%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU806^1 : 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 : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:37:21 AM UTC 2026
% Result : Theorem 34.78s 6.30s
% Output : Refutation 34.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 17
% Syntax : Number of formulae : 115 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 6887 (1992 equ; 0 cnn)
% Maximal formula atoms : 323 ( 59 avg)
% Number of connectives : 3624 ( 182 ~; 150 |;1039 &; 603 @)
% ( 15 <=>;1635 =>; 0 <=; 0 <~>)
% Maximal formula depth : 328 ( 27 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 572 ( 569 usr; 338 con; 0-6 aty)
% Number of variables : 223 ( 10 ^; 159 !; 54 ?; 223 :)
% 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_323,type,
breln1: $i > $i > $o ).
thf(func_def_325,type,
breln1Set: $i > $i ).
thf(func_def_327,type,
transitive: $i > $i > $o ).
thf(func_def_328,type,
antisymmetric: $i > $i > $o ).
thf(func_def_329,type,
reflexive: $i > $i > $o ).
thf(func_def_330,type,
refltransitive: $i > $i > $o ).
thf(func_def_331,type,
refllinearorder: $i > $i > $o ).
thf(func_def_332,type,
reflwellordering: $i > $i > $o ).
thf(func_def_338,type,
breln1invset: $i > $i > $i ).
thf(func_def_342,type,
breln1compset: $i > $i > $i > $i ).
thf(func_def_360,type,
image1: $i > ( $i > $i ) > $i ).
thf(func_def_364,type,
injective: $i > $i > $i > $o ).
thf(func_def_365,type,
injFuncSet: $i > $i > $i ).
thf(func_def_369,type,
surjective: $i > $i > $i > $o ).
thf(func_def_370,type,
surjFuncSet: $i > $i > $i ).
thf(func_def_391,type,
sP1: $i > $i > $o ).
thf(func_def_392,type,
sP2: $i > $o ).
thf(func_def_393,type,
sP3: $i > $i > $o ).
thf(func_def_394,type,
sP4: $i > $i > $o ).
thf(func_def_397,type,
sP7: $i > $i > $i > $o ).
thf(func_def_398,type,
sP8: $i > $i > $i > $o ).
thf(func_def_401,type,
sP11: $i > $i > $i > $o > $o ).
thf(func_def_406,type,
sP16: $i > $i > $i > $i > $o ).
thf(func_def_412,type,
sK22: $i > $o ).
thf(func_def_443,type,
sK53: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_444,type,
sK54: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_447,type,
sK57: $i > $o ).
thf(func_def_448,type,
sK58: $i > $o ).
thf(func_def_449,type,
sK59: $i > ( $i > $o ) > $i ).
thf(func_def_450,type,
sK60: $i > $o ).
thf(func_def_468,type,
sK78: $i > $i ).
thf(func_def_494,type,
sK104: $i > $o ).
thf(func_def_495,type,
sK105: $i > $i ).
thf(func_def_496,type,
sK106: ( $i > $o ) > $i ).
thf(func_def_497,type,
sK107: $i > $o ).
thf(func_def_500,type,
sK110: $i > ( $i > $o ) > $i ).
thf(func_def_501,type,
sK111: $i > ( $i > $o ) > $i ).
thf(func_def_512,type,
sK122: $i > $o ).
thf(func_def_514,type,
sK124: $i > $i > $i ).
thf(func_def_515,type,
sK125: $i > $i > $i ).
thf(func_def_516,type,
sK126: $i > $i > $i ).
thf(func_def_517,type,
sK127: $i > $i > $i ).
thf(func_def_518,type,
sK128: $i > $i > $i > $i ).
thf(func_def_519,type,
sK129: $i > $i ).
thf(func_def_520,type,
sK130: $i > $i ).
thf(func_def_521,type,
sK131: $i > $i ).
thf(func_def_522,type,
sK132: $i > $i ).
thf(func_def_523,type,
sK133: $i > $i > $i ).
thf(func_def_524,type,
sK134: $i > $i > $i > $i ).
thf(func_def_525,type,
sK135: $i > $i > $i > $i ).
thf(func_def_526,type,
sK136: $i > $i > $i ).
thf(func_def_527,type,
sK137: $i > $i > $i ).
thf(func_def_528,type,
sK138: $i > $i ).
thf(func_def_529,type,
sK139: $i > $i > $i ).
thf(func_def_531,type,
sK141: $i > $i ).
thf(func_def_532,type,
sK142: $i > $i ).
thf(func_def_544,type,
sK154: $o > $i > $i > $i > $i > $i > $i ).
thf(func_def_572,type,
sK182: $i > $o ).
thf(func_def_574,type,
sK184: $i > ( $i > $o ) > $i ).
thf(func_def_581,type,
sK191: $i > $i > $i ).
thf(func_def_582,type,
sK192: $i > $i > $i ).
thf(func_def_584,type,
sK194: $i > $o ).
thf(func_def_591,type,
sK201: $i > $i > $o ).
thf(func_def_592,type,
sK202: $i > $i ).
thf(func_def_593,type,
sK203: $i > $i ).
thf(func_def_594,type,
sK204: ( $i > $i > $o ) > $i > $i ).
thf(func_def_595,type,
sK205: ( $i > $i > $o ) > $i > $i ).
thf(func_def_596,type,
sK206: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_598,type,
sK208: $i > $i > $o ).
thf(func_def_617,type,
sK227: $i > $o ).
thf(func_def_618,type,
sK228: $i > $o ).
thf(func_def_619,type,
sK229: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_620,type,
sK230: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_637,type,
sK247: $i > $i > $o ).
thf(func_def_651,type,
sK261: $i > $i > $i > $i ).
thf(func_def_652,type,
sK262: $i > $i > $i > $i ).
thf(func_def_663,type,
sK273: $i > $i ).
thf(func_def_676,type,
sK286: $i > $i > $i ).
thf(func_def_679,type,
sK289: $i > $i > $o ).
thf(func_def_708,type,
sK318: $i > $i ).
thf(func_def_712,type,
sK322: $i > $i > ( $i > $i ) > $i ).
thf(func_def_724,type,
sK334: $i > $i > $i ).
thf(func_def_739,type,
sK349: $i > $i ).
thf(func_def_757,type,
sK367: $i > $i > $i > $i ).
thf(func_def_761,type,
sK371: $i > $i > $i > $i ).
thf(func_def_762,type,
sK372: $i > ( $i > $i ) > $i > $i ).
thf(func_def_764,type,
sK374: $i > $i ).
thf(func_def_770,type,
sK380: $i > $i > $o ).
thf(func_def_773,type,
sK383: $i > $o ).
thf(func_def_775,type,
sK385: ( $i > $o ) > $i > $i > $i ).
thf(func_def_776,type,
sK386: ( $i > $o ) > $i > $i > $i ).
thf(func_def_784,type,
sK394: $i > $o ).
thf(func_def_792,type,
sK402: $i > $i ).
thf(func_def_794,type,
sK404: ( $i > $i ) > $i > $i > $i ).
thf(func_def_807,type,
sK417: $i > $i > $i ).
thf(func_def_829,type,
sK439: $i > $o ).
thf(func_def_832,type,
sK442: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_833,type,
sK443: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_837,type,
sK447: $i > $o ).
thf(func_def_839,type,
sK449: $i > $i > $o ).
thf(func_def_842,type,
sK452: $i > $i ).
thf(func_def_850,type,
sK460: $i > $i > $i ).
thf(func_def_866,type,
sK476: $i > $i > $o ).
thf(func_def_869,type,
sK479: $i > $o ).
thf(func_def_901,type,
sK511: $i > $i > $i > $i > $i ).
thf(func_def_902,type,
sK512: $i > $i > $i > $i > $i ).
thf(func_def_908,type,
sK518: $i > $o ).
thf(func_def_910,type,
sK520: ( $i > $o ) > $i > $i ).
thf(func_def_919,type,
sK529: $i > ( $i > $i ) > $i > $i ).
thf(func_def_921,type,
sK531: $i > $i ).
thf(func_def_936,type,
sK546: $i > $i ).
thf(func_def_938,type,
sK548: $i > ( $i > $i ) > $i > $i > $i ).
thf(func_def_939,type,
sK549: ( $i > $i ) > $i > $i > $i ).
thf(func_def_941,type,
sK551: $i > $i > $o ).
thf(func_def_955,type,
sK565: $i > $i > $i ).
thf(func_def_956,type,
sK566: $i > ( $i > $i ) > $i > $i ).
thf(func_def_958,type,
sK568: $i > $i ).
thf(func_def_966,type,
sK576: $i > $o ).
thf(func_def_969,type,
sK579: $i > ( $i > $o ) > $i ).
thf(func_def_974,type,
sK584: $i > $o ).
thf(func_def_981,type,
sK591: $i > $o ).
thf(func_def_997,type,
sK607: $i > $i > $i > $i ).
thf(func_def_998,type,
sK608: $i > $i > $i > $i ).
thf(func_def_999,type,
sK609: $i > $i > $i > $i ).
thf(func_def_1000,type,
sK610: $i > $i > $i > $i ).
thf(func_def_1003,type,
sK613: ( $i > $i ) > $i > $i ).
thf(func_def_1004,type,
sK614: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1006,type,
sK616: $i > $i ).
thf(func_def_1007,type,
sK617: $i > $i ).
thf(func_def_1008,type,
sK618: $i > $i ).
thf(func_def_1066,type,
sK676: $i > $i > $i ).
thf(func_def_1071,type,
sK681: $i > $o ).
thf(func_def_1085,type,
sK695: $i > $o ).
thf(func_def_1087,type,
sK697: ( $i > $o ) > $i > $i ).
thf(func_def_1088,type,
sK698: ( $i > $o ) > $i > $i ).
thf(func_def_1095,type,
sK705: $i > $i > $i > $i > $i ).
thf(func_def_1120,type,
sK730: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1123,type,
sK733: $i > $i ).
thf(func_def_1127,type,
sK737: $i > $i ).
thf(func_def_1134,type,
sK744: $i > $i ).
thf(func_def_1137,type,
sK747: $i > $o ).
thf(func_def_1139,type,
sK749: ( $i > $o ) > $i > $i > $i ).
thf(func_def_1140,type,
sK750: ( $i > $o ) > $i > $i > $i ).
thf(func_def_1172,type,
sK782: $i > $i > $i > $i > $i > $i ).
thf(func_def_1178,type,
sK788: $i > $i > $i > $i > $i ).
thf(func_def_1181,type,
sK791: $i > $i > $o ).
thf(func_def_1186,type,
sK796: $o > $i > $i > $i ).
thf(func_def_1190,type,
sK800: ( $i > $o ) > $i ).
thf(func_def_1191,type,
sK801: $i > $o ).
thf(func_def_1195,type,
sK805: $i > $o ).
thf(func_def_1197,type,
sK807: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_1198,type,
sK808: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_1208,type,
sK818: $i > $o ).
thf(func_def_1212,type,
sK822: $i > $i ).
thf(func_def_1213,type,
sK823: $i > $i ).
thf(func_def_1214,type,
sK824: $i > $o ).
thf(func_def_1216,type,
sK826: $i > ( $i > $o ) > $i ).
thf(func_def_1224,type,
sK834: $i > $i > $i > $i > $i ).
thf(func_def_1225,type,
sK835: $i > $i > $i > $i > $i ).
thf(func_def_1226,type,
sK836: $i > $i > $i > $i > $i ).
thf(func_def_1227,type,
sK837: $i > $i > $i > $i > $i ).
thf(func_def_1228,type,
sK838: $i > $i > $i > $i > $i ).
thf(func_def_1240,type,
sK850: $i > $o ).
thf(func_def_1242,type,
sK852: ( $i > $o ) > $i ).
thf(func_def_1243,type,
sK853: ( $i > $o ) > $i ).
thf(func_def_1250,type,
sK860: $i > $i > $i > $i ).
thf(func_def_1270,type,
sK880: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1273,type,
sK883: $i > $i ).
thf(func_def_1274,type,
sK884: $i > ( $i > $o ) > $i ).
thf(func_def_1275,type,
sK885: $i > $o ).
thf(func_def_1295,type,
sK905: $i > $i > $i > $i ).
thf(func_def_1296,type,
sK906: $i > $i > $i > $i ).
thf(func_def_1321,type,
sK931: $i > $o ).
thf(func_def_1323,type,
sK933: $i > ( $i > $o ) > $i > $i ).
thf(func_def_1328,type,
sK938: $i > $o ).
thf(func_def_1333,type,
sK943: $i > $i ).
thf(func_def_1337,type,
sK947: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1338,type,
sK948: $i > $o ).
thf(func_def_1339,type,
sK949: $i > $o ).
thf(func_def_1340,type,
sK950: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1341,type,
sK951: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1345,type,
sK955: $i > $i > $i ).
thf(func_def_1351,type,
sK961: $i > $o ).
thf(func_def_1353,type,
sK963: ( $i > $o ) > $i > $i ).
thf(func_def_1355,type,
sK965: $i > $o ).
thf(func_def_1357,type,
sK967: ( $i > $o ) > $i > $i ).
thf(func_def_1381,type,
sK991: $i > $i > $i ).
thf(func_def_1401,type,
sK1011: $i > $i > $i > $i ).
thf(func_def_1410,type,
sK1020: $i > $o ).
thf(func_def_1422,type,
sK1032: $i > $o ).
thf(func_def_1423,type,
sK1033: $i > $i ).
thf(func_def_1424,type,
sK1034: ( $i > $o ) > $i ).
thf(func_def_1425,type,
sK1035: $i > $i ).
thf(func_def_1431,type,
sK1041: $i > ( $i > $o ) > $i ).
thf(func_def_1432,type,
sK1042: $i > $o ).
thf(func_def_1443,type,
sK1053: $i > $o ).
thf(func_def_1468,type,
ph1078:
!>[X0: $tType] : X0 ).
thf(f11438,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f11435]) ).
thf(f11435,plain,
$true != $true,
inference(superposition,[status(thm)],[f11333,f3373]) ).
thf(f3373,plain,
( $true
= ( in @ sK28 @ sK28 ) ),
inference(cnf_transformation,[status(thm)],[f1465]) ).
thf(f1465,plain,
( ( setunionE2 = $true )
& ( secondinupair = $true )
& ( inPowerset = $true )
& ( complementTI1 = $true )
& ( subbreln = $true )
& ( contrasubsetT2 = $true )
& ( brelnall2 = $true )
& ( setminusSubset1 = $true )
& ( emptysetsubset = $true )
& ( ex1I2 = $true )
& ( contraSubsetComplement = $true )
& ( ksndsingleton = $true )
& ( sepSubset = $true )
& ( setminusIRneg = $true )
& ( complementTcontraSubset = $true )
& ( injFuncSetFuncIn = $true )
& ( breln1unionprop = $true )
& ( foundation2 = $true )
& ( inCongP = $true )
& ( theeq = $true )
& ( setextsub = $true )
& ( quantDeMorgan3 = $true )
& ( setunionsingleton1 = $true )
& ( setukpairinjL1 = $true )
& ( breln1compprop = $true )
& ( ex1E2 = $true )
& ( singletonsswitch = $true )
& ( subsetI1 = $true )
& ( dsetconstrER = $true )
& ( exuE1 = $true )
& ( binunionIR = $true )
& ( $true
= ( in @ sK28 @ sK28 ) )
& ( woz2B = $true )
& ( infuncsetfunc = $true )
& ( image1Ex = $true )
& ( breln1invE = $true )
& ( emptyI = $true )
& ( kpairsurjEq = $true )
& ( subsetTrans = $true )
& ( woz13rule0 = $true )
& ( setminusILneg = $true )
& ( setukpairinjL = $true )
& ( setukpairinjR2 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( upairset2E = $true )
& ( quantDeMorgan4 = $true )
& ( singletonsubset = $true )
& ( setminusELneg = $true )
& ( ifp = $true )
& ( ap2apEq2 = $true )
& ( ifSingleton = $true )
& ( notequalI1 = $true )
& ( breln1invprop = $true )
& ( subsetemptysetimpeq = $true )
& ( setukpairIL = $true )
& ( subsetRefl = $true )
& ( lamp = $true )
& ( setminusT_lem = $true )
& ( sepInPowerset = $true )
& ( upairsubunion = $true )
& ( ap2p = $true )
& ( notinemptyset = $true )
& ( contrasubsetT = $true )
& ( injFuncSetFuncInj = $true )
& ( symdiffE = $true )
& ( setOfPairsIsBReln = $true )
& ( binintersectSubset1 = $true )
& ( wellorderingAx = $true )
& ( binintersectSubset5 = $true )
& ( choice2fnsingleton = $true )
& ( binintersectRsub = $true )
& ( woz1_3 = $true )
& ( iftrueorfalse = $true )
& ( eta2 = $true )
& ( demorgan1b = $true )
& ( woz2W = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( binintersectER = $true )
& ( woz2Ex = $true )
& ( surjFuncSetFuncIn = $true )
& ( emptyinPowerset = $true )
& ( complementImpComplementIntersect = $true )
& ( omegaIndAx = $true )
& ( demorgan1a = $true )
& ( binintersectI = $true )
& ( binintersectSubset2 = $true )
& ( ex1I = $true )
& ( singletoninpowunion = $true )
& ( noeltsimpempty = $true )
& ( iftrueProp2 = $true )
& ( binunionT_lem = $true )
& ( cartprodsndin = $true )
& ( contrasubsetT3 = $true )
& ( cartprodmempaircEq = $true )
& ( subsetE2 = $true )
& ( dpsetconstrEL1 = $true )
& ( doubleComplementSub1 = $true )
& ( emptyset__Cong = $true )
& ( ksndpairEq = $true )
& ( upairsetIR = $true )
& ( leftInvIsSurj = $true )
& ( dsetconstrEL = $true )
& ( cartprodmempair = $true )
& ( powersetE1 = $true )
& ( cartprodpairmemEL = $true )
& ( setukpairinjR = $true )
& ( woz13rule1 = $true )
& ( setadjoinSub = $true )
& ( exuI3 = $true )
& ( upairsetIL = $true )
& ( cartprodfstpairEq = $true )
& ( vacuousDall = $true )
& ( breln1unionEcases = $true )
& ( exuE3u = $true )
& ( demorgan2b2 = $true )
& ( kfstsingleton = $true )
& ( powersetE = $true )
& ( app = $true )
& ( dpsetconstrEL2 = $true )
& ( woz13rule4 = $true )
& ( exuI2 = $true )
& ( emptysetAx = $true )
& ( subsetTI = $true )
& ( in__Cong = $true )
& ( prop2setE = $true )
& ( setOfPairsIsBReln1 = $true )
& ( setminusER = $true )
& ( breln1compI = $true )
& ( funcextLem = $true )
& ( setukpairinjR11 = $true )
& ( dpsetconstrSub = $true )
& ( setminusEL = $true )
& ( image1Ex1 = $true )
& ( image1I = $true )
& ( image1E = $true )
& ( setminusERneg = $true )
& ( demorgan2a1 = $true )
& ( iffalseProp2 = $true )
& ( demorgan2a2 = $true )
& ( symdiffIneg2 = $true )
& ( dpsetconstrI = $true )
& ( breln1unionCommutes = $true )
& ( exu__Cong = $true )
& ( descr__Cong = $true )
& ( woz1_5 = $true )
& ( woz13rule3 = $true )
& ( cartprodfstin = $true )
& ( contrasubsetT1 = $true )
& ( breln1all1 = $true )
& ( demorgan2a = $true )
& ( breln1unionI = $true )
& ( breln1compEex = $true )
& ( brelnall1 = $true )
& ( exuI1 = $true )
& ( setadjoinSub2 = $true )
& ( subsetI2 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( breln1all2 = $true )
& ( dpsetconstrERa = $true )
& ( complementTE1 = $true )
& ( binunionLsub = $true )
& ( funcGraphProp3 = $true )
& ( binunionIL = $true )
& ( eqbreln1 = $true )
& ( binintersectT_lem = $true )
& ( setukpairinjR1 = $true )
& ( ubforcartprodlem2 = $true )
& ( notequalI2 = $true )
& ( exuE2 = $true )
& ( omegaSAx = $true )
& ( powersetsubset = $true )
& ( powersetT_lem = $true )
& ( powersetAx = $true )
& ( binunionTILcontra = $true )
& ( symdiffI1 = $true )
& ( woz1_1 = $true )
& ( singletoninpowerset = $true )
& ( eta1 = $true )
& ( emptysetimpfalse = $true )
& ( nonemptyI1 = $true )
& ( doubleComplementE1 = $true )
& ( cartprodsndpairEq = $true )
& ( omega0Ax = $true )
& ( ex1E1 = $true )
& ( complementTnotintersectT = $true )
& ( breln1SetBreln1 = $true )
& ( setminusI = $true )
& ( cartprodpairin = $true )
& ( setunionsingleton = $true )
& ( breln1unionIR = $true )
& ( demorgan2 = $true )
& ( bs114d = $true )
& ( binintersectSubset4 = $true )
& ( notdexE = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( binintersectTELcontra = $true )
& ( theprop = $true )
& ( binunionTEcontra = $true )
& ( notsubsetI = $true )
& ( ubforcartprodlem3 = $true )
& ( setoftrueEq = $true )
& ( eqinunit = $true )
& ( funcGraphProp2 = $true )
& ( doubleComplementEq = $true )
& ( setextAx = $true )
& ( demorgan2b = $true )
& ( funcext = $true )
& ( nonemptyImpWitness = $true )
& ( lam2lamEq = $true )
& ( beta2 = $true )
& ( symdiffIneg1 = $true )
& ( powersetTI1 = $true )
& ( setadjoinOr = $true )
& ( kpairp = $true )
& ( setadjoinIR = $true )
& ( funcext2 = $true )
& ( iffalse = $true )
& ( eqimpsubset1 = $true )
& ( lamProp = $true )
& ( notdallE = $true )
& ( binintersectEL = $true )
& ( eqimpsubset2 = $true )
& ( binintersectLsub = $true )
& ( complementT_lem = $true )
& ( upairinpowunion = $true )
& ( iftrue = $true )
& ( ubforcartprodlem1 = $true )
& ( breln1unionE = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( binintersectTERcontra = $true )
& ( woz1_2 = $true )
& ( setminusLsub = $true )
& ( exuEu = $true )
& ( upairsetE = $true )
& ( upairequniteq = $true )
& ( breln1compE = $true )
& ( replAx = $true )
& ( cartprodmempair1 = $true )
& ( setadjoinE = $true )
& ( singletonsuniq = $true )
& ( binunionTE = $true )
& ( descrp = $true )
& ( funcGraphProp4 = $true )
& ( nonemptyI = $true )
& ( setadjoin__Cong = $true )
& ( eqbreln = $true )
& ( binunionEcases = $true )
& ( binunionTIRcontra = $true )
& ( iffalseProp1 = $true )
& ( binunionRsub = $true )
& ( disjointsetsI1 = $true )
& ( surjFuncSetFuncSurj = $true )
& ( iftrueProp1 = $true )
& ( complementSubsetComplementIntersect = $true )
& ( setminusSubset2 = $true )
& ( exuE3e = $true )
& ( setukpairinjR12 = $true )
& ( emptyE1 = $true )
& ( woz13rule2 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( subsetE = $true )
& ( funcImageSingleton = $true )
& ( emptyinunitempty = $true )
& ( funcGraphProp1 = $true )
& ( demorgan1 = $true )
& ( powersetI = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( powersetI1 = $true )
& ( lam2p = $true )
& ( surjCantorThm = $true )
& ( subset2powerset = $true )
& ( breln1invI = $true )
& ( image1Equiv = $true )
& ( upairset2IR = $true )
& ( setunionAx = $true )
& ( setunionsingleton2 = $true )
& ( funcinfuncset = $true )
& ( doubleComplementSub2 = $true )
& ( kfstpairEq = $true )
& ( inIntersectImpInUnion = $true )
& ( woz1_4 = $true )
& ( setunionE = $true )
& ( cartprodpairmemER = $true )
& ( emptysetE = $true )
& ( notinsingleton = $true )
& ( foundationAx = $true )
& ( woz2A = $true )
& ( setextT = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( powersetTE1 = $true )
& ( setunion__Cong = $true )
& ( cartprodpairsurjEq = $true )
& ( setukpairinjL2 = $true )
& ( dsetconstr__Cong = $true )
& ( setunionI = $true )
& ( quantDeMorgan1 = $true )
& ( apProp = $true )
& ( nonemptyE1 = $true )
& ( setadjoinIL = $true )
& ( binintersectSubset3 = $true )
& ( singletonprop = $true )
& ( dpsetconstrER = $true )
& ( kpairiskpair = $true )
& ( uniqinunit = $true )
& ( ap2apEq1 = $true )
& ( emptyInPowerset = $true )
& ( setext = $true )
& ( powerset__Cong = $true )
& ( injFuncInInjFuncSet = $true )
& ( beta1 = $true )
& ( setadjoinAx = $true )
& ( quantDeMorgan2 = $true )
& ( setbeta = $true )
& ( symdiffI2 = $true )
& ( subbreln1 = $true )
& ( breln1unionIL = $true )
& ( subPowSU = $true )
& ( doubleComplementI1 = $true )
& ( binunionE = $true )
& ( omega__Cong = $true )
& ( dsetconstrI = $true )
& ( setukpairIR = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f1366,f1464]) ).
thf(f1464,plain,
( ? [X0: $i] :
( $true
= ( in @ X0 @ X0 ) )
=> ( $true
= ( in @ sK28 @ sK28 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1366,plain,
( ( setunionE2 = $true )
& ( secondinupair = $true )
& ( inPowerset = $true )
& ( complementTI1 = $true )
& ( subbreln = $true )
& ( contrasubsetT2 = $true )
& ( brelnall2 = $true )
& ( setminusSubset1 = $true )
& ( emptysetsubset = $true )
& ( ex1I2 = $true )
& ( contraSubsetComplement = $true )
& ( ksndsingleton = $true )
& ( sepSubset = $true )
& ( setminusIRneg = $true )
& ( complementTcontraSubset = $true )
& ( injFuncSetFuncIn = $true )
& ( breln1unionprop = $true )
& ( foundation2 = $true )
& ( inCongP = $true )
& ( theeq = $true )
& ( setextsub = $true )
& ( quantDeMorgan3 = $true )
& ( setunionsingleton1 = $true )
& ( setukpairinjL1 = $true )
& ( breln1compprop = $true )
& ( ex1E2 = $true )
& ( singletonsswitch = $true )
& ( subsetI1 = $true )
& ( dsetconstrER = $true )
& ( exuE1 = $true )
& ( binunionIR = $true )
& ? [X0: $i] :
( $true
= ( in @ X0 @ X0 ) )
& ( woz2B = $true )
& ( infuncsetfunc = $true )
& ( image1Ex = $true )
& ( breln1invE = $true )
& ( emptyI = $true )
& ( kpairsurjEq = $true )
& ( subsetTrans = $true )
& ( woz13rule0 = $true )
& ( setminusILneg = $true )
& ( setukpairinjL = $true )
& ( setukpairinjR2 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( upairset2E = $true )
& ( quantDeMorgan4 = $true )
& ( singletonsubset = $true )
& ( setminusELneg = $true )
& ( ifp = $true )
& ( ap2apEq2 = $true )
& ( ifSingleton = $true )
& ( notequalI1 = $true )
& ( breln1invprop = $true )
& ( subsetemptysetimpeq = $true )
& ( setukpairIL = $true )
& ( subsetRefl = $true )
& ( lamp = $true )
& ( setminusT_lem = $true )
& ( sepInPowerset = $true )
& ( upairsubunion = $true )
& ( ap2p = $true )
& ( notinemptyset = $true )
& ( contrasubsetT = $true )
& ( injFuncSetFuncInj = $true )
& ( symdiffE = $true )
& ( setOfPairsIsBReln = $true )
& ( binintersectSubset1 = $true )
& ( wellorderingAx = $true )
& ( binintersectSubset5 = $true )
& ( choice2fnsingleton = $true )
& ( binintersectRsub = $true )
& ( woz1_3 = $true )
& ( iftrueorfalse = $true )
& ( eta2 = $true )
& ( demorgan1b = $true )
& ( woz2W = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( binintersectER = $true )
& ( woz2Ex = $true )
& ( surjFuncSetFuncIn = $true )
& ( emptyinPowerset = $true )
& ( complementImpComplementIntersect = $true )
& ( omegaIndAx = $true )
& ( demorgan1a = $true )
& ( binintersectI = $true )
& ( binintersectSubset2 = $true )
& ( ex1I = $true )
& ( singletoninpowunion = $true )
& ( noeltsimpempty = $true )
& ( iftrueProp2 = $true )
& ( binunionT_lem = $true )
& ( cartprodsndin = $true )
& ( contrasubsetT3 = $true )
& ( cartprodmempaircEq = $true )
& ( subsetE2 = $true )
& ( dpsetconstrEL1 = $true )
& ( doubleComplementSub1 = $true )
& ( emptyset__Cong = $true )
& ( ksndpairEq = $true )
& ( upairsetIR = $true )
& ( leftInvIsSurj = $true )
& ( dsetconstrEL = $true )
& ( cartprodmempair = $true )
& ( powersetE1 = $true )
& ( cartprodpairmemEL = $true )
& ( setukpairinjR = $true )
& ( woz13rule1 = $true )
& ( setadjoinSub = $true )
& ( exuI3 = $true )
& ( upairsetIL = $true )
& ( cartprodfstpairEq = $true )
& ( vacuousDall = $true )
& ( breln1unionEcases = $true )
& ( exuE3u = $true )
& ( demorgan2b2 = $true )
& ( kfstsingleton = $true )
& ( powersetE = $true )
& ( app = $true )
& ( dpsetconstrEL2 = $true )
& ( woz13rule4 = $true )
& ( exuI2 = $true )
& ( emptysetAx = $true )
& ( subsetTI = $true )
& ( in__Cong = $true )
& ( prop2setE = $true )
& ( setOfPairsIsBReln1 = $true )
& ( setminusER = $true )
& ( breln1compI = $true )
& ( funcextLem = $true )
& ( setukpairinjR11 = $true )
& ( dpsetconstrSub = $true )
& ( setminusEL = $true )
& ( image1Ex1 = $true )
& ( image1I = $true )
& ( image1E = $true )
& ( setminusERneg = $true )
& ( demorgan2a1 = $true )
& ( iffalseProp2 = $true )
& ( demorgan2a2 = $true )
& ( symdiffIneg2 = $true )
& ( dpsetconstrI = $true )
& ( breln1unionCommutes = $true )
& ( exu__Cong = $true )
& ( descr__Cong = $true )
& ( woz1_5 = $true )
& ( woz13rule3 = $true )
& ( cartprodfstin = $true )
& ( contrasubsetT1 = $true )
& ( breln1all1 = $true )
& ( demorgan2a = $true )
& ( breln1unionI = $true )
& ( breln1compEex = $true )
& ( brelnall1 = $true )
& ( exuI1 = $true )
& ( setadjoinSub2 = $true )
& ( subsetI2 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( breln1all2 = $true )
& ( dpsetconstrERa = $true )
& ( complementTE1 = $true )
& ( binunionLsub = $true )
& ( funcGraphProp3 = $true )
& ( binunionIL = $true )
& ( eqbreln1 = $true )
& ( binintersectT_lem = $true )
& ( setukpairinjR1 = $true )
& ( ubforcartprodlem2 = $true )
& ( notequalI2 = $true )
& ( exuE2 = $true )
& ( omegaSAx = $true )
& ( powersetsubset = $true )
& ( powersetT_lem = $true )
& ( powersetAx = $true )
& ( binunionTILcontra = $true )
& ( symdiffI1 = $true )
& ( woz1_1 = $true )
& ( singletoninpowerset = $true )
& ( eta1 = $true )
& ( emptysetimpfalse = $true )
& ( nonemptyI1 = $true )
& ( doubleComplementE1 = $true )
& ( cartprodsndpairEq = $true )
& ( omega0Ax = $true )
& ( ex1E1 = $true )
& ( complementTnotintersectT = $true )
& ( breln1SetBreln1 = $true )
& ( setminusI = $true )
& ( cartprodpairin = $true )
& ( setunionsingleton = $true )
& ( breln1unionIR = $true )
& ( demorgan2 = $true )
& ( bs114d = $true )
& ( binintersectSubset4 = $true )
& ( notdexE = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( binintersectTELcontra = $true )
& ( theprop = $true )
& ( binunionTEcontra = $true )
& ( notsubsetI = $true )
& ( ubforcartprodlem3 = $true )
& ( setoftrueEq = $true )
& ( eqinunit = $true )
& ( funcGraphProp2 = $true )
& ( doubleComplementEq = $true )
& ( setextAx = $true )
& ( demorgan2b = $true )
& ( funcext = $true )
& ( nonemptyImpWitness = $true )
& ( lam2lamEq = $true )
& ( beta2 = $true )
& ( symdiffIneg1 = $true )
& ( powersetTI1 = $true )
& ( setadjoinOr = $true )
& ( kpairp = $true )
& ( setadjoinIR = $true )
& ( funcext2 = $true )
& ( iffalse = $true )
& ( eqimpsubset1 = $true )
& ( lamProp = $true )
& ( notdallE = $true )
& ( binintersectEL = $true )
& ( eqimpsubset2 = $true )
& ( binintersectLsub = $true )
& ( complementT_lem = $true )
& ( upairinpowunion = $true )
& ( iftrue = $true )
& ( ubforcartprodlem1 = $true )
& ( breln1unionE = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( binintersectTERcontra = $true )
& ( woz1_2 = $true )
& ( setminusLsub = $true )
& ( exuEu = $true )
& ( upairsetE = $true )
& ( upairequniteq = $true )
& ( breln1compE = $true )
& ( replAx = $true )
& ( cartprodmempair1 = $true )
& ( setadjoinE = $true )
& ( singletonsuniq = $true )
& ( binunionTE = $true )
& ( descrp = $true )
& ( funcGraphProp4 = $true )
& ( nonemptyI = $true )
& ( setadjoin__Cong = $true )
& ( eqbreln = $true )
& ( binunionEcases = $true )
& ( binunionTIRcontra = $true )
& ( iffalseProp1 = $true )
& ( binunionRsub = $true )
& ( disjointsetsI1 = $true )
& ( surjFuncSetFuncSurj = $true )
& ( iftrueProp1 = $true )
& ( complementSubsetComplementIntersect = $true )
& ( setminusSubset2 = $true )
& ( exuE3e = $true )
& ( setukpairinjR12 = $true )
& ( emptyE1 = $true )
& ( woz13rule2 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( subsetE = $true )
& ( funcImageSingleton = $true )
& ( emptyinunitempty = $true )
& ( funcGraphProp1 = $true )
& ( demorgan1 = $true )
& ( powersetI = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( powersetI1 = $true )
& ( lam2p = $true )
& ( surjCantorThm = $true )
& ( subset2powerset = $true )
& ( breln1invI = $true )
& ( image1Equiv = $true )
& ( upairset2IR = $true )
& ( setunionAx = $true )
& ( setunionsingleton2 = $true )
& ( funcinfuncset = $true )
& ( doubleComplementSub2 = $true )
& ( kfstpairEq = $true )
& ( inIntersectImpInUnion = $true )
& ( woz1_4 = $true )
& ( setunionE = $true )
& ( cartprodpairmemER = $true )
& ( emptysetE = $true )
& ( notinsingleton = $true )
& ( foundationAx = $true )
& ( woz2A = $true )
& ( setextT = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( powersetTE1 = $true )
& ( setunion__Cong = $true )
& ( cartprodpairsurjEq = $true )
& ( setukpairinjL2 = $true )
& ( dsetconstr__Cong = $true )
& ( setunionI = $true )
& ( quantDeMorgan1 = $true )
& ( apProp = $true )
& ( nonemptyE1 = $true )
& ( setadjoinIL = $true )
& ( binintersectSubset3 = $true )
& ( singletonprop = $true )
& ( dpsetconstrER = $true )
& ( kpairiskpair = $true )
& ( uniqinunit = $true )
& ( ap2apEq1 = $true )
& ( emptyInPowerset = $true )
& ( setext = $true )
& ( powerset__Cong = $true )
& ( injFuncInInjFuncSet = $true )
& ( beta1 = $true )
& ( setadjoinAx = $true )
& ( quantDeMorgan2 = $true )
& ( setbeta = $true )
& ( symdiffI2 = $true )
& ( subbreln1 = $true )
& ( breln1unionIL = $true )
& ( subPowSU = $true )
& ( doubleComplementI1 = $true )
& ( binunionE = $true )
& ( omega__Cong = $true )
& ( dsetconstrI = $true )
& ( setukpairIR = $true ) ),
inference(flattening,[status(thm)],[f1365]) ).
thf(f1365,plain,
( ? [X0: $i] :
( $true
= ( in @ X0 @ X0 ) )
& ( foundation2 = $true )
& ( surjCantorThm = $true )
& ( leftInvIsSurj = $true )
& ( surjFuncSetFuncSurj = $true )
& ( surjFuncSetFuncIn = $true )
& ( injFuncSetFuncInj = $true )
& ( injFuncSetFuncIn = $true )
& ( injFuncInInjFuncSet = $true )
& ( image1I = $true )
& ( image1E = $true )
& ( image1Equiv = $true )
& ( image1Ex1 = $true )
& ( image1Ex = $true )
& ( woz2B = $true )
& ( woz2A = $true )
& ( woz2W = $true )
& ( woz2Ex = $true )
& ( breln1unionCommutes = $true )
& ( breln1unionEcases = $true )
& ( breln1unionE = $true )
& ( breln1unionI = $true )
& ( breln1unionIR = $true )
& ( breln1unionIL = $true )
& ( breln1unionprop = $true )
& ( breln1compEex = $true )
& ( breln1compE = $true )
& ( breln1compI = $true )
& ( breln1compprop = $true )
& ( breln1invE = $true )
& ( breln1invI = $true )
& ( breln1invprop = $true )
& ( eqbreln1 = $true )
& ( subbreln1 = $true )
& ( breln1all1 = $true )
& ( setOfPairsIsBReln1 = $true )
& ( choice2fnsingleton = $true )
& ( breln1SetBreln1 = $true )
& ( breln1all2 = $true )
& ( woz1_5 = $true )
& ( woz1_4 = $true )
& ( woz1_3 = $true )
& ( woz1_2 = $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)],[f972]) ).
thf(f972,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 )
=> ( ( woz1_2 = $true )
=> ( ( woz1_3 = $true )
=> ( ( woz1_4 = $true )
=> ( ( woz1_5 = $true )
=> ( ( breln1all2 = $true )
=> ( ( breln1SetBreln1 = $true )
=> ( ( choice2fnsingleton = $true )
=> ( ( setOfPairsIsBReln1 = $true )
=> ( ( breln1all1 = $true )
=> ( ( subbreln1 = $true )
=> ( ( eqbreln1 = $true )
=> ( ( breln1invprop = $true )
=> ( ( breln1invI = $true )
=> ( ( breln1invE = $true )
=> ( ( breln1compprop = $true )
=> ( ( breln1compI = $true )
=> ( ( breln1compE = $true )
=> ( ( breln1compEex = $true )
=> ( ( breln1unionprop = $true )
=> ( ( breln1unionIL = $true )
=> ( ( breln1unionIR = $true )
=> ( ( breln1unionI = $true )
=> ( ( breln1unionE = $true )
=> ( ( breln1unionEcases = $true )
=> ( ( breln1unionCommutes = $true )
=> ( ( woz2Ex = $true )
=> ( ( woz2W = $true )
=> ( ( woz2A = $true )
=> ( ( woz2B = $true )
=> ( ( image1Ex = $true )
=> ( ( image1Ex1 = $true )
=> ( ( image1Equiv = $true )
=> ( ( image1E = $true )
=> ( ( image1I = $true )
=> ( ( injFuncInInjFuncSet = $true )
=> ( ( injFuncSetFuncIn = $true )
=> ( ( injFuncSetFuncInj = $true )
=> ( ( surjFuncSetFuncIn = $true )
=> ( ( surjFuncSetFuncSurj = $true )
=> ( ( leftInvIsSurj = $true )
=> ( ( surjCantorThm = $true )
=> ( ( foundation2 = $true )
=> ! [X0: $i] :
( $true
!= ( in @ X0 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f913]) ).
thf(f913,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 )
=> ( ( woz1_2 = $true )
=> ( ( woz1_3 = $true )
=> ( ( woz1_4 = $true )
=> ( ( woz1_5 = $true )
=> ( ( breln1all2 = $true )
=> ( ( breln1SetBreln1 = $true )
=> ( ( choice2fnsingleton = $true )
=> ( ( setOfPairsIsBReln1 = $true )
=> ( ( breln1all1 = $true )
=> ( ( subbreln1 = $true )
=> ( ( eqbreln1 = $true )
=> ( ( breln1invprop = $true )
=> ( ( breln1invI = $true )
=> ( ( breln1invE = $true )
=> ( ( breln1compprop = $true )
=> ( ( breln1compI = $true )
=> ( ( breln1compE = $true )
=> ( ( breln1compEex = $true )
=> ( ( breln1unionprop = $true )
=> ( ( breln1unionIL = $true )
=> ( ( breln1unionIR = $true )
=> ( ( breln1unionI = $true )
=> ( ( breln1unionE = $true )
=> ( ( breln1unionEcases = $true )
=> ( ( breln1unionCommutes = $true )
=> ( ( woz2Ex = $true )
=> ( ( woz2W = $true )
=> ( ( woz2A = $true )
=> ( ( woz2B = $true )
=> ( ( image1Ex = $true )
=> ( ( image1Ex1 = $true )
=> ( ( image1Equiv = $true )
=> ( ( image1E = $true )
=> ( ( image1I = $true )
=> ( ( injFuncInInjFuncSet = $true )
=> ( ( injFuncSetFuncIn = $true )
=> ( ( injFuncSetFuncInj = $true )
=> ( ( surjFuncSetFuncIn = $true )
=> ( ( surjFuncSetFuncSurj = $true )
=> ( ( leftInvIsSurj = $true )
=> ( ( surjCantorThm = $true )
=> ( ( foundation2 = $true )
=> ! [X0: $i] :
( $true
!= ( in @ X0 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f912]) ).
thf(f912,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
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( breln1compprop
=> ( breln1compI
=> ( breln1compE
=> ( breln1compEex
=> ( breln1unionprop
=> ( breln1unionIL
=> ( breln1unionIR
=> ( breln1unionI
=> ( breln1unionE
=> ( breln1unionEcases
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ( woz2B
=> ( image1Ex
=> ( image1Ex1
=> ( image1Equiv
=> ( image1E
=> ( image1I
=> ( injFuncInInjFuncSet
=> ( injFuncSetFuncIn
=> ( injFuncSetFuncInj
=> ( surjFuncSetFuncIn
=> ( surjFuncSetFuncSurj
=> ( leftInvIsSurj
=> ( surjCantorThm
=> ( foundation2
=> ! [X0: $i] :
~ ( in @ X0 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f326]) ).
thf(f326,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
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( breln1compprop
=> ( breln1compI
=> ( breln1compE
=> ( breln1compEex
=> ( breln1unionprop
=> ( breln1unionIL
=> ( breln1unionIR
=> ( breln1unionI
=> ( breln1unionE
=> ( breln1unionEcases
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ( woz2B
=> ( image1Ex
=> ( image1Ex1
=> ( image1Equiv
=> ( image1E
=> ( image1I
=> ( injFuncInInjFuncSet
=> ( injFuncSetFuncIn
=> ( injFuncSetFuncInj
=> ( surjFuncSetFuncIn
=> ( surjFuncSetFuncSurj
=> ( leftInvIsSurj
=> ( surjCantorThm
=> ( foundation2
=> ! [X3: $i] :
~ ( in @ X3 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f325]) ).
thf(f325,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
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( breln1compprop
=> ( breln1compI
=> ( breln1compE
=> ( breln1compEex
=> ( breln1unionprop
=> ( breln1unionIL
=> ( breln1unionIR
=> ( breln1unionI
=> ( breln1unionE
=> ( breln1unionEcases
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ( woz2B
=> ( image1Ex
=> ( image1Ex1
=> ( image1Equiv
=> ( image1E
=> ( image1I
=> ( injFuncInInjFuncSet
=> ( injFuncSetFuncIn
=> ( injFuncSetFuncInj
=> ( surjFuncSetFuncIn
=> ( surjFuncSetFuncSurj
=> ( leftInvIsSurj
=> ( surjCantorThm
=> ( foundation2
=> ! [X3: $i] :
~ ( in @ X3 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yv4wus1g2e/DTF2THF_4600.p',notinself) ).
thf(f11333,plain,
! [X0: $i] :
( $true
!= ( in @ X0 @ X0 ) ),
inference(forward_demodulation,[status(thm)],[f11332,f7832]) ).
thf(f7832,plain,
! [X0: $i] :
( ( sK273 @ ( setadjoin @ X0 @ emptyset ) )
= X0 ),
inference(subsumption_resolution,[status(thm)],[f7774,f7577]) ).
thf(f7577,plain,
! [X0: $i,X1: $i] :
( emptyset
!= ( setadjoin @ X0 @ X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f7575]) ).
thf(f7575,plain,
! [X0: $i,X1: $i] :
( ( emptyset
!= ( setadjoin @ X0 @ X1 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f6333,f6499]) ).
thf(f6499,plain,
! [X4: $i,X5: $i] :
( $true
= ( in @ X4 @ ( setadjoin @ X4 @ X5 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f6178]) ).
thf(f6178,plain,
! [X4: $i,X5: $i] :
( ( $true != $true )
| ( $true
= ( in @ X4 @ ( setadjoin @ X4 @ X5 ) ) ) ),
inference(equality_resolution,[status(thm)],[f5441]) ).
thf(f5441,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setadjoin @ X3 @ X5 ) )
= $true )
| ( X3 != X4 )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f4048,f3093]) ).
thf(f3093,plain,
setadjoinAx = $true,
inference(cnf_transformation,[status(thm)],[f1465]) ).
thf(f4048,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setadjoin @ X3 @ X5 ) )
= $true )
| ( X3 != X4 )
| ( setadjoinAx != $true ) ),
inference(cnf_transformation,[status(thm)],[f2189]) ).
thf(f2189,plain,
( ( ( setadjoinAx = $true )
| ( ( ( $true
!= ( in @ sK507 @ ( setadjoin @ sK506 @ sK508 ) ) )
| ( ( sK506 != sK507 )
& ( $true
!= ( in @ sK507 @ sK508 ) ) ) )
& ( ( $true
= ( in @ sK507 @ ( setadjoin @ sK506 @ sK508 ) ) )
| ( sK506 = sK507 )
| ( $true
= ( in @ sK507 @ sK508 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( X3 = X4 )
| ( $true
= ( in @ X4 @ X5 ) )
| ( ( in @ X4 @ ( setadjoin @ X3 @ X5 ) )
!= $true ) )
& ( ( ( in @ X4 @ ( setadjoin @ X3 @ X5 ) )
= $true )
| ( ( X3 != X4 )
& ( $true
!= ( in @ X4 @ X5 ) ) ) ) )
| ( setadjoinAx != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK506,sK507,sK508])],[f2187,f2188]) ).
thf(f2188,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( $true
!= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) )
| ( ( X0 != X1 )
& ( $true
!= ( in @ X1 @ X2 ) ) ) )
& ( ( $true
= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) )
| ( X0 = X1 )
| ( $true
= ( in @ X1 @ X2 ) ) ) )
=> ( ( ( $true
!= ( in @ sK507 @ ( setadjoin @ sK506 @ sK508 ) ) )
| ( ( sK506 != sK507 )
& ( $true
!= ( in @ sK507 @ sK508 ) ) ) )
& ( ( $true
= ( in @ sK507 @ ( setadjoin @ sK506 @ sK508 ) ) )
| ( sK506 = sK507 )
| ( $true
= ( in @ sK507 @ sK508 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2187,plain,
( ( ( setadjoinAx = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( $true
!= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) )
| ( ( X0 != X1 )
& ( $true
!= ( in @ X1 @ X2 ) ) ) )
& ( ( $true
= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) )
| ( X0 = X1 )
| ( $true
= ( in @ X1 @ X2 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( X3 = X4 )
| ( $true
= ( in @ X4 @ X5 ) )
| ( ( in @ X4 @ ( setadjoin @ X3 @ X5 ) )
!= $true ) )
& ( ( ( in @ X4 @ ( setadjoin @ X3 @ X5 ) )
= $true )
| ( ( X3 != X4 )
& ( $true
!= ( in @ X4 @ X5 ) ) ) ) )
| ( setadjoinAx != $true ) ) ),
inference(rectify,[status(thm)],[f2186]) ).
thf(f2186,plain,
( ( ( setadjoinAx = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( $true
!= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) )
| ( ( X0 != X1 )
& ( $true
!= ( in @ X1 @ X2 ) ) ) )
& ( ( $true
= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) )
| ( X0 = X1 )
| ( $true
= ( in @ X1 @ X2 ) ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( X0 = X1 )
| ( $true
= ( in @ X1 @ X2 ) )
| ( $true
!= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) ) )
& ( ( $true
= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) )
| ( ( X0 != X1 )
& ( $true
!= ( in @ X1 @ X2 ) ) ) ) )
| ( setadjoinAx != $true ) ) ),
inference(flattening,[status(thm)],[f2185]) ).
thf(f2185,plain,
( ( ( setadjoinAx = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( $true
!= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) )
| ( ( X0 != X1 )
& ( $true
!= ( in @ X1 @ X2 ) ) ) )
& ( ( $true
= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) )
| ( X0 = X1 )
| ( $true
= ( in @ X1 @ X2 ) ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( X0 = X1 )
| ( $true
= ( in @ X1 @ X2 ) )
| ( $true
!= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) ) )
& ( ( $true
= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) )
| ( ( X0 != X1 )
& ( $true
!= ( in @ X1 @ X2 ) ) ) ) )
| ( setadjoinAx != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f933]) ).
thf(f933,plain,
( ( setadjoinAx = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( X0 = X1 )
| ( $true
= ( in @ X1 @ X2 ) ) )
<=> ( $true
= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f932]) ).
thf(f932,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( ( X0 = X1 )
| ( in @ X1 @ X2 ) )
<=> ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) )
= setadjoinAx ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X1: $i,X2: $i,X3: $i] :
( ( ( ( X1 = X2 )
| ( in @ X2 @ X3 ) )
<=> ( in @ X2 @ ( setadjoin @ X1 @ X3 ) ) )
= setadjoinAx ),
file('/export/starexec/sandbox2/tmp/tmp.yv4wus1g2e/DTF2THF_4600.p',setadjoinAx) ).
thf(f6333,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ X0 ) )
| ( emptyset != X0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f6332]) ).
thf(f6332,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( emptyset = X0 ) )
| ( $true
!= ( in @ X1 @ X0 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f6331]) ).
thf(f6331,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ X0 ) )
| ( ( emptyset != X0 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f6330]) ).
thf(f6330,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] : ( emptyset != Y0 )
@ X0 ) )
| ( $true
!= ( in @ X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f5706]) ).
thf(f5706,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( in @ X1 @ X0 ) )
| ( $true
= ( ^ [Y0: $i] : ( emptyset != Y0 )
@ X0 ) ) ),
inference(definition_unfolding,[status(thm)],[f4365,f3477,f3224]) ).
thf(f3224,plain,
nonemptyI1 = $true,
inference(cnf_transformation,[status(thm)],[f1465]) ).
thf(f3477,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f705]) ).
thf(f705,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f704]) ).
thf(f704,plain,
( ( ^ [X0: $i] : ( emptyset != X0 ) )
= nonempty ),
inference(rectify,[status(thm)],[f27]) ).
thf(f27,axiom,
( ( ^ [X1: $i] : ( emptyset != X1 ) )
= nonempty ),
file('/export/starexec/sandbox2/tmp/tmp.yv4wus1g2e/DTF2THF_4600.p',nonempty) ).
thf(f4365,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ X0 ) )
| ( ( nonempty @ X0 )
= $true )
| ( nonemptyI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f2536]) ).
thf(f2536,plain,
( ( ! [X0: $i] :
( ! [X1: $i] :
( $true
!= ( in @ X1 @ X0 ) )
| ( ( nonempty @ X0 )
= $true ) )
| ( nonemptyI1 != $true ) )
& ( ( nonemptyI1 = $true )
| ( ( $true
= ( in @ sK735 @ sK734 ) )
& ( $true
!= ( nonempty @ sK734 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK734,sK735])],[f2533,f2535,f2534]) ).
thf(f2534,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( $true
= ( in @ X3 @ X2 ) )
& ( $true
!= ( nonempty @ X2 ) ) )
=> ( ? [X3: $i] :
( $true
= ( in @ X3 @ sK734 ) )
& ( $true
!= ( nonempty @ sK734 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2535,plain,
( ? [X3: $i] :
( $true
= ( in @ X3 @ sK734 ) )
=> ( $true
= ( in @ sK735 @ sK734 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2533,plain,
( ( ! [X0: $i] :
( ! [X1: $i] :
( $true
!= ( in @ X1 @ X0 ) )
| ( ( nonempty @ X0 )
= $true ) )
| ( nonemptyI1 != $true ) )
& ( ( nonemptyI1 = $true )
| ? [X2: $i] :
( ? [X3: $i] :
( $true
= ( in @ X3 @ X2 ) )
& ( $true
!= ( nonempty @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f2532]) ).
thf(f2532,plain,
( ( ! [X0: $i] :
( ! [X1: $i] :
( $true
!= ( in @ X1 @ X0 ) )
| ( ( nonempty @ X0 )
= $true ) )
| ( nonemptyI1 != $true ) )
& ( ( nonemptyI1 = $true )
| ? [X0: $i] :
( ? [X1: $i] :
( $true
= ( in @ X1 @ X0 ) )
& ( ( nonempty @ X0 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f1318]) ).
thf(f1318,plain,
( ! [X0: $i] :
( ! [X1: $i] :
( $true
!= ( in @ X1 @ X0 ) )
| ( ( nonempty @ X0 )
= $true ) )
<=> ( nonemptyI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f587]) ).
thf(f587,plain,
( ( nonemptyI1 = $true )
<=> ! [X0: $i] :
( ? [X1: $i] :
( $true
= ( in @ X1 @ X0 ) )
=> ( ( nonempty @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f586]) ).
thf(f586,plain,
( nonemptyI1
= ( ! [X0: $i] :
( ? [X1: $i] : ( in @ X1 @ X0 )
=> ( nonempty @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f30]) ).
thf(f30,axiom,
( nonemptyI1
= ( ! [X3: $i] :
( ? [X1: $i] : ( in @ X1 @ X3 )
=> ( nonempty @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yv4wus1g2e/DTF2THF_4600.p',nonemptyI1) ).
thf(f7774,plain,
! [X0: $i] :
( ( ( sK273 @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( emptyset
= ( setadjoin @ X0 @ emptyset ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f7753]) ).
thf(f7753,plain,
! [X0: $i] :
( ( ( sK273 @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( emptyset
= ( setadjoin @ X0 @ emptyset ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f6486,f6416]) ).
thf(f6416,plain,
! [X2: $i] :
( ( ( in @ ( sK273 @ X2 ) @ X2 )
= $true )
| ( emptyset = X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f6415]) ).
thf(f6415,plain,
! [X2: $i] :
( ( $true
= ( emptyset = X2 ) )
| ( ( in @ ( sK273 @ X2 ) @ X2 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f6414]) ).
thf(f6414,plain,
! [X2: $i] :
( ( ( in @ ( sK273 @ X2 ) @ X2 )
= $true )
| ( $true
!= ( emptyset != X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f6413]) ).
thf(f6413,plain,
! [X2: $i] :
( ( ( in @ ( sK273 @ X2 ) @ X2 )
= $true )
| ( $true
!= ( ^ [Y0: $i] : ( emptyset != Y0 )
@ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f5145]) ).
thf(f5145,plain,
! [X2: $i] :
( ( $true != $true )
| ( $true
!= ( ^ [Y0: $i] : ( emptyset != Y0 )
@ X2 ) )
| ( ( in @ ( sK273 @ X2 ) @ X2 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f3748,f3477,f3387]) ).
thf(f3387,plain,
foundation2 = $true,
inference(cnf_transformation,[status(thm)],[f1465]) ).
thf(f3748,plain,
! [X2: $i] :
( ( ( in @ ( sK273 @ X2 ) @ X2 )
= $true )
| ( $true
!= ( nonempty @ X2 ) )
| ( foundation2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f1840]) ).
thf(f1840,plain,
( ( ( foundation2 = $true )
| ( ! [X1: $i] :
( ( emptyset
!= ( binintersect @ X1 @ sK272 ) )
| ( ( in @ X1 @ sK272 )
!= $true ) )
& ( $true
= ( nonempty @ sK272 ) ) ) )
& ( ! [X2: $i] :
( ( ( emptyset
= ( binintersect @ ( sK273 @ X2 ) @ X2 ) )
& ( ( in @ ( sK273 @ X2 ) @ X2 )
= $true ) )
| ( $true
!= ( nonempty @ X2 ) ) )
| ( foundation2 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK272,sK273])],[f1837,f1839,f1838]) ).
thf(f1838,plain,
( ? [X0: $i] :
( ! [X1: $i] :
( ( emptyset
!= ( binintersect @ X1 @ X0 ) )
| ( $true
!= ( in @ X1 @ X0 ) ) )
& ( ( nonempty @ X0 )
= $true ) )
=> ( ! [X1: $i] :
( ( emptyset
!= ( binintersect @ X1 @ sK272 ) )
| ( ( in @ X1 @ sK272 )
!= $true ) )
& ( $true
= ( nonempty @ sK272 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1839,plain,
! [X2: $i] :
( ? [X3: $i] :
( ( emptyset
= ( binintersect @ X3 @ X2 ) )
& ( $true
= ( in @ X3 @ X2 ) ) )
=> ( ( emptyset
= ( binintersect @ ( sK273 @ X2 ) @ X2 ) )
& ( ( in @ ( sK273 @ X2 ) @ X2 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1837,plain,
( ( ( foundation2 = $true )
| ? [X0: $i] :
( ! [X1: $i] :
( ( emptyset
!= ( binintersect @ X1 @ X0 ) )
| ( $true
!= ( in @ X1 @ X0 ) ) )
& ( ( nonempty @ X0 )
= $true ) ) )
& ( ! [X2: $i] :
( ? [X3: $i] :
( ( emptyset
= ( binintersect @ X3 @ X2 ) )
& ( $true
= ( in @ X3 @ X2 ) ) )
| ( $true
!= ( nonempty @ X2 ) ) )
| ( foundation2 != $true ) ) ),
inference(rectify,[status(thm)],[f1836]) ).
thf(f1836,plain,
( ( ( foundation2 = $true )
| ? [X0: $i] :
( ! [X1: $i] :
( ( emptyset
!= ( binintersect @ X1 @ X0 ) )
| ( $true
!= ( in @ X1 @ X0 ) ) )
& ( ( nonempty @ X0 )
= $true ) ) )
& ( ! [X0: $i] :
( ? [X1: $i] :
( ( emptyset
= ( binintersect @ X1 @ X0 ) )
& ( $true
= ( in @ X1 @ X0 ) ) )
| ( ( nonempty @ X0 )
!= $true ) )
| ( foundation2 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f1353]) ).
