.33/1.64 = ( ! [A: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ ( setunion @ A ) )
% 0.33/1.64 <=> ? [B: $i] :
% 0.33/1.64 ( ( in @ Xx @ B )
% 0.33/1.64 & ( in @ B @ A ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(omega_type,type,
% 0.33/1.64 omega: $i ).
% 0.33/1.64
% 0.33/1.64 thf(omega0Ax_type,type,
% 0.33/1.64 omega0Ax: $o ).
% 0.33/1.64
% 0.33/1.64 thf(omega0Ax,definition,
% 0.33/1.64 ( omega0Ax
% 0.33/1.64 = ( in @ emptyset @ omega ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(omegaSAx_type,type,
% 0.33/1.64 omegaSAx: $o ).
% 0.33/1.64
% 0.33/1.64 thf(omegaSAx,definition,
% 0.33/1.64 ( omegaSAx
% 0.33/1.64 = ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ omega )
% 0.33/1.64 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(omegaIndAx_type,type,
% 0.33/1.64 omegaIndAx: $o ).
% 0.33/1.64
% 0.33/1.64 thf(omegaIndAx,definition,
% 0.33/1.64 ( omegaIndAx
% 0.33/1.64 = ( ! [A: $i] :
% 0.33/1.64 ( ( ( in @ emptyset @ A )
% 0.33/1.64 & ! [Xx: $i] :
% 0.33/1.64 ( ( ( in @ Xx @ omega )
% 0.33/1.64 & ( in @ Xx @ A ) )
% 0.33/1.64 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ omega )
% 0.33/1.64 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(replAx_type,type,
% 0.33/1.64 replAx: $o ).
% 0.33/1.64
% 0.33/1.64 thf(replAx,definition,
% 0.33/1.64 ( replAx
% 0.33/1.64 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.33/1.64 ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( exu
% 0.33/1.64 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.33/1.64 => ? [B: $i] :
% 0.33/1.64 ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ B )
% 0.33/1.64 <=> ? [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ A )
% 0.33/1.64 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(foundationAx_type,type,
% 0.33/1.64 foundationAx: $o ).
% 0.33/1.64
% 0.33/1.64 thf(foundationAx,definition,
% 0.33/1.64 ( foundationAx
% 0.33/1.64 = ( ! [A: $i] :
% 0.33/1.64 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.33/1.64 => ? [B: $i] :
% 0.33/1.64 ( ( in @ B @ A )
% 0.33/1.64 & ~ ? [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ B )
% 0.33/1.64 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(wellorderingAx_type,type,
% 0.33/1.64 wellorderingAx: $o ).
% 0.33/1.64
% 0.33/1.64 thf(wellorderingAx,definition,
% 0.33/1.64 ( wellorderingAx
% 0.33/1.64 = ( ! [A: $i] :
% 0.33/1.64 ? [B: $i] :
% 0.33/1.64 ( ! [C: $i] :
% 0.33/1.64 ( ( in @ C @ B )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ C )
% 0.33/1.64 => ( in @ Xx @ A ) ) )
% 0.33/1.64 & ! [Xx: $i,Xy: $i] :
% 0.33/1.64 ( ( ( in @ Xx @ A )
% 0.33/1.64 & ( in @ Xy @ A ) )
% 0.33/1.64 => ( ! [C: $i] :
% 0.33/1.64 ( ( in @ C @ B )
% 0.33/1.64 => ( ( in @ Xx @ C )
% 0.33/1.64 <=> ( in @ Xy @ C ) ) )
% 0.33/1.64 => ( Xx = Xy ) ) )
% 0.33/1.64 & ! [C: $i,D: $i] :
% 0.33/1.64 ( ( ( in @ C @ B )
% 0.33/1.64 & ( in @ D @ B ) )
% 0.33/1.64 => ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ C )
% 0.33/1.64 => ( in @ Xx @ D ) )
% 0.33/1.64 | ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ D )
% 0.33/1.64 => ( in @ Xx @ C ) ) ) )
% 0.33/1.64 & ! [C: $i] :
% 0.33/1.64 ( ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ C )
% 0.33/1.64 => ( in @ Xx @ A ) )
% 0.33/1.64 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.33/1.64 => ? [D: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ D @ B )
% 0.33/1.64 & ( in @ Xx @ C )
% 0.33/1.64 & ~ ? [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ D )
% 0.33/1.64 & ( in @ Xy @ C ) )
% 0.33/1.64 & ! [E: $i] :
% 0.33/1.64 ( ( in @ E @ B )
% 0.33/1.64 => ( ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ E )
% 0.33/1.64 => ( in @ Xy @ D ) )
% 0.33/1.64 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(descr_type,type,
% 0.33/1.64 descr: ( $i > $o ) > $i ).
% 0.33/1.64
% 0.33/1.64 thf(descrp_type,type,
% 0.33/1.64 descrp: $o ).
% 0.33/1.64
% 0.33/1.64 thf(descrp,definition,
% 0.33/1.64 ( descrp
% 0.33/1.64 = ( ! [Xphi: $i > $o] :
% 0.33/1.64 ( ( exu
% 0.33/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/1.64 => ( Xphi
% 0.33/1.64 @ ( descr
% 0.33/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(dsetconstr_type,type,
% 0.33/1.64 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.33/1.64
% 0.33/1.64 thf(dsetconstrI_type,type,
% 0.33/1.64 dsetconstrI: $o ).
% 0.33/1.64
% 0.33/1.64 thf(dsetconstrI,definition,
% 0.33/1.64 ( dsetconstrI
% 0.33/1.64 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( Xphi @ Xx )
% 0.33/1.64 => ( in @ Xx
% 0.33/1.64 @ ( dsetconstr @ A
% 0.33/1.64 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(dsetconstrEL_type,type,
% 0.33/1.64 dsetconstrEL: $o ).
% 0.33/1.64
% 0.33/1.64 thf(dsetconstrEL,definition,
% 0.33/1.64 ( dsetconstrEL
% 0.33/1.64 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx
% 0.33/1.64 @ ( dsetconstr @ A
% 0.33/1.64 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.33/1.64 => ( in @ Xx @ A ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(dsetconstrER_type,type,
% 0.33/1.64 dsetconstrER: $o ).
% 0.33/1.64
% 0.33/1.64 thf(dsetconstrER,definition,
% 0.33/1.64 ( dsetconstrER
% 0.33/1.64 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx
% 0.33/1.64 @ ( dsetconstr @ A
% 0.33/1.64 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.33/1.64 => ( Xphi @ Xx ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(exuE1_type,type,
% 0.33/1.64 exuE1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(exuE1,definition,
% 0.33/1.64 ( exuE1
% 0.33/1.64 = ( ! [Xphi: $i > $o] :
% 0.33/1.64 ( ( exu
% 0.33/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/1.64 => ? [Xx: $i] :
% 0.33/1.64 ( ( Xphi @ Xx )
% 0.33/1.64 & ! [Xy: $i] :
% 0.33/1.64 ( ( Xphi @ Xy )
% 0.33/1.64 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(prop2set_type,type,
% 0.33/1.64 prop2set: $o > $i ).
% 0.33/1.64
% 0.33/1.64 thf(prop2setE_type,type,
% 0.33/1.64 prop2setE: $o ).
% 0.33/1.64
% 0.33/1.64 thf(prop2setE,definition,
% 0.33/1.64 ( prop2setE
% 0.33/1.64 = ( ! [Xphi: $o,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.33/1.64 => Xphi ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(emptysetE_type,type,
% 0.33/1.64 emptysetE: $o ).
% 0.33/1.64
% 0.33/1.64 thf(emptysetE,definition,
% 0.33/1.64 ( emptysetE
% 0.33/1.64 = ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ emptyset )
% 0.33/1.64 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(emptysetimpfalse_type,type,
% 0.33/1.64 emptysetimpfalse: $o ).
% 0.33/1.64
% 0.33/1.64 thf(emptysetimpfalse,definition,
% 0.33/1.64 ( emptysetimpfalse
% 0.33/1.64 = ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ emptyset )
% 0.33/1.64 => $false ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(notinemptyset_type,type,
% 0.33/1.64 notinemptyset: $o ).
% 0.33/1.64
% 0.33/1.64 thf(notinemptyset,definition,
% 0.33/1.64 ( notinemptyset
% 0.33/1.64 = ( ! [Xx: $i] :
% 0.33/1.64 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(exuE3e_type,type,
% 0.33/1.64 exuE3e: $o ).
% 0.33/1.64
% 0.33/1.64 thf(exuE3e,definition,
% 0.33/1.64 ( exuE3e
% 0.33/1.64 = ( ! [Xphi: $i > $o] :
% 0.33/1.64 ( ( exu
% 0.33/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/1.64 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setext_type,type,
% 0.33/1.64 setext: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setext,definition,
% 0.33/1.64 ( setext
% 0.33/1.64 = ( ! [A: $i,B: $i] :
% 0.33/1.64 ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( in @ Xx @ B ) )
% 0.33/1.64 => ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ B )
% 0.33/1.64 => ( in @ Xx @ A ) )
% 0.33/1.64 => ( A = B ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(emptyI_type,type,
% 0.33/1.64 emptyI: $o ).
% 0.33/1.64
% 0.33/1.64 thf(emptyI,definition,
% 0.33/1.64 ( emptyI
% 0.33/1.64 = ( ! [A: $i] :
% 0.33/1.64 ( ! [Xx: $i] :
% 0.33/1.64 ~ ( in @ Xx @ A )
% 0.33/1.64 => ( A = emptyset ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(noeltsimpempty_type,type,
% 0.33/1.64 noeltsimpempty: $o ).
% 0.33/1.64
% 0.33/1.64 thf(noeltsimpempty,definition,
% 0.33/1.64 ( noeltsimpempty
% 0.33/1.64 = ( ! [A: $i] :
% 0.33/1.64 ( ! [Xx: $i] :
% 0.33/1.64 ~ ( in @ Xx @ A )
% 0.33/1.64 => ( A = emptyset ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setbeta_type,type,
% 0.33/1.64 setbeta: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setbeta,definition,
% 0.33/1.64 ( setbeta
% 0.33/1.64 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( in @ Xx
% 0.33/1.64 @ ( dsetconstr @ A
% 0.33/1.64 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.33/1.64 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(nonempty_type,type,
% 0.33/1.64 nonempty: $i > $o ).
% 0.33/1.64
% 0.33/1.64 thf(nonempty,definition,
% 0.33/1.64 ( nonempty
% 0.33/1.64 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(nonemptyE1_type,type,
% 0.33/1.64 nonemptyE1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(nonemptyE1,definition,
% 0.33/1.64 ( nonemptyE1
% 0.33/1.64 = ( ! [A: $i] :
% 0.33/1.64 ( ( nonempty @ A )
% 0.33/1.64 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(nonemptyI_type,type,
% 0.33/1.64 nonemptyI: $o ).
% 0.33/1.64
% 0.33/1.64 thf(nonemptyI,definition,
% 0.33/1.64 ( nonemptyI
% 0.33/1.64 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( Xphi @ Xx )
% 0.33/1.64 => ( nonempty
% 0.33/1.64 @ ( dsetconstr @ A
% 0.33/1.64 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(nonemptyI1_type,type,
% 0.33/1.64 nonemptyI1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(nonemptyI1,definition,
% 0.33/1.64 ( nonemptyI1
% 0.33/1.64 = ( ! [A: $i] :
% 0.33/1.64 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.33/1.64 => ( nonempty @ A ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setadjoinIL_type,type,
% 0.33/1.64 setadjoinIL: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setadjoinIL,definition,
% 0.33/1.64 ( setadjoinIL
% 0.33/1.64 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(emptyinunitempty_type,type,
% 0.33/1.64 emptyinunitempty: $o ).
% 0.33/1.64
% 0.33/1.64 thf(emptyinunitempty,definition,
% 0.33/1.64 ( emptyinunitempty
% 0.33/1.64 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setadjoinIR_type,type,
% 0.33/1.64 setadjoinIR: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setadjoinIR,definition,
% 0.33/1.64 ( setadjoinIR
% 0.33/1.64 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ A )
% 0.33/1.64 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setadjoinE_type,type,
% 0.33/1.64 setadjoinE: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setadjoinE,definition,
% 0.33/1.64 ( setadjoinE
% 0.33/1.64 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.33/1.64 => ! [Xphi: $o] :
% 0.33/1.64 ( ( ( Xy = Xx )
% 0.33/1.64 => Xphi )
% 0.33/1.64 => ( ( ( in @ Xy @ A )
% 0.33/1.64 => Xphi )
% 0.33/1.64 => Xphi ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setadjoinOr_type,type,
% 0.33/1.64 setadjoinOr: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setadjoinOr,definition,
% 0.33/1.64 ( setadjoinOr
% 0.33/1.64 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.33/1.64 => ( ( Xy = Xx )
% 0.33/1.64 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setoftrueEq_type,type,
% 0.33/1.64 setoftrueEq: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setoftrueEq,definition,
% 0.33/1.64 ( setoftrueEq
% 0.33/1.64 = ( ! [A: $i] :
% 0.33/1.64 ( ( dsetconstr @ A
% 0.33/1.64 @ ^ [Xx: $i] : $true )
% 0.33/1.64 = A ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(powersetI_type,type,
% 0.33/1.64 powersetI: $o ).
% 0.33/1.64
% 0.33/1.64 thf(powersetI,definition,
% 0.33/1.64 ( powersetI
% 0.33/1.64 = ( ! [A: $i,B: $i] :
% 0.33/1.64 ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ B )
% 0.33/1.64 => ( in @ Xx @ A ) )
% 0.33/1.64 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(emptyinPowerset_type,type,
% 0.33/1.64 emptyinPowerset: $o ).
% 0.33/1.64
% 0.33/1.64 thf(emptyinPowerset,definition,
% 0.33/1.64 ( emptyinPowerset
% 0.33/1.64 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(emptyInPowerset_type,type,
% 0.33/1.64 emptyInPowerset: $o ).
% 0.33/1.64
% 0.33/1.64 thf(emptyInPowerset,definition,
% 0.33/1.64 ( emptyInPowerset
% 0.33/1.64 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(powersetE_type,type,
% 0.33/1.64 powersetE: $o ).
% 0.33/1.64
% 0.33/1.64 thf(powersetE,definition,
% 0.33/1.64 ( powersetE
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ B @ ( powerset @ A ) )
% 0.33/1.64 => ( ( in @ Xx @ B )
% 0.33/1.64 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setunionI_type,type,
% 0.33/1.64 setunionI: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setunionI,definition,
% 0.33/1.64 ( setunionI
% 0.33/1.64 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.33/1.64 ( ( in @ Xx @ B )
% 0.33/1.64 => ( ( in @ B @ A )
% 0.33/1.64 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setunionE_type,type,
% 0.33/1.64 setunionE: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setunionE,definition,
% 0.33/1.64 ( setunionE
% 0.33/1.64 = ( ! [A: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ ( setunion @ A ) )
% 0.33/1.64 => ! [Xphi: $o] :
% 0.33/1.64 ( ! [B: $i] :
% 0.33/1.64 ( ( in @ Xx @ B )
% 0.33/1.64 => ( ( in @ B @ A )
% 0.33/1.64 => Xphi ) )
% 0.33/1.64 => Xphi ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(subPowSU_type,type,
% 0.33/1.64 subPowSU: $o ).
% 0.33/1.64
% 0.33/1.64 thf(subPowSU,definition,
% 0.33/1.64 ( subPowSU
% 0.33/1.64 = ( ! [A: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(exuE2_type,type,
% 0.33/1.64 exuE2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(exuE2,definition,
% 0.33/1.64 ( exuE2
% 0.33/1.64 = ( ! [Xphi: $i > $o] :
% 0.33/1.64 ( ( exu
% 0.33/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/1.64 => ? [Xx: $i] :
% 0.33/1.64 ! [Xy: $i] :
% 0.33/1.64 ( ( Xphi @ Xy )
% 0.33/1.64 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(nonemptyImpWitness_type,type,
% 0.33/1.64 nonemptyImpWitness: $o ).
% 0.33/1.64
% 0.33/1.64 thf(nonemptyImpWitness,definition,
% 0.33/1.64 ( nonemptyImpWitness
% 0.33/1.64 = ( ! [A: $i] :
% 0.33/1.64 ( ( nonempty @ A )
% 0.33/1.64 => ? [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 & $true ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(uniqinunit_type,type,
% 0.33/1.64 uniqinunit: $o ).
% 0.33/1.64
% 0.33/1.64 thf(uniqinunit,definition,
% 0.33/1.64 ( uniqinunit
% 0.33/1.64 = ( ! [Xx: $i,Xy: $i] :
% 0.33/1.64 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.33/1.64 => ( Xx = Xy ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(notinsingleton_type,type,
% 0.33/1.64 notinsingleton: $o ).
% 0.33/1.64
% 0.33/1.64 thf(notinsingleton,definition,
% 0.33/1.64 ( notinsingleton
% 0.33/1.64 = ( ! [Xx: $i,Xy: $i] :
% 0.33/1.64 ( ( Xx != Xy )
% 0.33/1.64 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(eqinunit_type,type,
% 0.33/1.64 eqinunit: $o ).
% 0.33/1.64
% 0.33/1.64 thf(eqinunit,definition,
% 0.33/1.64 ( eqinunit
% 0.33/1.64 = ( ! [Xx: $i,Xy: $i] :
% 0.33/1.64 ( ( Xx = Xy )
% 0.33/1.64 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(singletonsswitch_type,type,
% 0.33/1.64 singletonsswitch: $o ).
% 0.33/1.64
% 0.33/1.64 thf(singletonsswitch,definition,
% 0.33/1.64 ( singletonsswitch
% 0.33/1.64 = ( ! [Xx: $i,Xy: $i] :
% 0.33/1.64 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.33/1.64 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(upairsetE_type,type,
% 0.33/1.64 upairsetE: $o ).
% 0.33/1.64
% 0.33/1.64 thf(upairsetE,definition,
% 0.33/1.64 ( upairsetE
% 0.33/1.64 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.33/1.64 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.33/1.64 => ( ( Xz = Xx )
% 0.33/1.64 | ( Xz = Xy ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(upairsetIL_type,type,
% 0.33/1.64 upairsetIL: $o ).
% 0.33/1.64
% 0.33/1.64 thf(upairsetIL,definition,
% 0.33/1.64 ( upairsetIL
% 0.33/1.64 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(upairsetIR_type,type,
% 0.33/1.64 upairsetIR: $o ).
% 0.33/1.64
% 0.33/1.64 thf(upairsetIR,definition,
% 0.33/1.64 ( upairsetIR
% 0.33/1.64 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(emptyE1_type,type,
% 0.33/1.64 emptyE1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(emptyE1,definition,
% 0.33/1.64 ( emptyE1
% 0.33/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 0.33/1.64 ( ? [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 & ( Xphi @ Xx ) )
% 0.33/1.64 => ( ( ( dsetconstr @ A
% 0.33/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/1.64 = emptyset )
% 0.33/1.64 => $false ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(vacuousDall_type,type,
% 0.33/1.64 vacuousDall: $o ).
% 0.33/1.64
% 0.33/1.64 thf(vacuousDall,definition,
% 0.33/1.64 ( vacuousDall
% 0.33/1.64 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ emptyset )
% 0.33/1.64 => ( Xphi @ Xx ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(quantDeMorgan1_type,type,
% 0.33/1.64 quantDeMorgan1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(quantDeMorgan1,definition,
% 0.33/1.64 ( quantDeMorgan1
% 0.33/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 0.33/1.64 ( ~ ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( Xphi @ Xx ) )
% 0.33/1.64 => ? [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(quantDeMorgan2_type,type,
% 0.33/1.64 quantDeMorgan2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(quantDeMorgan2,definition,
% 0.33/1.64 ( quantDeMorgan2
% 0.33/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 0.33/1.64 ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ~ ( Xphi @ Xx ) )
% 0.33/1.64 => ~ ? [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(quantDeMorgan3_type,type,
% 0.33/1.64 quantDeMorgan3: $o ).
% 0.33/1.64
% 0.33/1.64 thf(quantDeMorgan3,definition,
% 0.33/1.64 ( quantDeMorgan3
% 0.33/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 0.33/1.64 ( ~ ? [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 & ( Xphi @ Xx ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(quantDeMorgan4_type,type,
% 0.33/1.64 quantDeMorgan4: $o ).
% 0.33/1.64
% 0.33/1.64 thf(quantDeMorgan4,definition,
% 0.33/1.64 ( quantDeMorgan4
% 0.33/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 0.33/1.64 ( ? [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 & ~ ( Xphi @ Xx ) )
% 0.33/1.64 => ~ ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(prop2setI_type,type,
% 0.33/1.64 prop2setI: $o ).
% 0.33/1.64
% 0.33/1.64 thf(prop2setI,definition,
% 0.33/1.64 ( prop2setI
% 0.33/1.64 = ( ! [Xphi: $o] :
% 0.33/1.64 ( Xphi
% 0.33/1.64 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(set2prop_type,type,
% 0.33/1.64 set2prop: $i > $o ).
% 0.33/1.64
% 0.33/1.64 thf(prop2set2propI_type,type,
% 0.33/1.64 prop2set2propI: $o ).
% 0.33/1.64
% 0.33/1.64 thf(prop2set2propI,definition,
% 0.33/1.64 ( prop2set2propI
% 0.33/1.64 = ( ! [Xphi: $o] :
% 0.33/1.64 ( Xphi
% 0.33/1.64 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(notdexE_type,type,
% 0.33/1.64 notdexE: $o ).
% 0.33/1.64
% 0.33/1.64 thf(notdexE,definition,
% 0.33/1.64 ( notdexE
% 0.33/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 0.33/1.64 ( ~ ? [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 & ( Xphi @ Xx ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(notdallE_type,type,
% 0.33/1.64 notdallE: $o ).
% 0.33/1.64
% 0.33/1.64 thf(notdallE,definition,
% 0.33/1.64 ( notdallE
% 0.33/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 0.33/1.64 ( ~ ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( Xphi @ Xx ) )
% 0.33/1.64 => ? [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(exuI1_type,type,
% 0.33/1.64 exuI1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(exuI1,definition,
% 0.33/1.64 ( exuI1
% 0.33/1.64 = ( ! [Xphi: $i > $o] :
% 0.33/1.64 ( ? [Xx: $i] :
% 0.33/1.64 ( ( Xphi @ Xx )
% 0.33/1.64 & ! [Xy: $i] :
% 0.33/1.64 ( ( Xphi @ Xy )
% 0.33/1.64 => ( Xx = Xy ) ) )
% 0.33/1.64 => ( exu
% 0.33/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(exuI3_type,type,
% 0.33/1.64 exuI3: $o ).
% 0.33/1.64
% 0.33/1.64 thf(exuI3,definition,
% 0.33/1.64 ( exuI3
% 0.33/1.64 = ( ! [Xphi: $i > $o] :
% 0.33/1.64 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.33/1.64 => ( ! [Xx: $i,Xy: $i] :
% 0.33/1.64 ( ( Xphi @ Xx )
% 0.33/1.64 => ( ( Xphi @ Xy )
% 0.33/1.64 => ( Xx = Xy ) ) )
% 0.33/1.64 => ( exu
% 0.33/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(exuI2_type,type,
% 0.33/1.64 exuI2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(exuI2,definition,
% 0.33/1.64 ( exuI2
% 0.33/1.64 = ( ! [Xphi: $i > $o] :
% 0.33/1.64 ( ? [Xx: $i] :
% 0.33/1.64 ! [Xy: $i] :
% 0.33/1.64 ( ( Xphi @ Xy )
% 0.33/1.64 <=> ( Xy = Xx ) )
% 0.33/1.64 => ( exu
% 0.33/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(inCongP_type,type,
% 0.33/1.64 inCongP: $o ).
% 0.33/1.64
% 0.33/1.64 thf(inCongP,definition,
% 0.33/1.64 ( inCongP
% 0.33/1.64 = ( ! [A: $i,B: $i] :
% 0.33/1.64 ( ( A = B )
% 0.33/1.64 => ! [Xx: $i,Xy: $i] :
% 0.33/1.64 ( ( Xx = Xy )
% 0.33/1.64 => ( ( in @ Xx @ A )
% 0.33/1.64 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(in__Cong_type,type,
% 0.33/1.64 in__Cong: $o ).
% 0.33/1.64
% 0.33/1.64 thf(in__Cong,definition,
% 0.33/1.64 ( in__Cong
% 0.33/1.64 = ( ! [A: $i,B: $i] :
% 0.33/1.64 ( ( A = B )
% 0.33/1.64 => ! [Xx: $i,Xy: $i] :
% 0.33/1.64 ( ( Xx = Xy )
% 0.33/1.64 => ( ( in @ Xx @ A )
% 0.33/1.64 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(exuE3u_type,type,
% 0.33/1.64 exuE3u: $o ).
% 0.33/1.64
% 0.33/1.64 thf(exuE3u,definition,
% 0.33/1.64 ( exuE3u
% 0.33/1.64 = ( ! [Xphi: $i > $o] :
% 0.33/1.64 ( ( exu
% 0.33/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/1.64 => ! [Xx: $i,Xy: $i] :
% 0.33/1.64 ( ( Xphi @ Xx )
% 0.33/1.64 => ( ( Xphi @ Xy )
% 0.33/1.64 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(exu__Cong_type,type,
% 0.33/1.64 exu__Cong: $o ).
% 0.33/1.64
% 0.33/1.64 thf(exu__Cong,definition,
% 0.33/1.64 ( exu__Cong
% 0.33/1.64 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.33/1.64 ( ! [Xx: $i,Xy: $i] :
% 0.33/1.64 ( ( Xx = Xy )
% 0.33/1.64 => ( ( Xphi @ Xx )
% 0.33/1.64 <=> ( Xpsi @ Xy ) ) )
% 0.33/1.64 => ( ( exu
% 0.33/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/1.64 <=> ( exu
% 0.33/1.64 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(emptyset__Cong_type,type,
% 0.33/1.64 emptyset__Cong: $o ).
% 0.33/1.64
% 0.33/1.64 thf(emptyset__Cong,definition,
% 0.33/1.64 ( emptyset__Cong
% 0.33/1.64 = ( emptyset = emptyset ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setadjoin__Cong_type,type,
% 0.33/1.64 setadjoin__Cong: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setadjoin__Cong,definition,
% 0.33/1.64 ( setadjoin__Cong
% 0.33/1.64 = ( ! [Xx: $i,Xy: $i] :
% 0.33/1.64 ( ( Xx = Xy )
% 0.33/1.64 => ! [Xz: $i,Xu: $i] :
% 0.33/1.64 ( ( Xz = Xu )
% 0.33/1.64 => ( ( setadjoin @ Xx @ Xz )
% 0.33/1.64 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(powerset__Cong_type,type,
% 0.33/1.64 powerset__Cong: $o ).
% 0.33/1.64
% 0.33/1.64 thf(powerset__Cong,definition,
% 0.33/1.64 ( powerset__Cong
% 0.33/1.64 = ( ! [A: $i,B: $i] :
% 0.33/1.64 ( ( A = B )
% 0.33/1.64 => ( ( powerset @ A )
% 0.33/1.64 = ( powerset @ B ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setunion__Cong_type,type,
% 0.33/1.64 setunion__Cong: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setunion__Cong,definition,
% 0.33/1.64 ( setunion__Cong
% 0.33/1.64 = ( ! [A: $i,B: $i] :
% 0.33/1.64 ( ( A = B )
% 0.33/1.64 => ( ( setunion @ A )
% 0.33/1.64 = ( setunion @ B ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(omega__Cong_type,type,
% 0.33/1.64 omega__Cong: $o ).
% 0.33/1.64
% 0.33/1.64 thf(omega__Cong,definition,
% 0.33/1.64 ( omega__Cong
% 0.33/1.64 = ( omega = omega ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(exuEu_type,type,
% 0.33/1.64 exuEu: $o ).
% 0.33/1.64
% 0.33/1.64 thf(exuEu,definition,
% 0.33/1.64 ( exuEu
% 0.33/1.64 = ( ! [Xphi: $i > $o] :
% 0.33/1.64 ( ( exu
% 0.33/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/1.64 => ! [Xx: $i,Xy: $i] :
% 0.33/1.64 ( ( Xphi @ Xx )
% 0.33/1.64 => ( ( Xphi @ Xy )
% 0.33/1.64 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(descr__Cong_type,type,
% 0.33/1.64 descr__Cong: $o ).
% 0.33/1.64
% 0.33/1.64 thf(descr__Cong,definition,
% 0.33/1.64 ( descr__Cong
% 0.33/1.64 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.33/1.64 ( ! [Xx: $i,Xy: $i] :
% 0.33/1.64 ( ( Xx = Xy )
% 0.33/1.64 => ( ( Xphi @ Xx )
% 0.33/1.64 <=> ( Xpsi @ Xy ) ) )
% 0.33/1.64 => ( ( exu
% 0.33/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/1.64 => ( ( exu
% 0.33/1.64 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.33/1.64 => ( ( descr
% 0.33/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/1.64 = ( descr
% 0.33/1.64 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(dsetconstr__Cong_type,type,
% 0.33/1.64 dsetconstr__Cong: $o ).
% 0.33/1.64
% 0.33/1.64 thf(dsetconstr__Cong,definition,
% 0.33/1.64 ( dsetconstr__Cong
% 0.33/1.64 = ( ! [A: $i,B: $i] :
% 0.33/1.64 ( ( A = B )
% 0.33/1.64 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.33/1.64 ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ B )
% 0.33/1.64 => ( ( Xx = Xy )
% 0.33/1.64 => ( ( Xphi @ Xx )
% 0.33/1.64 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.33/1.64 => ( ( dsetconstr @ A
% 0.33/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/1.64 = ( dsetconstr @ B
% 0.33/1.64 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(subset_type,type,
% 0.33/1.64 subset: $i > $i > $o ).
% 0.33/1.64
% 0.33/1.64 thf(disjoint_type,type,
% 0.33/1.64 disjoint: $i > $i > $o ).
% 0.33/1.64
% 0.33/1.64 thf(setsmeet_type,type,
% 0.33/1.64 setsmeet: $i > $i > $o ).
% 0.33/1.64
% 0.33/1.64 thf(subsetI1_type,type,
% 0.33/1.64 subsetI1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(subsetI1,definition,
% 0.33/1.64 ( subsetI1
% 0.33/1.64 = ( ! [A: $i,B: $i] :
% 0.33/1.64 ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( in @ Xx @ B ) )
% 0.33/1.64 => ( subset @ A @ B ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(eqimpsubset2_type,type,
% 0.33/1.64 eqimpsubset2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(eqimpsubset2,definition,
% 0.33/1.64 ( eqimpsubset2
% 0.33/1.64 = ( ! [A: $i,B: $i] :
% 0.33/1.64 ( ( A = B )
% 0.33/1.64 => ( subset @ B @ A ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(eqimpsubset1_type,type,
% 0.33/1.64 eqimpsubset1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(eqimpsubset1,definition,
% 0.33/1.64 ( eqimpsubset1
% 0.33/1.64 = ( ! [A: $i,B: $i] :
% 0.33/1.64 ( ( A = B )
% 0.33/1.64 => ( subset @ A @ B ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(subsetI2_type,type,
% 0.33/1.64 subsetI2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(subsetI2,definition,
% 0.33/1.64 ( subsetI2
% 0.33/1.64 = ( ! [A: $i,B: $i] :
% 0.33/1.64 ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( in @ Xx @ B ) )
% 0.33/1.64 => ( subset @ A @ B ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(emptysetsubset_type,type,
% 0.33/1.64 emptysetsubset: $o ).
% 0.33/1.64
% 0.33/1.64 thf(emptysetsubset,definition,
% 0.33/1.64 ( emptysetsubset
% 0.33/1.64 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(subsetE_type,type,
% 0.33/1.64 subsetE: $o ).
% 0.33/1.64
% 0.33/1.64 thf(subsetE,definition,
% 0.33/1.64 ( subsetE
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ( subset @ A @ B )
% 0.33/1.64 => ( ( in @ Xx @ A )
% 0.33/1.64 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(subsetE2_type,type,
% 0.33/1.64 subsetE2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(subsetE2,definition,
% 0.33/1.64 ( subsetE2
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ( subset @ A @ B )
% 0.33/1.64 => ( ~ ( in @ Xx @ B )
% 0.33/1.64 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(notsubsetI_type,type,
% 0.33/1.64 notsubsetI: $o ).
% 0.33/1.64
% 0.33/1.64 thf(notsubsetI,definition,
% 0.33/1.64 ( notsubsetI
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ~ ( in @ Xx @ B )
% 0.33/1.64 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(notequalI1_type,type,
% 0.33/1.64 notequalI1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(notequalI1,definition,
% 0.33/1.64 ( notequalI1
% 0.33/1.64 = ( ! [A: $i,B: $i] :
% 0.33/1.64 ( ~ ( subset @ A @ B )
% 0.33/1.64 => ( A != B ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(notequalI2_type,type,
% 0.33/1.64 notequalI2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(notequalI2,definition,
% 0.33/1.64 ( notequalI2
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ~ ( in @ Xx @ B )
% 0.33/1.64 => ( A != B ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(subsetRefl_type,type,
% 0.33/1.64 subsetRefl: $o ).
% 0.33/1.64
% 0.33/1.64 thf(subsetRefl,definition,
% 0.33/1.64 ( subsetRefl
% 0.33/1.64 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(subsetTrans_type,type,
% 0.33/1.64 subsetTrans: $o ).
% 0.33/1.64
% 0.33/1.64 thf(subsetTrans,definition,
% 0.33/1.64 ( subsetTrans
% 0.33/1.64 = ( ! [A: $i,B: $i,C: $i] :
% 0.33/1.64 ( ( subset @ A @ B )
% 0.33/1.64 => ( ( subset @ B @ C )
% 0.33/1.64 => ( subset @ A @ C ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setadjoinSub_type,type,
% 0.33/1.64 setadjoinSub: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setadjoinSub,definition,
% 0.33/1.64 ( setadjoinSub
% 0.33/1.64 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setadjoinSub2_type,type,
% 0.33/1.64 setadjoinSub2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setadjoinSub2,definition,
% 0.33/1.64 ( setadjoinSub2
% 0.33/1.64 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.33/1.64 ( ( subset @ A @ B )
% 0.33/1.64 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(subset2powerset_type,type,
% 0.33/1.64 subset2powerset: $o ).
% 0.33/1.64
% 0.33/1.64 thf(subset2powerset,definition,
% 0.33/1.64 ( subset2powerset
% 0.33/1.64 = ( ! [A: $i,B: $i] :
% 0.33/1.64 ( ( subset @ A @ B )
% 0.33/1.64 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setextsub_type,type,
% 0.33/1.64 setextsub: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setextsub,definition,
% 0.33/1.64 ( setextsub
% 0.33/1.64 = ( ! [A: $i,B: $i] :
% 0.33/1.64 ( ( subset @ A @ B )
% 0.33/1.64 => ( ( subset @ B @ A )
% 0.33/1.64 => ( A = B ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(subsetemptysetimpeq_type,type,
% 0.33/1.64 subsetemptysetimpeq: $o ).
% 0.33/1.64
% 0.33/1.64 thf(subsetemptysetimpeq,definition,
% 0.33/1.64 ( subsetemptysetimpeq
% 0.33/1.64 = ( ! [A: $i] :
% 0.33/1.64 ( ( subset @ A @ emptyset )
% 0.33/1.64 => ( A = emptyset ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(powersetI1_type,type,
% 0.33/1.64 powersetI1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(powersetI1,definition,
% 0.33/1.64 ( powersetI1
% 0.33/1.64 = ( ! [A: $i,B: $i] :
% 0.33/1.64 ( ( subset @ B @ A )
% 0.33/1.64 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(powersetE1_type,type,
% 0.33/1.64 powersetE1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(powersetE1,definition,
% 0.33/1.64 ( powersetE1
% 0.33/1.64 = ( ! [A: $i,B: $i] :
% 0.33/1.64 ( ( in @ B @ ( powerset @ A ) )
% 0.33/1.64 => ( subset @ B @ A ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(inPowerset_type,type,
% 0.33/1.64 inPowerset: $o ).
% 0.33/1.64
% 0.33/1.64 thf(inPowerset,definition,
% 0.33/1.64 ( inPowerset
% 0.33/1.64 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(powersetsubset_type,type,
% 0.33/1.64 powersetsubset: $o ).
% 0.33/1.64
% 0.33/1.64 thf(powersetsubset,definition,
% 0.33/1.64 ( powersetsubset
% 0.33/1.64 = ( ! [A: $i,B: $i] :
% 0.33/1.64 ( ( subset @ A @ B )
% 0.33/1.64 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(sepInPowerset_type,type,
% 0.33/1.64 sepInPowerset: $o ).
% 0.33/1.64
% 0.33/1.64 thf(sepInPowerset,definition,
% 0.33/1.64 ( sepInPowerset
% 0.33/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 0.33/1.64 ( in
% 0.33/1.64 @ ( dsetconstr @ A
% 0.33/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/1.64 @ ( powerset @ A ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(sepSubset_type,type,
% 0.33/1.64 sepSubset: $o ).
% 0.33/1.64
% 0.33/1.64 thf(sepSubset,definition,
% 0.33/1.64 ( sepSubset
% 0.33/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 0.33/1.64 ( subset
% 0.33/1.64 @ ( dsetconstr @ A
% 0.33/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/1.64 @ A ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(binunion_type,type,
% 0.33/1.64 binunion: $i > $i > $i ).
% 0.33/1.64
% 0.33/1.64 thf(binunionIL_type,type,
% 0.33/1.64 binunionIL: $o ).
% 0.33/1.64
% 0.33/1.64 thf(binunionIL,definition,
% 0.33/1.64 ( binunionIL
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(upairset2IR_type,type,
% 0.33/1.64 upairset2IR: $o ).
% 0.33/1.64
% 0.33/1.64 thf(upairset2IR,definition,
% 0.33/1.64 ( upairset2IR
% 0.33/1.64 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(binunionIR_type,type,
% 0.33/1.64 binunionIR: $o ).
% 0.33/1.64
% 0.33/1.64 thf(binunionIR,definition,
% 0.33/1.64 ( binunionIR
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ B )
% 0.33/1.64 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(binunionEcases_type,type,
% 0.33/1.64 binunionEcases: $o ).
% 0.33/1.64
% 0.33/1.64 thf(binunionEcases,definition,
% 0.33/1.64 ( binunionEcases
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.33/1.64 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.33/1.64 => ( ( ( in @ Xx @ A )
% 0.33/1.64 => Xphi )
% 0.33/1.64 => ( ( ( in @ Xx @ B )
% 0.33/1.64 => Xphi )
% 0.33/1.64 => Xphi ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(binunionE_type,type,
% 0.33/1.64 binunionE: $o ).
% 0.33/1.64
% 0.33/1.64 thf(binunionE,definition,
% 0.33/1.64 ( binunionE
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.33/1.64 => ( ( in @ Xx @ A )
% 0.33/1.64 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(binunionLsub_type,type,
% 0.33/1.64 binunionLsub: $o ).
% 0.33/1.64
% 0.33/1.64 thf(binunionLsub,definition,
% 0.33/1.64 ( binunionLsub
% 0.33/1.64 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(binunionRsub_type,type,
% 0.33/1.64 binunionRsub: $o ).
% 0.33/1.64
% 0.33/1.64 thf(binunionRsub,definition,
% 0.33/1.64 ( binunionRsub
% 0.33/1.64 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(binintersect_type,type,
% 0.33/1.64 binintersect: $i > $i > $i ).
% 0.33/1.64
% 0.33/1.64 thf(binintersectI_type,type,
% 0.33/1.64 binintersectI: $o ).
% 0.33/1.64
% 0.33/1.64 thf(binintersectI,definition,
% 0.33/1.64 ( binintersectI
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( in @ Xx @ B )
% 0.33/1.64 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(binintersectSubset5_type,type,
% 0.33/1.64 binintersectSubset5: $o ).
% 0.33/1.64
% 0.33/1.64 thf(binintersectSubset5,definition,
% 0.33/1.64 ( binintersectSubset5
% 0.33/1.64 = ( ! [A: $i,B: $i,C: $i] :
% 0.33/1.64 ( ( subset @ C @ A )
% 0.33/1.64 => ( ( subset @ C @ B )
% 0.33/1.64 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(binintersectEL_type,type,
% 0.33/1.64 binintersectEL: $o ).
% 0.33/1.64
% 0.33/1.64 thf(binintersectEL,definition,
% 0.33/1.64 ( binintersectEL
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.33/1.64 => ( in @ Xx @ A ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(binintersectLsub_type,type,
% 0.33/1.64 binintersectLsub: $o ).
% 0.33/1.64
% 0.33/1.64 thf(binintersectLsub,definition,
% 0.33/1.64 ( binintersectLsub
% 0.33/1.64 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(binintersectSubset2_type,type,
% 0.33/1.64 binintersectSubset2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(binintersectSubset2,definition,
% 0.33/1.64 ( binintersectSubset2
% 0.33/1.64 = ( ! [A: $i,B: $i] :
% 0.33/1.64 ( ( subset @ A @ B )
% 0.33/1.64 => ( ( binintersect @ A @ B )
% 0.33/1.64 = A ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(binintersectSubset3_type,type,
% 0.33/1.64 binintersectSubset3: $o ).
% 0.33/1.64
% 0.33/1.64 thf(binintersectSubset3,definition,
% 0.33/1.64 ( binintersectSubset3
% 0.33/1.64 = ( ! [A: $i,B: $i] :
% 0.33/1.64 ( ( ( binintersect @ A @ B )
% 0.33/1.64 = B )
% 0.33/1.64 => ( subset @ B @ A ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(binintersectER_type,type,
% 0.33/1.64 binintersectER: $o ).
% 0.33/1.64
% 0.33/1.64 thf(binintersectER,definition,
% 0.33/1.64 ( binintersectER
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.33/1.64 => ( in @ Xx @ B ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(disjointsetsI1_type,type,
% 0.33/1.64 disjointsetsI1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(disjointsetsI1,definition,
% 0.33/1.64 ( disjointsetsI1
% 0.33/1.64 = ( ! [A: $i,B: $i] :
% 0.33/1.64 ( ~ ? [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 & ( in @ Xx @ B ) )
% 0.33/1.64 => ( ( binintersect @ A @ B )
% 0.33/1.64 = emptyset ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(binintersectRsub_type,type,
% 0.33/1.64 binintersectRsub: $o ).
% 0.33/1.64
% 0.33/1.64 thf(binintersectRsub,definition,
% 0.33/1.64 ( binintersectRsub
% 0.33/1.64 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(binintersectSubset4_type,type,
% 0.33/1.64 binintersectSubset4: $o ).
% 0.33/1.64
% 0.33/1.64 thf(binintersectSubset4,definition,
% 0.33/1.64 ( binintersectSubset4
% 0.33/1.64 = ( ! [A: $i,B: $i] :
% 0.33/1.64 ( ( subset @ B @ A )
% 0.33/1.64 => ( ( binintersect @ A @ B )
% 0.33/1.64 = B ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(binintersectSubset1_type,type,
% 0.33/1.64 binintersectSubset1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(binintersectSubset1,definition,
% 0.33/1.64 ( binintersectSubset1
% 0.33/1.64 = ( ! [A: $i,B: $i] :
% 0.33/1.64 ( ( ( binintersect @ A @ B )
% 0.33/1.64 = A )
% 0.33/1.64 => ( subset @ A @ B ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(bs114d_type,type,
% 0.33/1.64 bs114d: $o ).
% 0.33/1.64
% 0.33/1.64 thf(bs114d,definition,
% 0.33/1.64 ( bs114d
% 0.33/1.64 = ( ! [A: $i,B: $i,C: $i] :
% 0.33/1.64 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.33/1.64 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(regular_type,type,
% 0.33/1.64 regular: $i > $o ).
% 0.33/1.64
% 0.33/1.64 thf(setminus_type,type,
% 0.33/1.64 setminus: $i > $i > $i ).
% 0.33/1.64
% 0.33/1.64 thf(setminusI_type,type,
% 0.33/1.64 setminusI: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setminusI,definition,
% 0.33/1.64 ( setminusI
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ~ ( in @ Xx @ B )
% 0.33/1.64 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setminusEL_type,type,
% 0.33/1.64 setminusEL: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setminusEL,definition,
% 0.33/1.64 ( setminusEL
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.33/1.64 => ( in @ Xx @ A ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setminusER_type,type,
% 0.33/1.64 setminusER: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setminusER,definition,
% 0.33/1.64 ( setminusER
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.33/1.64 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setminusSubset2_type,type,
% 0.33/1.64 setminusSubset2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setminusSubset2,definition,
% 0.33/1.64 ( setminusSubset2
% 0.33/1.64 = ( ! [A: $i,B: $i] :
% 0.33/1.64 ( ( subset @ A @ B )
% 0.33/1.64 => ( ( setminus @ A @ B )
% 0.33/1.64 = emptyset ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setminusERneg_type,type,
% 0.33/1.64 setminusERneg: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setminusERneg,definition,
% 0.33/1.64 ( setminusERneg
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.33/1.64 => ( ( in @ Xx @ A )
% 0.33/1.64 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setminusELneg_type,type,
% 0.33/1.64 setminusELneg: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setminusELneg,definition,
% 0.33/1.64 ( setminusELneg
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.33/1.64 => ( ~ ( in @ Xx @ B )
% 0.33/1.64 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setminusILneg_type,type,
% 0.33/1.64 setminusILneg: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setminusILneg,definition,
% 0.33/1.64 ( setminusILneg
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ~ ( in @ Xx @ A )
% 0.33/1.64 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setminusIRneg_type,type,
% 0.33/1.64 setminusIRneg: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setminusIRneg,definition,
% 0.33/1.64 ( setminusIRneg
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ B )
% 0.33/1.64 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setminusLsub_type,type,
% 0.33/1.64 setminusLsub: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setminusLsub,definition,
% 0.33/1.64 ( setminusLsub
% 0.33/1.64 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setminusSubset1_type,type,
% 0.33/1.64 setminusSubset1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setminusSubset1,definition,
% 0.33/1.64 ( setminusSubset1
% 0.33/1.64 = ( ! [A: $i,B: $i] :
% 0.33/1.64 ( ( ( setminus @ A @ B )
% 0.33/1.64 = emptyset )
% 0.33/1.64 => ( subset @ A @ B ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(symdiff_type,type,
% 0.33/1.64 symdiff: $i > $i > $i ).
% 0.33/1.64
% 0.33/1.64 thf(symdiffE_type,type,
% 0.33/1.64 symdiffE: $o ).
% 0.33/1.64
% 0.33/1.64 thf(symdiffE,definition,
% 0.33/1.64 ( symdiffE
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.33/1.64 => ! [Xphi: $o] :
% 0.33/1.64 ( ( ( in @ Xx @ A )
% 0.33/1.64 => ( ~ ( in @ Xx @ B )
% 0.33/1.64 => Xphi ) )
% 0.33/1.64 => ( ( ~ ( in @ Xx @ A )
% 0.33/1.64 => ( ( in @ Xx @ B )
% 0.33/1.64 => Xphi ) )
% 0.33/1.64 => Xphi ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(symdiffI1_type,type,
% 0.33/1.64 symdiffI1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(symdiffI1,definition,
% 0.33/1.64 ( symdiffI1
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ~ ( in @ Xx @ B )
% 0.33/1.64 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(symdiffI2_type,type,
% 0.33/1.64 symdiffI2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(symdiffI2,definition,
% 0.33/1.64 ( symdiffI2
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ~ ( in @ Xx @ A )
% 0.33/1.64 => ( ( in @ Xx @ B )
% 0.33/1.64 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(symdiffIneg1_type,type,
% 0.33/1.64 symdiffIneg1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(symdiffIneg1,definition,
% 0.33/1.64 ( symdiffIneg1
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( in @ Xx @ B )
% 0.33/1.64 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(symdiffIneg2_type,type,
% 0.33/1.64 symdiffIneg2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(symdiffIneg2,definition,
% 0.33/1.64 ( symdiffIneg2
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ~ ( in @ Xx @ A )
% 0.33/1.64 => ( ~ ( in @ Xx @ B )
% 0.33/1.64 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(iskpair_type,type,
% 0.33/1.64 iskpair: $i > $o ).
% 0.33/1.64
% 0.33/1.64 thf(secondinupair_type,type,
% 0.33/1.64 secondinupair: $o ).
% 0.33/1.64
% 0.33/1.64 thf(secondinupair,definition,
% 0.33/1.64 ( secondinupair
% 0.33/1.64 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setukpairIL_type,type,
% 0.33/1.64 setukpairIL: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setukpairIL,definition,
% 0.33/1.64 ( setukpairIL
% 0.33/1.64 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setukpairIR_type,type,
% 0.33/1.64 setukpairIR: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setukpairIR,definition,
% 0.33/1.64 ( setukpairIR
% 0.33/1.64 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(kpairiskpair_type,type,
% 0.33/1.64 kpairiskpair: $o ).
% 0.33/1.64
% 0.33/1.64 thf(kpairiskpair,definition,
% 0.33/1.64 ( kpairiskpair
% 0.33/1.64 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(kpair_type,type,
% 0.33/1.64 kpair: $i > $i > $i ).
% 0.33/1.64
% 0.33/1.64 thf(kpairp_type,type,
% 0.33/1.64 kpairp: $o ).
% 0.33/1.64
% 0.33/1.64 thf(kpairp,definition,
% 0.33/1.64 ( kpairp
% 0.33/1.64 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(cartprod_type,type,
% 0.33/1.64 cartprod: $i > $i > $i ).
% 0.33/1.64
% 0.33/1.64 thf(singletonsubset_type,type,
% 0.33/1.64 singletonsubset: $o ).
% 0.33/1.64
% 0.33/1.64 thf(singletonsubset,definition,
% 0.33/1.64 ( singletonsubset
% 0.33/1.64 = ( ! [A: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(singletoninpowerset_type,type,
% 0.33/1.64 singletoninpowerset: $o ).
% 0.33/1.64
% 0.33/1.64 thf(singletoninpowerset,definition,
% 0.33/1.64 ( singletoninpowerset
% 0.33/1.64 = ( ! [A: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(singletoninpowunion_type,type,
% 0.33/1.64 singletoninpowunion: $o ).
% 0.33/1.64
% 0.33/1.64 thf(singletoninpowunion,definition,
% 0.33/1.64 ( singletoninpowunion
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(upairset2E_type,type,
% 0.33/1.64 upairset2E: $o ).
% 0.33/1.64
% 0.33/1.64 thf(upairset2E,definition,
% 0.33/1.64 ( upairset2E
% 0.33/1.64 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.33/1.64 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.33/1.64 => ( ( Xz = Xx )
% 0.33/1.64 | ( Xz = Xy ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(upairsubunion_type,type,
% 0.33/1.64 upairsubunion: $o ).
% 0.33/1.64
% 0.33/1.64 thf(upairsubunion,definition,
% 0.33/1.64 ( upairsubunion
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ B )
% 0.33/1.64 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(upairinpowunion_type,type,
% 0.33/1.64 upairinpowunion: $o ).
% 0.33/1.64
% 0.33/1.64 thf(upairinpowunion,definition,
% 0.33/1.64 ( upairinpowunion
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ B )
% 0.33/1.64 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(ubforcartprodlem1_type,type,
% 0.33/1.64 ubforcartprodlem1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(ubforcartprodlem1,definition,
% 0.33/1.64 ( ubforcartprodlem1
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ B )
% 0.33/1.64 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(ubforcartprodlem2_type,type,
% 0.33/1.64 ubforcartprodlem2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(ubforcartprodlem2,definition,
% 0.33/1.64 ( ubforcartprodlem2
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ B )
% 0.33/1.64 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(ubforcartprodlem3_type,type,
% 0.33/1.64 ubforcartprodlem3: $o ).
% 0.33/1.64
% 0.33/1.64 thf(ubforcartprodlem3,definition,
% 0.33/1.64 ( ubforcartprodlem3
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ B )
% 0.33/1.64 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(cartprodpairin_type,type,
% 0.33/1.64 cartprodpairin: $o ).
% 0.33/1.64
% 0.33/1.64 thf(cartprodpairin,definition,
% 0.33/1.64 ( cartprodpairin
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ B )
% 0.33/1.64 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(cartprodmempair1_type,type,
% 0.33/1.64 cartprodmempair1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(cartprodmempair1,definition,
% 0.33/1.64 ( cartprodmempair1
% 0.33/1.64 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.33/1.64 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.33/1.64 => ? [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 & ? [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ B )
% 0.33/1.64 & ( Xu
% 0.33/1.64 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(cartprodmempair_type,type,
% 0.33/1.64 cartprodmempair: $o ).
% 0.33/1.64
% 0.33/1.64 thf(cartprodmempair,definition,
% 0.33/1.64 ( cartprodmempair
% 0.33/1.64 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.33/1.64 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.33/1.64 => ( iskpair @ Xu ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setunionE2_type,type,
% 0.33/1.64 setunionE2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setunionE2,definition,
% 0.33/1.64 ( setunionE2
% 0.33/1.64 = ( ! [A: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ ( setunion @ A ) )
% 0.33/1.64 => ? [X: $i] :
% 0.33/1.64 ( ( in @ X @ A )
% 0.33/1.64 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setunionsingleton1_type,type,
% 0.33/1.64 setunionsingleton1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setunionsingleton1,definition,
% 0.33/1.64 ( setunionsingleton1
% 0.33/1.64 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setunionsingleton2_type,type,
% 0.33/1.64 setunionsingleton2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setunionsingleton2,definition,
% 0.33/1.64 ( setunionsingleton2
% 0.33/1.64 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setunionsingleton_type,type,
% 0.33/1.64 setunionsingleton: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setunionsingleton,definition,
% 0.33/1.64 ( setunionsingleton
% 0.33/1.64 = ( ! [Xx: $i] :
% 0.33/1.64 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.33/1.64 = Xx ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(singleton_type,type,
% 0.33/1.64 singleton: $i > $o ).
% 0.33/1.64
% 0.33/1.64 thf(singletonprop_type,type,
% 0.33/1.64 singletonprop: $o ).
% 0.33/1.64
% 0.33/1.64 thf(singletonprop,definition,
% 0.33/1.64 ( singletonprop
% 0.33/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 0.33/1.64 ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ A )
% 0.33/1.64 => ( ( Xphi @ Xx )
% 0.33/1.64 => ( ( Xphi @ Xy )
% 0.33/1.64 => ( Xx = Xy ) ) ) ) )
% 0.33/1.64 => ( ? [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 & ( Xphi @ Xx ) )
% 0.33/1.64 => ( singleton
% 0.33/1.64 @ ( dsetconstr @ A
% 0.33/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(ex1_type,type,
% 0.33/1.64 ex1: $i > ( $i > $o ) > $o ).
% 0.33/1.64
% 0.33/1.64 thf(ex1,definition,
% 0.33/1.64 ( ex1
% 0.33/1.64 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.33/1.64 ( singleton
% 0.33/1.64 @ ( dsetconstr @ A
% 0.33/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(ex1E1_type,type,
% 0.33/1.64 ex1E1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(ex1E1,definition,
% 0.33/1.64 ( ex1E1
% 0.33/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 0.33/1.64 ( ( ex1 @ A
% 0.33/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/1.64 => ? [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(ex1I_type,type,
% 0.33/1.64 ex1I: $o ).
% 0.33/1.64
% 0.33/1.64 thf(ex1I,definition,
% 0.33/1.64 ( ex1I
% 0.33/1.64 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( Xphi @ Xx )
% 0.33/1.64 => ( ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ A )
% 0.33/1.64 => ( ( Xphi @ Xy )
% 0.33/1.64 => ( Xy = Xx ) ) )
% 0.33/1.64 => ( ex1 @ A
% 0.33/1.64 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(ex1I2_type,type,
% 0.33/1.64 ex1I2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(ex1I2,definition,
% 0.33/1.64 ( ex1I2
% 0.33/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 0.33/1.64 ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ A )
% 0.33/1.64 => ( ( Xphi @ Xx )
% 0.33/1.64 => ( ( Xphi @ Xy )
% 0.33/1.64 => ( Xx = Xy ) ) ) ) )
% 0.33/1.64 => ( ? [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 & ( Xphi @ Xx ) )
% 0.33/1.64 => ( ex1 @ A
% 0.33/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(singletonsuniq_type,type,
% 0.33/1.64 singletonsuniq: $o ).
% 0.33/1.64
% 0.33/1.64 thf(singletonsuniq,definition,
% 0.33/1.64 ( singletonsuniq
% 0.33/1.64 = ( ! [Xx: $i,Xy: $i] :
% 0.33/1.64 ( ( ( setadjoin @ Xx @ emptyset )
% 0.33/1.64 = ( setadjoin @ Xy @ emptyset ) )
% 0.33/1.64 => ( Xx = Xy ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(atmost1p_type,type,
% 0.33/1.64 atmost1p: $i > $o ).
% 0.33/1.64
% 0.33/1.64 thf(atleast2p_type,type,
% 0.33/1.64 atleast2p: $i > $o ).
% 0.33/1.64
% 0.33/1.64 thf(atmost2p_type,type,
% 0.33/1.64 atmost2p: $i > $o ).
% 0.33/1.64
% 0.33/1.64 thf(upairsetp_type,type,
% 0.33/1.64 upairsetp: $i > $o ).
% 0.33/1.64
% 0.33/1.64 thf(setukpairinjL1_type,type,
% 0.33/1.64 setukpairinjL1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setukpairinjL1,definition,
% 0.33/1.64 ( setukpairinjL1
% 0.33/1.64 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.33/1.64 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.33/1.64 => ( Xx = Xz ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(kfstsingleton_type,type,
% 0.33/1.64 kfstsingleton: $o ).
% 0.33/1.64
% 0.33/1.64 thf(kfstsingleton,definition,
% 0.33/1.64 ( kfstsingleton
% 0.33/1.64 = ( ! [Xu: $i] :
% 0.33/1.64 ( ( iskpair @ Xu )
% 0.33/1.64 => ( singleton
% 0.33/1.64 @ ( dsetconstr @ ( setunion @ Xu )
% 0.33/1.64 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(theprop_type,type,
% 0.33/1.64 theprop: $o ).
% 0.33/1.64
% 0.33/1.64 thf(theprop,definition,
% 0.33/1.64 ( theprop
% 0.33/1.64 = ( ! [X: $i] :
% 0.33/1.64 ( ( singleton @ X )
% 0.33/1.64 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(kfst_type,type,
% 0.33/1.64 kfst: $i > $i ).
% 0.33/1.64
% 0.33/1.64 thf(kfstpairEq_type,type,
% 0.33/1.64 kfstpairEq: $o ).
% 0.33/1.64
% 0.33/1.64 thf(kfstpairEq,definition,
% 0.33/1.64 ( kfstpairEq
% 0.33/1.64 = ( ! [Xx: $i,Xy: $i] :
% 0.33/1.64 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.33/1.64 = Xx ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(cartprodfstin_type,type,
% 0.33/1.64 cartprodfstin: $o ).
% 0.33/1.64
% 0.33/1.64 thf(cartprodfstin,definition,
% 0.33/1.64 ( cartprodfstin
% 0.33/1.64 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.33/1.64 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.33/1.64 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setukpairinjL2_type,type,
% 0.33/1.64 setukpairinjL2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setukpairinjL2,definition,
% 0.33/1.64 ( setukpairinjL2
% 0.33/1.64 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.33/1.64 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.33/1.64 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.33/1.64 => ( Xx = Xz ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setukpairinjL_type,type,
% 0.33/1.64 setukpairinjL: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setukpairinjL,definition,
% 0.33/1.64 ( setukpairinjL
% 0.33/1.64 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.33/1.64 ( ( ( kpair @ Xx @ Xy )
% 0.33/1.64 = ( kpair @ Xz @ Xu ) )
% 0.33/1.64 => ( Xx = Xz ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setukpairinjR11_type,type,
% 0.33/1.64 setukpairinjR11: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setukpairinjR11,definition,
% 0.33/1.64 ( setukpairinjR11
% 0.33/1.64 = ( ! [Xx: $i,Xy: $i] :
% 0.33/1.64 ( ( Xx = Xy )
% 0.33/1.64 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.33/1.64 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setukpairinjR12_type,type,
% 0.33/1.64 setukpairinjR12: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setukpairinjR12,definition,
% 0.33/1.64 ( setukpairinjR12
% 0.33/1.64 = ( ! [Xx: $i,Xy: $i] :
% 0.33/1.64 ( ( Xx = Xy )
% 0.33/1.64 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.33/1.64 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setukpairinjR1_type,type,
% 0.33/1.64 setukpairinjR1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setukpairinjR1,definition,
% 0.33/1.64 ( setukpairinjR1
% 0.33/1.64 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.33/1.64 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.33/1.64 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.33/1.64 => ( ( Xz = Xu )
% 0.33/1.64 => ( Xy = Xu ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(upairequniteq_type,type,
% 0.33/1.64 upairequniteq: $o ).
% 0.33/1.64
% 0.33/1.64 thf(upairequniteq,definition,
% 0.33/1.64 ( upairequniteq
% 0.33/1.64 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.33/1.64 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.33/1.64 = ( setadjoin @ Xz @ emptyset ) )
% 0.33/1.64 => ( Xx = Xy ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setukpairinjR2_type,type,
% 0.33/1.64 setukpairinjR2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setukpairinjR2,definition,
% 0.33/1.64 ( setukpairinjR2
% 0.33/1.64 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.33/1.64 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.33/1.64 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.33/1.64 => ( Xy = Xu ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setukpairinjR_type,type,
% 0.33/1.64 setukpairinjR: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setukpairinjR,definition,
% 0.33/1.64 ( setukpairinjR
% 0.33/1.64 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.33/1.64 ( ( ( kpair @ Xx @ Xy )
% 0.33/1.64 = ( kpair @ Xz @ Xu ) )
% 0.33/1.64 => ( Xy = Xu ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(ksndsingleton_type,type,
% 0.33/1.64 ksndsingleton: $o ).
% 0.33/1.64
% 0.33/1.64 thf(ksndsingleton,definition,
% 0.33/1.64 ( ksndsingleton
% 0.33/1.64 = ( ! [Xu: $i] :
% 0.33/1.64 ( ( iskpair @ Xu )
% 0.33/1.64 => ( singleton
% 0.33/1.64 @ ( dsetconstr @ ( setunion @ Xu )
% 0.33/1.64 @ ^ [Xx: $i] :
% 0.33/1.64 ( Xu
% 0.33/1.64 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(ksnd_type,type,
% 0.33/1.64 ksnd: $i > $i ).
% 0.33/1.64
% 0.33/1.64 thf(ksndpairEq_type,type,
% 0.33/1.64 ksndpairEq: $o ).
% 0.33/1.64
% 0.33/1.64 thf(ksndpairEq,definition,
% 0.33/1.64 ( ksndpairEq
% 0.33/1.64 = ( ! [Xx: $i,Xy: $i] :
% 0.33/1.64 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.33/1.64 = Xy ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(kpairsurjEq_type,type,
% 0.33/1.64 kpairsurjEq: $o ).