thf(f1353,plain,
( ( foundation2 = $true )
<=> ! [X0: $i] :
( ? [X1: $i] :
( ( emptyset
= ( binintersect @ X1 @ X0 ) )
& ( $true
= ( in @ X1 @ X0 ) ) )
| ( ( nonempty @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f373]) ).
thf(f373,plain,
( ( foundation2 = $true )
<=> ! [X0: $i] :
( ( ( nonempty @ X0 )
= $true )
=> ? [X1: $i] :
( ( emptyset
= ( binintersect @ X1 @ X0 ) )
& ( $true
= ( in @ X1 @ X0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f372]) ).
thf(f372,plain,
! [X0: $i] :
( ( ( nonempty @ X0 )
=> ? [X1: $i] :
( ( emptyset
= ( binintersect @ X1 @ X0 ) )
& ( in @ X1 @ X0 ) ) )
= foundation2 ),
inference(rectify,[status(thm)],[f324]) ).
thf(f324,axiom,
! [X3: $i] :
( ( ( nonempty @ X3 )
=> ? [X11: $i] :
( ( emptyset
= ( binintersect @ X11 @ X3 ) )
& ( in @ X11 @ X3 ) ) )
= foundation2 ),
file('/export/starexec/sandbox2/tmp/tmp.yv4wus1g2e/DTF2THF_4600.p',foundation2) ).
thf(f6486,plain,
! [X2: $i,X3: $i] :
( ( $true
!= ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
| ( X2 = X3 ) ),
inference(trivial_inequality_removal,[status(thm)],[f5885]) ).
thf(f5885,plain,
! [X2: $i,X3: $i] :
( ( $true != $true )
| ( X2 = X3 )
| ( $true
!= ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
inference(definition_unfolding,[status(thm)],[f4575,f3119]) ).
thf(f3119,plain,
notinsingleton = $true,
inference(cnf_transformation,[status(thm)],[f1465]) ).
thf(f4575,plain,
! [X2: $i,X3: $i] :
( ( X2 = X3 )
| ( $true
!= ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
| ( notinsingleton != $true ) ),
inference(cnf_transformation,[status(thm)],[f2767]) ).
thf(f2767,plain,
( ( ( notinsingleton = $true )
| ( ( sK879 != sK878 )
& ( ( in @ sK878 @ ( setadjoin @ sK879 @ emptyset ) )
= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
| ( $true
!= ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) )
| ( notinsingleton != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK878,sK879])],[f2765,f2766]) ).
thf(f2766,plain,
( ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true ) )
=> ( ( sK879 != sK878 )
& ( ( in @ sK878 @ ( setadjoin @ sK879 @ emptyset ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2765,plain,
( ( ( notinsingleton = $true )
| ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
| ( $true
!= ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) )
| ( notinsingleton != $true ) ) ),
inference(rectify,[status(thm)],[f2764]) ).
thf(f2764,plain,
( ( ( notinsingleton = $true )
| ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true ) ) )
& ( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true ) )
| ( notinsingleton != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f1389]) ).
thf(f1389,plain,
( ( notinsingleton = $true )
<=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f984]) ).
thf(f984,plain,
( ! [X0: $i,X1: $i] :
( ( X0 != X1 )
=> ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true ) )
<=> ( notinsingleton = $true ) ),
inference(flattening,[status(thm)],[f355]) ).
thf(f355,plain,
( ! [X0: $i,X1: $i] :
( ( X0 != X1 )
=> ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true ) )
<=> ( notinsingleton = $true ) ),
inference(fool_elimination,[status(thm)],[f354]) ).
thf(f354,plain,
! [X0: $i,X1: $i] :
( ( ( X0 != X1 )
=> ~ ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= notinsingleton ),
inference(rectify,[status(thm)],[f47]) ).
thf(f47,axiom,
! [X2: $i,X1: $i] :
( ( ( X1 != X2 )
=> ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
= notinsingleton ),
file('/export/starexec/sandbox2/tmp/tmp.yv4wus1g2e/DTF2THF_4600.p',notinsingleton) ).
thf(f11332,plain,
! [X0: $i] :
( $true
!= ( in @ X0 @ ( sK273 @ ( setadjoin @ X0 @ emptyset ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f11326,f7577]) ).
thf(f11326,plain,
! [X0: $i] :
( ( emptyset
= ( setadjoin @ X0 @ emptyset ) )
| ( $true
!= ( in @ X0 @ ( sK273 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f11323]) ).
thf(f11323,plain,
! [X0: $i] :
( ( emptyset
= ( setadjoin @ X0 @ emptyset ) )
| ( $true
!= ( in @ X0 @ ( sK273 @ ( setadjoin @ X0 @ emptyset ) ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f7666,f6597]) ).
thf(f6597,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ ( setadjoin @ X1 @ emptyset ) @ X0 )
= $true )
| ( $true
!= ( in @ X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f5874]) ).
thf(f5874,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ ( setadjoin @ X1 @ emptyset ) @ X0 )
= $true )
| ( $true != $true )
| ( $true
!= ( in @ X1 @ X0 ) ) ),
inference(definition_unfolding,[status(thm)],[f4568,f3358]) ).
thf(f3358,plain,
singletonsubset = $true,
inference(cnf_transformation,[status(thm)],[f1465]) ).
thf(f4568,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ ( setadjoin @ X1 @ emptyset ) @ X0 )
= $true )
| ( $true
!= ( in @ X1 @ X0 ) )
| ( singletonsubset != $true ) ),
inference(cnf_transformation,[status(thm)],[f2758]) ).
thf(f2758,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ ( setadjoin @ X1 @ emptyset ) @ X0 )
= $true )
| ( $true
!= ( in @ X1 @ X0 ) ) )
| ( singletonsubset != $true ) )
& ( ( singletonsubset = $true )
| ( ( ( subset @ ( setadjoin @ sK875 @ emptyset ) @ sK874 )
!= $true )
& ( ( in @ sK875 @ sK874 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK874,sK875])],[f2756,f2757]) ).
thf(f2757,plain,
( ? [X2: $i,X3: $i] :
( ( $true
!= ( subset @ ( setadjoin @ X3 @ emptyset ) @ X2 ) )
& ( $true
= ( in @ X3 @ X2 ) ) )
=> ( ( ( subset @ ( setadjoin @ sK875 @ emptyset ) @ sK874 )
!= $true )
& ( ( in @ sK875 @ sK874 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2756,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ ( setadjoin @ X1 @ emptyset ) @ X0 )
= $true )
| ( $true
!= ( in @ X1 @ X0 ) ) )
| ( singletonsubset != $true ) )
& ( ( singletonsubset = $true )
| ? [X2: $i,X3: $i] :
( ( $true
!= ( subset @ ( setadjoin @ X3 @ emptyset ) @ X2 ) )
& ( $true
= ( in @ X3 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f2755]) ).
thf(f2755,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ ( setadjoin @ X1 @ emptyset ) @ X0 )
= $true )
| ( $true
!= ( in @ X1 @ X0 ) ) )
| ( singletonsubset != $true ) )
& ( ( singletonsubset = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ ( setadjoin @ X1 @ emptyset ) @ X0 )
!= $true )
& ( $true
= ( in @ X1 @ X0 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f1156]) ).
thf(f1156,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ ( setadjoin @ X1 @ emptyset ) @ X0 )
= $true )
| ( $true
!= ( in @ X1 @ X0 ) ) )
<=> ( singletonsubset = $true ) ),
inference(ennf_transformation,[status(thm)],[f811]) ).
thf(f811,plain,
( ( singletonsubset = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
=> ( ( subset @ ( setadjoin @ X1 @ emptyset ) @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f810]) ).
thf(f810,plain,
( singletonsubset
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ ( setadjoin @ X1 @ emptyset ) @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f140]) ).
thf(f140,axiom,
( singletonsubset
= ( ! [X3: $i,X1: $i] :
( ( in @ X1 @ X3 )
=> ( subset @ ( setadjoin @ X1 @ emptyset ) @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yv4wus1g2e/DTF2THF_4600.p',singletonsubset) ).
thf(f7666,plain,
! [X0: $i] :
( ( ( subset @ X0 @ ( sK273 @ X0 ) )
!= $true )
| ( emptyset = X0 ) ),
inference(duplicate_literal_removal,[status(thm)],[f7661]) ).
thf(f7661,plain,
! [X0: $i] :
( ( ( subset @ X0 @ ( sK273 @ X0 ) )
!= $true )
| ( emptyset = X0 )
| ( emptyset = X0 ) ),
inference(superposition,[status(thm)],[f6613,f6408]) ).
thf(f6408,plain,
! [X2: $i,X3: $i] :
( ( ( binintersect @ X2 @ X3 )
= X3 )
| ( $true
!= ( subset @ X3 @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f5124]) ).
thf(f5124,plain,
! [X2: $i,X3: $i] :
( ( ( binintersect @ X2 @ X3 )
= X3 )
| ( $true != $true )
| ( $true
!= ( subset @ X3 @ X2 ) ) ),
inference(definition_unfolding,[status(thm)],[f3728,f3211]) ).
thf(f3211,plain,
binintersectSubset4 = $true,
inference(cnf_transformation,[status(thm)],[f1465]) ).
thf(f3728,plain,
! [X2: $i,X3: $i] :
( ( $true
!= ( subset @ X3 @ X2 ) )
| ( ( binintersect @ X2 @ X3 )
= X3 )
| ( binintersectSubset4 != $true ) ),
inference(cnf_transformation,[status(thm)],[f1815]) ).
thf(f1815,plain,
( ( ( binintersectSubset4 = $true )
| ( ( $true
= ( subset @ sK256 @ sK255 ) )
& ( ( binintersect @ sK255 @ sK256 )
!= sK256 ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
!= ( subset @ X3 @ X2 ) )
| ( ( binintersect @ X2 @ X3 )
= X3 ) )
| ( binintersectSubset4 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK255,sK256])],[f1813,f1814]) ).
thf(f1814,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
& ( ( binintersect @ X0 @ X1 )
!= X1 ) )
=> ( ( $true
= ( subset @ sK256 @ sK255 ) )
& ( ( binintersect @ sK255 @ sK256 )
!= sK256 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1813,plain,
( ( ( binintersectSubset4 = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
& ( ( binintersect @ X0 @ X1 )
!= X1 ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
!= ( subset @ X3 @ X2 ) )
| ( ( binintersect @ X2 @ X3 )
= X3 ) )
| ( binintersectSubset4 != $true ) ) ),
inference(rectify,[status(thm)],[f1812]) ).
thf(f1812,plain,
( ( ( binintersectSubset4 = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
& ( ( binintersect @ X0 @ X1 )
!= X1 ) ) )
& ( ! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ X0 ) )
| ( ( binintersect @ X0 @ X1 )
= X1 ) )
| ( binintersectSubset4 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f1317]) ).
thf(f1317,plain,
( ( binintersectSubset4 = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ X0 ) )
| ( ( binintersect @ X0 @ X1 )
= X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f935]) ).
thf(f935,plain,
( ( binintersectSubset4 = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
=> ( ( binintersect @ X0 @ X1 )
= X1 ) ) ),
inference(fool_elimination,[status(thm)],[f934]) ).
thf(f934,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
=> ( ( binintersect @ X0 @ X1 )
= X1 ) )
= binintersectSubset4 ),
inference(rectify,[status(thm)],[f117]) ).
thf(f117,axiom,
! [X3: $i,X4: $i] :
( ( ( subset @ X4 @ X3 )
=> ( ( binintersect @ X3 @ X4 )
= X4 ) )
= binintersectSubset4 ),
file('/export/starexec/sandbox2/tmp/tmp.yv4wus1g2e/DTF2THF_4600.p',binintersectSubset4) ).
thf(f6613,plain,
! [X2: $i] :
( ( emptyset
= ( binintersect @ ( sK273 @ X2 ) @ X2 ) )
| ( emptyset = X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f6612]) ).
thf(f6612,plain,
! [X2: $i] :
( ( emptyset
= ( binintersect @ ( sK273 @ X2 ) @ X2 ) )
| ( $true
= ( emptyset = X2 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f6611]) ).
thf(f6611,plain,
! [X2: $i] :
( ( $true
!= ( emptyset != X2 ) )
| ( emptyset
= ( binintersect @ ( sK273 @ X2 ) @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f6610]) ).
thf(f6610,plain,
! [X2: $i] :
( ( emptyset
= ( binintersect @ ( sK273 @ X2 ) @ X2 ) )
| ( $true
!= ( ^ [Y0: $i] : ( emptyset != Y0 )
@ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f5144]) ).
thf(f5144,plain,
! [X2: $i] :
( ( $true
!= ( ^ [Y0: $i] : ( emptyset != Y0 )
@ X2 ) )
| ( emptyset
= ( binintersect @ ( sK273 @ X2 ) @ X2 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f3749,f3477,f3387]) ).
thf(f3749,plain,
! [X2: $i] :
( ( emptyset
= ( binintersect @ ( sK273 @ X2 ) @ X2 ) )
| ( $true
!= ( nonempty @ X2 ) )
| ( foundation2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f1840]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU806^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n025.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 12:34:42 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.42 ---- Original DTF file ---
% 0.17/0.42 thf(spec,logic,$$dhol).
% 0.17/0.42 %------------------------------------------------------------------------------
% 0.17/0.42 % File : SEU806^1 : TPTP v9.2.1. Released v3.7.0.
% 0.17/0.42 % Domain : Set Theory
% 0.17/0.42 % Problem : The Foundation Axiom
% 0.17/0.42 % Version : Especial.
% 0.17/0.42 % English : (! A:i.~(in A A))
% 0.17/0.42
% 0.17/0.42 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.17/0.42 % Source : [Bro08]
% 0.17/0.42 % Names : ZFC308g [Bro08]
% 0.17/0.42
% 0.17/0.42 % Status : Theorem
% 0.17/0.42 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.40 v8.2.0, 0.46 v8.1.0, 0.27 v7.5.0, 0.29 v7.4.0, 0.33 v7.3.0, 0.44 v7.2.0, 0.38 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.57 v6.1.0, 0.86 v5.5.0, 1.00 v3.7.0
% 0.17/0.42 % Syntax : Number of formulae : 700 ( 324 unt; 375 typ; 324 def)
% 0.17/0.42 % Number of atoms : 1998 ( 466 equ; 0 cnn)
% 0.17/0.42 % Maximal formula atoms : 323 ( 6 avg)
% 0.17/0.42 % Number of connectives : 4387 ( 75 ~; 14 |; 54 &;3194 @)
% 0.17/0.42 % ( 17 <=>;1033 =>; 0 <=; 0 <~>)
% 0.17/0.42 % Maximal formula depth : 327 ( 2 avg)
% 0.17/0.42 % Number of types : 2 ( 0 usr)
% 0.17/0.42 % Number of type conns : 176 ( 176 >; 0 *; 0 +; 0 <<)
% 0.17/0.42 % Number of symbols : 378 ( 375 usr; 326 con; 0-4 aty)
% 0.17/0.42 % Number of variables : 1144 ( 75 ^;1025 !; 44 ?;1144 :)
% 0.17/0.42 % SPC : TH0_THM_EQU_NAR
% 0.17/0.42
% 0.17/0.42 % Comments : http://mathgate.info/detsetitem.php?id=435
% 0.17/0.42 %------------------------------------------------------------------------------
% 0.17/0.42 thf(in_type,type,
% 0.17/0.42 in: $i > $i > $o ).
% 0.17/0.42
% 0.17/0.42 thf(exu_type,type,
% 0.17/0.42 exu: ( $i > $o ) > $o ).
% 0.17/0.42
% 0.17/0.42 thf(exu,definition,
% 0.17/0.42 ( exu
% 0.17/0.42 = ( ^ [Xphi: $i > $o] :
% 0.17/0.42 ? [Xx: $i] :
% 0.17/0.42 ( ( Xphi @ Xx )
% 0.17/0.42 & ! [Xy: $i] :
% 0.17/0.42 ( ( Xphi @ Xy )
% 0.17/0.42 => ( Xx = Xy ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setextAx_type,type,
% 0.17/0.42 setextAx: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setextAx,definition,
% 0.17/0.42 ( setextAx
% 0.17/0.42 = ( ! [A: $i,B: $i] :
% 0.17/0.42 ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 <=> ( in @ Xx @ B ) )
% 0.17/0.42 => ( A = B ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(emptyset_type,type,
% 0.17/0.42 emptyset: $i ).
% 0.17/0.42
% 0.17/0.42 thf(emptysetAx_type,type,
% 0.17/0.42 emptysetAx: $o ).
% 0.17/0.42
% 0.17/0.42 thf(emptysetAx,definition,
% 0.17/0.42 ( emptysetAx
% 0.17/0.42 = ( ! [Xx: $i] :
% 0.17/0.42 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setadjoin_type,type,
% 0.17/0.42 setadjoin: $i > $i > $i ).
% 0.17/0.42
% 0.17/0.42 thf(setadjoinAx_type,type,
% 0.17/0.42 setadjoinAx: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setadjoinAx,definition,
% 0.17/0.42 ( setadjoinAx
% 0.17/0.42 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.17/0.42 <=> ( ( Xy = Xx )
% 0.17/0.42 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(powerset_type,type,
% 0.17/0.42 powerset: $i > $i ).
% 0.17/0.42
% 0.17/0.42 thf(powersetAx_type,type,
% 0.17/0.42 powersetAx: $o ).
% 0.17/0.42
% 0.17/0.42 thf(powersetAx,definition,
% 0.17/0.42 ( powersetAx
% 0.17/0.42 = ( ! [A: $i,B: $i] :
% 0.17/0.42 ( ( in @ B @ ( powerset @ A ) )
% 0.17/0.42 <=> ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ B )
% 0.17/0.42 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setunion_type,type,
% 0.17/0.42 setunion: $i > $i ).
% 0.17/0.42
% 0.17/0.42 thf(setunionAx_type,type,
% 0.17/0.42 setunionAx: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setunionAx,definition,
% 0.17/0.42 ( setunionAx
% 0.17/0.42 = ( ! [A: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ ( setunion @ A ) )
% 0.17/0.42 <=> ? [B: $i] :
% 0.17/0.42 ( ( in @ Xx @ B )
% 0.17/0.42 & ( in @ B @ A ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(omega_type,type,
% 0.17/0.42 omega: $i ).
% 0.17/0.42
% 0.17/0.42 thf(omega0Ax_type,type,
% 0.17/0.42 omega0Ax: $o ).
% 0.17/0.42
% 0.17/0.42 thf(omega0Ax,definition,
% 0.17/0.42 ( omega0Ax
% 0.17/0.42 = ( in @ emptyset @ omega ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(omegaSAx_type,type,
% 0.17/0.42 omegaSAx: $o ).
% 0.17/0.42
% 0.17/0.42 thf(omegaSAx,definition,
% 0.17/0.42 ( omegaSAx
% 0.17/0.42 = ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ omega )
% 0.17/0.42 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(omegaIndAx_type,type,
% 0.17/0.42 omegaIndAx: $o ).
% 0.17/0.42
% 0.17/0.42 thf(omegaIndAx,definition,
% 0.17/0.42 ( omegaIndAx
% 0.17/0.42 = ( ! [A: $i] :
% 0.17/0.42 ( ( ( in @ emptyset @ A )
% 0.17/0.42 & ! [Xx: $i] :
% 0.17/0.42 ( ( ( in @ Xx @ omega )
% 0.17/0.42 & ( in @ Xx @ A ) )
% 0.17/0.42 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ omega )
% 0.17/0.42 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(replAx_type,type,
% 0.17/0.42 replAx: $o ).
% 0.17/0.42
% 0.17/0.42 thf(replAx,definition,
% 0.17/0.42 ( replAx
% 0.17/0.42 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.17/0.42 ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( exu
% 0.17/0.42 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.17/0.42 => ? [B: $i] :
% 0.17/0.42 ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ B )
% 0.17/0.42 <=> ? [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(foundationAx_type,type,
% 0.17/0.42 foundationAx: $o ).
% 0.17/0.42
% 0.17/0.42 thf(foundationAx,definition,
% 0.17/0.42 ( foundationAx
% 0.17/0.42 = ( ! [A: $i] :
% 0.17/0.42 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.17/0.42 => ? [B: $i] :
% 0.17/0.42 ( ( in @ B @ A )
% 0.17/0.42 & ~ ? [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ B )
% 0.17/0.42 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(wellorderingAx_type,type,
% 0.17/0.42 wellorderingAx: $o ).
% 0.17/0.42
% 0.17/0.42 thf(wellorderingAx,definition,
% 0.17/0.42 ( wellorderingAx
% 0.17/0.42 = ( ! [A: $i] :
% 0.17/0.42 ? [B: $i] :
% 0.17/0.42 ( ! [C: $i] :
% 0.17/0.42 ( ( in @ C @ B )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ C )
% 0.17/0.42 => ( in @ Xx @ A ) ) )
% 0.17/0.42 & ! [Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( ( in @ Xx @ A )
% 0.17/0.42 & ( in @ Xy @ A ) )
% 0.17/0.42 => ( ! [C: $i] :
% 0.17/0.42 ( ( in @ C @ B )
% 0.17/0.42 => ( ( in @ Xx @ C )
% 0.17/0.42 <=> ( in @ Xy @ C ) ) )
% 0.17/0.42 => ( Xx = Xy ) ) )
% 0.17/0.42 & ! [C: $i,D: $i] :
% 0.17/0.42 ( ( ( in @ C @ B )
% 0.17/0.42 & ( in @ D @ B ) )
% 0.17/0.42 => ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ C )
% 0.17/0.42 => ( in @ Xx @ D ) )
% 0.17/0.42 | ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ D )
% 0.17/0.42 => ( in @ Xx @ C ) ) ) )
% 0.17/0.42 & ! [C: $i] :
% 0.17/0.42 ( ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ C )
% 0.17/0.42 => ( in @ Xx @ A ) )
% 0.17/0.42 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.17/0.42 => ? [D: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ D @ B )
% 0.17/0.42 & ( in @ Xx @ C )
% 0.17/0.42 & ~ ? [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ D )
% 0.17/0.42 & ( in @ Xy @ C ) )
% 0.17/0.42 & ! [E: $i] :
% 0.17/0.42 ( ( in @ E @ B )
% 0.17/0.42 => ( ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ E )
% 0.17/0.42 => ( in @ Xy @ D ) )
% 0.17/0.42 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(descr_type,type,
% 0.17/0.42 descr: ( $i > $o ) > $i ).
% 0.17/0.42
% 0.17/0.42 thf(descrp_type,type,
% 0.17/0.42 descrp: $o ).
% 0.17/0.42
% 0.17/0.42 thf(descrp,definition,
% 0.17/0.42 ( descrp
% 0.17/0.42 = ( ! [Xphi: $i > $o] :
% 0.17/0.42 ( ( exu
% 0.17/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.42 => ( Xphi
% 0.17/0.42 @ ( descr
% 0.17/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(dsetconstr_type,type,
% 0.17/0.42 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.17/0.42
% 0.17/0.42 thf(dsetconstrI_type,type,
% 0.17/0.42 dsetconstrI: $o ).
% 0.17/0.42
% 0.17/0.42 thf(dsetconstrI,definition,
% 0.17/0.42 ( dsetconstrI
% 0.17/0.42 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( Xphi @ Xx )
% 0.17/0.42 => ( in @ Xx
% 0.17/0.42 @ ( dsetconstr @ A
% 0.17/0.42 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(dsetconstrEL_type,type,
% 0.17/0.42 dsetconstrEL: $o ).
% 0.17/0.42
% 0.17/0.42 thf(dsetconstrEL,definition,
% 0.17/0.42 ( dsetconstrEL
% 0.17/0.42 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx
% 0.17/0.42 @ ( dsetconstr @ A
% 0.17/0.42 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.17/0.42 => ( in @ Xx @ A ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(dsetconstrER_type,type,
% 0.17/0.42 dsetconstrER: $o ).
% 0.17/0.42
% 0.17/0.42 thf(dsetconstrER,definition,
% 0.17/0.42 ( dsetconstrER
% 0.17/0.42 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx
% 0.17/0.42 @ ( dsetconstr @ A
% 0.17/0.42 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.17/0.42 => ( Xphi @ Xx ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(exuE1_type,type,
% 0.17/0.42 exuE1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(exuE1,definition,
% 0.17/0.42 ( exuE1
% 0.17/0.42 = ( ! [Xphi: $i > $o] :
% 0.17/0.42 ( ( exu
% 0.17/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.42 => ? [Xx: $i] :
% 0.17/0.42 ( ( Xphi @ Xx )
% 0.17/0.42 & ! [Xy: $i] :
% 0.17/0.42 ( ( Xphi @ Xy )
% 0.17/0.42 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(prop2set_type,type,
% 0.17/0.42 prop2set: $o > $i ).
% 0.17/0.42
% 0.17/0.42 thf(prop2setE_type,type,
% 0.17/0.42 prop2setE: $o ).
% 0.17/0.42
% 0.17/0.42 thf(prop2setE,definition,
% 0.17/0.42 ( prop2setE
% 0.17/0.42 = ( ! [Xphi: $o,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.17/0.42 => Xphi ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(emptysetE_type,type,
% 0.17/0.42 emptysetE: $o ).
% 0.17/0.42
% 0.17/0.42 thf(emptysetE,definition,
% 0.17/0.42 ( emptysetE
% 0.17/0.42 = ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ emptyset )
% 0.17/0.42 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(emptysetimpfalse_type,type,
% 0.17/0.42 emptysetimpfalse: $o ).
% 0.17/0.42
% 0.17/0.42 thf(emptysetimpfalse,definition,
% 0.17/0.42 ( emptysetimpfalse
% 0.17/0.42 = ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ emptyset )
% 0.17/0.42 => $false ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(notinemptyset_type,type,
% 0.17/0.42 notinemptyset: $o ).
% 0.17/0.42
% 0.17/0.42 thf(notinemptyset,definition,
% 0.17/0.42 ( notinemptyset
% 0.17/0.42 = ( ! [Xx: $i] :
% 0.17/0.42 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(exuE3e_type,type,
% 0.17/0.42 exuE3e: $o ).
% 0.17/0.42
% 0.17/0.42 thf(exuE3e,definition,
% 0.17/0.42 ( exuE3e
% 0.17/0.42 = ( ! [Xphi: $i > $o] :
% 0.17/0.42 ( ( exu
% 0.17/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.42 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setext_type,type,
% 0.17/0.42 setext: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setext,definition,
% 0.17/0.42 ( setext
% 0.17/0.42 = ( ! [A: $i,B: $i] :
% 0.17/0.42 ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( in @ Xx @ B ) )
% 0.17/0.42 => ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ B )
% 0.17/0.42 => ( in @ Xx @ A ) )
% 0.17/0.42 => ( A = B ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(emptyI_type,type,
% 0.17/0.42 emptyI: $o ).
% 0.17/0.42
% 0.17/0.42 thf(emptyI,definition,
% 0.17/0.42 ( emptyI
% 0.17/0.42 = ( ! [A: $i] :
% 0.17/0.42 ( ! [Xx: $i] :
% 0.17/0.42 ~ ( in @ Xx @ A )
% 0.17/0.42 => ( A = emptyset ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(noeltsimpempty_type,type,
% 0.17/0.42 noeltsimpempty: $o ).
% 0.17/0.42
% 0.17/0.42 thf(noeltsimpempty,definition,
% 0.17/0.42 ( noeltsimpempty
% 0.17/0.42 = ( ! [A: $i] :
% 0.17/0.42 ( ! [Xx: $i] :
% 0.17/0.42 ~ ( in @ Xx @ A )
% 0.17/0.42 => ( A = emptyset ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setbeta_type,type,
% 0.17/0.42 setbeta: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setbeta,definition,
% 0.17/0.42 ( setbeta
% 0.17/0.42 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( in @ Xx
% 0.17/0.42 @ ( dsetconstr @ A
% 0.17/0.42 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.17/0.42 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(nonempty_type,type,
% 0.17/0.42 nonempty: $i > $o ).
% 0.17/0.42
% 0.17/0.42 thf(nonempty,definition,
% 0.17/0.42 ( nonempty
% 0.17/0.42 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(nonemptyE1_type,type,
% 0.17/0.42 nonemptyE1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(nonemptyE1,definition,
% 0.17/0.42 ( nonemptyE1
% 0.17/0.42 = ( ! [A: $i] :
% 0.17/0.42 ( ( nonempty @ A )
% 0.17/0.42 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(nonemptyI_type,type,
% 0.17/0.42 nonemptyI: $o ).
% 0.17/0.42
% 0.17/0.42 thf(nonemptyI,definition,
% 0.17/0.42 ( nonemptyI
% 0.17/0.42 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( Xphi @ Xx )
% 0.17/0.42 => ( nonempty
% 0.17/0.42 @ ( dsetconstr @ A
% 0.17/0.42 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(nonemptyI1_type,type,
% 0.17/0.42 nonemptyI1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(nonemptyI1,definition,
% 0.17/0.42 ( nonemptyI1
% 0.17/0.42 = ( ! [A: $i] :
% 0.17/0.42 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.17/0.42 => ( nonempty @ A ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setadjoinIL_type,type,
% 0.17/0.42 setadjoinIL: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setadjoinIL,definition,
% 0.17/0.42 ( setadjoinIL
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(emptyinunitempty_type,type,
% 0.17/0.42 emptyinunitempty: $o ).
% 0.17/0.42
% 0.17/0.42 thf(emptyinunitempty,definition,
% 0.17/0.42 ( emptyinunitempty
% 0.17/0.42 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setadjoinIR_type,type,
% 0.17/0.42 setadjoinIR: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setadjoinIR,definition,
% 0.17/0.42 ( setadjoinIR
% 0.17/0.42 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setadjoinE_type,type,
% 0.17/0.42 setadjoinE: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setadjoinE,definition,
% 0.17/0.42 ( setadjoinE
% 0.17/0.42 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.17/0.42 => ! [Xphi: $o] :
% 0.17/0.42 ( ( ( Xy = Xx )
% 0.17/0.42 => Xphi )
% 0.17/0.42 => ( ( ( in @ Xy @ A )
% 0.17/0.42 => Xphi )
% 0.17/0.42 => Xphi ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setadjoinOr_type,type,
% 0.17/0.42 setadjoinOr: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setadjoinOr,definition,
% 0.17/0.42 ( setadjoinOr
% 0.17/0.42 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.17/0.42 => ( ( Xy = Xx )
% 0.17/0.42 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setoftrueEq_type,type,
% 0.17/0.42 setoftrueEq: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setoftrueEq,definition,
% 0.17/0.42 ( setoftrueEq
% 0.17/0.42 = ( ! [A: $i] :
% 0.17/0.42 ( ( dsetconstr @ A
% 0.17/0.42 @ ^ [Xx: $i] : $true )
% 0.17/0.42 = A ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(powersetI_type,type,
% 0.17/0.42 powersetI: $o ).
% 0.17/0.42
% 0.17/0.42 thf(powersetI,definition,
% 0.17/0.42 ( powersetI
% 0.17/0.42 = ( ! [A: $i,B: $i] :
% 0.17/0.42 ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ B )
% 0.17/0.42 => ( in @ Xx @ A ) )
% 0.17/0.42 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(emptyinPowerset_type,type,
% 0.17/0.42 emptyinPowerset: $o ).
% 0.17/0.42
% 0.17/0.42 thf(emptyinPowerset,definition,
% 0.17/0.42 ( emptyinPowerset
% 0.17/0.42 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(emptyInPowerset_type,type,
% 0.17/0.42 emptyInPowerset: $o ).
% 0.17/0.42
% 0.17/0.42 thf(emptyInPowerset,definition,
% 0.17/0.42 ( emptyInPowerset
% 0.17/0.42 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(powersetE_type,type,
% 0.17/0.42 powersetE: $o ).
% 0.17/0.42
% 0.17/0.42 thf(powersetE,definition,
% 0.17/0.42 ( powersetE
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ B @ ( powerset @ A ) )
% 0.17/0.42 => ( ( in @ Xx @ B )
% 0.17/0.42 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setunionI_type,type,
% 0.17/0.42 setunionI: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setunionI,definition,
% 0.17/0.42 ( setunionI
% 0.17/0.42 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.17/0.42 ( ( in @ Xx @ B )
% 0.17/0.42 => ( ( in @ B @ A )
% 0.17/0.42 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setunionE_type,type,
% 0.17/0.42 setunionE: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setunionE,definition,
% 0.17/0.42 ( setunionE
% 0.17/0.42 = ( ! [A: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ ( setunion @ A ) )
% 0.17/0.42 => ! [Xphi: $o] :
% 0.17/0.42 ( ! [B: $i] :
% 0.17/0.42 ( ( in @ Xx @ B )
% 0.17/0.42 => ( ( in @ B @ A )
% 0.17/0.42 => Xphi ) )
% 0.17/0.42 => Xphi ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(subPowSU_type,type,
% 0.17/0.42 subPowSU: $o ).
% 0.17/0.42
% 0.17/0.42 thf(subPowSU,definition,
% 0.17/0.42 ( subPowSU
% 0.17/0.42 = ( ! [A: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(exuE2_type,type,
% 0.17/0.42 exuE2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(exuE2,definition,
% 0.17/0.42 ( exuE2
% 0.17/0.42 = ( ! [Xphi: $i > $o] :
% 0.17/0.42 ( ( exu
% 0.17/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.42 => ? [Xx: $i] :
% 0.17/0.42 ! [Xy: $i] :
% 0.17/0.42 ( ( Xphi @ Xy )
% 0.17/0.42 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(nonemptyImpWitness_type,type,
% 0.17/0.42 nonemptyImpWitness: $o ).
% 0.17/0.42
% 0.17/0.42 thf(nonemptyImpWitness,definition,
% 0.17/0.42 ( nonemptyImpWitness
% 0.17/0.42 = ( ! [A: $i] :
% 0.17/0.42 ( ( nonempty @ A )
% 0.17/0.42 => ? [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 & $true ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(uniqinunit_type,type,
% 0.17/0.42 uniqinunit: $o ).
% 0.17/0.42
% 0.17/0.42 thf(uniqinunit,definition,
% 0.17/0.42 ( uniqinunit
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.17/0.42 => ( Xx = Xy ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(notinsingleton_type,type,
% 0.17/0.42 notinsingleton: $o ).
% 0.17/0.42
% 0.17/0.42 thf(notinsingleton,definition,
% 0.17/0.42 ( notinsingleton
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( Xx != Xy )
% 0.17/0.42 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(eqinunit_type,type,
% 0.17/0.42 eqinunit: $o ).
% 0.17/0.42
% 0.17/0.42 thf(eqinunit,definition,
% 0.17/0.42 ( eqinunit
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( Xx = Xy )
% 0.17/0.42 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(singletonsswitch_type,type,
% 0.17/0.42 singletonsswitch: $o ).
% 0.17/0.42
% 0.17/0.42 thf(singletonsswitch,definition,
% 0.17/0.42 ( singletonsswitch
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.17/0.42 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(upairsetE_type,type,
% 0.17/0.42 upairsetE: $o ).
% 0.17/0.42
% 0.17/0.42 thf(upairsetE,definition,
% 0.17/0.42 ( upairsetE
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.17/0.42 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.17/0.42 => ( ( Xz = Xx )
% 0.17/0.42 | ( Xz = Xy ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(upairsetIL_type,type,
% 0.17/0.42 upairsetIL: $o ).
% 0.17/0.42
% 0.17/0.42 thf(upairsetIL,definition,
% 0.17/0.42 ( upairsetIL
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(upairsetIR_type,type,
% 0.17/0.42 upairsetIR: $o ).
% 0.17/0.42
% 0.17/0.42 thf(upairsetIR,definition,
% 0.17/0.42 ( upairsetIR
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(emptyE1_type,type,
% 0.17/0.42 emptyE1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(emptyE1,definition,
% 0.17/0.42 ( emptyE1
% 0.17/0.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.42 ( ? [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 & ( Xphi @ Xx ) )
% 0.17/0.42 => ( ( ( dsetconstr @ A
% 0.17/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.42 = emptyset )
% 0.17/0.42 => $false ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(vacuousDall_type,type,
% 0.17/0.42 vacuousDall: $o ).
% 0.17/0.42
% 0.17/0.42 thf(vacuousDall,definition,
% 0.17/0.42 ( vacuousDall
% 0.17/0.42 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ emptyset )
% 0.17/0.42 => ( Xphi @ Xx ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(quantDeMorgan1_type,type,
% 0.17/0.42 quantDeMorgan1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(quantDeMorgan1,definition,
% 0.17/0.42 ( quantDeMorgan1
% 0.17/0.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.42 ( ~ ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( Xphi @ Xx ) )
% 0.17/0.42 => ? [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(quantDeMorgan2_type,type,
% 0.17/0.42 quantDeMorgan2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(quantDeMorgan2,definition,
% 0.17/0.42 ( quantDeMorgan2
% 0.17/0.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.42 ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ~ ( Xphi @ Xx ) )
% 0.17/0.42 => ~ ? [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(quantDeMorgan3_type,type,
% 0.17/0.42 quantDeMorgan3: $o ).
% 0.17/0.42
% 0.17/0.42 thf(quantDeMorgan3,definition,
% 0.17/0.42 ( quantDeMorgan3
% 0.17/0.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.42 ( ~ ? [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 & ( Xphi @ Xx ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(quantDeMorgan4_type,type,
% 0.17/0.42 quantDeMorgan4: $o ).
% 0.17/0.42
% 0.17/0.42 thf(quantDeMorgan4,definition,
% 0.17/0.42 ( quantDeMorgan4
% 0.17/0.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.42 ( ? [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 & ~ ( Xphi @ Xx ) )
% 0.17/0.42 => ~ ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(prop2setI_type,type,
% 0.17/0.42 prop2setI: $o ).
% 0.17/0.42
% 0.17/0.42 thf(prop2setI,definition,
% 0.17/0.42 ( prop2setI
% 0.17/0.42 = ( ! [Xphi: $o] :
% 0.17/0.42 ( Xphi
% 0.17/0.42 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(set2prop_type,type,
% 0.17/0.42 set2prop: $i > $o ).
% 0.17/0.42
% 0.17/0.42 thf(prop2set2propI_type,type,
% 0.17/0.42 prop2set2propI: $o ).
% 0.17/0.42
% 0.17/0.42 thf(prop2set2propI,definition,
% 0.17/0.42 ( prop2set2propI
% 0.17/0.42 = ( ! [Xphi: $o] :
% 0.17/0.42 ( Xphi
% 0.17/0.42 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(notdexE_type,type,
% 0.17/0.42 notdexE: $o ).
% 0.17/0.42
% 0.17/0.42 thf(notdexE,definition,
% 0.17/0.42 ( notdexE
% 0.17/0.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.42 ( ~ ? [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 & ( Xphi @ Xx ) )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(notdallE_type,type,
% 0.17/0.42 notdallE: $o ).
% 0.17/0.42
% 0.17/0.42 thf(notdallE,definition,
% 0.17/0.42 ( notdallE
% 0.17/0.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.42 ( ~ ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( Xphi @ Xx ) )
% 0.17/0.42 => ? [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(exuI1_type,type,
% 0.17/0.42 exuI1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(exuI1,definition,
% 0.17/0.42 ( exuI1
% 0.17/0.42 = ( ! [Xphi: $i > $o] :
% 0.17/0.42 ( ? [Xx: $i] :
% 0.17/0.42 ( ( Xphi @ Xx )
% 0.17/0.42 & ! [Xy: $i] :
% 0.17/0.42 ( ( Xphi @ Xy )
% 0.17/0.42 => ( Xx = Xy ) ) )
% 0.17/0.42 => ( exu
% 0.17/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(exuI3_type,type,
% 0.17/0.42 exuI3: $o ).
% 0.17/0.42
% 0.17/0.42 thf(exuI3,definition,
% 0.17/0.42 ( exuI3
% 0.17/0.42 = ( ! [Xphi: $i > $o] :
% 0.17/0.42 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.17/0.42 => ( ! [Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( Xphi @ Xx )
% 0.17/0.42 => ( ( Xphi @ Xy )
% 0.17/0.42 => ( Xx = Xy ) ) )
% 0.17/0.42 => ( exu
% 0.17/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(exuI2_type,type,
% 0.17/0.42 exuI2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(exuI2,definition,
% 0.17/0.42 ( exuI2
% 0.17/0.42 = ( ! [Xphi: $i > $o] :
% 0.17/0.42 ( ? [Xx: $i] :
% 0.17/0.42 ! [Xy: $i] :
% 0.17/0.42 ( ( Xphi @ Xy )
% 0.17/0.42 <=> ( Xy = Xx ) )
% 0.17/0.42 => ( exu
% 0.17/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(inCongP_type,type,
% 0.17/0.42 inCongP: $o ).
% 0.17/0.42
% 0.17/0.42 thf(inCongP,definition,
% 0.17/0.42 ( inCongP
% 0.17/0.42 = ( ! [A: $i,B: $i] :
% 0.17/0.42 ( ( A = B )
% 0.17/0.42 => ! [Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( Xx = Xy )
% 0.17/0.42 => ( ( in @ Xx @ A )
% 0.17/0.42 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(in__Cong_type,type,
% 0.17/0.42 in__Cong: $o ).
% 0.17/0.42
% 0.17/0.42 thf(in__Cong,definition,
% 0.17/0.42 ( in__Cong
% 0.17/0.42 = ( ! [A: $i,B: $i] :
% 0.17/0.42 ( ( A = B )
% 0.17/0.42 => ! [Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( Xx = Xy )
% 0.17/0.42 => ( ( in @ Xx @ A )
% 0.17/0.42 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(exuE3u_type,type,
% 0.17/0.42 exuE3u: $o ).
% 0.17/0.42
% 0.17/0.42 thf(exuE3u,definition,
% 0.17/0.42 ( exuE3u
% 0.17/0.42 = ( ! [Xphi: $i > $o] :
% 0.17/0.42 ( ( exu
% 0.17/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.42 => ! [Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( Xphi @ Xx )
% 0.17/0.42 => ( ( Xphi @ Xy )
% 0.17/0.42 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(exu__Cong_type,type,
% 0.17/0.42 exu__Cong: $o ).
% 0.17/0.42
% 0.17/0.42 thf(exu__Cong,definition,
% 0.17/0.42 ( exu__Cong
% 0.17/0.42 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.17/0.42 ( ! [Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( Xx = Xy )
% 0.17/0.42 => ( ( Xphi @ Xx )
% 0.17/0.42 <=> ( Xpsi @ Xy ) ) )
% 0.17/0.42 => ( ( exu
% 0.17/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.42 <=> ( exu
% 0.17/0.42 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(emptyset__Cong_type,type,
% 0.17/0.42 emptyset__Cong: $o ).
% 0.17/0.42
% 0.17/0.42 thf(emptyset__Cong,definition,
% 0.17/0.42 ( emptyset__Cong
% 0.17/0.42 = ( emptyset = emptyset ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setadjoin__Cong_type,type,
% 0.17/0.42 setadjoin__Cong: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setadjoin__Cong,definition,
% 0.17/0.42 ( setadjoin__Cong
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( Xx = Xy )
% 0.17/0.42 => ! [Xz: $i,Xu: $i] :
% 0.17/0.42 ( ( Xz = Xu )
% 0.17/0.42 => ( ( setadjoin @ Xx @ Xz )
% 0.17/0.42 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(powerset__Cong_type,type,
% 0.17/0.42 powerset__Cong: $o ).
% 0.17/0.42
% 0.17/0.42 thf(powerset__Cong,definition,
% 0.17/0.42 ( powerset__Cong
% 0.17/0.42 = ( ! [A: $i,B: $i] :
% 0.17/0.42 ( ( A = B )
% 0.17/0.42 => ( ( powerset @ A )
% 0.17/0.42 = ( powerset @ B ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setunion__Cong_type,type,
% 0.17/0.42 setunion__Cong: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setunion__Cong,definition,
% 0.17/0.42 ( setunion__Cong
% 0.17/0.42 = ( ! [A: $i,B: $i] :
% 0.17/0.42 ( ( A = B )
% 0.17/0.42 => ( ( setunion @ A )
% 0.17/0.42 = ( setunion @ B ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(omega__Cong_type,type,
% 0.17/0.42 omega__Cong: $o ).
% 0.17/0.42
% 0.17/0.42 thf(omega__Cong,definition,
% 0.17/0.42 ( omega__Cong
% 0.17/0.42 = ( omega = omega ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(exuEu_type,type,
% 0.17/0.42 exuEu: $o ).
% 0.17/0.42
% 0.17/0.42 thf(exuEu,definition,
% 0.17/0.42 ( exuEu
% 0.17/0.42 = ( ! [Xphi: $i > $o] :
% 0.17/0.42 ( ( exu
% 0.17/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.42 => ! [Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( Xphi @ Xx )
% 0.17/0.42 => ( ( Xphi @ Xy )
% 0.17/0.42 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(descr__Cong_type,type,
% 0.17/0.42 descr__Cong: $o ).
% 0.17/0.42
% 0.17/0.42 thf(descr__Cong,definition,
% 0.17/0.42 ( descr__Cong
% 0.17/0.42 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.17/0.42 ( ! [Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( Xx = Xy )
% 0.17/0.42 => ( ( Xphi @ Xx )
% 0.17/0.42 <=> ( Xpsi @ Xy ) ) )
% 0.17/0.42 => ( ( exu
% 0.17/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.42 => ( ( exu
% 0.17/0.42 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.17/0.42 => ( ( descr
% 0.17/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.42 = ( descr
% 0.17/0.42 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(dsetconstr__Cong_type,type,
% 0.17/0.42 dsetconstr__Cong: $o ).
% 0.17/0.42
% 0.17/0.42 thf(dsetconstr__Cong,definition,
% 0.17/0.42 ( dsetconstr__Cong
% 0.17/0.42 = ( ! [A: $i,B: $i] :
% 0.17/0.42 ( ( A = B )
% 0.17/0.42 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.17/0.42 ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ B )
% 0.17/0.42 => ( ( Xx = Xy )
% 0.17/0.42 => ( ( Xphi @ Xx )
% 0.17/0.42 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.17/0.42 => ( ( dsetconstr @ A
% 0.17/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.42 = ( dsetconstr @ B
% 0.17/0.42 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(subset_type,type,
% 0.17/0.42 subset: $i > $i > $o ).
% 0.17/0.42
% 0.17/0.42 thf(disjoint_type,type,
% 0.17/0.42 disjoint: $i > $i > $o ).
% 0.17/0.42
% 0.17/0.42 thf(setsmeet_type,type,
% 0.17/0.42 setsmeet: $i > $i > $o ).
% 0.17/0.42
% 0.17/0.42 thf(subsetI1_type,type,
% 0.17/0.42 subsetI1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(subsetI1,definition,
% 0.17/0.42 ( subsetI1
% 0.17/0.42 = ( ! [A: $i,B: $i] :
% 0.17/0.42 ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( in @ Xx @ B ) )
% 0.17/0.42 => ( subset @ A @ B ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(eqimpsubset2_type,type,
% 0.17/0.42 eqimpsubset2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(eqimpsubset2,definition,
% 0.17/0.42 ( eqimpsubset2
% 0.17/0.42 = ( ! [A: $i,B: $i] :
% 0.17/0.42 ( ( A = B )
% 0.17/0.42 => ( subset @ B @ A ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(eqimpsubset1_type,type,
% 0.17/0.42 eqimpsubset1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(eqimpsubset1,definition,
% 0.17/0.42 ( eqimpsubset1
% 0.17/0.42 = ( ! [A: $i,B: $i] :
% 0.17/0.42 ( ( A = B )
% 0.17/0.42 => ( subset @ A @ B ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(subsetI2_type,type,
% 0.17/0.42 subsetI2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(subsetI2,definition,
% 0.17/0.42 ( subsetI2
% 0.17/0.42 = ( ! [A: $i,B: $i] :
% 0.17/0.42 ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( in @ Xx @ B ) )
% 0.17/0.42 => ( subset @ A @ B ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(emptysetsubset_type,type,
% 0.17/0.42 emptysetsubset: $o ).
% 0.17/0.42
% 0.17/0.42 thf(emptysetsubset,definition,
% 0.17/0.42 ( emptysetsubset
% 0.17/0.42 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(subsetE_type,type,
% 0.17/0.42 subsetE: $o ).
% 0.17/0.42
% 0.17/0.42 thf(subsetE,definition,
% 0.17/0.42 ( subsetE
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( subset @ A @ B )
% 0.17/0.42 => ( ( in @ Xx @ A )
% 0.17/0.42 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(subsetE2_type,type,
% 0.17/0.42 subsetE2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(subsetE2,definition,
% 0.17/0.42 ( subsetE2
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( subset @ A @ B )
% 0.17/0.42 => ( ~ ( in @ Xx @ B )
% 0.17/0.42 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(notsubsetI_type,type,
% 0.17/0.42 notsubsetI: $o ).
% 0.17/0.42
% 0.17/0.42 thf(notsubsetI,definition,
% 0.17/0.42 ( notsubsetI
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ~ ( in @ Xx @ B )
% 0.17/0.42 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(notequalI1_type,type,
% 0.17/0.42 notequalI1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(notequalI1,definition,
% 0.17/0.42 ( notequalI1
% 0.17/0.42 = ( ! [A: $i,B: $i] :
% 0.17/0.42 ( ~ ( subset @ A @ B )
% 0.17/0.42 => ( A != B ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(notequalI2_type,type,
% 0.17/0.42 notequalI2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(notequalI2,definition,
% 0.17/0.42 ( notequalI2
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ~ ( in @ Xx @ B )
% 0.17/0.42 => ( A != B ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(subsetRefl_type,type,
% 0.17/0.42 subsetRefl: $o ).
% 0.17/0.42
% 0.17/0.42 thf(subsetRefl,definition,
% 0.17/0.42 ( subsetRefl
% 0.17/0.42 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(subsetTrans_type,type,
% 0.17/0.42 subsetTrans: $o ).
% 0.17/0.42
% 0.17/0.42 thf(subsetTrans,definition,
% 0.17/0.42 ( subsetTrans
% 0.17/0.42 = ( ! [A: $i,B: $i,C: $i] :
% 0.17/0.42 ( ( subset @ A @ B )
% 0.17/0.42 => ( ( subset @ B @ C )
% 0.17/0.42 => ( subset @ A @ C ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setadjoinSub_type,type,
% 0.17/0.42 setadjoinSub: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setadjoinSub,definition,
% 0.17/0.42 ( setadjoinSub
% 0.17/0.42 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setadjoinSub2_type,type,
% 0.17/0.42 setadjoinSub2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setadjoinSub2,definition,
% 0.17/0.42 ( setadjoinSub2
% 0.17/0.42 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.17/0.42 ( ( subset @ A @ B )
% 0.17/0.42 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(subset2powerset_type,type,
% 0.17/0.42 subset2powerset: $o ).
% 0.17/0.42
% 0.17/0.42 thf(subset2powerset,definition,
% 0.17/0.42 ( subset2powerset
% 0.17/0.42 = ( ! [A: $i,B: $i] :
% 0.17/0.42 ( ( subset @ A @ B )
% 0.17/0.42 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setextsub_type,type,
% 0.17/0.42 setextsub: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setextsub,definition,
% 0.17/0.42 ( setextsub
% 0.17/0.42 = ( ! [A: $i,B: $i] :
% 0.17/0.42 ( ( subset @ A @ B )
% 0.17/0.42 => ( ( subset @ B @ A )
% 0.17/0.42 => ( A = B ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(subsetemptysetimpeq_type,type,
% 0.17/0.42 subsetemptysetimpeq: $o ).
% 0.17/0.42
% 0.17/0.42 thf(subsetemptysetimpeq,definition,
% 0.17/0.42 ( subsetemptysetimpeq
% 0.17/0.42 = ( ! [A: $i] :
% 0.17/0.42 ( ( subset @ A @ emptyset )
% 0.17/0.42 => ( A = emptyset ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(powersetI1_type,type,
% 0.17/0.42 powersetI1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(powersetI1,definition,
% 0.17/0.42 ( powersetI1
% 0.17/0.42 = ( ! [A: $i,B: $i] :
% 0.17/0.42 ( ( subset @ B @ A )
% 0.17/0.42 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(powersetE1_type,type,
% 0.17/0.42 powersetE1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(powersetE1,definition,
% 0.17/0.42 ( powersetE1
% 0.17/0.42 = ( ! [A: $i,B: $i] :
% 0.17/0.42 ( ( in @ B @ ( powerset @ A ) )
% 0.17/0.42 => ( subset @ B @ A ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(inPowerset_type,type,
% 0.17/0.42 inPowerset: $o ).
% 0.17/0.42
% 0.17/0.42 thf(inPowerset,definition,
% 0.17/0.42 ( inPowerset
% 0.17/0.42 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(powersetsubset_type,type,
% 0.17/0.42 powersetsubset: $o ).
% 0.17/0.42
% 0.17/0.42 thf(powersetsubset,definition,
% 0.17/0.42 ( powersetsubset
% 0.17/0.42 = ( ! [A: $i,B: $i] :
% 0.17/0.42 ( ( subset @ A @ B )
% 0.17/0.42 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(sepInPowerset_type,type,
% 0.17/0.42 sepInPowerset: $o ).
% 0.17/0.42
% 0.17/0.42 thf(sepInPowerset,definition,
% 0.17/0.42 ( sepInPowerset
% 0.17/0.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.42 ( in
% 0.17/0.42 @ ( dsetconstr @ A
% 0.17/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.42 @ ( powerset @ A ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(sepSubset_type,type,
% 0.17/0.42 sepSubset: $o ).
% 0.17/0.42
% 0.17/0.42 thf(sepSubset,definition,
% 0.17/0.42 ( sepSubset
% 0.17/0.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.42 ( subset
% 0.17/0.42 @ ( dsetconstr @ A
% 0.17/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.42 @ A ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(binunion_type,type,
% 0.17/0.42 binunion: $i > $i > $i ).
% 0.17/0.42
% 0.17/0.42 thf(binunionIL_type,type,
% 0.17/0.42 binunionIL: $o ).
% 0.17/0.42
% 0.17/0.42 thf(binunionIL,definition,
% 0.17/0.42 ( binunionIL
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(upairset2IR_type,type,
% 0.17/0.42 upairset2IR: $o ).
% 0.17/0.42
% 0.17/0.42 thf(upairset2IR,definition,
% 0.17/0.42 ( upairset2IR
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(binunionIR_type,type,
% 0.17/0.42 binunionIR: $o ).
% 0.17/0.42
% 0.17/0.42 thf(binunionIR,definition,
% 0.17/0.42 ( binunionIR
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ B )
% 0.17/0.42 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(binunionEcases_type,type,
% 0.17/0.42 binunionEcases: $o ).
% 0.17/0.42
% 0.17/0.42 thf(binunionEcases,definition,
% 0.17/0.42 ( binunionEcases
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.17/0.42 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.17/0.42 => ( ( ( in @ Xx @ A )
% 0.17/0.42 => Xphi )
% 0.17/0.42 => ( ( ( in @ Xx @ B )
% 0.17/0.42 => Xphi )
% 0.17/0.42 => Xphi ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(binunionE_type,type,
% 0.17/0.42 binunionE: $o ).
% 0.17/0.42
% 0.17/0.42 thf(binunionE,definition,
% 0.17/0.42 ( binunionE
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.17/0.42 => ( ( in @ Xx @ A )
% 0.17/0.42 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(binunionLsub_type,type,
% 0.17/0.42 binunionLsub: $o ).
% 0.17/0.42
% 0.17/0.42 thf(binunionLsub,definition,
% 0.17/0.42 ( binunionLsub
% 0.17/0.42 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(binunionRsub_type,type,
% 0.17/0.42 binunionRsub: $o ).
% 0.17/0.42
% 0.17/0.42 thf(binunionRsub,definition,
% 0.17/0.42 ( binunionRsub
% 0.17/0.42 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(binintersect_type,type,
% 0.17/0.42 binintersect: $i > $i > $i ).
% 0.17/0.42
% 0.17/0.42 thf(binintersectI_type,type,
% 0.17/0.42 binintersectI: $o ).
% 0.17/0.42
% 0.17/0.42 thf(binintersectI,definition,
% 0.17/0.42 ( binintersectI
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( in @ Xx @ B )
% 0.17/0.42 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(binintersectSubset5_type,type,
% 0.17/0.42 binintersectSubset5: $o ).
% 0.17/0.42
% 0.17/0.42 thf(binintersectSubset5,definition,
% 0.17/0.42 ( binintersectSubset5
% 0.17/0.42 = ( ! [A: $i,B: $i,C: $i] :
% 0.17/0.42 ( ( subset @ C @ A )
% 0.17/0.42 => ( ( subset @ C @ B )
% 0.17/0.42 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(binintersectEL_type,type,
% 0.17/0.42 binintersectEL: $o ).
% 0.17/0.42
% 0.17/0.42 thf(binintersectEL,definition,
% 0.17/0.42 ( binintersectEL
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.17/0.42 => ( in @ Xx @ A ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(binintersectLsub_type,type,
% 0.17/0.42 binintersectLsub: $o ).
% 0.17/0.42
% 0.17/0.42 thf(binintersectLsub,definition,
% 0.17/0.42 ( binintersectLsub
% 0.17/0.42 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(binintersectSubset2_type,type,
% 0.17/0.42 binintersectSubset2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(binintersectSubset2,definition,
% 0.17/0.42 ( binintersectSubset2
% 0.17/0.42 = ( ! [A: $i,B: $i] :
% 0.17/0.42 ( ( subset @ A @ B )
% 0.17/0.42 => ( ( binintersect @ A @ B )
% 0.17/0.42 = A ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(binintersectSubset3_type,type,
% 0.17/0.42 binintersectSubset3: $o ).
% 0.17/0.42
% 0.17/0.42 thf(binintersectSubset3,definition,
% 0.17/0.42 ( binintersectSubset3
% 0.17/0.42 = ( ! [A: $i,B: $i] :
% 0.17/0.42 ( ( ( binintersect @ A @ B )
% 0.17/0.42 = B )
% 0.17/0.42 => ( subset @ B @ A ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(binintersectER_type,type,
% 0.17/0.42 binintersectER: $o ).
% 0.17/0.42
% 0.17/0.42 thf(binintersectER,definition,
% 0.17/0.42 ( binintersectER
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.17/0.42 => ( in @ Xx @ B ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(disjointsetsI1_type,type,
% 0.17/0.42 disjointsetsI1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(disjointsetsI1,definition,
% 0.17/0.42 ( disjointsetsI1
% 0.17/0.42 = ( ! [A: $i,B: $i] :
% 0.17/0.42 ( ~ ? [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 & ( in @ Xx @ B ) )
% 0.17/0.42 => ( ( binintersect @ A @ B )
% 0.17/0.42 = emptyset ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(binintersectRsub_type,type,
% 0.17/0.42 binintersectRsub: $o ).
% 0.17/0.42
% 0.17/0.42 thf(binintersectRsub,definition,
% 0.17/0.42 ( binintersectRsub
% 0.17/0.42 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(binintersectSubset4_type,type,
% 0.17/0.42 binintersectSubset4: $o ).