% 0.33/1.64
% 0.33/1.64 thf(kpairsurjEq,definition,
% 0.33/1.64 ( kpairsurjEq
% 0.33/1.64 = ( ! [Xu: $i] :
% 0.33/1.64 ( ( iskpair @ Xu )
% 0.33/1.64 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.33/1.64 = Xu ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(cartprodsndin_type,type,
% 0.33/1.64 cartprodsndin: $o ).
% 0.33/1.64
% 0.33/1.64 thf(cartprodsndin,definition,
% 0.33/1.64 ( cartprodsndin
% 0.33/1.64 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.33/1.64 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.33/1.64 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(cartprodpairmemEL_type,type,
% 0.33/1.64 cartprodpairmemEL: $o ).
% 0.33/1.64
% 0.33/1.64 thf(cartprodpairmemEL,definition,
% 0.33/1.64 ( cartprodpairmemEL
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.33/1.64 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.33/1.64 => ( in @ Xx @ A ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(cartprodpairmemER_type,type,
% 0.33/1.64 cartprodpairmemER: $o ).
% 0.33/1.64
% 0.33/1.64 thf(cartprodpairmemER,definition,
% 0.33/1.64 ( cartprodpairmemER
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.33/1.64 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.33/1.64 => ( in @ Xy @ B ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(cartprodmempaircEq_type,type,
% 0.33/1.64 cartprodmempaircEq: $o ).
% 0.33/1.64
% 0.33/1.64 thf(cartprodmempaircEq,definition,
% 0.33/1.64 ( cartprodmempaircEq
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ B )
% 0.33/1.64 => ( ( kpair @ Xx @ Xy )
% 0.33/1.64 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(cartprodfstpairEq_type,type,
% 0.33/1.64 cartprodfstpairEq: $o ).
% 0.33/1.64
% 0.33/1.64 thf(cartprodfstpairEq,definition,
% 0.33/1.64 ( cartprodfstpairEq
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ B )
% 0.33/1.64 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.33/1.64 = Xx ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(cartprodsndpairEq_type,type,
% 0.33/1.64 cartprodsndpairEq: $o ).
% 0.33/1.64
% 0.33/1.64 thf(cartprodsndpairEq,definition,
% 0.33/1.64 ( cartprodsndpairEq
% 0.33/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ B )
% 0.33/1.64 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.33/1.64 = Xy ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(cartprodpairsurjEq_type,type,
% 0.33/1.64 cartprodpairsurjEq: $o ).
% 0.33/1.64
% 0.33/1.64 thf(cartprodpairsurjEq,definition,
% 0.33/1.64 ( cartprodpairsurjEq
% 0.33/1.64 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.33/1.64 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.33/1.64 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.33/1.64 = Xu ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(breln_type,type,
% 0.33/1.64 breln: $i > $i > $i > $o ).
% 0.33/1.64
% 0.33/1.64 thf(breln,definition,
% 0.33/1.64 ( breln
% 0.33/1.64 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(dpsetconstr_type,type,
% 0.33/1.64 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.33/1.64
% 0.33/1.64 thf(dpsetconstrI_type,type,
% 0.33/1.64 dpsetconstrI: $o ).
% 0.33/1.64
% 0.33/1.64 thf(dpsetconstrI,definition,
% 0.33/1.64 ( dpsetconstrI
% 0.33/1.64 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ B )
% 0.33/1.64 => ( ( Xphi @ Xx @ Xy )
% 0.33/1.64 => ( in @ ( kpair @ Xx @ Xy )
% 0.33/1.64 @ ( dpsetconstr @ A @ B
% 0.33/1.64 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(dpsetconstrSub_type,type,
% 0.33/1.64 dpsetconstrSub: $o ).
% 0.33/1.64
% 0.33/1.64 thf(dpsetconstrSub,definition,
% 0.33/1.64 ( dpsetconstrSub
% 0.33/1.64 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.33/1.64 ( subset
% 0.33/1.64 @ ( dpsetconstr @ A @ B
% 0.33/1.64 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.33/1.64 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setOfPairsIsBReln_type,type,
% 0.33/1.64 setOfPairsIsBReln: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setOfPairsIsBReln,definition,
% 0.33/1.64 ( setOfPairsIsBReln
% 0.33/1.64 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.33/1.64 ( breln @ A @ B
% 0.33/1.64 @ ( dpsetconstr @ A @ B
% 0.33/1.64 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(dpsetconstrERa_type,type,
% 0.33/1.64 dpsetconstrERa: $o ).
% 0.33/1.64
% 0.33/1.64 thf(dpsetconstrERa,definition,
% 0.33/1.64 ( dpsetconstrERa
% 0.33/1.64 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ B )
% 0.33/1.64 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.33/1.64 @ ( dpsetconstr @ A @ B
% 0.33/1.64 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.33/1.64 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(dpsetconstrEL1_type,type,
% 0.33/1.64 dpsetconstrEL1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(dpsetconstrEL1,definition,
% 0.33/1.64 ( dpsetconstrEL1
% 0.33/1.64 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.33/1.64 ( ( in @ ( kpair @ Xx @ Xy )
% 0.33/1.64 @ ( dpsetconstr @ A @ B
% 0.33/1.64 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.33/1.64 => ( in @ Xx @ A ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(dpsetconstrEL2_type,type,
% 0.33/1.64 dpsetconstrEL2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(dpsetconstrEL2,definition,
% 0.33/1.64 ( dpsetconstrEL2
% 0.33/1.64 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.33/1.64 ( ( in @ ( kpair @ Xx @ Xy )
% 0.33/1.64 @ ( dpsetconstr @ A @ B
% 0.33/1.64 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.33/1.64 => ( in @ Xy @ B ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(dpsetconstrER_type,type,
% 0.33/1.64 dpsetconstrER: $o ).
% 0.33/1.64
% 0.33/1.64 thf(dpsetconstrER,definition,
% 0.33/1.64 ( dpsetconstrER
% 0.33/1.64 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.33/1.64 ( ( in @ ( kpair @ Xx @ Xy )
% 0.33/1.64 @ ( dpsetconstr @ A @ B
% 0.33/1.64 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.33/1.64 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(func_type,type,
% 0.33/1.64 func: $i > $i > $i > $o ).
% 0.33/1.64
% 0.33/1.64 thf(funcSet_type,type,
% 0.33/1.64 funcSet: $i > $i > $i ).
% 0.33/1.64
% 0.33/1.64 thf(funcImageSingleton_type,type,
% 0.33/1.64 funcImageSingleton: $o ).
% 0.33/1.64
% 0.33/1.64 thf(funcImageSingleton,definition,
% 0.33/1.64 ( funcImageSingleton
% 0.33/1.64 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/1.64 ( ( func @ A @ B @ Xf )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( singleton
% 0.33/1.64 @ ( dsetconstr @ B
% 0.33/1.64 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(apProp_type,type,
% 0.33/1.64 apProp: $o ).
% 0.33/1.64
% 0.33/1.64 thf(apProp,definition,
% 0.33/1.64 ( apProp
% 0.33/1.64 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/1.64 ( ( func @ A @ B @ Xf )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( in
% 0.33/1.64 @ ( setunion
% 0.33/1.64 @ ( dsetconstr @ B
% 0.33/1.64 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.33/1.64 @ B ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(ap_type,type,
% 0.33/1.64 ap: $i > $i > $i > $i > $i ).
% 0.33/1.64
% 0.33/1.64 thf(app_type,type,
% 0.33/1.64 app: $o ).
% 0.33/1.64
% 0.33/1.64 thf(app,definition,
% 0.33/1.64 ( app
% 0.33/1.64 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/1.64 ( ( func @ A @ B @ Xf )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(infuncsetfunc_type,type,
% 0.33/1.64 infuncsetfunc: $o ).
% 0.33/1.64
% 0.33/1.64 thf(infuncsetfunc,definition,
% 0.33/1.64 ( infuncsetfunc
% 0.33/1.64 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/1.64 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.33/1.64 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(ap2p_type,type,
% 0.33/1.64 ap2p: $o ).
% 0.33/1.64
% 0.33/1.64 thf(ap2p,definition,
% 0.33/1.64 ( ap2p
% 0.33/1.64 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/1.64 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(funcinfuncset_type,type,
% 0.33/1.64 funcinfuncset: $o ).
% 0.33/1.64
% 0.33/1.64 thf(funcinfuncset,definition,
% 0.33/1.64 ( funcinfuncset
% 0.33/1.64 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/1.64 ( ( func @ A @ B @ Xf )
% 0.33/1.64 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(lamProp_type,type,
% 0.33/1.64 lamProp: $o ).
% 0.33/1.64
% 0.33/1.64 thf(lamProp,definition,
% 0.33/1.64 ( lamProp
% 0.33/1.64 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.33/1.64 ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.33/1.64 => ( func @ A @ B
% 0.33/1.64 @ ( dpsetconstr @ A @ B
% 0.33/1.64 @ ^ [Xx: $i,Xy: $i] :
% 0.33/1.64 ( ( Xf @ Xx )
% 0.33/1.64 = Xy ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(lam_type,type,
% 0.33/1.64 lam: $i > $i > ( $i > $i ) > $i ).
% 0.33/1.64
% 0.33/1.64 thf(lamp_type,type,
% 0.33/1.64 lamp: $o ).
% 0.33/1.64
% 0.33/1.64 thf(lamp,definition,
% 0.33/1.64 ( lamp
% 0.33/1.64 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.33/1.64 ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.33/1.64 => ( func @ A @ B
% 0.33/1.64 @ ( lam @ A @ B
% 0.33/1.64 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(lam2p_type,type,
% 0.33/1.64 lam2p: $o ).
% 0.33/1.64
% 0.33/1.64 thf(lam2p,definition,
% 0.33/1.64 ( lam2p
% 0.33/1.64 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.33/1.64 ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.33/1.64 => ( in
% 0.33/1.64 @ ( lam @ A @ B
% 0.33/1.64 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.33/1.64 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(brelnall1_type,type,
% 0.33/1.64 brelnall1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(brelnall1,definition,
% 0.33/1.64 ( brelnall1
% 0.33/1.64 = ( ! [A: $i,B: $i,R: $i] :
% 0.33/1.64 ( ( breln @ A @ B @ R )
% 0.33/1.64 => ! [Xphi: $i > $o] :
% 0.33/1.64 ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ B )
% 0.33/1.64 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.33/1.64 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ R )
% 0.33/1.64 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(brelnall2_type,type,
% 0.33/1.64 brelnall2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(brelnall2,definition,
% 0.33/1.64 ( brelnall2
% 0.33/1.64 = ( ! [A: $i,B: $i,R: $i] :
% 0.33/1.64 ( ( breln @ A @ B @ R )
% 0.33/1.64 => ! [Xphi: $i > $o] :
% 0.33/1.64 ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ B )
% 0.33/1.64 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.33/1.64 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ R )
% 0.33/1.64 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(ex1E2_type,type,
% 0.33/1.64 ex1E2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(ex1E2,definition,
% 0.33/1.64 ( ex1E2
% 0.33/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 0.33/1.64 ( ( ex1 @ A
% 0.33/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ A )
% 0.33/1.64 => ( ( Xphi @ Xx )
% 0.33/1.64 => ( ( Xphi @ Xy )
% 0.33/1.64 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(funcGraphProp1_type,type,
% 0.33/1.64 funcGraphProp1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(funcGraphProp1,definition,
% 0.33/1.64 ( funcGraphProp1
% 0.33/1.64 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/1.64 ( ( func @ A @ B @ Xf )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(funcGraphProp3_type,type,
% 0.33/1.64 funcGraphProp3: $o ).
% 0.33/1.64
% 0.33/1.64 thf(funcGraphProp3,definition,
% 0.33/1.64 ( funcGraphProp3
% 0.33/1.64 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/1.64 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(funcGraphProp2_type,type,
% 0.33/1.64 funcGraphProp2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(funcGraphProp2,definition,
% 0.33/1.64 ( funcGraphProp2
% 0.33/1.64 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/1.64 ( ( func @ A @ B @ Xf )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ B )
% 0.33/1.64 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.33/1.64 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.33/1.64 = Xy ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(funcextLem_type,type,
% 0.33/1.64 funcextLem: $o ).
% 0.33/1.64
% 0.33/1.64 thf(funcextLem,definition,
% 0.33/1.64 ( funcextLem
% 0.33/1.64 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/1.64 ( ( func @ A @ B @ Xf )
% 0.33/1.64 => ! [Xg: $i] :
% 0.33/1.64 ( ( func @ A @ B @ Xg )
% 0.33/1.64 => ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.33/1.64 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ B )
% 0.33/1.64 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 0.33/1.64 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(funcGraphProp4_type,type,
% 0.33/1.64 funcGraphProp4: $o ).
% 0.33/1.64
% 0.33/1.64 thf(funcGraphProp4,definition,
% 0.33/1.64 ( funcGraphProp4
% 0.33/1.64 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/1.64 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ B )
% 0.33/1.64 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.33/1.64 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.33/1.64 = Xy ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(subbreln_type,type,
% 0.33/1.64 subbreln: $o ).
% 0.33/1.64
% 0.33/1.64 thf(subbreln,definition,
% 0.33/1.64 ( subbreln
% 0.33/1.64 = ( ! [A: $i,B: $i,R: $i] :
% 0.33/1.64 ( ( breln @ A @ B @ R )
% 0.33/1.64 => ! [S: $i] :
% 0.33/1.64 ( ( breln @ A @ B @ S )
% 0.33/1.64 => ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ B )
% 0.33/1.64 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.33/1.64 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.33/1.64 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(eqbreln_type,type,
% 0.33/1.64 eqbreln: $o ).
% 0.33/1.64
% 0.33/1.64 thf(eqbreln,definition,
% 0.33/1.64 ( eqbreln
% 0.33/1.64 = ( ! [A: $i,B: $i,R: $i] :
% 0.33/1.64 ( ( breln @ A @ B @ R )
% 0.33/1.64 => ! [S: $i] :
% 0.33/1.64 ( ( breln @ A @ B @ S )
% 0.33/1.64 => ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ B )
% 0.33/1.64 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.33/1.64 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.33/1.64 => ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ B )
% 0.33/1.64 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.33/1.64 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.33/1.64 => ( R = S ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(funcext_type,type,
% 0.33/1.64 funcext: $o ).
% 0.33/1.64
% 0.33/1.64 thf(funcext,definition,
% 0.33/1.64 ( funcext
% 0.33/1.64 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/1.64 ( ( func @ A @ B @ Xf )
% 0.33/1.64 => ! [Xg: $i] :
% 0.33/1.64 ( ( func @ A @ B @ Xg )
% 0.33/1.64 => ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.33/1.64 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.33/1.64 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(funcext2_type,type,
% 0.33/1.64 funcext2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(funcext2,definition,
% 0.33/1.64 ( funcext2
% 0.33/1.64 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/1.64 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.33/1.64 => ! [Xg: $i] :
% 0.33/1.64 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 0.33/1.64 => ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.33/1.64 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.33/1.64 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(ap2apEq1_type,type,
% 0.33/1.64 ap2apEq1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(ap2apEq1,definition,
% 0.33/1.64 ( ap2apEq1
% 0.33/1.64 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/1.64 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.33/1.64 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(ap2apEq2_type,type,
% 0.33/1.64 ap2apEq2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(ap2apEq2,definition,
% 0.33/1.64 ( ap2apEq2
% 0.33/1.64 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/1.64 ( ( func @ A @ B @ Xf )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.33/1.64 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(beta1_type,type,
% 0.33/1.64 beta1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(beta1,definition,
% 0.33/1.64 ( beta1
% 0.33/1.64 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.33/1.64 ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( ap @ A @ B
% 0.33/1.64 @ ( lam @ A @ B
% 0.33/1.64 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.33/1.64 @ Xx )
% 0.33/1.64 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(eta1_type,type,
% 0.33/1.64 eta1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(eta1,definition,
% 0.33/1.64 ( eta1
% 0.33/1.64 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/1.64 ( ( func @ A @ B @ Xf )
% 0.33/1.64 => ( ( lam @ A @ B
% 0.33/1.64 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.33/1.64 = Xf ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(lam2lamEq_type,type,
% 0.33/1.64 lam2lamEq: $o ).
% 0.33/1.64
% 0.33/1.64 thf(lam2lamEq,definition,
% 0.33/1.64 ( lam2lamEq
% 0.33/1.64 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.33/1.64 ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.33/1.64 => ( ( lam @ A @ B
% 0.33/1.64 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.33/1.64 = ( lam @ A @ B
% 0.33/1.64 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(beta2_type,type,
% 0.33/1.64 beta2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(beta2,definition,
% 0.33/1.64 ( beta2
% 0.33/1.64 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.33/1.64 ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( ap @ A @ B
% 0.33/1.64 @ ( lam @ A @ B
% 0.33/1.64 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.33/1.64 @ Xx )
% 0.33/1.64 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(eta2_type,type,
% 0.33/1.64 eta2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(eta2,definition,
% 0.33/1.64 ( eta2
% 0.33/1.64 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/1.64 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.33/1.64 => ( ( lam @ A @ B
% 0.33/1.64 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.33/1.64 = Xf ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(iffalseProp1_type,type,
% 0.33/1.64 iffalseProp1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(iffalseProp1,definition,
% 0.33/1.64 ( iffalseProp1
% 0.33/1.64 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ A )
% 0.33/1.64 => ( ~ Xphi
% 0.33/1.64 => ( in @ Xy
% 0.33/1.64 @ ( dsetconstr @ A
% 0.33/1.64 @ ^ [Xz: $i] :
% 0.33/1.64 ( ( Xphi
% 0.33/1.64 & ( Xz = Xx ) )
% 0.33/1.64 | ( ~ Xphi
% 0.33/1.64 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(iffalseProp2_type,type,
% 0.33/1.64 iffalseProp2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(iffalseProp2,definition,
% 0.33/1.64 ( iffalseProp2
% 0.33/1.64 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ A )
% 0.33/1.64 => ( ~ Xphi
% 0.33/1.64 => ( ( dsetconstr @ A
% 0.33/1.64 @ ^ [Xz: $i] :
% 0.33/1.64 ( ( Xphi
% 0.33/1.64 & ( Xz = Xx ) )
% 0.33/1.64 | ( ~ Xphi
% 0.33/1.64 & ( Xz = Xy ) ) ) )
% 0.33/1.64 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(iftrueProp1_type,type,
% 0.33/1.64 iftrueProp1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(iftrueProp1,definition,
% 0.33/1.64 ( iftrueProp1
% 0.33/1.64 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ A )
% 0.33/1.64 => ( Xphi
% 0.33/1.64 => ( in @ Xx
% 0.33/1.64 @ ( dsetconstr @ A
% 0.33/1.64 @ ^ [Xz: $i] :
% 0.33/1.64 ( ( Xphi
% 0.33/1.64 & ( Xz = Xx ) )
% 0.33/1.64 | ( ~ Xphi
% 0.33/1.64 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(iftrueProp2_type,type,
% 0.33/1.64 iftrueProp2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(iftrueProp2,definition,
% 0.33/1.64 ( iftrueProp2
% 0.33/1.64 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ A )
% 0.33/1.64 => ( Xphi
% 0.33/1.64 => ( ( dsetconstr @ A
% 0.33/1.64 @ ^ [Xz: $i] :
% 0.33/1.64 ( ( Xphi
% 0.33/1.64 & ( Xz = Xx ) )
% 0.33/1.64 | ( ~ Xphi
% 0.33/1.64 & ( Xz = Xy ) ) ) )
% 0.33/1.64 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(ifSingleton_type,type,
% 0.33/1.64 ifSingleton: $o ).
% 0.33/1.64
% 0.33/1.64 thf(ifSingleton,definition,
% 0.33/1.64 ( ifSingleton
% 0.33/1.64 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ A )
% 0.33/1.64 => ( singleton
% 0.33/1.64 @ ( dsetconstr @ A
% 0.33/1.64 @ ^ [Xz: $i] :
% 0.33/1.64 ( ( Xphi
% 0.33/1.64 & ( Xz = Xx ) )
% 0.33/1.64 | ( ~ Xphi
% 0.33/1.64 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(if_type,type,
% 0.33/1.64 if: $i > $o > $i > $i > $i ).
% 0.33/1.64
% 0.33/1.64 thf(ifp_type,type,
% 0.33/1.64 ifp: $o ).
% 0.33/1.64
% 0.33/1.64 thf(ifp,definition,
% 0.33/1.64 ( ifp
% 0.33/1.64 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ A )
% 0.33/1.64 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(theeq_type,type,
% 0.33/1.64 theeq: $o ).
% 0.33/1.64
% 0.33/1.64 thf(theeq,definition,
% 0.33/1.64 ( theeq
% 0.33/1.64 = ( ! [X: $i] :
% 0.33/1.64 ( ( singleton @ X )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ X )
% 0.33/1.64 => ( ( setunion @ X )
% 0.33/1.64 = Xx ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(iftrue_type,type,
% 0.33/1.64 iftrue: $o ).
% 0.33/1.64
% 0.33/1.64 thf(iftrue,definition,
% 0.33/1.64 ( iftrue
% 0.33/1.64 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ A )
% 0.33/1.64 => ( Xphi
% 0.33/1.64 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.33/1.64 = Xx ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(iffalse_type,type,
% 0.33/1.64 iffalse: $o ).
% 0.33/1.64
% 0.33/1.64 thf(iffalse,definition,
% 0.33/1.64 ( iffalse
% 0.33/1.64 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ A )
% 0.33/1.64 => ( ~ Xphi
% 0.33/1.64 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.33/1.64 = Xy ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(iftrueorfalse_type,type,
% 0.33/1.64 iftrueorfalse: $o ).
% 0.33/1.64
% 0.33/1.64 thf(iftrueorfalse,definition,
% 0.33/1.64 ( iftrueorfalse
% 0.33/1.64 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ! [Xy: $i] :
% 0.33/1.64 ( ( in @ Xy @ A )
% 0.33/1.64 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(binintersectT_lem_type,type,
% 0.33/1.64 binintersectT_lem: $o ).
% 0.33/1.64
% 0.33/1.64 thf(binintersectT_lem,definition,
% 0.33/1.64 ( binintersectT_lem
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(binunionT_lem_type,type,
% 0.33/1.64 binunionT_lem: $o ).
% 0.33/1.64
% 0.33/1.64 thf(binunionT_lem,definition,
% 0.33/1.64 ( binunionT_lem
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(powersetT_lem_type,type,
% 0.33/1.64 powersetT_lem: $o ).
% 0.33/1.64
% 0.33/1.64 thf(powersetT_lem,definition,
% 0.33/1.64 ( powersetT_lem
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setminusT_lem_type,type,
% 0.33/1.64 setminusT_lem: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setminusT_lem,definition,
% 0.33/1.64 ( setminusT_lem
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(complementT_lem_type,type,
% 0.33/1.64 complementT_lem: $o ).
% 0.33/1.64
% 0.33/1.64 thf(complementT_lem,definition,
% 0.33/1.64 ( complementT_lem
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(setextT_type,type,
% 0.33/1.64 setextT: $o ).
% 0.33/1.64
% 0.33/1.64 thf(setextT,definition,
% 0.33/1.64 ( setextT
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( in @ Xx @ X )
% 0.33/1.64 => ( in @ Xx @ Y ) ) )
% 0.33/1.64 => ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( in @ Xx @ Y )
% 0.33/1.64 => ( in @ Xx @ X ) ) )
% 0.33/1.64 => ( X = Y ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(subsetTI_type,type,
% 0.33/1.64 subsetTI: $o ).
% 0.33/1.64
% 0.33/1.64 thf(subsetTI,definition,
% 0.33/1.64 ( subsetTI
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( in @ Xx @ X )
% 0.33/1.64 => ( in @ Xx @ Y ) ) )
% 0.33/1.64 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(powersetTI1_type,type,
% 0.33/1.64 powersetTI1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(powersetTI1,definition,
% 0.33/1.64 ( powersetTI1
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ( ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( in @ Xx @ X )
% 0.33/1.64 => ( in @ Xx @ Y ) ) )
% 0.33/1.64 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(powersetTE1_type,type,
% 0.33/1.64 powersetTE1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(powersetTE1,definition,
% 0.33/1.64 ( powersetTE1
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( in @ X @ ( powerset @ Y ) )
% 0.33/1.64 => ( ( in @ Xx @ X )
% 0.33/1.64 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(complementTI1_type,type,
% 0.33/1.64 complementTI1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(complementTI1,definition,
% 0.33/1.64 ( complementTI1
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( in @ Xx @ X )
% 0.33/1.64 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(complementTE1_type,type,
% 0.33/1.64 complementTE1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(complementTE1,definition,
% 0.33/1.64 ( complementTE1
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 0.33/1.64 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(binintersectTELcontra_type,type,
% 0.33/1.64 binintersectTELcontra: $o ).
% 0.33/1.64
% 0.33/1.64 thf(binintersectTELcontra,definition,
% 0.33/1.64 ( binintersectTELcontra
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ~ ( in @ Xx @ X )
% 0.33/1.64 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(binintersectTERcontra_type,type,
% 0.33/1.64 binintersectTERcontra: $o ).
% 0.33/1.64
% 0.33/1.64 thf(binintersectTERcontra,definition,
% 0.33/1.64 ( binintersectTERcontra
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ~ ( in @ Xx @ Y )
% 0.33/1.64 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(contrasubsetT_type,type,
% 0.33/1.64 contrasubsetT: $o ).
% 0.33/1.64
% 0.33/1.64 thf(contrasubsetT,definition,
% 0.33/1.64 ( contrasubsetT
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.33/1.64 => ( ( in @ Xx @ Y )
% 0.33/1.64 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(contrasubsetT1_type,type,
% 0.33/1.64 contrasubsetT1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(contrasubsetT1,definition,
% 0.33/1.64 ( contrasubsetT1
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( subset @ X @ Y )
% 0.33/1.64 => ( ~ ( in @ Xx @ Y )
% 0.33/1.64 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(contrasubsetT2_type,type,
% 0.33/1.64 contrasubsetT2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(contrasubsetT2,definition,
% 0.33/1.64 ( contrasubsetT2
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ( ( subset @ X @ Y )
% 0.33/1.64 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(contrasubsetT3_type,type,
% 0.33/1.64 contrasubsetT3: $o ).
% 0.33/1.64
% 0.33/1.64 thf(contrasubsetT3,definition,
% 0.33/1.64 ( contrasubsetT3
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 0.33/1.64 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(doubleComplementI1_type,type,
% 0.33/1.64 doubleComplementI1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(doubleComplementI1,definition,
% 0.33/1.64 ( doubleComplementI1
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( in @ Xx @ X )
% 0.33/1.64 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(doubleComplementE1_type,type,
% 0.33/1.64 doubleComplementE1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(doubleComplementE1,definition,
% 0.33/1.64 ( doubleComplementE1
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 0.33/1.64 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(doubleComplementSub1_type,type,
% 0.33/1.64 doubleComplementSub1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(doubleComplementSub1,definition,
% 0.33/1.64 ( doubleComplementSub1
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(doubleComplementSub2_type,type,
% 0.33/1.64 doubleComplementSub2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(doubleComplementSub2,definition,
% 0.33/1.64 ( doubleComplementSub2
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(doubleComplementEq_type,type,
% 0.33/1.64 doubleComplementEq: $o ).
% 0.33/1.64
% 0.33/1.64 thf(doubleComplementEq,definition,
% 0.33/1.64 ( doubleComplementEq
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ( X
% 0.33/1.64 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(complementTnotintersectT_type,type,
% 0.33/1.64 complementTnotintersectT: $o ).
% 0.33/1.64
% 0.33/1.64 thf(complementTnotintersectT,definition,
% 0.33/1.64 ( complementTnotintersectT
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.33/1.64 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(complementImpComplementIntersect_type,type,
% 0.33/1.64 complementImpComplementIntersect: $o ).
% 0.33/1.64
% 0.33/1.64 thf(complementImpComplementIntersect,definition,
% 0.33/1.64 ( complementImpComplementIntersect
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.33/1.64 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(complementSubsetComplementIntersect_type,type,
% 0.33/1.64 complementSubsetComplementIntersect: $o ).
% 0.33/1.64
% 0.33/1.64 thf(complementSubsetComplementIntersect,definition,
% 0.33/1.64 ( complementSubsetComplementIntersect
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(complementInPowersetComplementIntersect_type,type,
% 0.33/1.64 complementInPowersetComplementIntersect: $o ).
% 0.33/1.64
% 0.33/1.64 thf(complementInPowersetComplementIntersect,definition,
% 0.33/1.64 ( complementInPowersetComplementIntersect
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(contraSubsetComplement_type,type,
% 0.33/1.64 contraSubsetComplement: $o ).
% 0.33/1.64
% 0.33/1.64 thf(contraSubsetComplement,definition,
% 0.33/1.64 ( contraSubsetComplement
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( in @ Xx @ Y )
% 0.33/1.64 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(complementTcontraSubset_type,type,
% 0.33/1.64 complementTcontraSubset: $o ).
% 0.33/1.64
% 0.33/1.64 thf(complementTcontraSubset,definition,
% 0.33/1.64 ( complementTcontraSubset
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.33/1.64 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(binunionTILcontra_type,type,
% 0.33/1.64 binunionTILcontra: $o ).
% 0.33/1.64
% 0.33/1.64 thf(binunionTILcontra,definition,
% 0.33/1.64 ( binunionTILcontra
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.33/1.64 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(binunionTIRcontra_type,type,
% 0.33/1.64 binunionTIRcontra: $o ).
% 0.33/1.64
% 0.33/1.64 thf(binunionTIRcontra,definition,
% 0.33/1.64 ( binunionTIRcontra
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.33/1.64 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(inIntersectImpInUnion_type,type,
% 0.33/1.64 inIntersectImpInUnion: $o ).
% 0.33/1.64
% 0.33/1.64 thf(inIntersectImpInUnion,definition,
% 0.33/1.64 ( inIntersectImpInUnion
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Z: $i] :
% 0.33/1.64 ( ( in @ Z @ ( powerset @ A ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.33/1.64 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(inIntersectImpInUnion2_type,type,
% 0.33/1.64 inIntersectImpInUnion2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(inIntersectImpInUnion2,definition,
% 0.33/1.64 ( inIntersectImpInUnion2
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Z: $i] :
% 0.33/1.64 ( ( in @ Z @ ( powerset @ A ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.33/1.64 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(inIntersectImpInIntersectUnions_type,type,
% 0.33/1.64 inIntersectImpInIntersectUnions: $o ).
% 0.33/1.64
% 0.33/1.64 thf(inIntersectImpInIntersectUnions,definition,
% 0.33/1.64 ( inIntersectImpInIntersectUnions
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Z: $i] :
% 0.33/1.64 ( ( in @ Z @ ( powerset @ A ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.33/1.64 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(intersectInPowersetIntersectUnions_type,type,
% 0.33/1.64 intersectInPowersetIntersectUnions: $o ).
% 0.33/1.64
% 0.33/1.64 thf(intersectInPowersetIntersectUnions,definition,
% 0.33/1.64 ( intersectInPowersetIntersectUnions
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Z: $i] :
% 0.33/1.64 ( ( in @ Z @ ( powerset @ A ) )
% 0.33/1.64 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(inComplementUnionImpNotIn1_type,type,
% 0.33/1.64 inComplementUnionImpNotIn1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(inComplementUnionImpNotIn1,definition,
% 0.33/1.64 ( inComplementUnionImpNotIn1
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.33/1.64 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(inComplementUnionImpInComplement1_type,type,
% 0.33/1.64 inComplementUnionImpInComplement1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(inComplementUnionImpInComplement1,definition,
% 0.33/1.64 ( inComplementUnionImpInComplement1
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.33/1.64 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(binunionTE_type,type,
% 0.33/1.64 binunionTE: $o ).
% 0.33/1.64
% 0.33/1.64 thf(binunionTE,definition,
% 0.33/1.64 ( binunionTE
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Xphi: $o,Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.33/1.64 => ( ( ( in @ Xx @ X )
% 0.33/1.64 => Xphi )
% 0.33/1.64 => ( ( ( in @ Xx @ Y )
% 0.33/1.64 => Xphi )
% 0.33/1.64 => Xphi ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(binunionTEcontra_type,type,
% 0.33/1.64 binunionTEcontra: $o ).
% 0.33/1.64
% 0.33/1.64 thf(binunionTEcontra,definition,
% 0.33/1.64 ( binunionTEcontra
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ~ ( in @ Xx @ X )
% 0.33/1.64 => ( ~ ( in @ Xx @ Y )
% 0.33/1.64 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(demorgan2a1_type,type,
% 0.33/1.64 demorgan2a1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(demorgan2a1,definition,
% 0.33/1.64 ( demorgan2a1
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.33/1.64 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(complementUnionInPowersetComplement_type,type,
% 0.33/1.64 complementUnionInPowersetComplement: $o ).
% 0.33/1.64
% 0.33/1.64 thf(complementUnionInPowersetComplement,definition,
% 0.33/1.64 ( complementUnionInPowersetComplement
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(demorgan2a2_type,type,
% 0.33/1.64 demorgan2a2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(demorgan2a2,definition,
% 0.33/1.64 ( demorgan2a2
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.33/1.64 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(demorgan1a_type,type,
% 0.33/1.64 demorgan1a: $o ).
% 0.33/1.64
% 0.33/1.64 thf(demorgan1a,definition,
% 0.33/1.64 ( demorgan1a
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 0.33/1.64 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(demorgan1b_type,type,
% 0.33/1.64 demorgan1b: $o ).
% 0.33/1.64
% 0.33/1.64 thf(demorgan1b,definition,
% 0.33/1.64 ( demorgan1b
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.33/1.64 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(demorgan1_type,type,
% 0.33/1.64 demorgan1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(demorgan1,definition,
% 0.33/1.64 ( demorgan1
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 0.33/1.64 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(demorgan2a_type,type,
% 0.33/1.64 demorgan2a: $o ).
% 0.33/1.64
% 0.33/1.64 thf(demorgan2a,definition,
% 0.33/1.64 ( demorgan2a
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.33/1.64 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(demorgan2b2_type,type,
% 0.33/1.64 demorgan2b2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(demorgan2b2,definition,
% 0.33/1.64 ( demorgan2b2
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.33/1.64 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 0.33/1.64 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(demorgan2b_type,type,
% 0.33/1.64 demorgan2b: $o ).
% 0.33/1.64
% 0.33/1.64 thf(demorgan2b,definition,
% 0.33/1.64 ( demorgan2b
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ A )
% 0.33/1.64 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.33/1.64 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(demorgan2_type,type,
% 0.33/1.64 demorgan2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(demorgan2,definition,
% 0.33/1.64 ( demorgan2
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 0.33/1.64 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(woz13rule0_type,type,
% 0.33/1.64 woz13rule0: $o ).
% 0.33/1.64
% 0.33/1.64 thf(woz13rule0,definition,
% 0.33/1.64 ( woz13rule0
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Xx: $i] :
% 0.33/1.64 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.33/1.64 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(woz13rule1_type,type,
% 0.33/1.64 woz13rule1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(woz13rule1,definition,
% 0.33/1.64 ( woz13rule1
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Z: $i] :
% 0.33/1.64 ( ( in @ Z @ ( powerset @ A ) )
% 0.33/1.64 => ( ( subset @ X @ Z )
% 0.33/1.64 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(woz13rule2_type,type,
% 0.33/1.64 woz13rule2: $o ).
% 0.33/1.64
% 0.33/1.64 thf(woz13rule2,definition,
% 0.33/1.64 ( woz13rule2
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Z: $i] :
% 0.33/1.64 ( ( in @ Z @ ( powerset @ A ) )
% 0.33/1.64 => ( ( subset @ Y @ Z )
% 0.33/1.64 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(woz13rule3_type,type,
% 0.33/1.64 woz13rule3: $o ).
% 0.33/1.64
% 0.33/1.64 thf(woz13rule3,definition,
% 0.33/1.64 ( woz13rule3
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Z: $i] :
% 0.33/1.64 ( ( in @ Z @ ( powerset @ A ) )
% 0.33/1.64 => ( ( subset @ X @ Y )
% 0.33/1.64 => ( ( subset @ X @ Z )
% 0.33/1.64 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(woz13rule4_type,type,
% 0.33/1.64 woz13rule4: $o ).
% 0.33/1.64
% 0.33/1.64 thf(woz13rule4,definition,
% 0.33/1.64 ( woz13rule4
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Z: $i] :
% 0.33/1.64 ( ( in @ Z @ ( powerset @ A ) )
% 0.33/1.64 => ! [W: $i] :
% 0.33/1.64 ( ( in @ W @ ( powerset @ A ) )
% 0.33/1.64 => ( ( subset @ X @ Z )
% 0.33/1.64 => ( ( subset @ Y @ W )
% 0.33/1.64 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(woz1_1_type,type,
% 0.33/1.64 woz1_1: $o ).
% 0.33/1.64
% 0.33/1.64 thf(woz1_1,definition,
% 0.33/1.64 ( woz1_1
% 0.33/1.64 = ( ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.33/1.64
% 0.33/1.64 thf(woz1_2,conjecture,
% 0.33/1.64 ( setextAx
% 0.33/1.64 => ( emptysetAx
% 0.33/1.64 => ( setadjoinAx
% 0.33/1.64 => ( powersetAx
% 0.33/1.64 => ( setunionAx
% 0.33/1.64 => ( omega0Ax
% 0.33/1.64 => ( omegaSAx
% 0.33/1.64 => ( omegaIndAx
% 0.33/1.64 => ( replAx
% 0.33/1.64 => ( foundationAx
% 0.33/1.64 => ( wellorderingAx
% 0.33/1.64 => ( descrp
% 0.33/1.64 => ( dsetconstrI
% 0.33/1.64 => ( dsetconstrEL
% 0.33/1.64 => ( dsetconstrER
% 0.33/1.64 => ( exuE1
% 0.33/1.64 => ( prop2setE
% 0.33/1.64 => ( emptysetE
% 0.33/1.64 => ( emptysetimpfalse
% 0.33/1.64 => ( notinemptyset
% 0.33/1.64 => ( exuE3e
% 0.33/1.64 => ( setext
% 0.33/1.64 => ( emptyI
% 0.33/1.64 => ( noeltsimpempty
% 0.33/1.64 => ( setbeta
% 0.33/1.64 => ( nonemptyE1
% 0.33/1.64 => ( nonemptyI
% 0.33/1.64 => ( nonemptyI1
% 0.33/1.64 => ( setadjoinIL
% 0.33/1.64 => ( emptyinunitempty
% 0.33/1.64 => ( setadjoinIR
% 0.33/1.64 => ( setadjoinE
% 0.33/1.64 => ( setadjoinOr
% 0.33/1.64 => ( setoftrueEq
% 0.33/1.64 => ( powersetI
% 0.33/1.64 => ( emptyinPowerset
% 0.33/1.64 => ( emptyInPowerset
% 0.33/1.64 => ( powersetE
% 0.33/1.64 => ( setunionI
% 0.33/1.64 => ( setunionE
% 0.33/1.64 => ( subPowSU
% 0.33/1.64 => ( exuE2
% 0.33/1.64 => ( nonemptyImpWitness
% 0.33/1.64 => ( uniqinunit
% 0.33/1.64 => ( notinsingleton
% 0.33/1.64 => ( eqinunit
% 0.33/1.64 => ( singletonsswitch
% 0.33/1.64 => ( upairsetE
% 0.33/1.64 => ( upairsetIL
% 0.33/1.64 => ( upairsetIR
% 0.33/1.64 => ( emptyE1
% 0.33/1.64 => ( vacuousDall
% 0.33/1.64 => ( quantDeMorgan1
% 0.33/1.64 => ( quantDeMorgan2
% 0.33/1.64 => ( quantDeMorgan3
% 0.33/1.64 => ( quantDeMorgan4
% 0.33/1.64 => ( prop2setI
% 0.33/1.64 => ( prop2set2propI
% 0.33/1.64 => ( notdexE
% 0.33/1.64 => ( notdallE
% 0.33/1.64 => ( exuI1
% 0.33/1.64 => ( exuI3
% 0.33/1.64 => ( exuI2
% 0.33/1.64 => ( inCongP
% 0.33/1.64 => ( in__Cong
% 0.33/1.64 => ( exuE3u
% 0.33/1.64 => ( exu__Cong
% 0.33/1.64 => ( emptyset__Cong
% 0.33/1.64 => ( setadjoin__Cong
% 0.33/1.64 => ( powerset__Cong
% 0.33/1.64 => ( setunion__Cong
% 0.33/1.64 => ( omega__Cong
% 0.33/1.64 => ( exuEu
% 0.33/1.64 => ( descr__Cong
% 0.33/1.64 => ( dsetconstr__Cong
% 0.33/1.64 => ( subsetI1
% 0.33/1.64 => ( eqimpsubset2
% 0.33/1.64 => ( eqimpsubset1
% 0.33/1.64 => ( subsetI2
% 0.33/1.64 => ( emptysetsubset
% 0.33/1.64 => ( subsetE
% 0.33/1.64 => ( subsetE2
% 0.33/1.64 => ( notsubsetI
% 0.33/1.64 => ( notequalI1
% 0.33/1.64 => ( notequalI2
% 0.33/1.64 => ( subsetRefl
% 0.33/1.64 => ( subsetTrans
% 0.33/1.64 => ( setadjoinSub
% 0.33/1.64 => ( setadjoinSub2
% 0.33/1.64 => ( subset2powerset
% 0.33/1.64 => ( setextsub
% 0.33/1.64 => ( subsetemptysetimpeq
% 0.33/1.64 => ( powersetI1
% 0.33/1.64 => ( powersetE1
% 0.33/1.64 => ( inPowerset
% 0.33/1.64 => ( powersetsubset
% 0.33/1.64 => ( sepInPowerset
% 0.33/1.64 => ( sepSubset
% 0.33/1.64 => ( binunionIL
% 0.33/1.64 => ( upairset2IR
% 0.33/1.64 => ( binunionIR
% 0.33/1.64 => ( binunionEcases
% 0.33/1.64 => ( binunionE
% 0.33/1.64 => ( binunionLsub
% 0.33/1.64 => ( binunionRsub
% 0.33/1.64 => ( binintersectI
% 0.33/1.64 => ( binintersectSubset5
% 0.33/1.64 => ( binintersectEL
% 0.33/1.64 => ( binintersectLsub
% 0.33/1.64 => ( binintersectSubset2
% 0.33/1.64 => ( binintersectSubset3
% 0.33/1.64 => ( binintersectER
% 0.33/1.64 => ( disjointsetsI1
% 0.33/1.64 => ( binintersectRsub
% 0.33/1.64 => ( binintersectSubset4
% 0.33/1.64 => ( binintersectSubset1
% 0.33/1.64 => ( bs114d
% 0.33/1.64 => ( setminusI
% 0.33/1.64 => ( setminusEL
% 0.33/1.64 => ( setminusER
% 0.33/1.64 => ( setminusSubset2
% 0.33/1.64 => ( setminusERneg
% 0.33/1.64 => ( setminusELneg
% 0.33/1.64 => ( setminusILneg
% 0.33/1.64 => ( setminusIRneg
% 0.33/1.64 => ( setminusLsub
% 0.33/1.64 => ( setminusSubset1
% 0.33/1.64 => ( symdiffE
% 0.33/1.64 => ( symdiffI1
% 0.33/1.64 => ( symdiffI2
% 0.33/1.64 => ( symdiffIneg1
% 0.33/1.64 => ( symdiffIneg2
% 0.33/1.64 => ( secondinupair
% 0.33/1.64 => ( setukpairIL
% 0.33/1.64 => ( setukpairIR
% 0.33/1.64 => ( kpairiskpair
% 0.33/1.64 => ( kpairp
% 0.33/1.64 => ( singletonsubset
% 0.33/1.64 => ( singletoninpowerset
% 0.33/1.64 => ( singletoninpowunion
% 0.33/1.64 => ( upairset2E
% 0.33/1.64 => ( upairsubunion
% 0.33/1.64 => ( upairinpowunion
% 0.33/1.64 => ( ubforcartprodlem1
% 0.33/1.64 => ( ubforcartprodlem2
% 0.33/1.64 => ( ubforcartprodlem3
% 0.33/1.64 => ( cartprodpairin
% 0.33/1.64 => ( cartprodmempair1
% 0.33/1.64 => ( cartprodmempair
% 0.33/1.64 => ( setunionE2
% 0.33/1.64 => ( setunionsingleton1
% 0.33/1.64 => ( setunionsingleton2
% 0.33/1.64 => ( setunionsingleton
% 0.33/1.64 => ( singletonprop
% 0.33/1.64 => ( ex1E1
% 0.33/1.64 => ( ex1I
% 0.33/1.64 => ( ex1I2
% 0.33/1.64 => ( singletonsuniq
% 0.33/1.64 => ( setukpairinjL1
% 0.33/1.64 => ( kfstsingleton
% 0.33/1.64 => ( theprop
% 0.33/1.64 => ( kfstpairEq
% 0.33/1.64 => ( cartprodfstin
% 0.33/1.64 => ( setukpairinjL2
% 0.33/1.64 => ( setukpairinjL
% 0.33/1.64 => ( setukpairinjR11
% 0.33/1.64 => ( setukpairinjR12
% 0.33/1.64 => ( setukpairinjR1
% 0.33/1.64 => ( upairequniteq
% 0.33/1.64 => ( setukpairinjR2
% 0.33/1.64 => ( setukpairinjR
% 0.33/1.64 => ( ksndsingleton
% 0.33/1.64 => ( ksndpairEq
% 0.33/1.64 => ( kpairsurjEq
% 0.33/1.64 => ( cartprodsndin
% 0.33/1.64 => ( cartprodpairmemEL
% 0.33/1.64 => ( cartprodpairmemER
% 0.33/1.64 => ( cartprodmempaircEq
% 0.33/1.64 => ( cartprodfstpairEq
% 0.33/1.64 => ( cartprodsndpairEq
% 0.33/1.64 => ( cartprodpairsurjEq
% 0.33/1.64 => ( dpsetconstrI
% 0.33/1.64 => ( dpsetconstrSub
% 0.33/1.64 => ( setOfPairsIsBReln
% 0.33/1.64 => ( dpsetconstrERa
% 0.33/1.64 => ( dpsetconstrEL1
% 0.33/1.64 => ( dpsetconstrEL2
% 0.33/1.64 => ( dpsetconstrER
% 0.33/1.64 => ( funcImageSingleton
% 0.33/1.64 => ( apProp
% 0.33/1.64 => ( app
% 0.33/1.64 => ( infuncsetfunc
% 0.33/1.64 => ( ap2p
% 0.33/1.64 => ( funcinfuncset
% 0.33/1.64 => ( lamProp
% 0.33/1.64 => ( lamp
% 0.33/1.64 => ( lam2p
% 0.33/1.64 => ( brelnall1
% 0.33/1.64 => ( brelnall2
% 0.33/1.64 => ( ex1E2
% 0.33/1.64 => ( funcGraphProp1
% 0.33/1.64 => ( funcGraphProp3
% 0.33/1.64 => ( funcGraphProp2
% 0.33/1.64 => ( funcextLem
% 0.33/1.64 => ( funcGraphProp4
% 0.33/1.64 => ( subbreln
% 0.33/1.64 => ( eqbreln
% 0.33/1.64 => ( funcext
% 0.33/1.64 => ( funcext2
% 0.33/1.64 => ( ap2apEq1
% 0.33/1.64 => ( ap2apEq2
% 0.33/1.64 => ( beta1
% 0.33/1.64 => ( eta1
% 0.33/1.64 => ( lam2lamEq
% 0.33/1.64 => ( beta2
% 0.33/1.64 => ( eta2
% 0.33/1.64 => ( iffalseProp1
% 0.33/1.64 => ( iffalseProp2
% 0.33/1.64 => ( iftrueProp1
% 0.33/1.64 => ( iftrueProp2
% 0.33/1.64 => ( ifSingleton
% 0.33/1.64 => ( ifp
% 0.33/1.64 => ( theeq
% 0.33/1.64 => ( iftrue
% 0.33/1.64 => ( iffalse
% 0.33/1.64 => ( iftrueorfalse
% 0.33/1.64 => ( binintersectT_lem
% 0.33/1.64 => ( binunionT_lem
% 0.33/1.64 => ( powersetT_lem
% 0.33/1.64 => ( setminusT_lem
% 0.33/1.64 => ( complementT_lem
% 0.33/1.64 => ( setextT
% 0.33/1.64 => ( subsetTI
% 0.33/1.64 => ( powersetTI1
% 0.33/1.64 => ( powersetTE1
% 0.33/1.64 => ( complementTI1
% 0.33/1.64 => ( complementTE1
% 0.33/1.64 => ( binintersectTELcontra
% 0.33/1.64 => ( binintersectTERcontra
% 0.33/1.64 => ( contrasubsetT
% 0.33/1.64 => ( contrasubsetT1
% 0.33/1.64 => ( contrasubsetT2
% 0.33/1.64 => ( contrasubsetT3
% 0.33/1.64 => ( doubleComplementI1
% 0.33/1.64 => ( doubleComplementE1
% 0.33/1.64 => ( doubleComplementSub1
% 0.33/1.64 => ( doubleComplementSub2
% 0.33/1.64 => ( doubleComplementEq
% 0.33/1.64 => ( complementTnotintersectT
% 0.33/1.64 => ( complementImpComplementIntersect
% 0.33/1.64 => ( complementSubsetComplementIntersect
% 0.33/1.64 => ( complementInPowersetComplementIntersect
% 0.33/1.64 => ( contraSubsetComplement
% 0.33/1.64 => ( complementTcontraSubset
% 0.33/1.64 => ( binunionTILcontra
% 0.33/1.64 => ( binunionTIRcontra
% 0.33/1.64 => ( inIntersectImpInUnion
% 0.33/1.64 => ( inIntersectImpInUnion2
% 0.33/1.64 => ( inIntersectImpInIntersectUnions
% 0.33/1.64 => ( intersectInPowersetIntersectUnions
% 0.33/1.64 => ( inComplementUnionImpNotIn1
% 0.33/1.64 => ( inComplementUnionImpInComplement1
% 0.33/1.64 => ( binunionTE
% 0.33/1.64 => ( binunionTEcontra
% 0.33/1.64 => ( demorgan2a1
% 0.33/1.64 => ( complementUnionInPowersetComplement
% 0.33/1.64 => ( demorgan2a2
% 0.33/1.64 => ( demorgan1a
% 0.33/1.64 => ( demorgan1b
% 0.33/1.64 => ( demorgan1
% 0.33/1.64 => ( demorgan2a
% 0.33/1.64 => ( demorgan2b2
% 0.33/1.64 => ( demorgan2b
% 0.33/1.64 => ( demorgan2
% 0.33/1.64 => ( woz13rule0
% 0.33/1.64 => ( woz13rule1
% 0.33/1.64 => ( woz13rule2
% 0.33/1.64 => ( woz13rule3
% 0.33/1.64 => ( woz13rule4
% 0.33/1.64 => ( woz1_1
% 0.33/1.64 => ! [A: $i,X: $i] :
% 0.33/1.64 ( ( in @ X @ ( powerset @ A ) )
% 0.33/1.64 => ! [Y: $i] :
% 0.33/1.64 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/1.64 => ! [Z: $i] :
% 0.33/1.64 ( ( in @ Z @ ( powerset @ A ) )
% 0.33/1.64 => ! [W: $i] :
% 0.33/1.64 ( ( in @ W @ ( powerset @ A ) )
% 0.33/1.64 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 0.33/1.64 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/1.64 ------------------------
% 0.33/1.68 % (10296)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_10139 for (2999ds/4Mi)
% 0.33/1.68 % (10298)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10139 for (2999ds/2Mi)
% 0.33/1.68 % (10297)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_10139 for (2999ds/27Mi)
% 0.33/1.68 % (10298)Instruction limit reached!
% 0.33/1.68 % (10298)------------------------------
% 0.33/1.68 % (10298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.68 % (10298)Termination reason: Unknown
% 0.33/1.68 % (10298)Termination phase: shuffling
% 0.33/1.68
% 0.33/1.68 % (10298)Memory used [KB]: 1535
% 0.33/1.68 % (10298)Time elapsed: 0.002 s
% 0.33/1.68 % (10298)Instructions burned: 2 (million)
% 0.33/1.68 % (10298)------------------------------
% 0.33/1.68 % (10298)------------------------------
% 0.33/1.68 % (10299)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_10139 for (2999ds/2Mi)
% 0.33/1.68 % (10295)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10139 for (2999ds/183Mi)
% 0.33/1.68 % (10296)Instruction limit reached!
% 0.33/1.68 % (10296)------------------------------
% 0.33/1.68 % (10296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.68 % (10296)Termination reason: Unknown
% 0.33/1.68 % (10296)Termination phase: shuffling
% 0.33/1.68
% 0.33/1.68 % (10296)Memory used [KB]: 1535
% 0.33/1.68 % (10296)Time elapsed: 0.003 s
% 0.33/1.68 % (10296)Instructions burned: 5 (million)
% 0.33/1.68 % (10296)------------------------------
% 0.33/1.68 % (10296)------------------------------
% 0.33/1.68 % (10299)Instruction limit reached!
% 0.33/1.68 % (10299)------------------------------
% 0.33/1.68 % (10299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.68 % (10299)Termination reason: Unknown
% 0.33/1.68 % (10299)Termination phase: shuffling
% 0.33/1.68
% 0.33/1.68 % (10299)Memory used [KB]: 1535
% 0.33/1.68 % (10299)Time elapsed: 0.002 s
% 0.33/1.68 % (10299)Instructions burned: 3 (million)
% 0.33/1.68 % (10299)------------------------------
% 0.33/1.68 % (10299)------------------------------
% 0.33/1.68 % (10301)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10139 for (2999ds/18Mi)
% 0.33/1.68 % (10297)Instruction limit reached!
% 0.33/1.68 % (10297)------------------------------
% 0.33/1.68 % (10297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.68 % (10297)Termination reason: Unknown
% 0.33/1.68 % (10297)Termination phase: shuffling
% 0.33/1.68
% 0.33/1.68 % (10297)Memory used [KB]: 1918
% 0.33/1.68 % (10297)Time elapsed: 0.009 s
% 0.33/1.68 % (10297)Instructions burned: 28 (million)
% 0.33/1.68 % (10297)------------------------------
% 0.33/1.68 % (10297)------------------------------
% 0.33/1.68 % (10300)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_10139 for (2999ds/275Mi)
% 0.33/1.68 % (10301)Instruction limit reached!
% 0.33/1.68 % (10301)------------------------------
% 0.33/1.68 % (10301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.68 % (10301)Termination reason: Unknown
% 0.33/1.68 % (10301)Termination phase: shuffling
% 0.33/1.68
% 0.33/1.68 % (10301)Memory used [KB]: 1791
% 0.33/1.68 % (10301)Time elapsed: 0.007 s
% 0.33/1.68 % (10301)Instructions burned: 19 (million)
% 0.33/1.68 % (10301)------------------------------
% 0.33/1.68 % (10301)------------------------------
% 0.33/1.69 % (10303)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10139 for (2999ds/3Mi)
% 0.33/1.69 % (10304)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_10139 for (2999ds/37Mi)
% 0.33/1.69 % (10303)Instruction limit reached!
% 0.33/1.69 % (10303)------------------------------
% 0.33/1.69 % (10303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.69 % (10303)Termination reason: Unknown
% 0.33/1.69 % (10303)Termination phase: shuffling
% 0.33/1.69
% 0.33/1.69 % (10303)Memory used [KB]: 1535
% 0.33/1.69 % (10303)Time elapsed: 0.002 s
% 0.33/1.69 % (10303)Instructions burned: 3 (million)
% 0.33/1.69 % (10303)------------------------------
% 0.33/1.69 % (10303)------------------------------
% 0.33/1.69 % (10305)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_10139 for (2999ds/15Mi)
% 0.33/1.69 % (10305)Instruction limit reached!
% 0.33/1.69 % (10305)------------------------------
% 0.33/1.69 % (10305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.69 % (10305)Termination reason: Unknown
% 0.33/1.69 % (10305)Termination phase: shuffling
% 0.33/1.69
% 0.33/1.69 % (10305)Memory used [KB]: 1791
% 0.33/1.69 % (10305)Time elapsed: 0.006 s
% 0.33/1.69 % (10305)Instructions burned: 15 (million)
% 0.33/1.69 % (10305)------------------------------
% 0.33/1.69 % (10305)------------------------------
% 0.33/1.69 % (10306)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_10139 for (2999ds/3Mi)
% 0.33/1.70 % (10306)Instruction limit reached!
% 0.33/1.70 % (10306)------------------------------
% 0.33/1.70 % (10306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.70 % (10306)Termination reason: Unknown
% 0.33/1.70 % (10306)Termination phase: shuffling
% 0.33/1.70
% 0.33/1.70 % (10306)Memory used [KB]: 1535
% 0.33/1.70 % (10306)Time elapsed: 0.003 s
% 0.33/1.70 % (10306)Instructions burned: 3 (million)
% 0.33/1.70 % (10306)------------------------------
% 0.33/1.70 % (10306)------------------------------
% 0.33/1.70 % (10307)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_10139 for (2999ds/1041Mi)
% 3.13/1.70 % (10304)Instruction limit reached!
% 3.13/1.70 % (10304)------------------------------
% 3.13/1.70 % (10304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.70 % (10304)Termination reason: Unknown
% 3.13/1.70 % (10304)Termination phase: shuffling
% 3.13/1.70
% 3.13/1.70 % (10304)Memory used [KB]: 2302
% 3.13/1.70 % (10304)Time elapsed: 0.015 s
% 3.13/1.70 % (10304)Instructions burned: 37 (million)
% 3.13/1.70 % (10304)------------------------------
% 3.13/1.70 % (10304)------------------------------
% 3.13/1.70 % (10308)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_10139 for (2999ds/7Mi)
% 3.13/1.70 % (10316)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_10139 for (2999ds/16Mi)
% 3.13/1.70 % (10308)Instruction limit reached!
% 3.13/1.70 % (10308)------------------------------
% 3.13/1.70 % (10308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.70 % (10308)Termination reason: Unknown
% 3.13/1.70 % (10308)Termination phase: shuffling
% 3.13/1.70
% 3.13/1.70 % (10308)Memory used [KB]: 1663
% 3.13/1.70 % (10308)Time elapsed: 0.005 s
% 3.13/1.70 % (10308)Instructions burned: 8 (million)
% 3.13/1.70 % (10308)------------------------------
% 3.13/1.70 % (10308)------------------------------
% 3.13/1.71 % (10316)Instruction limit reached!
% 3.13/1.71 % (10316)------------------------------
% 3.13/1.71 % (10316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.71 % (10316)Termination reason: Unknown
% 3.13/1.71 % (10316)Termination phase: shuffling
% 3.13/1.71
% 3.13/1.71 % (10316)Memory used [KB]: 1791
% 3.13/1.71 % (10316)Time elapsed: 0.006 s
% 3.13/1.71 % (10316)Instructions burned: 16 (million)
% 3.13/1.71 % (10316)------------------------------
% 3.13/1.71 % (10316)------------------------------
% 3.13/1.71 % (10317)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_10139 for (2999ds/3Mi)
% 3.13/1.71 % (10317)Instruction limit reached!
% 3.13/1.71 % (10317)------------------------------
% 3.13/1.71 % (10317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.71 % (10317)Termination reason: Unknown
% 3.13/1.71 % (10317)Termination phase: shuffling
% 3.13/1.71
% 3.13/1.71 % (10317)Memory used [KB]: 1535
% 3.13/1.71 % (10317)Time elapsed: 0.003 s
% 3.13/1.71 % (10317)Instructions burned: 6 (million)
% 3.13/1.71 % (10317)------------------------------
% 3.13/1.71 % (10317)------------------------------
% 3.13/1.72 % (10318)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_10139 for (2999ds/3Mi)
% 3.13/1.72 % (10318)Instruction limit reached!
% 3.13/1.72 % (10318)------------------------------
% 3.13/1.72 % (10318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.72 % (10318)Termination reason: Unknown
% 3.13/1.72 % (10318)Termination phase: shuffling
% 3.13/1.72
% 3.13/1.72 % (10318)Memory used [KB]: 1535
% 3.13/1.72 % (10318)Time elapsed: 0.003 s
% 3.13/1.72 % (10318)Instructions burned: 3 (million)
% 3.13/1.72 % (10318)------------------------------
% 3.13/1.72 % (10318)------------------------------
% 3.13/1.72 % (10319)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_10139 for (2999ds/7Mi)
% 3.13/1.72 % (10324)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_10139 for (2999ds/4Mi)
% 3.13/1.72 % (10324)Instruction limit reached!
% 3.13/1.72 % (10324)------------------------------
% 3.13/1.72 % (10324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.72 % (10324)Termination reason: Unknown
% 3.13/1.72 % (10324)Termination phase: shuffling
% 3.13/1.72
% 3.13/1.72 % (10324)Memory used [KB]: 1535
% 3.13/1.72 % (10324)Time elapsed: 0.003 s
% 3.13/1.72 % (10324)Instructions burned: 6 (million)
% 3.13/1.72 % (10324)------------------------------
% 3.13/1.72 % (10324)------------------------------
% 3.13/1.72 % (10319)Instruction limit reached!
% 3.13/1.72 % (10319)------------------------------
% 3.13/1.72 % (10319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.72 % (10319)Termination reason: Unknown
% 3.13/1.72 % (10319)Termination phase: shuffling
% 3.13/1.72
% 3.13/1.72 % (10319)Memory used [KB]: 1663
% 3.13/1.72 % (10319)Time elapsed: 0.005 s
% 3.13/1.72 % (10319)Instructions burned: 8 (million)
% 3.13/1.72 % (10319)------------------------------
% 3.13/1.72 % (10319)------------------------------
% 3.13/1.73 % (10322)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_10139 for (2999ds/3Mi)
% 3.13/1.73 % (10322)Instruction limit reached!
% 3.13/1.73 % (10322)------------------------------
% 3.13/1.73 % (10322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.73 % (10322)Termination reason: Unknown
% 3.13/1.73 % (10322)Termination phase: shuffling
% 3.13/1.73
% 3.13/1.73 % (10322)Memory used [KB]: 1535
% 3.13/1.73 % (10322)Time elapsed: 0.004 s
% 3.13/1.73 % (10322)Instructions burned: 4 (million)
% 3.13/1.73 % (10322)------------------------------
% 3.13/1.73 % (10322)------------------------------
% 3.13/1.73 % (10328)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_10139 for (2999ds/710Mi)
% 3.13/1.74 % (10329)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_10139 for (2999ds/6Mi)
% 3.13/1.74 % (10325)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_10139 for (2999ds/18Mi)
% 3.13/1.74 % (10329)Instruction limit reached!
% 3.13/1.74 % (10329)------------------------------
% 3.13/1.74 % (10329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.74 % (10329)Termination reason: Unknown
% 3.13/1.74 % (10329)Termination phase: shuffling
% 3.13/1.74
% 3.13/1.74 % (10329)Memory used [KB]: 1535
% 3.13/1.74 % (10329)Time elapsed: 0.005 s
% 3.13/1.74 % (10329)Instructions burned: 7 (million)
% 3.13/1.74 % (10329)------------------------------
% 3.13/1.74 % (10329)------------------------------
% 3.13/1.75 % (10295)Instruction limit reached!