% 0.17/0.42
% 0.17/0.42 thf(binintersectSubset4,definition,
% 0.17/0.42 ( binintersectSubset4
% 0.17/0.42 = ( ! [A: $i,B: $i] :
% 0.17/0.42 ( ( subset @ B @ A )
% 0.17/0.42 => ( ( binintersect @ A @ B )
% 0.17/0.42 = B ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(binintersectSubset1_type,type,
% 0.17/0.42 binintersectSubset1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(binintersectSubset1,definition,
% 0.17/0.42 ( binintersectSubset1
% 0.17/0.42 = ( ! [A: $i,B: $i] :
% 0.17/0.42 ( ( ( binintersect @ A @ B )
% 0.17/0.42 = A )
% 0.17/0.42 => ( subset @ A @ B ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(bs114d_type,type,
% 0.17/0.42 bs114d: $o ).
% 0.17/0.42
% 0.17/0.42 thf(bs114d,definition,
% 0.17/0.42 ( bs114d
% 0.17/0.42 = ( ! [A: $i,B: $i,C: $i] :
% 0.17/0.42 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.17/0.42 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(regular_type,type,
% 0.17/0.42 regular: $i > $o ).
% 0.17/0.42
% 0.17/0.42 thf(setminus_type,type,
% 0.17/0.42 setminus: $i > $i > $i ).
% 0.17/0.42
% 0.17/0.42 thf(setminusI_type,type,
% 0.17/0.42 setminusI: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setminusI,definition,
% 0.17/0.42 ( setminusI
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ~ ( in @ Xx @ B )
% 0.17/0.42 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setminusEL_type,type,
% 0.17/0.42 setminusEL: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setminusEL,definition,
% 0.17/0.42 ( setminusEL
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.17/0.42 => ( in @ Xx @ A ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setminusER_type,type,
% 0.17/0.42 setminusER: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setminusER,definition,
% 0.17/0.42 ( setminusER
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.17/0.42 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setminusSubset2_type,type,
% 0.17/0.42 setminusSubset2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setminusSubset2,definition,
% 0.17/0.42 ( setminusSubset2
% 0.17/0.42 = ( ! [A: $i,B: $i] :
% 0.17/0.42 ( ( subset @ A @ B )
% 0.17/0.42 => ( ( setminus @ A @ B )
% 0.17/0.42 = emptyset ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setminusERneg_type,type,
% 0.17/0.42 setminusERneg: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setminusERneg,definition,
% 0.17/0.42 ( setminusERneg
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.17/0.42 => ( ( in @ Xx @ A )
% 0.17/0.42 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setminusELneg_type,type,
% 0.17/0.42 setminusELneg: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setminusELneg,definition,
% 0.17/0.42 ( setminusELneg
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.17/0.42 => ( ~ ( in @ Xx @ B )
% 0.17/0.42 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setminusILneg_type,type,
% 0.17/0.42 setminusILneg: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setminusILneg,definition,
% 0.17/0.42 ( setminusILneg
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ~ ( in @ Xx @ A )
% 0.17/0.42 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setminusIRneg_type,type,
% 0.17/0.42 setminusIRneg: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setminusIRneg,definition,
% 0.17/0.42 ( setminusIRneg
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ B )
% 0.17/0.42 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setminusLsub_type,type,
% 0.17/0.42 setminusLsub: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setminusLsub,definition,
% 0.17/0.42 ( setminusLsub
% 0.17/0.42 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setminusSubset1_type,type,
% 0.17/0.42 setminusSubset1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setminusSubset1,definition,
% 0.17/0.42 ( setminusSubset1
% 0.17/0.42 = ( ! [A: $i,B: $i] :
% 0.17/0.42 ( ( ( setminus @ A @ B )
% 0.17/0.42 = emptyset )
% 0.17/0.42 => ( subset @ A @ B ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(symdiff_type,type,
% 0.17/0.42 symdiff: $i > $i > $i ).
% 0.17/0.42
% 0.17/0.42 thf(symdiffE_type,type,
% 0.17/0.42 symdiffE: $o ).
% 0.17/0.42
% 0.17/0.42 thf(symdiffE,definition,
% 0.17/0.42 ( symdiffE
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.17/0.42 => ! [Xphi: $o] :
% 0.17/0.42 ( ( ( in @ Xx @ A )
% 0.17/0.42 => ( ~ ( in @ Xx @ B )
% 0.17/0.42 => Xphi ) )
% 0.17/0.42 => ( ( ~ ( in @ Xx @ A )
% 0.17/0.42 => ( ( in @ Xx @ B )
% 0.17/0.42 => Xphi ) )
% 0.17/0.42 => Xphi ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(symdiffI1_type,type,
% 0.17/0.42 symdiffI1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(symdiffI1,definition,
% 0.17/0.42 ( symdiffI1
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ~ ( in @ Xx @ B )
% 0.17/0.42 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(symdiffI2_type,type,
% 0.17/0.42 symdiffI2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(symdiffI2,definition,
% 0.17/0.42 ( symdiffI2
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ~ ( in @ Xx @ A )
% 0.17/0.42 => ( ( in @ Xx @ B )
% 0.17/0.42 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(symdiffIneg1_type,type,
% 0.17/0.42 symdiffIneg1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(symdiffIneg1,definition,
% 0.17/0.42 ( symdiffIneg1
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( in @ Xx @ B )
% 0.17/0.42 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(symdiffIneg2_type,type,
% 0.17/0.42 symdiffIneg2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(symdiffIneg2,definition,
% 0.17/0.42 ( symdiffIneg2
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ~ ( in @ Xx @ A )
% 0.17/0.42 => ( ~ ( in @ Xx @ B )
% 0.17/0.42 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(iskpair_type,type,
% 0.17/0.42 iskpair: $i > $o ).
% 0.17/0.42
% 0.17/0.42 thf(secondinupair_type,type,
% 0.17/0.42 secondinupair: $o ).
% 0.17/0.42
% 0.17/0.42 thf(secondinupair,definition,
% 0.17/0.42 ( secondinupair
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setukpairIL_type,type,
% 0.17/0.42 setukpairIL: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setukpairIL,definition,
% 0.17/0.42 ( setukpairIL
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setukpairIR_type,type,
% 0.17/0.42 setukpairIR: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setukpairIR,definition,
% 0.17/0.42 ( setukpairIR
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(kpairiskpair_type,type,
% 0.17/0.42 kpairiskpair: $o ).
% 0.17/0.42
% 0.17/0.42 thf(kpairiskpair,definition,
% 0.17/0.42 ( kpairiskpair
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(kpair_type,type,
% 0.17/0.42 kpair: $i > $i > $i ).
% 0.17/0.42
% 0.17/0.42 thf(kpairp_type,type,
% 0.17/0.42 kpairp: $o ).
% 0.17/0.42
% 0.17/0.42 thf(kpairp,definition,
% 0.17/0.42 ( kpairp
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(cartprod_type,type,
% 0.17/0.42 cartprod: $i > $i > $i ).
% 0.17/0.42
% 0.17/0.42 thf(singletonsubset_type,type,
% 0.17/0.42 singletonsubset: $o ).
% 0.17/0.42
% 0.17/0.42 thf(singletonsubset,definition,
% 0.17/0.42 ( singletonsubset
% 0.17/0.42 = ( ! [A: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(singletoninpowerset_type,type,
% 0.17/0.42 singletoninpowerset: $o ).
% 0.17/0.42
% 0.17/0.42 thf(singletoninpowerset,definition,
% 0.17/0.42 ( singletoninpowerset
% 0.17/0.42 = ( ! [A: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(singletoninpowunion_type,type,
% 0.17/0.42 singletoninpowunion: $o ).
% 0.17/0.42
% 0.17/0.42 thf(singletoninpowunion,definition,
% 0.17/0.42 ( singletoninpowunion
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(upairset2E_type,type,
% 0.17/0.42 upairset2E: $o ).
% 0.17/0.42
% 0.17/0.42 thf(upairset2E,definition,
% 0.17/0.42 ( upairset2E
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.17/0.42 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.17/0.42 => ( ( Xz = Xx )
% 0.17/0.42 | ( Xz = Xy ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(upairsubunion_type,type,
% 0.17/0.42 upairsubunion: $o ).
% 0.17/0.42
% 0.17/0.42 thf(upairsubunion,definition,
% 0.17/0.42 ( upairsubunion
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ B )
% 0.17/0.42 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(upairinpowunion_type,type,
% 0.17/0.42 upairinpowunion: $o ).
% 0.17/0.42
% 0.17/0.42 thf(upairinpowunion,definition,
% 0.17/0.42 ( upairinpowunion
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ B )
% 0.17/0.42 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(ubforcartprodlem1_type,type,
% 0.17/0.42 ubforcartprodlem1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(ubforcartprodlem1,definition,
% 0.17/0.42 ( ubforcartprodlem1
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ B )
% 0.17/0.42 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(ubforcartprodlem2_type,type,
% 0.17/0.42 ubforcartprodlem2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(ubforcartprodlem2,definition,
% 0.17/0.42 ( ubforcartprodlem2
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ B )
% 0.17/0.42 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(ubforcartprodlem3_type,type,
% 0.17/0.42 ubforcartprodlem3: $o ).
% 0.17/0.42
% 0.17/0.42 thf(ubforcartprodlem3,definition,
% 0.17/0.42 ( ubforcartprodlem3
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ B )
% 0.17/0.42 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodpairin_type,type,
% 0.17/0.42 cartprodpairin: $o ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodpairin,definition,
% 0.17/0.42 ( cartprodpairin
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ B )
% 0.17/0.42 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodmempair1_type,type,
% 0.17/0.42 cartprodmempair1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodmempair1,definition,
% 0.17/0.42 ( cartprodmempair1
% 0.17/0.42 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.17/0.42 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.17/0.42 => ? [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 & ? [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ B )
% 0.17/0.42 & ( Xu
% 0.17/0.42 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodmempair_type,type,
% 0.17/0.42 cartprodmempair: $o ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodmempair,definition,
% 0.17/0.42 ( cartprodmempair
% 0.17/0.42 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.17/0.42 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.17/0.42 => ( iskpair @ Xu ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setunionE2_type,type,
% 0.17/0.42 setunionE2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setunionE2,definition,
% 0.17/0.42 ( setunionE2
% 0.17/0.42 = ( ! [A: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ ( setunion @ A ) )
% 0.17/0.42 => ? [X: $i] :
% 0.17/0.42 ( ( in @ X @ A )
% 0.17/0.42 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setunionsingleton1_type,type,
% 0.17/0.42 setunionsingleton1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setunionsingleton1,definition,
% 0.17/0.42 ( setunionsingleton1
% 0.17/0.42 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setunionsingleton2_type,type,
% 0.17/0.42 setunionsingleton2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setunionsingleton2,definition,
% 0.17/0.42 ( setunionsingleton2
% 0.17/0.42 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setunionsingleton_type,type,
% 0.17/0.42 setunionsingleton: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setunionsingleton,definition,
% 0.17/0.42 ( setunionsingleton
% 0.17/0.42 = ( ! [Xx: $i] :
% 0.17/0.42 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.17/0.42 = Xx ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(singleton_type,type,
% 0.17/0.42 singleton: $i > $o ).
% 0.17/0.42
% 0.17/0.42 thf(singletonprop_type,type,
% 0.17/0.42 singletonprop: $o ).
% 0.17/0.42
% 0.17/0.42 thf(singletonprop,definition,
% 0.17/0.42 ( singletonprop
% 0.17/0.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.42 ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 => ( ( Xphi @ Xx )
% 0.17/0.42 => ( ( Xphi @ Xy )
% 0.17/0.42 => ( Xx = Xy ) ) ) ) )
% 0.17/0.42 => ( ? [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 & ( Xphi @ Xx ) )
% 0.17/0.42 => ( singleton
% 0.17/0.42 @ ( dsetconstr @ A
% 0.17/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(ex1_type,type,
% 0.17/0.42 ex1: $i > ( $i > $o ) > $o ).
% 0.17/0.42
% 0.17/0.42 thf(ex1E1_type,type,
% 0.17/0.42 ex1E1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(ex1E1,definition,
% 0.17/0.42 ( ex1E1
% 0.17/0.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.42 ( ( ex1 @ A
% 0.17/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.42 => ? [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(ex1I_type,type,
% 0.17/0.42 ex1I: $o ).
% 0.17/0.42
% 0.17/0.42 thf(ex1I,definition,
% 0.17/0.42 ( ex1I
% 0.17/0.42 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( ( Xphi @ Xx )
% 0.17/0.42 => ( ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 => ( ( Xphi @ Xy )
% 0.17/0.42 => ( Xy = Xx ) ) )
% 0.17/0.42 => ( ex1 @ A
% 0.17/0.42 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(ex1I2_type,type,
% 0.17/0.42 ex1I2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(ex1I2,definition,
% 0.17/0.42 ( ex1I2
% 0.17/0.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.42 ( ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ A )
% 0.17/0.42 => ( ( Xphi @ Xx )
% 0.17/0.42 => ( ( Xphi @ Xy )
% 0.17/0.42 => ( Xx = Xy ) ) ) ) )
% 0.17/0.42 => ( ? [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 & ( Xphi @ Xx ) )
% 0.17/0.42 => ( ex1 @ A
% 0.17/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(singletonsuniq_type,type,
% 0.17/0.42 singletonsuniq: $o ).
% 0.17/0.42
% 0.17/0.42 thf(singletonsuniq,definition,
% 0.17/0.42 ( singletonsuniq
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( ( setadjoin @ Xx @ emptyset )
% 0.17/0.42 = ( setadjoin @ Xy @ emptyset ) )
% 0.17/0.42 => ( Xx = Xy ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(atmost1p_type,type,
% 0.17/0.42 atmost1p: $i > $o ).
% 0.17/0.42
% 0.17/0.42 thf(atleast2p_type,type,
% 0.17/0.42 atleast2p: $i > $o ).
% 0.17/0.42
% 0.17/0.42 thf(atmost2p_type,type,
% 0.17/0.42 atmost2p: $i > $o ).
% 0.17/0.42
% 0.17/0.42 thf(upairsetp_type,type,
% 0.17/0.42 upairsetp: $i > $o ).
% 0.17/0.42
% 0.17/0.42 thf(setukpairinjL1_type,type,
% 0.17/0.42 setukpairinjL1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setukpairinjL1,definition,
% 0.17/0.42 ( setukpairinjL1
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.17/0.42 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.17/0.42 => ( Xx = Xz ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(kfstsingleton_type,type,
% 0.17/0.42 kfstsingleton: $o ).
% 0.17/0.42
% 0.17/0.42 thf(kfstsingleton,definition,
% 0.17/0.42 ( kfstsingleton
% 0.17/0.42 = ( ! [Xu: $i] :
% 0.17/0.42 ( ( iskpair @ Xu )
% 0.17/0.42 => ( singleton
% 0.17/0.42 @ ( dsetconstr @ ( setunion @ Xu )
% 0.17/0.42 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(theprop_type,type,
% 0.17/0.42 theprop: $o ).
% 0.17/0.42
% 0.17/0.42 thf(theprop,definition,
% 0.17/0.42 ( theprop
% 0.17/0.42 = ( ! [X: $i] :
% 0.17/0.42 ( ( singleton @ X )
% 0.17/0.42 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(kfst_type,type,
% 0.17/0.42 kfst: $i > $i ).
% 0.17/0.42
% 0.17/0.42 thf(kfstpairEq_type,type,
% 0.17/0.42 kfstpairEq: $o ).
% 0.17/0.42
% 0.17/0.42 thf(kfstpairEq,definition,
% 0.17/0.42 ( kfstpairEq
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.17/0.42 = Xx ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodfstin_type,type,
% 0.17/0.42 cartprodfstin: $o ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodfstin,definition,
% 0.17/0.42 ( cartprodfstin
% 0.17/0.42 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.17/0.42 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.17/0.42 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setukpairinjL2_type,type,
% 0.17/0.42 setukpairinjL2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setukpairinjL2,definition,
% 0.17/0.42 ( setukpairinjL2
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.17/0.42 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.17/0.42 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.17/0.42 => ( Xx = Xz ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setukpairinjL_type,type,
% 0.17/0.42 setukpairinjL: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setukpairinjL,definition,
% 0.17/0.42 ( setukpairinjL
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.17/0.42 ( ( ( kpair @ Xx @ Xy )
% 0.17/0.42 = ( kpair @ Xz @ Xu ) )
% 0.17/0.42 => ( Xx = Xz ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setukpairinjR11_type,type,
% 0.17/0.42 setukpairinjR11: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setukpairinjR11,definition,
% 0.17/0.42 ( setukpairinjR11
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( Xx = Xy )
% 0.17/0.42 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.17/0.42 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setukpairinjR12_type,type,
% 0.17/0.42 setukpairinjR12: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setukpairinjR12,definition,
% 0.17/0.42 ( setukpairinjR12
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( Xx = Xy )
% 0.17/0.42 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.17/0.42 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setukpairinjR1_type,type,
% 0.17/0.42 setukpairinjR1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setukpairinjR1,definition,
% 0.17/0.42 ( setukpairinjR1
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.17/0.42 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.17/0.42 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.17/0.42 => ( ( Xz = Xu )
% 0.17/0.42 => ( Xy = Xu ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(upairequniteq_type,type,
% 0.17/0.42 upairequniteq: $o ).
% 0.17/0.42
% 0.17/0.42 thf(upairequniteq,definition,
% 0.17/0.42 ( upairequniteq
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.17/0.42 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.17/0.42 = ( setadjoin @ Xz @ emptyset ) )
% 0.17/0.42 => ( Xx = Xy ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setukpairinjR2_type,type,
% 0.17/0.42 setukpairinjR2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setukpairinjR2,definition,
% 0.17/0.42 ( setukpairinjR2
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.17/0.42 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.17/0.42 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.17/0.42 => ( Xy = Xu ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setukpairinjR_type,type,
% 0.17/0.42 setukpairinjR: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setukpairinjR,definition,
% 0.17/0.42 ( setukpairinjR
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.17/0.42 ( ( ( kpair @ Xx @ Xy )
% 0.17/0.42 = ( kpair @ Xz @ Xu ) )
% 0.17/0.42 => ( Xy = Xu ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(ksndsingleton_type,type,
% 0.17/0.42 ksndsingleton: $o ).
% 0.17/0.42
% 0.17/0.42 thf(ksndsingleton,definition,
% 0.17/0.42 ( ksndsingleton
% 0.17/0.42 = ( ! [Xu: $i] :
% 0.17/0.42 ( ( iskpair @ Xu )
% 0.17/0.42 => ( singleton
% 0.17/0.42 @ ( dsetconstr @ ( setunion @ Xu )
% 0.17/0.42 @ ^ [Xx: $i] :
% 0.17/0.42 ( Xu
% 0.17/0.42 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(ksnd_type,type,
% 0.17/0.42 ksnd: $i > $i ).
% 0.17/0.42
% 0.17/0.42 thf(ksndpairEq_type,type,
% 0.17/0.42 ksndpairEq: $o ).
% 0.17/0.42
% 0.17/0.42 thf(ksndpairEq,definition,
% 0.17/0.42 ( ksndpairEq
% 0.17/0.42 = ( ! [Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.17/0.42 = Xy ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(kpairsurjEq_type,type,
% 0.17/0.42 kpairsurjEq: $o ).
% 0.17/0.42
% 0.17/0.42 thf(kpairsurjEq,definition,
% 0.17/0.42 ( kpairsurjEq
% 0.17/0.42 = ( ! [Xu: $i] :
% 0.17/0.42 ( ( iskpair @ Xu )
% 0.17/0.42 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.17/0.42 = Xu ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodsndin_type,type,
% 0.17/0.42 cartprodsndin: $o ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodsndin,definition,
% 0.17/0.42 ( cartprodsndin
% 0.17/0.42 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.17/0.42 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.17/0.42 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodpairmemEL_type,type,
% 0.17/0.42 cartprodpairmemEL: $o ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodpairmemEL,definition,
% 0.17/0.42 ( cartprodpairmemEL
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.17/0.42 => ( in @ Xx @ A ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodpairmemER_type,type,
% 0.17/0.42 cartprodpairmemER: $o ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodpairmemER,definition,
% 0.17/0.42 ( cartprodpairmemER
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.17/0.42 => ( in @ Xy @ B ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodmempaircEq_type,type,
% 0.17/0.42 cartprodmempaircEq: $o ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodmempaircEq,definition,
% 0.17/0.42 ( cartprodmempaircEq
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ B )
% 0.17/0.42 => ( ( kpair @ Xx @ Xy )
% 0.17/0.42 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodfstpairEq_type,type,
% 0.17/0.42 cartprodfstpairEq: $o ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodfstpairEq,definition,
% 0.17/0.42 ( cartprodfstpairEq
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ B )
% 0.17/0.42 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.17/0.42 = Xx ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodsndpairEq_type,type,
% 0.17/0.42 cartprodsndpairEq: $o ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodsndpairEq,definition,
% 0.17/0.42 ( cartprodsndpairEq
% 0.17/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ B )
% 0.17/0.42 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.17/0.42 = Xy ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodpairsurjEq_type,type,
% 0.17/0.42 cartprodpairsurjEq: $o ).
% 0.17/0.42
% 0.17/0.42 thf(cartprodpairsurjEq,definition,
% 0.17/0.42 ( cartprodpairsurjEq
% 0.17/0.42 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.17/0.42 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.17/0.42 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.17/0.42 = Xu ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(breln_type,type,
% 0.17/0.42 breln: $i > $i > $i > $o ).
% 0.17/0.42
% 0.17/0.42 thf(dpsetconstr_type,type,
% 0.17/0.42 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.17/0.42
% 0.17/0.42 thf(dpsetconstrI_type,type,
% 0.17/0.42 dpsetconstrI: $o ).
% 0.17/0.42
% 0.17/0.42 thf(dpsetconstrI,definition,
% 0.17/0.42 ( dpsetconstrI
% 0.17/0.42 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ B )
% 0.17/0.42 => ( ( Xphi @ Xx @ Xy )
% 0.17/0.42 => ( in @ ( kpair @ Xx @ Xy )
% 0.17/0.42 @ ( dpsetconstr @ A @ B
% 0.17/0.42 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(dpsetconstrSub_type,type,
% 0.17/0.42 dpsetconstrSub: $o ).
% 0.17/0.42
% 0.17/0.42 thf(dpsetconstrSub,definition,
% 0.17/0.42 ( dpsetconstrSub
% 0.17/0.42 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.17/0.42 ( subset
% 0.17/0.42 @ ( dpsetconstr @ A @ B
% 0.17/0.42 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.17/0.42 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(setOfPairsIsBReln_type,type,
% 0.17/0.42 setOfPairsIsBReln: $o ).
% 0.17/0.42
% 0.17/0.42 thf(setOfPairsIsBReln,definition,
% 0.17/0.42 ( setOfPairsIsBReln
% 0.17/0.42 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.17/0.42 ( breln @ A @ B
% 0.17/0.42 @ ( dpsetconstr @ A @ B
% 0.17/0.42 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(dpsetconstrERa_type,type,
% 0.17/0.42 dpsetconstrERa: $o ).
% 0.17/0.42
% 0.17/0.42 thf(dpsetconstrERa,definition,
% 0.17/0.42 ( dpsetconstrERa
% 0.17/0.42 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ! [Xy: $i] :
% 0.17/0.42 ( ( in @ Xy @ B )
% 0.17/0.42 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.17/0.42 @ ( dpsetconstr @ A @ B
% 0.17/0.42 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.17/0.42 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(dpsetconstrEL1_type,type,
% 0.17/0.42 dpsetconstrEL1: $o ).
% 0.17/0.42
% 0.17/0.42 thf(dpsetconstrEL1,definition,
% 0.17/0.42 ( dpsetconstrEL1
% 0.17/0.42 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( in @ ( kpair @ Xx @ Xy )
% 0.17/0.42 @ ( dpsetconstr @ A @ B
% 0.17/0.42 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.17/0.42 => ( in @ Xx @ A ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(dpsetconstrEL2_type,type,
% 0.17/0.42 dpsetconstrEL2: $o ).
% 0.17/0.42
% 0.17/0.42 thf(dpsetconstrEL2,definition,
% 0.17/0.42 ( dpsetconstrEL2
% 0.17/0.42 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( in @ ( kpair @ Xx @ Xy )
% 0.17/0.42 @ ( dpsetconstr @ A @ B
% 0.17/0.42 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.17/0.42 => ( in @ Xy @ B ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(dpsetconstrER_type,type,
% 0.17/0.42 dpsetconstrER: $o ).
% 0.17/0.42
% 0.17/0.42 thf(dpsetconstrER,definition,
% 0.17/0.42 ( dpsetconstrER
% 0.17/0.42 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.17/0.42 ( ( in @ ( kpair @ Xx @ Xy )
% 0.17/0.42 @ ( dpsetconstr @ A @ B
% 0.17/0.42 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.17/0.42 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(func_type,type,
% 0.17/0.42 func: $i > $i > $i > $o ).
% 0.17/0.42
% 0.17/0.42 thf(funcSet_type,type,
% 0.17/0.42 funcSet: $i > $i > $i ).
% 0.17/0.42
% 0.17/0.42 thf(funcImageSingleton_type,type,
% 0.17/0.42 funcImageSingleton: $o ).
% 0.17/0.42
% 0.17/0.42 thf(funcImageSingleton,definition,
% 0.17/0.42 ( funcImageSingleton
% 0.17/0.42 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.42 ( ( func @ A @ B @ Xf )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( singleton
% 0.17/0.42 @ ( dsetconstr @ B
% 0.17/0.42 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.17/0.42
% 0.17/0.42 thf(apProp_type,type,
% 0.17/0.42 apProp: $o ).
% 0.17/0.42
% 0.17/0.42 thf(apProp,definition,
% 0.17/0.42 ( apProp
% 0.17/0.42 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.42 ( ( func @ A @ B @ Xf )
% 0.17/0.42 => ! [Xx: $i] :
% 0.17/0.42 ( ( in @ Xx @ A )
% 0.17/0.42 => ( in
% 0.17/0.42 @ ( setunion
% 0.17/0.42 @ ( dsetconstr @ B
% 0.17/0.42 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.17/0.42 @ B ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(ap_type,type,
% 0.17/0.43 ap: $i > $i > $i > $i > $i ).
% 0.17/0.43
% 0.17/0.43 thf(app_type,type,
% 0.17/0.43 app: $o ).
% 0.17/0.43
% 0.17/0.43 thf(app,definition,
% 0.17/0.43 ( app
% 0.17/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.43 ( ( func @ A @ B @ Xf )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(infuncsetfunc_type,type,
% 0.17/0.43 infuncsetfunc: $o ).
% 0.17/0.43
% 0.17/0.43 thf(infuncsetfunc,definition,
% 0.17/0.43 ( infuncsetfunc
% 0.17/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.43 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.17/0.43 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(ap2p_type,type,
% 0.17/0.43 ap2p: $o ).
% 0.17/0.43
% 0.17/0.43 thf(ap2p,definition,
% 0.17/0.43 ( ap2p
% 0.17/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.43 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(funcinfuncset_type,type,
% 0.17/0.43 funcinfuncset: $o ).
% 0.17/0.43
% 0.17/0.43 thf(funcinfuncset,definition,
% 0.17/0.43 ( funcinfuncset
% 0.17/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.43 ( ( func @ A @ B @ Xf )
% 0.17/0.43 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(lamProp_type,type,
% 0.17/0.43 lamProp: $o ).
% 0.17/0.43
% 0.17/0.43 thf(lamProp,definition,
% 0.17/0.43 ( lamProp
% 0.17/0.43 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.17/0.43 ( ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.17/0.43 => ( func @ A @ B
% 0.17/0.43 @ ( dpsetconstr @ A @ B
% 0.17/0.43 @ ^ [Xx: $i,Xy: $i] :
% 0.17/0.43 ( ( Xf @ Xx )
% 0.17/0.43 = Xy ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(lam_type,type,
% 0.17/0.43 lam: $i > $i > ( $i > $i ) > $i ).
% 0.17/0.43
% 0.17/0.43 thf(lamp_type,type,
% 0.17/0.43 lamp: $o ).
% 0.17/0.43
% 0.17/0.43 thf(lamp,definition,
% 0.17/0.43 ( lamp
% 0.17/0.43 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.17/0.43 ( ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.17/0.43 => ( func @ A @ B
% 0.17/0.43 @ ( lam @ A @ B
% 0.17/0.43 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(lam2p_type,type,
% 0.17/0.43 lam2p: $o ).
% 0.17/0.43
% 0.17/0.43 thf(lam2p,definition,
% 0.17/0.43 ( lam2p
% 0.17/0.43 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.17/0.43 ( ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.17/0.43 => ( in
% 0.17/0.43 @ ( lam @ A @ B
% 0.17/0.43 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.17/0.43 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(brelnall1_type,type,
% 0.17/0.43 brelnall1: $o ).
% 0.17/0.43
% 0.17/0.43 thf(brelnall1,definition,
% 0.17/0.43 ( brelnall1
% 0.17/0.43 = ( ! [A: $i,B: $i,R: $i] :
% 0.17/0.43 ( ( breln @ A @ B @ R )
% 0.17/0.43 => ! [Xphi: $i > $o] :
% 0.17/0.43 ( ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ B )
% 0.17/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.17/0.43 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ R )
% 0.17/0.43 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(brelnall2_type,type,
% 0.17/0.43 brelnall2: $o ).
% 0.17/0.43
% 0.17/0.43 thf(brelnall2,definition,
% 0.17/0.43 ( brelnall2
% 0.17/0.43 = ( ! [A: $i,B: $i,R: $i] :
% 0.17/0.43 ( ( breln @ A @ B @ R )
% 0.17/0.43 => ! [Xphi: $i > $o] :
% 0.17/0.43 ( ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ B )
% 0.17/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.17/0.43 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ R )
% 0.17/0.43 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(ex1E2_type,type,
% 0.17/0.43 ex1E2: $o ).
% 0.17/0.43
% 0.17/0.43 thf(ex1E2,definition,
% 0.17/0.43 ( ex1E2
% 0.17/0.43 = ( ! [A: $i,Xphi: $i > $o] :
% 0.17/0.43 ( ( ex1 @ A
% 0.17/0.43 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 => ( ( Xphi @ Xx )
% 0.17/0.43 => ( ( Xphi @ Xy )
% 0.17/0.43 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(funcGraphProp1_type,type,
% 0.17/0.43 funcGraphProp1: $o ).
% 0.17/0.43
% 0.17/0.43 thf(funcGraphProp1,definition,
% 0.17/0.43 ( funcGraphProp1
% 0.17/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.43 ( ( func @ A @ B @ Xf )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(funcGraphProp3_type,type,
% 0.17/0.43 funcGraphProp3: $o ).
% 0.17/0.43
% 0.17/0.43 thf(funcGraphProp3,definition,
% 0.17/0.43 ( funcGraphProp3
% 0.17/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.43 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(funcGraphProp2_type,type,
% 0.17/0.43 funcGraphProp2: $o ).
% 0.17/0.43
% 0.17/0.43 thf(funcGraphProp2,definition,
% 0.17/0.43 ( funcGraphProp2
% 0.17/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.43 ( ( func @ A @ B @ Xf )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ B )
% 0.17/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.17/0.43 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.17/0.43 = Xy ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(funcextLem_type,type,
% 0.17/0.43 funcextLem: $o ).
% 0.17/0.43
% 0.17/0.43 thf(funcextLem,definition,
% 0.17/0.43 ( funcextLem
% 0.17/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.43 ( ( func @ A @ B @ Xf )
% 0.17/0.43 => ! [Xg: $i] :
% 0.17/0.43 ( ( func @ A @ B @ Xg )
% 0.17/0.43 => ( ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.17/0.43 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ B )
% 0.17/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 0.17/0.43 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(funcGraphProp4_type,type,
% 0.17/0.43 funcGraphProp4: $o ).
% 0.17/0.43
% 0.17/0.43 thf(funcGraphProp4,definition,
% 0.17/0.43 ( funcGraphProp4
% 0.17/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.43 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ B )
% 0.17/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.17/0.43 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.17/0.43 = Xy ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(subbreln_type,type,
% 0.17/0.43 subbreln: $o ).
% 0.17/0.43
% 0.17/0.43 thf(subbreln,definition,
% 0.17/0.43 ( subbreln
% 0.17/0.43 = ( ! [A: $i,B: $i,R: $i] :
% 0.17/0.43 ( ( breln @ A @ B @ R )
% 0.17/0.43 => ! [S: $i] :
% 0.17/0.43 ( ( breln @ A @ B @ S )
% 0.17/0.43 => ( ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ B )
% 0.17/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.17/0.43 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.17/0.43 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(eqbreln_type,type,
% 0.17/0.43 eqbreln: $o ).
% 0.17/0.43
% 0.17/0.43 thf(eqbreln,definition,
% 0.17/0.43 ( eqbreln
% 0.17/0.43 = ( ! [A: $i,B: $i,R: $i] :
% 0.17/0.43 ( ( breln @ A @ B @ R )
% 0.17/0.43 => ! [S: $i] :
% 0.17/0.43 ( ( breln @ A @ B @ S )
% 0.17/0.43 => ( ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ B )
% 0.17/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.17/0.43 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.17/0.43 => ( ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ B )
% 0.17/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.17/0.43 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.17/0.43 => ( R = S ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(funcext_type,type,
% 0.17/0.43 funcext: $o ).
% 0.17/0.43
% 0.17/0.43 thf(funcext,definition,
% 0.17/0.43 ( funcext
% 0.17/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.43 ( ( func @ A @ B @ Xf )
% 0.17/0.43 => ! [Xg: $i] :
% 0.17/0.43 ( ( func @ A @ B @ Xg )
% 0.17/0.43 => ( ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.17/0.43 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.17/0.43 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(funcext2_type,type,
% 0.17/0.43 funcext2: $o ).
% 0.17/0.43
% 0.17/0.43 thf(funcext2,definition,
% 0.17/0.43 ( funcext2
% 0.17/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.43 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.17/0.43 => ! [Xg: $i] :
% 0.17/0.43 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 0.17/0.43 => ( ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.17/0.43 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.17/0.43 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(ap2apEq1_type,type,
% 0.17/0.43 ap2apEq1: $o ).
% 0.17/0.43
% 0.17/0.43 thf(ap2apEq1,definition,
% 0.17/0.43 ( ap2apEq1
% 0.17/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.43 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.17/0.43 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(ap2apEq2_type,type,
% 0.17/0.43 ap2apEq2: $o ).
% 0.17/0.43
% 0.17/0.43 thf(ap2apEq2,definition,
% 0.17/0.43 ( ap2apEq2
% 0.17/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.43 ( ( func @ A @ B @ Xf )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.17/0.43 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(beta1_type,type,
% 0.17/0.43 beta1: $o ).
% 0.17/0.43
% 0.17/0.43 thf(beta1,definition,
% 0.17/0.43 ( beta1
% 0.17/0.43 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.17/0.43 ( ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( ap @ A @ B
% 0.17/0.43 @ ( lam @ A @ B
% 0.17/0.43 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.17/0.43 @ Xx )
% 0.17/0.43 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(eta1_type,type,
% 0.17/0.43 eta1: $o ).
% 0.17/0.43
% 0.17/0.43 thf(eta1,definition,
% 0.17/0.43 ( eta1
% 0.17/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.43 ( ( func @ A @ B @ Xf )
% 0.17/0.43 => ( ( lam @ A @ B
% 0.17/0.43 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.17/0.43 = Xf ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(lam2lamEq_type,type,
% 0.17/0.43 lam2lamEq: $o ).
% 0.17/0.43
% 0.17/0.43 thf(lam2lamEq,definition,
% 0.17/0.43 ( lam2lamEq
% 0.17/0.43 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.17/0.43 ( ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.17/0.43 => ( ( lam @ A @ B
% 0.17/0.43 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.17/0.43 = ( lam @ A @ B
% 0.17/0.43 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(beta2_type,type,
% 0.17/0.43 beta2: $o ).
% 0.17/0.43
% 0.17/0.43 thf(beta2,definition,
% 0.17/0.43 ( beta2
% 0.17/0.43 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.17/0.43 ( ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( ap @ A @ B
% 0.17/0.43 @ ( lam @ A @ B
% 0.17/0.43 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.17/0.43 @ Xx )
% 0.17/0.43 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(eta2_type,type,
% 0.17/0.43 eta2: $o ).
% 0.17/0.43
% 0.17/0.43 thf(eta2,definition,
% 0.17/0.43 ( eta2
% 0.17/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.43 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.17/0.43 => ( ( lam @ A @ B
% 0.17/0.43 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.17/0.43 = Xf ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(iffalseProp1_type,type,
% 0.17/0.43 iffalseProp1: $o ).
% 0.17/0.43
% 0.17/0.43 thf(iffalseProp1,definition,
% 0.17/0.43 ( iffalseProp1
% 0.17/0.43 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 => ( ~ Xphi
% 0.17/0.43 => ( in @ Xy
% 0.17/0.43 @ ( dsetconstr @ A
% 0.17/0.43 @ ^ [Xz: $i] :
% 0.17/0.43 ( ( Xphi
% 0.17/0.43 & ( Xz = Xx ) )
% 0.17/0.43 | ( ~ Xphi
% 0.17/0.43 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(iffalseProp2_type,type,
% 0.17/0.43 iffalseProp2: $o ).
% 0.17/0.43
% 0.17/0.43 thf(iffalseProp2,definition,
% 0.17/0.43 ( iffalseProp2
% 0.17/0.43 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 => ( ~ Xphi
% 0.17/0.43 => ( ( dsetconstr @ A
% 0.17/0.43 @ ^ [Xz: $i] :
% 0.17/0.43 ( ( Xphi
% 0.17/0.43 & ( Xz = Xx ) )
% 0.17/0.43 | ( ~ Xphi
% 0.17/0.43 & ( Xz = Xy ) ) ) )
% 0.17/0.43 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(iftrueProp1_type,type,
% 0.17/0.43 iftrueProp1: $o ).
% 0.17/0.43
% 0.17/0.43 thf(iftrueProp1,definition,
% 0.17/0.43 ( iftrueProp1
% 0.17/0.43 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 => ( Xphi
% 0.17/0.43 => ( in @ Xx
% 0.17/0.43 @ ( dsetconstr @ A
% 0.17/0.43 @ ^ [Xz: $i] :
% 0.17/0.43 ( ( Xphi
% 0.17/0.43 & ( Xz = Xx ) )
% 0.17/0.43 | ( ~ Xphi
% 0.17/0.43 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(iftrueProp2_type,type,
% 0.17/0.43 iftrueProp2: $o ).
% 0.17/0.43
% 0.17/0.43 thf(iftrueProp2,definition,
% 0.17/0.43 ( iftrueProp2
% 0.17/0.43 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 => ( Xphi
% 0.17/0.43 => ( ( dsetconstr @ A
% 0.17/0.43 @ ^ [Xz: $i] :
% 0.17/0.43 ( ( Xphi
% 0.17/0.43 & ( Xz = Xx ) )
% 0.17/0.43 | ( ~ Xphi
% 0.17/0.43 & ( Xz = Xy ) ) ) )
% 0.17/0.43 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(ifSingleton_type,type,
% 0.17/0.43 ifSingleton: $o ).
% 0.17/0.43
% 0.17/0.43 thf(ifSingleton,definition,
% 0.17/0.43 ( ifSingleton
% 0.17/0.43 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 => ( singleton
% 0.17/0.43 @ ( dsetconstr @ A
% 0.17/0.43 @ ^ [Xz: $i] :
% 0.17/0.43 ( ( Xphi
% 0.17/0.43 & ( Xz = Xx ) )
% 0.17/0.43 | ( ~ Xphi
% 0.17/0.43 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(if_type,type,
% 0.17/0.43 if: $i > $o > $i > $i > $i ).
% 0.17/0.43
% 0.17/0.43 thf(ifp_type,type,
% 0.17/0.43 ifp: $o ).
% 0.17/0.43
% 0.17/0.43 thf(ifp,definition,
% 0.17/0.43 ( ifp
% 0.17/0.43 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(theeq_type,type,
% 0.17/0.43 theeq: $o ).
% 0.17/0.43
% 0.17/0.43 thf(theeq,definition,
% 0.17/0.43 ( theeq
% 0.17/0.43 = ( ! [X: $i] :
% 0.17/0.43 ( ( singleton @ X )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ X )
% 0.17/0.43 => ( ( setunion @ X )
% 0.17/0.43 = Xx ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(iftrue_type,type,
% 0.17/0.43 iftrue: $o ).
% 0.17/0.43
% 0.17/0.43 thf(iftrue,definition,
% 0.17/0.43 ( iftrue
% 0.17/0.43 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 => ( Xphi
% 0.17/0.43 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.17/0.43 = Xx ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(iffalse_type,type,
% 0.17/0.43 iffalse: $o ).
% 0.17/0.43
% 0.17/0.43 thf(iffalse,definition,
% 0.17/0.43 ( iffalse
% 0.17/0.43 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 => ( ~ Xphi
% 0.17/0.43 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.17/0.43 = Xy ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(iftrueorfalse_type,type,
% 0.17/0.43 iftrueorfalse: $o ).
% 0.17/0.43
% 0.17/0.43 thf(iftrueorfalse,definition,
% 0.17/0.43 ( iftrueorfalse
% 0.17/0.43 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(binintersectT_lem_type,type,
% 0.17/0.43 binintersectT_lem: $o ).
% 0.17/0.43
% 0.17/0.43 thf(binintersectT_lem,definition,
% 0.17/0.43 ( binintersectT_lem
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(binunionT_lem_type,type,
% 0.17/0.43 binunionT_lem: $o ).
% 0.17/0.43
% 0.17/0.43 thf(binunionT_lem,definition,
% 0.17/0.43 ( binunionT_lem
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(powersetT_lem_type,type,
% 0.17/0.43 powersetT_lem: $o ).
% 0.17/0.43
% 0.17/0.43 thf(powersetT_lem,definition,
% 0.17/0.43 ( powersetT_lem
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(setminusT_lem_type,type,
% 0.17/0.43 setminusT_lem: $o ).
% 0.17/0.43
% 0.17/0.43 thf(setminusT_lem,definition,
% 0.17/0.43 ( setminusT_lem
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(complementT_lem_type,type,
% 0.17/0.43 complementT_lem: $o ).
% 0.17/0.43
% 0.17/0.43 thf(complementT_lem,definition,
% 0.17/0.43 ( complementT_lem
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(setextT_type,type,
% 0.17/0.43 setextT: $o ).
% 0.17/0.43
% 0.17/0.43 thf(setextT,definition,
% 0.17/0.43 ( setextT
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ( ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( in @ Xx @ X )
% 0.17/0.43 => ( in @ Xx @ Y ) ) )
% 0.17/0.43 => ( ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( in @ Xx @ Y )
% 0.17/0.43 => ( in @ Xx @ X ) ) )
% 0.17/0.43 => ( X = Y ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(subsetTI_type,type,
% 0.17/0.43 subsetTI: $o ).
% 0.17/0.43
% 0.17/0.43 thf(subsetTI,definition,
% 0.17/0.43 ( subsetTI
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ( ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( in @ Xx @ X )
% 0.17/0.43 => ( in @ Xx @ Y ) ) )
% 0.17/0.43 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(powersetTI1_type,type,
% 0.17/0.43 powersetTI1: $o ).
% 0.17/0.43
% 0.17/0.43 thf(powersetTI1,definition,
% 0.17/0.43 ( powersetTI1
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ( ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( in @ Xx @ X )
% 0.17/0.43 => ( in @ Xx @ Y ) ) )
% 0.17/0.43 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(powersetTE1_type,type,
% 0.17/0.43 powersetTE1: $o ).
% 0.17/0.43
% 0.17/0.43 thf(powersetTE1,definition,
% 0.17/0.43 ( powersetTE1
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( in @ X @ ( powerset @ Y ) )
% 0.17/0.43 => ( ( in @ Xx @ X )
% 0.17/0.43 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(complementTI1_type,type,
% 0.17/0.43 complementTI1: $o ).
% 0.17/0.43
% 0.17/0.43 thf(complementTI1,definition,
% 0.17/0.43 ( complementTI1
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( in @ Xx @ X )
% 0.17/0.43 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(complementTE1_type,type,
% 0.17/0.43 complementTE1: $o ).
% 0.17/0.43
% 0.17/0.43 thf(complementTE1,definition,
% 0.17/0.43 ( complementTE1
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 0.17/0.43 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(binintersectTELcontra_type,type,
% 0.17/0.43 binintersectTELcontra: $o ).
% 0.17/0.43
% 0.17/0.43 thf(binintersectTELcontra,definition,
% 0.17/0.43 ( binintersectTELcontra
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ~ ( in @ Xx @ X )
% 0.17/0.43 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(binintersectTERcontra_type,type,
% 0.17/0.43 binintersectTERcontra: $o ).
% 0.17/0.43
% 0.17/0.43 thf(binintersectTERcontra,definition,
% 0.17/0.43 ( binintersectTERcontra
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ~ ( in @ Xx @ Y )
% 0.17/0.43 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(contrasubsetT_type,type,
% 0.17/0.43 contrasubsetT: $o ).
% 0.17/0.43
% 0.17/0.43 thf(contrasubsetT,definition,
% 0.17/0.43 ( contrasubsetT
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.17/0.43 => ( ( in @ Xx @ Y )
% 0.17/0.43 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(contrasubsetT1_type,type,
% 0.17/0.43 contrasubsetT1: $o ).
% 0.17/0.43
% 0.17/0.43 thf(contrasubsetT1,definition,
% 0.17/0.43 ( contrasubsetT1
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( subset @ X @ Y )
% 0.17/0.43 => ( ~ ( in @ Xx @ Y )
% 0.17/0.43 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(contrasubsetT2_type,type,
% 0.17/0.43 contrasubsetT2: $o ).
% 0.17/0.43
% 0.17/0.43 thf(contrasubsetT2,definition,
% 0.17/0.43 ( contrasubsetT2
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ( ( subset @ X @ Y )
% 0.17/0.43 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(contrasubsetT3_type,type,
% 0.17/0.43 contrasubsetT3: $o ).
% 0.17/0.43
% 0.17/0.43 thf(contrasubsetT3,definition,
% 0.17/0.43 ( contrasubsetT3
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 0.17/0.43 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(doubleComplementI1_type,type,
% 0.17/0.43 doubleComplementI1: $o ).
% 0.17/0.43
% 0.17/0.43 thf(doubleComplementI1,definition,
% 0.17/0.43 ( doubleComplementI1
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( in @ Xx @ X )
% 0.17/0.43 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(doubleComplementE1_type,type,
% 0.17/0.43 doubleComplementE1: $o ).
% 0.17/0.43
% 0.17/0.43 thf(doubleComplementE1,definition,
% 0.17/0.43 ( doubleComplementE1
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 0.17/0.43 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(doubleComplementSub1_type,type,
% 0.17/0.43 doubleComplementSub1: $o ).
% 0.17/0.43
% 0.17/0.43 thf(doubleComplementSub1,definition,
% 0.17/0.43 ( doubleComplementSub1
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(doubleComplementSub2_type,type,
% 0.17/0.43 doubleComplementSub2: $o ).
% 0.17/0.43
% 0.17/0.43 thf(doubleComplementSub2,definition,
% 0.17/0.43 ( doubleComplementSub2
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(doubleComplementEq_type,type,
% 0.17/0.43 doubleComplementEq: $o ).
% 0.17/0.43
% 0.17/0.43 thf(doubleComplementEq,definition,
% 0.17/0.43 ( doubleComplementEq
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ( X
% 0.17/0.43 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(complementTnotintersectT_type,type,
% 0.17/0.43 complementTnotintersectT: $o ).
% 0.17/0.43
% 0.17/0.43 thf(complementTnotintersectT,definition,
% 0.17/0.43 ( complementTnotintersectT
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.17/0.43 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(complementImpComplementIntersect_type,type,
% 0.17/0.43 complementImpComplementIntersect: $o ).
% 0.17/0.43
% 0.17/0.43 thf(complementImpComplementIntersect,definition,
% 0.17/0.43 ( complementImpComplementIntersect
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.17/0.43 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(complementSubsetComplementIntersect_type,type,
% 0.17/0.43 complementSubsetComplementIntersect: $o ).
% 0.17/0.43
% 0.17/0.43 thf(complementSubsetComplementIntersect,definition,
% 0.17/0.43 ( complementSubsetComplementIntersect
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(complementInPowersetComplementIntersect_type,type,
% 0.17/0.43 complementInPowersetComplementIntersect: $o ).
% 0.17/0.43
% 0.17/0.43 thf(complementInPowersetComplementIntersect,definition,
% 0.17/0.43 ( complementInPowersetComplementIntersect
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(contraSubsetComplement_type,type,
% 0.17/0.43 contraSubsetComplement: $o ).
% 0.17/0.43
% 0.17/0.43 thf(contraSubsetComplement,definition,
% 0.17/0.43 ( contraSubsetComplement
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( in @ Xx @ Y )
% 0.17/0.43 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(complementTcontraSubset_type,type,
% 0.17/0.43 complementTcontraSubset: $o ).
% 0.17/0.43
% 0.17/0.43 thf(complementTcontraSubset,definition,
% 0.17/0.43 ( complementTcontraSubset
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.17/0.43 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(binunionTILcontra_type,type,
% 0.17/0.43 binunionTILcontra: $o ).
% 0.17/0.43
% 0.17/0.43 thf(binunionTILcontra,definition,
% 0.17/0.43 ( binunionTILcontra
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.17/0.43 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(binunionTIRcontra_type,type,
% 0.17/0.43 binunionTIRcontra: $o ).
% 0.17/0.43
% 0.17/0.43 thf(binunionTIRcontra,definition,
% 0.17/0.43 ( binunionTIRcontra
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.17/0.43 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(inIntersectImpInUnion_type,type,
% 0.17/0.43 inIntersectImpInUnion: $o ).
% 0.17/0.43
% 0.17/0.43 thf(inIntersectImpInUnion,definition,
% 0.17/0.43 ( inIntersectImpInUnion
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Z: $i] :
% 0.17/0.43 ( ( in @ Z @ ( powerset @ A ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.17/0.43 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(inIntersectImpInUnion2_type,type,
% 0.17/0.43 inIntersectImpInUnion2: $o ).
% 0.17/0.43
% 0.17/0.43 thf(inIntersectImpInUnion2,definition,
% 0.17/0.43 ( inIntersectImpInUnion2
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Z: $i] :
% 0.17/0.43 ( ( in @ Z @ ( powerset @ A ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.17/0.43 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(inIntersectImpInIntersectUnions_type,type,
% 0.17/0.43 inIntersectImpInIntersectUnions: $o ).
% 0.17/0.43
% 0.17/0.43 thf(inIntersectImpInIntersectUnions,definition,
% 0.17/0.43 ( inIntersectImpInIntersectUnions
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Z: $i] :
% 0.17/0.43 ( ( in @ Z @ ( powerset @ A ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.17/0.43 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(intersectInPowersetIntersectUnions_type,type,
% 0.17/0.43 intersectInPowersetIntersectUnions: $o ).
% 0.17/0.43
% 0.17/0.43 thf(intersectInPowersetIntersectUnions,definition,
% 0.17/0.43 ( intersectInPowersetIntersectUnions
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Z: $i] :
% 0.17/0.43 ( ( in @ Z @ ( powerset @ A ) )
% 0.17/0.43 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(inComplementUnionImpNotIn1_type,type,
% 0.17/0.43 inComplementUnionImpNotIn1: $o ).
% 0.17/0.43
% 0.17/0.43 thf(inComplementUnionImpNotIn1,definition,
% 0.17/0.43 ( inComplementUnionImpNotIn1
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.17/0.43 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(inComplementUnionImpInComplement1_type,type,
% 0.17/0.43 inComplementUnionImpInComplement1: $o ).
% 0.17/0.43
% 0.17/0.43 thf(inComplementUnionImpInComplement1,definition,
% 0.17/0.43 ( inComplementUnionImpInComplement1
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.17/0.43 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(binunionTE_type,type,
% 0.17/0.43 binunionTE: $o ).
% 0.17/0.43
% 0.17/0.43 thf(binunionTE,definition,
% 0.17/0.43 ( binunionTE
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Xphi: $o,Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.17/0.43 => ( ( ( in @ Xx @ X )
% 0.17/0.43 => Xphi )
% 0.17/0.43 => ( ( ( in @ Xx @ Y )
% 0.17/0.43 => Xphi )
% 0.17/0.43 => Xphi ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(binunionTEcontra_type,type,
% 0.17/0.43 binunionTEcontra: $o ).
% 0.17/0.43
% 0.17/0.43 thf(binunionTEcontra,definition,
% 0.17/0.43 ( binunionTEcontra
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ~ ( in @ Xx @ X )
% 0.17/0.43 => ( ~ ( in @ Xx @ Y )
% 0.17/0.43 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(demorgan2a1_type,type,
% 0.17/0.43 demorgan2a1: $o ).
% 0.17/0.43
% 0.17/0.43 thf(demorgan2a1,definition,
% 0.17/0.43 ( demorgan2a1
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.17/0.43 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(complementUnionInPowersetComplement_type,type,
% 0.17/0.43 complementUnionInPowersetComplement: $o ).
% 0.17/0.43
% 0.17/0.43 thf(complementUnionInPowersetComplement,definition,
% 0.17/0.43 ( complementUnionInPowersetComplement
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(demorgan2a2_type,type,
% 0.17/0.43 demorgan2a2: $o ).
% 0.17/0.43
% 0.17/0.43 thf(demorgan2a2,definition,
% 0.17/0.43 ( demorgan2a2
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.17/0.43 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(demorgan1a_type,type,
% 0.17/0.43 demorgan1a: $o ).
% 0.17/0.43
% 0.17/0.43 thf(demorgan1a,definition,
% 0.17/0.43 ( demorgan1a
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 0.17/0.43 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(demorgan1b_type,type,
% 0.17/0.43 demorgan1b: $o ).
% 0.17/0.43
% 0.17/0.43 thf(demorgan1b,definition,
% 0.17/0.43 ( demorgan1b
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.17/0.43 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(demorgan1_type,type,
% 0.17/0.43 demorgan1: $o ).
% 0.17/0.43
% 0.17/0.43 thf(demorgan1,definition,
% 0.17/0.43 ( demorgan1
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 0.17/0.43 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(demorgan2a_type,type,
% 0.17/0.43 demorgan2a: $o ).
% 0.17/0.43
% 0.17/0.43 thf(demorgan2a,definition,
% 0.17/0.43 ( demorgan2a
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.17/0.43 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(demorgan2b2_type,type,
% 0.17/0.43 demorgan2b2: $o ).
% 0.17/0.43
% 0.17/0.43 thf(demorgan2b2,definition,
% 0.17/0.43 ( demorgan2b2
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.17/0.43 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 0.17/0.43 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(demorgan2b_type,type,
% 0.17/0.43 demorgan2b: $o ).
% 0.17/0.43
% 0.17/0.43 thf(demorgan2b,definition,
% 0.17/0.43 ( demorgan2b
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.17/0.43 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(demorgan2_type,type,
% 0.17/0.43 demorgan2: $o ).
% 0.17/0.43
% 0.17/0.43 thf(demorgan2,definition,
% 0.17/0.43 ( demorgan2
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 0.17/0.43 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(woz13rule0_type,type,
% 0.17/0.43 woz13rule0: $o ).
% 0.17/0.43
% 0.17/0.43 thf(woz13rule0,definition,
% 0.17/0.43 ( woz13rule0
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.17/0.43 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(woz13rule1_type,type,
% 0.17/0.43 woz13rule1: $o ).
% 0.17/0.43
% 0.17/0.43 thf(woz13rule1,definition,
% 0.17/0.43 ( woz13rule1
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Z: $i] :
% 0.17/0.43 ( ( in @ Z @ ( powerset @ A ) )
% 0.17/0.43 => ( ( subset @ X @ Z )
% 0.17/0.43 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(woz13rule2_type,type,
% 0.17/0.43 woz13rule2: $o ).
% 0.17/0.43
% 0.17/0.43 thf(woz13rule2,definition,
% 0.17/0.43 ( woz13rule2
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Z: $i] :
% 0.17/0.43 ( ( in @ Z @ ( powerset @ A ) )
% 0.17/0.43 => ( ( subset @ Y @ Z )
% 0.17/0.43 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(woz13rule3_type,type,
% 0.17/0.43 woz13rule3: $o ).
% 0.17/0.43
% 0.17/0.43 thf(woz13rule3,definition,
% 0.17/0.43 ( woz13rule3
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Z: $i] :
% 0.17/0.43 ( ( in @ Z @ ( powerset @ A ) )
% 0.17/0.43 => ( ( subset @ X @ Y )
% 0.17/0.43 => ( ( subset @ X @ Z )
% 0.17/0.43 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(woz13rule4_type,type,
% 0.17/0.43 woz13rule4: $o ).
% 0.17/0.43
% 0.17/0.43 thf(woz13rule4,definition,
% 0.17/0.43 ( woz13rule4
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Z: $i] :
% 0.17/0.43 ( ( in @ Z @ ( powerset @ A ) )
% 0.17/0.43 => ! [W: $i] :
% 0.17/0.43 ( ( in @ W @ ( powerset @ A ) )
% 0.17/0.43 => ( ( subset @ X @ Z )
% 0.17/0.43 => ( ( subset @ Y @ W )
% 0.17/0.43 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(woz1_1_type,type,
% 0.17/0.43 woz1_1: $o ).
% 0.17/0.43
% 0.17/0.43 thf(woz1_1,definition,
% 0.17/0.43 ( woz1_1
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(woz1_2_type,type,
% 0.17/0.43 woz1_2: $o ).
% 0.17/0.43
% 0.17/0.43 thf(woz1_2,definition,
% 0.17/0.43 ( woz1_2
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Z: $i] :
% 0.17/0.43 ( ( in @ Z @ ( powerset @ A ) )
% 0.17/0.43 => ! [W: $i] :
% 0.17/0.43 ( ( in @ W @ ( powerset @ A ) )
% 0.17/0.43 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 0.17/0.43 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(woz1_3_type,type,
% 0.17/0.43 woz1_3: $o ).
% 0.17/0.43
% 0.17/0.43 thf(woz1_3,definition,
% 0.17/0.43 ( woz1_3
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ! [Z: $i] :
% 0.17/0.43 ( ( in @ Z @ ( powerset @ A ) )
% 0.17/0.43 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(woz1_4_type,type,
% 0.17/0.43 woz1_4: $o ).
% 0.17/0.43
% 0.17/0.43 thf(woz1_4,definition,
% 0.17/0.43 ( woz1_4
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.17/0.43 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(woz1_5_type,type,
% 0.17/0.43 woz1_5: $o ).
% 0.17/0.43
% 0.17/0.43 thf(woz1_5,definition,
% 0.17/0.43 ( woz1_5
% 0.17/0.43 = ( ! [A: $i,X: $i] :
% 0.17/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.17/0.43 => ! [Y: $i] :
% 0.17/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.17/0.43 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(breln1_type,type,
% 0.17/0.43 breln1: $i > $i > $o ).
% 0.17/0.43
% 0.17/0.43 thf(breln1all2_type,type,
% 0.17/0.43 breln1all2: $o ).