% 3.13/1.75 % (10295)------------------------------
% 3.13/1.75 % (10295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.75 % (10295)Termination reason: Unknown
% 3.13/1.75 % (10295)Termination phase: Saturation
% 3.13/1.75
% 3.13/1.75 % (10295)Memory used [KB]: 7419
% 3.13/1.75 % (10295)Time elapsed: 0.072 s
% 3.13/1.75 % (10295)Instructions burned: 183 (million)
% 3.13/1.75 % (10295)------------------------------
% 3.13/1.75 % (10295)------------------------------
% 3.13/1.75 % (10325)Instruction limit reached!
% 3.13/1.75 % (10325)------------------------------
% 3.13/1.75 % (10325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.75 % (10325)Termination reason: Unknown
% 3.13/1.75 % (10325)Termination phase: shuffling
% 3.13/1.75
% 3.13/1.75 % (10325)Memory used [KB]: 1791
% 3.13/1.75 % (10325)Time elapsed: 0.012 s
% 3.13/1.75 % (10325)Instructions burned: 19 (million)
% 3.13/1.75 % (10325)------------------------------
% 3.13/1.75 % (10325)------------------------------
% 3.13/1.75 % (10331)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_10139 for (2999ds/902Mi)
% 3.13/1.75 % (10335)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_10139 for (2999ds/21Mi)
% 3.13/1.76 % (10335)Instruction limit reached!
% 3.13/1.76 % (10335)------------------------------
% 3.13/1.76 % (10335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.76 % (10335)Termination reason: Unknown
% 3.13/1.76 % (10335)Termination phase: shuffling
% 3.13/1.76
% 3.13/1.76 % (10335)Memory used [KB]: 1918
% 3.13/1.76 % (10335)Time elapsed: 0.008 s
% 3.13/1.76 % (10335)Instructions burned: 23 (million)
% 3.13/1.76 % (10335)------------------------------
% 3.13/1.76 % (10335)------------------------------
% 3.13/1.76 % (10336)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_10139 for (2999ds/5Mi)
% 3.13/1.77 % (10336)Instruction limit reached!
% 3.13/1.77 % (10336)------------------------------
% 3.13/1.77 % (10336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.77 % (10336)Termination reason: Unknown
% 3.13/1.77 % (10336)Termination phase: shuffling
% 3.13/1.77
% 3.13/1.77 % (10336)Memory used [KB]: 1535
% 3.13/1.77 % (10336)Time elapsed: 0.004 s
% 3.13/1.77 % (10336)Instructions burned: 5 (million)
% 3.13/1.77 % (10336)------------------------------
% 3.13/1.77 % (10336)------------------------------
% 3.13/1.77 % (10339)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_10139 for (2999ds/6Mi)
% 3.13/1.77 % (10342)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_10139 for (2998ds/377Mi)
% 3.13/1.77 % (10339)Instruction limit reached!
% 3.13/1.77 % (10339)------------------------------
% 3.13/1.77 % (10339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.77 % (10339)Termination reason: Unknown
% 3.13/1.77 % (10339)Termination phase: shuffling
% 3.13/1.77
% 3.13/1.77 % (10339)Memory used [KB]: 1663
% 3.13/1.77 % (10339)Time elapsed: 0.004 s
% 3.13/1.77 % (10339)Instructions burned: 8 (million)
% 3.13/1.77 % (10339)------------------------------
% 3.13/1.77 % (10339)------------------------------
% 3.13/1.78 % (10346)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_10139 for (2998ds/19Mi)
% 3.13/1.79 % (10346)Instruction limit reached!
% 3.13/1.79 % (10346)------------------------------
% 3.13/1.79 % (10346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.79 % (10346)Termination reason: Unknown
% 3.13/1.79 % (10346)Termination phase: shuffling
% 3.13/1.79
% 3.13/1.79 % (10346)Memory used [KB]: 1791
% 3.13/1.79 % (10346)Time elapsed: 0.008 s
% 3.13/1.79 % (10346)Instructions burned: 19 (million)
% 3.13/1.79 % (10346)------------------------------
% 3.13/1.79 % (10346)------------------------------
% 3.13/1.79 % (10345)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_10139 for (2998ds/779Mi)
% 3.13/1.81 % (10350)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_10139 for (2998ds/879Mi)
% 3.13/1.82 % (10300)Instruction limit reached!
% 3.13/1.82 % (10300)------------------------------
% 3.13/1.82 % (10300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.82 % (10300)Termination reason: Unknown
% 3.13/1.82 % (10300)Termination phase: Saturation
% 3.13/1.82
% 3.13/1.82 % (10300)Memory used [KB]: 10106
% 3.13/1.82 % (10300)Time elapsed: 0.142 s
% 3.13/1.82 % (10300)Instructions burned: 276 (million)
% 3.13/1.82 % (10300)------------------------------
% 3.13/1.82 % (10300)------------------------------
% 3.13/1.84 % (10355)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_10139 for (2998ds/17Mi)
% 3.13/1.85 % (10355)Instruction limit reached!
% 3.13/1.85 % (10355)------------------------------
% 3.13/1.85 % (10355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.85 % (10355)Termination reason: Unknown
% 3.13/1.85 % (10355)Termination phase: shuffling
% 3.13/1.85
% 3.13/1.85 % (10355)Memory used [KB]: 1791
% 3.13/1.85 % (10355)Time elapsed: 0.010 s
% 3.13/1.85 % (10355)Instructions burned: 17 (million)
% 3.13/1.85 % (10355)------------------------------
% 3.13/1.85 % (10355)------------------------------
% 3.13/1.87 % (10358)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_10139 for (2998ds/3Mi)
% 3.13/1.87 % (10358)Instruction limit reached!
% 3.13/1.87 % (10358)------------------------------
% 3.13/1.87 % (10358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.87 % (10358)Termination reason: Unknown
% 3.13/1.87 % (10358)Termination phase: shuffling
% 3.13/1.87
% 3.13/1.87 % (10358)Memory used [KB]: 1535
% 3.13/1.87 % (10358)Time elapsed: 0.004 s
% 3.13/1.87 % (10358)Instructions burned: 5 (million)
% 3.13/1.87 % (10358)------------------------------
% 3.13/1.87 % (10358)------------------------------
% 3.13/1.89 % (10360)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_10139 for (2997ds/30Mi)
% 3.13/1.90 % (10360)Instruction limit reached!
% 3.13/1.90 % (10360)------------------------------
% 3.13/1.90 % (10360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.90 % (10360)Termination reason: Unknown
% 3.13/1.90 % (10360)Termination phase: shuffling
% 3.13/1.90
% 3.13/1.90 % (10360)Memory used [KB]: 2174
% 3.13/1.90 % (10360)Time elapsed: 0.015 s
% 3.13/1.90 % (10360)Instructions burned: 32 (million)
% 3.13/1.90 % (10360)------------------------------
% 3.13/1.90 % (10360)------------------------------
% 3.13/1.91 % (10362)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_10139 for (2997ds/127Mi)
% 3.13/1.94 % (10342)Instruction limit reached!
% 3.13/1.94 % (10342)------------------------------
% 3.13/1.94 % (10342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.94 % (10342)Termination reason: Unknown
% 3.13/1.94 % (10342)Termination phase: Saturation
% 3.13/1.94
% 3.13/1.94 % (10342)Memory used [KB]: 9466
% 3.13/1.94 % (10342)Time elapsed: 0.169 s
% 3.13/1.94 % (10342)Instructions burned: 377 (million)
% 3.13/1.94 % (10342)------------------------------
% 3.13/1.94 % (10342)------------------------------
% 3.13/1.96 % (10364)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_10139 for (2997ds/100Mi)
% 3.13/1.96 % (10362)Instruction limit reached!
% 3.13/1.96 % (10362)------------------------------
% 3.13/1.96 % (10362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.96 % (10362)Termination reason: Unknown
% 3.13/1.96 % (10362)Termination phase: Property scanning
% 3.13/1.96
% 3.13/1.96 % (10362)Memory used [KB]: 2686
% 3.13/1.96 % (10362)Time elapsed: 0.051 s
% 3.13/1.96 % (10362)Instructions burned: 128 (million)
% 3.13/1.96 % (10362)------------------------------
% 3.13/1.96 % (10362)------------------------------
% 3.13/1.98 % (10365)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_10139 for (2996ds/3Mi)
% 3.13/1.98 % (10365)Instruction limit reached!
% 3.13/1.98 % (10365)------------------------------
% 3.13/1.98 % (10365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.98 % (10365)Termination reason: Unknown
% 3.13/1.98 % (10365)Termination phase: shuffling
% 3.13/1.98
% 3.13/1.98 % (10365)Memory used [KB]: 1535
% 3.13/1.98 % (10365)Time elapsed: 0.003 s
% 3.13/1.98 % (10365)Instructions burned: 5 (million)
% 3.13/1.98 % (10365)------------------------------
% 3.13/1.98 % (10365)------------------------------
% 3.13/1.99 % (10368)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_10139 for (2996ds/20Mi)
% 3.13/1.99 % (10364)Instruction limit reached!
% 3.13/1.99 % (10364)------------------------------
% 3.13/1.99 % (10364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.99 % (10364)Termination reason: Unknown
% 3.13/1.99 % (10364)Termination phase: Property scanning
% 3.13/1.99
% 3.13/1.99 % (10364)Memory used [KB]: 2686
% 3.13/1.99 % (10364)Time elapsed: 0.036 s
% 3.13/1.99 % (10364)Instructions burned: 103 (million)
% 3.13/1.99 % (10364)------------------------------
% 3.13/1.99 % (10364)------------------------------
% 3.13/2.00 % (10368)Instruction limit reached!
% 3.13/2.00 % (10368)------------------------------
% 3.13/2.00 % (10368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/2.00 % (10368)Termination reason: Unknown
% 3.13/2.00 % (10368)Termination phase: shuffling
% 3.13/2.00
% 3.13/2.00 % (10368)Memory used [KB]: 1791
% 3.13/2.00 % (10368)Time elapsed: 0.008 s
% 3.13/2.00 % (10368)Instructions burned: 20 (million)
% 3.13/2.00 % (10368)------------------------------
% 3.13/2.00 % (10368)------------------------------
% 3.13/2.00 % (10369)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_10139 for (2996ds/86Mi)
% 3.13/2.01 % (10370)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_10139 for (2996ds/107Mi)
% 5.44/2.02 % (10369)Instruction limit reached!
% 5.44/2.02 % (10369)------------------------------
% 5.44/2.02 % (10369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.44/2.02 % (10369)Termination reason: Unknown
% 5.44/2.02 % (10369)Termination phase: Property scanning
% 5.44/2.02
% 5.44/2.02 % (10369)Memory used [KB]: 2686
% 5.44/2.02 % (10369)Time elapsed: 0.024 s
% 5.44/2.02 % (10369)Instructions burned: 88 (million)
% 5.44/2.02 % (10369)------------------------------
% 5.44/2.02 % (10369)------------------------------
% 5.44/2.03 % (10371)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_10139 for (2996ds/39Mi)
% 5.44/2.04 % (10370)Instruction limit reached!
% 5.44/2.04 % (10370)------------------------------
% 5.44/2.04 % (10370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.44/2.04 % (10370)Termination reason: Unknown
% 5.44/2.04 % (10370)Termination phase: Preprocessing 1
% 5.44/2.04
% 5.44/2.04 % (10370)Memory used [KB]: 2558
% 5.44/2.04 % (10370)Time elapsed: 0.031 s
% 5.44/2.04 % (10370)Instructions burned: 107 (million)
% 5.44/2.04 % (10370)------------------------------
% 5.44/2.04 % (10370)------------------------------
% 5.44/2.04 % (10328)Instruction limit reached!
% 5.44/2.04 % (10328)------------------------------
% 5.44/2.04 % (10328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.44/2.04 % (10328)Termination reason: Unknown
% 5.44/2.04 % (10328)Termination phase: Saturation
% 5.44/2.04
% 5.44/2.04 % (10328)Memory used [KB]: 10746
% 5.44/2.04 % (10328)Time elapsed: 0.305 s
% 5.44/2.04 % (10328)Instructions burned: 710 (million)
% 5.44/2.04 % (10328)------------------------------
% 5.44/2.04 % (10328)------------------------------
% 5.44/2.04 % (10345)Instruction limit reached!
% 5.44/2.04 % (10345)------------------------------
% 5.44/2.04 % (10345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.44/2.04 % (10345)Termination reason: Unknown
% 5.44/2.04 % (10345)Termination phase: Saturation
% 5.44/2.04
% 5.44/2.04 % (10345)Memory used [KB]: 7675
% 5.44/2.04 % (10345)Time elapsed: 0.251 s
% 5.44/2.04 % (10345)Instructions burned: 782 (million)
% 5.44/2.04 % (10345)------------------------------
% 5.44/2.04 % (10345)------------------------------
% 5.44/2.04 % (10371)Instruction limit reached!
% 5.44/2.04 % (10371)------------------------------
% 5.44/2.04 % (10371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.44/2.04 % (10371)Termination reason: Unknown
% 5.44/2.04 % (10371)Termination phase: shuffling
% 5.44/2.04
% 5.44/2.04 % (10371)Memory used [KB]: 2302
% 5.44/2.04 % (10371)Time elapsed: 0.012 s
% 5.44/2.04 % (10371)Instructions burned: 39 (million)
% 5.44/2.04 % (10371)------------------------------
% 5.44/2.04 % (10371)------------------------------
% 5.44/2.05 % (10372)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_10139 for (2996ds/448Mi)
% 5.44/2.05 % (10373)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_10139 for (2996ds/46Mi)
% 5.44/2.05 % (10374)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_10139 for (2996ds/98Mi)
% 5.44/2.05 % (10375)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_10139 for (2996ds/507Mi)
% 5.44/2.05 % (10307)Instruction limit reached!
% 5.44/2.05 % (10307)------------------------------
% 5.44/2.05 % (10307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.44/2.05 % (10307)Termination reason: Unknown
% 5.44/2.05 % (10307)Termination phase: Saturation
% 5.44/2.05
% 5.44/2.05 % (10307)Memory used [KB]: 15863
% 5.44/2.05 % (10307)Time elapsed: 0.359 s
% 5.44/2.05 % (10307)Instructions burned: 1043 (million)
% 5.44/2.05 % (10307)------------------------------
% 5.44/2.05 % (10307)------------------------------
% 5.44/2.06 % (10373)Instruction limit reached!
% 5.44/2.06 % (10373)------------------------------
% 5.44/2.06 % (10373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.44/2.06 % (10373)Termination reason: Unknown
% 5.44/2.06 % (10373)Termination phase: shuffling
% 5.44/2.06
% 5.44/2.06 % (10373)Memory used [KB]: 2430
% 5.44/2.06 % (10373)Time elapsed: 0.014 s
% 5.44/2.06 % (10373)Instructions burned: 47 (million)
% 5.44/2.06 % (10373)------------------------------
% 5.44/2.06 % (10373)------------------------------
% 5.44/2.06 % (10376)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_10139 for (2996ds/149Mi)
% 5.44/2.07 % (10377)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_10139 for (2996ds/39Mi)
% 5.44/2.07 % (10374)Instruction limit reached!
% 5.44/2.07 % (10374)------------------------------
% 5.44/2.07 % (10374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.44/2.07 % (10374)Termination reason: Unknown
% 5.44/2.07 % (10374)Termination phase: Property scanning
% 5.44/2.07
% 5.44/2.07 % (10374)Memory used [KB]: 2558
% 5.44/2.07 % (10374)Time elapsed: 0.027 s
% 5.44/2.07 % (10374)Instructions burned: 100 (million)
% 5.44/2.07 % (10374)------------------------------
% 5.44/2.07 % (10374)------------------------------
% 5.44/2.08 % (10377)Instruction limit reached!
% 5.44/2.08 % (10377)------------------------------
% 5.44/2.08 % (10377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.44/2.08 % (10377)Termination reason: Unknown
% 5.44/2.08 % (10377)Termination phase: shuffling
% 5.44/2.08
% 5.44/2.08 % (10377)Memory used [KB]: 2302
% 5.44/2.08 % (10377)Time elapsed: 0.012 s
% 5.44/2.08 % (10377)Instructions burned: 41 (million)
% 5.44/2.08 % (10377)------------------------------
% 5.44/2.08 % (10377)------------------------------
% 5.44/2.08 % (10378)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_10139 for (2995ds/6Mi)
% 5.44/2.08 % (10378)Instruction limit reached!
% 5.44/2.08 % (10378)------------------------------
% 5.44/2.08 % (10378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.44/2.08 % (10378)Termination reason: Unknown
% 5.44/2.08 % (10378)Termination phase: shuffling
% 5.44/2.08
% 5.44/2.08 % (10378)Memory used [KB]: 1535
% 5.44/2.08 % (10378)Time elapsed: 0.003 s
% 5.44/2.08 % (10378)Instructions burned: 7 (million)
% 5.44/2.08 % (10378)------------------------------
% 5.44/2.08 % (10378)------------------------------
% 5.44/2.09 % (10379)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_10139 for (2995ds/1087Mi)
% 5.44/2.09 % (10380)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_10139 for (2995ds/47Mi)
% 5.44/2.10 % (10376)Instruction limit reached!
% 5.44/2.10 % (10376)------------------------------
% 5.44/2.10 % (10376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.44/2.10 % (10376)Termination reason: Unknown
% 5.44/2.10 % (10376)Termination phase: Twee Goal Transformation
% 5.44/2.10
% 5.44/2.10 % (10376)Memory used [KB]: 3326
% 5.44/2.10 % (10376)Time elapsed: 0.040 s
% 5.44/2.10 % (10376)Instructions burned: 150 (million)
% 5.44/2.10 % (10376)------------------------------
% 5.44/2.10 % (10376)------------------------------
% 5.44/2.11 % (10380)Instruction limit reached!
% 5.44/2.11 % (10380)------------------------------
% 5.44/2.11 % (10380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.44/2.11 % (10380)Termination reason: Unknown
% 5.44/2.11 % (10380)Termination phase: shuffling
% 5.44/2.11
% 5.44/2.11 % (10380)Memory used [KB]: 2430
% 5.44/2.11 % (10380)Time elapsed: 0.015 s
% 5.44/2.11 % (10380)Instructions burned: 50 (million)
% 5.44/2.11 % (10380)------------------------------
% 5.44/2.11 % (10380)------------------------------
% 5.44/2.11 % (10331)Instruction limit reached!
% 5.44/2.11 % (10331)------------------------------
% 5.44/2.11 % (10331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.44/2.11 % (10331)Termination reason: Unknown
% 5.44/2.11 % (10331)Termination phase: Saturation
% 5.44/2.11
% 5.44/2.11 % (10331)Memory used [KB]: 12920
% 5.44/2.11 % (10331)Time elapsed: 0.365 s
% 5.44/2.11 % (10331)Instructions burned: 904 (million)
% 5.44/2.11 % (10331)------------------------------
% 5.44/2.11 % (10331)------------------------------
% 5.65/2.11 % (10384)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_10139 for (2995ds/44Mi)
% 5.65/2.12 % (10386)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_10139 for (2995ds/432Mi)
% 5.65/2.12 % (10389)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_10139 for (2995ds/62Mi)
% 5.65/2.13 % (10384)Instruction limit reached!
% 5.65/2.13 % (10384)------------------------------
% 5.65/2.13 % (10384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.13 % (10384)Termination reason: Unknown
% 5.65/2.13 % (10384)Termination phase: shuffling
% 5.65/2.13
% 5.65/2.13 % (10384)Memory used [KB]: 2430
% 5.65/2.13 % (10384)Time elapsed: 0.014 s
% 5.65/2.13 % (10384)Instructions burned: 46 (million)
% 5.65/2.13 % (10384)------------------------------
% 5.65/2.13 % (10384)------------------------------
% 5.65/2.13 % (10350)Instruction limit reached!
% 5.65/2.13 % (10350)------------------------------
% 5.65/2.13 % (10350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.13 % (10350)Termination reason: Unknown
% 5.65/2.13 % (10350)Termination phase: Saturation
% 5.65/2.13
% 5.65/2.13 % (10350)Memory used [KB]: 9978
% 5.65/2.13 % (10350)Time elapsed: 0.324 s
% 5.65/2.13 % (10350)Instructions burned: 880 (million)
% 5.65/2.13 % (10350)------------------------------
% 5.65/2.13 % (10350)------------------------------
% 5.65/2.13 % (10397)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_10139 for (2995ds/31Mi)
% 5.65/2.14 % (10389)Instruction limit reached!
% 5.65/2.14 % (10389)------------------------------
% 5.65/2.14 % (10389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.14 % (10389)Termination reason: Unknown
% 5.65/2.14 % (10389)Termination phase: Property scanning
% 5.65/2.14
% 5.65/2.14 % (10389)Memory used [KB]: 2558
% 5.65/2.14 % (10389)Time elapsed: 0.018 s
% 5.65/2.14 % (10389)Instructions burned: 62 (million)
% 5.65/2.14 % (10389)------------------------------
% 5.65/2.14 % (10389)------------------------------
% 5.65/2.14 % (10401)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_10139 for (2995ds/96Mi)
% 5.65/2.14 % (10397)Instruction limit reached!
% 5.65/2.14 % (10397)------------------------------
% 5.65/2.14 % (10397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.14 % (10397)Termination reason: Unknown
% 5.65/2.14 % (10397)Termination phase: shuffling
% 5.65/2.14
% 5.65/2.14 % (10397)Memory used [KB]: 2174
% 5.65/2.14 % (10397)Time elapsed: 0.010 s
% 5.65/2.14 % (10397)Instructions burned: 33 (million)
% 5.65/2.14 % (10397)------------------------------
% 5.65/2.14 % (10397)------------------------------
% 5.65/2.15 % (10406)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_10139 for (2995ds/453Mi)
% 5.65/2.15 % (10409)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_10139 for (2995ds/71Mi)
% 5.65/2.16 % (10372)Instruction limit reached!
% 5.65/2.16 % (10372)------------------------------
% 5.65/2.16 % (10372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.16 % (10372)Termination reason: Unknown
% 5.65/2.16 % (10372)Termination phase: Saturation
% 5.65/2.16
% 5.65/2.16 % (10372)Memory used [KB]: 7547
% 5.65/2.16 % (10372)Time elapsed: 0.113 s
% 5.65/2.16 % (10372)Instructions burned: 451 (million)
% 5.65/2.16 % (10372)------------------------------
% 5.65/2.16 % (10372)------------------------------
% 5.65/2.17 % (10401)Instruction limit reached!
% 5.65/2.17 % (10401)------------------------------
% 5.65/2.17 % (10401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.17 % (10401)Termination reason: Unknown
% 5.65/2.17 % (10401)Termination phase: Property scanning
% 5.65/2.17
% 5.65/2.17 % (10401)Memory used [KB]: 2686
% 5.65/2.17 % (10401)Time elapsed: 0.026 s
% 5.65/2.17 % (10401)Instructions burned: 96 (million)
% 5.65/2.17 % (10401)------------------------------
% 5.65/2.17 % (10401)------------------------------
% 5.65/2.17 % (10417)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_10139 for (2994ds/83Mi)
% 5.65/2.17 % (10409)Instruction limit reached!
% 5.65/2.17 % (10409)------------------------------
% 5.65/2.17 % (10409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.17 % (10409)Termination reason: Unknown
% 5.65/2.17 % (10409)Termination phase: Property scanning
% 5.65/2.17
% 5.65/2.17 % (10409)Memory used [KB]: 2558
% 5.65/2.17 % (10409)Time elapsed: 0.021 s
% 5.65/2.17 % (10409)Instructions burned: 74 (million)
% 5.65/2.17 % (10409)------------------------------
% 5.65/2.17 % (10409)------------------------------
% 5.65/2.18 % (10424)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_10139 for (2994ds/11Mi)
% 5.65/2.18 % (10424)Instruction limit reached!
% 5.65/2.18 % (10424)------------------------------
% 5.65/2.18 % (10424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.18 % (10424)Termination reason: Unknown
% 5.65/2.18 % (10424)Termination phase: shuffling
% 5.65/2.18
% 5.65/2.18 % (10424)Memory used [KB]: 1791
% 5.65/2.18 % (10424)Time elapsed: 0.005 s
% 5.65/2.18 % (10424)Instructions burned: 13 (million)
% 5.65/2.18 % (10424)------------------------------
% 5.65/2.18 % (10424)------------------------------
% 5.65/2.18 % (10429)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_10139 for (2994ds/41Mi)
% 5.65/2.19 % (10431)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_10139 for (2994ds/6Mi)
% 5.65/2.19 % (10417)Instruction limit reached!
% 5.65/2.19 % (10417)------------------------------
% 5.65/2.19 % (10417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.19 % (10417)Termination reason: Unknown
% 5.65/2.19 % (10417)Termination phase: Property scanning
% 5.65/2.19
% 5.65/2.19 % (10417)Memory used [KB]: 2558
% 5.65/2.19 % (10417)Time elapsed: 0.023 s
% 5.65/2.19 % (10417)Instructions burned: 83 (million)
% 5.65/2.19 % (10417)------------------------------
% 5.65/2.19 % (10417)------------------------------
% 5.65/2.19 % (10431)Instruction limit reached!
% 5.65/2.19 % (10431)------------------------------
% 5.65/2.19 % (10431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.19 % (10431)Termination reason: Unknown
% 5.65/2.19 % (10431)Termination phase: shuffling
% 5.65/2.19
% 5.65/2.19 % (10431)Memory used [KB]: 1535
% 5.65/2.19 % (10431)Time elapsed: 0.003 s
% 5.65/2.19 % (10431)Instructions burned: 7 (million)
% 5.65/2.19 % (10431)------------------------------
% 5.65/2.19 % (10431)------------------------------
% 5.65/2.19 % (10429)Instruction limit reached!
% 5.65/2.19 % (10429)------------------------------
% 5.65/2.19 % (10429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.19 % (10429)Termination reason: Unknown
% 5.65/2.19 % (10429)Termination phase: shuffling
% 5.65/2.19
% 5.65/2.19 % (10429)Memory used [KB]: 2302
% 5.65/2.19 % (10429)Time elapsed: 0.012 s
% 5.65/2.19 % (10429)Instructions burned: 42 (million)
% 5.65/2.19 % (10429)------------------------------
% 5.65/2.19 % (10429)------------------------------
% 6.41/2.20 % (10435)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_10139 for (2994ds/150Mi)
% 6.41/2.20 % (10375)Instruction limit reached!
% 6.41/2.20 % (10375)------------------------------
% 6.41/2.20 % (10375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.20 % (10375)Termination reason: Unknown
% 6.41/2.20 % (10375)Termination phase: Saturation
% 6.41/2.20
% 6.41/2.20 % (10375)Memory used [KB]: 8187
% 6.41/2.20 % (10375)Time elapsed: 0.148 s
% 6.41/2.20 % (10375)Instructions burned: 508 (million)
% 6.41/2.20 % (10375)------------------------------
% 6.41/2.20 % (10375)------------------------------
% 6.41/2.20 % (10437)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_10139 for (2994ds/343Mi)
% 6.41/2.20 % (10439)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_10139 for (2994ds/109Mi)
% 6.41/2.21 % (10443)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_10139 for (2994ds/253Mi)
% 6.41/2.23 % (10386)Instruction limit reached!
% 6.41/2.23 % (10386)------------------------------
% 6.41/2.23 % (10386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.23 % (10386)Termination reason: Unknown
% 6.41/2.23 % (10386)Termination phase: Saturation
% 6.41/2.23
% 6.41/2.23 % (10386)Memory used [KB]: 3070
% 6.41/2.23 % (10386)Time elapsed: 0.110 s
% 6.41/2.23 % (10386)Instructions burned: 434 (million)
% 6.41/2.23 % (10386)------------------------------
% 6.41/2.23 % (10386)------------------------------
% 6.41/2.23 % (10439)Instruction limit reached!
% 6.41/2.23 % (10439)------------------------------
% 6.41/2.23 % (10439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.23 % (10439)Termination reason: Unknown
% 6.41/2.23 % (10439)Termination phase: Property scanning
% 6.41/2.23
% 6.41/2.23 % (10439)Memory used [KB]: 2686
% 6.41/2.23 % (10439)Time elapsed: 0.030 s
% 6.41/2.23 % (10439)Instructions burned: 111 (million)
% 6.41/2.23 % (10439)------------------------------
% 6.41/2.23 % (10439)------------------------------
% 6.41/2.24 % (10453)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_10139 for (2994ds/140Mi)
% 6.41/2.24 % (10455)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_10139 for (2994ds/614Mi)
% 6.41/2.24 % (10435)Instruction limit reached!
% 6.41/2.24 % (10435)------------------------------
% 6.41/2.24 % (10435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.24 % (10435)Termination reason: Unknown
% 6.41/2.24 % (10435)Termination phase: Property scanning
% 6.41/2.24
% 6.41/2.24 % (10435)Memory used [KB]: 4861
% 6.41/2.24 % (10435)Time elapsed: 0.045 s
% 6.41/2.24 % (10435)Instructions burned: 150 (million)
% 6.41/2.24 % (10435)------------------------------
% 6.41/2.24 % (10435)------------------------------
% 6.41/2.25 % (10464)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_10139 for (2994ds/202Mi)
% 6.41/2.26 % (10406)Instruction limit reached!
% 6.41/2.26 % (10406)------------------------------
% 6.41/2.26 % (10406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.26 % (10406)Termination reason: Unknown
% 6.41/2.26 % (10406)Termination phase: Saturation
% 6.41/2.26
% 6.41/2.26 % (10406)Memory used [KB]: 7547
% 6.41/2.26 % (10406)Time elapsed: 0.115 s
% 6.41/2.26 % (10406)Instructions burned: 456 (million)
% 6.41/2.26 % (10406)------------------------------
% 6.41/2.26 % (10406)------------------------------
% 6.41/2.27 % (10469)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_10139 for (2993ds/339Mi)
% 6.41/2.27 % (10453)Instruction limit reached!
% 6.41/2.27 % (10453)------------------------------
% 6.41/2.27 % (10453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.27 % (10453)Termination reason: Unknown
% 6.41/2.27 % (10453)Termination phase: Property scanning
% 6.41/2.27
% 6.41/2.27 % (10453)Memory used [KB]: 2814
% 6.41/2.27 % (10453)Time elapsed: 0.038 s
% 6.41/2.27 % (10453)Instructions burned: 140 (million)
% 6.41/2.27 % (10453)------------------------------
% 6.41/2.27 % (10453)------------------------------
% 6.41/2.28 % (10443)Instruction limit reached!
% 6.41/2.28 % (10443)------------------------------
% 6.41/2.28 % (10443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.28 % (10443)Termination reason: Unknown
% 6.41/2.28 % (10443)Termination phase: Saturation
% 6.41/2.28
% 6.41/2.28 % (10443)Memory used [KB]: 9978
% 6.41/2.28 % (10443)Time elapsed: 0.073 s
% 6.41/2.28 % (10443)Instructions burned: 253 (million)
% 6.41/2.28 % (10443)------------------------------
% 6.41/2.28 % (10443)------------------------------
% 6.41/2.28 % (10478)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_10139 for (2993ds/283Mi)
% 6.41/2.29 % (10437)Instruction limit reached!
% 6.41/2.29 % (10437)------------------------------
% 6.41/2.29 % (10437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.29 % (10437)Termination reason: Unknown
% 6.41/2.29 % (10437)Termination phase: Saturation
% 6.41/2.29
% 6.41/2.29 % (10437)Memory used [KB]: 8443
% 6.41/2.29 % (10437)Time elapsed: 0.091 s
% 6.41/2.29 % (10437)Instructions burned: 344 (million)
% 6.41/2.29 % (10437)------------------------------
% 6.41/2.29 % (10437)------------------------------
% 6.41/2.29 % (10485)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_10139 for (2993ds/134Mi)
% 7.12/2.30 % (10488)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_10139 for (2993ds/298Mi)
% 7.12/2.31 % (10464)Instruction limit reached!
% 7.12/2.31 % (10464)------------------------------
% 7.12/2.31 % (10464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.12/2.31 % (10464)Termination reason: Unknown
% 7.12/2.31 % (10464)Termination phase: Property scanning
% 7.12/2.31
% 7.12/2.31 % (10464)Memory used [KB]: 4989
% 7.12/2.31 % (10464)Time elapsed: 0.058 s
% 7.12/2.31 % (10464)Instructions burned: 206 (million)
% 7.12/2.31 % (10464)------------------------------
% 7.12/2.31 % (10464)------------------------------
% 7.12/2.32 % (10500)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_10139 for (2993ds/192Mi)
% 7.12/2.33 % (10485)Instruction limit reached!
% 7.12/2.33 % (10485)------------------------------
% 7.12/2.33 % (10485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.12/2.33 % (10485)Termination reason: Unknown
% 7.12/2.33 % (10485)Termination phase: Property scanning
% 7.12/2.33
% 7.12/2.33 % (10485)Memory used [KB]: 2814
% 7.12/2.33 % (10485)Time elapsed: 0.036 s
% 7.12/2.33 % (10485)Instructions burned: 135 (million)
% 7.12/2.33 % (10485)------------------------------
% 7.12/2.33 % (10485)------------------------------
% 7.12/2.34 % (10512)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_10139 for (2993ds/258Mi)
% 7.12/2.35 % (10478)Instruction limit reached!
% 7.12/2.35 % (10478)------------------------------
% 7.12/2.35 % (10478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.12/2.35 % (10478)Termination reason: Unknown
% 7.12/2.35 % (10478)Termination phase: Saturation
% 7.12/2.35
% 7.12/2.35 % (10478)Memory used [KB]: 7419
% 7.12/2.35 % (10478)Time elapsed: 0.072 s
% 7.12/2.35 % (10478)Instructions burned: 283 (million)
% 7.12/2.35 % (10478)------------------------------
% 7.12/2.35 % (10478)------------------------------
% 7.12/2.36 % (10525)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_10139 for (2993ds/90Mi)
% 7.12/2.37 % (10469)Instruction limit reached!
% 7.12/2.37 % (10469)------------------------------
% 7.12/2.37 % (10469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.12/2.37 % (10469)Termination reason: Unknown
% 7.12/2.37 % (10469)Termination phase: Saturation
% 7.12/2.37
% 7.12/2.37 % (10469)Memory used [KB]: 8315
% 7.12/2.37 % (10469)Time elapsed: 0.095 s
% 7.12/2.37 % (10469)Instructions burned: 341 (million)
% 7.12/2.37 % (10469)------------------------------
% 7.12/2.37 % (10469)------------------------------
% 7.12/2.37 % (10500)Instruction limit reached!
% 7.12/2.37 % (10500)------------------------------
% 7.12/2.37 % (10500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.12/2.37 % (10500)Termination reason: Unknown
% 7.12/2.37 % (10500)Termination phase: Saturation
% 7.12/2.37
% 7.12/2.37 % (10500)Memory used [KB]: 7547
% 7.12/2.37 % (10500)Time elapsed: 0.051 s
% 7.12/2.37 % (10500)Instructions burned: 194 (million)
% 7.12/2.37 % (10500)------------------------------
% 7.12/2.37 % (10500)------------------------------
% 7.12/2.37 % (10488)Instruction limit reached!
% 7.12/2.37 % (10488)------------------------------
% 7.12/2.37 % (10488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.12/2.37 % (10488)Termination reason: Unknown
% 7.12/2.37 % (10488)Termination phase: Saturation
% 7.12/2.37
% 7.12/2.37 % (10488)Memory used [KB]: 7547
% 7.12/2.37 % (10488)Time elapsed: 0.076 s
% 7.12/2.37 % (10488)Instructions burned: 301 (million)
% 7.12/2.37 % (10488)------------------------------
% 7.12/2.37 % (10488)------------------------------
% 7.12/2.38 % (10531)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_10139 for (2992ds/231Mi)
% 7.12/2.38 % (10532)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_10139 for (2992ds/458Mi)
% 7.12/2.38 % (10536)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_10139 for (2992ds/31Mi)
% 7.12/2.39 % (10525)Instruction limit reached!
% 7.12/2.39 % (10525)------------------------------
% 7.12/2.39 % (10525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.12/2.39 % (10525)Termination reason: Unknown
% 7.12/2.39 % (10525)Termination phase: Property scanning
% 7.12/2.39
% 7.12/2.39 % (10525)Memory used [KB]: 2686
% 7.12/2.39 % (10525)Time elapsed: 0.025 s
% 7.12/2.39 % (10525)Instructions burned: 90 (million)
% 7.12/2.39 % (10525)------------------------------
% 7.12/2.39 % (10525)------------------------------
% 7.12/2.39 % (10536)Instruction limit reached!
% 7.12/2.39 % (10536)------------------------------
% 7.12/2.39 % (10536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.12/2.39 % (10536)Termination reason: Unknown
% 7.12/2.39 % (10536)Termination phase: shuffling
% 7.12/2.39
% 7.12/2.39 % (10536)Memory used [KB]: 2046
% 7.12/2.39 % (10536)Time elapsed: 0.010 s
% 7.12/2.39 % (10536)Instructions burned: 32 (million)
% 7.12/2.39 % (10536)------------------------------
% 7.12/2.39 % (10536)------------------------------
% 7.12/2.40 % (10543)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_10139 for (2992ds/297Mi)
% 7.61/2.40 % (10512)Instruction limit reached!
% 7.61/2.40 % (10512)------------------------------
% 7.61/2.40 % (10512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.61/2.40 % (10512)Termination reason: Unknown
% 7.61/2.40 % (10512)Termination phase: Saturation
% 7.61/2.40
% 7.61/2.40 % (10512)Memory used [KB]: 7931
% 7.61/2.40 % (10512)Time elapsed: 0.068 s
% 7.61/2.40 % (10512)Instructions burned: 259 (million)
% 7.61/2.40 % (10512)------------------------------
% 7.61/2.40 % (10512)------------------------------
% 7.61/2.40 % (10548)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_10139 for (2992ds/987Mi)
% 7.61/2.41 % (10552)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_10139 for (2992ds/182Mi)
% 7.61/2.42 % (10455)Instruction limit reached!
% 7.61/2.42 % (10455)------------------------------
% 7.61/2.42 % (10455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.61/2.42 % (10455)Termination reason: Unknown
% 7.61/2.42 % (10455)Termination phase: Saturation
% 7.61/2.42
% 7.61/2.42 % (10455)Memory used [KB]: 9978
% 7.61/2.42 % (10455)Time elapsed: 0.178 s
% 7.61/2.42 % (10455)Instructions burned: 614 (million)
% 7.61/2.42 % (10455)------------------------------
% 7.61/2.42 % (10455)------------------------------
% 7.61/2.43 % (10559)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_10139 for (2992ds/182Mi)
% 7.61/2.43 % (10379)Instruction limit reached!
% 7.61/2.43 % (10379)------------------------------
% 7.61/2.43 % (10379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.61/2.43 % (10379)Termination reason: Unknown
% 7.61/2.43 % (10379)Termination phase: Saturation
% 7.61/2.43
% 7.61/2.43 % (10379)Memory used [KB]: 12537
% 7.61/2.43 % (10379)Time elapsed: 0.363 s
% 7.61/2.43 % (10379)Instructions burned: 1087 (million)
% 7.61/2.43 % (10379)------------------------------
% 7.61/2.43 % (10379)------------------------------
% 7.61/2.43 % (10531)Instruction limit reached!
% 7.61/2.43 % (10531)------------------------------
% 7.61/2.43 % (10531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.61/2.43 % (10531)Termination reason: Unknown
% 7.61/2.43 % (10531)Termination phase: Saturation
% 7.61/2.43
% 7.61/2.43 % (10531)Memory used [KB]: 8443
% 7.61/2.43 % (10531)Time elapsed: 0.061 s
% 7.61/2.43 % (10531)Instructions burned: 232 (million)
% 7.61/2.43 % (10531)------------------------------
% 7.61/2.43 % (10531)------------------------------
% 7.61/2.44 % (10564)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_10139 for (2992ds/154Mi)
% 7.61/2.44 % (10566)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_10139 for (2992ds/79Mi)
% 7.61/2.46 % (10552)Instruction limit reached!
% 7.61/2.46 % (10552)------------------------------
% 7.61/2.46 % (10552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.61/2.46 % (10552)Termination reason: Unknown
% 7.61/2.46 % (10552)Termination phase: Saturation
% 7.61/2.46
% 7.61/2.46 % (10552)Memory used [KB]: 7419
% 7.61/2.46 % (10552)Time elapsed: 0.050 s
% 7.61/2.46 % (10552)Instructions burned: 185 (million)
% 7.61/2.46 % (10552)------------------------------
% 7.61/2.46 % (10552)------------------------------
% 7.61/2.47 % (10566)Instruction limit reached!
% 7.61/2.47 % (10566)------------------------------
% 7.61/2.47 % (10566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.61/2.47 % (10566)Termination reason: Unknown
% 7.61/2.47 % (10566)Termination phase: Property scanning
% 7.61/2.47
% 7.61/2.47 % (10566)Memory used [KB]: 2558
% 7.61/2.47 % (10566)Time elapsed: 0.022 s
% 7.61/2.47 % (10566)Instructions burned: 80 (million)
% 7.61/2.47 % (10566)------------------------------
% 7.61/2.47 % (10566)------------------------------
% 7.61/2.47 % (10543)Instruction limit reached!
% 7.61/2.47 % (10543)------------------------------
% 7.61/2.47 % (10543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.61/2.47 % (10543)Termination reason: Unknown
% 7.61/2.47 % (10543)Termination phase: Saturation
% 7.61/2.47
% 7.61/2.47 % (10543)Memory used [KB]: 7547
% 7.61/2.47 % (10543)Time elapsed: 0.075 s
% 7.61/2.47 % (10543)Instructions burned: 299 (million)
% 7.61/2.47 % (10543)------------------------------
% 7.61/2.47 % (10543)------------------------------
% 7.61/2.47 % (10576)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_10139 for (2992ds/216Mi)
% 7.61/2.48 % (10580)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_10139 for (2992ds/114Mi)
% 7.61/2.48 % (10559)Instruction limit reached!
% 7.61/2.48 % (10559)------------------------------
% 7.61/2.48 % (10559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.61/2.48 % (10559)Termination reason: Unknown
% 7.61/2.48 % (10559)Termination phase: Property scanning
% 7.61/2.48
% 7.61/2.48 % (10559)Memory used [KB]: 4989
% 7.61/2.48 % (10559)Time elapsed: 0.052 s
% 7.61/2.48 % (10559)Instructions burned: 182 (million)
% 7.61/2.48 % (10559)------------------------------
% 7.61/2.48 % (10559)------------------------------
% 7.61/2.48 % (10564)Instruction limit reached!
% 7.61/2.48 % (10564)------------------------------
% 7.61/2.48 % (10564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.61/2.48 % (10564)Termination reason: Unknown
% 7.61/2.48 % (10564)Termination phase: Property scanning
% 7.61/2.48
% 7.61/2.48 % (10564)Memory used [KB]: 2686
% 7.61/2.48 % (10564)Time elapsed: 0.040 s
% 7.61/2.48 % (10564)Instructions burned: 157 (million)
% 7.61/2.48 % (10564)------------------------------
% 7.61/2.48 % (10564)------------------------------
% 7.61/2.48 % (10583)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_10139 for (2991ds/922Mi)
% 7.61/2.49 % (10587)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_10139 for (2991ds/182Mi)
% 7.61/2.49 % (10588)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_10139 for (2991ds/164Mi)
% 8.58/2.50 % (10580)Instruction limit reached!
% 8.58/2.50 % (10580)------------------------------
% 8.58/2.50 % (10580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.58/2.50 % (10580)Termination reason: Unknown
% 8.58/2.50 % (10580)Termination phase: Property scanning
% 8.58/2.50
% 8.58/2.51 % (10580)Memory used [KB]: 2686
% 8.58/2.51 % (10580)Time elapsed: 0.031 s
% 8.58/2.51 % (10580)Instructions burned: 117 (million)
% 8.58/2.51 % (10580)------------------------------
% 8.58/2.51 % (10580)------------------------------
% 8.58/2.51 % (10532)Instruction limit reached!
% 8.58/2.51 % (10532)------------------------------
% 8.58/2.51 % (10532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.58/2.51 % (10532)Termination reason: Unknown
% 8.58/2.51 % (10532)Termination phase: Saturation
% 8.58/2.51
% 8.58/2.51 % (10532)Memory used [KB]: 9722
% 8.58/2.51 % (10532)Time elapsed: 0.128 s
% 8.58/2.51 % (10532)Instructions burned: 460 (million)
% 8.58/2.51 % (10532)------------------------------
% 8.58/2.51 % (10532)------------------------------
% 8.58/2.51 % (10595)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_10139 for (2991ds/50Mi)
% 8.58/2.52 % (10597)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_10139 for (2991ds/368Mi)
% 8.58/2.52 % (10576)Instruction limit reached!
% 8.58/2.52 % (10576)------------------------------
% 8.58/2.52 % (10576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.58/2.52 % (10576)Termination reason: Unknown
% 8.58/2.52 % (10576)Termination phase: Saturation
% 8.58/2.52
% 8.58/2.52 % (10576)Memory used [KB]: 7547
% 8.58/2.52 % (10576)Time elapsed: 0.055 s
% 8.58/2.52 % (10576)Instructions burned: 219 (million)
% 8.58/2.52 % (10576)------------------------------
% 8.58/2.52 % (10576)------------------------------
% 8.58/2.53 % (10595)Instruction limit reached!
% 8.58/2.53 % (10595)------------------------------
% 8.58/2.53 % (10595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.58/2.53 % (10595)Termination reason: Unknown
% 8.58/2.53 % (10595)Termination phase: shuffling
% 8.58/2.53
% 8.58/2.53 % (10595)Memory used [KB]: 2430
% 8.58/2.53 % (10595)Time elapsed: 0.015 s
% 8.58/2.53 % (10595)Instructions burned: 52 (million)
% 8.58/2.53 % (10595)------------------------------
% 8.58/2.53 % (10595)------------------------------
% 8.58/2.53 % (10588)Instruction limit reached!
% 8.58/2.53 % (10588)------------------------------
% 8.58/2.53 % (10588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.58/2.53 % (10588)Termination reason: Unknown
% 8.58/2.53 % (10588)Termination phase: Property scanning
% 8.58/2.53
% 8.58/2.53 % (10588)Memory used [KB]: 2814
% 8.58/2.53 % (10588)Time elapsed: 0.042 s
% 8.58/2.53 % (10588)Instructions burned: 165 (million)
% 8.58/2.53 % (10588)------------------------------
% 8.58/2.53 % (10588)------------------------------
% 8.58/2.53 % (10587)Instruction limit reached!
% 8.58/2.53 % (10587)------------------------------
% 8.58/2.53 % (10587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.58/2.53 % (10587)Termination reason: Unknown
% 8.58/2.53 % (10587)Termination phase: Saturation
% 8.58/2.53
% 8.58/2.53 % (10587)Memory used [KB]: 7419
% 8.58/2.53 % (10587)Time elapsed: 0.046 s
% 8.58/2.53 % (10587)Instructions burned: 182 (million)
% 8.58/2.53 % (10587)------------------------------
% 8.58/2.53 % (10587)------------------------------
% 8.58/2.53 % (10607)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_10139 for (2991ds/1021Mi)
% 8.58/2.54 % (10610)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_10139 for (2991ds/267Mi)
% 8.58/2.54 % (10612)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_10139 for (2991ds/204Mi)
% 8.58/2.54 % (10613)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_10139 for (2991ds/26Mi)
% 8.58/2.55 % (10613)Instruction limit reached!
% 8.58/2.55 % (10613)------------------------------
% 8.58/2.55 % (10613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.58/2.55 % (10613)Termination reason: Unknown
% 8.58/2.55 % (10613)Termination phase: shuffling
% 8.58/2.55
% 8.58/2.55 % (10613)Memory used [KB]: 2174
% 8.58/2.55 % (10613)Time elapsed: 0.009 s
% 8.58/2.55 % (10613)Instructions burned: 29 (million)
% 8.58/2.55 % (10613)------------------------------
% 8.58/2.55 % (10613)------------------------------
% 8.58/2.56 % (10619)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_10139 for (2990ds/53Mi)
% 8.58/2.57 % (10619)Instruction limit reached!
% 8.58/2.57 % (10619)------------------------------
% 8.58/2.57 % (10619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.58/2.57 % (10619)Termination reason: Unknown
% 8.58/2.57 % (10619)Termination phase: shuffling
% 8.58/2.57
% 8.58/2.57 % (10619)Memory used [KB]: 2430
% 8.58/2.57 % (10619)Time elapsed: 0.015 s
% 8.58/2.57 % (10619)Instructions burned: 53 (million)
% 8.58/2.57 % (10619)------------------------------
% 8.58/2.57 % (10619)------------------------------
% 8.58/2.58 % (10637)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_10139 for (2990ds/4436Mi)
% 8.58/2.59 % (10612)Instruction limit reached!
% 8.58/2.59 % (10612)------------------------------
% 8.58/2.59 % (10612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.58/2.59 % (10612)Termination reason: Unknown
% 8.58/2.59 % (10612)Termination phase: Saturation
% 8.58/2.59
% 8.58/2.59 % (10612)Memory used [KB]: 7291
% 8.58/2.59 % (10612)Time elapsed: 0.052 s
% 8.58/2.59 % (10612)Instructions burned: 206 (million)
% 8.58/2.59 % (10612)------------------------------
% 8.58/2.59 % (10612)------------------------------
% 9.05/2.60 % (10649)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_10139 for (2990ds/1539Mi)
% 9.05/2.60 % (10610)Instruction limit reached!
% 9.05/2.60 % (10610)------------------------------
% 9.05/2.60 % (10610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.05/2.60 % (10610)Termination reason: Unknown
% 9.05/2.60 % (10610)Termination phase: Saturation
% 9.05/2.60
% 9.05/2.61 % (10610)Memory used [KB]: 7419
% 9.05/2.61 % (10610)Time elapsed: 0.068 s
% 9.05/2.61 % (10610)Instructions burned: 270 (million)
% 9.05/2.61 % (10610)------------------------------
% 9.05/2.61 % (10610)------------------------------
% 9.05/2.61 % (10597)Instruction limit reached!
% 9.05/2.61 % (10597)------------------------------
% 9.05/2.61 % (10597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.05/2.61 % (10597)Termination reason: Unknown
% 9.05/2.61 % (10597)Termination phase: Saturation
% 9.05/2.61
% 9.05/2.61 % (10597)Memory used [KB]: 9466
% 9.05/2.61 % (10597)Time elapsed: 0.100 s
% 9.05/2.61 % (10597)Instructions burned: 369 (million)
% 9.05/2.61 % (10597)------------------------------
% 9.05/2.61 % (10597)------------------------------
% 9.05/2.61 % (10655)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_10139 for (2990ds/408Mi)
% 9.05/2.62 % (10661)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_10139 for (2990ds/5205Mi)
% 9.05/2.65 % (10548)Instruction limit reached!
% 9.05/2.65 % (10548)------------------------------
% 9.05/2.65 % (10548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.05/2.65 % (10548)Termination reason: Unknown
% 9.05/2.65 % (10548)Termination phase: Saturation
% 9.05/2.65
% 9.05/2.65 % (10548)Memory used [KB]: 16119
% 9.05/2.65 % (10548)Time elapsed: 0.251 s
% 9.05/2.65 % (10548)Instructions burned: 989 (million)
% 9.05/2.65 % (10548)------------------------------
% 9.05/2.65 % (10548)------------------------------
% 9.05/2.66 % (10662)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_10139 for (2990ds/1913Mi)
% 9.49/2.72 % (10655)First to succeed.
% 9.49/2.72 % (10655)Refutation found. Thanks to Tanya!
% 9.49/2.72 % SZS status Theorem for DTF2THF_10139
% 9.49/2.72 % SZS output start Proof for DTF2THF_10139
% 9.49/2.72 thf(func_def_0, type, in: $i > $i > $o).
% 9.49/2.72 thf(func_def_1, type, exu: ($i > $o) > $o).
% 9.49/2.72 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 9.49/2.72 thf(func_def_8, type, powerset: $i > $i).
% 9.49/2.72 thf(func_def_10, type, setunion: $i > $i).
% 9.49/2.72 thf(func_def_19, type, descr: ($i > $o) > $i).
% 9.49/2.72 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 9.49/2.72 thf(func_def_26, type, prop2set: $o > $i).
% 9.49/2.72 thf(func_def_36, type, nonempty: $i > $o).
% 9.49/2.72 thf(func_def_69, type, set2prop: $i > $o).
% 9.49/2.72 thf(func_def_88, type, subset: $i > $i > $o).
% 9.49/2.72 thf(func_def_89, type, disjoint: $i > $i > $o).
% 9.49/2.72 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 9.49/2.72 thf(func_def_114, type, binunion: $i > $i > $i).
% 9.49/2.72 thf(func_def_122, type, binintersect: $i > $i > $i).
% 9.49/2.72 thf(func_def_135, type, regular: $i > $o).
% 9.49/2.72 thf(func_def_136, type, setminus: $i > $i > $i).
% 9.49/2.72 thf(func_def_147, type, symdiff: $i > $i > $i).
% 9.49/2.72 thf(func_def_153, type, iskpair: $i > $o).
% 9.49/2.72 thf(func_def_158, type, kpair: $i > $i > $i).
% 9.49/2.72 thf(func_def_160, type, cartprod: $i > $i > $i).
% 9.49/2.72 thf(func_def_177, type, singleton: $i > $o).
% 9.49/2.72 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 9.49/2.72 thf(func_def_184, type, atmost1p: $i > $o).
% 9.49/2.72 thf(func_def_185, type, atleast2p: $i > $o).
% 9.49/2.72 thf(func_def_186, type, atmost2p: $i > $o).
% 9.49/2.72 thf(func_def_187, type, upairsetp: $i > $o).
% 9.49/2.72 thf(func_def_191, type, kfst: $i > $i).
% 9.49/2.72 thf(func_def_203, type, ksnd: $i > $i).
% 9.49/2.72 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 9.49/2.72 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 9.49/2.72 thf(func_def_222, type, func: $i > $i > $i > $o).
% 9.49/2.72 thf(func_def_223, type, funcSet: $i > $i > $i).
% 9.49/2.72 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 9.49/2.72 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 9.49/2.72 thf(func_def_259, type, if: $i > $o > $i > $i > $i).
% 9.49/2.72 thf(func_def_334, type, sP2: $i > $i > $i > $o).
% 9.49/2.72 thf(func_def_335, type, sP3: $i > $i > $i > $i > $o).
% 9.49/2.72 thf(func_def_338, type, sP6: $i > $i > $o).
% 9.49/2.72 thf(func_def_339, type, sP7: $i > $o).
% 9.49/2.72 thf(func_def_340, type, sP8: $i > $i > $o).
% 9.49/2.72 thf(func_def_341, type, sP9: $i > $i > $o).
% 9.49/2.72 thf(func_def_343, type, sP11: $i > $i > $i > $o > $o).
% 9.49/2.72 thf(func_def_345, type, sK13: $i > $i > $i).
% 9.49/2.72 thf(func_def_362, type, sK30: $i > $i > $i > $i).
% 9.49/2.72 thf(func_def_363, type, sK31: $i > $i > $i > $i).
% 9.49/2.72 thf(func_def_378, type, sK46: $i > $o).
% 9.49/2.72 thf(func_def_393, type, sK61: $i > ($i > $i) > $i > $i).
% 9.49/2.72 thf(func_def_395, type, sK63: $i > $i).
% 9.49/2.72 thf(func_def_406, type, sK74: $i > $o).
% 9.49/2.72 thf(func_def_427, type, sK95: $i > $i).
% 9.49/2.72 thf(func_def_429, type, sK97: ($i > $o) > $i > $i > $i > $i).
% 9.49/2.72 thf(func_def_430, type, sK98: ($i > $o) > $i > $i > $i > $i).
% 9.49/2.72 thf(func_def_434, type, sK102: $i > $o).
% 9.49/2.72 thf(func_def_449, type, sK117: $i > $i > $i > $i > $i).
% 9.49/2.72 thf(func_def_454, type, sK122: ($i > $o) > $i > $i).
% 9.49/2.72 thf(func_def_456, type, sK124: $i > $o).
% 9.49/2.72 thf(func_def_459, type, sK127: $i > $i).
% 9.49/2.72 thf(func_def_482, type, sK150: $i > $o).
% 9.49/2.72 thf(func_def_489, type, sK157: $i > ($i > $o) > $i).
% 9.49/2.72 thf(func_def_490, type, sK158: $i > $o).
% 9.49/2.72 thf(func_def_497, type, sK165: $i > $i > $o).
% 9.49/2.72 thf(func_def_506, type, sK174: $i > $i > $i).
% 9.49/2.72 thf(func_def_511, type, sK179: $i > $i).
% 9.49/2.72 thf(func_def_515, type, sK183: $i > $i > $i).
% 9.49/2.72 thf(func_def_531, type, sK199: $i > $i > $i).
% 9.49/2.72 thf(func_def_557, type, sK225: $i > $i).
% 9.49/2.72 thf(func_def_558, type, sK226: $i > $i).
% 9.49/2.72 thf(func_def_573, type, sK241: $i > $o).
% 9.49/2.72 thf(func_def_574, type, sK242: $i > $o).
% 9.49/2.72 thf(func_def_575, type, sK243: ($i > $o) > ($i > $o) > $i > $i > $i).
% 9.49/2.72 thf(func_def_576, type, sK244: ($i > $o) > ($i > $o) > $i > $i > $i).
% 9.49/2.72 thf(func_def_584, type, sK252: ($i > $o) > ($i > $o) > $i).
% 9.49/2.72 thf(func_def_585, type, sK253: ($i > $o) > ($i > $o) > $i).
% 9.49/2.72 thf(func_def_586, type, sK254: $i > $o).
% 9.49/2.72 thf(func_def_587, type, sK255: $i > $o).
% 9.49/2.72 thf(func_def_589, type, sK257: $i > $i).
% 9.49/2.72 thf(func_def_591, type, sK259: $i > ($i > $i) > $i > $i).
% 9.49/2.72 thf(func_def_600, type, sK268: $i > $o).
% 9.49/2.72 thf(func_def_610, type, sK278: $i > $o).
% 9.49/2.72 thf(func_def_613, type, sK281: $i > $i > ($i > $o) > $i).
% 9.49/2.72 thf(func_def_614, type, sK282: $i > $o).
% 9.49/2.72 thf(func_def_618, type, sK286: ($i > $o) > $i).
% 9.49/2.72 thf(func_def_619, type, sK287: $i > $o).
% 9.49/2.72 thf(func_def_620, type, sK288: $i > $i).
% 9.49/2.72 thf(func_def_623, type, sK291: $i > $i > $i).
% 9.49/2.72 thf(func_def_624, type, sK292: $i > $i > $i).
% 9.49/2.72 thf(func_def_645, type, sK313: $i > $i > $i > $i > $i).
% 9.49/2.72 thf(func_def_674, type, sK342: $i > $i > $i > $i > $i).
% 9.49/2.72 thf(func_def_675, type, sK343: $i > $i > $i > $i > $i).
% 9.49/2.72 thf(func_def_683, type, sK351: $i > $i > $i > $i).
% 9.49/2.72 thf(func_def_687, type, sK355: $i > $i > $i > $i).
% 9.49/2.72 thf(func_def_698, type, sK366: $i > $o).
% 9.49/2.72 thf(func_def_699, type, sK367: $i > $o).
% 9.49/2.72 thf(func_def_700, type, sK368: ($i > $o) > ($i > $o) > $i).
% 9.49/2.72 thf(func_def_701, type, sK369: ($i > $o) > ($i > $o) > $i).
% 9.49/2.72 thf(func_def_712, type, sK380: $i > $o).
% 9.49/2.72 thf(func_def_714, type, sK382: ($i > $o) > $i > $i).
% 9.49/2.72 thf(func_def_723, type, sK391: $i > $o).
% 9.49/2.72 thf(func_def_725, type, sK393: ($i > $o) > $i).
% 9.49/2.72 thf(func_def_726, type, sK394: ($i > $o) > $i).
% 9.49/2.72 thf(func_def_741, type, sK409: $i > $i > ($i > $i) > $i).
% 9.49/2.72 thf(func_def_742, type, sK410: $i > $i).
% 9.49/2.72 thf(func_def_751, type, sK419: $i > $o).
% 9.49/2.72 thf(func_def_762, type, sK430: $i > $i).
% 9.49/2.72 thf(func_def_781, type, sK449: ($i > $o) > $i > $i).
% 9.49/2.72 thf(func_def_783, type, sK451: $i > $o).
% 9.49/2.72 thf(func_def_806, type, sK474: $i > $i > $i).
% 9.49/2.72 thf(func_def_835, type, sK503: $i > $o).
% 9.49/2.72 thf(func_def_839, type, sK507: $i > $i > $o).
% 9.49/2.72 thf(func_def_853, type, sK521: ($i > $o) > $i > $i).
% 9.49/2.72 thf(func_def_855, type, sK523: $i > $o).
% 9.49/2.72 thf(func_def_860, type, sK528: $i > $o).
% 9.49/2.72 thf(func_def_862, type, sK530: ($i > $o) > $i > $i > $i > $i).
% 9.49/2.72 thf(func_def_863, type, sK531: ($i > $o) > $i > $i > $i > $i).
% 9.49/2.72 thf(func_def_864, type, sK532: $i > $o).
% 9.49/2.72 thf(func_def_867, type, sK535: $i > $o).
% 9.49/2.72 thf(func_def_869, type, sK537: ($i > $o) > $i > $i).
% 9.49/2.72 thf(func_def_871, type, sK539: $i > $o).
% 9.49/2.72 thf(func_def_874, type, sK542: $i > ($i > $o) > $i).
% 9.49/2.72 thf(func_def_915, type, sK583: $i > $o).
% 9.49/2.72 thf(func_def_917, type, sK585: $i > ($i > $o) > $i).
% 9.49/2.72 thf(func_def_922, type, sK590: $i > $i > $i > $i > $i).
% 9.49/2.72 thf(func_def_923, type, sK591: $i > $i > $i > $i > $i).
% 9.49/2.72 thf(func_def_924, type, sK592: $i > $i > $i > $i > $i).
% 9.49/2.72 thf(func_def_925, type, sK593: $i > $i > $i > $i > $i).
% 9.49/2.72 thf(func_def_927, type, sK595: $i > $o).
% 9.49/2.72 thf(func_def_929, type, sK597: ($i > $o) > $i > $i).
% 9.49/2.72 thf(func_def_930, type, sK598: ($i > $o) > $i > $i).
% 9.49/2.72 thf(func_def_931, type, sK599: $i > ($i > $o) > $i).
% 9.49/2.72 thf(func_def_932, type, sK600: $i > $o).
% 9.49/2.72 thf(func_def_937, type, sK605: ($i > $o) > $i).
% 9.49/2.72 thf(func_def_938, type, sK606: $i > $o).