% 0.17/0.43
% 0.17/0.43 thf(breln1all2,definition,
% 0.17/0.43 ( breln1all2
% 0.17/0.43 = ( ! [A: $i,R: $i] :
% 0.17/0.43 ( ( breln1 @ A @ R )
% 0.17/0.43 => ! [Xphi: $i > $o] :
% 0.17/0.43 ( ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.17/0.43 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ R )
% 0.17/0.43 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(breln1Set_type,type,
% 0.17/0.43 breln1Set: $i > $i ).
% 0.17/0.43
% 0.17/0.43 thf(breln1SetBreln1_type,type,
% 0.17/0.43 breln1SetBreln1: $o ).
% 0.17/0.43
% 0.17/0.43 thf(breln1SetBreln1,definition,
% 0.17/0.43 ( breln1SetBreln1
% 0.17/0.43 = ( ! [A: $i,R: $i] :
% 0.17/0.43 ( ( in @ R @ ( breln1Set @ A ) )
% 0.17/0.43 => ( breln1 @ A @ R ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(transitive_type,type,
% 0.17/0.43 transitive: $i > $i > $o ).
% 0.17/0.43
% 0.17/0.43 thf(antisymmetric_type,type,
% 0.17/0.43 antisymmetric: $i > $i > $o ).
% 0.17/0.43
% 0.17/0.43 thf(reflexive_type,type,
% 0.17/0.43 reflexive: $i > $i > $o ).
% 0.17/0.43
% 0.17/0.43 thf(refltransitive_type,type,
% 0.17/0.43 refltransitive: $i > $i > $o ).
% 0.17/0.43
% 0.17/0.43 thf(refllinearorder_type,type,
% 0.17/0.43 refllinearorder: $i > $i > $o ).
% 0.17/0.43
% 0.17/0.43 thf(reflwellordering_type,type,
% 0.17/0.43 reflwellordering: $i > $i > $o ).
% 0.17/0.43
% 0.17/0.43 thf(choice2fnsingleton_type,type,
% 0.17/0.43 choice2fnsingleton: $o ).
% 0.17/0.43
% 0.17/0.43 thf(choice2fnsingleton,definition,
% 0.17/0.43 ( choice2fnsingleton
% 0.17/0.43 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.17/0.43 ( ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ? [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ B )
% 0.17/0.43 & ( Xphi @ Xx @ Xy ) ) )
% 0.17/0.43 => ! [R: $i] :
% 0.17/0.43 ( ( in @ R @ ( breln1Set @ B ) )
% 0.17/0.43 => ( ( reflwellordering @ B @ R )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( singleton
% 0.17/0.43 @ ( dsetconstr @ B
% 0.17/0.43 @ ^ [Xy: $i] :
% 0.17/0.43 ( ( Xphi @ Xx @ Xy )
% 0.17/0.43 & ! [Xz: $i] :
% 0.17/0.43 ( ( in @ Xz @ B )
% 0.17/0.43 => ( ( Xphi @ Xx @ Xz )
% 0.17/0.43 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(setOfPairsIsBReln1_type,type,
% 0.17/0.43 setOfPairsIsBReln1: $o ).
% 0.17/0.43
% 0.17/0.43 thf(setOfPairsIsBReln1,definition,
% 0.17/0.43 ( setOfPairsIsBReln1
% 0.17/0.43 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 0.17/0.43 ( breln1 @ A
% 0.17/0.43 @ ( dpsetconstr @ A @ A
% 0.17/0.43 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(breln1all1_type,type,
% 0.17/0.43 breln1all1: $o ).
% 0.17/0.43
% 0.17/0.43 thf(breln1all1,definition,
% 0.17/0.43 ( breln1all1
% 0.17/0.43 = ( ! [A: $i,R: $i] :
% 0.17/0.43 ( ( breln1 @ A @ R )
% 0.17/0.43 => ! [Xphi: $i > $o] :
% 0.17/0.43 ( ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.17/0.43 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ R )
% 0.17/0.43 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(subbreln1_type,type,
% 0.17/0.43 subbreln1: $o ).
% 0.17/0.43
% 0.17/0.43 thf(subbreln1,definition,
% 0.17/0.43 ( subbreln1
% 0.17/0.43 = ( ! [A: $i,R: $i] :
% 0.17/0.43 ( ( breln1 @ A @ R )
% 0.17/0.43 => ! [S: $i] :
% 0.17/0.43 ( ( breln1 @ A @ S )
% 0.17/0.43 => ( ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.17/0.43 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.17/0.43 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(eqbreln1_type,type,
% 0.17/0.43 eqbreln1: $o ).
% 0.17/0.43
% 0.17/0.43 thf(eqbreln1,definition,
% 0.17/0.43 ( eqbreln1
% 0.17/0.43 = ( ! [A: $i,R: $i] :
% 0.17/0.43 ( ( breln1 @ A @ R )
% 0.17/0.43 => ! [S: $i] :
% 0.17/0.43 ( ( breln1 @ A @ S )
% 0.17/0.43 => ( ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.17/0.43 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.17/0.43 => ( ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.17/0.43 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.17/0.43 => ( R = S ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(breln1invset_type,type,
% 0.17/0.43 breln1invset: $i > $i > $i ).
% 0.17/0.43
% 0.17/0.43 thf(breln1invprop_type,type,
% 0.17/0.43 breln1invprop: $o ).
% 0.17/0.43
% 0.17/0.43 thf(breln1invprop,definition,
% 0.17/0.43 ( breln1invprop
% 0.17/0.43 = ( ! [A: $i,R: $i] :
% 0.17/0.43 ( ( breln1 @ A @ R )
% 0.17/0.43 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(breln1invI_type,type,
% 0.17/0.43 breln1invI: $o ).
% 0.17/0.43
% 0.17/0.43 thf(breln1invI,definition,
% 0.17/0.43 ( breln1invI
% 0.17/0.43 = ( ! [A: $i,R: $i] :
% 0.17/0.43 ( ( breln1 @ A @ R )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.17/0.43 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(breln1invE_type,type,
% 0.17/0.43 breln1invE: $o ).
% 0.17/0.43
% 0.17/0.43 thf(breln1invE,definition,
% 0.17/0.43 ( breln1invE
% 0.17/0.43 = ( ! [A: $i,R: $i] :
% 0.17/0.43 ( ( breln1 @ A @ R )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 0.17/0.43 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(breln1compset_type,type,
% 0.17/0.43 breln1compset: $i > $i > $i > $i ).
% 0.17/0.43
% 0.17/0.43 thf(breln1compprop_type,type,
% 0.17/0.43 breln1compprop: $o ).
% 0.17/0.43
% 0.17/0.43 thf(breln1compprop,definition,
% 0.17/0.43 ( breln1compprop
% 0.17/0.43 = ( ! [A: $i,R: $i] :
% 0.17/0.43 ( ( breln1 @ A @ R )
% 0.17/0.43 => ! [S: $i] :
% 0.17/0.43 ( ( breln1 @ A @ S )
% 0.17/0.43 => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(breln1compI_type,type,
% 0.17/0.43 breln1compI: $o ).
% 0.17/0.43
% 0.17/0.43 thf(breln1compI,definition,
% 0.17/0.43 ( breln1compI
% 0.17/0.43 = ( ! [A: $i,R: $i] :
% 0.17/0.43 ( ( breln1 @ A @ R )
% 0.17/0.43 => ! [S: $i] :
% 0.17/0.43 ( ( breln1 @ A @ S )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 => ! [Xz: $i] :
% 0.17/0.43 ( ( in @ Xz @ A )
% 0.17/0.43 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.17/0.43 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 0.17/0.43 => ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(breln1compE_type,type,
% 0.17/0.43 breln1compE: $o ).
% 0.17/0.43
% 0.17/0.43 thf(breln1compE,definition,
% 0.17/0.43 ( breln1compE
% 0.17/0.43 = ( ! [A: $i,R: $i] :
% 0.17/0.43 ( ( breln1 @ A @ R )
% 0.17/0.43 => ! [S: $i] :
% 0.17/0.43 ( ( breln1 @ A @ S )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 0.17/0.43 => ? [Xz: $i] :
% 0.17/0.43 ( ( in @ Xz @ A )
% 0.17/0.43 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.17/0.43 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(breln1compEex_type,type,
% 0.17/0.43 breln1compEex: $o ).
% 0.17/0.43
% 0.17/0.43 thf(breln1compEex,definition,
% 0.17/0.43 ( breln1compEex
% 0.17/0.43 = ( ! [A: $i,R: $i] :
% 0.17/0.43 ( ( breln1 @ A @ R )
% 0.17/0.43 => ! [S: $i] :
% 0.17/0.43 ( ( breln1 @ A @ S )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 0.17/0.43 => ! [Xphi: $o] :
% 0.17/0.43 ( ! [Xz: $i] :
% 0.17/0.43 ( ( in @ Xz @ A )
% 0.17/0.43 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.17/0.43 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 0.17/0.43 => Xphi ) ) )
% 0.17/0.43 => Xphi ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(breln1unionprop_type,type,
% 0.17/0.43 breln1unionprop: $o ).
% 0.17/0.43
% 0.17/0.43 thf(breln1unionprop,definition,
% 0.17/0.43 ( breln1unionprop
% 0.17/0.43 = ( ! [A: $i,R: $i] :
% 0.17/0.43 ( ( breln1 @ A @ R )
% 0.17/0.43 => ! [S: $i] :
% 0.17/0.43 ( ( breln1 @ A @ S )
% 0.17/0.43 => ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(breln1unionIL_type,type,
% 0.17/0.43 breln1unionIL: $o ).
% 0.17/0.43
% 0.17/0.43 thf(breln1unionIL,definition,
% 0.17/0.43 ( breln1unionIL
% 0.17/0.43 = ( ! [A: $i,R: $i] :
% 0.17/0.43 ( ( breln1 @ A @ R )
% 0.17/0.43 => ! [S: $i] :
% 0.17/0.43 ( ( breln1 @ A @ S )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.17/0.43 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(breln1unionIR_type,type,
% 0.17/0.43 breln1unionIR: $o ).
% 0.17/0.43
% 0.17/0.43 thf(breln1unionIR,definition,
% 0.17/0.43 ( breln1unionIR
% 0.17/0.43 = ( ! [A: $i,R: $i] :
% 0.17/0.43 ( ( breln1 @ A @ R )
% 0.17/0.43 => ! [S: $i] :
% 0.17/0.43 ( ( breln1 @ A @ S )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.17/0.43 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(breln1unionI_type,type,
% 0.17/0.43 breln1unionI: $o ).
% 0.17/0.43
% 0.17/0.43 thf(breln1unionI,definition,
% 0.17/0.43 ( breln1unionI
% 0.17/0.43 = ( ! [A: $i,R: $i] :
% 0.17/0.43 ( ( breln1 @ A @ R )
% 0.17/0.43 => ! [S: $i] :
% 0.17/0.43 ( ( breln1 @ A @ S )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.17/0.43 | ( in @ ( kpair @ Xx @ Xy ) @ S ) )
% 0.17/0.43 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(breln1unionE_type,type,
% 0.17/0.43 breln1unionE: $o ).
% 0.17/0.43
% 0.17/0.43 thf(breln1unionE,definition,
% 0.17/0.43 ( breln1unionE
% 0.17/0.43 = ( ! [A: $i,R: $i] :
% 0.17/0.43 ( ( breln1 @ A @ R )
% 0.17/0.43 => ! [S: $i] :
% 0.17/0.43 ( ( breln1 @ A @ S )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 0.17/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.17/0.43 | ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(breln1unionEcases_type,type,
% 0.17/0.43 breln1unionEcases: $o ).
% 0.17/0.43
% 0.17/0.43 thf(breln1unionEcases,definition,
% 0.17/0.43 ( breln1unionEcases
% 0.17/0.43 = ( ! [A: $i,R: $i] :
% 0.17/0.43 ( ( breln1 @ A @ R )
% 0.17/0.43 => ! [S: $i] :
% 0.17/0.43 ( ( breln1 @ A @ S )
% 0.17/0.43 => ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ! [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 0.17/0.43 => ! [Xphi: $o] :
% 0.17/0.43 ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.17/0.43 => Xphi )
% 0.17/0.43 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.17/0.43 => Xphi )
% 0.17/0.43 => Xphi ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(breln1unionCommutes_type,type,
% 0.17/0.43 breln1unionCommutes: $o ).
% 0.17/0.43
% 0.17/0.43 thf(breln1unionCommutes,definition,
% 0.17/0.43 ( breln1unionCommutes
% 0.17/0.43 = ( ! [A: $i,R: $i] :
% 0.17/0.43 ( ( breln1 @ A @ R )
% 0.17/0.43 => ! [S: $i] :
% 0.17/0.43 ( ( breln1 @ A @ S )
% 0.17/0.43 => ( ( binunion @ R @ S )
% 0.17/0.43 = ( binunion @ S @ R ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(woz2Ex_type,type,
% 0.17/0.43 woz2Ex: $o ).
% 0.17/0.43
% 0.17/0.43 thf(woz2Ex,definition,
% 0.17/0.43 ( woz2Ex
% 0.17/0.43 = ( ! [A: $i,R: $i] :
% 0.17/0.43 ( ( breln1 @ A @ R )
% 0.17/0.43 => ( R
% 0.17/0.43 = ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(woz2W_type,type,
% 0.17/0.43 woz2W: $o ).
% 0.17/0.43
% 0.17/0.43 thf(woz2W,definition,
% 0.17/0.43 ( woz2W
% 0.17/0.43 = ( ! [A: $i,R: $i] :
% 0.17/0.43 ( ( breln1 @ A @ R )
% 0.17/0.43 => ! [S: $i] :
% 0.17/0.43 ( ( breln1 @ A @ S )
% 0.17/0.43 => ( ( breln1invset @ A @ ( breln1compset @ A @ R @ S ) )
% 0.17/0.43 = ( breln1compset @ A @ ( breln1invset @ A @ S ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(woz2A_type,type,
% 0.17/0.43 woz2A: $o ).
% 0.17/0.43
% 0.17/0.43 thf(woz2A,definition,
% 0.17/0.43 ( woz2A
% 0.17/0.43 = ( ! [A: $i,R: $i] :
% 0.17/0.43 ( ( breln1 @ A @ R )
% 0.17/0.43 => ! [S: $i] :
% 0.17/0.43 ( ( breln1 @ A @ S )
% 0.17/0.43 => ! [T: $i] :
% 0.17/0.43 ( ( breln1 @ A @ T )
% 0.17/0.43 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 0.17/0.43 = ( binunion @ ( breln1compset @ A @ R @ T ) @ ( breln1compset @ A @ S @ T ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(woz2B_type,type,
% 0.17/0.43 woz2B: $o ).
% 0.17/0.43
% 0.17/0.43 thf(woz2B,definition,
% 0.17/0.43 ( woz2B
% 0.17/0.43 = ( ! [A: $i,R: $i] :
% 0.17/0.43 ( ( breln1 @ A @ R )
% 0.17/0.43 => ! [S: $i] :
% 0.17/0.43 ( ( breln1 @ A @ S )
% 0.17/0.43 => ! [T: $i] :
% 0.17/0.43 ( ( breln1 @ A @ T )
% 0.17/0.43 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 0.17/0.43 = ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ S ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(image1Ex_type,type,
% 0.17/0.43 image1Ex: $o ).
% 0.17/0.43
% 0.17/0.43 thf(image1Ex,definition,
% 0.17/0.43 ( image1Ex
% 0.17/0.43 = ( ! [A: $i,Xf: $i > $i] :
% 0.17/0.43 ? [B: $i] :
% 0.17/0.43 ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ B )
% 0.17/0.43 <=> ? [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 & ( Xx
% 0.17/0.43 = ( Xf @ Xy ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(image1Ex1_type,type,
% 0.17/0.43 image1Ex1: $o ).
% 0.17/0.43
% 0.17/0.43 thf(image1Ex1,definition,
% 0.17/0.43 ( image1Ex1
% 0.17/0.43 = ( ! [A: $i,Xf: $i > $i] :
% 0.17/0.43 ( exu
% 0.17/0.43 @ ^ [B: $i] :
% 0.17/0.43 ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ B )
% 0.17/0.43 <=> ? [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 & ( Xx
% 0.17/0.43 = ( Xf @ Xy ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(image1_type,type,
% 0.17/0.43 image1: $i > ( $i > $i ) > $i ).
% 0.17/0.43
% 0.17/0.43 thf(image1Equiv_type,type,
% 0.17/0.43 image1Equiv: $o ).
% 0.17/0.43
% 0.17/0.43 thf(image1Equiv,definition,
% 0.17/0.43 ( image1Equiv
% 0.17/0.43 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 0.17/0.43 ( ( in @ Xx
% 0.17/0.43 @ ( image1 @ A
% 0.17/0.43 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 0.17/0.43 <=> ? [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 & ( Xx
% 0.17/0.43 = ( Xf @ Xy ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(image1E_type,type,
% 0.17/0.43 image1E: $o ).
% 0.17/0.43
% 0.17/0.43 thf(image1E,definition,
% 0.17/0.43 ( image1E
% 0.17/0.43 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 0.17/0.43 ( ( in @ Xx
% 0.17/0.43 @ ( image1 @ A
% 0.17/0.43 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 0.17/0.43 => ? [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 & ( Xx
% 0.17/0.43 = ( Xf @ Xy ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(image1I_type,type,
% 0.17/0.43 image1I: $o ).
% 0.17/0.43
% 0.17/0.43 thf(image1I,definition,
% 0.17/0.43 ( image1I
% 0.17/0.43 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 0.17/0.43 ( ? [Xy: $i] :
% 0.17/0.43 ( ( in @ Xy @ A )
% 0.17/0.43 & ( Xx
% 0.17/0.43 = ( Xf @ Xy ) ) )
% 0.17/0.43 => ( in @ Xx
% 0.17/0.43 @ ( image1 @ A
% 0.17/0.43 @ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(injective_type,type,
% 0.17/0.43 injective: $i > $i > $i > $o ).
% 0.17/0.43
% 0.17/0.43 thf(injFuncSet_type,type,
% 0.17/0.43 injFuncSet: $i > $i > $i ).
% 0.17/0.43
% 0.17/0.43 thf(injFuncInInjFuncSet_type,type,
% 0.17/0.43 injFuncInInjFuncSet: $o ).
% 0.17/0.43
% 0.17/0.43 thf(injFuncInInjFuncSet,definition,
% 0.17/0.43 ( injFuncInInjFuncSet
% 0.17/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.43 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.17/0.43 => ( ( injective @ A @ B @ Xf )
% 0.17/0.43 => ( in @ Xf @ ( injFuncSet @ A @ B ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(injFuncSetFuncIn_type,type,
% 0.17/0.43 injFuncSetFuncIn: $o ).
% 0.17/0.43
% 0.17/0.43 thf(injFuncSetFuncIn,definition,
% 0.17/0.43 ( injFuncSetFuncIn
% 0.17/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.43 ( ( in @ Xf @ ( injFuncSet @ A @ B ) )
% 0.17/0.43 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(injFuncSetFuncInj_type,type,
% 0.17/0.43 injFuncSetFuncInj: $o ).
% 0.17/0.43
% 0.17/0.43 thf(injFuncSetFuncInj,definition,
% 0.17/0.43 ( injFuncSetFuncInj
% 0.17/0.43 = ( ! [Xx: $i,Xy: $i,Xf: $i] :
% 0.17/0.43 ( ( in @ Xf @ ( injFuncSet @ Xx @ Xy ) )
% 0.17/0.43 => ( injective @ Xx @ Xy @ Xf ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(surjective_type,type,
% 0.17/0.43 surjective: $i > $i > $i > $o ).
% 0.17/0.43
% 0.17/0.43 thf(surjFuncSet_type,type,
% 0.17/0.43 surjFuncSet: $i > $i > $i ).
% 0.17/0.43
% 0.17/0.43 thf(surjFuncSetFuncIn_type,type,
% 0.17/0.43 surjFuncSetFuncIn: $o ).
% 0.17/0.43
% 0.17/0.43 thf(surjFuncSetFuncIn,definition,
% 0.17/0.43 ( surjFuncSetFuncIn
% 0.17/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.17/0.43 ( ( in @ Xf @ ( surjFuncSet @ A @ B ) )
% 0.17/0.43 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(surjFuncSetFuncSurj_type,type,
% 0.17/0.43 surjFuncSetFuncSurj: $o ).
% 0.17/0.43
% 0.17/0.43 thf(surjFuncSetFuncSurj,definition,
% 0.17/0.43 ( surjFuncSetFuncSurj
% 0.17/0.43 = ( ! [Xx: $i,Xy: $i,Xf: $i] :
% 0.17/0.43 ( ( in @ Xf @ ( surjFuncSet @ Xx @ Xy ) )
% 0.17/0.43 => ( surjective @ Xx @ Xy @ Xf ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(leftInvIsSurj_type,type,
% 0.17/0.43 leftInvIsSurj: $o ).
% 0.17/0.43
% 0.17/0.43 thf(leftInvIsSurj,definition,
% 0.17/0.43 ( leftInvIsSurj
% 0.17/0.43 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.17/0.43 ( ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.17/0.43 => ! [Xg: $i] :
% 0.17/0.43 ( ( in @ Xg @ ( funcSet @ B @ A ) )
% 0.17/0.43 => ( ! [Xx: $i] :
% 0.17/0.43 ( ( in @ Xx @ A )
% 0.17/0.43 => ( ( ap @ B @ A @ Xg @ ( Xf @ Xx ) )
% 0.17/0.43 = Xx ) )
% 0.17/0.43 => ( surjective @ B @ A @ Xg ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(surjCantorThm_type,type,
% 0.17/0.43 surjCantorThm: $o ).
% 0.17/0.43
% 0.17/0.43 thf(surjCantorThm,definition,
% 0.17/0.43 ( surjCantorThm
% 0.17/0.43 = ( ! [A: $i,Xf: $i] :
% 0.17/0.43 ( ( in @ Xf @ ( funcSet @ A @ ( powerset @ A ) ) )
% 0.17/0.43 => ~ ( surjective @ A @ ( powerset @ A ) @ Xf ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(foundation2_type,type,
% 0.17/0.43 foundation2: $o ).
% 0.17/0.43
% 0.17/0.43 thf(foundation2,definition,
% 0.17/0.43 ( foundation2
% 0.17/0.43 = ( ! [A: $i] :
% 0.17/0.43 ( ( nonempty @ A )
% 0.17/0.43 => ? [X: $i] :
% 0.17/0.43 ( ( in @ X @ A )
% 0.17/0.43 & ( ( binintersect @ X @ A )
% 0.17/0.43 = emptyset ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 thf(notinself,conjecture,
% 0.17/0.43 ( setextAx
% 0.17/0.43 => ( emptysetAx
% 0.17/0.43 => ( setadjoinAx
% 0.17/0.43 => ( powersetAx
% 0.17/0.43 => ( setunionAx
% 0.17/0.43 => ( omega0Ax
% 0.17/0.43 => ( omegaSAx
% 0.17/0.43 => ( omegaIndAx
% 0.17/0.43 => ( replAx
% 0.17/0.43 => ( foundationAx
% 0.17/0.43 => ( wellorderingAx
% 0.17/0.43 => ( descrp
% 0.17/0.43 => ( dsetconstrI
% 0.17/0.43 => ( dsetconstrEL
% 0.17/0.43 => ( dsetconstrER
% 0.17/0.43 => ( exuE1
% 0.17/0.43 => ( prop2setE
% 0.17/0.43 => ( emptysetE
% 0.17/0.43 => ( emptysetimpfalse
% 0.17/0.43 => ( notinemptyset
% 0.17/0.43 => ( exuE3e
% 0.17/0.43 => ( setext
% 0.17/0.43 => ( emptyI
% 0.17/0.43 => ( noeltsimpempty
% 0.17/0.43 => ( setbeta
% 0.17/0.43 => ( nonemptyE1
% 0.17/0.43 => ( nonemptyI
% 0.17/0.43 => ( nonemptyI1
% 0.17/0.43 => ( setadjoinIL
% 0.17/0.43 => ( emptyinunitempty
% 0.17/0.43 => ( setadjoinIR
% 0.17/0.43 => ( setadjoinE
% 0.17/0.43 => ( setadjoinOr
% 0.17/0.43 => ( setoftrueEq
% 0.17/0.43 => ( powersetI
% 0.17/0.43 => ( emptyinPowerset
% 0.17/0.43 => ( emptyInPowerset
% 0.17/0.43 => ( powersetE
% 0.17/0.43 => ( setunionI
% 0.17/0.43 => ( setunionE
% 0.17/0.43 => ( subPowSU
% 0.17/0.43 => ( exuE2
% 0.17/0.43 => ( nonemptyImpWitness
% 0.17/0.43 => ( uniqinunit
% 0.17/0.43 => ( notinsingleton
% 0.17/0.43 => ( eqinunit
% 0.17/0.43 => ( singletonsswitch
% 0.17/0.43 => ( upairsetE
% 0.17/0.43 => ( upairsetIL
% 0.17/0.43 => ( upairsetIR
% 0.17/0.43 => ( emptyE1
% 0.17/0.43 => ( vacuousDall
% 0.17/0.43 => ( quantDeMorgan1
% 0.17/0.43 => ( quantDeMorgan2
% 0.17/0.43 => ( quantDeMorgan3
% 0.17/0.43 => ( quantDeMorgan4
% 0.17/0.43 => ( prop2setI
% 0.17/0.43 => ( prop2set2propI
% 0.17/0.43 => ( notdexE
% 0.17/0.43 => ( notdallE
% 0.17/0.43 => ( exuI1
% 0.17/0.43 => ( exuI3
% 0.17/0.43 => ( exuI2
% 0.17/0.43 => ( inCongP
% 0.17/0.43 => ( in__Cong
% 0.17/0.43 => ( exuE3u
% 0.17/0.43 => ( exu__Cong
% 0.17/0.43 => ( emptyset__Cong
% 0.17/0.43 => ( setadjoin__Cong
% 0.17/0.43 => ( powerset__Cong
% 0.17/0.43 => ( setunion__Cong
% 0.17/0.43 => ( omega__Cong
% 0.17/0.43 => ( exuEu
% 0.17/0.43 => ( descr__Cong
% 0.17/0.43 => ( dsetconstr__Cong
% 0.17/0.43 => ( subsetI1
% 0.17/0.43 => ( eqimpsubset2
% 0.17/0.43 => ( eqimpsubset1
% 0.17/0.43 => ( subsetI2
% 0.17/0.43 => ( emptysetsubset
% 0.17/0.43 => ( subsetE
% 0.17/0.43 => ( subsetE2
% 0.17/0.43 => ( notsubsetI
% 0.17/0.43 => ( notequalI1
% 0.17/0.43 => ( notequalI2
% 0.17/0.43 => ( subsetRefl
% 0.17/0.43 => ( subsetTrans
% 0.17/0.43 => ( setadjoinSub
% 0.17/0.43 => ( setadjoinSub2
% 0.17/0.43 => ( subset2powerset
% 0.17/0.43 => ( setextsub
% 0.17/0.43 => ( subsetemptysetimpeq
% 0.17/0.43 => ( powersetI1
% 0.17/0.43 => ( powersetE1
% 0.17/0.43 => ( inPowerset
% 0.17/0.43 => ( powersetsubset
% 0.17/0.43 => ( sepInPowerset
% 0.17/0.43 => ( sepSubset
% 0.17/0.43 => ( binunionIL
% 0.17/0.43 => ( upairset2IR
% 0.17/0.43 => ( binunionIR
% 0.17/0.43 => ( binunionEcases
% 0.17/0.43 => ( binunionE
% 0.17/0.43 => ( binunionLsub
% 0.17/0.43 => ( binunionRsub
% 0.17/0.43 => ( binintersectI
% 0.17/0.43 => ( binintersectSubset5
% 0.17/0.43 => ( binintersectEL
% 0.17/0.43 => ( binintersectLsub
% 0.17/0.43 => ( binintersectSubset2
% 0.17/0.43 => ( binintersectSubset3
% 0.17/0.43 => ( binintersectER
% 0.17/0.43 => ( disjointsetsI1
% 0.17/0.43 => ( binintersectRsub
% 0.17/0.43 => ( binintersectSubset4
% 0.17/0.43 => ( binintersectSubset1
% 0.17/0.43 => ( bs114d
% 0.17/0.43 => ( setminusI
% 0.17/0.43 => ( setminusEL
% 0.17/0.43 => ( setminusER
% 0.17/0.43 => ( setminusSubset2
% 0.17/0.43 => ( setminusERneg
% 0.17/0.43 => ( setminusELneg
% 0.17/0.43 => ( setminusILneg
% 0.17/0.43 => ( setminusIRneg
% 0.17/0.43 => ( setminusLsub
% 0.17/0.43 => ( setminusSubset1
% 0.17/0.43 => ( symdiffE
% 0.17/0.43 => ( symdiffI1
% 0.17/0.43 => ( symdiffI2
% 0.17/0.43 => ( symdiffIneg1
% 0.17/0.43 => ( symdiffIneg2
% 0.17/0.43 => ( secondinupair
% 0.17/0.43 => ( setukpairIL
% 0.17/0.43 => ( setukpairIR
% 0.17/0.43 => ( kpairiskpair
% 0.17/0.43 => ( kpairp
% 0.17/0.43 => ( singletonsubset
% 0.17/0.43 => ( singletoninpowerset
% 0.17/0.43 => ( singletoninpowunion
% 0.17/0.43 => ( upairset2E
% 0.17/0.43 => ( upairsubunion
% 0.17/0.43 => ( upairinpowunion
% 0.17/0.43 => ( ubforcartprodlem1
% 0.17/0.43 => ( ubforcartprodlem2
% 0.17/0.43 => ( ubforcartprodlem3
% 0.17/0.43 => ( cartprodpairin
% 0.17/0.43 => ( cartprodmempair1
% 0.17/0.43 => ( cartprodmempair
% 0.17/0.43 => ( setunionE2
% 0.17/0.43 => ( setunionsingleton1
% 0.17/0.43 => ( setunionsingleton2
% 0.17/0.43 => ( setunionsingleton
% 0.17/0.43 => ( singletonprop
% 0.17/0.43 => ( ex1E1
% 0.17/0.43 => ( ex1I
% 0.17/0.43 => ( ex1I2
% 0.17/0.43 => ( singletonsuniq
% 0.17/0.43 => ( setukpairinjL1
% 0.17/0.43 => ( kfstsingleton
% 0.17/0.43 => ( theprop
% 0.17/0.43 => ( kfstpairEq
% 0.17/0.43 => ( cartprodfstin
% 0.17/0.43 => ( setukpairinjL2
% 0.17/0.43 => ( setukpairinjL
% 0.17/0.43 => ( setukpairinjR11
% 0.17/0.43 => ( setukpairinjR12
% 0.17/0.43 => ( setukpairinjR1
% 0.17/0.43 => ( upairequniteq
% 0.17/0.43 => ( setukpairinjR2
% 0.17/0.43 => ( setukpairinjR
% 0.17/0.43 => ( ksndsingleton
% 0.17/0.43 => ( ksndpairEq
% 0.17/0.43 => ( kpairsurjEq
% 0.17/0.43 => ( cartprodsndin
% 0.17/0.43 => ( cartprodpairmemEL
% 0.17/0.43 => ( cartprodpairmemER
% 0.17/0.43 => ( cartprodmempaircEq
% 0.17/0.43 => ( cartprodfstpairEq
% 0.17/0.43 => ( cartprodsndpairEq
% 0.17/0.43 => ( cartprodpairsurjEq
% 0.17/0.43 => ( dpsetconstrI
% 0.17/0.43 => ( dpsetconstrSub
% 0.17/0.43 => ( setOfPairsIsBReln
% 0.17/0.43 => ( dpsetconstrERa
% 0.17/0.43 => ( dpsetconstrEL1
% 0.17/0.43 => ( dpsetconstrEL2
% 0.17/0.43 => ( dpsetconstrER
% 0.17/0.43 => ( funcImageSingleton
% 0.17/0.43 => ( apProp
% 0.17/0.43 => ( app
% 0.17/0.43 => ( infuncsetfunc
% 0.17/0.43 => ( ap2p
% 0.17/0.43 => ( funcinfuncset
% 0.17/0.43 => ( lamProp
% 0.17/0.43 => ( lamp
% 0.17/0.43 => ( lam2p
% 0.17/0.43 => ( brelnall1
% 0.17/0.43 => ( brelnall2
% 0.17/0.43 => ( ex1E2
% 0.17/0.43 => ( funcGraphProp1
% 0.17/0.43 => ( funcGraphProp3
% 0.17/0.43 => ( funcGraphProp2
% 0.17/0.43 => ( funcextLem
% 0.17/0.43 => ( funcGraphProp4
% 0.17/0.43 => ( subbreln
% 0.17/0.43 => ( eqbreln
% 0.17/0.43 => ( funcext
% 0.17/0.43 => ( funcext2
% 0.17/0.43 => ( ap2apEq1
% 0.17/0.43 => ( ap2apEq2
% 0.17/0.43 => ( beta1
% 0.17/0.43 => ( eta1
% 0.17/0.43 => ( lam2lamEq
% 0.17/0.43 => ( beta2
% 0.17/0.43 => ( eta2
% 0.17/0.43 => ( iffalseProp1
% 0.17/0.43 => ( iffalseProp2
% 0.17/0.43 => ( iftrueProp1
% 0.17/0.43 => ( iftrueProp2
% 0.17/0.43 => ( ifSingleton
% 0.17/0.43 => ( ifp
% 0.17/0.43 => ( theeq
% 0.17/0.43 => ( iftrue
% 0.17/0.43 => ( iffalse
% 0.17/0.43 => ( iftrueorfalse
% 0.17/0.43 => ( binintersectT_lem
% 0.17/0.43 => ( binunionT_lem
% 0.17/0.43 => ( powersetT_lem
% 0.17/0.43 => ( setminusT_lem
% 0.17/0.43 => ( complementT_lem
% 0.17/0.43 => ( setextT
% 0.17/0.43 => ( subsetTI
% 0.17/0.43 => ( powersetTI1
% 0.17/0.43 => ( powersetTE1
% 0.17/0.43 => ( complementTI1
% 0.17/0.43 => ( complementTE1
% 0.17/0.43 => ( binintersectTELcontra
% 0.17/0.43 => ( binintersectTERcontra
% 0.17/0.43 => ( contrasubsetT
% 0.17/0.43 => ( contrasubsetT1
% 0.17/0.43 => ( contrasubsetT2
% 0.17/0.43 => ( contrasubsetT3
% 0.17/0.43 => ( doubleComplementI1
% 0.17/0.43 => ( doubleComplementE1
% 0.17/0.43 => ( doubleComplementSub1
% 0.17/0.43 => ( doubleComplementSub2
% 0.17/0.43 => ( doubleComplementEq
% 0.17/0.43 => ( complementTnotintersectT
% 0.17/0.43 => ( complementImpComplementIntersect
% 0.17/0.43 => ( complementSubsetComplementIntersect
% 0.17/0.43 => ( complementInPowersetComplementIntersect
% 0.17/0.43 => ( contraSubsetComplement
% 0.17/0.43 => ( complementTcontraSubset
% 0.17/0.43 => ( binunionTILcontra
% 0.17/0.43 => ( binunionTIRcontra
% 0.17/0.43 => ( inIntersectImpInUnion
% 0.17/0.43 => ( inIntersectImpInUnion2
% 0.17/0.43 => ( inIntersectImpInIntersectUnions
% 0.17/0.43 => ( intersectInPowersetIntersectUnions
% 0.17/0.43 => ( inComplementUnionImpNotIn1
% 0.17/0.43 => ( inComplementUnionImpInComplement1
% 0.17/0.43 => ( binunionTE
% 0.17/0.43 => ( binunionTEcontra
% 0.17/0.43 => ( demorgan2a1
% 0.17/0.43 => ( complementUnionInPowersetComplement
% 0.17/0.43 => ( demorgan2a2
% 0.17/0.43 => ( demorgan1a
% 0.17/0.43 => ( demorgan1b
% 0.17/0.43 => ( demorgan1
% 0.17/0.43 => ( demorgan2a
% 0.17/0.43 => ( demorgan2b2
% 0.17/0.43 => ( demorgan2b
% 0.17/0.43 => ( demorgan2
% 0.17/0.43 => ( woz13rule0
% 0.17/0.43 => ( woz13rule1
% 0.17/0.43 => ( woz13rule2
% 0.17/0.43 => ( woz13rule3
% 0.17/0.43 => ( woz13rule4
% 0.17/0.43 => ( woz1_1
% 0.17/0.43 => ( woz1_2
% 0.17/0.43 => ( woz1_3
% 0.17/0.43 => ( woz1_4
% 0.17/0.43 => ( woz1_5
% 0.17/0.43 => ( breln1all2
% 0.17/0.43 => ( breln1SetBreln1
% 0.17/0.43 => ( choice2fnsingleton
% 0.17/0.43 => ( setOfPairsIsBReln1
% 0.17/0.43 => ( breln1all1
% 0.17/0.43 => ( subbreln1
% 0.17/0.43 => ( eqbreln1
% 0.17/0.43 => ( breln1invprop
% 0.17/0.43 => ( breln1invI
% 0.17/0.43 => ( breln1invE
% 0.17/0.43 => ( breln1compprop
% 0.17/0.43 => ( breln1compI
% 0.17/0.43 => ( breln1compE
% 0.17/0.43 => ( breln1compEex
% 0.17/0.43 => ( breln1unionprop
% 0.17/0.43 => ( breln1unionIL
% 0.17/0.43 => ( breln1unionIR
% 0.17/0.43 => ( breln1unionI
% 0.17/0.43 => ( breln1unionE
% 0.17/0.43 => ( breln1unionEcases
% 0.17/0.43 => ( breln1unionCommutes
% 0.17/0.43 => ( woz2Ex
% 0.17/0.43 => ( woz2W
% 0.17/0.43 => ( woz2A
% 0.17/0.43 => ( woz2B
% 0.17/0.43 => ( image1Ex
% 0.17/0.43 => ( image1Ex1
% 0.17/0.43 => ( image1Equiv
% 0.17/0.43 => ( image1E
% 0.17/0.43 => ( image1I
% 0.17/0.43 => ( injFuncInInjFuncSet
% 0.17/0.43 => ( injFuncSetFuncIn
% 0.17/0.43 => ( injFuncSetFuncInj
% 0.17/0.43 => ( surjFuncSetFuncIn
% 0.17/0.43 => ( surjFuncSetFuncSurj
% 0.17/0.43 => ( leftInvIsSurj
% 0.17/0.43 => ( surjCantorThm
% 0.17/0.43 => ( foundation2
% 0.17/0.43 => ! [A: $i] :
% 0.17/0.43 ~ ( in @ A @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.43
% 0.17/0.43 %------------------------------------------------------------------------------
% 0.17/0.43 ------------------------
% 2.77/1.47 ---- Embedded in THF ---
% 2.77/1.47 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.77/1.47 %%% Generated on Tue Feb 24 12:34:43 EST 2026
% 2.77/1.47 %%% using '$$dhol' embedding, version 1.3.0.
% 2.77/1.47 %%% Logic specification used:
% 2.77/1.47 %%% thf(spec, logic, $$dhol).
% 2.77/1.47
% 2.77/1.47 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.yv4wus1g2e/DTF2DTF4600.p
% See solution above
% 2.77/1.47 ------------------------
% 2.99/1.51 ---- Cleaned THF ---
% 2.99/1.51 thf(in_type,type,
% 2.99/1.51 in: $i > $i > $o ).
% 2.99/1.51
% 2.99/1.51 thf(exu_type,type,
% 2.99/1.51 exu: ( $i > $o ) > $o ).
% 2.99/1.51
% 2.99/1.51 thf(exu,definition,
% 2.99/1.51 ( exu
% 2.99/1.51 = ( ^ [Xphi: $i > $o] :
% 2.99/1.51 ? [Xx: $i] :
% 2.99/1.51 ( ( Xphi @ Xx )
% 2.99/1.51 & ! [Xy: $i] :
% 2.99/1.51 ( ( Xphi @ Xy )
% 2.99/1.51 => ( Xx = Xy ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setextAx_type,type,
% 2.99/1.51 setextAx: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setextAx,definition,
% 2.99/1.51 ( setextAx
% 2.99/1.51 = ( ! [A: $i,B: $i] :
% 2.99/1.51 ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 <=> ( in @ Xx @ B ) )
% 2.99/1.51 => ( A = B ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(emptyset_type,type,
% 2.99/1.51 emptyset: $i ).
% 2.99/1.51
% 2.99/1.51 thf(emptysetAx_type,type,
% 2.99/1.51 emptysetAx: $o ).
% 2.99/1.51
% 2.99/1.51 thf(emptysetAx,definition,
% 2.99/1.51 ( emptysetAx
% 2.99/1.51 = ( ! [Xx: $i] :
% 2.99/1.51 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setadjoin_type,type,
% 2.99/1.51 setadjoin: $i > $i > $i ).
% 2.99/1.51
% 2.99/1.51 thf(setadjoinAx_type,type,
% 2.99/1.51 setadjoinAx: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setadjoinAx,definition,
% 2.99/1.51 ( setadjoinAx
% 2.99/1.51 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.99/1.51 <=> ( ( Xy = Xx )
% 2.99/1.51 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(powerset_type,type,
% 2.99/1.51 powerset: $i > $i ).
% 2.99/1.51
% 2.99/1.51 thf(powersetAx_type,type,
% 2.99/1.51 powersetAx: $o ).
% 2.99/1.51
% 2.99/1.51 thf(powersetAx,definition,
% 2.99/1.51 ( powersetAx
% 2.99/1.51 = ( ! [A: $i,B: $i] :
% 2.99/1.51 ( ( in @ B @ ( powerset @ A ) )
% 2.99/1.51 <=> ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ B )
% 2.99/1.51 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setunion_type,type,
% 2.99/1.51 setunion: $i > $i ).
% 2.99/1.51
% 2.99/1.51 thf(setunionAx_type,type,
% 2.99/1.51 setunionAx: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setunionAx,definition,
% 2.99/1.51 ( setunionAx
% 2.99/1.51 = ( ! [A: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ ( setunion @ A ) )
% 2.99/1.51 <=> ? [B: $i] :
% 2.99/1.51 ( ( in @ Xx @ B )
% 2.99/1.51 & ( in @ B @ A ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(omega_type,type,
% 2.99/1.51 omega: $i ).
% 2.99/1.51
% 2.99/1.51 thf(omega0Ax_type,type,
% 2.99/1.51 omega0Ax: $o ).
% 2.99/1.51
% 2.99/1.51 thf(omega0Ax,definition,
% 2.99/1.51 ( omega0Ax
% 2.99/1.51 = ( in @ emptyset @ omega ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(omegaSAx_type,type,
% 2.99/1.51 omegaSAx: $o ).
% 2.99/1.51
% 2.99/1.51 thf(omegaSAx,definition,
% 2.99/1.51 ( omegaSAx
% 2.99/1.51 = ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ omega )
% 2.99/1.51 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(omegaIndAx_type,type,
% 2.99/1.51 omegaIndAx: $o ).
% 2.99/1.51
% 2.99/1.51 thf(omegaIndAx,definition,
% 2.99/1.51 ( omegaIndAx
% 2.99/1.51 = ( ! [A: $i] :
% 2.99/1.51 ( ( ( in @ emptyset @ A )
% 2.99/1.51 & ! [Xx: $i] :
% 2.99/1.51 ( ( ( in @ Xx @ omega )
% 2.99/1.51 & ( in @ Xx @ A ) )
% 2.99/1.51 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.99/1.51 => ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ omega )
% 2.99/1.51 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(replAx_type,type,
% 2.99/1.51 replAx: $o ).
% 2.99/1.51
% 2.99/1.51 thf(replAx,definition,
% 2.99/1.51 ( replAx
% 2.99/1.51 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.99/1.51 ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( exu
% 2.99/1.51 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.99/1.51 => ? [B: $i] :
% 2.99/1.51 ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ B )
% 2.99/1.51 <=> ? [Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ A )
% 2.99/1.51 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(foundationAx_type,type,
% 2.99/1.51 foundationAx: $o ).
% 2.99/1.51
% 2.99/1.51 thf(foundationAx,definition,
% 2.99/1.51 ( foundationAx
% 2.99/1.51 = ( ! [A: $i] :
% 2.99/1.51 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.99/1.51 => ? [B: $i] :
% 2.99/1.51 ( ( in @ B @ A )
% 2.99/1.51 & ~ ? [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ B )
% 2.99/1.51 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(wellorderingAx_type,type,
% 2.99/1.51 wellorderingAx: $o ).
% 2.99/1.51
% 2.99/1.51 thf(wellorderingAx,definition,
% 2.99/1.51 ( wellorderingAx
% 2.99/1.51 = ( ! [A: $i] :
% 2.99/1.51 ? [B: $i] :
% 2.99/1.51 ( ! [C: $i] :
% 2.99/1.51 ( ( in @ C @ B )
% 2.99/1.51 => ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ C )
% 2.99/1.51 => ( in @ Xx @ A ) ) )
% 2.99/1.51 & ! [Xx: $i,Xy: $i] :
% 2.99/1.51 ( ( ( in @ Xx @ A )
% 2.99/1.51 & ( in @ Xy @ A ) )
% 2.99/1.51 => ( ! [C: $i] :
% 2.99/1.51 ( ( in @ C @ B )
% 2.99/1.51 => ( ( in @ Xx @ C )
% 2.99/1.51 <=> ( in @ Xy @ C ) ) )
% 2.99/1.51 => ( Xx = Xy ) ) )
% 2.99/1.51 & ! [C: $i,D: $i] :
% 2.99/1.51 ( ( ( in @ C @ B )
% 2.99/1.51 & ( in @ D @ B ) )
% 2.99/1.51 => ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ C )
% 2.99/1.51 => ( in @ Xx @ D ) )
% 2.99/1.51 | ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ D )
% 2.99/1.51 => ( in @ Xx @ C ) ) ) )
% 2.99/1.51 & ! [C: $i] :
% 2.99/1.51 ( ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ C )
% 2.99/1.51 => ( in @ Xx @ A ) )
% 2.99/1.51 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.99/1.51 => ? [D: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ D @ B )
% 2.99/1.51 & ( in @ Xx @ C )
% 2.99/1.51 & ~ ? [Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ D )
% 2.99/1.51 & ( in @ Xy @ C ) )
% 2.99/1.51 & ! [E: $i] :
% 2.99/1.51 ( ( in @ E @ B )
% 2.99/1.51 => ( ! [Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ E )
% 2.99/1.51 => ( in @ Xy @ D ) )
% 2.99/1.51 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(descr_type,type,
% 2.99/1.51 descr: ( $i > $o ) > $i ).
% 2.99/1.51
% 2.99/1.51 thf(descrp_type,type,
% 2.99/1.51 descrp: $o ).
% 2.99/1.51
% 2.99/1.51 thf(descrp,definition,
% 2.99/1.51 ( descrp
% 2.99/1.51 = ( ! [Xphi: $i > $o] :
% 2.99/1.51 ( ( exu
% 2.99/1.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.51 => ( Xphi
% 2.99/1.51 @ ( descr
% 2.99/1.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(dsetconstr_type,type,
% 2.99/1.51 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.99/1.51
% 2.99/1.51 thf(dsetconstrI_type,type,
% 2.99/1.51 dsetconstrI: $o ).
% 2.99/1.51
% 2.99/1.51 thf(dsetconstrI,definition,
% 2.99/1.51 ( dsetconstrI
% 2.99/1.51 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( ( Xphi @ Xx )
% 2.99/1.51 => ( in @ Xx
% 2.99/1.51 @ ( dsetconstr @ A
% 2.99/1.51 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(dsetconstrEL_type,type,
% 2.99/1.51 dsetconstrEL: $o ).
% 2.99/1.51
% 2.99/1.51 thf(dsetconstrEL,definition,
% 2.99/1.51 ( dsetconstrEL
% 2.99/1.51 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx
% 2.99/1.51 @ ( dsetconstr @ A
% 2.99/1.51 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.99/1.51 => ( in @ Xx @ A ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(dsetconstrER_type,type,
% 2.99/1.51 dsetconstrER: $o ).
% 2.99/1.51
% 2.99/1.51 thf(dsetconstrER,definition,
% 2.99/1.51 ( dsetconstrER
% 2.99/1.51 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx
% 2.99/1.51 @ ( dsetconstr @ A
% 2.99/1.51 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.99/1.51 => ( Xphi @ Xx ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(exuE1_type,type,
% 2.99/1.51 exuE1: $o ).
% 2.99/1.51
% 2.99/1.51 thf(exuE1,definition,
% 2.99/1.51 ( exuE1
% 2.99/1.51 = ( ! [Xphi: $i > $o] :
% 2.99/1.51 ( ( exu
% 2.99/1.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.51 => ? [Xx: $i] :
% 2.99/1.51 ( ( Xphi @ Xx )
% 2.99/1.51 & ! [Xy: $i] :
% 2.99/1.51 ( ( Xphi @ Xy )
% 2.99/1.51 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(prop2set_type,type,
% 2.99/1.51 prop2set: $o > $i ).
% 2.99/1.51
% 2.99/1.51 thf(prop2setE_type,type,
% 2.99/1.51 prop2setE: $o ).
% 2.99/1.51
% 2.99/1.51 thf(prop2setE,definition,
% 2.99/1.51 ( prop2setE
% 2.99/1.51 = ( ! [Xphi: $o,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.99/1.51 => Xphi ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(emptysetE_type,type,
% 2.99/1.51 emptysetE: $o ).
% 2.99/1.51
% 2.99/1.51 thf(emptysetE,definition,
% 2.99/1.51 ( emptysetE
% 2.99/1.51 = ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ emptyset )
% 2.99/1.51 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(emptysetimpfalse_type,type,
% 2.99/1.51 emptysetimpfalse: $o ).
% 2.99/1.51
% 2.99/1.51 thf(emptysetimpfalse,definition,
% 2.99/1.51 ( emptysetimpfalse
% 2.99/1.51 = ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ emptyset )
% 2.99/1.51 => $false ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(notinemptyset_type,type,
% 2.99/1.51 notinemptyset: $o ).
% 2.99/1.51
% 2.99/1.51 thf(notinemptyset,definition,
% 2.99/1.51 ( notinemptyset
% 2.99/1.51 = ( ! [Xx: $i] :
% 2.99/1.51 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(exuE3e_type,type,
% 2.99/1.51 exuE3e: $o ).
% 2.99/1.51
% 2.99/1.51 thf(exuE3e,definition,
% 2.99/1.51 ( exuE3e
% 2.99/1.51 = ( ! [Xphi: $i > $o] :
% 2.99/1.51 ( ( exu
% 2.99/1.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.51 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setext_type,type,
% 2.99/1.51 setext: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setext,definition,
% 2.99/1.51 ( setext
% 2.99/1.51 = ( ! [A: $i,B: $i] :
% 2.99/1.51 ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( in @ Xx @ B ) )
% 2.99/1.51 => ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ B )
% 2.99/1.51 => ( in @ Xx @ A ) )
% 2.99/1.51 => ( A = B ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(emptyI_type,type,
% 2.99/1.51 emptyI: $o ).
% 2.99/1.51
% 2.99/1.51 thf(emptyI,definition,
% 2.99/1.51 ( emptyI
% 2.99/1.51 = ( ! [A: $i] :
% 2.99/1.51 ( ! [Xx: $i] :
% 2.99/1.51 ~ ( in @ Xx @ A )
% 2.99/1.51 => ( A = emptyset ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(noeltsimpempty_type,type,
% 2.99/1.51 noeltsimpempty: $o ).
% 2.99/1.51
% 2.99/1.51 thf(noeltsimpempty,definition,
% 2.99/1.51 ( noeltsimpempty
% 2.99/1.51 = ( ! [A: $i] :
% 2.99/1.51 ( ! [Xx: $i] :
% 2.99/1.51 ~ ( in @ Xx @ A )
% 2.99/1.51 => ( A = emptyset ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setbeta_type,type,
% 2.99/1.51 setbeta: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setbeta,definition,
% 2.99/1.51 ( setbeta
% 2.99/1.51 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( ( in @ Xx
% 2.99/1.51 @ ( dsetconstr @ A
% 2.99/1.51 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.99/1.51 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(nonempty_type,type,
% 2.99/1.51 nonempty: $i > $o ).
% 2.99/1.51
% 2.99/1.51 thf(nonempty,definition,
% 2.99/1.51 ( nonempty
% 2.99/1.51 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(nonemptyE1_type,type,
% 2.99/1.51 nonemptyE1: $o ).
% 2.99/1.51
% 2.99/1.51 thf(nonemptyE1,definition,
% 2.99/1.51 ( nonemptyE1
% 2.99/1.51 = ( ! [A: $i] :
% 2.99/1.51 ( ( nonempty @ A )
% 2.99/1.51 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(nonemptyI_type,type,
% 2.99/1.51 nonemptyI: $o ).
% 2.99/1.51
% 2.99/1.51 thf(nonemptyI,definition,
% 2.99/1.51 ( nonemptyI
% 2.99/1.51 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( ( Xphi @ Xx )
% 2.99/1.51 => ( nonempty
% 2.99/1.51 @ ( dsetconstr @ A
% 2.99/1.51 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(nonemptyI1_type,type,
% 2.99/1.51 nonemptyI1: $o ).
% 2.99/1.51
% 2.99/1.51 thf(nonemptyI1,definition,
% 2.99/1.51 ( nonemptyI1
% 2.99/1.51 = ( ! [A: $i] :
% 2.99/1.51 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.99/1.51 => ( nonempty @ A ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setadjoinIL_type,type,
% 2.99/1.51 setadjoinIL: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setadjoinIL,definition,
% 2.99/1.51 ( setadjoinIL
% 2.99/1.51 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(emptyinunitempty_type,type,
% 2.99/1.51 emptyinunitempty: $o ).
% 2.99/1.51
% 2.99/1.51 thf(emptyinunitempty,definition,
% 2.99/1.51 ( emptyinunitempty
% 2.99/1.51 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setadjoinIR_type,type,
% 2.99/1.51 setadjoinIR: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setadjoinIR,definition,
% 2.99/1.51 ( setadjoinIR
% 2.99/1.51 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ A )
% 2.99/1.51 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setadjoinE_type,type,
% 2.99/1.51 setadjoinE: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setadjoinE,definition,
% 2.99/1.51 ( setadjoinE
% 2.99/1.51 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.99/1.51 => ! [Xphi: $o] :
% 2.99/1.51 ( ( ( Xy = Xx )
% 2.99/1.51 => Xphi )
% 2.99/1.51 => ( ( ( in @ Xy @ A )
% 2.99/1.51 => Xphi )
% 2.99/1.51 => Xphi ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setadjoinOr_type,type,
% 2.99/1.51 setadjoinOr: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setadjoinOr,definition,
% 2.99/1.51 ( setadjoinOr
% 2.99/1.51 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.99/1.51 => ( ( Xy = Xx )
% 2.99/1.51 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setoftrueEq_type,type,
% 2.99/1.51 setoftrueEq: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setoftrueEq,definition,
% 2.99/1.51 ( setoftrueEq
% 2.99/1.51 = ( ! [A: $i] :
% 2.99/1.51 ( ( dsetconstr @ A
% 2.99/1.51 @ ^ [Xx: $i] : $true )
% 2.99/1.51 = A ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(powersetI_type,type,
% 2.99/1.51 powersetI: $o ).
% 2.99/1.51
% 2.99/1.51 thf(powersetI,definition,
% 2.99/1.51 ( powersetI
% 2.99/1.51 = ( ! [A: $i,B: $i] :
% 2.99/1.51 ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ B )
% 2.99/1.51 => ( in @ Xx @ A ) )
% 2.99/1.51 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(emptyinPowerset_type,type,
% 2.99/1.51 emptyinPowerset: $o ).
% 2.99/1.51
% 2.99/1.51 thf(emptyinPowerset,definition,
% 2.99/1.51 ( emptyinPowerset
% 2.99/1.51 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(emptyInPowerset_type,type,
% 2.99/1.51 emptyInPowerset: $o ).
% 2.99/1.51
% 2.99/1.51 thf(emptyInPowerset,definition,
% 2.99/1.51 ( emptyInPowerset
% 2.99/1.51 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(powersetE_type,type,
% 2.99/1.51 powersetE: $o ).
% 2.99/1.51
% 2.99/1.51 thf(powersetE,definition,
% 2.99/1.51 ( powersetE
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ B @ ( powerset @ A ) )
% 2.99/1.51 => ( ( in @ Xx @ B )
% 2.99/1.51 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setunionI_type,type,
% 2.99/1.51 setunionI: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setunionI,definition,
% 2.99/1.51 ( setunionI
% 2.99/1.51 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.99/1.51 ( ( in @ Xx @ B )
% 2.99/1.51 => ( ( in @ B @ A )
% 2.99/1.51 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setunionE_type,type,
% 2.99/1.51 setunionE: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setunionE,definition,
% 2.99/1.51 ( setunionE
% 2.99/1.51 = ( ! [A: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ ( setunion @ A ) )
% 2.99/1.51 => ! [Xphi: $o] :
% 2.99/1.51 ( ! [B: $i] :
% 2.99/1.51 ( ( in @ Xx @ B )
% 2.99/1.51 => ( ( in @ B @ A )
% 2.99/1.51 => Xphi ) )
% 2.99/1.51 => Xphi ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(subPowSU_type,type,
% 2.99/1.51 subPowSU: $o ).
% 2.99/1.51
% 2.99/1.51 thf(subPowSU,definition,
% 2.99/1.51 ( subPowSU
% 2.99/1.51 = ( ! [A: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(exuE2_type,type,
% 2.99/1.51 exuE2: $o ).
% 2.99/1.51
% 2.99/1.51 thf(exuE2,definition,
% 2.99/1.51 ( exuE2
% 2.99/1.51 = ( ! [Xphi: $i > $o] :
% 2.99/1.51 ( ( exu
% 2.99/1.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.51 => ? [Xx: $i] :
% 2.99/1.51 ! [Xy: $i] :
% 2.99/1.51 ( ( Xphi @ Xy )
% 2.99/1.51 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(nonemptyImpWitness_type,type,
% 2.99/1.51 nonemptyImpWitness: $o ).
% 2.99/1.51
% 2.99/1.51 thf(nonemptyImpWitness,definition,
% 2.99/1.51 ( nonemptyImpWitness
% 2.99/1.51 = ( ! [A: $i] :
% 2.99/1.51 ( ( nonempty @ A )
% 2.99/1.51 => ? [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 & $true ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(uniqinunit_type,type,
% 2.99/1.51 uniqinunit: $o ).
% 2.99/1.51
% 2.99/1.51 thf(uniqinunit,definition,
% 2.99/1.51 ( uniqinunit
% 2.99/1.51 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.51 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.99/1.51 => ( Xx = Xy ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(notinsingleton_type,type,
% 2.99/1.51 notinsingleton: $o ).
% 2.99/1.51
% 2.99/1.51 thf(notinsingleton,definition,
% 2.99/1.51 ( notinsingleton
% 2.99/1.51 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.51 ( ( Xx != Xy )
% 2.99/1.51 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(eqinunit_type,type,
% 2.99/1.51 eqinunit: $o ).
% 2.99/1.51
% 2.99/1.51 thf(eqinunit,definition,
% 2.99/1.51 ( eqinunit
% 2.99/1.51 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.51 ( ( Xx = Xy )
% 2.99/1.51 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(singletonsswitch_type,type,
% 2.99/1.51 singletonsswitch: $o ).
% 2.99/1.51
% 2.99/1.51 thf(singletonsswitch,definition,
% 2.99/1.51 ( singletonsswitch
% 2.99/1.51 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.51 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.99/1.51 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(upairsetE_type,type,
% 2.99/1.51 upairsetE: $o ).
% 2.99/1.51
% 2.99/1.51 thf(upairsetE,definition,
% 2.99/1.51 ( upairsetE
% 2.99/1.51 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.99/1.51 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.99/1.51 => ( ( Xz = Xx )
% 2.99/1.51 | ( Xz = Xy ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(upairsetIL_type,type,
% 2.99/1.51 upairsetIL: $o ).
% 2.99/1.51
% 2.99/1.51 thf(upairsetIL,definition,
% 2.99/1.51 ( upairsetIL
% 2.99/1.51 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(upairsetIR_type,type,
% 2.99/1.51 upairsetIR: $o ).
% 2.99/1.51
% 2.99/1.51 thf(upairsetIR,definition,
% 2.99/1.51 ( upairsetIR
% 2.99/1.51 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(emptyE1_type,type,
% 2.99/1.51 emptyE1: $o ).
% 2.99/1.51
% 2.99/1.51 thf(emptyE1,definition,
% 2.99/1.51 ( emptyE1
% 2.99/1.51 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.51 ( ? [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 & ( Xphi @ Xx ) )
% 2.99/1.51 => ( ( ( dsetconstr @ A
% 2.99/1.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.51 = emptyset )
% 2.99/1.51 => $false ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(vacuousDall_type,type,
% 2.99/1.51 vacuousDall: $o ).
% 2.99/1.51
% 2.99/1.51 thf(vacuousDall,definition,
% 2.99/1.51 ( vacuousDall
% 2.99/1.51 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ emptyset )
% 2.99/1.51 => ( Xphi @ Xx ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(quantDeMorgan1_type,type,
% 2.99/1.51 quantDeMorgan1: $o ).
% 2.99/1.51
% 2.99/1.51 thf(quantDeMorgan1,definition,
% 2.99/1.51 ( quantDeMorgan1
% 2.99/1.51 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.51 ( ~ ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( Xphi @ Xx ) )
% 2.99/1.51 => ? [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(quantDeMorgan2_type,type,
% 2.99/1.51 quantDeMorgan2: $o ).
% 2.99/1.51
% 2.99/1.51 thf(quantDeMorgan2,definition,
% 2.99/1.51 ( quantDeMorgan2
% 2.99/1.51 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.51 ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ~ ( Xphi @ Xx ) )
% 2.99/1.51 => ~ ? [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(quantDeMorgan3_type,type,
% 2.99/1.51 quantDeMorgan3: $o ).
% 2.99/1.51
% 2.99/1.51 thf(quantDeMorgan3,definition,
% 2.99/1.51 ( quantDeMorgan3
% 2.99/1.51 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.51 ( ~ ? [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 & ( Xphi @ Xx ) )
% 2.99/1.51 => ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(quantDeMorgan4_type,type,
% 2.99/1.51 quantDeMorgan4: $o ).
% 2.99/1.51
% 2.99/1.51 thf(quantDeMorgan4,definition,
% 2.99/1.51 ( quantDeMorgan4
% 2.99/1.51 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.51 ( ? [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 & ~ ( Xphi @ Xx ) )
% 2.99/1.51 => ~ ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(prop2setI_type,type,
% 2.99/1.51 prop2setI: $o ).
% 2.99/1.51
% 2.99/1.51 thf(prop2setI,definition,
% 2.99/1.51 ( prop2setI
% 2.99/1.51 = ( ! [Xphi: $o] :
% 2.99/1.51 ( Xphi
% 2.99/1.51 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(set2prop_type,type,
% 2.99/1.51 set2prop: $i > $o ).
% 2.99/1.51
% 2.99/1.51 thf(prop2set2propI_type,type,
% 2.99/1.51 prop2set2propI: $o ).
% 2.99/1.51
% 2.99/1.51 thf(prop2set2propI,definition,
% 2.99/1.51 ( prop2set2propI
% 2.99/1.51 = ( ! [Xphi: $o] :
% 2.99/1.51 ( Xphi
% 2.99/1.51 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(notdexE_type,type,
% 2.99/1.51 notdexE: $o ).
% 2.99/1.51
% 2.99/1.51 thf(notdexE,definition,
% 2.99/1.51 ( notdexE
% 2.99/1.51 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.51 ( ~ ? [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 & ( Xphi @ Xx ) )
% 2.99/1.51 => ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(notdallE_type,type,
% 2.99/1.51 notdallE: $o ).
% 2.99/1.51
% 2.99/1.51 thf(notdallE,definition,
% 2.99/1.51 ( notdallE
% 2.99/1.51 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.51 ( ~ ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( Xphi @ Xx ) )
% 2.99/1.51 => ? [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(exuI1_type,type,
% 2.99/1.51 exuI1: $o ).
% 2.99/1.51
% 2.99/1.51 thf(exuI1,definition,
% 2.99/1.51 ( exuI1
% 2.99/1.51 = ( ! [Xphi: $i > $o] :
% 2.99/1.51 ( ? [Xx: $i] :
% 2.99/1.51 ( ( Xphi @ Xx )
% 2.99/1.51 & ! [Xy: $i] :
% 2.99/1.51 ( ( Xphi @ Xy )
% 2.99/1.51 => ( Xx = Xy ) ) )
% 2.99/1.51 => ( exu
% 2.99/1.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(exuI3_type,type,
% 2.99/1.51 exuI3: $o ).
% 2.99/1.51
% 2.99/1.51 thf(exuI3,definition,
% 2.99/1.51 ( exuI3
% 2.99/1.51 = ( ! [Xphi: $i > $o] :
% 2.99/1.51 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.99/1.51 => ( ! [Xx: $i,Xy: $i] :
% 2.99/1.51 ( ( Xphi @ Xx )
% 2.99/1.51 => ( ( Xphi @ Xy )
% 2.99/1.51 => ( Xx = Xy ) ) )
% 2.99/1.51 => ( exu
% 2.99/1.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(exuI2_type,type,
% 2.99/1.51 exuI2: $o ).
% 2.99/1.51
% 2.99/1.51 thf(exuI2,definition,
% 2.99/1.51 ( exuI2
% 2.99/1.51 = ( ! [Xphi: $i > $o] :
% 2.99/1.51 ( ? [Xx: $i] :
% 2.99/1.51 ! [Xy: $i] :
% 2.99/1.51 ( ( Xphi @ Xy )
% 2.99/1.51 <=> ( Xy = Xx ) )
% 2.99/1.51 => ( exu
% 2.99/1.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(inCongP_type,type,
% 2.99/1.51 inCongP: $o ).
% 2.99/1.51
% 2.99/1.51 thf(inCongP,definition,
% 2.99/1.51 ( inCongP
% 2.99/1.51 = ( ! [A: $i,B: $i] :
% 2.99/1.51 ( ( A = B )
% 2.99/1.51 => ! [Xx: $i,Xy: $i] :
% 2.99/1.51 ( ( Xx = Xy )
% 2.99/1.51 => ( ( in @ Xx @ A )
% 2.99/1.51 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(in__Cong_type,type,
% 2.99/1.51 in__Cong: $o ).
% 2.99/1.51
% 2.99/1.51 thf(in__Cong,definition,
% 2.99/1.51 ( in__Cong
% 2.99/1.51 = ( ! [A: $i,B: $i] :
% 2.99/1.51 ( ( A = B )
% 2.99/1.51 => ! [Xx: $i,Xy: $i] :
% 2.99/1.51 ( ( Xx = Xy )
% 2.99/1.51 => ( ( in @ Xx @ A )
% 2.99/1.51 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(exuE3u_type,type,
% 2.99/1.51 exuE3u: $o ).
% 2.99/1.51
% 2.99/1.51 thf(exuE3u,definition,
% 2.99/1.51 ( exuE3u
% 2.99/1.51 = ( ! [Xphi: $i > $o] :
% 2.99/1.51 ( ( exu
% 2.99/1.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.51 => ! [Xx: $i,Xy: $i] :
% 2.99/1.51 ( ( Xphi @ Xx )
% 2.99/1.51 => ( ( Xphi @ Xy )
% 2.99/1.51 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(exu__Cong_type,type,
% 2.99/1.51 exu__Cong: $o ).
% 2.99/1.51
% 2.99/1.51 thf(exu__Cong,definition,
% 2.99/1.51 ( exu__Cong
% 2.99/1.51 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.99/1.51 ( ! [Xx: $i,Xy: $i] :
% 2.99/1.51 ( ( Xx = Xy )
% 2.99/1.51 => ( ( Xphi @ Xx )
% 2.99/1.51 <=> ( Xpsi @ Xy ) ) )
% 2.99/1.51 => ( ( exu
% 2.99/1.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.51 <=> ( exu
% 2.99/1.51 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(emptyset__Cong_type,type,
% 2.99/1.51 emptyset__Cong: $o ).
% 2.99/1.51
% 2.99/1.51 thf(emptyset__Cong,definition,
% 2.99/1.51 ( emptyset__Cong
% 2.99/1.51 = ( emptyset = emptyset ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setadjoin__Cong_type,type,
% 2.99/1.51 setadjoin__Cong: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setadjoin__Cong,definition,
% 2.99/1.51 ( setadjoin__Cong
% 2.99/1.51 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.51 ( ( Xx = Xy )
% 2.99/1.51 => ! [Xz: $i,Xu: $i] :
% 2.99/1.51 ( ( Xz = Xu )
% 2.99/1.51 => ( ( setadjoin @ Xx @ Xz )
% 2.99/1.51 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(powerset__Cong_type,type,
% 2.99/1.51 powerset__Cong: $o ).
% 2.99/1.51
% 2.99/1.51 thf(powerset__Cong,definition,
% 2.99/1.51 ( powerset__Cong
% 2.99/1.51 = ( ! [A: $i,B: $i] :
% 2.99/1.51 ( ( A = B )
% 2.99/1.51 => ( ( powerset @ A )
% 2.99/1.51 = ( powerset @ B ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setunion__Cong_type,type,
% 2.99/1.51 setunion__Cong: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setunion__Cong,definition,
% 2.99/1.51 ( setunion__Cong
% 2.99/1.51 = ( ! [A: $i,B: $i] :
% 2.99/1.51 ( ( A = B )
% 2.99/1.51 => ( ( setunion @ A )
% 2.99/1.51 = ( setunion @ B ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(omega__Cong_type,type,
% 2.99/1.51 omega__Cong: $o ).
% 2.99/1.51
% 2.99/1.51 thf(omega__Cong,definition,
% 2.99/1.51 ( omega__Cong
% 2.99/1.51 = ( omega = omega ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(exuEu_type,type,
% 2.99/1.51 exuEu: $o ).
% 2.99/1.51
% 2.99/1.51 thf(exuEu,definition,
% 2.99/1.51 ( exuEu
% 2.99/1.51 = ( ! [Xphi: $i > $o] :
% 2.99/1.51 ( ( exu
% 2.99/1.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.51 => ! [Xx: $i,Xy: $i] :
% 2.99/1.51 ( ( Xphi @ Xx )
% 2.99/1.51 => ( ( Xphi @ Xy )
% 2.99/1.51 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(descr__Cong_type,type,
% 2.99/1.51 descr__Cong: $o ).
% 2.99/1.51
% 2.99/1.51 thf(descr__Cong,definition,
% 2.99/1.51 ( descr__Cong
% 2.99/1.51 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.99/1.51 ( ! [Xx: $i,Xy: $i] :
% 2.99/1.51 ( ( Xx = Xy )
% 2.99/1.51 => ( ( Xphi @ Xx )
% 2.99/1.51 <=> ( Xpsi @ Xy ) ) )
% 2.99/1.51 => ( ( exu
% 2.99/1.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.51 => ( ( exu
% 2.99/1.51 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.99/1.51 => ( ( descr
% 2.99/1.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.51 = ( descr
% 2.99/1.51 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(dsetconstr__Cong_type,type,
% 2.99/1.51 dsetconstr__Cong: $o ).
% 2.99/1.51
% 2.99/1.51 thf(dsetconstr__Cong,definition,
% 2.99/1.51 ( dsetconstr__Cong
% 2.99/1.51 = ( ! [A: $i,B: $i] :
% 2.99/1.51 ( ( A = B )
% 2.99/1.51 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.99/1.51 ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ! [Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ B )
% 2.99/1.51 => ( ( Xx = Xy )
% 2.99/1.51 => ( ( Xphi @ Xx )
% 2.99/1.51 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.99/1.51 => ( ( dsetconstr @ A
% 2.99/1.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.51 = ( dsetconstr @ B
% 2.99/1.51 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(subset_type,type,
% 2.99/1.51 subset: $i > $i > $o ).
% 2.99/1.51
% 2.99/1.51 thf(disjoint_type,type,
% 2.99/1.51 disjoint: $i > $i > $o ).
% 2.99/1.51
% 2.99/1.51 thf(setsmeet_type,type,
% 2.99/1.51 setsmeet: $i > $i > $o ).
% 2.99/1.51
% 2.99/1.51 thf(subsetI1_type,type,
% 2.99/1.51 subsetI1: $o ).
% 2.99/1.51
% 2.99/1.51 thf(subsetI1,definition,
% 2.99/1.51 ( subsetI1
% 2.99/1.51 = ( ! [A: $i,B: $i] :
% 2.99/1.51 ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( in @ Xx @ B ) )
% 2.99/1.51 => ( subset @ A @ B ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(eqimpsubset2_type,type,
% 2.99/1.51 eqimpsubset2: $o ).
% 2.99/1.51
% 2.99/1.51 thf(eqimpsubset2,definition,
% 2.99/1.51 ( eqimpsubset2
% 2.99/1.51 = ( ! [A: $i,B: $i] :
% 2.99/1.51 ( ( A = B )
% 2.99/1.51 => ( subset @ B @ A ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(eqimpsubset1_type,type,
% 2.99/1.51 eqimpsubset1: $o ).
% 2.99/1.51
% 2.99/1.51 thf(eqimpsubset1,definition,
% 2.99/1.51 ( eqimpsubset1
% 2.99/1.51 = ( ! [A: $i,B: $i] :
% 2.99/1.51 ( ( A = B )
% 2.99/1.51 => ( subset @ A @ B ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(subsetI2_type,type,
% 2.99/1.51 subsetI2: $o ).
% 2.99/1.51
% 2.99/1.51 thf(subsetI2,definition,
% 2.99/1.51 ( subsetI2
% 2.99/1.51 = ( ! [A: $i,B: $i] :
% 2.99/1.51 ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( in @ Xx @ B ) )
% 2.99/1.51 => ( subset @ A @ B ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(emptysetsubset_type,type,
% 2.99/1.51 emptysetsubset: $o ).
% 2.99/1.51
% 2.99/1.51 thf(emptysetsubset,definition,
% 2.99/1.51 ( emptysetsubset
% 2.99/1.51 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(subsetE_type,type,
% 2.99/1.51 subsetE: $o ).
% 2.99/1.51
% 2.99/1.51 thf(subsetE,definition,
% 2.99/1.51 ( subsetE
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ( subset @ A @ B )
% 2.99/1.51 => ( ( in @ Xx @ A )
% 2.99/1.51 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(subsetE2_type,type,
% 2.99/1.51 subsetE2: $o ).
% 2.99/1.51
% 2.99/1.51 thf(subsetE2,definition,
% 2.99/1.51 ( subsetE2
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ( subset @ A @ B )
% 2.99/1.51 => ( ~ ( in @ Xx @ B )
% 2.99/1.51 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(notsubsetI_type,type,
% 2.99/1.51 notsubsetI: $o ).
% 2.99/1.51
% 2.99/1.51 thf(notsubsetI,definition,
% 2.99/1.51 ( notsubsetI
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( ~ ( in @ Xx @ B )
% 2.99/1.51 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(notequalI1_type,type,
% 2.99/1.51 notequalI1: $o ).
% 2.99/1.51
% 2.99/1.51 thf(notequalI1,definition,
% 2.99/1.51 ( notequalI1
% 2.99/1.51 = ( ! [A: $i,B: $i] :
% 2.99/1.51 ( ~ ( subset @ A @ B )
% 2.99/1.51 => ( A != B ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(notequalI2_type,type,
% 2.99/1.51 notequalI2: $o ).
% 2.99/1.51
% 2.99/1.51 thf(notequalI2,definition,
% 2.99/1.51 ( notequalI2
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( ~ ( in @ Xx @ B )
% 2.99/1.51 => ( A != B ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(subsetRefl_type,type,
% 2.99/1.51 subsetRefl: $o ).
% 2.99/1.51
% 2.99/1.51 thf(subsetRefl,definition,
% 2.99/1.51 ( subsetRefl
% 2.99/1.51 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(subsetTrans_type,type,
% 2.99/1.51 subsetTrans: $o ).
% 2.99/1.51
% 2.99/1.51 thf(subsetTrans,definition,
% 2.99/1.51 ( subsetTrans
% 2.99/1.51 = ( ! [A: $i,B: $i,C: $i] :
% 2.99/1.51 ( ( subset @ A @ B )
% 2.99/1.51 => ( ( subset @ B @ C )
% 2.99/1.51 => ( subset @ A @ C ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setadjoinSub_type,type,
% 2.99/1.51 setadjoinSub: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setadjoinSub,definition,
% 2.99/1.51 ( setadjoinSub
% 2.99/1.51 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setadjoinSub2_type,type,
% 2.99/1.51 setadjoinSub2: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setadjoinSub2,definition,
% 2.99/1.51 ( setadjoinSub2
% 2.99/1.51 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.99/1.51 ( ( subset @ A @ B )
% 2.99/1.51 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(subset2powerset_type,type,
% 2.99/1.51 subset2powerset: $o ).
% 2.99/1.51
% 2.99/1.51 thf(subset2powerset,definition,
% 2.99/1.51 ( subset2powerset
% 2.99/1.51 = ( ! [A: $i,B: $i] :
% 2.99/1.51 ( ( subset @ A @ B )
% 2.99/1.51 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setextsub_type,type,
% 2.99/1.51 setextsub: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setextsub,definition,
% 2.99/1.51 ( setextsub
% 2.99/1.51 = ( ! [A: $i,B: $i] :
% 2.99/1.51 ( ( subset @ A @ B )
% 2.99/1.51 => ( ( subset @ B @ A )
% 2.99/1.51 => ( A = B ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(subsetemptysetimpeq_type,type,
% 2.99/1.51 subsetemptysetimpeq: $o ).
% 2.99/1.51
% 2.99/1.51 thf(subsetemptysetimpeq,definition,
% 2.99/1.51 ( subsetemptysetimpeq
% 2.99/1.51 = ( ! [A: $i] :
% 2.99/1.51 ( ( subset @ A @ emptyset )
% 2.99/1.51 => ( A = emptyset ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(powersetI1_type,type,
% 2.99/1.51 powersetI1: $o ).
% 2.99/1.51
% 2.99/1.51 thf(powersetI1,definition,
% 2.99/1.51 ( powersetI1
% 2.99/1.51 = ( ! [A: $i,B: $i] :
% 2.99/1.51 ( ( subset @ B @ A )
% 2.99/1.51 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(powersetE1_type,type,
% 2.99/1.51 powersetE1: $o ).
% 2.99/1.51
% 2.99/1.51 thf(powersetE1,definition,
% 2.99/1.51 ( powersetE1
% 2.99/1.51 = ( ! [A: $i,B: $i] :
% 2.99/1.51 ( ( in @ B @ ( powerset @ A ) )
% 2.99/1.51 => ( subset @ B @ A ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(inPowerset_type,type,
% 2.99/1.51 inPowerset: $o ).
% 2.99/1.51
% 2.99/1.51 thf(inPowerset,definition,
% 2.99/1.51 ( inPowerset
% 2.99/1.51 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(powersetsubset_type,type,
% 2.99/1.51 powersetsubset: $o ).
% 2.99/1.51
% 2.99/1.51 thf(powersetsubset,definition,
% 2.99/1.51 ( powersetsubset
% 2.99/1.51 = ( ! [A: $i,B: $i] :
% 2.99/1.51 ( ( subset @ A @ B )
% 2.99/1.51 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(sepInPowerset_type,type,
% 2.99/1.51 sepInPowerset: $o ).
% 2.99/1.51
% 2.99/1.51 thf(sepInPowerset,definition,
% 2.99/1.51 ( sepInPowerset
% 2.99/1.51 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.51 ( in
% 2.99/1.51 @ ( dsetconstr @ A
% 2.99/1.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.51 @ ( powerset @ A ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(sepSubset_type,type,
% 2.99/1.51 sepSubset: $o ).
% 2.99/1.51
% 2.99/1.51 thf(sepSubset,definition,
% 2.99/1.51 ( sepSubset
% 2.99/1.51 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.51 ( subset
% 2.99/1.51 @ ( dsetconstr @ A
% 2.99/1.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.51 @ A ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(binunion_type,type,
% 2.99/1.51 binunion: $i > $i > $i ).
% 2.99/1.51
% 2.99/1.51 thf(binunionIL_type,type,
% 2.99/1.51 binunionIL: $o ).
% 2.99/1.51
% 2.99/1.51 thf(binunionIL,definition,
% 2.99/1.51 ( binunionIL
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(upairset2IR_type,type,
% 2.99/1.51 upairset2IR: $o ).
% 2.99/1.51
% 2.99/1.51 thf(upairset2IR,definition,
% 2.99/1.51 ( upairset2IR
% 2.99/1.51 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(binunionIR_type,type,
% 2.99/1.51 binunionIR: $o ).
% 2.99/1.51
% 2.99/1.51 thf(binunionIR,definition,
% 2.99/1.51 ( binunionIR
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ B )
% 2.99/1.51 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(binunionEcases_type,type,
% 2.99/1.51 binunionEcases: $o ).
% 2.99/1.51
% 2.99/1.51 thf(binunionEcases,definition,
% 2.99/1.51 ( binunionEcases
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.99/1.51 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.99/1.51 => ( ( ( in @ Xx @ A )
% 2.99/1.51 => Xphi )
% 2.99/1.51 => ( ( ( in @ Xx @ B )
% 2.99/1.51 => Xphi )
% 2.99/1.51 => Xphi ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(binunionE_type,type,
% 2.99/1.51 binunionE: $o ).
% 2.99/1.51
% 2.99/1.51 thf(binunionE,definition,
% 2.99/1.51 ( binunionE
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.99/1.51 => ( ( in @ Xx @ A )
% 2.99/1.51 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(binunionLsub_type,type,
% 2.99/1.51 binunionLsub: $o ).
% 2.99/1.51
% 2.99/1.51 thf(binunionLsub,definition,
% 2.99/1.51 ( binunionLsub
% 2.99/1.51 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(binunionRsub_type,type,
% 2.99/1.51 binunionRsub: $o ).
% 2.99/1.51
% 2.99/1.51 thf(binunionRsub,definition,
% 2.99/1.51 ( binunionRsub
% 2.99/1.51 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(binintersect_type,type,
% 2.99/1.51 binintersect: $i > $i > $i ).
% 2.99/1.51
% 2.99/1.51 thf(binintersectI_type,type,
% 2.99/1.51 binintersectI: $o ).
% 2.99/1.51
% 2.99/1.51 thf(binintersectI,definition,
% 2.99/1.51 ( binintersectI
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( ( in @ Xx @ B )
% 2.99/1.51 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(binintersectSubset5_type,type,
% 2.99/1.51 binintersectSubset5: $o ).
% 2.99/1.51
% 2.99/1.51 thf(binintersectSubset5,definition,
% 2.99/1.51 ( binintersectSubset5
% 2.99/1.51 = ( ! [A: $i,B: $i,C: $i] :
% 2.99/1.51 ( ( subset @ C @ A )
% 2.99/1.51 => ( ( subset @ C @ B )
% 2.99/1.51 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(binintersectEL_type,type,
% 2.99/1.51 binintersectEL: $o ).
% 2.99/1.51
% 2.99/1.51 thf(binintersectEL,definition,
% 2.99/1.51 ( binintersectEL
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.99/1.51 => ( in @ Xx @ A ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(binintersectLsub_type,type,
% 2.99/1.51 binintersectLsub: $o ).
% 2.99/1.51
% 2.99/1.51 thf(binintersectLsub,definition,
% 2.99/1.51 ( binintersectLsub
% 2.99/1.51 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(binintersectSubset2_type,type,
% 2.99/1.51 binintersectSubset2: $o ).
% 2.99/1.51
% 2.99/1.51 thf(binintersectSubset2,definition,
% 2.99/1.51 ( binintersectSubset2
% 2.99/1.51 = ( ! [A: $i,B: $i] :
% 2.99/1.51 ( ( subset @ A @ B )
% 2.99/1.51 => ( ( binintersect @ A @ B )
% 2.99/1.51 = A ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(binintersectSubset3_type,type,
% 2.99/1.51 binintersectSubset3: $o ).
% 2.99/1.51
% 2.99/1.51 thf(binintersectSubset3,definition,
% 2.99/1.51 ( binintersectSubset3
% 2.99/1.51 = ( ! [A: $i,B: $i] :
% 2.99/1.51 ( ( ( binintersect @ A @ B )
% 2.99/1.51 = B )
% 2.99/1.51 => ( subset @ B @ A ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(binintersectER_type,type,
% 2.99/1.51 binintersectER: $o ).
% 2.99/1.51
% 2.99/1.51 thf(binintersectER,definition,
% 2.99/1.51 ( binintersectER
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.99/1.51 => ( in @ Xx @ B ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(disjointsetsI1_type,type,
% 2.99/1.51 disjointsetsI1: $o ).
% 2.99/1.51
% 2.99/1.51 thf(disjointsetsI1,definition,
% 2.99/1.51 ( disjointsetsI1
% 2.99/1.51 = ( ! [A: $i,B: $i] :
% 2.99/1.51 ( ~ ? [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 & ( in @ Xx @ B ) )
% 2.99/1.51 => ( ( binintersect @ A @ B )
% 2.99/1.51 = emptyset ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(binintersectRsub_type,type,
% 2.99/1.51 binintersectRsub: $o ).
% 2.99/1.51
% 2.99/1.51 thf(binintersectRsub,definition,
% 2.99/1.51 ( binintersectRsub
% 2.99/1.51 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(binintersectSubset4_type,type,
% 2.99/1.51 binintersectSubset4: $o ).
% 2.99/1.51
% 2.99/1.51 thf(binintersectSubset4,definition,
% 2.99/1.51 ( binintersectSubset4
% 2.99/1.51 = ( ! [A: $i,B: $i] :
% 2.99/1.51 ( ( subset @ B @ A )
% 2.99/1.51 => ( ( binintersect @ A @ B )
% 2.99/1.51 = B ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(binintersectSubset1_type,type,
% 2.99/1.51 binintersectSubset1: $o ).
% 2.99/1.51
% 2.99/1.51 thf(binintersectSubset1,definition,
% 2.99/1.51 ( binintersectSubset1
% 2.99/1.51 = ( ! [A: $i,B: $i] :
% 2.99/1.51 ( ( ( binintersect @ A @ B )
% 2.99/1.51 = A )
% 2.99/1.51 => ( subset @ A @ B ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(bs114d_type,type,
% 2.99/1.51 bs114d: $o ).
% 2.99/1.51
% 2.99/1.51 thf(bs114d,definition,
% 2.99/1.51 ( bs114d
% 2.99/1.51 = ( ! [A: $i,B: $i,C: $i] :
% 2.99/1.51 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.99/1.51 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(regular_type,type,
% 2.99/1.51 regular: $i > $o ).
% 2.99/1.51
% 2.99/1.51 thf(setminus_type,type,
% 2.99/1.51 setminus: $i > $i > $i ).
% 2.99/1.51
% 2.99/1.51 thf(setminusI_type,type,
% 2.99/1.51 setminusI: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setminusI,definition,
% 2.99/1.51 ( setminusI
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( ~ ( in @ Xx @ B )
% 2.99/1.51 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setminusEL_type,type,
% 2.99/1.51 setminusEL: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setminusEL,definition,
% 2.99/1.51 ( setminusEL
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.99/1.51 => ( in @ Xx @ A ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setminusER_type,type,
% 2.99/1.51 setminusER: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setminusER,definition,
% 2.99/1.51 ( setminusER
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.99/1.51 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setminusSubset2_type,type,
% 2.99/1.51 setminusSubset2: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setminusSubset2,definition,
% 2.99/1.51 ( setminusSubset2
% 2.99/1.51 = ( ! [A: $i,B: $i] :
% 2.99/1.51 ( ( subset @ A @ B )
% 2.99/1.51 => ( ( setminus @ A @ B )
% 2.99/1.51 = emptyset ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setminusERneg_type,type,
% 2.99/1.51 setminusERneg: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setminusERneg,definition,
% 2.99/1.51 ( setminusERneg
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.99/1.51 => ( ( in @ Xx @ A )
% 2.99/1.51 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setminusELneg_type,type,
% 2.99/1.51 setminusELneg: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setminusELneg,definition,
% 2.99/1.51 ( setminusELneg
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.99/1.51 => ( ~ ( in @ Xx @ B )
% 2.99/1.51 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setminusILneg_type,type,
% 2.99/1.51 setminusILneg: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setminusILneg,definition,
% 2.99/1.51 ( setminusILneg
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ~ ( in @ Xx @ A )
% 2.99/1.51 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setminusIRneg_type,type,
% 2.99/1.51 setminusIRneg: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setminusIRneg,definition,
% 2.99/1.51 ( setminusIRneg
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ B )
% 2.99/1.51 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setminusLsub_type,type,
% 2.99/1.51 setminusLsub: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setminusLsub,definition,
% 2.99/1.51 ( setminusLsub
% 2.99/1.51 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setminusSubset1_type,type,
% 2.99/1.51 setminusSubset1: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setminusSubset1,definition,
% 2.99/1.51 ( setminusSubset1
% 2.99/1.51 = ( ! [A: $i,B: $i] :
% 2.99/1.51 ( ( ( setminus @ A @ B )
% 2.99/1.51 = emptyset )
% 2.99/1.51 => ( subset @ A @ B ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(symdiff_type,type,
% 2.99/1.51 symdiff: $i > $i > $i ).
% 2.99/1.51
% 2.99/1.51 thf(symdiffE_type,type,
% 2.99/1.51 symdiffE: $o ).
% 2.99/1.51
% 2.99/1.51 thf(symdiffE,definition,
% 2.99/1.51 ( symdiffE
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.99/1.51 => ! [Xphi: $o] :
% 2.99/1.51 ( ( ( in @ Xx @ A )
% 2.99/1.51 => ( ~ ( in @ Xx @ B )
% 2.99/1.51 => Xphi ) )
% 2.99/1.51 => ( ( ~ ( in @ Xx @ A )
% 2.99/1.51 => ( ( in @ Xx @ B )
% 2.99/1.51 => Xphi ) )
% 2.99/1.51 => Xphi ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(symdiffI1_type,type,
% 2.99/1.51 symdiffI1: $o ).
% 2.99/1.51
% 2.99/1.51 thf(symdiffI1,definition,
% 2.99/1.51 ( symdiffI1
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( ~ ( in @ Xx @ B )
% 2.99/1.51 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(symdiffI2_type,type,
% 2.99/1.51 symdiffI2: $o ).
% 2.99/1.51
% 2.99/1.51 thf(symdiffI2,definition,
% 2.99/1.51 ( symdiffI2
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ~ ( in @ Xx @ A )
% 2.99/1.51 => ( ( in @ Xx @ B )
% 2.99/1.51 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(symdiffIneg1_type,type,
% 2.99/1.51 symdiffIneg1: $o ).
% 2.99/1.51
% 2.99/1.51 thf(symdiffIneg1,definition,
% 2.99/1.51 ( symdiffIneg1
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( ( in @ Xx @ B )
% 2.99/1.51 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(symdiffIneg2_type,type,
% 2.99/1.51 symdiffIneg2: $o ).
% 2.99/1.51
% 2.99/1.51 thf(symdiffIneg2,definition,
% 2.99/1.51 ( symdiffIneg2
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ~ ( in @ Xx @ A )
% 2.99/1.51 => ( ~ ( in @ Xx @ B )
% 2.99/1.51 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(iskpair_type,type,
% 2.99/1.51 iskpair: $i > $o ).
% 2.99/1.51
% 2.99/1.51 thf(secondinupair_type,type,
% 2.99/1.51 secondinupair: $o ).
% 2.99/1.51
% 2.99/1.51 thf(secondinupair,definition,
% 2.99/1.51 ( secondinupair
% 2.99/1.51 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setukpairIL_type,type,
% 2.99/1.51 setukpairIL: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setukpairIL,definition,
% 2.99/1.51 ( setukpairIL
% 2.99/1.51 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setukpairIR_type,type,
% 2.99/1.51 setukpairIR: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setukpairIR,definition,
% 2.99/1.51 ( setukpairIR
% 2.99/1.51 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(kpairiskpair_type,type,
% 2.99/1.51 kpairiskpair: $o ).
% 2.99/1.51
% 2.99/1.51 thf(kpairiskpair,definition,
% 2.99/1.51 ( kpairiskpair
% 2.99/1.51 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(kpair_type,type,
% 2.99/1.51 kpair: $i > $i > $i ).
% 2.99/1.51
% 2.99/1.51 thf(kpairp_type,type,
% 2.99/1.51 kpairp: $o ).
% 2.99/1.51
% 2.99/1.51 thf(kpairp,definition,
% 2.99/1.51 ( kpairp
% 2.99/1.51 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(cartprod_type,type,
% 2.99/1.51 cartprod: $i > $i > $i ).
% 2.99/1.51
% 2.99/1.51 thf(singletonsubset_type,type,
% 2.99/1.51 singletonsubset: $o ).
% 2.99/1.51
% 2.99/1.51 thf(singletonsubset,definition,
% 2.99/1.51 ( singletonsubset
% 2.99/1.51 = ( ! [A: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(singletoninpowerset_type,type,
% 2.99/1.51 singletoninpowerset: $o ).
% 2.99/1.51
% 2.99/1.51 thf(singletoninpowerset,definition,
% 2.99/1.51 ( singletoninpowerset
% 2.99/1.51 = ( ! [A: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(singletoninpowunion_type,type,
% 2.99/1.51 singletoninpowunion: $o ).
% 2.99/1.51
% 2.99/1.51 thf(singletoninpowunion,definition,
% 2.99/1.51 ( singletoninpowunion
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(upairset2E_type,type,
% 2.99/1.51 upairset2E: $o ).
% 2.99/1.51
% 2.99/1.51 thf(upairset2E,definition,
% 2.99/1.51 ( upairset2E
% 2.99/1.51 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.99/1.51 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.99/1.51 => ( ( Xz = Xx )
% 2.99/1.51 | ( Xz = Xy ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(upairsubunion_type,type,
% 2.99/1.51 upairsubunion: $o ).
% 2.99/1.51
% 2.99/1.51 thf(upairsubunion,definition,
% 2.99/1.51 ( upairsubunion
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ! [Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ B )
% 2.99/1.51 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(upairinpowunion_type,type,
% 2.99/1.51 upairinpowunion: $o ).
% 2.99/1.51
% 2.99/1.51 thf(upairinpowunion,definition,
% 2.99/1.51 ( upairinpowunion
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ! [Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ B )
% 2.99/1.51 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(ubforcartprodlem1_type,type,
% 2.99/1.51 ubforcartprodlem1: $o ).
% 2.99/1.51
% 2.99/1.51 thf(ubforcartprodlem1,definition,
% 2.99/1.51 ( ubforcartprodlem1
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ! [Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ B )
% 2.99/1.51 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(ubforcartprodlem2_type,type,
% 2.99/1.51 ubforcartprodlem2: $o ).
% 2.99/1.51
% 2.99/1.51 thf(ubforcartprodlem2,definition,
% 2.99/1.51 ( ubforcartprodlem2
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ! [Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ B )
% 2.99/1.51 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(ubforcartprodlem3_type,type,
% 2.99/1.51 ubforcartprodlem3: $o ).
% 2.99/1.51
% 2.99/1.51 thf(ubforcartprodlem3,definition,
% 2.99/1.51 ( ubforcartprodlem3
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ! [Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ B )
% 2.99/1.51 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(cartprodpairin_type,type,
% 2.99/1.51 cartprodpairin: $o ).
% 2.99/1.51
% 2.99/1.51 thf(cartprodpairin,definition,
% 2.99/1.51 ( cartprodpairin
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ! [Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ B )
% 2.99/1.51 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(cartprodmempair1_type,type,
% 2.99/1.51 cartprodmempair1: $o ).
% 2.99/1.51
% 2.99/1.51 thf(cartprodmempair1,definition,
% 2.99/1.51 ( cartprodmempair1
% 2.99/1.51 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.99/1.51 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.99/1.51 => ? [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 & ? [Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ B )
% 2.99/1.51 & ( Xu
% 2.99/1.51 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(cartprodmempair_type,type,
% 2.99/1.51 cartprodmempair: $o ).
% 2.99/1.51
% 2.99/1.51 thf(cartprodmempair,definition,
% 2.99/1.51 ( cartprodmempair
% 2.99/1.51 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.99/1.51 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.99/1.51 => ( iskpair @ Xu ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setunionE2_type,type,
% 2.99/1.51 setunionE2: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setunionE2,definition,
% 2.99/1.51 ( setunionE2
% 2.99/1.51 = ( ! [A: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ ( setunion @ A ) )
% 2.99/1.51 => ? [X: $i] :
% 2.99/1.51 ( ( in @ X @ A )
% 2.99/1.51 & ( in @ Xx @ X ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setunionsingleton1_type,type,
% 2.99/1.51 setunionsingleton1: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setunionsingleton1,definition,
% 2.99/1.51 ( setunionsingleton1
% 2.99/1.51 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setunionsingleton2_type,type,
% 2.99/1.51 setunionsingleton2: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setunionsingleton2,definition,
% 2.99/1.51 ( setunionsingleton2
% 2.99/1.51 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setunionsingleton_type,type,
% 2.99/1.51 setunionsingleton: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setunionsingleton,definition,
% 2.99/1.51 ( setunionsingleton
% 2.99/1.51 = ( ! [Xx: $i] :
% 2.99/1.51 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 2.99/1.51 = Xx ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(singleton_type,type,
% 2.99/1.51 singleton: $i > $o ).
% 2.99/1.51
% 2.99/1.51 thf(singletonprop_type,type,
% 2.99/1.51 singletonprop: $o ).
% 2.99/1.51
% 2.99/1.51 thf(singletonprop,definition,
% 2.99/1.51 ( singletonprop
% 2.99/1.51 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.51 ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ! [Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ A )
% 2.99/1.51 => ( ( Xphi @ Xx )
% 2.99/1.51 => ( ( Xphi @ Xy )
% 2.99/1.51 => ( Xx = Xy ) ) ) ) )
% 2.99/1.51 => ( ? [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 & ( Xphi @ Xx ) )
% 2.99/1.51 => ( singleton
% 2.99/1.51 @ ( dsetconstr @ A
% 2.99/1.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(ex1_type,type,
% 2.99/1.51 ex1: $i > ( $i > $o ) > $o ).
% 2.99/1.51
% 2.99/1.51 thf(ex1E1_type,type,
% 2.99/1.51 ex1E1: $o ).
% 2.99/1.51
% 2.99/1.51 thf(ex1E1,definition,
% 2.99/1.51 ( ex1E1
% 2.99/1.51 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.51 ( ( ex1 @ A
% 2.99/1.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.51 => ? [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(ex1I_type,type,
% 2.99/1.51 ex1I: $o ).
% 2.99/1.51
% 2.99/1.51 thf(ex1I,definition,
% 2.99/1.51 ( ex1I
% 2.99/1.51 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( ( Xphi @ Xx )
% 2.99/1.51 => ( ! [Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ A )
% 2.99/1.51 => ( ( Xphi @ Xy )
% 2.99/1.51 => ( Xy = Xx ) ) )
% 2.99/1.51 => ( ex1 @ A
% 2.99/1.51 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(ex1I2_type,type,
% 2.99/1.51 ex1I2: $o ).
% 2.99/1.51
% 2.99/1.51 thf(ex1I2,definition,
% 2.99/1.51 ( ex1I2
% 2.99/1.51 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.51 ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ! [Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ A )
% 2.99/1.51 => ( ( Xphi @ Xx )
% 2.99/1.51 => ( ( Xphi @ Xy )
% 2.99/1.51 => ( Xx = Xy ) ) ) ) )
% 2.99/1.51 => ( ? [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 & ( Xphi @ Xx ) )
% 2.99/1.51 => ( ex1 @ A
% 2.99/1.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(singletonsuniq_type,type,
% 2.99/1.51 singletonsuniq: $o ).
% 2.99/1.51
% 2.99/1.51 thf(singletonsuniq,definition,
% 2.99/1.51 ( singletonsuniq
% 2.99/1.51 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.51 ( ( ( setadjoin @ Xx @ emptyset )
% 2.99/1.51 = ( setadjoin @ Xy @ emptyset ) )
% 2.99/1.51 => ( Xx = Xy ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(atmost1p_type,type,
% 2.99/1.51 atmost1p: $i > $o ).
% 2.99/1.51
% 2.99/1.51 thf(atleast2p_type,type,
% 2.99/1.51 atleast2p: $i > $o ).
% 2.99/1.51
% 2.99/1.51 thf(atmost2p_type,type,
% 2.99/1.51 atmost2p: $i > $o ).
% 2.99/1.51
% 2.99/1.51 thf(upairsetp_type,type,
% 2.99/1.51 upairsetp: $i > $o ).
% 2.99/1.51
% 2.99/1.51 thf(setukpairinjL1_type,type,
% 2.99/1.51 setukpairinjL1: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setukpairinjL1,definition,
% 2.99/1.51 ( setukpairinjL1
% 2.99/1.51 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.99/1.51 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 2.99/1.51 => ( Xx = Xz ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(kfstsingleton_type,type,
% 2.99/1.51 kfstsingleton: $o ).
% 2.99/1.51
% 2.99/1.51 thf(kfstsingleton,definition,
% 2.99/1.51 ( kfstsingleton
% 2.99/1.51 = ( ! [Xu: $i] :
% 2.99/1.51 ( ( iskpair @ Xu )
% 2.99/1.51 => ( singleton
% 2.99/1.51 @ ( dsetconstr @ ( setunion @ Xu )
% 2.99/1.51 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(theprop_type,type,
% 2.99/1.51 theprop: $o ).
% 2.99/1.51
% 2.99/1.51 thf(theprop,definition,
% 2.99/1.51 ( theprop
% 2.99/1.51 = ( ! [X: $i] :
% 2.99/1.51 ( ( singleton @ X )
% 2.99/1.51 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(kfst_type,type,
% 2.99/1.51 kfst: $i > $i ).
% 2.99/1.51
% 2.99/1.51 thf(kfstpairEq_type,type,
% 2.99/1.51 kfstpairEq: $o ).
% 2.99/1.51
% 2.99/1.51 thf(kfstpairEq,definition,
% 2.99/1.51 ( kfstpairEq
% 2.99/1.51 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.51 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.99/1.51 = Xx ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(cartprodfstin_type,type,
% 2.99/1.51 cartprodfstin: $o ).
% 2.99/1.51
% 2.99/1.51 thf(cartprodfstin,definition,
% 2.99/1.51 ( cartprodfstin
% 2.99/1.51 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.99/1.51 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.99/1.51 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setukpairinjL2_type,type,
% 2.99/1.51 setukpairinjL2: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setukpairinjL2,definition,
% 2.99/1.51 ( setukpairinjL2
% 2.99/1.51 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.99/1.51 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.99/1.51 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.99/1.51 => ( Xx = Xz ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setukpairinjL_type,type,
% 2.99/1.51 setukpairinjL: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setukpairinjL,definition,
% 2.99/1.51 ( setukpairinjL
% 2.99/1.51 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.99/1.51 ( ( ( kpair @ Xx @ Xy )
% 2.99/1.51 = ( kpair @ Xz @ Xu ) )
% 2.99/1.51 => ( Xx = Xz ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setukpairinjR11_type,type,
% 2.99/1.51 setukpairinjR11: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setukpairinjR11,definition,
% 2.99/1.51 ( setukpairinjR11
% 2.99/1.51 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.51 ( ( Xx = Xy )
% 2.99/1.51 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.99/1.51 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setukpairinjR12_type,type,
% 2.99/1.51 setukpairinjR12: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setukpairinjR12,definition,
% 2.99/1.51 ( setukpairinjR12
% 2.99/1.51 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.51 ( ( Xx = Xy )
% 2.99/1.51 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.99/1.51 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setukpairinjR1_type,type,
% 2.99/1.51 setukpairinjR1: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setukpairinjR1,definition,
% 2.99/1.51 ( setukpairinjR1
% 2.99/1.51 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.99/1.51 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.99/1.51 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.99/1.51 => ( ( Xz = Xu )
% 2.99/1.51 => ( Xy = Xu ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(upairequniteq_type,type,
% 2.99/1.51 upairequniteq: $o ).
% 2.99/1.51
% 2.99/1.51 thf(upairequniteq,definition,
% 2.99/1.51 ( upairequniteq
% 2.99/1.51 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.99/1.51 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.99/1.51 = ( setadjoin @ Xz @ emptyset ) )
% 2.99/1.51 => ( Xx = Xy ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setukpairinjR2_type,type,
% 2.99/1.51 setukpairinjR2: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setukpairinjR2,definition,
% 2.99/1.51 ( setukpairinjR2
% 2.99/1.51 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.99/1.51 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.99/1.51 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.99/1.51 => ( Xy = Xu ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setukpairinjR_type,type,
% 2.99/1.51 setukpairinjR: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setukpairinjR,definition,
% 2.99/1.51 ( setukpairinjR
% 2.99/1.51 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.99/1.51 ( ( ( kpair @ Xx @ Xy )
% 2.99/1.51 = ( kpair @ Xz @ Xu ) )
% 2.99/1.51 => ( Xy = Xu ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(ksndsingleton_type,type,
% 2.99/1.51 ksndsingleton: $o ).
% 2.99/1.51
% 2.99/1.51 thf(ksndsingleton,definition,
% 2.99/1.51 ( ksndsingleton
% 2.99/1.51 = ( ! [Xu: $i] :
% 2.99/1.51 ( ( iskpair @ Xu )
% 2.99/1.51 => ( singleton
% 2.99/1.51 @ ( dsetconstr @ ( setunion @ Xu )
% 2.99/1.51 @ ^ [Xx: $i] :
% 2.99/1.51 ( Xu
% 2.99/1.51 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(ksnd_type,type,
% 2.99/1.51 ksnd: $i > $i ).
% 2.99/1.51
% 2.99/1.51 thf(ksndpairEq_type,type,
% 2.99/1.51 ksndpairEq: $o ).
% 2.99/1.51
% 2.99/1.51 thf(ksndpairEq,definition,
% 2.99/1.51 ( ksndpairEq
% 2.99/1.51 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.51 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.99/1.51 = Xy ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(kpairsurjEq_type,type,
% 2.99/1.51 kpairsurjEq: $o ).
% 2.99/1.51
% 2.99/1.51 thf(kpairsurjEq,definition,
% 2.99/1.51 ( kpairsurjEq
% 2.99/1.51 = ( ! [Xu: $i] :
% 2.99/1.51 ( ( iskpair @ Xu )
% 2.99/1.51 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.99/1.51 = Xu ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(cartprodsndin_type,type,
% 2.99/1.51 cartprodsndin: $o ).
% 2.99/1.51
% 2.99/1.51 thf(cartprodsndin,definition,
% 2.99/1.51 ( cartprodsndin
% 2.99/1.51 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.99/1.51 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.99/1.51 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(cartprodpairmemEL_type,type,
% 2.99/1.51 cartprodpairmemEL: $o ).
% 2.99/1.51
% 2.99/1.51 thf(cartprodpairmemEL,definition,
% 2.99/1.51 ( cartprodpairmemEL
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.99/1.51 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.99/1.51 => ( in @ Xx @ A ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(cartprodpairmemER_type,type,
% 2.99/1.51 cartprodpairmemER: $o ).
% 2.99/1.51
% 2.99/1.51 thf(cartprodpairmemER,definition,
% 2.99/1.51 ( cartprodpairmemER
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.99/1.51 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.99/1.51 => ( in @ Xy @ B ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(cartprodmempaircEq_type,type,
% 2.99/1.51 cartprodmempaircEq: $o ).
% 2.99/1.51
% 2.99/1.51 thf(cartprodmempaircEq,definition,
% 2.99/1.51 ( cartprodmempaircEq
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ! [Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ B )
% 2.99/1.51 => ( ( kpair @ Xx @ Xy )
% 2.99/1.51 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(cartprodfstpairEq_type,type,
% 2.99/1.51 cartprodfstpairEq: $o ).
% 2.99/1.51
% 2.99/1.51 thf(cartprodfstpairEq,definition,
% 2.99/1.51 ( cartprodfstpairEq
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ! [Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ B )
% 2.99/1.51 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.99/1.51 = Xx ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(cartprodsndpairEq_type,type,
% 2.99/1.51 cartprodsndpairEq: $o ).
% 2.99/1.51
% 2.99/1.51 thf(cartprodsndpairEq,definition,
% 2.99/1.51 ( cartprodsndpairEq
% 2.99/1.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ! [Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ B )
% 2.99/1.51 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.99/1.51 = Xy ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(cartprodpairsurjEq_type,type,
% 2.99/1.51 cartprodpairsurjEq: $o ).
% 2.99/1.51
% 2.99/1.51 thf(cartprodpairsurjEq,definition,
% 2.99/1.51 ( cartprodpairsurjEq
% 2.99/1.51 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.99/1.51 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.99/1.51 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.99/1.51 = Xu ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(breln_type,type,
% 2.99/1.51 breln: $i > $i > $i > $o ).
% 2.99/1.51
% 2.99/1.51 thf(dpsetconstr_type,type,
% 2.99/1.51 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 2.99/1.51
% 2.99/1.51 thf(dpsetconstrI_type,type,
% 2.99/1.51 dpsetconstrI: $o ).
% 2.99/1.51
% 2.99/1.51 thf(dpsetconstrI,definition,
% 2.99/1.51 ( dpsetconstrI
% 2.99/1.51 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ! [Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ B )
% 2.99/1.51 => ( ( Xphi @ Xx @ Xy )
% 2.99/1.51 => ( in @ ( kpair @ Xx @ Xy )
% 2.99/1.51 @ ( dpsetconstr @ A @ B
% 2.99/1.51 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(dpsetconstrSub_type,type,
% 2.99/1.51 dpsetconstrSub: $o ).
% 2.99/1.51
% 2.99/1.51 thf(dpsetconstrSub,definition,
% 2.99/1.51 ( dpsetconstrSub
% 2.99/1.51 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.99/1.51 ( subset
% 2.99/1.51 @ ( dpsetconstr @ A @ B
% 2.99/1.51 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 2.99/1.51 @ ( cartprod @ A @ B ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(setOfPairsIsBReln_type,type,
% 2.99/1.51 setOfPairsIsBReln: $o ).
% 2.99/1.51
% 2.99/1.51 thf(setOfPairsIsBReln,definition,
% 2.99/1.51 ( setOfPairsIsBReln
% 2.99/1.51 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.99/1.51 ( breln @ A @ B
% 2.99/1.51 @ ( dpsetconstr @ A @ B
% 2.99/1.51 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(dpsetconstrERa_type,type,
% 2.99/1.51 dpsetconstrERa: $o ).
% 2.99/1.51
% 2.99/1.51 thf(dpsetconstrERa,definition,
% 2.99/1.51 ( dpsetconstrERa
% 2.99/1.51 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ! [Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ B )
% 2.99/1.51 => ( ( in @ ( kpair @ Xx @ Xy )
% 2.99/1.51 @ ( dpsetconstr @ A @ B
% 2.99/1.51 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.99/1.51 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(dpsetconstrEL1_type,type,
% 2.99/1.51 dpsetconstrEL1: $o ).
% 2.99/1.51
% 2.99/1.51 thf(dpsetconstrEL1,definition,
% 2.99/1.51 ( dpsetconstrEL1
% 2.99/1.51 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.99/1.51 ( ( in @ ( kpair @ Xx @ Xy )
% 2.99/1.51 @ ( dpsetconstr @ A @ B
% 2.99/1.51 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.99/1.51 => ( in @ Xx @ A ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(dpsetconstrEL2_type,type,
% 2.99/1.51 dpsetconstrEL2: $o ).
% 2.99/1.51
% 2.99/1.51 thf(dpsetconstrEL2,definition,
% 2.99/1.51 ( dpsetconstrEL2
% 2.99/1.51 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.99/1.51 ( ( in @ ( kpair @ Xx @ Xy )
% 2.99/1.51 @ ( dpsetconstr @ A @ B
% 2.99/1.51 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.99/1.51 => ( in @ Xy @ B ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(dpsetconstrER_type,type,
% 2.99/1.51 dpsetconstrER: $o ).
% 2.99/1.51
% 2.99/1.51 thf(dpsetconstrER,definition,
% 2.99/1.51 ( dpsetconstrER
% 2.99/1.51 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.99/1.51 ( ( in @ ( kpair @ Xx @ Xy )
% 2.99/1.51 @ ( dpsetconstr @ A @ B
% 2.99/1.51 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.99/1.51 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(func_type,type,
% 2.99/1.51 func: $i > $i > $i > $o ).
% 2.99/1.51
% 2.99/1.51 thf(funcSet_type,type,
% 2.99/1.51 funcSet: $i > $i > $i ).
% 2.99/1.51
% 2.99/1.51 thf(funcImageSingleton_type,type,
% 2.99/1.51 funcImageSingleton: $o ).
% 2.99/1.51
% 2.99/1.51 thf(funcImageSingleton,definition,
% 2.99/1.51 ( funcImageSingleton
% 2.99/1.51 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.51 ( ( func @ A @ B @ Xf )
% 2.99/1.51 => ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( singleton
% 2.99/1.51 @ ( dsetconstr @ B
% 2.99/1.51 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(apProp_type,type,
% 2.99/1.51 apProp: $o ).
% 2.99/1.51
% 2.99/1.51 thf(apProp,definition,
% 2.99/1.51 ( apProp
% 2.99/1.51 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.51 ( ( func @ A @ B @ Xf )
% 2.99/1.51 => ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( in
% 2.99/1.51 @ ( setunion
% 2.99/1.51 @ ( dsetconstr @ B
% 2.99/1.51 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 2.99/1.51 @ B ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(ap_type,type,
% 2.99/1.51 ap: $i > $i > $i > $i > $i ).
% 2.99/1.51
% 2.99/1.51 thf(app_type,type,
% 2.99/1.51 app: $o ).
% 2.99/1.51
% 2.99/1.51 thf(app,definition,
% 2.99/1.51 ( app
% 2.99/1.51 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.51 ( ( func @ A @ B @ Xf )
% 2.99/1.51 => ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(infuncsetfunc_type,type,
% 2.99/1.51 infuncsetfunc: $o ).
% 2.99/1.51
% 2.99/1.51 thf(infuncsetfunc,definition,
% 2.99/1.51 ( infuncsetfunc
% 2.99/1.51 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.51 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.99/1.51 => ( func @ A @ B @ Xf ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(ap2p_type,type,
% 2.99/1.51 ap2p: $o ).
% 2.99/1.51
% 2.99/1.51 thf(ap2p,definition,
% 2.99/1.51 ( ap2p
% 2.99/1.51 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.51 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.99/1.51 => ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(funcinfuncset_type,type,
% 2.99/1.51 funcinfuncset: $o ).
% 2.99/1.51
% 2.99/1.51 thf(funcinfuncset,definition,
% 2.99/1.51 ( funcinfuncset
% 2.99/1.51 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.51 ( ( func @ A @ B @ Xf )
% 2.99/1.51 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(lamProp_type,type,
% 2.99/1.51 lamProp: $o ).
% 2.99/1.51
% 2.99/1.51 thf(lamProp,definition,
% 2.99/1.51 ( lamProp
% 2.99/1.51 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.99/1.51 ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.99/1.51 => ( func @ A @ B
% 2.99/1.51 @ ( dpsetconstr @ A @ B
% 2.99/1.51 @ ^ [Xx: $i,Xy: $i] :
% 2.99/1.51 ( ( Xf @ Xx )
% 2.99/1.51 = Xy ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(lam_type,type,
% 2.99/1.51 lam: $i > $i > ( $i > $i ) > $i ).
% 2.99/1.51
% 2.99/1.51 thf(lamp_type,type,
% 2.99/1.51 lamp: $o ).
% 2.99/1.51
% 2.99/1.51 thf(lamp,definition,
% 2.99/1.51 ( lamp
% 2.99/1.51 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.99/1.51 ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.99/1.51 => ( func @ A @ B
% 2.99/1.51 @ ( lam @ A @ B
% 2.99/1.51 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(lam2p_type,type,
% 2.99/1.51 lam2p: $o ).
% 2.99/1.51
% 2.99/1.51 thf(lam2p,definition,
% 2.99/1.51 ( lam2p
% 2.99/1.51 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.99/1.51 ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.99/1.51 => ( in
% 2.99/1.51 @ ( lam @ A @ B
% 2.99/1.51 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 2.99/1.51 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(brelnall1_type,type,
% 2.99/1.51 brelnall1: $o ).
% 2.99/1.51
% 2.99/1.51 thf(brelnall1,definition,
% 2.99/1.51 ( brelnall1
% 2.99/1.51 = ( ! [A: $i,B: $i,R: $i] :
% 2.99/1.51 ( ( breln @ A @ B @ R )
% 2.99/1.51 => ! [Xphi: $i > $o] :
% 2.99/1.51 ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ! [Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ B )
% 2.99/1.51 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.99/1.51 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.99/1.51 => ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ R )
% 2.99/1.51 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(brelnall2_type,type,
% 2.99/1.51 brelnall2: $o ).
% 2.99/1.51
% 2.99/1.51 thf(brelnall2,definition,
% 2.99/1.51 ( brelnall2
% 2.99/1.51 = ( ! [A: $i,B: $i,R: $i] :
% 2.99/1.51 ( ( breln @ A @ B @ R )
% 2.99/1.51 => ! [Xphi: $i > $o] :
% 2.99/1.51 ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ! [Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ B )
% 2.99/1.51 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.99/1.51 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.99/1.51 => ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ R )
% 2.99/1.51 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(ex1E2_type,type,
% 2.99/1.51 ex1E2: $o ).
% 2.99/1.51
% 2.99/1.51 thf(ex1E2,definition,
% 2.99/1.51 ( ex1E2
% 2.99/1.51 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.51 ( ( ex1 @ A
% 2.99/1.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.51 => ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ! [Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ A )
% 2.99/1.51 => ( ( Xphi @ Xx )
% 2.99/1.51 => ( ( Xphi @ Xy )
% 2.99/1.51 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(funcGraphProp1_type,type,
% 2.99/1.51 funcGraphProp1: $o ).