% 9.49/2.72 thf(func_def_940, type, sK608: $i > $i > $o).
% 9.49/2.72 thf(func_def_948, type, sK616: $o > $i > $i > $i).
% 9.49/2.72 thf(func_def_970, type, sK638: $i > $o).
% 9.49/2.72 thf(func_def_987, type, sK655: $i > $i > $i).
% 9.49/2.72 thf(func_def_988, type, sK656: $i > $i > $i).
% 9.49/2.72 thf(func_def_989, type, sK657: $i > $i > $i).
% 9.49/2.72 thf(func_def_990, type, sK658: $i > $i > $i).
% 9.49/2.72 thf(func_def_991, type, sK659: $i > $i > $i > $i).
% 9.49/2.72 thf(func_def_992, type, sK660: $i > $i).
% 9.49/2.72 thf(func_def_993, type, sK661: $i > $i).
% 9.49/2.72 thf(func_def_994, type, sK662: $i > $i).
% 9.49/2.72 thf(func_def_995, type, sK663: $i > $i).
% 9.49/2.72 thf(func_def_996, type, sK664: $i > $i > $i > $i).
% 9.49/2.72 thf(func_def_997, type, sK665: $i > $i > $i > $i).
% 9.49/2.72 thf(func_def_998, type, sK666: $i > $i > $i).
% 9.49/2.72 thf(func_def_999, type, sK667: $i > $i > $i).
% 9.49/2.72 thf(func_def_1000, type, sK668: $i > $i > $i).
% 9.49/2.72 thf(func_def_1002, type, sK670: $i > $i).
% 9.49/2.72 thf(func_def_1003, type, sK671: $i > $i).
% 9.49/2.72 thf(func_def_1004, type, sK672: $i > $i).
% 9.49/2.72 thf(func_def_1005, type, sK673: $i > $i > $i).
% 9.49/2.72 thf(func_def_1013, type, sK681: $i > $i > $i > $i).
% 9.49/2.72 thf(func_def_1019, type, sK687: $i > $o).
% 9.49/2.72 thf(func_def_1021, type, sK689: ($i > $o) > $i > $i).
% 9.49/2.72 thf(func_def_1022, type, sK690: ($i > $o) > $i > $i).
% 9.49/2.72 thf(func_def_1032, type, sK700: $i > $i > $o).
% 9.49/2.72 thf(func_def_1039, type, sK707: $i > $i > $i).
% 9.49/2.72 thf(func_def_1040, type, sK708: $i > $i > $i).
% 9.49/2.72 thf(func_def_1047, type, sK715: $i > $i).
% 9.49/2.72 thf(func_def_1048, type, sK716: ($i > $i) > $i > $i > $i).
% 9.49/2.72 thf(func_def_1057, type, sK725: $i > $o).
% 9.49/2.72 thf(func_def_1063, type, sK731: $i > $i > $o).
% 9.49/2.72 thf(func_def_1075, type, sK743: $i > $i > $i > $i).
% 9.49/2.72 thf(func_def_1084, type, sK752: $i > $i).
% 9.49/2.72 thf(func_def_1098, type, sK766: $i > $o).
% 9.49/2.72 thf(func_def_1129, type, sK797: $i > $i > $o).
% 9.49/2.72 thf(func_def_1130, type, sK798: $i > $i).
% 9.49/2.72 thf(func_def_1131, type, sK799: $i > $i).
% 9.49/2.72 thf(func_def_1132, type, sK800: ($i > $i > $o) > $i > $i).
% 9.49/2.72 thf(func_def_1133, type, sK801: $i > ($i > $i > $o) > $i > $i).
% 9.49/2.72 thf(func_def_1134, type, sK802: ($i > $i > $o) > $i > $i).
% 9.49/2.72 thf(func_def_1149, type, sK817: $i > $i > $o).
% 9.49/2.72 thf(func_def_1152, type, sK820: $i > $i > $i).
% 9.49/2.72 thf(func_def_1162, type, sK830: $i > $o).
% 9.49/2.72 thf(func_def_1182, type, sK850: $i > $o).
% 9.49/2.72 thf(func_def_1183, type, sK851: $i > $i).
% 9.49/2.72 thf(func_def_1184, type, sK852: ($i > $o) > $i).
% 9.49/2.72 thf(func_def_1185, type, sK853: $i > $o).
% 9.49/2.72 thf(func_def_1192, type, sK860: $i > $i > $i > $i > $i).
% 9.49/2.72 thf(func_def_1219, type, sK887: $i > $i).
% 9.49/2.72 thf(func_def_1221, type, sK889: ($i > $i) > $i > $i > $i).
% 9.49/2.72 thf(func_def_1231, type, sK899: $i > $i > $o).
% 9.49/2.72 thf(func_def_1234, type, sK902: $i > $i).
% 9.49/2.72 thf(func_def_1237, type, sK905: $i > $i > ($i > $i) > $i).
% 9.49/2.72 thf(func_def_1246, type, ph914: !>[X0: $tType]:(X0)).
% 9.49/2.72 thf(f4460,plain,(
% 9.49/2.72 $false),
% 9.49/2.72 inference(avatar_sat_refutation,[status(thm)],[f4408,f4430,f4457])).
% 9.49/2.72 thf(f4457,plain,(
% 9.49/2.72 spl913_8),
% 9.49/2.72 inference(avatar_contradiction_clause,[status(thm)],[f4456])).
% 9.49/2.72 thf(f4456,plain,(
% 9.49/2.72 $false | spl913_8),
% 9.49/2.72 inference(subsumption_resolution,[status(thm)],[f4455,f2798])).
% 9.49/2.72 thf(f2798,plain,(
% 9.49/2.72 ((in @ sK27 @ (powerset @ sK26)) = $true)),
% 9.49/2.72 inference(cnf_transformation,[status(thm)],[f1287])).
% 9.49/2.72 thf(f1287,plain,(
% 9.49/2.72 (doubleComplementEq = $true) & (dpsetconstrEL1 = $true) & (demorgan2 = $true) & (theeq = $true) & (binintersectT_lem = $true) & (setminusILneg = $true) & (singletonprop = $true) & (contraSubsetComplement = $true) & (setukpairinjR12 = $true) & (setadjoinIR = $true) & (ifSingleton = $true) & (iffalse = $true) & (setoftrueEq = $true) & (ap2apEq2 = $true) & (subsetI1 = $true) & (cartprodpairsurjEq = $true) & (descr__Cong = $true) & (emptyinPowerset = $true) & (powersetE = $true) & (eqinunit = $true) & (powersetTE1 = $true) & (eta2 = $true) & (quantDeMorgan4 = $true) & (exuE3e = $true) & (eqimpsubset1 = $true) & (nonemptyI1 = $true) & (woz13rule2 = $true) & (ubforcartprodlem2 = $true) & (nonemptyE1 = $true) & (intersectInPowersetIntersectUnions = $true) & (woz13rule0 = $true) & (setminusEL = $true) & (quantDeMorgan1 = $true) & (binintersectSubset4 = $true) & (setadjoinE = $true) & (nonemptyImpWitness = $true) & (cartprodmempaircEq = $true) & (prop2set2propI = $true) & (subsetI2 = $true) & (kpairsurjEq = $true) & (funcinfuncset = $true) & (setminusERneg = $true) & (singletoninpowerset = $true) & (powersetI1 = $true) & (powersetTI1 = $true) & (dpsetconstrSub = $true) & (prop2setE = $true) & (setminusELneg = $true) & (singletonsswitch = $true) & (emptyE1 = $true) & (quantDeMorgan3 = $true) & (app = $true) & (setukpairinjR = $true) & (demorgan2b = $true) & (woz13rule1 = $true) & (symdiffI1 = $true) & (setukpairIL = $true) & (binunionTIRcontra = $true) & (cartprodsndin = $true) & (ap2p = $true) & (setunionE = $true) & (funcImageSingleton = $true) & (setminusT_lem = $true) & (setunionsingleton = $true) & (subsetTrans = $true) & (emptyinunitempty = $true) & (dsetconstrER = $true) & (upairsetIR = $true) & (complementTcontraSubset = $true) & (demorgan1 = $true) & (setadjoinAx = $true) & (binunionRsub = $true) & (setadjoinIL = $true) & (setminusSubset2 = $true) & (binunionE = $true) & (noeltsimpempty = $true) & (beta2 = $true) & (iftrue = $true) & (inPowerset = $true) & (notdallE = $true) & (sepInPowerset = $true) & (notequalI1 = $true) & (uniqinunit = $true) & (powersetT_lem = $true) & (setminusLsub = $true) & (demorgan2a2 = $true) & (binintersectSubset5 = $true) & (dpsetconstrI = $true) & (cartprodfstin = $true) & (binintersectSubset2 = $true) & (cartprodmempair = $true) & (complementTnotintersectT = $true) & (symdiffIneg2 = $true) & (replAx = $true) & (setminusER = $true) & (notdexE = $true) & (subsetemptysetimpeq = $true) & (setukpairIR = $true) & (setbeta = $true) & (woz13rule4 = $true) & (binunionT_lem = $true) & (setextT = $true) & (setOfPairsIsBReln = $true) & (subsetRefl = $true) & (inComplementUnionImpNotIn1 = $true) & (setukpairinjL1 = $true) & (symdiffI2 = $true) & (subPowSU = $true) & (exuE3u = $true) & (binintersectRsub = $true) & (emptyI = $true) & (subsetE2 = $true) & (bs114d = $true) & (complementInPowersetComplementIntersect = $true) & (binintersectLsub = $true) & (inIntersectImpInIntersectUnions = $true) & (dpsetconstrEL2 = $true) & (prop2setI = $true) & (lam2p = $true) & (setukpairinjL2 = $true) & (complementTE1 = $true) & (singletonsuniq = $true) & (contrasubsetT1 = $true) & (notinemptyset = $true) & (emptyset__Cong = $true) & (powersetI = $true) & (setminusI = $true) & (setextAx = $true) & (demorgan2b2 = $true) & (singletonsubset = $true) & (setunionI = $true) & (funcGraphProp2 = $true) & (nonemptyI = $true) & (funcext2 = $true) & (exu__Cong = $true) & (binunionLsub = $true) & (inIntersectImpInUnion2 = $true) & (ubforcartprodlem3 = $true) & (upairsetIL = $true) & (binintersectTERcontra = $true) & (eqbreln = $true) & (subset2powerset = $true) & (funcGraphProp3 = $true) & (powersetAx = $true) & (binintersectSubset1 = $true) & (lam2lamEq = $true) & (subbreln = $true) & ((((((in @ sK29 @ (powerset @ sK26)) = $true) & ((setminus @ sK26 @ (binintersect @ (binunion @ sK25 @ sK27) @ (binunion @ sK28 @ sK29))) != (binunion @ (binintersect @ (setminus @ sK26 @ sK25) @ (setminus @ sK26 @ sK27)) @ (binintersect @ (setminus @ sK26 @ sK28) @ (setminus @ sK26 @ sK29))))) & ((in @ sK28 @ (powerset @ sK26)) = $true)) & ((in @ sK27 @ (powerset @ sK26)) = $true)) & ((in @ sK25 @ (powerset @ sK26)) = $true)) & (binunionIL = $true) & (theprop = $true) & (notequalI2 = $true) & (disjointsetsI1 = $true) & (iffalseProp2 = $true) & (iftrueProp1 = $true) & (kpairp = $true) & (kfstsingleton = $true) & (demorgan1a = $true) & (upairequniteq = $true) & (brelnall2 = $true) & (dsetconstr__Cong = $true) & (upairsetE = $true) & (quantDeMorgan2 = $true) & (setadjoin__Cong = $true) & (subsetE = $true) & (ap2apEq1 = $true) & (ksndpairEq = $true) & (setextsub = $true) & (exuI1 = $true) & (dsetconstrEL = $true) & (binintersectER = $true) & (complementImpComplementIntersect = $true) & (eta1 = $true) & (ex1E1 = $true) & (wellorderingAx = $true) & (cartprodpairin = $true) & (iffalseProp1 = $true) & (omega__Cong = $true) & (doubleComplementI1 = $true) & (doubleComplementSub2 = $true) & (setunion__Cong = $true) & (emptysetAx = $true) & (ifp = $true) & (omegaSAx = $true) & (setunionsingleton2 = $true) & (secondinupair = $true) & (setadjoinSub2 = $true) & (beta1 = $true) & (cartprodmempair1 = $true) & (cartprodpairmemER = $true) & (exuE1 = $true) & (cartprodpairmemEL = $true) & (in__Cong = $true) & (descrp = $true) & (setukpairinjR1 = $true) & (complementT_lem = $true) & (ksndsingleton = $true) & (powersetE1 = $true) & (setext = $true) & (lamProp = $true) & (inIntersectImpInUnion = $true) & (emptyInPowerset = $true) & (setunionAx = $true) & (notsubsetI = $true) & (woz13rule3 = $true) & (demorgan2a = $true) & (exuI2 = $true) & (apProp = $true) & (exuI3 = $true) & (setunionE2 = $true) & (foundationAx = $true) & (symdiffIneg1 = $true) & (brelnall1 = $true) & (setunionsingleton1 = $true) & (powersetsubset = $true) & (powerset__Cong = $true) & (binintersectI = $true) & (cartprodfstpairEq = $true) & (setukpairinjR2 = $true) & (doubleComplementE1 = $true) & (omegaIndAx = $true) & (binunionIR = $true) & (emptysetsubset = $true) & (singletoninpowunion = $true) & (contrasubsetT = $true) & (binunionTILcontra = $true) & (funcGraphProp1 = $true) & (binunionEcases = $true) & (setadjoinOr = $true) & (cartprodsndpairEq = $true) & (setukpairinjR11 = $true) & (doubleComplementSub1 = $true) & (binintersectEL = $true) & (symdiffE = $true) & (setukpairinjL = $true) & (exuE2 = $true) & (funcGraphProp4 = $true) & (binunionTEcontra = $true) & (demorgan1b = $true) & (infuncsetfunc = $true) & (dsetconstrI = $true) & (notinsingleton = $true) & (upairsubunion = $true) & (sepSubset = $true) & (ex1I2 = $true) & (iftrueProp2 = $true) & (binunionTE = $true) & (upairinpowunion = $true) & (complementTI1 = $true) & (inComplementUnionImpInComplement1 = $true) & (contrasubsetT2 = $true) & (demorgan2a1 = $true) & (lamp = $true) & (iftrueorfalse = $true) & (vacuousDall = $true) & (ubforcartprodlem1 = $true) & (funcextLem = $true) & (subsetTI = $true) & (dpsetconstrERa = $true) & (upairset2E = $true) & (setadjoinSub = $true) & (omega0Ax = $true) & (exuEu = $true) & (dpsetconstrER = $true) & (contrasubsetT3 = $true) & (complementSubsetComplementIntersect = $true) & (funcext = $true) & (kfstpairEq = $true) & (setminusIRneg = $true) & (eqimpsubset2 = $true) & (kpairiskpair = $true) & (setminusSubset1 = $true) & (ex1I = $true) & (emptysetimpfalse = $true) & (binintersectTELcontra = $true) & (emptysetE = $true) & (binintersectSubset3 = $true) & (upairset2IR = $true) & (woz1_1 = $true) & (ex1E2 = $true) & (complementUnionInPowersetComplement = $true) & (inCongP = $true)),
% 9.49/2.72 inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26,sK27,sK28,sK29])],[f1200,f1286,f1285,f1284,f1283])).
% 9.49/2.72 thf(f1283,plain,(
% 9.49/2.72 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ (powerset @ X1)) = $true) & ((setminus @ X1 @ (binintersect @ (binunion @ X0 @ X2) @ (binunion @ X3 @ X4))) != (binunion @ (binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)) @ (binintersect @ (setminus @ X1 @ X3) @ (setminus @ X1 @ X4))))) & ((in @ X3 @ (powerset @ X1)) = $true)) & ($true = (in @ X2 @ (powerset @ X1)))) & ((in @ X0 @ (powerset @ X1)) = $true)) => (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ (powerset @ sK26)) = $true) & ((setminus @ sK26 @ (binintersect @ (binunion @ sK25 @ X2) @ (binunion @ X3 @ X4))) != (binunion @ (binintersect @ (setminus @ sK26 @ sK25) @ (setminus @ sK26 @ X2)) @ (binintersect @ (setminus @ sK26 @ X3) @ (setminus @ sK26 @ X4))))) & ((in @ X3 @ (powerset @ sK26)) = $true)) & ($true = (in @ X2 @ (powerset @ sK26)))) & ((in @ sK25 @ (powerset @ sK26)) = $true))),
% 9.49/2.72 introduced(definition,[],[choice_axiom])).
% 9.49/2.72 thf(f1284,plain,(
% 9.49/2.72 ? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ (powerset @ sK26)) = $true) & ((setminus @ sK26 @ (binintersect @ (binunion @ sK25 @ X2) @ (binunion @ X3 @ X4))) != (binunion @ (binintersect @ (setminus @ sK26 @ sK25) @ (setminus @ sK26 @ X2)) @ (binintersect @ (setminus @ sK26 @ X3) @ (setminus @ sK26 @ X4))))) & ((in @ X3 @ (powerset @ sK26)) = $true)) & ($true = (in @ X2 @ (powerset @ sK26)))) => (? [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ (powerset @ sK26)) = $true) & ((binunion @ (binintersect @ (setminus @ sK26 @ sK25) @ (setminus @ sK26 @ sK27)) @ (binintersect @ (setminus @ sK26 @ X3) @ (setminus @ sK26 @ X4))) != (setminus @ sK26 @ (binintersect @ (binunion @ sK25 @ sK27) @ (binunion @ X3 @ X4))))) & ((in @ X3 @ (powerset @ sK26)) = $true)) & ((in @ sK27 @ (powerset @ sK26)) = $true))),
% 9.49/2.72 introduced(definition,[],[choice_axiom])).
% 9.49/2.72 thf(f1285,plain,(
% 9.49/2.72 ? [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ (powerset @ sK26)) = $true) & ((binunion @ (binintersect @ (setminus @ sK26 @ sK25) @ (setminus @ sK26 @ sK27)) @ (binintersect @ (setminus @ sK26 @ X3) @ (setminus @ sK26 @ X4))) != (setminus @ sK26 @ (binintersect @ (binunion @ sK25 @ sK27) @ (binunion @ X3 @ X4))))) & ((in @ X3 @ (powerset @ sK26)) = $true)) => (? [X4 : $i] : (((in @ X4 @ (powerset @ sK26)) = $true) & ((binunion @ (binintersect @ (setminus @ sK26 @ sK25) @ (setminus @ sK26 @ sK27)) @ (binintersect @ (setminus @ sK26 @ sK28) @ (setminus @ sK26 @ X4))) != (setminus @ sK26 @ (binintersect @ (binunion @ sK25 @ sK27) @ (binunion @ sK28 @ X4))))) & ((in @ sK28 @ (powerset @ sK26)) = $true))),
% 9.49/2.72 introduced(definition,[],[choice_axiom])).
% 9.49/2.72 thf(f1286,plain,(
% 9.49/2.72 ? [X4 : $i] : (((in @ X4 @ (powerset @ sK26)) = $true) & ((binunion @ (binintersect @ (setminus @ sK26 @ sK25) @ (setminus @ sK26 @ sK27)) @ (binintersect @ (setminus @ sK26 @ sK28) @ (setminus @ sK26 @ X4))) != (setminus @ sK26 @ (binintersect @ (binunion @ sK25 @ sK27) @ (binunion @ sK28 @ X4))))) => (((in @ sK29 @ (powerset @ sK26)) = $true) & ((setminus @ sK26 @ (binintersect @ (binunion @ sK25 @ sK27) @ (binunion @ sK28 @ sK29))) != (binunion @ (binintersect @ (setminus @ sK26 @ sK25) @ (setminus @ sK26 @ sK27)) @ (binintersect @ (setminus @ sK26 @ sK28) @ (setminus @ sK26 @ sK29)))))),
% 9.49/2.72 introduced(definition,[],[choice_axiom])).
% 9.49/2.72 thf(f1200,plain,(
% 9.49/2.72 (doubleComplementEq = $true) & (dpsetconstrEL1 = $true) & (demorgan2 = $true) & (theeq = $true) & (binintersectT_lem = $true) & (setminusILneg = $true) & (singletonprop = $true) & (contraSubsetComplement = $true) & (setukpairinjR12 = $true) & (setadjoinIR = $true) & (ifSingleton = $true) & (iffalse = $true) & (setoftrueEq = $true) & (ap2apEq2 = $true) & (subsetI1 = $true) & (cartprodpairsurjEq = $true) & (descr__Cong = $true) & (emptyinPowerset = $true) & (powersetE = $true) & (eqinunit = $true) & (powersetTE1 = $true) & (eta2 = $true) & (quantDeMorgan4 = $true) & (exuE3e = $true) & (eqimpsubset1 = $true) & (nonemptyI1 = $true) & (woz13rule2 = $true) & (ubforcartprodlem2 = $true) & (nonemptyE1 = $true) & (intersectInPowersetIntersectUnions = $true) & (woz13rule0 = $true) & (setminusEL = $true) & (quantDeMorgan1 = $true) & (binintersectSubset4 = $true) & (setadjoinE = $true) & (nonemptyImpWitness = $true) & (cartprodmempaircEq = $true) & (prop2set2propI = $true) & (subsetI2 = $true) & (kpairsurjEq = $true) & (funcinfuncset = $true) & (setminusERneg = $true) & (singletoninpowerset = $true) & (powersetI1 = $true) & (powersetTI1 = $true) & (dpsetconstrSub = $true) & (prop2setE = $true) & (setminusELneg = $true) & (singletonsswitch = $true) & (emptyE1 = $true) & (quantDeMorgan3 = $true) & (app = $true) & (setukpairinjR = $true) & (demorgan2b = $true) & (woz13rule1 = $true) & (symdiffI1 = $true) & (setukpairIL = $true) & (binunionTIRcontra = $true) & (cartprodsndin = $true) & (ap2p = $true) & (setunionE = $true) & (funcImageSingleton = $true) & (setminusT_lem = $true) & (setunionsingleton = $true) & (subsetTrans = $true) & (emptyinunitempty = $true) & (dsetconstrER = $true) & (upairsetIR = $true) & (complementTcontraSubset = $true) & (demorgan1 = $true) & (setadjoinAx = $true) & (binunionRsub = $true) & (setadjoinIL = $true) & (setminusSubset2 = $true) & (binunionE = $true) & (noeltsimpempty = $true) & (beta2 = $true) & (iftrue = $true) & (inPowerset = $true) & (notdallE = $true) & (sepInPowerset = $true) & (notequalI1 = $true) & (uniqinunit = $true) & (powersetT_lem = $true) & (setminusLsub = $true) & (demorgan2a2 = $true) & (binintersectSubset5 = $true) & (dpsetconstrI = $true) & (cartprodfstin = $true) & (binintersectSubset2 = $true) & (cartprodmempair = $true) & (complementTnotintersectT = $true) & (symdiffIneg2 = $true) & (replAx = $true) & (setminusER = $true) & (notdexE = $true) & (subsetemptysetimpeq = $true) & (setukpairIR = $true) & (setbeta = $true) & (woz13rule4 = $true) & (binunionT_lem = $true) & (setextT = $true) & (setOfPairsIsBReln = $true) & (subsetRefl = $true) & (inComplementUnionImpNotIn1 = $true) & (setukpairinjL1 = $true) & (symdiffI2 = $true) & (subPowSU = $true) & (exuE3u = $true) & (binintersectRsub = $true) & (emptyI = $true) & (subsetE2 = $true) & (bs114d = $true) & (complementInPowersetComplementIntersect = $true) & (binintersectLsub = $true) & (inIntersectImpInIntersectUnions = $true) & (dpsetconstrEL2 = $true) & (prop2setI = $true) & (lam2p = $true) & (setukpairinjL2 = $true) & (complementTE1 = $true) & (singletonsuniq = $true) & (contrasubsetT1 = $true) & (notinemptyset = $true) & (emptyset__Cong = $true) & (powersetI = $true) & (setminusI = $true) & (setextAx = $true) & (demorgan2b2 = $true) & (singletonsubset = $true) & (setunionI = $true) & (funcGraphProp2 = $true) & (nonemptyI = $true) & (funcext2 = $true) & (exu__Cong = $true) & (binunionLsub = $true) & (inIntersectImpInUnion2 = $true) & (ubforcartprodlem3 = $true) & (upairsetIL = $true) & (binintersectTERcontra = $true) & (eqbreln = $true) & (subset2powerset = $true) & (funcGraphProp3 = $true) & (powersetAx = $true) & (binintersectSubset1 = $true) & (lam2lamEq = $true) & (subbreln = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ (powerset @ X1)) = $true) & ((setminus @ X1 @ (binintersect @ (binunion @ X0 @ X2) @ (binunion @ X3 @ X4))) != (binunion @ (binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)) @ (binintersect @ (setminus @ X1 @ X3) @ (setminus @ X1 @ X4))))) & ((in @ X3 @ (powerset @ X1)) = $true)) & ($true = (in @ X2 @ (powerset @ X1)))) & ((in @ X0 @ (powerset @ X1)) = $true)) & (binunionIL = $true) & (theprop = $true) & (notequalI2 = $true) & (disjointsetsI1 = $true) & (iffalseProp2 = $true) & (iftrueProp1 = $true) & (kpairp = $true) & (kfstsingleton = $true) & (demorgan1a = $true) & (upairequniteq = $true) & (brelnall2 = $true) & (dsetconstr__Cong = $true) & (upairsetE = $true) & (quantDeMorgan2 = $true) & (setadjoin__Cong = $true) & (subsetE = $true) & (ap2apEq1 = $true) & (ksndpairEq = $true) & (setextsub = $true) & (exuI1 = $true) & (dsetconstrEL = $true) & (binintersectER = $true) & (complementImpComplementIntersect = $true) & (eta1 = $true) & (ex1E1 = $true) & (wellorderingAx = $true) & (cartprodpairin = $true) & (iffalseProp1 = $true) & (omega__Cong = $true) & (doubleComplementI1 = $true) & (doubleComplementSub2 = $true) & (setunion__Cong = $true) & (emptysetAx = $true) & (ifp = $true) & (omegaSAx = $true) & (setunionsingleton2 = $true) & (secondinupair = $true) & (setadjoinSub2 = $true) & (beta1 = $true) & (cartprodmempair1 = $true) & (cartprodpairmemER = $true) & (exuE1 = $true) & (cartprodpairmemEL = $true) & (in__Cong = $true) & (descrp = $true) & (setukpairinjR1 = $true) & (complementT_lem = $true) & (ksndsingleton = $true) & (powersetE1 = $true) & (setext = $true) & (lamProp = $true) & (inIntersectImpInUnion = $true) & (emptyInPowerset = $true) & (setunionAx = $true) & (notsubsetI = $true) & (woz13rule3 = $true) & (demorgan2a = $true) & (exuI2 = $true) & (apProp = $true) & (exuI3 = $true) & (setunionE2 = $true) & (foundationAx = $true) & (symdiffIneg1 = $true) & (brelnall1 = $true) & (setunionsingleton1 = $true) & (powersetsubset = $true) & (powerset__Cong = $true) & (binintersectI = $true) & (cartprodfstpairEq = $true) & (setukpairinjR2 = $true) & (doubleComplementE1 = $true) & (omegaIndAx = $true) & (binunionIR = $true) & (emptysetsubset = $true) & (singletoninpowunion = $true) & (contrasubsetT = $true) & (binunionTILcontra = $true) & (funcGraphProp1 = $true) & (binunionEcases = $true) & (setadjoinOr = $true) & (cartprodsndpairEq = $true) & (setukpairinjR11 = $true) & (doubleComplementSub1 = $true) & (binintersectEL = $true) & (symdiffE = $true) & (setukpairinjL = $true) & (exuE2 = $true) & (funcGraphProp4 = $true) & (binunionTEcontra = $true) & (demorgan1b = $true) & (infuncsetfunc = $true) & (dsetconstrI = $true) & (notinsingleton = $true) & (upairsubunion = $true) & (sepSubset = $true) & (ex1I2 = $true) & (iftrueProp2 = $true) & (binunionTE = $true) & (upairinpowunion = $true) & (complementTI1 = $true) & (inComplementUnionImpInComplement1 = $true) & (contrasubsetT2 = $true) & (demorgan2a1 = $true) & (lamp = $true) & (iftrueorfalse = $true) & (vacuousDall = $true) & (ubforcartprodlem1 = $true) & (funcextLem = $true) & (subsetTI = $true) & (dpsetconstrERa = $true) & (upairset2E = $true) & (setadjoinSub = $true) & (omega0Ax = $true) & (exuEu = $true) & (dpsetconstrER = $true) & (contrasubsetT3 = $true) & (complementSubsetComplementIntersect = $true) & (funcext = $true) & (kfstpairEq = $true) & (setminusIRneg = $true) & (eqimpsubset2 = $true) & (kpairiskpair = $true) & (setminusSubset1 = $true) & (ex1I = $true) & (emptysetimpfalse = $true) & (binintersectTELcontra = $true) & (emptysetE = $true) & (binintersectSubset3 = $true) & (upairset2IR = $true) & (woz1_1 = $true) & (ex1E2 = $true) & (complementUnionInPowersetComplement = $true) & (inCongP = $true)),
% 9.49/2.72 inference(flattening,[status(thm)],[f1199])).
% 9.49/2.72 thf(f1199,plain,(
% 9.49/2.72 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ (powerset @ X1)) = $true) & ((setminus @ X1 @ (binintersect @ (binunion @ X0 @ X2) @ (binunion @ X3 @ X4))) != (binunion @ (binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)) @ (binintersect @ (setminus @ X1 @ X3) @ (setminus @ X1 @ X4))))) & ((in @ X3 @ (powerset @ X1)) = $true)) & ($true = (in @ X2 @ (powerset @ X1)))) & ((in @ X0 @ (powerset @ X1)) = $true)) & (woz1_1 = $true)) & (woz13rule4 = $true)) & (woz13rule3 = $true)) & (woz13rule2 = $true)) & (woz13rule1 = $true)) & (woz13rule0 = $true)) & (demorgan2 = $true)) & (demorgan2b = $true)) & (demorgan2b2 = $true)) & (demorgan2a = $true)) & (demorgan1 = $true)) & (demorgan1b = $true)) & (demorgan1a = $true)) & (demorgan2a2 = $true)) & (complementUnionInPowersetComplement = $true)) & (demorgan2a1 = $true)) & (binunionTEcontra = $true)) & (binunionTE = $true)) & (inComplementUnionImpInComplement1 = $true)) & (inComplementUnionImpNotIn1 = $true)) & (intersectInPowersetIntersectUnions = $true)) & (inIntersectImpInIntersectUnions = $true)) & (inIntersectImpInUnion2 = $true)) & (inIntersectImpInUnion = $true)) & (binunionTIRcontra = $true)) & (binunionTILcontra = $true)) & (complementTcontraSubset = $true)) & (contraSubsetComplement = $true)) & (complementInPowersetComplementIntersect = $true)) & (complementSubsetComplementIntersect = $true)) & (complementImpComplementIntersect = $true)) & (complementTnotintersectT = $true)) & (doubleComplementEq = $true)) & (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)),
% 9.49/2.72 inference(ennf_transformation,[status(thm)],[f614])).