% 2.99/1.51
% 2.99/1.51 thf(funcGraphProp1,definition,
% 2.99/1.51 ( funcGraphProp1
% 2.99/1.51 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.51 ( ( func @ A @ B @ Xf )
% 2.99/1.51 => ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(funcGraphProp3_type,type,
% 2.99/1.51 funcGraphProp3: $o ).
% 2.99/1.51
% 2.99/1.51 thf(funcGraphProp3,definition,
% 2.99/1.51 ( funcGraphProp3
% 2.99/1.51 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.51 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.99/1.51 => ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(funcGraphProp2_type,type,
% 2.99/1.51 funcGraphProp2: $o ).
% 2.99/1.51
% 2.99/1.51 thf(funcGraphProp2,definition,
% 2.99/1.51 ( funcGraphProp2
% 2.99/1.51 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.51 ( ( func @ A @ B @ Xf )
% 2.99/1.51 => ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ! [Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ B )
% 2.99/1.51 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 2.99/1.51 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.99/1.51 = Xy ) ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(funcextLem_type,type,
% 2.99/1.51 funcextLem: $o ).
% 2.99/1.51
% 2.99/1.51 thf(funcextLem,definition,
% 2.99/1.51 ( funcextLem
% 2.99/1.51 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.51 ( ( func @ A @ B @ Xf )
% 2.99/1.51 => ! [Xg: $i] :
% 2.99/1.51 ( ( func @ A @ B @ Xg )
% 2.99/1.51 => ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.99/1.51 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.99/1.51 => ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ! [Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ B )
% 2.99/1.51 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 2.99/1.51 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(funcGraphProp4_type,type,
% 2.99/1.51 funcGraphProp4: $o ).
% 2.99/1.51
% 2.99/1.51 thf(funcGraphProp4,definition,
% 2.99/1.51 ( funcGraphProp4
% 2.99/1.51 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.51 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.99/1.51 => ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ! [Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ B )
% 2.99/1.51 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 2.99/1.51 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.99/1.51 = Xy ) ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(subbreln_type,type,
% 2.99/1.51 subbreln: $o ).
% 2.99/1.51
% 2.99/1.51 thf(subbreln,definition,
% 2.99/1.51 ( subbreln
% 2.99/1.51 = ( ! [A: $i,B: $i,R: $i] :
% 2.99/1.51 ( ( breln @ A @ B @ R )
% 2.99/1.51 => ! [S: $i] :
% 2.99/1.51 ( ( breln @ A @ B @ S )
% 2.99/1.51 => ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ! [Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ B )
% 2.99/1.51 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.99/1.51 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.99/1.51 => ( subset @ R @ S ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(eqbreln_type,type,
% 2.99/1.51 eqbreln: $o ).
% 2.99/1.51
% 2.99/1.51 thf(eqbreln,definition,
% 2.99/1.51 ( eqbreln
% 2.99/1.51 = ( ! [A: $i,B: $i,R: $i] :
% 2.99/1.51 ( ( breln @ A @ B @ R )
% 2.99/1.51 => ! [S: $i] :
% 2.99/1.51 ( ( breln @ A @ B @ S )
% 2.99/1.51 => ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ! [Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ B )
% 2.99/1.51 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.99/1.51 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.99/1.51 => ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ! [Xy: $i] :
% 2.99/1.51 ( ( in @ Xy @ B )
% 2.99/1.51 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 2.99/1.51 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 2.99/1.51 => ( R = S ) ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(funcext_type,type,
% 2.99/1.51 funcext: $o ).
% 2.99/1.51
% 2.99/1.51 thf(funcext,definition,
% 2.99/1.51 ( funcext
% 2.99/1.51 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.51 ( ( func @ A @ B @ Xf )
% 2.99/1.51 => ! [Xg: $i] :
% 2.99/1.51 ( ( func @ A @ B @ Xg )
% 2.99/1.51 => ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.99/1.51 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.99/1.51 => ( Xf = Xg ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(funcext2_type,type,
% 2.99/1.51 funcext2: $o ).
% 2.99/1.51
% 2.99/1.51 thf(funcext2,definition,
% 2.99/1.51 ( funcext2
% 2.99/1.51 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.51 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.99/1.51 => ! [Xg: $i] :
% 2.99/1.51 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 2.99/1.51 => ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.99/1.51 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.99/1.51 => ( Xf = Xg ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(ap2apEq1_type,type,
% 2.99/1.51 ap2apEq1: $o ).
% 2.99/1.51
% 2.99/1.51 thf(ap2apEq1,definition,
% 2.99/1.51 ( ap2apEq1
% 2.99/1.51 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.51 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.99/1.51 => ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.99/1.51 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(ap2apEq2_type,type,
% 2.99/1.51 ap2apEq2: $o ).
% 2.99/1.51
% 2.99/1.51 thf(ap2apEq2,definition,
% 2.99/1.51 ( ap2apEq2
% 2.99/1.51 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.51 ( ( func @ A @ B @ Xf )
% 2.99/1.51 => ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.99/1.51 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(beta1_type,type,
% 2.99/1.51 beta1: $o ).
% 2.99/1.51
% 2.99/1.51 thf(beta1,definition,
% 2.99/1.51 ( beta1
% 2.99/1.51 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.99/1.51 ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.99/1.51 => ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( ( ap @ A @ B
% 2.99/1.51 @ ( lam @ A @ B
% 2.99/1.51 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 2.99/1.51 @ Xx )
% 2.99/1.51 = ( Xf @ Xx ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(eta1_type,type,
% 2.99/1.51 eta1: $o ).
% 2.99/1.51
% 2.99/1.51 thf(eta1,definition,
% 2.99/1.51 ( eta1
% 2.99/1.51 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.51 ( ( func @ A @ B @ Xf )
% 2.99/1.51 => ( ( lam @ A @ B
% 2.99/1.51 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 2.99/1.51 = Xf ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(lam2lamEq_type,type,
% 2.99/1.51 lam2lamEq: $o ).
% 2.99/1.51
% 2.99/1.51 thf(lam2lamEq,definition,
% 2.99/1.51 ( lam2lamEq
% 2.99/1.51 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.99/1.51 ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.99/1.51 => ( ( lam @ A @ B
% 2.99/1.51 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 2.99/1.51 = ( lam @ A @ B
% 2.99/1.51 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(beta2_type,type,
% 2.99/1.51 beta2: $o ).
% 2.99/1.51
% 2.99/1.51 thf(beta2,definition,
% 2.99/1.51 ( beta2
% 2.99/1.51 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.99/1.51 ( ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.99/1.51 => ! [Xx: $i] :
% 2.99/1.51 ( ( in @ Xx @ A )
% 2.99/1.51 => ( ( ap @ A @ B
% 2.99/1.51 @ ( lam @ A @ B
% 2.99/1.51 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 2.99/1.51 @ Xx )
% 2.99/1.51 = ( Xf @ Xx ) ) ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(eta2_type,type,
% 2.99/1.51 eta2: $o ).
% 2.99/1.51
% 2.99/1.51 thf(eta2,definition,
% 2.99/1.51 ( eta2
% 2.99/1.51 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.51 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.99/1.51 => ( ( lam @ A @ B
% 2.99/1.51 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 2.99/1.51 = Xf ) ) ) ) ).
% 2.99/1.51
% 2.99/1.51 thf(iffalseProp1_type,type,
% 2.99/1.51 iffalseProp1: $o ).
% 2.99/1.51
% 2.99/1.51 thf(iffalseProp1,definition,
% 2.99/1.52 ( iffalseProp1
% 2.99/1.52 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ! [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ A )
% 2.99/1.52 => ( ~ Xphi
% 2.99/1.52 => ( in @ Xy
% 2.99/1.52 @ ( dsetconstr @ A
% 2.99/1.52 @ ^ [Xz: $i] :
% 2.99/1.52 ( ( Xphi
% 2.99/1.52 & ( Xz = Xx ) )
% 2.99/1.52 | ( ~ Xphi
% 2.99/1.52 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(iffalseProp2_type,type,
% 2.99/1.52 iffalseProp2: $o ).
% 2.99/1.52
% 2.99/1.52 thf(iffalseProp2,definition,
% 2.99/1.52 ( iffalseProp2
% 2.99/1.52 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ! [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ A )
% 2.99/1.52 => ( ~ Xphi
% 2.99/1.52 => ( ( dsetconstr @ A
% 2.99/1.52 @ ^ [Xz: $i] :
% 2.99/1.52 ( ( Xphi
% 2.99/1.52 & ( Xz = Xx ) )
% 2.99/1.52 | ( ~ Xphi
% 2.99/1.52 & ( Xz = Xy ) ) ) )
% 2.99/1.52 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(iftrueProp1_type,type,
% 2.99/1.52 iftrueProp1: $o ).
% 2.99/1.52
% 2.99/1.52 thf(iftrueProp1,definition,
% 2.99/1.52 ( iftrueProp1
% 2.99/1.52 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ! [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ A )
% 2.99/1.52 => ( Xphi
% 2.99/1.52 => ( in @ Xx
% 2.99/1.52 @ ( dsetconstr @ A
% 2.99/1.52 @ ^ [Xz: $i] :
% 2.99/1.52 ( ( Xphi
% 2.99/1.52 & ( Xz = Xx ) )
% 2.99/1.52 | ( ~ Xphi
% 2.99/1.52 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(iftrueProp2_type,type,
% 2.99/1.52 iftrueProp2: $o ).
% 2.99/1.52
% 2.99/1.52 thf(iftrueProp2,definition,
% 2.99/1.52 ( iftrueProp2
% 2.99/1.52 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ! [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ A )
% 2.99/1.52 => ( Xphi
% 2.99/1.52 => ( ( dsetconstr @ A
% 2.99/1.52 @ ^ [Xz: $i] :
% 2.99/1.52 ( ( Xphi
% 2.99/1.52 & ( Xz = Xx ) )
% 2.99/1.52 | ( ~ Xphi
% 2.99/1.52 & ( Xz = Xy ) ) ) )
% 2.99/1.52 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(ifSingleton_type,type,
% 2.99/1.52 ifSingleton: $o ).
% 2.99/1.52
% 2.99/1.52 thf(ifSingleton,definition,
% 2.99/1.52 ( ifSingleton
% 2.99/1.52 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ! [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ A )
% 2.99/1.52 => ( singleton
% 2.99/1.52 @ ( dsetconstr @ A
% 2.99/1.52 @ ^ [Xz: $i] :
% 2.99/1.52 ( ( Xphi
% 2.99/1.52 & ( Xz = Xx ) )
% 2.99/1.52 | ( ~ Xphi
% 2.99/1.52 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(if_type,type,
% 2.99/1.52 if: $i > $o > $i > $i > $i ).
% 2.99/1.52
% 2.99/1.52 thf(ifp_type,type,
% 2.99/1.52 ifp: $o ).
% 2.99/1.52
% 2.99/1.52 thf(ifp,definition,
% 2.99/1.52 ( ifp
% 2.99/1.52 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ! [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ A )
% 2.99/1.52 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(theeq_type,type,
% 2.99/1.52 theeq: $o ).
% 2.99/1.52
% 2.99/1.52 thf(theeq,definition,
% 2.99/1.52 ( theeq
% 2.99/1.52 = ( ! [X: $i] :
% 2.99/1.52 ( ( singleton @ X )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ X )
% 2.99/1.52 => ( ( setunion @ X )
% 2.99/1.52 = Xx ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(iftrue_type,type,
% 2.99/1.52 iftrue: $o ).
% 2.99/1.52
% 2.99/1.52 thf(iftrue,definition,
% 2.99/1.52 ( iftrue
% 2.99/1.52 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ! [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ A )
% 2.99/1.52 => ( Xphi
% 2.99/1.52 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 2.99/1.52 = Xx ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(iffalse_type,type,
% 2.99/1.52 iffalse: $o ).
% 2.99/1.52
% 2.99/1.52 thf(iffalse,definition,
% 2.99/1.52 ( iffalse
% 2.99/1.52 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ! [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ A )
% 2.99/1.52 => ( ~ Xphi
% 2.99/1.52 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 2.99/1.52 = Xy ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(iftrueorfalse_type,type,
% 2.99/1.52 iftrueorfalse: $o ).
% 2.99/1.52
% 2.99/1.52 thf(iftrueorfalse,definition,
% 2.99/1.52 ( iftrueorfalse
% 2.99/1.52 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ! [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ A )
% 2.99/1.52 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(binintersectT_lem_type,type,
% 2.99/1.52 binintersectT_lem: $o ).
% 2.99/1.52
% 2.99/1.52 thf(binintersectT_lem,definition,
% 2.99/1.52 ( binintersectT_lem
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(binunionT_lem_type,type,
% 2.99/1.52 binunionT_lem: $o ).
% 2.99/1.52
% 2.99/1.52 thf(binunionT_lem,definition,
% 2.99/1.52 ( binunionT_lem
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(powersetT_lem_type,type,
% 2.99/1.52 powersetT_lem: $o ).
% 2.99/1.52
% 2.99/1.52 thf(powersetT_lem,definition,
% 2.99/1.52 ( powersetT_lem
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(setminusT_lem_type,type,
% 2.99/1.52 setminusT_lem: $o ).
% 2.99/1.52
% 2.99/1.52 thf(setminusT_lem,definition,
% 2.99/1.52 ( setminusT_lem
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(complementT_lem_type,type,
% 2.99/1.52 complementT_lem: $o ).
% 2.99/1.52
% 2.99/1.52 thf(complementT_lem,definition,
% 2.99/1.52 ( complementT_lem
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(setextT_type,type,
% 2.99/1.52 setextT: $o ).
% 2.99/1.52
% 2.99/1.52 thf(setextT,definition,
% 2.99/1.52 ( setextT
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ( ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ( in @ Xx @ X )
% 2.99/1.52 => ( in @ Xx @ Y ) ) )
% 2.99/1.52 => ( ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ( in @ Xx @ Y )
% 2.99/1.52 => ( in @ Xx @ X ) ) )
% 2.99/1.52 => ( X = Y ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(subsetTI_type,type,
% 2.99/1.52 subsetTI: $o ).
% 2.99/1.52
% 2.99/1.52 thf(subsetTI,definition,
% 2.99/1.52 ( subsetTI
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ( ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ( in @ Xx @ X )
% 2.99/1.52 => ( in @ Xx @ Y ) ) )
% 2.99/1.52 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(powersetTI1_type,type,
% 2.99/1.52 powersetTI1: $o ).
% 2.99/1.52
% 2.99/1.52 thf(powersetTI1,definition,
% 2.99/1.52 ( powersetTI1
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ( ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ( in @ Xx @ X )
% 2.99/1.52 => ( in @ Xx @ Y ) ) )
% 2.99/1.52 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(powersetTE1_type,type,
% 2.99/1.52 powersetTE1: $o ).
% 2.99/1.52
% 2.99/1.52 thf(powersetTE1,definition,
% 2.99/1.52 ( powersetTE1
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ( in @ X @ ( powerset @ Y ) )
% 2.99/1.52 => ( ( in @ Xx @ X )
% 2.99/1.52 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(complementTI1_type,type,
% 2.99/1.52 complementTI1: $o ).
% 2.99/1.52
% 2.99/1.52 thf(complementTI1,definition,
% 2.99/1.52 ( complementTI1
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ( in @ Xx @ X )
% 2.99/1.52 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(complementTE1_type,type,
% 2.99/1.52 complementTE1: $o ).
% 2.99/1.52
% 2.99/1.52 thf(complementTE1,definition,
% 2.99/1.52 ( complementTE1
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 2.99/1.52 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(binintersectTELcontra_type,type,
% 2.99/1.52 binintersectTELcontra: $o ).
% 2.99/1.52
% 2.99/1.52 thf(binintersectTELcontra,definition,
% 2.99/1.52 ( binintersectTELcontra
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ~ ( in @ Xx @ X )
% 2.99/1.52 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(binintersectTERcontra_type,type,
% 2.99/1.52 binintersectTERcontra: $o ).
% 2.99/1.52
% 2.99/1.52 thf(binintersectTERcontra,definition,
% 2.99/1.52 ( binintersectTERcontra
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ~ ( in @ Xx @ Y )
% 2.99/1.52 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(contrasubsetT_type,type,
% 2.99/1.52 contrasubsetT: $o ).
% 2.99/1.52
% 2.99/1.52 thf(contrasubsetT,definition,
% 2.99/1.52 ( contrasubsetT
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.99/1.52 => ( ( in @ Xx @ Y )
% 2.99/1.52 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(contrasubsetT1_type,type,
% 2.99/1.52 contrasubsetT1: $o ).
% 2.99/1.52
% 2.99/1.52 thf(contrasubsetT1,definition,
% 2.99/1.52 ( contrasubsetT1
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ( subset @ X @ Y )
% 2.99/1.52 => ( ~ ( in @ Xx @ Y )
% 2.99/1.52 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(contrasubsetT2_type,type,
% 2.99/1.52 contrasubsetT2: $o ).
% 2.99/1.52
% 2.99/1.52 thf(contrasubsetT2,definition,
% 2.99/1.52 ( contrasubsetT2
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ( ( subset @ X @ Y )
% 2.99/1.52 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(contrasubsetT3_type,type,
% 2.99/1.52 contrasubsetT3: $o ).
% 2.99/1.52
% 2.99/1.52 thf(contrasubsetT3,definition,
% 2.99/1.52 ( contrasubsetT3
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 2.99/1.52 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(doubleComplementI1_type,type,
% 2.99/1.52 doubleComplementI1: $o ).
% 2.99/1.52
% 2.99/1.52 thf(doubleComplementI1,definition,
% 2.99/1.52 ( doubleComplementI1
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ( in @ Xx @ X )
% 2.99/1.52 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(doubleComplementE1_type,type,
% 2.99/1.52 doubleComplementE1: $o ).
% 2.99/1.52
% 2.99/1.52 thf(doubleComplementE1,definition,
% 2.99/1.52 ( doubleComplementE1
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 2.99/1.52 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(doubleComplementSub1_type,type,
% 2.99/1.52 doubleComplementSub1: $o ).
% 2.99/1.52
% 2.99/1.52 thf(doubleComplementSub1,definition,
% 2.99/1.52 ( doubleComplementSub1
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(doubleComplementSub2_type,type,
% 2.99/1.52 doubleComplementSub2: $o ).
% 2.99/1.52
% 2.99/1.52 thf(doubleComplementSub2,definition,
% 2.99/1.52 ( doubleComplementSub2
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(doubleComplementEq_type,type,
% 2.99/1.52 doubleComplementEq: $o ).
% 2.99/1.52
% 2.99/1.52 thf(doubleComplementEq,definition,
% 2.99/1.52 ( doubleComplementEq
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ( X
% 2.99/1.52 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(complementTnotintersectT_type,type,
% 2.99/1.52 complementTnotintersectT: $o ).
% 2.99/1.52
% 2.99/1.52 thf(complementTnotintersectT,definition,
% 2.99/1.52 ( complementTnotintersectT
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 2.99/1.52 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(complementImpComplementIntersect_type,type,
% 2.99/1.52 complementImpComplementIntersect: $o ).
% 2.99/1.52
% 2.99/1.52 thf(complementImpComplementIntersect,definition,
% 2.99/1.52 ( complementImpComplementIntersect
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 2.99/1.52 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(complementSubsetComplementIntersect_type,type,
% 2.99/1.52 complementSubsetComplementIntersect: $o ).
% 2.99/1.52
% 2.99/1.52 thf(complementSubsetComplementIntersect,definition,
% 2.99/1.52 ( complementSubsetComplementIntersect
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(complementInPowersetComplementIntersect_type,type,
% 2.99/1.52 complementInPowersetComplementIntersect: $o ).
% 2.99/1.52
% 2.99/1.52 thf(complementInPowersetComplementIntersect,definition,
% 2.99/1.52 ( complementInPowersetComplementIntersect
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(contraSubsetComplement_type,type,
% 2.99/1.52 contraSubsetComplement: $o ).
% 2.99/1.52
% 2.99/1.52 thf(contraSubsetComplement,definition,
% 2.99/1.52 ( contraSubsetComplement
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ( in @ Xx @ Y )
% 2.99/1.52 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(complementTcontraSubset_type,type,
% 2.99/1.52 complementTcontraSubset: $o ).
% 2.99/1.52
% 2.99/1.52 thf(complementTcontraSubset,definition,
% 2.99/1.52 ( complementTcontraSubset
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.99/1.52 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(binunionTILcontra_type,type,
% 2.99/1.52 binunionTILcontra: $o ).
% 2.99/1.52
% 2.99/1.52 thf(binunionTILcontra,definition,
% 2.99/1.52 ( binunionTILcontra
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 2.99/1.52 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(binunionTIRcontra_type,type,
% 2.99/1.52 binunionTIRcontra: $o ).
% 2.99/1.52
% 2.99/1.52 thf(binunionTIRcontra,definition,
% 2.99/1.52 ( binunionTIRcontra
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 2.99/1.52 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(inIntersectImpInUnion_type,type,
% 2.99/1.52 inIntersectImpInUnion: $o ).
% 2.99/1.52
% 2.99/1.52 thf(inIntersectImpInUnion,definition,
% 2.99/1.52 ( inIntersectImpInUnion
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Z: $i] :
% 2.99/1.52 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 2.99/1.52 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(inIntersectImpInUnion2_type,type,
% 2.99/1.52 inIntersectImpInUnion2: $o ).
% 2.99/1.52
% 2.99/1.52 thf(inIntersectImpInUnion2,definition,
% 2.99/1.52 ( inIntersectImpInUnion2
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Z: $i] :
% 2.99/1.52 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 2.99/1.52 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(inIntersectImpInIntersectUnions_type,type,
% 2.99/1.52 inIntersectImpInIntersectUnions: $o ).
% 2.99/1.52
% 2.99/1.52 thf(inIntersectImpInIntersectUnions,definition,
% 2.99/1.52 ( inIntersectImpInIntersectUnions
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Z: $i] :
% 2.99/1.52 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 2.99/1.52 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(intersectInPowersetIntersectUnions_type,type,
% 2.99/1.52 intersectInPowersetIntersectUnions: $o ).
% 2.99/1.52
% 2.99/1.52 thf(intersectInPowersetIntersectUnions,definition,
% 2.99/1.52 ( intersectInPowersetIntersectUnions
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Z: $i] :
% 2.99/1.52 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.52 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(inComplementUnionImpNotIn1_type,type,
% 2.99/1.52 inComplementUnionImpNotIn1: $o ).
% 2.99/1.52
% 2.99/1.52 thf(inComplementUnionImpNotIn1,definition,
% 2.99/1.52 ( inComplementUnionImpNotIn1
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.99/1.52 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(inComplementUnionImpInComplement1_type,type,
% 2.99/1.52 inComplementUnionImpInComplement1: $o ).
% 2.99/1.52
% 2.99/1.52 thf(inComplementUnionImpInComplement1,definition,
% 2.99/1.52 ( inComplementUnionImpInComplement1
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.99/1.52 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(binunionTE_type,type,
% 2.99/1.52 binunionTE: $o ).
% 2.99/1.52
% 2.99/1.52 thf(binunionTE,definition,
% 2.99/1.52 ( binunionTE
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Xphi: $o,Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 2.99/1.52 => ( ( ( in @ Xx @ X )
% 2.99/1.52 => Xphi )
% 2.99/1.52 => ( ( ( in @ Xx @ Y )
% 2.99/1.52 => Xphi )
% 2.99/1.52 => Xphi ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(binunionTEcontra_type,type,
% 2.99/1.52 binunionTEcontra: $o ).
% 2.99/1.52
% 2.99/1.52 thf(binunionTEcontra,definition,
% 2.99/1.52 ( binunionTEcontra
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ~ ( in @ Xx @ X )
% 2.99/1.52 => ( ~ ( in @ Xx @ Y )
% 2.99/1.52 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(demorgan2a1_type,type,
% 2.99/1.52 demorgan2a1: $o ).
% 2.99/1.52
% 2.99/1.52 thf(demorgan2a1,definition,
% 2.99/1.52 ( demorgan2a1
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.99/1.52 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(complementUnionInPowersetComplement_type,type,
% 2.99/1.52 complementUnionInPowersetComplement: $o ).
% 2.99/1.52
% 2.99/1.52 thf(complementUnionInPowersetComplement,definition,
% 2.99/1.52 ( complementUnionInPowersetComplement
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(demorgan2a2_type,type,
% 2.99/1.52 demorgan2a2: $o ).
% 2.99/1.52
% 2.99/1.52 thf(demorgan2a2,definition,
% 2.99/1.52 ( demorgan2a2
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.99/1.52 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(demorgan1a_type,type,
% 2.99/1.52 demorgan1a: $o ).
% 2.99/1.52
% 2.99/1.52 thf(demorgan1a,definition,
% 2.99/1.52 ( demorgan1a
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 2.99/1.52 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(demorgan1b_type,type,
% 2.99/1.52 demorgan1b: $o ).
% 2.99/1.52
% 2.99/1.52 thf(demorgan1b,definition,
% 2.99/1.52 ( demorgan1b
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 2.99/1.52 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(demorgan1_type,type,
% 2.99/1.52 demorgan1: $o ).
% 2.99/1.52
% 2.99/1.52 thf(demorgan1,definition,
% 2.99/1.52 ( demorgan1
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 2.99/1.52 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(demorgan2a_type,type,
% 2.99/1.52 demorgan2a: $o ).
% 2.99/1.52
% 2.99/1.52 thf(demorgan2a,definition,
% 2.99/1.52 ( demorgan2a
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.99/1.52 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(demorgan2b2_type,type,
% 2.99/1.52 demorgan2b2: $o ).
% 2.99/1.52
% 2.99/1.52 thf(demorgan2b2,definition,
% 2.99/1.52 ( demorgan2b2
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 2.99/1.52 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 2.99/1.52 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(demorgan2b_type,type,
% 2.99/1.52 demorgan2b: $o ).
% 2.99/1.52
% 2.99/1.52 thf(demorgan2b,definition,
% 2.99/1.52 ( demorgan2b
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 2.99/1.52 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(demorgan2_type,type,
% 2.99/1.52 demorgan2: $o ).
% 2.99/1.52
% 2.99/1.52 thf(demorgan2,definition,
% 2.99/1.52 ( demorgan2
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 2.99/1.52 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(woz13rule0_type,type,
% 2.99/1.52 woz13rule0: $o ).
% 2.99/1.52
% 2.99/1.52 thf(woz13rule0,definition,
% 2.99/1.52 ( woz13rule0
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 2.99/1.52 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(woz13rule1_type,type,
% 2.99/1.52 woz13rule1: $o ).
% 2.99/1.52
% 2.99/1.52 thf(woz13rule1,definition,
% 2.99/1.52 ( woz13rule1
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Z: $i] :
% 2.99/1.52 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.52 => ( ( subset @ X @ Z )
% 2.99/1.52 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(woz13rule2_type,type,
% 2.99/1.52 woz13rule2: $o ).
% 2.99/1.52
% 2.99/1.52 thf(woz13rule2,definition,
% 2.99/1.52 ( woz13rule2
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Z: $i] :
% 2.99/1.52 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.52 => ( ( subset @ Y @ Z )
% 2.99/1.52 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(woz13rule3_type,type,
% 2.99/1.52 woz13rule3: $o ).
% 2.99/1.52
% 2.99/1.52 thf(woz13rule3,definition,
% 2.99/1.52 ( woz13rule3
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Z: $i] :
% 2.99/1.52 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.52 => ( ( subset @ X @ Y )
% 2.99/1.52 => ( ( subset @ X @ Z )
% 2.99/1.52 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(woz13rule4_type,type,
% 2.99/1.52 woz13rule4: $o ).
% 2.99/1.52
% 2.99/1.52 thf(woz13rule4,definition,
% 2.99/1.52 ( woz13rule4
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Z: $i] :
% 2.99/1.52 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.52 => ! [W: $i] :
% 2.99/1.52 ( ( in @ W @ ( powerset @ A ) )
% 2.99/1.52 => ( ( subset @ X @ Z )
% 2.99/1.52 => ( ( subset @ Y @ W )
% 2.99/1.52 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(woz1_1_type,type,
% 2.99/1.52 woz1_1: $o ).
% 2.99/1.52
% 2.99/1.52 thf(woz1_1,definition,
% 2.99/1.52 ( woz1_1
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(woz1_2_type,type,
% 2.99/1.52 woz1_2: $o ).
% 2.99/1.52
% 2.99/1.52 thf(woz1_2,definition,
% 2.99/1.52 ( woz1_2
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Z: $i] :
% 2.99/1.52 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.52 => ! [W: $i] :
% 2.99/1.52 ( ( in @ W @ ( powerset @ A ) )
% 2.99/1.52 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 2.99/1.52 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(woz1_3_type,type,
% 2.99/1.52 woz1_3: $o ).
% 2.99/1.52
% 2.99/1.52 thf(woz1_3,definition,
% 2.99/1.52 ( woz1_3
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ! [Z: $i] :
% 2.99/1.52 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.52 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(woz1_4_type,type,
% 2.99/1.52 woz1_4: $o ).
% 2.99/1.52
% 2.99/1.52 thf(woz1_4,definition,
% 2.99/1.52 ( woz1_4
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.99/1.52 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(woz1_5_type,type,
% 2.99/1.52 woz1_5: $o ).
% 2.99/1.52
% 2.99/1.52 thf(woz1_5,definition,
% 2.99/1.52 ( woz1_5
% 2.99/1.52 = ( ! [A: $i,X: $i] :
% 2.99/1.52 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.52 => ! [Y: $i] :
% 2.99/1.52 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.52 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(breln1_type,type,
% 2.99/1.52 breln1: $i > $i > $o ).
% 2.99/1.52
% 2.99/1.52 thf(breln1all2_type,type,
% 2.99/1.52 breln1all2: $o ).
% 2.99/1.52
% 2.99/1.52 thf(breln1all2,definition,
% 2.99/1.52 ( breln1all2
% 2.99/1.52 = ( ! [A: $i,R: $i] :
% 2.99/1.52 ( ( breln1 @ A @ R )
% 2.99/1.52 => ! [Xphi: $i > $o] :
% 2.99/1.52 ( ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ! [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ A )
% 2.99/1.52 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.99/1.52 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ R )
% 2.99/1.52 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(breln1Set_type,type,
% 2.99/1.52 breln1Set: $i > $i ).
% 2.99/1.52
% 2.99/1.52 thf(breln1SetBreln1_type,type,
% 2.99/1.52 breln1SetBreln1: $o ).
% 2.99/1.52
% 2.99/1.52 thf(breln1SetBreln1,definition,
% 2.99/1.52 ( breln1SetBreln1
% 2.99/1.52 = ( ! [A: $i,R: $i] :
% 2.99/1.52 ( ( in @ R @ ( breln1Set @ A ) )
% 2.99/1.52 => ( breln1 @ A @ R ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(transitive_type,type,
% 2.99/1.52 transitive: $i > $i > $o ).
% 2.99/1.52
% 2.99/1.52 thf(antisymmetric_type,type,
% 2.99/1.52 antisymmetric: $i > $i > $o ).
% 2.99/1.52
% 2.99/1.52 thf(reflexive_type,type,
% 2.99/1.52 reflexive: $i > $i > $o ).
% 2.99/1.52
% 2.99/1.52 thf(refltransitive_type,type,
% 2.99/1.52 refltransitive: $i > $i > $o ).
% 2.99/1.52
% 2.99/1.52 thf(refllinearorder_type,type,
% 2.99/1.52 refllinearorder: $i > $i > $o ).
% 2.99/1.52
% 2.99/1.52 thf(reflwellordering_type,type,
% 2.99/1.52 reflwellordering: $i > $i > $o ).
% 2.99/1.52
% 2.99/1.52 thf(choice2fnsingleton_type,type,
% 2.99/1.52 choice2fnsingleton: $o ).
% 2.99/1.52
% 2.99/1.52 thf(choice2fnsingleton,definition,
% 2.99/1.52 ( choice2fnsingleton
% 2.99/1.52 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.99/1.52 ( ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ? [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ B )
% 2.99/1.52 & ( Xphi @ Xx @ Xy ) ) )
% 2.99/1.52 => ! [R: $i] :
% 2.99/1.52 ( ( in @ R @ ( breln1Set @ B ) )
% 2.99/1.52 => ( ( reflwellordering @ B @ R )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( singleton
% 2.99/1.52 @ ( dsetconstr @ B
% 2.99/1.52 @ ^ [Xy: $i] :
% 2.99/1.52 ( ( Xphi @ Xx @ Xy )
% 2.99/1.52 & ! [Xz: $i] :
% 2.99/1.52 ( ( in @ Xz @ B )
% 2.99/1.52 => ( ( Xphi @ Xx @ Xz )
% 2.99/1.52 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(setOfPairsIsBReln1_type,type,
% 2.99/1.52 setOfPairsIsBReln1: $o ).
% 2.99/1.52
% 2.99/1.52 thf(setOfPairsIsBReln1,definition,
% 2.99/1.52 ( setOfPairsIsBReln1
% 2.99/1.52 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 2.99/1.52 ( breln1 @ A
% 2.99/1.52 @ ( dpsetconstr @ A @ A
% 2.99/1.52 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(breln1all1_type,type,
% 2.99/1.52 breln1all1: $o ).
% 2.99/1.52
% 2.99/1.52 thf(breln1all1,definition,
% 2.99/1.52 ( breln1all1
% 2.99/1.52 = ( ! [A: $i,R: $i] :
% 2.99/1.52 ( ( breln1 @ A @ R )
% 2.99/1.52 => ! [Xphi: $i > $o] :
% 2.99/1.52 ( ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ! [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ A )
% 2.99/1.52 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.99/1.52 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ R )
% 2.99/1.52 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(subbreln1_type,type,
% 2.99/1.52 subbreln1: $o ).
% 2.99/1.52
% 2.99/1.52 thf(subbreln1,definition,
% 2.99/1.52 ( subbreln1
% 2.99/1.52 = ( ! [A: $i,R: $i] :
% 2.99/1.52 ( ( breln1 @ A @ R )
% 2.99/1.52 => ! [S: $i] :
% 2.99/1.52 ( ( breln1 @ A @ S )
% 2.99/1.52 => ( ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ! [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ A )
% 2.99/1.52 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.99/1.52 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.99/1.52 => ( subset @ R @ S ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(eqbreln1_type,type,
% 2.99/1.52 eqbreln1: $o ).
% 2.99/1.52
% 2.99/1.52 thf(eqbreln1,definition,
% 2.99/1.52 ( eqbreln1
% 2.99/1.52 = ( ! [A: $i,R: $i] :
% 2.99/1.52 ( ( breln1 @ A @ R )
% 2.99/1.52 => ! [S: $i] :
% 2.99/1.52 ( ( breln1 @ A @ S )
% 2.99/1.52 => ( ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ! [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ A )
% 2.99/1.52 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.99/1.52 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.99/1.52 => ( ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ! [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ A )
% 2.99/1.52 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 2.99/1.52 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 2.99/1.52 => ( R = S ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(breln1invset_type,type,
% 2.99/1.52 breln1invset: $i > $i > $i ).
% 2.99/1.52
% 2.99/1.52 thf(breln1invprop_type,type,
% 2.99/1.52 breln1invprop: $o ).
% 2.99/1.52
% 2.99/1.52 thf(breln1invprop,definition,
% 2.99/1.52 ( breln1invprop
% 2.99/1.52 = ( ! [A: $i,R: $i] :
% 2.99/1.52 ( ( breln1 @ A @ R )
% 2.99/1.52 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(breln1invI_type,type,
% 2.99/1.52 breln1invI: $o ).
% 2.99/1.52
% 2.99/1.52 thf(breln1invI,definition,
% 2.99/1.52 ( breln1invI
% 2.99/1.52 = ( ! [A: $i,R: $i] :
% 2.99/1.52 ( ( breln1 @ A @ R )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ! [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ A )
% 2.99/1.52 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.99/1.52 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(breln1invE_type,type,
% 2.99/1.52 breln1invE: $o ).
% 2.99/1.52
% 2.99/1.52 thf(breln1invE,definition,
% 2.99/1.52 ( breln1invE
% 2.99/1.52 = ( ! [A: $i,R: $i] :
% 2.99/1.52 ( ( breln1 @ A @ R )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ! [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ A )
% 2.99/1.52 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 2.99/1.52 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(breln1compset_type,type,
% 2.99/1.52 breln1compset: $i > $i > $i > $i ).
% 2.99/1.52
% 2.99/1.52 thf(breln1compprop_type,type,
% 2.99/1.52 breln1compprop: $o ).
% 2.99/1.52
% 2.99/1.52 thf(breln1compprop,definition,
% 2.99/1.52 ( breln1compprop
% 2.99/1.52 = ( ! [A: $i,R: $i] :
% 2.99/1.52 ( ( breln1 @ A @ R )
% 2.99/1.52 => ! [S: $i] :
% 2.99/1.52 ( ( breln1 @ A @ S )
% 2.99/1.52 => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(breln1compI_type,type,
% 2.99/1.52 breln1compI: $o ).
% 2.99/1.52
% 2.99/1.52 thf(breln1compI,definition,
% 2.99/1.52 ( breln1compI
% 2.99/1.52 = ( ! [A: $i,R: $i] :
% 2.99/1.52 ( ( breln1 @ A @ R )
% 2.99/1.52 => ! [S: $i] :
% 2.99/1.52 ( ( breln1 @ A @ S )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ! [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ A )
% 2.99/1.52 => ! [Xz: $i] :
% 2.99/1.52 ( ( in @ Xz @ A )
% 2.99/1.52 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 2.99/1.52 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 2.99/1.52 => ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(breln1compE_type,type,
% 2.99/1.52 breln1compE: $o ).
% 2.99/1.52
% 2.99/1.52 thf(breln1compE,definition,
% 2.99/1.52 ( breln1compE
% 2.99/1.52 = ( ! [A: $i,R: $i] :
% 2.99/1.52 ( ( breln1 @ A @ R )
% 2.99/1.52 => ! [S: $i] :
% 2.99/1.52 ( ( breln1 @ A @ S )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ! [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ A )
% 2.99/1.52 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 2.99/1.52 => ? [Xz: $i] :
% 2.99/1.52 ( ( in @ Xz @ A )
% 2.99/1.52 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 2.99/1.52 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(breln1compEex_type,type,
% 2.99/1.52 breln1compEex: $o ).
% 2.99/1.52
% 2.99/1.52 thf(breln1compEex,definition,
% 2.99/1.52 ( breln1compEex
% 2.99/1.52 = ( ! [A: $i,R: $i] :
% 2.99/1.52 ( ( breln1 @ A @ R )
% 2.99/1.52 => ! [S: $i] :
% 2.99/1.52 ( ( breln1 @ A @ S )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ! [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ A )
% 2.99/1.52 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 2.99/1.52 => ! [Xphi: $o] :
% 2.99/1.52 ( ! [Xz: $i] :
% 2.99/1.52 ( ( in @ Xz @ A )
% 2.99/1.52 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 2.99/1.52 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 2.99/1.52 => Xphi ) ) )
% 2.99/1.52 => Xphi ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(breln1unionprop_type,type,
% 2.99/1.52 breln1unionprop: $o ).
% 2.99/1.52
% 2.99/1.52 thf(breln1unionprop,definition,
% 2.99/1.52 ( breln1unionprop
% 2.99/1.52 = ( ! [A: $i,R: $i] :
% 2.99/1.52 ( ( breln1 @ A @ R )
% 2.99/1.52 => ! [S: $i] :
% 2.99/1.52 ( ( breln1 @ A @ S )
% 2.99/1.52 => ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(breln1unionIL_type,type,
% 2.99/1.52 breln1unionIL: $o ).
% 2.99/1.52
% 2.99/1.52 thf(breln1unionIL,definition,
% 2.99/1.52 ( breln1unionIL
% 2.99/1.52 = ( ! [A: $i,R: $i] :
% 2.99/1.52 ( ( breln1 @ A @ R )
% 2.99/1.52 => ! [S: $i] :
% 2.99/1.52 ( ( breln1 @ A @ S )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ! [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ A )
% 2.99/1.52 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.99/1.52 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(breln1unionIR_type,type,
% 2.99/1.52 breln1unionIR: $o ).
% 2.99/1.52
% 2.99/1.52 thf(breln1unionIR,definition,
% 2.99/1.52 ( breln1unionIR
% 2.99/1.52 = ( ! [A: $i,R: $i] :
% 2.99/1.52 ( ( breln1 @ A @ R )
% 2.99/1.52 => ! [S: $i] :
% 2.99/1.52 ( ( breln1 @ A @ S )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ! [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ A )
% 2.99/1.52 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 2.99/1.52 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(breln1unionI_type,type,
% 2.99/1.52 breln1unionI: $o ).
% 2.99/1.52
% 2.99/1.52 thf(breln1unionI,definition,
% 2.99/1.52 ( breln1unionI
% 2.99/1.52 = ( ! [A: $i,R: $i] :
% 2.99/1.52 ( ( breln1 @ A @ R )
% 2.99/1.52 => ! [S: $i] :
% 2.99/1.52 ( ( breln1 @ A @ S )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ! [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ A )
% 2.99/1.52 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.99/1.52 | ( in @ ( kpair @ Xx @ Xy ) @ S ) )
% 2.99/1.52 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(breln1unionE_type,type,
% 2.99/1.52 breln1unionE: $o ).
% 2.99/1.52
% 2.99/1.52 thf(breln1unionE,definition,
% 2.99/1.52 ( breln1unionE
% 2.99/1.52 = ( ! [A: $i,R: $i] :
% 2.99/1.52 ( ( breln1 @ A @ R )
% 2.99/1.52 => ! [S: $i] :
% 2.99/1.52 ( ( breln1 @ A @ S )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ! [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ A )
% 2.99/1.52 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 2.99/1.52 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.99/1.52 | ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(breln1unionEcases_type,type,
% 2.99/1.52 breln1unionEcases: $o ).
% 2.99/1.52
% 2.99/1.52 thf(breln1unionEcases,definition,
% 2.99/1.52 ( breln1unionEcases
% 2.99/1.52 = ( ! [A: $i,R: $i] :
% 2.99/1.52 ( ( breln1 @ A @ R )
% 2.99/1.52 => ! [S: $i] :
% 2.99/1.52 ( ( breln1 @ A @ S )
% 2.99/1.52 => ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ! [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ A )
% 2.99/1.52 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 2.99/1.52 => ! [Xphi: $o] :
% 2.99/1.52 ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.99/1.52 => Xphi )
% 2.99/1.52 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 2.99/1.52 => Xphi )
% 2.99/1.52 => Xphi ) ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(breln1unionCommutes_type,type,
% 2.99/1.52 breln1unionCommutes: $o ).
% 2.99/1.52
% 2.99/1.52 thf(breln1unionCommutes,definition,
% 2.99/1.52 ( breln1unionCommutes
% 2.99/1.52 = ( ! [A: $i,R: $i] :
% 2.99/1.52 ( ( breln1 @ A @ R )
% 2.99/1.52 => ! [S: $i] :
% 2.99/1.52 ( ( breln1 @ A @ S )
% 2.99/1.52 => ( ( binunion @ R @ S )
% 2.99/1.52 = ( binunion @ S @ R ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(woz2Ex_type,type,
% 2.99/1.52 woz2Ex: $o ).
% 2.99/1.52
% 2.99/1.52 thf(woz2Ex,definition,
% 2.99/1.52 ( woz2Ex
% 2.99/1.52 = ( ! [A: $i,R: $i] :
% 2.99/1.52 ( ( breln1 @ A @ R )
% 2.99/1.52 => ( R
% 2.99/1.52 = ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(woz2W_type,type,
% 2.99/1.52 woz2W: $o ).
% 2.99/1.52
% 2.99/1.52 thf(woz2W,definition,
% 2.99/1.52 ( woz2W
% 2.99/1.52 = ( ! [A: $i,R: $i] :
% 2.99/1.52 ( ( breln1 @ A @ R )
% 2.99/1.52 => ! [S: $i] :
% 2.99/1.52 ( ( breln1 @ A @ S )
% 2.99/1.52 => ( ( breln1invset @ A @ ( breln1compset @ A @ R @ S ) )
% 2.99/1.52 = ( breln1compset @ A @ ( breln1invset @ A @ S ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(woz2A_type,type,
% 2.99/1.52 woz2A: $o ).
% 2.99/1.52
% 2.99/1.52 thf(woz2A,definition,
% 2.99/1.52 ( woz2A
% 2.99/1.52 = ( ! [A: $i,R: $i] :
% 2.99/1.52 ( ( breln1 @ A @ R )
% 2.99/1.52 => ! [S: $i] :
% 2.99/1.52 ( ( breln1 @ A @ S )
% 2.99/1.52 => ! [T: $i] :
% 2.99/1.52 ( ( breln1 @ A @ T )
% 2.99/1.52 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 2.99/1.52 = ( binunion @ ( breln1compset @ A @ R @ T ) @ ( breln1compset @ A @ S @ T ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(woz2B_type,type,
% 2.99/1.52 woz2B: $o ).
% 2.99/1.52
% 2.99/1.52 thf(woz2B,definition,
% 2.99/1.52 ( woz2B
% 2.99/1.52 = ( ! [A: $i,R: $i] :
% 2.99/1.52 ( ( breln1 @ A @ R )
% 2.99/1.52 => ! [S: $i] :
% 2.99/1.52 ( ( breln1 @ A @ S )
% 2.99/1.52 => ! [T: $i] :
% 2.99/1.52 ( ( breln1 @ A @ T )
% 2.99/1.52 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 2.99/1.52 = ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ S ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(image1Ex_type,type,
% 2.99/1.52 image1Ex: $o ).
% 2.99/1.52
% 2.99/1.52 thf(image1Ex,definition,
% 2.99/1.52 ( image1Ex
% 2.99/1.52 = ( ! [A: $i,Xf: $i > $i] :
% 2.99/1.52 ? [B: $i] :
% 2.99/1.52 ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ B )
% 2.99/1.52 <=> ? [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ A )
% 2.99/1.52 & ( Xx
% 2.99/1.52 = ( Xf @ Xy ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(image1Ex1_type,type,
% 2.99/1.52 image1Ex1: $o ).
% 2.99/1.52
% 2.99/1.52 thf(image1Ex1,definition,
% 2.99/1.52 ( image1Ex1
% 2.99/1.52 = ( ! [A: $i,Xf: $i > $i] :
% 2.99/1.52 ( exu
% 2.99/1.52 @ ^ [B: $i] :
% 2.99/1.52 ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ B )
% 2.99/1.52 <=> ? [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ A )
% 2.99/1.52 & ( Xx
% 2.99/1.52 = ( Xf @ Xy ) ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(image1_type,type,
% 2.99/1.52 image1: $i > ( $i > $i ) > $i ).
% 2.99/1.52
% 2.99/1.52 thf(image1Equiv_type,type,
% 2.99/1.52 image1Equiv: $o ).
% 2.99/1.52
% 2.99/1.52 thf(image1Equiv,definition,
% 2.99/1.52 ( image1Equiv
% 2.99/1.52 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 2.99/1.52 ( ( in @ Xx
% 2.99/1.52 @ ( image1 @ A
% 2.99/1.52 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 2.99/1.52 <=> ? [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ A )
% 2.99/1.52 & ( Xx
% 2.99/1.52 = ( Xf @ Xy ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(image1E_type,type,
% 2.99/1.52 image1E: $o ).
% 2.99/1.52
% 2.99/1.52 thf(image1E,definition,
% 2.99/1.52 ( image1E
% 2.99/1.52 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 2.99/1.52 ( ( in @ Xx
% 2.99/1.52 @ ( image1 @ A
% 2.99/1.52 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 2.99/1.52 => ? [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ A )
% 2.99/1.52 & ( Xx
% 2.99/1.52 = ( Xf @ Xy ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(image1I_type,type,
% 2.99/1.52 image1I: $o ).
% 2.99/1.52
% 2.99/1.52 thf(image1I,definition,
% 2.99/1.52 ( image1I
% 2.99/1.52 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 2.99/1.52 ( ? [Xy: $i] :
% 2.99/1.52 ( ( in @ Xy @ A )
% 2.99/1.52 & ( Xx
% 2.99/1.52 = ( Xf @ Xy ) ) )
% 2.99/1.52 => ( in @ Xx
% 2.99/1.52 @ ( image1 @ A
% 2.99/1.52 @ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(injective_type,type,
% 2.99/1.52 injective: $i > $i > $i > $o ).
% 2.99/1.52
% 2.99/1.52 thf(injFuncSet_type,type,
% 2.99/1.52 injFuncSet: $i > $i > $i ).
% 2.99/1.52
% 2.99/1.52 thf(injFuncInInjFuncSet_type,type,
% 2.99/1.52 injFuncInInjFuncSet: $o ).
% 2.99/1.52
% 2.99/1.52 thf(injFuncInInjFuncSet,definition,
% 2.99/1.52 ( injFuncInInjFuncSet
% 2.99/1.52 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.52 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.99/1.52 => ( ( injective @ A @ B @ Xf )
% 2.99/1.52 => ( in @ Xf @ ( injFuncSet @ A @ B ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(injFuncSetFuncIn_type,type,
% 2.99/1.52 injFuncSetFuncIn: $o ).
% 2.99/1.52
% 2.99/1.52 thf(injFuncSetFuncIn,definition,
% 2.99/1.52 ( injFuncSetFuncIn
% 2.99/1.52 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.52 ( ( in @ Xf @ ( injFuncSet @ A @ B ) )
% 2.99/1.52 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(injFuncSetFuncInj_type,type,
% 2.99/1.52 injFuncSetFuncInj: $o ).
% 2.99/1.52
% 2.99/1.52 thf(injFuncSetFuncInj,definition,
% 2.99/1.52 ( injFuncSetFuncInj
% 2.99/1.52 = ( ! [Xx: $i,Xy: $i,Xf: $i] :
% 2.99/1.52 ( ( in @ Xf @ ( injFuncSet @ Xx @ Xy ) )
% 2.99/1.52 => ( injective @ Xx @ Xy @ Xf ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(surjective_type,type,
% 2.99/1.52 surjective: $i > $i > $i > $o ).
% 2.99/1.52
% 2.99/1.52 thf(surjFuncSet_type,type,
% 2.99/1.52 surjFuncSet: $i > $i > $i ).
% 2.99/1.52
% 2.99/1.52 thf(surjFuncSetFuncIn_type,type,
% 2.99/1.52 surjFuncSetFuncIn: $o ).
% 2.99/1.52
% 2.99/1.52 thf(surjFuncSetFuncIn,definition,
% 2.99/1.52 ( surjFuncSetFuncIn
% 2.99/1.52 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.52 ( ( in @ Xf @ ( surjFuncSet @ A @ B ) )
% 2.99/1.52 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(surjFuncSetFuncSurj_type,type,
% 2.99/1.52 surjFuncSetFuncSurj: $o ).
% 2.99/1.52
% 2.99/1.52 thf(surjFuncSetFuncSurj,definition,
% 2.99/1.52 ( surjFuncSetFuncSurj
% 2.99/1.52 = ( ! [Xx: $i,Xy: $i,Xf: $i] :
% 2.99/1.52 ( ( in @ Xf @ ( surjFuncSet @ Xx @ Xy ) )
% 2.99/1.52 => ( surjective @ Xx @ Xy @ Xf ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(leftInvIsSurj_type,type,
% 2.99/1.52 leftInvIsSurj: $o ).
% 2.99/1.52
% 2.99/1.52 thf(leftInvIsSurj,definition,
% 2.99/1.52 ( leftInvIsSurj
% 2.99/1.52 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.99/1.52 ( ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.99/1.52 => ! [Xg: $i] :
% 2.99/1.52 ( ( in @ Xg @ ( funcSet @ B @ A ) )
% 2.99/1.52 => ( ! [Xx: $i] :
% 2.99/1.52 ( ( in @ Xx @ A )
% 2.99/1.52 => ( ( ap @ B @ A @ Xg @ ( Xf @ Xx ) )
% 2.99/1.52 = Xx ) )
% 2.99/1.52 => ( surjective @ B @ A @ Xg ) ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(surjCantorThm_type,type,
% 2.99/1.52 surjCantorThm: $o ).
% 2.99/1.52
% 2.99/1.52 thf(surjCantorThm,definition,
% 2.99/1.52 ( surjCantorThm
% 2.99/1.52 = ( ! [A: $i,Xf: $i] :
% 2.99/1.52 ( ( in @ Xf @ ( funcSet @ A @ ( powerset @ A ) ) )
% 2.99/1.52 => ~ ( surjective @ A @ ( powerset @ A ) @ Xf ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(foundation2_type,type,
% 2.99/1.52 foundation2: $o ).
% 2.99/1.52
% 2.99/1.52 thf(foundation2,definition,
% 2.99/1.52 ( foundation2
% 2.99/1.52 = ( ! [A: $i] :
% 2.99/1.52 ( ( nonempty @ A )
% 2.99/1.52 => ? [X: $i] :
% 2.99/1.52 ( ( in @ X @ A )
% 2.99/1.52 & ( ( binintersect @ X @ A )
% 2.99/1.52 = emptyset ) ) ) ) ) ).
% 2.99/1.52
% 2.99/1.52 thf(notinself,conjecture,
% 2.99/1.52 ( setextAx
% 2.99/1.52 => ( emptysetAx
% 2.99/1.52 => ( setadjoinAx
% 2.99/1.52 => ( powersetAx
% 2.99/1.52 => ( setunionAx
% 2.99/1.52 => ( omega0Ax
% 2.99/1.52 => ( omegaSAx
% 2.99/1.52 => ( omegaIndAx
% 2.99/1.52 => ( replAx
% 2.99/1.52 => ( foundationAx
% 2.99/1.52 => ( wellorderingAx
% 2.99/1.52 => ( descrp
% 2.99/1.52 => ( dsetconstrI
% 2.99/1.52 => ( dsetconstrEL
% 2.99/1.52 => ( dsetconstrER
% 2.99/1.52 => ( exuE1
% 2.99/1.52 => ( prop2setE
% 2.99/1.52 => ( emptysetE
% 2.99/1.52 => ( emptysetimpfalse
% 2.99/1.52 => ( notinemptyset
% 2.99/1.52 => ( exuE3e
% 2.99/1.52 => ( setext
% 2.99/1.52 => ( emptyI
% 2.99/1.52 => ( noeltsimpempty
% 2.99/1.52 => ( setbeta
% 2.99/1.52 => ( nonemptyE1
% 2.99/1.52 => ( nonemptyI
% 2.99/1.52 => ( nonemptyI1
% 2.99/1.52 => ( setadjoinIL
% 2.99/1.52 => ( emptyinunitempty
% 2.99/1.52 => ( setadjoinIR
% 2.99/1.52 => ( setadjoinE
% 2.99/1.52 => ( setadjoinOr
% 2.99/1.52 => ( setoftrueEq
% 2.99/1.52 => ( powersetI
% 2.99/1.52 => ( emptyinPowerset
% 2.99/1.52 => ( emptyInPowerset
% 2.99/1.52 => ( powersetE
% 2.99/1.52 => ( setunionI
% 2.99/1.52 => ( setunionE
% 2.99/1.52 => ( subPowSU
% 2.99/1.52 => ( exuE2
% 2.99/1.52 => ( nonemptyImpWitness
% 2.99/1.52 => ( uniqinunit
% 2.99/1.52 => ( notinsingleton
% 2.99/1.52 => ( eqinunit
% 2.99/1.52 => ( singletonsswitch
% 2.99/1.52 => ( upairsetE
% 2.99/1.52 => ( upairsetIL
% 2.99/1.52 => ( upairsetIR
% 2.99/1.52 => ( emptyE1
% 2.99/1.52 => ( vacuousDall
% 2.99/1.52 => ( quantDeMorgan1
% 2.99/1.52 => ( quantDeMorgan2
% 2.99/1.52 => ( quantDeMorgan3
% 2.99/1.52 => ( quantDeMorgan4
% 2.99/1.52 => ( prop2setI
% 2.99/1.52 => ( prop2set2propI
% 2.99/1.52 => ( notdexE
% 2.99/1.52 => ( notdallE
% 2.99/1.52 => ( exuI1
% 2.99/1.52 => ( exuI3
% 2.99/1.52 => ( exuI2
% 2.99/1.52 => ( inCongP
% 2.99/1.52 => ( in__Cong
% 2.99/1.52 => ( exuE3u
% 2.99/1.52 => ( exu__Cong
% 2.99/1.52 => ( emptyset__Cong
% 2.99/1.52 => ( setadjoin__Cong
% 2.99/1.52 => ( powerset__Cong
% 2.99/1.52 => ( setunion__Cong
% 2.99/1.52 => ( omega__Cong
% 2.99/1.52 => ( exuEu
% 2.99/1.52 => ( descr__Cong
% 2.99/1.52 => ( dsetconstr__Cong
% 2.99/1.52 => ( subsetI1
% 2.99/1.52 => ( eqimpsubset2
% 2.99/1.52 => ( eqimpsubset1
% 2.99/1.52 => ( subsetI2
% 2.99/1.52 => ( emptysetsubset
% 2.99/1.52 => ( subsetE
% 2.99/1.52 => ( subsetE2
% 2.99/1.52 => ( notsubsetI
% 2.99/1.52 => ( notequalI1
% 2.99/1.52 => ( notequalI2
% 2.99/1.52 => ( subsetRefl
% 2.99/1.52 => ( subsetTrans
% 2.99/1.52 => ( setadjoinSub
% 2.99/1.52 => ( setadjoinSub2
% 2.99/1.52 => ( subset2powerset
% 2.99/1.52 => ( setextsub
% 2.99/1.52 => ( subsetemptysetimpeq
% 2.99/1.52 => ( powersetI1
% 2.99/1.52 => ( powersetE1
% 2.99/1.52 => ( inPowerset
% 2.99/1.52 => ( powersetsubset
% 2.99/1.52 => ( sepInPowerset
% 2.99/1.52 => ( sepSubset
% 2.99/1.52 => ( binunionIL
% 2.99/1.52 => ( upairset2IR
% 2.99/1.52 => ( binunionIR
% 2.99/1.52 => ( binunionEcases
% 2.99/1.52 => ( binunionE
% 2.99/1.52 => ( binunionLsub
% 2.99/1.52 => ( binunionRsub
% 2.99/1.52 => ( binintersectI
% 2.99/1.52 => ( binintersectSubset5
% 2.99/1.52 => ( binintersectEL
% 2.99/1.52 => ( binintersectLsub
% 2.99/1.52 => ( binintersectSubset2
% 2.99/1.52 => ( binintersectSubset3
% 2.99/1.52 => ( binintersectER
% 2.99/1.52 => ( disjointsetsI1
% 2.99/1.52 => ( binintersectRsub
% 2.99/1.52 => ( binintersectSubset4
% 2.99/1.52 => ( binintersectSubset1
% 2.99/1.52 => ( bs114d
% 2.99/1.52 => ( setminusI
% 2.99/1.52 => ( setminusEL
% 2.99/1.52 => ( setminusER
% 2.99/1.52 => ( setminusSubset2
% 2.99/1.52 => ( setminusERneg
% 2.99/1.52 => ( setminusELneg
% 2.99/1.52 => ( setminusILneg
% 2.99/1.52 => ( setminusIRneg
% 2.99/1.52 => ( setminusLsub
% 2.99/1.52 => ( setminusSubset1
% 2.99/1.52 => ( symdiffE
% 2.99/1.52 => ( symdiffI1
% 2.99/1.52 => ( symdiffI2
% 2.99/1.52 => ( symdiffIneg1
% 2.99/1.52 => ( symdiffIneg2
% 2.99/1.52 => ( secondinupair
% 2.99/1.52 => ( setukpairIL
% 2.99/1.52 => ( setukpairIR
% 2.99/1.52 => ( kpairiskpair
% 2.99/1.52 => ( kpairp
% 2.99/1.52 => ( singletonsubset
% 2.99/1.52 => ( singletoninpowerset
% 2.99/1.52 => ( singletoninpowunion
% 2.99/1.52 => ( upairset2E
% 2.99/1.52 => ( upairsubunion
% 2.99/1.52 => ( upairinpowunion
% 2.99/1.52 => ( ubforcartprodlem1
% 2.99/1.52 => ( ubforcartprodlem2
% 2.99/1.52 => ( ubforcartprodlem3
% 2.99/1.52 => ( cartprodpairin
% 2.99/1.52 => ( cartprodmempair1
% 2.99/1.52 => ( cartprodmempair
% 2.99/1.52 => ( setunionE2
% 2.99/1.52 => ( setunionsingleton1
% 2.99/1.52 => ( setunionsingleton2
% 2.99/1.52 => ( setunionsingleton
% 2.99/1.52 => ( singletonprop
% 2.99/1.52 => ( ex1E1
% 2.99/1.52 => ( ex1I
% 2.99/1.52 => ( ex1I2
% 2.99/1.52 => ( singletonsuniq
% 2.99/1.52 => ( setukpairinjL1
% 2.99/1.52 => ( kfstsingleton
% 2.99/1.52 => ( theprop
% 2.99/1.52 => ( kfstpairEq
% 2.99/1.52 => ( cartprodfstin
% 2.99/1.52 => ( setukpairinjL2
% 2.99/1.52 => ( setukpairinjL
% 2.99/1.52 => ( setukpairinjR11
% 2.99/1.52 => ( setukpairinjR12
% 2.99/1.52 => ( setukpairinjR1
% 2.99/1.52 => ( upairequniteq
% 2.99/1.52 => ( setukpairinjR2
% 2.99/1.52 => ( setukpairinjR
% 2.99/1.52 => ( ksndsingleton
% 2.99/1.52 => ( ksndpairEq
% 2.99/1.52 => ( kpairsurjEq
% 2.99/1.52 => ( cartprodsndin
% 2.99/1.52 => ( cartprodpairmemEL
% 2.99/1.52 => ( cartprodpairmemER
% 2.99/1.52 => ( cartprodmempaircEq
% 2.99/1.52 => ( cartprodfstpairEq
% 2.99/1.52 => ( cartprodsndpairEq
% 2.99/1.52 => ( cartprodpairsurjEq
% 2.99/1.52 => ( dpsetconstrI
% 2.99/1.52 => ( dpsetconstrSub
% 2.99/1.52 => ( setOfPairsIsBReln
% 2.99/1.52 => ( dpsetconstrERa
% 2.99/1.52 => ( dpsetconstrEL1
% 2.99/1.52 => ( dpsetconstrEL2
% 2.99/1.52 => ( dpsetconstrER
% 2.99/1.52 => ( funcImageSingleton
% 2.99/1.52 => ( apProp
% 2.99/1.52 => ( app
% 2.99/1.52 => ( infuncsetfunc
% 2.99/1.52 => ( ap2p
% 2.99/1.52 => ( funcinfuncset
% 2.99/1.52 => ( lamProp
% 2.99/1.52 => ( lamp
% 2.99/1.52 => ( lam2p
% 2.99/1.52 => ( brelnall1
% 2.99/1.52 => ( brelnall2
% 2.99/1.52 => ( ex1E2
% 2.99/1.52 => ( funcGraphProp1
% 2.99/1.52 => ( funcGraphProp3
% 2.99/1.52 => ( funcGraphProp2
% 2.99/1.52 => ( funcextLem
% 2.99/1.52 => ( funcGraphProp4
% 2.99/1.52 => ( subbreln
% 2.99/1.52 => ( eqbreln
% 2.99/1.52 => ( funcext
% 2.99/1.52 => ( funcext2
% 2.99/1.52 => ( ap2apEq1
% 2.99/1.52 => ( ap2apEq2
% 2.99/1.52 => ( beta1
% 2.99/1.52 => ( eta1
% 2.99/1.52 => ( lam2lamEq
% 2.99/1.52 => ( beta2
% 2.99/1.52 => ( eta2
% 2.99/1.52 => ( iffalseProp1
% 2.99/1.52 => ( iffalseProp2
% 2.99/1.52 => ( iftrueProp1
% 2.99/1.52 => ( iftrueProp2
% 2.99/1.52 => ( ifSingleton
% 2.99/1.52 => ( ifp
% 2.99/1.52 => ( theeq
% 2.99/1.52 => ( iftrue
% 2.99/1.52 => ( iffalse
% 2.99/1.52 => ( iftrueorfalse
% 2.99/1.52 => ( binintersectT_lem
% 2.99/1.52 => ( binunionT_lem
% 2.99/1.52 => ( powersetT_lem
% 2.99/1.52 => ( setminusT_lem
% 2.99/1.52 => ( complementT_lem
% 2.99/1.52 => ( setextT
% 2.99/1.52 => ( subsetTI
% 2.99/1.52 => ( powersetTI1
% 2.99/1.52 => ( powersetTE1
% 2.99/1.52 => ( complementTI1
% 2.99/1.52 => ( complementTE1
% 2.99/1.52 => ( binintersectTELcontra
% 2.99/1.52 => ( binintersectTERcontra
% 2.99/1.52 => ( contrasubsetT
% 2.99/1.52 => ( contrasubsetT1
% 2.99/1.52 => ( contrasubsetT2
% 2.99/1.52 => ( contrasubsetT3
% 2.99/1.52 => ( doubleComplementI1
% 2.99/1.52 => ( doubleComplementE1
% 2.99/1.52 => ( doubleComplementSub1
% 2.99/1.52 => ( doubleComplementSub2
% 2.99/1.52 => ( doubleComplementEq
% 2.99/1.52 => ( complementTnotintersectT
% 2.99/1.52 => ( complementImpComplementIntersect
% 2.99/1.52 => ( complementSubsetComplementIntersect
% 2.99/1.52 => ( complementInPowersetComplementIntersect
% 2.99/1.52 => ( contraSubsetComplement
% 2.99/1.52 => ( complementTcontraSubset
% 2.99/1.52 => ( binunionTILcontra
% 2.99/1.52 => ( binunionTIRcontra
% 2.99/1.52 => ( inIntersectImpInUnion
% 2.99/1.52 => ( inIntersectImpInUnion2
% 2.99/1.52 => ( inIntersectImpInIntersectUnions
% 2.99/1.52 => ( intersectInPowersetIntersectUnions
% 2.99/1.52 => ( inComplementUnionImpNotIn1
% 2.99/1.52 => ( inComplementUnionImpInComplement1
% 2.99/1.52 => ( binunionTE
% 2.99/1.52 => ( binunionTEcontra
% 2.99/1.52 => ( demorgan2a1
% 2.99/1.52 => ( complementUnionInPowersetComplement
% 2.99/1.52 => ( demorgan2a2
% 2.99/1.52 => ( demorgan1a
% 2.99/1.52 => ( demorgan1b
% 2.99/1.52 => ( demorgan1
% 2.99/1.52 => ( demorgan2a
% 2.99/1.52 => ( demorgan2b2
% 2.99/1.52 => ( demorgan2b
% 2.99/1.52 => ( demorgan2
% 2.99/1.52 => ( woz13rule0
% 2.99/1.52 => ( woz13rule1
% 2.99/1.52 => ( woz13rule2
% 2.99/1.52 => ( woz13rule3
% 2.99/1.52 => ( woz13rule4
% 2.99/1.52 => ( woz1_1
% 2.99/1.52 => ( woz1_2
% 2.99/1.52 => ( woz1_3
% 2.99/1.52 => ( woz1_4
% 2.99/1.52 => ( woz1_5
% 2.99/1.52 => ( breln1all2
% 2.99/1.52 => ( breln1SetBreln1
% 2.99/1.52 => ( choice2fnsingleton
% 2.99/1.52 => ( setOfPairsIsBReln1
% 2.99/1.52 => ( breln1all1
% 2.99/1.52 => ( subbreln1
% 2.99/1.52 => ( eqbreln1
% 2.99/1.52 => ( breln1invprop
% 2.99/1.52 => ( breln1invI
% 2.99/1.52 => ( breln1invE
% 2.99/1.52 => ( breln1compprop
% 2.99/1.52 => ( breln1compI
% 2.99/1.52 => ( breln1compE
% 2.99/1.52 => ( breln1compEex
% 2.99/1.52 => ( breln1unionprop
% 2.99/1.52 => ( breln1unionIL
% 2.99/1.52 => ( breln1unionIR
% 2.99/1.52 => ( breln1unionI
% 2.99/1.52 => ( breln1unionE
% 2.99/1.52 => ( breln1unionEcases
% 2.99/1.52 => ( breln1unionCommutes
% 2.99/1.52 => ( woz2Ex
% 2.99/1.52 => ( woz2W
% 2.99/1.52 => ( woz2A
% 2.99/1.52 => ( woz2B
% 2.99/1.52 => ( image1Ex
% 2.99/1.52 => ( image1Ex1
% 2.99/1.52 => ( image1Equiv
% 2.99/1.52 => ( image1E
% 2.99/1.52 => ( image1I
% 2.99/1.52 => ( injFuncInInjFuncSet
% 2.99/1.52 => ( injFuncSetFuncIn
% 2.99/1.52 => ( injFuncSetFuncInj
% 2.99/1.52 => ( surjFuncSetFuncIn
% 2.99/1.52 => ( surjFuncSetFuncSurj
% 2.99/1.52 => ( leftInvIsSurj
% 2.99/1.52 => ( surjCantorThm
% 2.99/1.52 => ( foundation2
% 2.99/1.52 => ! [A: $i] :
% 2.99/1.52 ~ ( in @ A @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.52 ------------------------
% 2.99/1.55 % (4702)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4600 for (2999ds/183Mi)
% 2.99/1.55 % (4706)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_4600 for (2999ds/2Mi)
% 2.99/1.55 % (4704)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_4600 for (2999ds/27Mi)
% 2.99/1.55 % (4703)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_4600 for (2999ds/4Mi)
% 2.99/1.55 % (4708)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4600 for (2999ds/18Mi)
% 2.99/1.55 % (4707)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_4600 for (2999ds/275Mi)
% 2.99/1.55 % (4705)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4600 for (2999ds/2Mi)
% 2.99/1.56 % (4705)Instruction limit reached!
% 2.99/1.56 % (4705)------------------------------
% 2.99/1.56 % (4705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.56 % (4705)Termination reason: Unknown
% 2.99/1.56 % (4706)Instruction limit reached!
% 2.99/1.56 % (4706)------------------------------
% 2.99/1.56 % (4706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.56 % (4705)Termination phase: shuffling
% 2.99/1.56
% 2.99/1.56 % (4705)Memory used [KB]: 1663
% 2.99/1.56 % (4705)Time elapsed: 0.003 s
% 2.99/1.56 % (4705)Instructions burned: 2 (million)
% 2.99/1.56 % (4705)------------------------------
% 2.99/1.56 % (4705)------------------------------
% 2.99/1.56 % (4706)Termination reason: Unknown
% 2.99/1.56 % (4706)Termination phase: shuffling
% 2.99/1.56
% 2.99/1.56 % (4706)Memory used [KB]: 1663
% 2.99/1.56 % (4706)Time elapsed: 0.003 s
% 2.99/1.56 % (4706)Instructions burned: 3 (million)
% 2.99/1.56 % (4706)------------------------------
% 2.99/1.56 % (4706)------------------------------
% 2.99/1.56 % (4703)Instruction limit reached!
% 2.99/1.56 % (4703)------------------------------
% 2.99/1.56 % (4703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.56 % (4703)Termination reason: Unknown
% 2.99/1.56 % (4703)Termination phase: shuffling
% 2.99/1.56
% 2.99/1.56 % (4703)Memory used [KB]: 1663
% 2.99/1.56 % (4703)Time elapsed: 0.004 s
% 2.99/1.56 % (4703)Instructions burned: 5 (million)
% 2.99/1.56 % (4703)------------------------------
% 2.99/1.56 % (4703)------------------------------
% 2.99/1.56 % (4708)Instruction limit reached!
% 2.99/1.56 % (4708)------------------------------
% 2.99/1.56 % (4708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.56 % (4708)Termination reason: Unknown
% 2.99/1.56 % (4708)Termination phase: shuffling
% 2.99/1.56
% 2.99/1.56 % (4708)Memory used [KB]: 1918
% 2.99/1.56 % (4708)Time elapsed: 0.011 s
% 2.99/1.56 % (4708)Instructions burned: 19 (million)
% 2.99/1.56 % (4708)------------------------------
% 2.99/1.56 % (4708)------------------------------
% 2.99/1.57 % (4704)Instruction limit reached!
% 2.99/1.57 % (4704)------------------------------
% 2.99/1.57 % (4704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.57 % (4704)Termination reason: Unknown
% 2.99/1.57 % (4704)Termination phase: shuffling
% 2.99/1.57
% 2.99/1.57 % (4704)Memory used [KB]: 2046
% 2.99/1.57 % (4704)Time elapsed: 0.014 s
% 2.99/1.57 % (4704)Instructions burned: 27 (million)
% 2.99/1.57 % (4704)------------------------------
% 2.99/1.57 % (4704)------------------------------
% 2.99/1.57 % (4711)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_4600 for (2999ds/37Mi)
% 2.99/1.57 % (4710)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_4600 for (2999ds/3Mi)
% 2.99/1.57 % (4712)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_4600 for (2999ds/15Mi)
% 2.99/1.57 % (4710)Instruction limit reached!
% 2.99/1.57 % (4710)------------------------------
% 2.99/1.57 % (4710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.57 % (4710)Termination reason: Unknown
% 2.99/1.57 % (4710)Termination phase: shuffling
% 2.99/1.57
% 2.99/1.57 % (4710)Memory used [KB]: 1663
% 2.99/1.57 % (4710)Time elapsed: 0.003 s
% 2.99/1.57 % (4710)Instructions burned: 3 (million)
% 2.99/1.57 % (4710)------------------------------
% 2.99/1.57 % (4710)------------------------------
% 2.99/1.58 % (4713)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_4600 for (2999ds/3Mi)
% 2.99/1.58 % (4712)Instruction limit reached!
% 2.99/1.58 % (4712)------------------------------
% 2.99/1.58 % (4712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.58 % (4712)Termination reason: Unknown
% 2.99/1.58 % (4712)Termination phase: shuffling
% 2.99/1.58
% 2.99/1.58 % (4712)Memory used [KB]: 1791
% 2.99/1.58 % (4712)Time elapsed: 0.009 s
% 2.99/1.58 % (4712)Instructions burned: 15 (million)
% 2.99/1.58 % (4712)------------------------------
% 2.99/1.58 % (4712)------------------------------
% 2.99/1.58 % (4713)Instruction limit reached!
% 2.99/1.58 % (4713)------------------------------
% 2.99/1.58 % (4713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.58 % (4713)Termination reason: Unknown
% 2.99/1.58 % (4713)Termination phase: shuffling
% 2.99/1.58
% 2.99/1.58 % (4713)Memory used [KB]: 1663
% 2.99/1.58 % (4713)Time elapsed: 0.003 s
% 2.99/1.58 % (4713)Instructions burned: 3 (million)
% 2.99/1.58 % (4713)------------------------------
% 2.99/1.58 % (4713)------------------------------
% 2.99/1.58 % (4714)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_4600 for (2999ds/1041Mi)
% 2.99/1.59 % (4711)Instruction limit reached!
% 2.99/1.59 % (4711)------------------------------
% 2.99/1.59 % (4711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.59 % (4711)Termination reason: Unknown
% 2.99/1.59 % (4711)Termination phase: shuffling
% 2.99/1.59
% 2.99/1.59 % (4711)Memory used [KB]: 2302
% 2.99/1.59 % (4711)Time elapsed: 0.018 s
% 2.99/1.59 % (4711)Instructions burned: 37 (million)
% 2.99/1.59 % (4711)------------------------------
% 2.99/1.59 % (4711)------------------------------
% 2.99/1.59 % (4716)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_4600 for (2999ds/7Mi)
% 2.99/1.59 % (4716)Instruction limit reached!
% 2.99/1.59 % (4716)------------------------------
% 2.99/1.59 % (4716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.99/1.59 % (4716)Termination reason: Unknown
% 2.99/1.59 % (4716)Termination phase: shuffling
% 2.99/1.59
% 2.99/1.59 % (4716)Memory used [KB]: 1663
% 2.99/1.59 % (4716)Time elapsed: 0.005 s
% 2.99/1.59 % (4716)Instructions burned: 8 (million)
% 2.99/1.59 % (4716)------------------------------
% 2.99/1.59 % (4716)------------------------------
% 3.03/1.60 % (4702)Instruction limit reached!
% 3.03/1.60 % (4702)------------------------------
% 3.03/1.60 % (4702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.60 % (4702)Termination reason: Unknown
% 3.03/1.60 % (4702)Termination phase: Property scanning
% 3.03/1.60
% 3.03/1.60 % (4702)Memory used [KB]: 3070
% 3.03/1.60 % (4702)Time elapsed: 0.050 s
% 3.03/1.60 % (4702)Instructions burned: 186 (million)
% 3.03/1.60 % (4702)------------------------------
% 3.03/1.60 % (4702)------------------------------
% 3.03/1.60 % (4718)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_4600 for (2999ds/3Mi)
% 3.03/1.60 % (4717)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_4600 for (2999ds/16Mi)
% 3.03/1.60 % (4718)Instruction limit reached!
% 3.03/1.60 % (4718)------------------------------
% 3.03/1.60 % (4718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.60 % (4718)Termination reason: Unknown
% 3.03/1.60 % (4718)Termination phase: shuffling
% 3.03/1.60
% 3.03/1.60 % (4718)Memory used [KB]: 1663
% 3.03/1.60 % (4718)Time elapsed: 0.004 s
% 3.03/1.60 % (4718)Instructions burned: 5 (million)
% 3.03/1.60 % (4718)------------------------------
% 3.03/1.60 % (4718)------------------------------
% 3.03/1.61 % (4717)Instruction limit reached!
% 3.03/1.61 % (4717)------------------------------
% 3.03/1.61 % (4717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.61 % (4717)Termination reason: Unknown
% 3.03/1.61 % (4717)Termination phase: shuffling
% 3.03/1.61
% 3.03/1.61 % (4717)Memory used [KB]: 1918
% 3.03/1.61 % (4717)Time elapsed: 0.009 s
% 3.03/1.61 % (4717)Instructions burned: 16 (million)
% 3.03/1.61 % (4717)------------------------------
% 3.03/1.61 % (4717)------------------------------
% 3.03/1.61 % (4721)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_4600 for (2999ds/3Mi)
% 3.03/1.61 % (4721)Instruction limit reached!
% 3.03/1.61 % (4721)------------------------------
% 3.03/1.61 % (4721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.61 % (4721)Termination reason: Unknown
% 3.03/1.61 % (4721)Termination phase: shuffling
% 3.03/1.61
% 3.03/1.61 % (4721)Memory used [KB]: 1663
% 3.03/1.61 % (4721)Time elapsed: 0.002 s
% 3.03/1.61 % (4721)Instructions burned: 3 (million)
% 3.03/1.61 % (4721)------------------------------
% 3.03/1.61 % (4721)------------------------------
% 3.03/1.61 % (4720)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_4600 for (2999ds/7Mi)
% 3.03/1.61 % (4719)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_4600 for (2999ds/3Mi)
% 3.03/1.61 % (4719)Instruction limit reached!
% 3.03/1.61 % (4719)------------------------------
% 3.03/1.61 % (4719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.61 % (4719)Termination reason: Unknown
% 3.03/1.61 % (4719)Termination phase: shuffling
% 3.03/1.61
% 3.03/1.61 % (4719)Memory used [KB]: 1663
% 3.03/1.61 % (4719)Time elapsed: 0.003 s
% 3.03/1.61 % (4719)Instructions burned: 3 (million)
% 3.03/1.61 % (4719)------------------------------
% 3.03/1.61 % (4719)------------------------------
% 3.03/1.61 % (4720)Instruction limit reached!
% 3.03/1.61 % (4720)------------------------------
% 3.03/1.61 % (4720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.61 % (4720)Termination reason: Unknown
% 3.03/1.61 % (4720)Termination phase: shuffling
% 3.03/1.61
% 3.03/1.61 % (4720)Memory used [KB]: 1663
% 3.03/1.61 % (4720)Time elapsed: 0.005 s
% 3.03/1.61 % (4720)Instructions burned: 8 (million)
% 3.03/1.61 % (4720)------------------------------
% 3.03/1.61 % (4720)------------------------------
% 3.03/1.62 % (4722)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_4600 for (2999ds/4Mi)
% 3.03/1.62 % (4723)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_4600 for (2999ds/18Mi)
% 3.03/1.62 % (4722)Instruction limit reached!
% 3.03/1.62 % (4722)------------------------------
% 3.03/1.62 % (4722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.62 % (4722)Termination reason: Unknown
% 3.03/1.62 % (4722)Termination phase: shuffling
% 3.03/1.62
% 3.03/1.62 % (4722)Memory used [KB]: 1663
% 3.03/1.62 % (4722)Time elapsed: 0.004 s
% 3.03/1.62 % (4722)Instructions burned: 5 (million)
% 3.03/1.62 % (4722)------------------------------
% 3.03/1.62 % (4722)------------------------------
% 3.03/1.62 % (4723)Instruction limit reached!
% 3.03/1.62 % (4723)------------------------------
% 3.03/1.62 % (4723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.62 % (4723)Termination reason: Unknown
% 3.03/1.62 % (4723)Termination phase: shuffling
% 3.03/1.62
% 3.03/1.62 % (4723)Memory used [KB]: 1918
% 3.03/1.62 % (4723)Time elapsed: 0.006 s
% 3.03/1.62 % (4723)Instructions burned: 18 (million)
% 3.03/1.62 % (4723)------------------------------
% 3.03/1.62 % (4723)------------------------------
% 3.03/1.62 % (4724)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_4600 for (2999ds/710Mi)
% 3.03/1.63 % (4725)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_4600 for (2999ds/6Mi)
% 3.03/1.63 % (4726)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_4600 for (2999ds/902Mi)
% 3.03/1.63 % (4725)Instruction limit reached!
% 3.03/1.63 % (4725)------------------------------
% 3.03/1.63 % (4725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.63 % (4725)Termination reason: Unknown
% 3.03/1.63 % (4725)Termination phase: shuffling
% 3.03/1.63
% 3.03/1.63 % (4725)Memory used [KB]: 1663
% 3.03/1.63 % (4725)Time elapsed: 0.004 s
% 3.03/1.63 % (4725)Instructions burned: 6 (million)
% 3.03/1.63 % (4725)------------------------------
% 3.03/1.63 % (4725)------------------------------
% 3.03/1.63 % (4728)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_4600 for (2999ds/5Mi)
% 3.03/1.63 % (4728)Instruction limit reached!
% 3.03/1.63 % (4728)------------------------------
% 3.03/1.63 % (4728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.63 % (4728)Termination reason: Unknown
% 3.03/1.63 % (4728)Termination phase: shuffling
% 3.03/1.63
% 3.03/1.63 % (4728)Memory used [KB]: 1663
% 3.03/1.63 % (4728)Time elapsed: 0.003 s
% 3.03/1.63 % (4728)Instructions burned: 7 (million)
% 3.03/1.63 % (4728)------------------------------
% 3.03/1.63 % (4728)------------------------------
% 3.03/1.63 % (4727)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_4600 for (2999ds/21Mi)
% 3.03/1.64 % (4730)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_4600 for (2999ds/377Mi)
% 3.03/1.64 % (4727)Instruction limit reached!
% 3.03/1.64 % (4727)------------------------------
% 3.03/1.64 % (4727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.64 % (4727)Termination reason: Unknown
% 3.03/1.64 % (4727)Termination phase: shuffling
% 3.03/1.64
% 3.03/1.64 % (4727)Memory used [KB]: 1918
% 3.03/1.64 % (4727)Time elapsed: 0.011 s
% 3.03/1.64 % (4727)Instructions burned: 21 (million)
% 3.03/1.64 % (4727)------------------------------
% 3.03/1.64 % (4727)------------------------------
% 3.03/1.65 % (4729)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_4600 for (2999ds/6Mi)
% 3.03/1.65 % (4729)Instruction limit reached!
% 3.03/1.65 % (4729)------------------------------
% 3.03/1.65 % (4729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.65 % (4729)Termination reason: Unknown
% 3.03/1.65 % (4729)Termination phase: shuffling
% 3.03/1.65
% 3.03/1.65 % (4729)Memory used [KB]: 1663
% 3.03/1.65 % (4729)Time elapsed: 0.004 s
% 3.03/1.65 % (4729)Instructions burned: 6 (million)
% 3.03/1.65 % (4729)------------------------------
% 3.03/1.65 % (4729)------------------------------
% 3.03/1.66 % (4731)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_4600 for (2998ds/779Mi)
% 3.03/1.66 % (4732)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_4600 for (2998ds/19Mi)
% 3.03/1.67 % (4732)Instruction limit reached!
% 3.03/1.67 % (4732)------------------------------
% 3.03/1.67 % (4732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.67 % (4732)Termination reason: Unknown
% 3.03/1.67 % (4732)Termination phase: shuffling
% 3.03/1.67
% 3.03/1.67 % (4732)Memory used [KB]: 1918
% 3.03/1.67 % (4732)Time elapsed: 0.010 s
% 3.03/1.67 % (4732)Instructions burned: 19 (million)
% 3.03/1.67 % (4732)------------------------------
% 3.03/1.67 % (4732)------------------------------
% 3.03/1.68 % (4707)Instruction limit reached!
% 3.03/1.68 % (4707)------------------------------
% 3.03/1.68 % (4707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.68 % (4707)Termination reason: Unknown
% 3.03/1.68 % (4707)Termination phase: Saturation
% 3.03/1.68
% 3.03/1.68 % (4707)Memory used [KB]: 6012
% 3.03/1.68 % (4707)Time elapsed: 0.128 s
% 3.03/1.68 % (4707)Instructions burned: 276 (million)
% 3.03/1.68 % (4707)------------------------------
% 3.03/1.68 % (4707)------------------------------
% 3.03/1.69 % (4733)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_4600 for (2998ds/879Mi)
% 3.03/1.70 % (4734)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_4600 for (2998ds/17Mi)
% 3.03/1.71 % (4734)Instruction limit reached!
% 3.03/1.71 % (4734)------------------------------
% 3.03/1.71 % (4734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.71 % (4734)Termination reason: Unknown
% 3.03/1.71 % (4734)Termination phase: shuffling
% 3.03/1.71
% 3.03/1.71 % (4734)Memory used [KB]: 1918
% 3.03/1.71 % (4734)Time elapsed: 0.010 s
% 3.03/1.71 % (4734)Instructions burned: 18 (million)
% 3.03/1.71 % (4734)------------------------------
% 3.03/1.71 % (4734)------------------------------
% 3.03/1.72 % (4735)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_4600 for (2998ds/3Mi)
% 3.03/1.72 % (4735)Instruction limit reached!
% 3.03/1.72 % (4735)------------------------------
% 3.03/1.72 % (4735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.72 % (4735)Termination reason: Unknown
% 3.03/1.72 % (4735)Termination phase: shuffling
% 3.03/1.72
% 3.03/1.72 % (4735)Memory used [KB]: 1663
% 3.03/1.72 % (4735)Time elapsed: 0.004 s
% 3.03/1.72 % (4735)Instructions burned: 5 (million)
% 3.03/1.72 % (4735)------------------------------
% 3.03/1.72 % (4735)------------------------------
% 3.03/1.74 % (4736)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_4600 for (2997ds/30Mi)
% 3.03/1.76 % (4736)Instruction limit reached!
% 3.03/1.76 % (4736)------------------------------
% 3.03/1.76 % (4736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.76 % (4736)Termination reason: Unknown
% 3.03/1.76 % (4736)Termination phase: shuffling
% 3.03/1.76
% 3.03/1.76 % (4736)Memory used [KB]: 2302
% 3.03/1.76 % (4736)Time elapsed: 0.016 s
% 3.03/1.76 % (4736)Instructions burned: 31 (million)
% 3.03/1.76 % (4736)------------------------------
% 3.03/1.76 % (4736)------------------------------
% 3.03/1.77 % (4730)Instruction limit reached!
% 3.03/1.77 % (4730)------------------------------
% 3.03/1.77 % (4730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.77 % (4730)Termination reason: Unknown
% 3.03/1.77 % (4730)Termination phase: Saturation
% 3.03/1.77
% 3.03/1.77 % (4730)Memory used [KB]: 9594
% 3.03/1.77 % (4730)Time elapsed: 0.127 s
% 3.03/1.77 % (4730)Instructions burned: 377 (million)
% 3.03/1.77 % (4730)------------------------------
% 3.03/1.77 % (4730)------------------------------
% 3.03/1.78 % (4737)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_4600 for (2997ds/127Mi)
% 3.03/1.79 % (4738)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_4600 for (2997ds/100Mi)
% 3.03/1.83 % (4738)Instruction limit reached!
% 3.03/1.83 % (4738)------------------------------
% 3.03/1.83 % (4738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.83 % (4738)Termination reason: Unknown
% 3.03/1.83 % (4738)Termination phase: shuffling
% 3.03/1.83
% 3.03/1.83 % (4738)Memory used [KB]: 2814
% 3.03/1.83 % (4738)Time elapsed: 0.047 s
% 3.03/1.83 % (4738)Instructions burned: 100 (million)
% 3.03/1.83 % (4738)------------------------------
% 3.03/1.83 % (4738)------------------------------
% 3.03/1.85 % (4739)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_4600 for (2996ds/3Mi)
% 3.03/1.85 % (4739)Instruction limit reached!
% 3.03/1.85 % (4739)------------------------------
% 3.03/1.85 % (4739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.85 % (4739)Termination reason: Unknown
% 3.03/1.85 % (4739)Termination phase: shuffling
% 3.03/1.85
% 3.03/1.85 % (4739)Memory used [KB]: 1663
% 3.03/1.85 % (4739)Time elapsed: 0.004 s
% 3.03/1.85 % (4739)Instructions burned: 4 (million)
% 3.03/1.85 % (4739)------------------------------
% 3.03/1.85 % (4739)------------------------------
% 3.03/1.85 % (4726)Refutation not found, incomplete strategy
% 3.03/1.85 % (4726)------------------------------
% 3.03/1.85 % (4726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.85 % (4737)Instruction limit reached!
% 3.03/1.85 % (4737)------------------------------
% 3.03/1.85 % (4737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.85 % (4726)Termination reason: Refutation not found, incomplete strategy
% 3.03/1.85
% 3.03/1.85 % (4737)Termination reason: Unknown
% 3.03/1.85
% 3.03/1.85 % (4726)Memory used [KB]: 11257
% 3.03/1.85 % (4737)Termination phase: Property scanning
% 3.03/1.85
% 3.03/1.85 % (4726)Time elapsed: 0.227 s
% 3.03/1.85 % (4737)Memory used [KB]: 2942
% 3.03/1.85 % (4726)Instructions burned: 471 (million)
% 3.03/1.85 % (4737)Time elapsed: 0.038 s
% 3.03/1.85 % (4726)------------------------------
% 3.03/1.85 % (4726)------------------------------
% 3.03/1.85 % (4737)Instructions burned: 127 (million)
% 3.03/1.85 % (4737)------------------------------
% 3.03/1.85 % (4737)------------------------------
% 3.03/1.87 % (4740)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_4600 for (2996ds/20Mi)
% 3.03/1.87 % (4741)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_4600 for (2996ds/86Mi)
% 3.03/1.87 % (4742)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_4600 for (2996ds/107Mi)
% 3.03/1.88 % (4740)Instruction limit reached!
% 3.03/1.88 % (4740)------------------------------
% 3.03/1.88 % (4740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.88 % (4740)Termination reason: Unknown
% 3.03/1.88 % (4740)Termination phase: shuffling
% 3.03/1.88
% 3.03/1.88 % (4740)Memory used [KB]: 1918
% 3.03/1.88 % (4740)Time elapsed: 0.012 s
% 3.03/1.88 % (4740)Instructions burned: 20 (million)
% 3.03/1.88 % (4740)------------------------------
% 3.03/1.88 % (4740)------------------------------
% 3.03/1.89 % (4743)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_4600 for (2996ds/39Mi)
% 3.03/1.91 % (4731)Instruction limit reached!
% 3.03/1.91 % (4731)------------------------------
% 3.03/1.91 % (4731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.91 % (4731)Termination reason: Unknown
% 3.03/1.91 % (4731)Termination phase: Saturation
% 3.03/1.91
% 3.03/1.91 % (4731)Memory used [KB]: 7931
% 3.03/1.91 % (4731)Time elapsed: 0.213 s
% 3.03/1.91 % (4731)Instructions burned: 782 (million)
% 3.03/1.91 % (4731)------------------------------
% 3.03/1.91 % (4731)------------------------------
% 3.03/1.91 % (4741)Instruction limit reached!
% 3.03/1.91 % (4741)------------------------------
% 3.03/1.91 % (4741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.91 % (4741)Termination reason: Unknown
% 3.03/1.91 % (4741)Termination phase: Property scanning
% 3.03/1.91
% 3.03/1.91 % (4741)Memory used [KB]: 2814
% 3.03/1.91 % (4741)Time elapsed: 0.041 s
% 3.03/1.91 % (4741)Instructions burned: 88 (million)
% 3.03/1.91 % (4741)------------------------------
% 3.03/1.91 % (4741)------------------------------
% 3.03/1.91 % (4743)Instruction limit reached!
% 3.03/1.91 % (4743)------------------------------
% 3.03/1.91 % (4743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.91 % (4743)Termination reason: Unknown
% 3.03/1.91 % (4743)Termination phase: shuffling
% 3.03/1.91
% 3.03/1.91 % (4743)Memory used [KB]: 2430
% 3.03/1.91 % (4743)Time elapsed: 0.020 s
% 3.03/1.91 % (4743)Instructions burned: 40 (million)
% 3.03/1.91 % (4743)------------------------------
% 3.03/1.91 % (4743)------------------------------
% 3.03/1.92 % (4744)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_4600 for (2996ds/448Mi)
% 3.03/1.92 % (4742)Instruction limit reached!
% 3.03/1.92 % (4742)------------------------------
% 3.03/1.92 % (4742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.92 % (4742)Termination reason: Unknown
% 3.03/1.92 % (4742)Termination phase: SInE selection
% 3.03/1.92
% 3.03/1.92 % (4742)Memory used [KB]: 2814
% 3.03/1.92 % (4742)Time elapsed: 0.049 s
% 3.03/1.92 % (4742)Instructions burned: 108 (million)
% 3.03/1.92 % (4742)------------------------------
% 3.03/1.92 % (4742)------------------------------
% 3.03/1.93 % (4745)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_4600 for (2996ds/46Mi)
% 3.03/1.94 % (4747)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_4600 for (2996ds/507Mi)
% 3.03/1.94 % (4746)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_4600 for (2996ds/98Mi)
% 3.03/1.95 % (4745)Instruction limit reached!
% 3.03/1.95 % (4745)------------------------------
% 3.03/1.95 % (4745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.95 % (4745)Termination reason: Unknown
% 3.03/1.95 % (4745)Termination phase: shuffling
% 3.03/1.95
% 3.03/1.95 % (4745)Memory used [KB]: 2430
% 3.03/1.95 % (4745)Time elapsed: 0.023 s
% 3.03/1.95 % (4745)Instructions burned: 47 (million)
% 3.03/1.95 % (4745)------------------------------
% 3.03/1.95 % (4745)------------------------------
% 3.03/1.97 % (4724)Instruction limit reached!
% 3.03/1.97 % (4724)------------------------------
% 3.03/1.97 % (4724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.97 % (4724)Termination reason: Unknown
% 3.03/1.97 % (4724)Termination phase: Saturation
% 3.03/1.97
% 3.03/1.97 % (4724)Memory used [KB]: 12537
% 3.03/1.97 % (4724)Time elapsed: 0.350 s
% 3.03/1.97 % (4724)Instructions burned: 710 (million)
% 3.03/1.97 % (4724)------------------------------
% 3.03/1.97 % (4724)------------------------------
% 3.03/1.97 % (4748)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_4600 for (2995ds/149Mi)
% 3.03/1.98 % (4746)Instruction limit reached!
% 3.03/1.98 % (4746)------------------------------
% 3.03/1.98 % (4746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.98 % (4746)Termination reason: Unknown
% 3.03/1.98 % (4746)Termination phase: Property scanning
% 3.03/1.98
% 3.03/1.98 % (4746)Memory used [KB]: 2814
% 3.03/1.98 % (4746)Time elapsed: 0.045 s
% 3.03/1.98 % (4746)Instructions burned: 98 (million)
% 3.03/1.98 % (4746)------------------------------
% 3.03/1.98 % (4746)------------------------------
% 3.03/1.99 % (4714)Instruction limit reached!
% 3.03/1.99 % (4714)------------------------------
% 3.03/1.99 % (4714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.99 % (4714)Termination reason: Unknown
% 3.03/1.99 % (4714)Termination phase: Saturation
% 3.03/1.99
% 3.03/1.99 % (4714)Memory used [KB]: 18677
% 3.03/1.99 % (4714)Time elapsed: 0.405 s
% 3.03/1.99 % (4714)Instructions burned: 1043 (million)
% 3.03/1.99 % (4714)------------------------------
% 3.03/1.99 % (4714)------------------------------
% 3.03/1.99 % (4749)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_4600 for (2995ds/39Mi)
% 3.03/2.00 % (4750)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_4600 for (2995ds/6Mi)
% 3.03/2.00 % (4750)Instruction limit reached!
% 3.03/2.00 % (4750)------------------------------
% 3.03/2.00 % (4750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/2.00 % (4750)Termination reason: Unknown
% 3.03/2.00 % (4750)Termination phase: shuffling
% 3.03/2.00
% 3.03/2.00 % (4750)Memory used [KB]: 1663
% 3.03/2.00 % (4750)Time elapsed: 0.005 s
% 3.03/2.00 % (4750)Instructions burned: 8 (million)
% 3.03/2.00 % (4750)------------------------------
% 3.03/2.00 % (4750)------------------------------
% 3.03/2.00 % (4751)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_4600 for (2995ds/1087Mi)
% 3.03/2.01 % (4749)Instruction limit reached!
% 3.03/2.01 % (4749)------------------------------
% 3.03/2.01 % (4749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/2.01 % (4749)Termination reason: Unknown
% 3.03/2.01 % (4749)Termination phase: shuffling
% 3.03/2.01
% 3.03/2.01 % (4749)Memory used [KB]: 2430
% 3.03/2.01 % (4749)Time elapsed: 0.021 s
% 3.03/2.01 % (4749)Instructions burned: 40 (million)
% 3.03/2.01 % (4749)------------------------------
% 3.03/2.01 % (4749)------------------------------
% 3.03/2.01 % (4748)Instruction limit reached!
% 3.03/2.01 % (4748)------------------------------
% 3.03/2.01 % (4748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/2.01 % (4748)Termination reason: Unknown
% 3.03/2.01 % (4748)Termination phase: Function definition elimination
% 3.03/2.01
% 3.03/2.01 % (4748)Memory used [KB]: 3070
% 3.03/2.01 % (4748)Time elapsed: 0.042 s
% 3.03/2.01 % (4748)Instructions burned: 151 (million)
% 3.03/2.01 % (4748)------------------------------
% 3.03/2.01 % (4748)------------------------------
% 3.03/2.02 % (4752)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_4600 for (2995ds/47Mi)
% 3.03/2.02 % (4753)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_4600 for (2995ds/44Mi)
% 6.19/2.03 % (4754)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_4600 for (2995ds/432Mi)
% 6.19/2.04 % (4752)Instruction limit reached!
% 6.19/2.04 % (4752)------------------------------
% 6.19/2.04 % (4752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.19/2.04 % (4752)Termination reason: Unknown
% 6.19/2.04 % (4752)Termination phase: shuffling
% 6.19/2.04
% 6.19/2.04 % (4752)Memory used [KB]: 2558
% 6.19/2.04 % (4752)Time elapsed: 0.023 s
% 6.19/2.04 % (4752)Instructions burned: 47 (million)
% 6.19/2.04 % (4752)------------------------------
% 6.19/2.04 % (4752)------------------------------
% 6.19/2.04 % (4753)Instruction limit reached!
% 6.19/2.04 % (4753)------------------------------
% 6.19/2.04 % (4753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.19/2.04 % (4753)Termination reason: Unknown
% 6.19/2.04 % (4753)Termination phase: shuffling
% 6.19/2.04
% 6.19/2.04 % (4753)Memory used [KB]: 2430
% 6.19/2.04 % (4753)Time elapsed: 0.022 s
% 6.19/2.04 % (4753)Instructions burned: 45 (million)
% 6.19/2.04 % (4753)------------------------------
% 6.19/2.04 % (4753)------------------------------
% 6.19/2.05 % (4755)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_4600 for (2994ds/62Mi)
% 6.19/2.06 % (4756)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_4600 for (2994ds/31Mi)
% 6.19/2.06 % (4755)Instruction limit reached!
% 6.19/2.06 % (4755)------------------------------
% 6.19/2.06 % (4755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.19/2.06 % (4755)Termination reason: Unknown
% 6.19/2.06 % (4755)Termination phase: shuffling
% 6.19/2.06
% 6.19/2.06 % (4755)Memory used [KB]: 2686
% 6.19/2.06 % (4755)Time elapsed: 0.018 s
% 6.19/2.06 % (4755)Instructions burned: 62 (million)
% 6.19/2.06 % (4755)------------------------------
% 6.19/2.06 % (4755)------------------------------
% 6.19/2.07 % (4757)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_4600 for (2994ds/96Mi)
% 6.19/2.08 % (4756)Instruction limit reached!
% 6.19/2.08 % (4756)------------------------------
% 6.19/2.08 % (4756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.19/2.08 % (4756)Termination reason: Unknown
% 6.19/2.08 % (4756)Termination phase: shuffling
% 6.19/2.08
% 6.19/2.08 % (4756)Memory used [KB]: 2302
% 6.19/2.08 % (4756)Time elapsed: 0.016 s
% 6.19/2.08 % (4756)Instructions burned: 31 (million)
% 6.19/2.08 % (4756)------------------------------
% 6.19/2.08 % (4756)------------------------------
% 6.19/2.08 % (4744)Instruction limit reached!
% 6.19/2.08 % (4744)------------------------------
% 6.19/2.08 % (4744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.19/2.08 % (4744)Termination reason: Unknown
% 6.19/2.08 % (4744)Termination phase: Saturation
% 6.19/2.08
% 6.19/2.08 % (4744)Memory used [KB]: 7803
% 6.19/2.08 % (4744)Time elapsed: 0.153 s
% 6.19/2.08 % (4744)Instructions burned: 450 (million)
% 6.19/2.08 % (4744)------------------------------
% 6.19/2.08 % (4744)------------------------------
% 6.19/2.09 % (4758)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_4600 for (2994ds/453Mi)
% 6.19/2.10 % (4733)Instruction limit reached!
% 6.19/2.10 % (4733)------------------------------
% 6.19/2.10 % (4733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.19/2.10 % (4733)Termination reason: Unknown
% 6.19/2.10 % (4733)Termination phase: Saturation
% 6.19/2.10
% 6.19/2.10 % (4733)Memory used [KB]: 10746
% 6.19/2.10 % (4733)Time elapsed: 0.408 s
% 6.19/2.10 % (4733)Instructions burned: 879 (million)
% 6.19/2.10 % (4733)------------------------------
% 6.19/2.10 % (4733)------------------------------
% 6.19/2.10 % (4759)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_4600 for (2994ds/71Mi)
% 6.19/2.11 % (4757)Instruction limit reached!
% 6.19/2.11 % (4757)------------------------------
% 6.19/2.11 % (4757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.19/2.11 % (4757)Termination reason: Unknown
% 6.19/2.11 % (4757)Termination phase: Property scanning
% 6.19/2.11
% 6.19/2.11 % (4757)Memory used [KB]: 2814
% 6.19/2.11 % (4757)Time elapsed: 0.033 s
% 6.19/2.11 % (4757)Instructions burned: 96 (million)
% 6.19/2.11 % (4757)------------------------------
% 6.19/2.11 % (4757)------------------------------
% 6.19/2.11 % (4760)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_4600 for (2994ds/83Mi)
% 6.19/2.12 % (4761)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_4600 for (2994ds/11Mi)
% 6.72/2.13 % (4761)Instruction limit reached!
% 6.72/2.13 % (4761)------------------------------
% 6.72/2.13 % (4761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.13 % (4761)Termination reason: Unknown
% 6.72/2.13 % (4761)Termination phase: shuffling
% 6.72/2.13 % (4760)Instruction limit reached!
% 6.72/2.13 % (4760)------------------------------
% 6.72/2.13 % (4760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.13 % (4760)Termination reason: Unknown
% 6.72/2.13 % (4760)Termination phase: Property scanning
% 6.72/2.13
% 6.72/2.13 % (4760)Memory used [KB]: 2814
% 6.72/2.13 % (4760)Time elapsed: 0.023 s
% 6.72/2.13 % (4760)Instructions burned: 83 (million)
% 6.72/2.13 % (4760)------------------------------
% 6.72/2.13 % (4760)------------------------------
% 6.72/2.13
% 6.72/2.13 % (4761)Memory used [KB]: 1791
% 6.72/2.13 % (4761)Time elapsed: 0.007 s
% 6.72/2.13 % (4761)Instructions burned: 11 (million)
% 6.72/2.13 % (4761)------------------------------
% 6.72/2.13 % (4761)------------------------------
% 6.72/2.13 % (4759)Instruction limit reached!
% 6.72/2.13 % (4759)------------------------------
% 6.72/2.13 % (4759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.13 % (4759)Termination reason: Unknown
% 6.72/2.13 % (4759)Termination phase: Property scanning
% 6.72/2.13
% 6.72/2.13 % (4759)Memory used [KB]: 2814
% 6.72/2.13 % (4759)Time elapsed: 0.034 s
% 6.72/2.13 % (4759)Instructions burned: 72 (million)
% 6.72/2.13 % (4759)------------------------------
% 6.72/2.13 % (4759)------------------------------
% 6.72/2.14 % (4762)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_4600 for (2994ds/41Mi)
% 6.72/2.14 % (4763)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_4600 for (2994ds/6Mi)
% 6.72/2.14 % (4764)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_4600 for (2994ds/150Mi)
% 6.72/2.15 % (4763)Instruction limit reached!
% 6.72/2.15 % (4763)------------------------------
% 6.72/2.15 % (4763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.15 % (4763)Termination reason: Unknown
% 6.72/2.15 % (4763)Termination phase: shuffling
% 6.72/2.15
% 6.72/2.15 % (4763)Memory used [KB]: 1663
% 6.72/2.15 % (4763)Time elapsed: 0.005 s
% 6.72/2.15 % (4763)Instructions burned: 8 (million)
% 6.72/2.15 % (4763)------------------------------
% 6.72/2.15 % (4763)------------------------------
% 6.72/2.15 % (4762)Instruction limit reached!
% 6.72/2.15 % (4762)------------------------------
% 6.72/2.15 % (4762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.15 % (4762)Termination reason: Unknown
% 6.72/2.15 % (4762)Termination phase: shuffling
% 6.72/2.15
% 6.72/2.15 % (4762)Memory used [KB]: 2430
% 6.72/2.15 % (4762)Time elapsed: 0.019 s
% 6.72/2.15 % (4762)Instructions burned: 42 (million)
% 6.72/2.15 % (4762)------------------------------
% 6.72/2.15 % (4762)------------------------------
% 6.72/2.16 % (4765)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_4600 for (2993ds/343Mi)
% 6.72/2.17 % (4766)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_4600 for (2993ds/109Mi)
% 6.72/2.17 % (4747)Instruction limit reached!
% 6.72/2.17 % (4747)------------------------------
% 6.72/2.17 % (4747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.17 % (4747)Termination reason: Unknown
% 6.72/2.17 % (4747)Termination phase: Saturation
% 6.72/2.17
% 6.72/2.17 % (4747)Memory used [KB]: 8443
% 6.72/2.17 % (4747)Time elapsed: 0.238 s
% 6.72/2.17 % (4747)Instructions burned: 508 (million)
% 6.72/2.17 % (4747)------------------------------
% 6.72/2.17 % (4747)------------------------------
% 6.72/2.19 % (4767)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_4600 for (2993ds/253Mi)
% 7.01/2.21 % (4754)Instruction limit reached!
% 7.01/2.21 % (4754)------------------------------
% 7.01/2.21 % (4754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.01/2.21 % (4754)Termination reason: Unknown
% 7.01/2.21 % (4754)Termination phase: Saturation
% 7.01/2.21
% 7.01/2.21 % (4754)Memory used [KB]: 3326
% 7.01/2.21 % (4754)Time elapsed: 0.180 s
% 7.01/2.21 % (4754)Instructions burned: 434 (million)
% 7.01/2.21 % (4754)------------------------------
% 7.01/2.21 % (4754)------------------------------
% 7.01/2.22 % (4764)Instruction limit reached!
% 7.01/2.22 % (4764)------------------------------
% 7.01/2.22 % (4764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.01/2.22 % (4764)Termination reason: Unknown
% 7.01/2.22 % (4764)Termination phase: Preprocessing 3
% 7.01/2.22
% 7.01/2.22 % (4764)Memory used [KB]: 5245
% 7.01/2.22 % (4764)Time elapsed: 0.073 s
% 7.01/2.22 % (4764)Instructions burned: 151 (million)
% 7.01/2.22 % (4764)------------------------------
% 7.01/2.22 % (4764)------------------------------
% 7.01/2.22 % (4766)Instruction limit reached!
% 7.01/2.22 % (4766)------------------------------
% 7.01/2.22 % (4766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.01/2.22 % (4766)Termination reason: Unknown
% 7.01/2.22 % (4766)Termination phase: SInE selection
% 7.01/2.22
% 7.01/2.22 % (4766)Memory used [KB]: 2814
% 7.01/2.22 % (4766)Time elapsed: 0.050 s
% 7.01/2.22 % (4766)Instructions burned: 111 (million)
% 7.01/2.22 % (4766)------------------------------
% 7.01/2.22 % (4766)------------------------------
% 7.01/2.22 % (4768)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_4600 for (2993ds/140Mi)
% 7.01/2.23 % (4769)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_4600 for (2993ds/614Mi)
% 7.01/2.24 % (4770)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_4600 for (2993ds/202Mi)
% 7.01/2.24 % (4758)Instruction limit reached!
% 7.01/2.24 % (4758)------------------------------
% 7.01/2.24 % (4758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.01/2.24 % (4758)Termination reason: Unknown
% 7.01/2.24 % (4758)Termination phase: Saturation
% 7.01/2.24
% 7.01/2.24 % (4758)Memory used [KB]: 7803
% 7.01/2.24 % (4758)Time elapsed: 0.153 s
% 7.01/2.24 % (4758)Instructions burned: 453 (million)
% 7.01/2.24 % (4758)------------------------------
% 7.01/2.24 % (4758)------------------------------
% 7.01/2.26 % (4765)Instruction limit reached!
% 7.01/2.26 % (4765)------------------------------
% 7.01/2.26 % (4765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.01/2.26 % (4765)Termination reason: Unknown
% 7.01/2.26 % (4765)Termination phase: Saturation
% 7.01/2.26
% 7.01/2.26 % (4765)Memory used [KB]: 8443
% 7.01/2.26 % (4765)Time elapsed: 0.099 s
% 7.01/2.26 % (4765)Instructions burned: 346 (million)
% 7.01/2.26 % (4765)------------------------------
% 7.01/2.26 % (4765)------------------------------
% 7.01/2.27 % (4772)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_4600 for (2992ds/283Mi)
% 7.01/2.27 % (4771)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_4600 for (2992ds/339Mi)
% 7.01/2.28 % (4768)Instruction limit reached!
% 7.01/2.28 % (4768)------------------------------
% 7.01/2.28 % (4768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.01/2.28 % (4768)Termination reason: Unknown
% 7.01/2.28 % (4768)Termination phase: Property scanning
% 7.01/2.28
% 7.01/2.28 % (4768)Memory used [KB]: 3070
% 7.01/2.28 % (4768)Time elapsed: 0.063 s
% 7.01/2.28 % (4768)Instructions burned: 140 (million)
% 7.01/2.29 % (4768)------------------------------
% 7.01/2.29 % (4768)------------------------------
% 7.82/2.30 % (4773)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_4600 for (2992ds/134Mi)
% 7.82/2.31 % (4767)Instruction limit reached!
% 7.82/2.31 % (4767)------------------------------
% 7.82/2.31 % (4767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.82/2.31 % (4767)Termination reason: Unknown
% 7.82/2.31 % (4767)Termination phase: Property scanning
% 7.82/2.31
% 7.82/2.31 % (4767)Memory used [KB]: 5884
% 7.82/2.31 % (4767)Time elapsed: 0.119 s
% 7.82/2.31 % (4767)Instructions burned: 253 (million)
% 7.82/2.31 % (4767)------------------------------
% 7.82/2.31 % (4767)------------------------------
% 7.82/2.32 % (4775)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_4600 for (2992ds/298Mi)
% 7.82/2.33 % (4770)Instruction limit reached!
% 7.82/2.33 % (4770)------------------------------
% 7.82/2.33 % (4770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.82/2.33 % (4770)Termination reason: Unknown
% 7.82/2.33 % (4770)Termination phase: Property scanning
% 7.82/2.33
% 7.82/2.33 % (4770)Memory used [KB]: 5756
% 7.82/2.33 % (4770)Time elapsed: 0.096 s
% 7.82/2.33 % (4770)Instructions burned: 204 (million)
% 7.82/2.33 % (4770)------------------------------
% 7.82/2.33 % (4770)------------------------------
% 7.82/2.35 % (4776)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_4600 for (2991ds/192Mi)
% 7.82/2.36 % (4773)Instruction limit reached!
% 7.82/2.36 % (4773)------------------------------
% 7.82/2.36 % (4773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.82/2.36 % (4773)Termination reason: Unknown
% 7.82/2.36 % (4773)Termination phase: Property scanning
% 7.82/2.36
% 7.82/2.36 % (4773)Memory used [KB]: 2942
% 7.82/2.36 % (4773)Time elapsed: 0.062 s
% 7.82/2.36 % (4773)Instructions burned: 134 (million)
% 7.82/2.36 % (4773)------------------------------
% 7.82/2.36 % (4773)------------------------------
% 7.82/2.37 % (4772)Instruction limit reached!
% 7.82/2.37 % (4772)------------------------------
% 7.82/2.37 % (4772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.82/2.37 % (4772)Termination reason: Unknown
% 7.82/2.37 % (4772)Termination phase: Saturation
% 7.82/2.37
% 7.82/2.37 % (4772)Memory used [KB]: 7675
% 7.82/2.37 % (4772)Time elapsed: 0.105 s
% 7.82/2.37 % (4772)Instructions burned: 283 (million)
% 7.82/2.37 % (4772)------------------------------
% 7.82/2.37 % (4772)------------------------------
% 7.82/2.38 % (4777)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_4600 for (2991ds/258Mi)
% 7.82/2.39 % (4778)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_4600 for (2991ds/90Mi)
% 8.35/2.42 % (4771)Instruction limit reached!
% 8.35/2.42 % (4771)------------------------------
% 8.35/2.42 % (4771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.35/2.42 % (4771)Termination reason: Unknown
% 8.35/2.42 % (4771)Termination phase: Saturation
% 8.35/2.42
% 8.35/2.42 % (4771)Memory used [KB]: 8315
% 8.35/2.42 % (4771)Time elapsed: 0.153 s
% 8.35/2.42 % (4771)Instructions burned: 339 (million)
% 8.35/2.42 % (4771)------------------------------
% 8.35/2.42 % (4771)------------------------------
% 8.35/2.43 % (4778)Instruction limit reached!
% 8.35/2.43 % (4778)------------------------------
% 8.35/2.43 % (4778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.35/2.43 % (4778)Termination reason: Unknown
% 8.35/2.43 % (4778)Termination phase: Property scanning
% 8.35/2.43
% 8.35/2.43 % (4778)Memory used [KB]: 2814
% 8.35/2.43 % (4778)Time elapsed: 0.042 s
% 8.35/2.43 % (4778)Instructions burned: 91 (million)
% 8.35/2.43 % (4778)------------------------------
% 8.35/2.43 % (4778)------------------------------
% 8.35/2.44 % (4779)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_4600 for (2990ds/231Mi)
% 8.35/2.45 % (4780)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_4600 for (2990ds/458Mi)
% 8.35/2.45 % (4775)Instruction limit reached!
% 8.35/2.45 % (4775)------------------------------
% 8.35/2.45 % (4775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.35/2.45 % (4775)Termination reason: Unknown
% 8.35/2.45 % (4775)Termination phase: Saturation
% 8.35/2.45
% 8.35/2.45 % (4775)Memory used [KB]: 7675
% 8.35/2.45 % (4775)Time elapsed: 0.127 s
% 8.35/2.45 % (4775)Instructions burned: 300 (million)
% 8.35/2.45 % (4775)------------------------------
% 8.35/2.45 % (4775)------------------------------
% 8.35/2.46 % (4776)Instruction limit reached!
% 8.35/2.46 % (4776)------------------------------
% 8.35/2.46 % (4776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.35/2.46 % (4776)Termination reason: Unknown
% 8.35/2.46 % (4776)Termination phase: Saturation
% 8.35/2.46
% 8.35/2.46 % (4776)Memory used [KB]: 7547
% 8.35/2.46 % (4776)Time elapsed: 0.055 s
% 8.35/2.46 % (4776)Instructions burned: 194 (million)
% 8.35/2.46 % (4776)------------------------------
% 8.35/2.46 % (4776)------------------------------
% 8.35/2.46 % (4781)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_4600 for (2990ds/31Mi)
% 8.35/2.47 % (4782)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_4600 for (2990ds/297Mi)
% 8.35/2.48 % (4781)Instruction limit reached!
% 8.35/2.48 % (4781)------------------------------
% 8.35/2.48 % (4781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.35/2.48 % (4781)Termination reason: Unknown
% 8.35/2.48 % (4781)Termination phase: shuffling
% 8.35/2.48
% 8.35/2.48 % (4781)Memory used [KB]: 2302
% 8.35/2.48 % (4781)Time elapsed: 0.016 s
% 8.35/2.48 % (4781)Instructions burned: 31 (million)
% 8.35/2.48 % (4781)------------------------------
% 8.35/2.48 % (4781)------------------------------
% 8.35/2.49 % (4769)Instruction limit reached!