% 9.49/2.72 thf(f614,plain,(
% 9.49/2.72 ~((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) => ((doubleComplementEq = $true) => ((complementTnotintersectT = $true) => ((complementImpComplementIntersect = $true) => ((complementSubsetComplementIntersect = $true) => ((complementInPowersetComplementIntersect = $true) => ((contraSubsetComplement = $true) => ((complementTcontraSubset = $true) => ((binunionTILcontra = $true) => ((binunionTIRcontra = $true) => ((inIntersectImpInUnion = $true) => ((inIntersectImpInUnion2 = $true) => ((inIntersectImpInIntersectUnions = $true) => ((intersectInPowersetIntersectUnions = $true) => ((inComplementUnionImpNotIn1 = $true) => ((inComplementUnionImpInComplement1 = $true) => ((binunionTE = $true) => ((binunionTEcontra = $true) => ((demorgan2a1 = $true) => ((complementUnionInPowersetComplement = $true) => ((demorgan2a2 = $true) => ((demorgan1a = $true) => ((demorgan1b = $true) => ((demorgan1 = $true) => ((demorgan2a = $true) => ((demorgan2b2 = $true) => ((demorgan2b = $true) => ((demorgan2 = $true) => ((woz13rule0 = $true) => ((woz13rule1 = $true) => ((woz13rule2 = $true) => ((woz13rule3 = $true) => ((woz13rule4 = $true) => ((woz1_1 = $true) => ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) => ! [X3 : $i] : (((in @ X3 @ (powerset @ X1)) = $true) => ! [X4 : $i] : (((in @ X4 @ (powerset @ X1)) = $true) => ((setminus @ X1 @ (binintersect @ (binunion @ X0 @ X2) @ (binunion @ X3 @ X4))) = (binunion @ (binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)) @ (binintersect @ (setminus @ X1 @ X3) @ (setminus @ X1 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 9.49/2.72 inference(fool_elimination,[status(thm)],[f613])).
% 9.49/2.72 thf(f613,plain,(
% 9.49/2.72 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X1)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X1)) => ((setminus @ X1 @ (binintersect @ (binunion @ X0 @ X2) @ (binunion @ X3 @ X4))) = (binunion @ (binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)) @ (binintersect @ (setminus @ X1 @ X3) @ (setminus @ X1 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 9.49/2.72 inference(rectify,[status(thm)],[f286])).
% 9.49/2.72 thf(f286,negated_conjecture,(
% 9.49/2.72 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => ! [X11 : $i,X3 : $i] : ((in @ X11 @ (powerset @ X3)) => ! [X16 : $i] : ((in @ X16 @ (powerset @ X3)) => ! [X17 : $i] : ((in @ X17 @ (powerset @ X3)) => ! [X18 : $i] : ((in @ X18 @ (powerset @ X3)) => ((setminus @ X3 @ (binintersect @ (binunion @ X11 @ X16) @ (binunion @ X17 @ X18))) = (binunion @ (binintersect @ (setminus @ X3 @ X11) @ (setminus @ X3 @ X16)) @ (binintersect @ (setminus @ X3 @ X17) @ (setminus @ X3 @ X18))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 9.49/2.72 inference(negated_conjecture,[status(cth)],[f285])).
% 9.49/2.72 thf(f285,conjecture,(
% 9.49/2.72 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => ! [X11 : $i,X3 : $i] : ((in @ X11 @ (powerset @ X3)) => ! [X16 : $i] : ((in @ X16 @ (powerset @ X3)) => ! [X17 : $i] : ((in @ X17 @ (powerset @ X3)) => ! [X18 : $i] : ((in @ X18 @ (powerset @ X3)) => ((setminus @ X3 @ (binintersect @ (binunion @ X11 @ X16) @ (binunion @ X17 @ X18))) = (binunion @ (binintersect @ (setminus @ X3 @ X11) @ (setminus @ X3 @ X16)) @ (binintersect @ (setminus @ X3 @ X17) @ (setminus @ X3 @ X18)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 9.49/2.72 file('/export/starexec/sandbox2/tmp/tmp.AAoQ5tR61a/DTF2THF_10139.p',woz1_2)).
% 9.49/2.72 thf(f4455,plain,(
% 9.49/2.72 ((in @ sK27 @ (powerset @ sK26)) != $true) | spl913_8),
% 9.49/2.72 inference(subsumption_resolution,[status(thm)],[f4454,f2848])).
% 9.49/2.72 thf(f2848,plain,(
% 9.49/2.72 (binunionT_lem = $true)),
% 9.49/2.72 inference(cnf_transformation,[status(thm)],[f1287])).
% 9.49/2.72 thf(f4454,plain,(
% 9.49/2.72 (binunionT_lem != $true) | ((in @ sK27 @ (powerset @ sK26)) != $true) | spl913_8),
% 9.49/2.72 inference(subsumption_resolution,[status(thm)],[f4445,f2797])).
% 9.49/2.72 thf(f2797,plain,(
% 9.49/2.72 ((in @ sK25 @ (powerset @ sK26)) = $true)),
% 9.49/2.72 inference(cnf_transformation,[status(thm)],[f1287])).
% 9.49/2.72 thf(f4445,plain,(
% 9.49/2.72 ((in @ sK25 @ (powerset @ sK26)) != $true) | ((in @ sK27 @ (powerset @ sK26)) != $true) | (binunionT_lem != $true) | spl913_8),
% 9.49/2.72 inference(trivial_inequality_removal,[status(thm)],[f4435])).
% 9.49/2.72 thf(f4435,plain,(
% 9.49/2.72 (binunionT_lem != $true) | ((in @ sK25 @ (powerset @ sK26)) != $true) | ($true != $true) | ((in @ sK27 @ (powerset @ sK26)) != $true) | spl913_8),
% 9.49/2.72 inference(superposition,[status(thm)],[f4407,f4052])).
% 9.49/2.72 thf(f4052,plain,(
% 9.49/2.72 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (binunion @ X1 @ X2) @ (powerset @ X0)) = $true) | (binunionT_lem != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true)) )),
% 9.49/2.72 inference(cnf_transformation,[status(thm)],[f2523])).
% 9.49/2.72 thf(f2523,plain,(
% 9.49/2.72 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ (binunion @ X1 @ X2) @ (powerset @ X0)) = $true) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) | (binunionT_lem != $true)) & ((binunionT_lem = $true) | ((($true != (in @ (binunion @ sK828 @ sK829) @ (powerset @ sK827))) & ((in @ sK829 @ (powerset @ sK827)) = $true)) & ((in @ sK828 @ (powerset @ sK827)) = $true)))),
% 9.49/2.72 inference(skolemisation,[status(esa),new_symbols(skolem,[sK827,sK828,sK829])],[f2520,f2522,f2521])).
% 9.49/2.72 thf(f2521,plain,(
% 9.49/2.72 ? [X3 : $i,X4 : $i] : (? [X5 : $i] : (($true != (in @ (binunion @ X4 @ X5) @ (powerset @ X3))) & ((in @ X5 @ (powerset @ X3)) = $true)) & ((in @ X4 @ (powerset @ X3)) = $true)) => (? [X5 : $i] : (($true != (in @ (binunion @ sK828 @ X5) @ (powerset @ sK827))) & ((in @ X5 @ (powerset @ sK827)) = $true)) & ((in @ sK828 @ (powerset @ sK827)) = $true))),
% 9.49/2.72 introduced(definition,[],[choice_axiom])).
% 9.49/2.72 thf(f2522,plain,(
% 9.49/2.72 ? [X5 : $i] : (($true != (in @ (binunion @ sK828 @ X5) @ (powerset @ sK827))) & ((in @ X5 @ (powerset @ sK827)) = $true)) => (($true != (in @ (binunion @ sK828 @ sK829) @ (powerset @ sK827))) & ((in @ sK829 @ (powerset @ sK827)) = $true))),
% 9.49/2.72 introduced(definition,[],[choice_axiom])).
% 9.49/2.72 thf(f2520,plain,(
% 9.49/2.72 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ (binunion @ X1 @ X2) @ (powerset @ X0)) = $true) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) | (binunionT_lem != $true)) & ((binunionT_lem = $true) | ? [X3 : $i,X4 : $i] : (? [X5 : $i] : (($true != (in @ (binunion @ X4 @ X5) @ (powerset @ X3))) & ((in @ X5 @ (powerset @ X3)) = $true)) & ((in @ X4 @ (powerset @ X3)) = $true)))),
% 9.49/2.72 inference(rectify,[status(thm)],[f2519])).
% 9.49/2.72 thf(f2519,plain,(
% 9.49/2.72 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ (binunion @ X1 @ X2) @ (powerset @ X0)) = $true) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) | (binunionT_lem != $true)) & ((binunionT_lem = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ (binunion @ X1 @ X2) @ (powerset @ X0)) != $true) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)))),
% 9.49/2.72 inference(nnf_transformation,[status(thm)],[f1089])).
% 9.49/2.72 thf(f1089,plain,(
% 9.49/2.72 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ (binunion @ X1 @ X2) @ (powerset @ X0)) = $true) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) <=> (binunionT_lem = $true)),
% 9.49/2.72 inference(ennf_transformation,[status(thm)],[f843])).
% 9.49/2.72 thf(f843,plain,(
% 9.49/2.72 ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ((in @ (binunion @ X1 @ X2) @ (powerset @ X0)) = $true))) <=> (binunionT_lem = $true)),
% 9.49/2.72 inference(fool_elimination,[status(thm)],[f842])).
% 9.49/2.72 thf(f842,plain,(
% 9.49/2.72 (binunionT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binunion @ X1 @ X2) @ (powerset @ X0)))))),
% 9.49/2.72 inference(rectify,[status(thm)],[f232])).
% 9.49/2.72 thf(f232,axiom,(
% 9.49/2.72 (binunionT_lem = ! [X3 : $i,X11 : $i] : ((in @ X11 @ (powerset @ X3)) => ! [X16 : $i] : ((in @ X16 @ (powerset @ X3)) => (in @ (binunion @ X11 @ X16) @ (powerset @ X3)))))),
% 9.49/2.72 file('/export/starexec/sandbox2/tmp/tmp.AAoQ5tR61a/DTF2THF_10139.p',binunionT_lem)).
% 9.49/2.72 thf(f4407,plain,(
% 9.49/2.72 ((in @ (binunion @ sK25 @ sK27) @ (powerset @ sK26)) != $true) | spl913_8),
% 9.49/2.72 inference(avatar_component_clause,[status(thm)],[f4405])).
% 9.49/2.72 thf(f4405,definition,(
% 9.49/2.72 spl913_8 <=> ((in @ (binunion @ sK25 @ sK27) @ (powerset @ sK26)) = $true)),
% 9.49/2.72 introduced(definition,[new_symbols(naming,[spl913_8])],[avatar_definition])).
% 9.49/2.72 thf(f4430,plain,(
% 9.49/2.72 spl913_7),
% 9.49/2.72 inference(avatar_contradiction_clause,[status(thm)],[f4429])).
% 9.49/2.72 thf(f4429,plain,(
% 9.49/2.72 $false | spl913_7),
% 9.49/2.72 inference(subsumption_resolution,[status(thm)],[f4428,f2848])).
% 9.49/2.72 thf(f4428,plain,(
% 9.49/2.72 (binunionT_lem != $true) | spl913_7),
% 9.49/2.72 inference(subsumption_resolution,[status(thm)],[f4427,f2799])).
% 9.49/2.72 thf(f2799,plain,(
% 9.49/2.72 ((in @ sK28 @ (powerset @ sK26)) = $true)),
% 9.49/2.72 inference(cnf_transformation,[status(thm)],[f1287])).
% 9.49/2.72 thf(f4427,plain,(
% 9.49/2.72 ((in @ sK28 @ (powerset @ sK26)) != $true) | (binunionT_lem != $true) | spl913_7),
% 9.49/2.72 inference(subsumption_resolution,[status(thm)],[f4423,f2801])).
% 9.49/2.72 thf(f2801,plain,(
% 9.49/2.72 ((in @ sK29 @ (powerset @ sK26)) = $true)),
% 9.49/2.72 inference(cnf_transformation,[status(thm)],[f1287])).
% 9.49/2.72 thf(f4423,plain,(
% 9.49/2.72 ((in @ sK29 @ (powerset @ sK26)) != $true) | (binunionT_lem != $true) | ((in @ sK28 @ (powerset @ sK26)) != $true) | spl913_7),
% 9.49/2.72 inference(trivial_inequality_removal,[status(thm)],[f4410])).
% 9.49/2.72 thf(f4410,plain,(
% 9.49/2.72 ((in @ sK28 @ (powerset @ sK26)) != $true) | (binunionT_lem != $true) | ((in @ sK29 @ (powerset @ sK26)) != $true) | ($true != $true) | spl913_7),
% 9.49/2.72 inference(superposition,[status(thm)],[f4403,f4052])).
% 9.49/2.72 thf(f4403,plain,(
% 9.49/2.72 ((in @ (binunion @ sK28 @ sK29) @ (powerset @ sK26)) != $true) | spl913_7),
% 9.49/2.72 inference(avatar_component_clause,[status(thm)],[f4401])).
% 9.49/2.72 thf(f4401,definition,(
% 9.49/2.72 spl913_7 <=> ((in @ (binunion @ sK28 @ sK29) @ (powerset @ sK26)) = $true)),
% 9.49/2.72 introduced(definition,[new_symbols(naming,[spl913_7])],[avatar_definition])).
% 9.49/2.72 thf(f4408,plain,(
% 9.49/2.72 ~spl913_7 | ~spl913_8),
% 9.49/2.72 inference(avatar_split_clause,[status(thm)],[f4399,f4405,f4401])).
% 9.49/2.72 thf(f4399,plain,(
% 9.49/2.72 ((in @ (binunion @ sK28 @ sK29) @ (powerset @ sK26)) != $true) | ((in @ (binunion @ sK25 @ sK27) @ (powerset @ sK26)) != $true)),
% 9.49/2.72 inference(subsumption_resolution,[status(thm)],[f4398,f2879])).
% 9.49/2.72 thf(f2879,plain,(
% 9.49/2.72 (demorgan1 = $true)),
% 9.49/2.72 inference(cnf_transformation,[status(thm)],[f1287])).
% 9.49/2.72 thf(f4398,plain,(
% 9.49/2.72 ((in @ (binunion @ sK25 @ sK27) @ (powerset @ sK26)) != $true) | ((in @ (binunion @ sK28 @ sK29) @ (powerset @ sK26)) != $true) | (demorgan1 != $true)),
% 9.49/2.72 inference(trivial_inequality_removal,[status(thm)],[f4397])).
% 9.49/2.72 thf(f4397,plain,(
% 9.49/2.72 (demorgan1 != $true) | ((in @ (binunion @ sK28 @ sK29) @ (powerset @ sK26)) != $true) | ((in @ (binunion @ sK25 @ sK27) @ (powerset @ sK26)) != $true) | ((setminus @ sK26 @ (binintersect @ (binunion @ sK25 @ sK27) @ (binunion @ sK28 @ sK29))) != (setminus @ sK26 @ (binintersect @ (binunion @ sK25 @ sK27) @ (binunion @ sK28 @ sK29))))),
% 9.49/2.72 inference(superposition,[status(thm)],[f4396,f3537])).
% 9.49/2.72 thf(f3537,plain,(
% 9.49/2.72 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) = (setminus @ X0 @ (binintersect @ X1 @ X2))) | (demorgan1 != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true)) )),
% 9.49/2.72 inference(cnf_transformation,[status(thm)],[f1965])).
% 9.49/2.72 thf(f1965,plain,(
% 9.49/2.72 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) = (setminus @ X0 @ (binintersect @ X1 @ X2)))) | ((in @ X1 @ (powerset @ X0)) != $true)) | (demorgan1 != $true)) & ((demorgan1 = $true) | ((((in @ sK466 @ (powerset @ sK464)) = $true) & ((binunion @ (setminus @ sK464 @ sK465) @ (setminus @ sK464 @ sK466)) != (setminus @ sK464 @ (binintersect @ sK465 @ sK466)))) & ((in @ sK465 @ (powerset @ sK464)) = $true)))),
% 9.49/2.72 inference(skolemisation,[status(esa),new_symbols(skolem,[sK464,sK465,sK466])],[f1962,f1964,f1963])).
% 9.49/2.72 thf(f1963,plain,(
% 9.49/2.72 ? [X3 : $i,X4 : $i] : (? [X5 : $i] : (((in @ X5 @ (powerset @ X3)) = $true) & ((binunion @ (setminus @ X3 @ X4) @ (setminus @ X3 @ X5)) != (setminus @ X3 @ (binintersect @ X4 @ X5)))) & ((in @ X4 @ (powerset @ X3)) = $true)) => (? [X5 : $i] : (((in @ X5 @ (powerset @ sK464)) = $true) & ((setminus @ sK464 @ (binintersect @ sK465 @ X5)) != (binunion @ (setminus @ sK464 @ sK465) @ (setminus @ sK464 @ X5)))) & ((in @ sK465 @ (powerset @ sK464)) = $true))),
% 9.49/2.72 introduced(definition,[],[choice_axiom])).
% 9.49/2.72 thf(f1964,plain,(
% 9.49/2.72 ? [X5 : $i] : (((in @ X5 @ (powerset @ sK464)) = $true) & ((setminus @ sK464 @ (binintersect @ sK465 @ X5)) != (binunion @ (setminus @ sK464 @ sK465) @ (setminus @ sK464 @ X5)))) => (((in @ sK466 @ (powerset @ sK464)) = $true) & ((binunion @ (setminus @ sK464 @ sK465) @ (setminus @ sK464 @ sK466)) != (setminus @ sK464 @ (binintersect @ sK465 @ sK466))))),
% 9.49/2.72 introduced(definition,[],[choice_axiom])).
% 9.49/2.72 thf(f1962,plain,(
% 9.49/2.72 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) = (setminus @ X0 @ (binintersect @ X1 @ X2)))) | ((in @ X1 @ (powerset @ X0)) != $true)) | (demorgan1 != $true)) & ((demorgan1 = $true) | ? [X3 : $i,X4 : $i] : (? [X5 : $i] : (((in @ X5 @ (powerset @ X3)) = $true) & ((binunion @ (setminus @ X3 @ X4) @ (setminus @ X3 @ X5)) != (setminus @ X3 @ (binintersect @ X4 @ X5)))) & ((in @ X4 @ (powerset @ X3)) = $true)))),
% 9.49/2.72 inference(rectify,[status(thm)],[f1961])).
% 9.49/2.72 thf(f1961,plain,(
% 9.49/2.72 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) = (setminus @ X0 @ (binintersect @ X1 @ X2)))) | ((in @ X1 @ (powerset @ X0)) != $true)) | (demorgan1 != $true)) & ((demorgan1 = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) & ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) != (setminus @ X0 @ (binintersect @ X1 @ X2)))) & ((in @ X1 @ (powerset @ X0)) = $true)))),
% 9.49/2.72 inference(nnf_transformation,[status(thm)],[f1079])).
% 9.49/2.72 thf(f1079,plain,(
% 9.49/2.72 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) = (setminus @ X0 @ (binintersect @ X1 @ X2)))) | ((in @ X1 @ (powerset @ X0)) != $true)) <=> (demorgan1 = $true)),
% 9.49/2.72 inference(ennf_transformation,[status(thm)],[f742])).
% 9.49/2.72 thf(f742,plain,(
% 9.49/2.72 ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) = (setminus @ X0 @ (binintersect @ X1 @ X2))))) <=> (demorgan1 = $true)),
% 9.49/2.72 inference(fool_elimination,[status(thm)],[f741])).
% 9.49/2.72 thf(f741,plain,(
% 9.49/2.72 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) = (setminus @ X0 @ (binintersect @ X1 @ X2))))) = demorgan1)),
% 9.49/2.72 inference(rectify,[status(thm)],[f274])).
% 9.49/2.72 thf(f274,axiom,(
% 9.49/2.72 (! [X3 : $i,X11 : $i] : ((in @ X11 @ (powerset @ X3)) => ! [X16 : $i] : ((in @ X16 @ (powerset @ X3)) => ((setminus @ X3 @ (binintersect @ X11 @ X16)) = (binunion @ (setminus @ X3 @ X11) @ (setminus @ X3 @ X16))))) = demorgan1)),
% 9.49/2.72 file('/export/starexec/sandbox2/tmp/tmp.AAoQ5tR61a/DTF2THF_10139.p',demorgan1)).
% 9.49/2.72 thf(f4396,plain,(
% 9.49/2.72 ((setminus @ sK26 @ (binintersect @ (binunion @ sK25 @ sK27) @ (binunion @ sK28 @ sK29))) != (binunion @ (setminus @ sK26 @ (binunion @ sK25 @ sK27)) @ (setminus @ sK26 @ (binunion @ sK28 @ sK29))))),
% 9.49/2.72 inference(subsumption_resolution,[status(thm)],[f4395,f2797])).
% 9.49/2.72 thf(f4395,plain,(
% 9.49/2.72 ((in @ sK25 @ (powerset @ sK26)) != $true) | ((setminus @ sK26 @ (binintersect @ (binunion @ sK25 @ sK27) @ (binunion @ sK28 @ sK29))) != (binunion @ (setminus @ sK26 @ (binunion @ sK25 @ sK27)) @ (setminus @ sK26 @ (binunion @ sK28 @ sK29))))),
% 9.49/2.72 inference(subsumption_resolution,[status(thm)],[f4394,f2946])).
% 9.49/2.72 thf(f2946,plain,(
% 9.49/2.72 (demorgan2 = $true)),
% 9.49/2.72 inference(cnf_transformation,[status(thm)],[f1287])).
% 9.49/2.72 thf(f4394,plain,(
% 9.49/2.72 (demorgan2 != $true) | ((in @ sK25 @ (powerset @ sK26)) != $true) | ((setminus @ sK26 @ (binintersect @ (binunion @ sK25 @ sK27) @ (binunion @ sK28 @ sK29))) != (binunion @ (setminus @ sK26 @ (binunion @ sK25 @ sK27)) @ (setminus @ sK26 @ (binunion @ sK28 @ sK29))))),
% 9.49/2.72 inference(subsumption_resolution,[status(thm)],[f4393,f2798])).
% 9.49/2.72 thf(f4393,plain,(
% 9.49/2.72 ((in @ sK27 @ (powerset @ sK26)) != $true) | ((setminus @ sK26 @ (binintersect @ (binunion @ sK25 @ sK27) @ (binunion @ sK28 @ sK29))) != (binunion @ (setminus @ sK26 @ (binunion @ sK25 @ sK27)) @ (setminus @ sK26 @ (binunion @ sK28 @ sK29)))) | (demorgan2 != $true) | ((in @ sK25 @ (powerset @ sK26)) != $true)),
% 9.49/2.72 inference(superposition,[status(thm)],[f4333,f3599])).
% 9.49/2.72 thf(f3599,plain,(
% 9.49/2.72 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((setminus @ X4 @ (binunion @ X3 @ X5)) = (binintersect @ (setminus @ X4 @ X3) @ (setminus @ X4 @ X5))) | (demorgan2 != $true) | ((in @ X5 @ (powerset @ X4)) != $true) | ((in @ X3 @ (powerset @ X4)) != $true)) )),
% 9.49/2.72 inference(cnf_transformation,[status(thm)],[f2041])).
% 9.49/2.72 thf(f2041,plain,(
% 9.49/2.72 ((demorgan2 = $true) | ((((setminus @ sK516 @ (binunion @ sK515 @ sK517)) != (binintersect @ (setminus @ sK516 @ sK515) @ (setminus @ sK516 @ sK517))) & ($true = (in @ sK517 @ (powerset @ sK516)))) & ($true = (in @ sK515 @ (powerset @ sK516))))) & (! [X3 : $i,X4 : $i] : (! [X5 : $i] : (((setminus @ X4 @ (binunion @ X3 @ X5)) = (binintersect @ (setminus @ X4 @ X3) @ (setminus @ X4 @ X5))) | ((in @ X5 @ (powerset @ X4)) != $true)) | ((in @ X3 @ (powerset @ X4)) != $true)) | (demorgan2 != $true))),
% 9.49/2.72 inference(skolemisation,[status(esa),new_symbols(skolem,[sK515,sK516,sK517])],[f2038,f2040,f2039])).
% 9.49/2.72 thf(f2039,plain,(
% 9.49/2.72 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)) != (setminus @ X1 @ (binunion @ X0 @ X2))) & ($true = (in @ X2 @ (powerset @ X1)))) & ((in @ X0 @ (powerset @ X1)) = $true)) => (? [X2 : $i] : (((binintersect @ (setminus @ sK516 @ sK515) @ (setminus @ sK516 @ X2)) != (setminus @ sK516 @ (binunion @ sK515 @ X2))) & ((in @ X2 @ (powerset @ sK516)) = $true)) & ($true = (in @ sK515 @ (powerset @ sK516))))),
% 9.49/2.72 introduced(definition,[],[choice_axiom])).
% 9.49/2.72 thf(f2040,plain,(
% 9.49/2.72 ? [X2 : $i] : (((binintersect @ (setminus @ sK516 @ sK515) @ (setminus @ sK516 @ X2)) != (setminus @ sK516 @ (binunion @ sK515 @ X2))) & ((in @ X2 @ (powerset @ sK516)) = $true)) => (((setminus @ sK516 @ (binunion @ sK515 @ sK517)) != (binintersect @ (setminus @ sK516 @ sK515) @ (setminus @ sK516 @ sK517))) & ($true = (in @ sK517 @ (powerset @ sK516))))),
% 9.49/2.72 introduced(definition,[],[choice_axiom])).
% 9.49/2.72 thf(f2038,plain,(
% 9.49/2.72 ((demorgan2 = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)) != (setminus @ X1 @ (binunion @ X0 @ X2))) & ($true = (in @ X2 @ (powerset @ X1)))) & ((in @ X0 @ (powerset @ X1)) = $true))) & (! [X3 : $i,X4 : $i] : (! [X5 : $i] : (((setminus @ X4 @ (binunion @ X3 @ X5)) = (binintersect @ (setminus @ X4 @ X3) @ (setminus @ X4 @ X5))) | ((in @ X5 @ (powerset @ X4)) != $true)) | ((in @ X3 @ (powerset @ X4)) != $true)) | (demorgan2 != $true))),
% 9.49/2.72 inference(rectify,[status(thm)],[f2037])).
% 9.49/2.72 thf(f2037,plain,(
% 9.49/2.72 ((demorgan2 = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (((binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)) != (setminus @ X1 @ (binunion @ X0 @ X2))) & ($true = (in @ X2 @ (powerset @ X1)))) & ((in @ X0 @ (powerset @ X1)) = $true))) & (! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)) = (setminus @ X1 @ (binunion @ X0 @ X2))) | ($true != (in @ X2 @ (powerset @ X1)))) | ((in @ X0 @ (powerset @ X1)) != $true)) | (demorgan2 != $true))),
% 9.49/2.72 inference(nnf_transformation,[status(thm)],[f1028])).
% 9.49/2.72 thf(f1028,plain,(
% 9.49/2.72 (demorgan2 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)) = (setminus @ X1 @ (binunion @ X0 @ X2))) | ($true != (in @ X2 @ (powerset @ X1)))) | ((in @ X0 @ (powerset @ X1)) != $true))),
% 9.49/2.72 inference(ennf_transformation,[status(thm)],[f395])).
% 9.49/2.72 thf(f395,plain,(
% 9.49/2.72 (demorgan2 = $true) <=> ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) => ((binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)) = (setminus @ X1 @ (binunion @ X0 @ X2)))))),
% 9.49/2.72 inference(fool_elimination,[status(thm)],[f394])).
% 9.49/2.72 thf(f394,plain,(
% 9.49/2.72 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ((binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)) = (setminus @ X1 @ (binunion @ X0 @ X2))))) = demorgan2)),
% 9.49/2.72 inference(rectify,[status(thm)],[f278])).
% 9.49/2.72 thf(f278,axiom,(
% 9.49/2.72 (! [X11 : $i,X3 : $i] : ((in @ X11 @ (powerset @ X3)) => ! [X16 : $i] : ((in @ X16 @ (powerset @ X3)) => ((setminus @ X3 @ (binunion @ X11 @ X16)) = (binintersect @ (setminus @ X3 @ X11) @ (setminus @ X3 @ X16))))) = demorgan2)),
% 9.49/2.72 file('/export/starexec/sandbox2/tmp/tmp.AAoQ5tR61a/DTF2THF_10139.p',demorgan2)).
% 9.49/2.72 thf(f4333,plain,(
% 9.49/2.72 ((setminus @ sK26 @ (binintersect @ (binunion @ sK25 @ sK27) @ (binunion @ sK28 @ sK29))) != (binunion @ (binintersect @ (setminus @ sK26 @ sK25) @ (setminus @ sK26 @ sK27)) @ (setminus @ sK26 @ (binunion @ sK28 @ sK29))))),
% 9.49/2.72 inference(subsumption_resolution,[status(thm)],[f4332,f2799])).
% 9.49/2.72 thf(f4332,plain,(
% 9.49/2.72 ((in @ sK28 @ (powerset @ sK26)) != $true) | ((setminus @ sK26 @ (binintersect @ (binunion @ sK25 @ sK27) @ (binunion @ sK28 @ sK29))) != (binunion @ (binintersect @ (setminus @ sK26 @ sK25) @ (setminus @ sK26 @ sK27)) @ (setminus @ sK26 @ (binunion @ sK28 @ sK29))))),
% 9.49/2.72 inference(subsumption_resolution,[status(thm)],[f4331,f2801])).
% 9.49/2.72 thf(f4331,plain,(
% 9.49/2.72 ((setminus @ sK26 @ (binintersect @ (binunion @ sK25 @ sK27) @ (binunion @ sK28 @ sK29))) != (binunion @ (binintersect @ (setminus @ sK26 @ sK25) @ (setminus @ sK26 @ sK27)) @ (setminus @ sK26 @ (binunion @ sK28 @ sK29)))) | ((in @ sK29 @ (powerset @ sK26)) != $true) | ((in @ sK28 @ (powerset @ sK26)) != $true)),
% 9.49/2.72 inference(subsumption_resolution,[status(thm)],[f4329,f2946])).
% 9.49/2.72 thf(f4329,plain,(
% 9.49/2.72 (demorgan2 != $true) | ((setminus @ sK26 @ (binintersect @ (binunion @ sK25 @ sK27) @ (binunion @ sK28 @ sK29))) != (binunion @ (binintersect @ (setminus @ sK26 @ sK25) @ (setminus @ sK26 @ sK27)) @ (setminus @ sK26 @ (binunion @ sK28 @ sK29)))) | ((in @ sK28 @ (powerset @ sK26)) != $true) | ((in @ sK29 @ (powerset @ sK26)) != $true)),
% 9.49/2.72 inference(superposition,[status(thm)],[f2800,f3599])).
% 9.49/2.72 thf(f2800,plain,(
% 9.49/2.72 ((setminus @ sK26 @ (binintersect @ (binunion @ sK25 @ sK27) @ (binunion @ sK28 @ sK29))) != (binunion @ (binintersect @ (setminus @ sK26 @ sK25) @ (setminus @ sK26 @ sK27)) @ (binintersect @ (setminus @ sK26 @ sK28) @ (setminus @ sK26 @ sK29))))),
% 9.49/2.72 inference(cnf_transformation,[status(thm)],[f1287])).
% 9.49/2.72 % SZS output end Proof for DTF2THF_10139
% 9.49/2.72 % (10655)------------------------------
% 9.49/2.72 % (10655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.49/2.72 % (10655)Termination reason: Refutation
% 9.49/2.72
% 9.49/2.72 % (10655)Memory used [KB]: 11257
% 9.49/2.72 % (10655)Time elapsed: 0.107 s
% 9.49/2.72 % (10655)Instructions burned: 346 (million)
% 9.49/2.72 % (10655)------------------------------
% 9.49/2.72 % (10655)------------------------------
% 9.49/2.72 % (10293)Success in time 1.069 s
%------------------------------------------------------------------------------