% 8.35/2.49 % (4769)------------------------------
% 8.35/2.49 % (4769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.35/2.49 % (4769)Termination reason: Unknown
% 8.35/2.49 % (4769)Termination phase: Saturation
% 8.35/2.49
% 8.35/2.49 % (4769)Memory used [KB]: 10490
% 8.35/2.49 % (4769)Time elapsed: 0.278 s
% 8.35/2.49 % (4769)Instructions burned: 615 (million)
% 8.35/2.49 % (4769)------------------------------
% 8.35/2.49 % (4769)------------------------------
% 8.35/2.49 % (4777)Instruction limit reached!
% 8.35/2.49 % (4777)------------------------------
% 8.35/2.49 % (4777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.35/2.49 % (4777)Termination reason: Unknown
% 8.35/2.49 % (4777)Termination phase: Saturation
% 8.35/2.49
% 8.35/2.49 % (4777)Memory used [KB]: 7931
% 8.35/2.49 % (4777)Time elapsed: 0.113 s
% 8.35/2.49 % (4777)Instructions burned: 259 (million)
% 8.35/2.49 % (4777)------------------------------
% 8.35/2.49 % (4777)------------------------------
% 8.35/2.50 % (4783)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_4600 for (2990ds/987Mi)
% 9.24/2.50 % (4784)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_4600 for (2990ds/182Mi)
% 9.24/2.51 % (4785)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_4600 for (2990ds/182Mi)
% 9.24/2.53 % (4779)Instruction limit reached!
% 9.24/2.53 % (4779)------------------------------
% 9.24/2.53 % (4779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.24/2.53 % (4779)Termination reason: Unknown
% 9.24/2.53 % (4779)Termination phase: Property scanning
% 9.24/2.53
% 9.24/2.53 % (4779)Memory used [KB]: 4349
% 9.24/2.53 % (4779)Time elapsed: 0.092 s
% 9.24/2.53 % (4779)Instructions burned: 232 (million)
% 9.24/2.53 % (4779)------------------------------
% 9.24/2.53 % (4779)------------------------------
% 9.24/2.54 % (4751)Instruction limit reached!
% 9.24/2.54 % (4751)------------------------------
% 9.24/2.54 % (4751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.24/2.54 % (4751)Termination reason: Unknown
% 9.24/2.54 % (4751)Termination phase: Saturation
% 9.24/2.54
% 9.24/2.54 % (4751)Memory used [KB]: 13304
% 9.24/2.54 % (4751)Time elapsed: 0.537 s
% 9.24/2.54 % (4751)Instructions burned: 1087 (million)
% 9.24/2.54 % (4751)------------------------------
% 9.24/2.54 % (4751)------------------------------
% 9.24/2.55 % (4786)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_4600 for (2989ds/154Mi)
% 9.24/2.55 % (4787)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_4600 for (2989ds/79Mi)
% 9.24/2.57 % (4787)Instruction limit reached!
% 9.24/2.57 % (4787)------------------------------
% 9.24/2.57 % (4787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.24/2.57 % (4787)Termination reason: Unknown
% 9.24/2.57 % (4787)Termination phase: Property scanning
% 9.24/2.57
% 9.24/2.57 % (4787)Memory used [KB]: 2814
% 9.24/2.57 % (4787)Time elapsed: 0.023 s
% 9.24/2.57 % (4787)Instructions burned: 82 (million)
% 9.24/2.57 % (4787)------------------------------
% 9.24/2.57 % (4787)------------------------------
% 9.24/2.58 % (4784)Instruction limit reached!
% 9.24/2.58 % (4784)------------------------------
% 9.24/2.58 % (4784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.24/2.58 % (4784)Termination reason: Unknown
% 9.24/2.58 % (4784)Termination phase: Property scanning
% 9.24/2.58
% 9.24/2.58 % (4784)Memory used [KB]: 3070
% 9.24/2.58 % (4784)Time elapsed: 0.082 s
% 9.24/2.58 % (4784)Instructions burned: 182 (million)
% 9.24/2.58 % (4784)------------------------------
% 9.24/2.58 % (4784)------------------------------
% 9.24/2.58 % (4785)Instruction limit reached!
% 9.24/2.58 % (4785)------------------------------
% 9.24/2.58 % (4785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.24/2.58 % (4785)Termination reason: Unknown
% 9.24/2.58 % (4785)Termination phase: Property scanning
% 9.24/2.58
% 9.24/2.58 % (4785)Memory used [KB]: 5756
% 9.24/2.58 % (4785)Time elapsed: 0.079 s
% 9.24/2.58 % (4785)Instructions burned: 182 (million)
% 9.24/2.58 % (4785)------------------------------
% 9.24/2.58 % (4785)------------------------------
% 9.24/2.59 % (4788)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_4600 for (2989ds/216Mi)
% 9.24/2.59 % (4790)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_4600 for (2989ds/922Mi)
% 9.24/2.60 % (4782)Instruction limit reached!
% 9.24/2.60 % (4782)------------------------------
% 9.24/2.60 % (4782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.24/2.60 % (4782)Termination reason: Unknown
% 9.24/2.60 % (4782)Termination phase: Saturation
% 9.24/2.60
% 9.24/2.60 % (4782)Memory used [KB]: 7675
% 9.24/2.60 % (4782)Time elapsed: 0.125 s
% 9.24/2.60 % (4782)Instructions burned: 298 (million)
% 9.24/2.60 % (4782)------------------------------
% 9.24/2.60 % (4782)------------------------------
% 9.63/2.60 % (4789)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_4600 for (2989ds/114Mi)
% 9.63/2.61 % (4791)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_4600 for (2989ds/182Mi)
% 9.63/2.61 % (4786)Instruction limit reached!
% 9.63/2.61 % (4786)------------------------------
% 9.63/2.61 % (4786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.63/2.61 % (4786)Termination reason: Unknown
% 9.63/2.61 % (4786)Termination phase: Function definition elimination
% 9.63/2.61
% 9.63/2.61 % (4786)Memory used [KB]: 2942
% 9.63/2.61 % (4786)Time elapsed: 0.069 s
% 9.63/2.61 % (4786)Instructions burned: 156 (million)
% 9.63/2.61 % (4786)------------------------------
% 9.63/2.61 % (4786)------------------------------
% 9.63/2.63 % (4792)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_4600 for (2989ds/164Mi)
% 9.63/2.63 % (4780)Instruction limit reached!
% 9.63/2.63 % (4780)------------------------------
% 9.63/2.63 % (4780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.63/2.63 % (4780)Termination reason: Unknown
% 9.63/2.63 % (4780)Termination phase: Saturation
% 9.63/2.63
% 9.63/2.63 % (4780)Memory used [KB]: 9722
% 9.63/2.63 % (4780)Time elapsed: 0.189 s
% 9.63/2.63 % (4780)Instructions burned: 458 (million)
% 9.63/2.63 % (4780)------------------------------
% 9.63/2.63 % (4780)------------------------------
% 9.63/2.65 % (4793)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_4600 for (2988ds/50Mi)
% 9.63/2.65 % (4789)Instruction limit reached!
% 9.63/2.65 % (4789)------------------------------
% 9.63/2.65 % (4789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.63/2.65 % (4789)Termination reason: Unknown
% 9.63/2.65 % (4789)Termination phase: Property scanning
% 9.63/2.65
% 9.63/2.65 % (4789)Memory used [KB]: 2942
% 9.63/2.65 % (4789)Time elapsed: 0.053 s
% 9.63/2.65 % (4789)Instructions burned: 115 (million)
% 9.63/2.65 % (4789)------------------------------
% 9.63/2.65 % (4789)------------------------------
% 9.63/2.66 % (4793)Instruction limit reached!
% 9.63/2.66 % (4793)------------------------------
% 9.63/2.66 % (4793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.63/2.66 % (4793)Termination reason: Unknown
% 9.63/2.66 % (4793)Termination phase: shuffling
% 9.63/2.66
% 9.63/2.66 % (4793)Memory used [KB]: 2558
% 9.63/2.66 % (4793)Time elapsed: 0.016 s
% 9.63/2.66 % (4793)Instructions burned: 51 (million)
% 9.63/2.66 % (4793)------------------------------
% 9.63/2.66 % (4793)------------------------------
% 9.63/2.66 % (4794)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_4600 for (2988ds/368Mi)
% 9.63/2.68 % (4791)Instruction limit reached!
% 9.63/2.68 % (4791)------------------------------
% 9.63/2.68 % (4791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.63/2.68 % (4791)Termination reason: Unknown
% 9.63/2.68 % (4791)Termination phase: Property scanning
% 9.63/2.68
% 9.63/2.68 % (4791)Memory used [KB]: 3198
% 9.63/2.68 % (4791)Time elapsed: 0.066 s
% 9.63/2.68 % (4791)Instructions burned: 182 (million)
% 9.63/2.68 % (4791)------------------------------
% 9.63/2.68 % (4791)------------------------------
% 9.63/2.68 % (4788)Instruction limit reached!
% 9.63/2.68 % (4788)------------------------------
% 9.63/2.68 % (4788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.63/2.68 % (4795)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_4600 for (2988ds/1021Mi)
% 9.63/2.68 % (4788)Termination reason: Unknown
% 9.63/2.68 % (4788)Termination phase: Property scanning
% 9.63/2.68
% 9.63/2.68 % (4788)Memory used [KB]: 3198
% 9.63/2.68 % (4788)Time elapsed: 0.092 s
% 9.63/2.68 % (4788)Instructions burned: 216 (million)
% 9.63/2.68 % (4788)------------------------------
% 9.63/2.68 % (4788)------------------------------
% 9.63/2.69 % (4796)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_4600 for (2988ds/267Mi)
% 9.63/2.69 % (4792)Instruction limit reached!
% 9.63/2.69 % (4792)------------------------------
% 9.63/2.69 % (4792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.63/2.69 % (4792)Termination reason: Unknown
% 9.63/2.69 % (4792)Termination phase: Property scanning
% 9.63/2.69
% 9.63/2.69 % (4792)Memory used [KB]: 2942
% 9.63/2.69 % (4792)Time elapsed: 0.062 s
% 9.63/2.69 % (4792)Instructions burned: 165 (million)
% 9.63/2.69 % (4792)------------------------------
% 9.63/2.69 % (4792)------------------------------
% 9.63/2.69 % (4797)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_4600 for (2988ds/204Mi)
% 10.40/2.71 % (4798)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_4600 for (2988ds/26Mi)
% 10.40/2.72 % (4798)Instruction limit reached!
% 10.40/2.72 % (4798)------------------------------
% 10.40/2.72 % (4798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.40/2.72 % (4798)Termination reason: Unknown
% 10.40/2.72 % (4798)Termination phase: shuffling
% 10.40/2.72
% 10.40/2.72 % (4798)Memory used [KB]: 2046
% 10.40/2.72 % (4798)Time elapsed: 0.013 s
% 10.40/2.72 % (4798)Instructions burned: 26 (million)
% 10.40/2.72 % (4798)------------------------------
% 10.40/2.72 % (4798)------------------------------
% 10.40/2.73 % (4799)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_4600 for (2988ds/53Mi)
% 10.40/2.76 % (4799)Instruction limit reached!
% 10.40/2.76 % (4799)------------------------------
% 10.40/2.76 % (4799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.40/2.76 % (4799)Termination reason: Unknown
% 10.40/2.76 % (4799)Termination phase: shuffling
% 10.40/2.76
% 10.40/2.76 % (4799)Memory used [KB]: 2558
% 10.40/2.76 % (4799)Time elapsed: 0.027 s
% 10.40/2.76 % (4799)Instructions burned: 54 (million)
% 10.40/2.76 % (4799)------------------------------
% 10.40/2.76 % (4799)------------------------------
% 10.40/2.78 % (4797)Instruction limit reached!
% 10.40/2.78 % (4797)------------------------------
% 10.40/2.78 % (4797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.40/2.78 % (4797)Termination reason: Unknown
% 10.40/2.78 % (4797)Termination phase: Property scanning
% 10.40/2.78
% 10.40/2.78 % (4797)Memory used [KB]: 3070
% 10.40/2.78 % (4797)Time elapsed: 0.087 s
% 10.40/2.78 % (4797)Instructions burned: 205 (million)
% 10.40/2.78 % (4797)------------------------------
% 10.40/2.78 % (4797)------------------------------
% 10.40/2.78 % (4800)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_4600 for (2987ds/4436Mi)
% 10.40/2.79 % (4796)Instruction limit reached!
% 10.40/2.79 % (4796)------------------------------
% 10.40/2.79 % (4796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.40/2.79 % (4796)Termination reason: Unknown
% 10.40/2.79 % (4796)Termination phase: Saturation
% 10.40/2.79
% 10.40/2.79 % (4796)Memory used [KB]: 7675
% 10.40/2.79 % (4796)Time elapsed: 0.109 s
% 10.40/2.79 % (4796)Instructions burned: 267 (million)
% 10.40/2.79 % (4796)------------------------------
% 10.40/2.79 % (4796)------------------------------
% 10.70/2.80 % (4802)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_4600 for (2987ds/1539Mi)
% 10.70/2.81 % (4807)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_4600 for (2987ds/408Mi)
% 10.70/2.82 % (4794)Instruction limit reached!
% 10.70/2.82 % (4794)------------------------------
% 10.70/2.82 % (4794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.70/2.82 % (4794)Termination reason: Unknown
% 10.70/2.82 % (4794)Termination phase: Saturation
% 10.70/2.82
% 10.70/2.82 % (4794)Memory used [KB]: 9466
% 10.70/2.82 % (4794)Time elapsed: 0.134 s
% 10.70/2.82 % (4794)Instructions burned: 369 (million)
% 10.70/2.82 % (4794)------------------------------
% 10.70/2.82 % (4794)------------------------------
% 10.70/2.84 % (4819)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_4600 for (2987ds/5205Mi)
% 10.70/2.85 % (4783)Instruction limit reached!
% 10.70/2.85 % (4783)------------------------------
% 10.70/2.85 % (4783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.70/2.85 % (4783)Termination reason: Unknown
% 10.70/2.85 % (4783)Termination phase: Saturation
% 10.70/2.85
% 10.70/2.85 % (4783)Memory used [KB]: 15223
% 10.70/2.85 % (4783)Time elapsed: 0.358 s
% 10.70/2.85 % (4783)Instructions burned: 988 (million)
% 10.70/2.85 % (4783)------------------------------
% 10.70/2.85 % (4783)------------------------------
% 10.70/2.87 % (4820)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_4600 for (2986ds/1913Mi)
% 11.23/2.97 % (4807)Instruction limit reached!
% 11.23/2.97 % (4807)------------------------------
% 11.23/2.97 % (4807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.23/2.97 % (4807)Termination reason: Unknown
% 11.23/2.97 % (4807)Termination phase: Saturation
% 11.23/2.97
% 11.23/2.97 % (4807)Memory used [KB]: 12025
% 11.23/2.97 % (4807)Time elapsed: 0.159 s
% 11.23/2.97 % (4807)Instructions burned: 410 (million)
% 11.23/2.97 % (4807)------------------------------
% 11.23/2.97 % (4807)------------------------------
% 11.23/2.98 % (4821)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_4600 for (2985ds/4350Mi)
% 11.23/3.02 % (4790)Instruction limit reached!
% 11.23/3.02 % (4790)------------------------------
% 11.23/3.02 % (4790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.23/3.02 % (4790)Termination reason: Unknown
% 11.23/3.02 % (4790)Termination phase: Saturation
% 11.23/3.02
% 11.23/3.02 % (4790)Memory used [KB]: 12792
% 11.23/3.02 % (4790)Time elapsed: 0.426 s
% 11.23/3.02 % (4790)Instructions burned: 923 (million)
% 11.23/3.02 % (4790)------------------------------
% 11.23/3.02 % (4790)------------------------------
% 13.01/3.04 % (4822)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_4600 for (2985ds/68Mi)
% 13.01/3.07 % (4822)Instruction limit reached!
% 13.01/3.07 % (4822)------------------------------
% 13.01/3.07 % (4822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.01/3.07 % (4822)Termination reason: Unknown
% 13.01/3.07 % (4822)Termination phase: Property scanning
% 13.01/3.07
% 13.01/3.07 % (4822)Memory used [KB]: 2814
% 13.01/3.07 % (4822)Time elapsed: 0.033 s
% 13.01/3.07 % (4822)Instructions burned: 68 (million)
% 13.01/3.07 % (4822)------------------------------
% 13.01/3.07 % (4822)------------------------------
% 13.01/3.09 % (4823)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_4600 for (2984ds/358Mi)
% 13.66/3.15 % (4795)Instruction limit reached!
% 13.66/3.15 % (4795)------------------------------
% 13.66/3.15 % (4795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.66/3.15 % (4795)Termination reason: Unknown
% 13.66/3.15 % (4795)Termination phase: Saturation
% 13.66/3.15
% 13.66/3.15 % (4795)Memory used [KB]: 13432
% 13.66/3.15 % (4795)Time elapsed: 0.473 s
% 13.66/3.15 % (4795)Instructions burned: 1022 (million)
% 13.66/3.15 % (4795)------------------------------
% 13.66/3.15 % (4795)------------------------------
% 13.66/3.17 % (4824)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_4600 for (2983ds/31Mi)
% 13.66/3.18 % (4824)Instruction limit reached!
% 13.66/3.18 % (4824)------------------------------
% 13.66/3.18 % (4824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.66/3.18 % (4824)Termination reason: Unknown
% 13.66/3.18 % (4824)Termination phase: shuffling
% 13.66/3.18
% 13.66/3.18 % (4824)Memory used [KB]: 2302
% 13.66/3.18 % (4824)Time elapsed: 0.016 s
% 13.66/3.18 % (4824)Instructions burned: 32 (million)
% 13.66/3.18 % (4824)------------------------------
% 13.66/3.18 % (4824)------------------------------
% 13.66/3.19 % (4823)Instruction limit reached!
% 13.66/3.19 % (4823)------------------------------
% 13.66/3.19 % (4823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.66/3.19 % (4823)Termination reason: Unknown
% 13.66/3.19 % (4823)Termination phase: Saturation
% 13.66/3.19
% 13.66/3.19 % (4823)Memory used [KB]: 8443
% 13.66/3.19 % (4823)Time elapsed: 0.106 s
% 13.66/3.19 % (4823)Instructions burned: 358 (million)
% 13.66/3.19 % (4823)------------------------------
% 13.66/3.19 % (4823)------------------------------
% 14.21/3.20 % (4825)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_4600 for (2983ds/279Mi)
% 14.21/3.21 % (4826)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_4600 for (2983ds/258Mi)
% 14.70/3.31 % (4826)Instruction limit reached!
% 14.70/3.31 % (4826)------------------------------
% 14.70/3.31 % (4826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.70/3.31 % (4826)Termination reason: Unknown
% 14.70/3.31 % (4826)Termination phase: Saturation
% 14.70/3.31
% 14.70/3.31 % (4826)Memory used [KB]: 8443
% 14.70/3.31 % (4826)Time elapsed: 0.110 s
% 14.70/3.31 % (4826)Instructions burned: 261 (million)
% 14.70/3.31 % (4826)------------------------------
% 14.70/3.31 % (4826)------------------------------
% 14.70/3.31 % (4825)Instruction limit reached!
% 14.70/3.31 % (4825)------------------------------
% 14.70/3.31 % (4825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.70/3.31 % (4825)Termination reason: Unknown
% 14.70/3.31 % (4825)Termination phase: Saturation
% 14.70/3.31
% 14.70/3.31 % (4825)Memory used [KB]: 7675
% 14.70/3.31 % (4825)Time elapsed: 0.118 s
% 14.70/3.31 % (4825)Instructions burned: 279 (million)
% 14.70/3.31 % (4825)------------------------------
% 14.70/3.31 % (4825)------------------------------
% 14.70/3.33 % (4827)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_4600 for (2982ds/26Mi)
% 14.70/3.33 % (4828)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_4600 for (2982ds/995Mi)
% 14.70/3.34 % (4827)Instruction limit reached!
% 14.70/3.34 % (4827)------------------------------
% 14.70/3.34 % (4827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.70/3.34 % (4827)Termination reason: Unknown
% 14.70/3.34 % (4827)Termination phase: shuffling
% 14.70/3.34
% 14.70/3.34 % (4827)Memory used [KB]: 2046
% 14.70/3.34 % (4827)Time elapsed: 0.014 s
% 14.70/3.34 % (4827)Instructions burned: 27 (million)
% 14.70/3.34 % (4827)------------------------------
% 14.70/3.34 % (4827)------------------------------
% 14.70/3.36 % (4829)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_4600 for (2981ds/373Mi)
% 15.46/3.49 % (4802)Instruction limit reached!
% 15.46/3.49 % (4802)------------------------------
% 15.46/3.49 % (4802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.46/3.49 % (4802)Termination reason: Unknown
% 15.46/3.49 % (4802)Termination phase: Saturation
% 15.46/3.49
% 15.46/3.49 % (4802)Memory used [KB]: 11385
% 15.46/3.49 % (4802)Time elapsed: 0.719 s
% 15.46/3.49 % (4802)Instructions burned: 1539 (million)
% 15.46/3.49 % (4802)------------------------------
% 15.46/3.49 % (4802)------------------------------
% 15.90/3.51 % (4831)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_4600 for (2980ds/253Mi)
% 15.90/3.53 % (4829)Instruction limit reached!
% 15.90/3.53 % (4829)------------------------------
% 15.90/3.53 % (4829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.90/3.53 % (4829)Termination reason: Unknown
% 15.90/3.53 % (4829)Termination phase: Saturation
% 15.90/3.53
% 15.90/3.53 % (4829)Memory used [KB]: 9594
% 15.90/3.53 % (4829)Time elapsed: 0.106 s
% 15.90/3.53 % (4829)Instructions burned: 375 (million)
% 15.90/3.53 % (4829)------------------------------
% 15.90/3.53 % (4829)------------------------------
% 15.90/3.54 % (4832)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_4600 for (2979ds/832Mi)
% 16.42/3.62 % (4831)Instruction limit reached!
% 16.42/3.62 % (4831)------------------------------
% 16.42/3.62 % (4831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.42/3.62 % (4831)Termination reason: Unknown
% 16.42/3.62 % (4831)Termination phase: Saturation
% 16.42/3.62
% 16.42/3.62 % (4831)Memory used [KB]: 7675
% 16.42/3.62 % (4831)Time elapsed: 0.108 s
% 16.42/3.62 % (4831)Instructions burned: 253 (million)
% 16.42/3.62 % (4831)------------------------------
% 16.42/3.62 % (4831)------------------------------
% 16.42/3.64 % (4833)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_4600 for (2979ds/668Mi)
% 16.91/3.72 % (4828)Instruction limit reached!
% 16.91/3.72 % (4828)------------------------------
% 16.91/3.72 % (4828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.91/3.72 % (4828)Termination reason: Unknown
% 16.91/3.72 % (4828)Termination phase: Saturation
% 16.91/3.72
% 16.91/3.72 % (4828)Memory used [KB]: 18421
% 16.91/3.72 % (4828)Time elapsed: 0.387 s
% 16.91/3.72 % (4828)Instructions burned: 996 (million)
% 16.91/3.72 % (4828)------------------------------
% 16.91/3.72 % (4828)------------------------------
% 16.91/3.74 % (4834)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_4600 for (2978ds/40Mi)
% 16.91/3.75 % (4834)Instruction limit reached!
% 16.91/3.75 % (4834)------------------------------
% 16.91/3.75 % (4834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.91/3.75 % (4834)Termination reason: Unknown
% 16.91/3.75 % (4834)Termination phase: shuffling
% 16.91/3.75
% 16.91/3.75 % (4834)Memory used [KB]: 2430
% 16.91/3.75 % (4834)Time elapsed: 0.020 s
% 16.91/3.75 % (4834)Instructions burned: 42 (million)
% 16.91/3.75 % (4834)------------------------------
% 16.91/3.75 % (4834)------------------------------
% 16.91/3.77 % (4832)Refutation not found, incomplete strategy
% 16.91/3.77 % (4832)------------------------------
% 16.91/3.77 % (4832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.91/3.77 % (4832)Termination reason: Refutation not found, incomplete strategy
% 16.91/3.77
% 16.91/3.77
% 16.91/3.77 % (4832)Memory used [KB]: 11897
% 16.91/3.77 % (4832)Time elapsed: 0.233 s
% 16.91/3.77 % (4832)Instructions burned: 510 (million)
% 16.91/3.77 % (4832)------------------------------
% 16.91/3.77 % (4832)------------------------------
% 16.91/3.77 % (4835)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_4600 for (2977ds/294Mi)
% 16.91/3.79 % (4836)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_4600 for (2977ds/187Mi)
% 17.94/3.81 % (4820)Instruction limit reached!
% 17.94/3.81 % (4820)------------------------------
% 17.94/3.81 % (4820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.94/3.81 % (4820)Termination reason: Unknown
% 17.94/3.81 % (4820)Termination phase: Saturation
% 17.94/3.81
% 17.94/3.81 % (4820)Memory used [KB]: 6652
% 17.94/3.81 % (4820)Time elapsed: 0.966 s
% 17.94/3.81 % (4820)Instructions burned: 1914 (million)
% 17.94/3.81 % (4820)------------------------------
% 17.94/3.81 % (4820)------------------------------
% 17.94/3.83 % (4837)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_4600 for (2977ds/371Mi)
% 17.94/3.87 % (4836)Instruction limit reached!
% 17.94/3.87 % (4836)------------------------------
% 17.94/3.87 % (4836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.94/3.87 % (4836)Termination reason: Unknown
% 17.94/3.87 % (4836)Termination phase: Property scanning
% 17.94/3.87
% 17.94/3.87 % (4836)Memory used [KB]: 3070
% 17.94/3.87 % (4836)Time elapsed: 0.083 s
% 17.94/3.87 % (4836)Instructions burned: 188 (million)
% 17.94/3.87 % (4836)------------------------------
% 17.94/3.87 % (4836)------------------------------
% 17.94/3.89 % (4838)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_4600 for (2976ds/1827Mi)
% 17.94/3.89 % (4835)Instruction limit reached!
% 17.94/3.89 % (4835)------------------------------
% 17.94/3.89 % (4835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.94/3.89 % (4835)Termination reason: Unknown
% 17.94/3.89 % (4835)Termination phase: Saturation
% 17.94/3.89
% 17.94/3.89 % (4835)Memory used [KB]: 7675
% 17.94/3.89 % (4835)Time elapsed: 0.124 s
% 17.94/3.89 % (4835)Instructions burned: 295 (million)
% 17.94/3.89 % (4835)------------------------------
% 17.94/3.89 % (4835)------------------------------
% 18.48/3.92 % (4839)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_4600 for (2976ds/70Mi)
% 18.48/3.95 % (4833)Instruction limit reached!
% 18.48/3.95 % (4833)------------------------------
% 18.48/3.95 % (4833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.48/3.95 % (4833)Termination reason: Unknown
% 18.48/3.95 % (4833)Termination phase: Saturation
% 18.48/3.95
% 18.48/3.95 % (4833)Memory used [KB]: 12281
% 18.48/3.95 % (4833)Time elapsed: 0.181 s
% 18.48/3.95 % (4833)Instructions burned: 670 (million)
% 18.48/3.95 % (4833)------------------------------
% 18.48/3.95 % (4833)------------------------------
% 18.48/3.96 % (4839)Instruction limit reached!
% 18.48/3.96 % (4839)------------------------------
% 18.48/3.96 % (4839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.48/3.96 % (4839)Termination reason: Unknown
% 18.48/3.96 % (4839)Termination phase: Property scanning
% 18.48/3.96
% 18.48/3.96 % (4839)Memory used [KB]: 2814
% 18.48/3.96 % (4839)Time elapsed: 0.024 s
% 18.48/3.96 % (4839)Instructions burned: 71 (million)
% 18.48/3.96 % (4839)------------------------------
% 18.48/3.96 % (4839)------------------------------
% 18.48/3.96 % (4840)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_4600 for (2975ds/316Mi)
% 18.48/3.98 % (4841)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_4600 for (2975ds/932Mi)
% 18.48/3.99 % (4837)Instruction limit reached!
% 18.48/3.99 % (4837)------------------------------
% 18.48/3.99 % (4837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.48/3.99 % (4837)Termination reason: Unknown
% 18.48/3.99 % (4837)Termination phase: Saturation
% 18.48/3.99
% 18.48/3.99 % (4837)Memory used [KB]: 9338
% 18.48/3.99 % (4837)Time elapsed: 0.163 s
% 18.48/3.99 % (4837)Instructions burned: 371 (million)
% 18.48/3.99 % (4837)------------------------------
% 18.48/3.99 % (4837)------------------------------
% 18.48/4.01 % (4842)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_4600 for (2975ds/4714Mi)
% 19.44/4.09 % (4840)Instruction limit reached!
% 19.44/4.09 % (4840)------------------------------
% 19.44/4.09 % (4840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.44/4.09 % (4840)Termination reason: Unknown
% 19.44/4.09 % (4840)Termination phase: Saturation
% 19.44/4.09
% 19.44/4.09 % (4840)Memory used [KB]: 7675
% 19.44/4.09 % (4840)Time elapsed: 0.094 s
% 19.44/4.09 % (4840)Instructions burned: 316 (million)
% 19.44/4.09 % (4840)------------------------------
% 19.44/4.09 % (4840)------------------------------
% 19.44/4.11 % (4844)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_4600 for (2974ds/8250Mi)
% 21.16/4.35 % (4841)Instruction limit reached!
% 21.16/4.35 % (4841)------------------------------
% 21.16/4.35 % (4841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.16/4.35 % (4841)Termination reason: Unknown
% 21.16/4.35 % (4841)Termination phase: Saturation
% 21.16/4.35
% 21.16/4.35 % (4841)Memory used [KB]: 15223
% 21.16/4.35 % (4841)Time elapsed: 0.344 s
% 21.16/4.35 % (4841)Instructions burned: 933 (million)
% 21.16/4.35 % (4841)------------------------------
% 21.16/4.35 % (4841)------------------------------
% 21.16/4.38 % (4845)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_4600 for (2971ds/770Mi)
% 22.23/4.58 % (4838)Instruction limit reached!
% 22.23/4.58 % (4838)------------------------------
% 22.23/4.58 % (4838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.23/4.58 % (4838)Termination reason: Unknown
% 22.23/4.58 % (4838)Termination phase: Saturation
% 22.23/4.58
% 22.23/4.58 % (4838)Memory used [KB]: 22131
% 22.23/4.58 % (4838)Time elapsed: 0.699 s
% 22.23/4.58 % (4838)Instructions burned: 1827 (million)
% 22.23/4.58 % (4838)------------------------------
% 22.23/4.58 % (4838)------------------------------
% 22.23/4.59 % (4846)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_4600 for (2969ds/794Mi)
% 23.15/4.71 % (4845)Instruction limit reached!
% 23.15/4.71 % (4845)------------------------------
% 23.15/4.71 % (4845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.15/4.71 % (4845)Termination reason: Unknown
% 23.15/4.71 % (4845)Termination phase: Saturation
% 23.15/4.71
% 23.15/4.71 % (4845)Memory used [KB]: 7931
% 23.15/4.71 % (4845)Time elapsed: 0.357 s
% 23.15/4.71 % (4845)Instructions burned: 772 (million)
% 23.15/4.71 % (4845)------------------------------
% 23.15/4.71 % (4845)------------------------------
% 23.15/4.72 % (4847)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_4600 for (2968ds/464Mi)
% 23.15/4.75 % (4819)Instruction limit reached!
% 23.15/4.75 % (4819)------------------------------
% 23.15/4.75 % (4819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.15/4.75 % (4819)Termination reason: Unknown
% 23.15/4.75 % (4819)Termination phase: Saturation
% 23.15/4.75
% 23.15/4.75 % (4819)Memory used [KB]: 19317
% 23.15/4.75 % (4819)Time elapsed: 1.932 s
% 23.15/4.75 % (4819)Instructions burned: 5207 (million)
% 23.15/4.75 % (4819)------------------------------
% 23.15/4.75 % (4819)------------------------------
% 23.15/4.77 % (4848)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_4600 for (2967ds/1376Mi)
% 24.15/4.91 % (4847)Instruction limit reached!
% 24.15/4.91 % (4847)------------------------------
% 24.15/4.91 % (4847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.15/4.91 % (4847)Termination reason: Unknown
% 24.15/4.91 % (4847)Termination phase: Saturation
% 24.15/4.91
% 24.15/4.91 % (4847)Memory used [KB]: 9722
% 24.15/4.91 % (4847)Time elapsed: 0.190 s
% 24.15/4.91 % (4847)Instructions burned: 465 (million)
% 24.15/4.91 % (4847)------------------------------
% 24.15/4.91 % (4847)------------------------------
% 24.15/4.93 % (4846)Instruction limit reached!
% 24.15/4.93 % (4846)------------------------------
% 24.15/4.93 % (4846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.15/4.93 % (4846)Termination reason: Unknown
% 24.15/4.93 % (4846)Termination phase: Saturation
% 24.15/4.93
% 24.15/4.93 % (4846)Memory used [KB]: 6396
% 24.15/4.93 % (4846)Time elapsed: 0.333 s
% 24.15/4.93 % (4846)Instructions burned: 794 (million)
% 24.15/4.93 % (4846)------------------------------
% 24.15/4.93 % (4846)------------------------------
% 24.15/4.93 % (4879)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_4600 for (2966ds/906Mi)
% 24.15/4.93 % (4800)Instruction limit reached!
% 24.15/4.93 % (4800)------------------------------
% 24.15/4.93 % (4800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.15/4.93 % (4800)Termination reason: Unknown
% 24.15/4.93 % (4800)Termination phase: Saturation
% 24.15/4.93
% 24.15/4.93 % (4800)Memory used [KB]: 15863
% 24.15/4.93 % (4800)Time elapsed: 2.175 s
% 24.15/4.93 % (4800)Instructions burned: 4436 (million)
% 24.15/4.93 % (4800)------------------------------
% 24.15/4.93 % (4800)------------------------------
% 24.15/4.94 % (4880)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_4600 for (2966ds/434Mi)
% 24.15/4.95 % (4881)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_4600 for (2966ds/865Mi)
% 24.15/5.01 % (4821)Instruction limit reached!
% 24.15/5.01 % (4821)------------------------------
% 24.15/5.01 % (4821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.15/5.01 % (4821)Termination reason: Unknown
% 24.15/5.01 % (4821)Termination phase: Saturation
% 24.15/5.01
% 24.15/5.01 % (4821)Memory used [KB]: 14072
% 24.15/5.01 % (4821)Time elapsed: 2.050 s
% 24.15/5.01 % (4821)Instructions burned: 4350 (million)
% 24.15/5.01 % (4821)------------------------------
% 24.15/5.01 % (4821)------------------------------
% 26.42/5.03 % (4882)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_4600 for (2965ds/593Mi)
% 27.03/5.14 % (4880)Instruction limit reached!
% 27.03/5.14 % (4880)------------------------------
% 27.03/5.14 % (4880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.03/5.14 % (4880)Termination reason: Unknown
% 27.03/5.14 % (4880)Termination phase: Saturation
% 27.03/5.14
% 27.03/5.14 % (4880)Memory used [KB]: 12025
% 27.03/5.14 % (4880)Time elapsed: 0.203 s
% 27.03/5.14 % (4880)Instructions burned: 435 (million)
% 27.03/5.14 % (4880)------------------------------
% 27.03/5.14 % (4880)------------------------------
% 27.03/5.15 % (4884)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_4600 for (2963ds/443Mi)
% 27.42/5.27 % (4882)Instruction limit reached!
% 27.42/5.27 % (4882)------------------------------
% 27.42/5.27 % (4882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.42/5.27 % (4882)Termination reason: Unknown
% 27.42/5.27 % (4882)Termination phase: Saturation
% 27.42/5.27
% 27.42/5.27 % (4882)Memory used [KB]: 7803
% 27.42/5.27 % (4882)Time elapsed: 0.242 s
% 27.42/5.27 % (4882)Instructions burned: 595 (million)
% 27.42/5.27 % (4882)------------------------------
% 27.42/5.27 % (4882)------------------------------
% 27.42/5.27 % (4884)Instruction limit reached!
% 27.42/5.27 % (4884)------------------------------
% 27.42/5.27 % (4884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.42/5.27 % (4884)Termination reason: Unknown
% 27.42/5.27 % (4884)Termination phase: Saturation
% 27.42/5.27
% 27.42/5.27 % (4884)Memory used [KB]: 9722
% 27.42/5.27 % (4884)Time elapsed: 0.120 s
% 27.42/5.27 % (4884)Instructions burned: 443 (million)
% 27.42/5.27 % (4884)------------------------------
% 27.42/5.27 % (4884)------------------------------
% 27.42/5.28 % (4886)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_4600 for (2962ds/327Mi)
% 27.42/5.28 % (4885)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_4600 for (2962ds/594Mi)
% 27.42/5.28 % (4848)Instruction limit reached!
% 27.42/5.28 % (4848)------------------------------
% 27.42/5.28 % (4848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.42/5.28 % (4848)Termination reason: Unknown
% 27.42/5.28 % (4848)Termination phase: Saturation
% 27.42/5.28
% 27.42/5.28 % (4848)Memory used [KB]: 10362
% 27.42/5.28 % (4848)Time elapsed: 0.517 s
% 27.42/5.28 % (4848)Instructions burned: 1376 (million)
% 27.42/5.28 % (4848)------------------------------
% 27.42/5.28 % (4848)------------------------------
% 28.30/5.30 % (4881)Instruction limit reached!
% 28.30/5.30 % (4881)------------------------------
% 28.30/5.30 % (4881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.30/5.30 % (4881)Termination reason: Unknown
% 28.30/5.30 % (4881)Termination phase: Saturation
% 28.30/5.30
% 28.30/5.30 % (4881)Memory used [KB]: 11001
% 28.30/5.30 % (4881)Time elapsed: 0.359 s
% 28.30/5.30 % (4881)Instructions burned: 865 (million)
% 28.30/5.30 % (4881)------------------------------
% 28.30/5.30 % (4881)------------------------------
% 28.30/5.31 % (4887)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_4600 for (2962ds/5411Mi)
% 28.30/5.32 % (4888)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_4600 for (2962ds/1762Mi)
% 28.30/5.35 % (4879)Instruction limit reached!
% 28.30/5.35 % (4879)------------------------------
% 28.30/5.35 % (4879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.30/5.35 % (4879)Termination reason: Unknown
% 28.30/5.35 % (4879)Termination phase: Saturation
% 28.30/5.35
% 28.30/5.35 % (4879)Memory used [KB]: 11641
% 28.30/5.35 % (4879)Time elapsed: 0.428 s
% 28.30/5.35 % (4879)Instructions burned: 906 (million)
% 28.30/5.35 % (4879)------------------------------
% 28.30/5.35 % (4879)------------------------------
% 28.30/5.37 % (4890)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_4600 for (2961ds/96Mi)
% 28.30/5.39 % (4886)Instruction limit reached!
% 28.30/5.39 % (4886)------------------------------
% 28.30/5.39 % (4886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.30/5.39 % (4886)Termination reason: Unknown
% 28.30/5.39 % (4886)Termination phase: Saturation
% 28.30/5.39
% 28.30/5.39 % (4886)Memory used [KB]: 11257
% 28.30/5.39 % (4886)Time elapsed: 0.117 s
% 28.30/5.39 % (4886)Instructions burned: 327 (million)
% 28.30/5.39 % (4886)------------------------------
% 28.30/5.39 % (4886)------------------------------
% 28.58/5.41 % (4890)Instruction limit reached!
% 28.58/5.41 % (4890)------------------------------
% 28.58/5.41 % (4890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.58/5.41 % (4890)Termination reason: Unknown
% 28.58/5.41 % (4890)Termination phase: Property scanning
% 28.58/5.41
% 28.58/5.41 % (4890)Memory used [KB]: 2814
% 28.58/5.41 % (4890)Time elapsed: 0.045 s
% 28.58/5.41 % (4890)Instructions burned: 97 (million)
% 28.58/5.41 % (4890)------------------------------
% 28.58/5.41 % (4890)------------------------------
% 28.58/5.42 % (4891)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_4600 for (2961ds/503Mi)
% 28.58/5.43 % (4892)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_4600 for (2961ds/90Mi)
% 28.58/5.47 % (4892)Instruction limit reached!
% 28.58/5.47 % (4892)------------------------------
% 28.58/5.47 % (4892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.58/5.47 % (4892)Termination reason: Unknown
% 28.58/5.47 % (4892)Termination phase: Property scanning
% 28.58/5.47
% 28.58/5.47 % (4892)Memory used [KB]: 2814
% 28.58/5.47 % (4892)Time elapsed: 0.044 s
% 28.58/5.47 % (4892)Instructions burned: 91 (million)
% 28.58/5.47 % (4892)------------------------------
% 28.58/5.47 % (4892)------------------------------
% 28.58/5.49 % (4893)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_4600 for (2960ds/593Mi)
% 29.03/5.51 % (4885)Instruction limit reached!
% 29.03/5.51 % (4885)------------------------------
% 29.03/5.51 % (4885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.03/5.51 % (4885)Termination reason: Unknown
% 29.03/5.51 % (4885)Termination phase: Saturation
% 29.03/5.51
% 29.03/5.51 % (4885)Memory used [KB]: 10234
% 29.03/5.51 % (4885)Time elapsed: 0.225 s
% 29.03/5.51 % (4885)Instructions burned: 595 (million)
% 29.03/5.51 % (4885)------------------------------
% 29.03/5.51 % (4885)------------------------------
% 29.03/5.52 % (4894)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_4600 for (2960ds/1512Mi)
% 29.47/5.62 % (4891)Instruction limit reached!
% 29.47/5.62 % (4891)------------------------------
% 29.47/5.62 % (4891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.47/5.62 % (4891)Termination reason: Unknown
% 29.47/5.62 % (4891)Termination phase: Saturation
% 29.47/5.62
% 29.47/5.62 % (4891)Memory used [KB]: 10106
% 29.47/5.62 % (4891)Time elapsed: 0.204 s
% 29.47/5.62 % (4891)Instructions burned: 503 (million)
% 29.47/5.62 % (4891)------------------------------
% 29.47/5.62 % (4891)------------------------------
% 29.47/5.64 % (4895)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_4600 for (2958ds/569Mi)
% 29.47/5.67 % (4842)Instruction limit reached!
% 29.47/5.67 % (4842)------------------------------
% 29.47/5.67 % (4842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.47/5.67 % (4842)Termination reason: Unknown
% 29.47/5.67 % (4842)Termination phase: Saturation
% 29.47/5.67
% 29.47/5.67 % (4842)Memory used [KB]: 7931
% 29.47/5.67 % (4842)Time elapsed: 1.662 s
% 29.47/5.67 % (4842)Instructions burned: 4714 (million)
% 29.47/5.67 % (4842)------------------------------
% 29.47/5.67 % (4842)------------------------------
% 29.47/5.68 % (4896)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_4600 for (2958ds/501Mi)
% 29.89/5.75 % (4893)Instruction limit reached!
% 29.89/5.75 % (4893)------------------------------
% 29.89/5.75 % (4893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.89/5.75 % (4893)Termination reason: Unknown
% 29.89/5.75 % (4893)Termination phase: Saturation
% 29.89/5.75
% 29.89/5.75 % (4893)Memory used [KB]: 10490
% 29.89/5.75 % (4893)Time elapsed: 0.262 s
% 29.89/5.75 % (4893)Instructions burned: 594 (million)
% 29.89/5.75 % (4893)------------------------------
% 29.89/5.75 % (4893)------------------------------
% 29.89/5.78 % (4897)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_4600 for (2957ds/562Mi)
% 30.26/5.84 % (4895)Instruction limit reached!
% 30.26/5.84 % (4895)------------------------------
% 30.26/5.84 % (4895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.26/5.84 % (4895)Termination reason: Unknown
% 30.26/5.84 % (4895)Termination phase: Saturation
% 30.26/5.84
% 30.26/5.84 % (4895)Memory used [KB]: 7803
% 30.26/5.84 % (4895)Time elapsed: 0.201 s
% 30.26/5.84 % (4895)Instructions burned: 571 (million)
% 30.26/5.84 % (4895)------------------------------
% 30.26/5.84 % (4895)------------------------------
% 30.26/5.86 % (4898)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_4600 for (2956ds/406Mi)
% 30.58/5.92 % (4896)Instruction limit reached!
% 30.58/5.92 % (4896)------------------------------
% 30.58/5.92 % (4896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.58/5.92 % (4896)Termination reason: Unknown
% 30.58/5.92 % (4896)Termination phase: Saturation
% 30.58/5.92
% 30.58/5.92 % (4896)Memory used [KB]: 11129
% 30.58/5.92 % (4896)Time elapsed: 0.238 s
% 30.58/5.92 % (4896)Instructions burned: 501 (million)
% 30.58/5.92 % (4896)------------------------------
% 30.58/5.92 % (4896)------------------------------
% 30.58/5.94 % (4899)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_4600 for (2955ds/582Mi)
% 30.58/5.96 % (4888)Instruction limit reached!
% 30.58/5.96 % (4888)------------------------------
% 30.58/5.96 % (4888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.58/5.96 % (4888)Termination reason: Unknown
% 30.58/5.96 % (4888)Termination phase: Saturation
% 30.58/5.96
% 30.58/5.96 % (4888)Memory used [KB]: 21875
% 30.58/5.96 % (4888)Time elapsed: 0.637 s
% 30.58/5.96 % (4888)Instructions burned: 1762 (million)
% 30.58/5.96 % (4888)------------------------------
% 30.58/5.96 % (4888)------------------------------
% 30.58/5.97 % (4900)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_4600 for (2955ds/456Mi)
% 30.58/6.00 % (4897)Instruction limit reached!
% 30.58/6.00 % (4897)------------------------------
% 30.58/6.00 % (4897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.58/6.00 % (4897)Termination reason: Unknown
% 30.58/6.00 % (4897)Termination phase: Saturation
% 30.58/6.00
% 30.58/6.00 % (4897)Memory used [KB]: 9594
% 30.58/6.00 % (4897)Time elapsed: 0.214 s
% 30.58/6.00 % (4897)Instructions burned: 563 (million)
% 30.58/6.00 % (4897)------------------------------
% 30.58/6.00 % (4897)------------------------------
% 30.58/6.01 % (4901)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_4600 for (2955ds/393Mi)
% 33.33/6.04 % (4898)Instruction limit reached!
% 33.33/6.04 % (4898)------------------------------
% 33.33/6.04 % (4898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.33/6.04 % (4898)Termination reason: Unknown
% 33.33/6.04 % (4898)Termination phase: Saturation
% 33.33/6.04
% 33.33/6.04 % (4898)Memory used [KB]: 7931
% 33.33/6.04 % (4898)Time elapsed: 0.186 s
% 33.33/6.04 % (4898)Instructions burned: 406 (million)
% 33.33/6.04 % (4898)------------------------------
% 33.33/6.04 % (4898)------------------------------
% 33.33/6.06 % (4902)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_4600 for (2954ds/1335Mi)
% 33.88/6.16 % (4900)Instruction limit reached!
% 33.88/6.16 % (4900)------------------------------
% 33.88/6.16 % (4900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.88/6.16 % (4900)Termination reason: Unknown
% 33.88/6.16 % (4900)Termination phase: Saturation
% 33.88/6.16
% 33.88/6.16 % (4900)Memory used [KB]: 9850
% 33.88/6.16 % (4900)Time elapsed: 0.191 s
% 33.88/6.16 % (4900)Instructions burned: 456 (million)
% 33.88/6.16 % (4900)------------------------------
% 33.88/6.16 % (4900)------------------------------
% 33.88/6.18 % (4903)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_4600 for (2953ds/3373Mi)
% 33.88/6.19 % (4901)Instruction limit reached!
% 33.88/6.19 % (4901)------------------------------
% 33.88/6.19 % (4901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.88/6.19 % (4901)Termination reason: Unknown
% 33.88/6.19 % (4901)Termination phase: Saturation
% 33.88/6.19
% 33.88/6.19 % (4901)Memory used [KB]: 9978
% 33.88/6.19 % (4901)Time elapsed: 0.176 s
% 33.88/6.19 % (4901)Instructions burned: 396 (million)
% 33.88/6.19 % (4901)------------------------------
% 33.88/6.19 % (4901)------------------------------
% 34.41/6.20 % (4904)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_4600 for (2953ds/474Mi)
% 34.41/6.21 % (4899)Instruction limit reached!
% 34.41/6.21 % (4899)------------------------------
% 34.41/6.21 % (4899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.41/6.21 % (4899)Termination reason: Unknown
% 34.41/6.21 % (4899)Termination phase: Saturation
% 34.41/6.21
% 34.41/6.21 % (4899)Memory used [KB]: 11385
% 34.41/6.21 % (4899)Time elapsed: 0.274 s
% 34.41/6.21 % (4899)Instructions burned: 582 (million)
% 34.41/6.21 % (4899)------------------------------
% 34.41/6.21 % (4899)------------------------------
% 34.41/6.23 % (4905)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_4600 for (2953ds/157Mi)
% 34.41/6.23 % (4894)Instruction limit reached!
% 34.41/6.23 % (4894)------------------------------
% 34.41/6.23 % (4894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.41/6.23 % (4894)Termination reason: Unknown
% 34.41/6.23 % (4894)Termination phase: Saturation
% 34.41/6.23
% 34.41/6.23 % (4894)Memory used [KB]: 13432
% 34.41/6.23 % (4894)Time elapsed: 0.710 s
% 34.41/6.23 % (4894)Instructions burned: 1512 (million)
% 34.41/6.23 % (4894)------------------------------
% 34.41/6.23 % (4894)------------------------------
% 34.41/6.25 % (4906)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_4600 for (2952ds/590Mi)
% 34.41/6.29 % (4887)First to succeed.
% 34.41/6.30 % (4905)Instruction limit reached!
% 34.41/6.30 % (4905)------------------------------
% 34.41/6.30 % (4905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.41/6.30 % (4905)Termination reason: Unknown
% 34.41/6.30 % (4905)Termination phase: Property scanning
% 34.41/6.30
% 34.41/6.30 % (4905)Memory used [KB]: 2814
% 34.41/6.30 % (4905)Time elapsed: 0.070 s
% 34.41/6.30 % (4905)Instructions burned: 159 (million)
% 34.41/6.30 % (4905)------------------------------
% 34.41/6.30 % (4905)------------------------------
% 34.78/6.30 % (4887)Refutation found. Thanks to Tanya!
% 34.78/6.30 % SZS status Theorem for DTF2THF_4600
% 34.78/6.30 % SZS output start Proof for DTF2THF_4600
% 34.78/6.30 thf(func_def_0, type, in: $i > $i > $o).
% 34.78/6.30 thf(func_def_1, type, exu: ($i > $o) > $o).
% 34.78/6.30 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 34.78/6.30 thf(func_def_8, type, powerset: $i > $i).
% 34.78/6.30 thf(func_def_10, type, setunion: $i > $i).
% 34.78/6.30 thf(func_def_19, type, descr: ($i > $o) > $i).
% 34.78/6.30 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 34.78/6.30 thf(func_def_26, type, prop2set: $o > $i).
% 34.78/6.30 thf(func_def_36, type, nonempty: $i > $o).
% 34.78/6.30 thf(func_def_69, type, set2prop: $i > $o).
% 34.78/6.30 thf(func_def_88, type, subset: $i > $i > $o).
% 34.78/6.30 thf(func_def_89, type, disjoint: $i > $i > $o).
% 34.78/6.30 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 34.78/6.30 thf(func_def_114, type, binunion: $i > $i > $i).
% 34.78/6.30 thf(func_def_122, type, binintersect: $i > $i > $i).
% 34.78/6.30 thf(func_def_135, type, regular: $i > $o).
% 34.78/6.30 thf(func_def_136, type, setminus: $i > $i > $i).
% 34.78/6.30 thf(func_def_147, type, symdiff: $i > $i > $i).
% 34.78/6.30 thf(func_def_153, type, iskpair: $i > $o).
% 34.78/6.30 thf(func_def_158, type, kpair: $i > $i > $i).
% 34.78/6.30 thf(func_def_160, type, cartprod: $i > $i > $i).
% 34.78/6.30 thf(func_def_177, type, singleton: $i > $o).
% 34.78/6.30 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 34.78/6.30 thf(func_def_184, type, atmost1p: $i > $o).
% 34.78/6.30 thf(func_def_185, type, atleast2p: $i > $o).
% 34.78/6.30 thf(func_def_186, type, atmost2p: $i > $o).
% 34.78/6.30 thf(func_def_187, type, upairsetp: $i > $o).
% 34.78/6.30 thf(func_def_191, type, kfst: $i > $i).
% 34.78/6.30 thf(func_def_203, type, ksnd: $i > $i).
% 34.78/6.30 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 34.78/6.30 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 34.78/6.30 thf(func_def_222, type, func: $i > $i > $i > $o).
% 34.78/6.30 thf(func_def_223, type, funcSet: $i > $i > $i).
% 34.78/6.30 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 34.78/6.30 thf(func_def_259, type, if: $i > $o > $i > $i > $i).
% 34.78/6.30 thf(func_def_323, type, breln1: $i > $i > $o).
% 34.78/6.30 thf(func_def_325, type, breln1Set: $i > $i).
% 34.78/6.30 thf(func_def_327, type, transitive: $i > $i > $o).
% 34.78/6.30 thf(func_def_328, type, antisymmetric: $i > $i > $o).
% 34.78/6.30 thf(func_def_329, type, reflexive: $i > $i > $o).
% 34.78/6.30 thf(func_def_330, type, refltransitive: $i > $i > $o).
% 34.78/6.30 thf(func_def_331, type, refllinearorder: $i > $i > $o).
% 34.78/6.30 thf(func_def_332, type, reflwellordering: $i > $i > $o).
% 34.78/6.30 thf(func_def_338, type, breln1invset: $i > $i > $i).
% 34.78/6.30 thf(func_def_342, type, breln1compset: $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_360, type, image1: $i > ($i > $i) > $i).
% 34.78/6.30 thf(func_def_364, type, injective: $i > $i > $i > $o).
% 34.78/6.30 thf(func_def_365, type, injFuncSet: $i > $i > $i).
% 34.78/6.30 thf(func_def_369, type, surjective: $i > $i > $i > $o).
% 34.78/6.30 thf(func_def_370, type, surjFuncSet: $i > $i > $i).
% 34.78/6.30 thf(func_def_391, type, sP1: $i > $i > $o).
% 34.78/6.30 thf(func_def_392, type, sP2: $i > $o).
% 34.78/6.30 thf(func_def_393, type, sP3: $i > $i > $o).
% 34.78/6.30 thf(func_def_394, type, sP4: $i > $i > $o).
% 34.78/6.30 thf(func_def_397, type, sP7: $i > $i > $i > $o).
% 34.78/6.30 thf(func_def_398, type, sP8: $i > $i > $i > $o).
% 34.78/6.30 thf(func_def_401, type, sP11: $i > $i > $i > $o > $o).
% 34.78/6.30 thf(func_def_406, type, sP16: $i > $i > $i > $i > $o).
% 34.78/6.30 thf(func_def_412, type, sK22: $i > $o).
% 34.78/6.30 thf(func_def_443, type, sK53: ($i > $o) > ($i > $o) > $i > $i > $i).
% 34.78/6.30 thf(func_def_444, type, sK54: ($i > $o) > ($i > $o) > $i > $i > $i).
% 34.78/6.30 thf(func_def_447, type, sK57: $i > $o).
% 34.78/6.30 thf(func_def_448, type, sK58: $i > $o).
% 34.78/6.30 thf(func_def_449, type, sK59: $i > ($i > $o) > $i).
% 34.78/6.30 thf(func_def_450, type, sK60: $i > $o).
% 34.78/6.30 thf(func_def_468, type, sK78: $i > $i).
% 34.78/6.30 thf(func_def_494, type, sK104: $i > $o).
% 34.78/6.30 thf(func_def_495, type, sK105: $i > $i).
% 34.78/6.30 thf(func_def_496, type, sK106: ($i > $o) > $i).
% 34.78/6.30 thf(func_def_497, type, sK107: $i > $o).
% 34.78/6.30 thf(func_def_500, type, sK110: $i > ($i > $o) > $i).
% 34.78/6.30 thf(func_def_501, type, sK111: $i > ($i > $o) > $i).
% 34.78/6.30 thf(func_def_512, type, sK122: $i > $o).
% 34.78/6.30 thf(func_def_514, type, sK124: $i > $i > $i).
% 34.78/6.30 thf(func_def_515, type, sK125: $i > $i > $i).
% 34.78/6.30 thf(func_def_516, type, sK126: $i > $i > $i).
% 34.78/6.30 thf(func_def_517, type, sK127: $i > $i > $i).
% 34.78/6.30 thf(func_def_518, type, sK128: $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_519, type, sK129: $i > $i).
% 34.78/6.30 thf(func_def_520, type, sK130: $i > $i).
% 34.78/6.30 thf(func_def_521, type, sK131: $i > $i).
% 34.78/6.30 thf(func_def_522, type, sK132: $i > $i).
% 34.78/6.30 thf(func_def_523, type, sK133: $i > $i > $i).
% 34.78/6.30 thf(func_def_524, type, sK134: $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_525, type, sK135: $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_526, type, sK136: $i > $i > $i).
% 34.78/6.30 thf(func_def_527, type, sK137: $i > $i > $i).
% 34.78/6.30 thf(func_def_528, type, sK138: $i > $i).
% 34.78/6.30 thf(func_def_529, type, sK139: $i > $i > $i).
% 34.78/6.30 thf(func_def_531, type, sK141: $i > $i).
% 34.78/6.30 thf(func_def_532, type, sK142: $i > $i).
% 34.78/6.30 thf(func_def_544, type, sK154: $o > $i > $i > $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_572, type, sK182: $i > $o).
% 34.78/6.30 thf(func_def_574, type, sK184: $i > ($i > $o) > $i).
% 34.78/6.30 thf(func_def_581, type, sK191: $i > $i > $i).
% 34.78/6.30 thf(func_def_582, type, sK192: $i > $i > $i).
% 34.78/6.30 thf(func_def_584, type, sK194: $i > $o).
% 34.78/6.30 thf(func_def_591, type, sK201: $i > $i > $o).
% 34.78/6.30 thf(func_def_592, type, sK202: $i > $i).
% 34.78/6.30 thf(func_def_593, type, sK203: $i > $i).
% 34.78/6.30 thf(func_def_594, type, sK204: ($i > $i > $o) > $i > $i).
% 34.78/6.30 thf(func_def_595, type, sK205: ($i > $i > $o) > $i > $i).
% 34.78/6.30 thf(func_def_596, type, sK206: $i > ($i > $i > $o) > $i > $i).
% 34.78/6.30 thf(func_def_598, type, sK208: $i > $i > $o).
% 34.78/6.30 thf(func_def_617, type, sK227: $i > $o).
% 34.78/6.30 thf(func_def_618, type, sK228: $i > $o).
% 34.78/6.30 thf(func_def_619, type, sK229: ($i > $o) > ($i > $o) > $i).
% 34.78/6.30 thf(func_def_620, type, sK230: ($i > $o) > ($i > $o) > $i).
% 34.78/6.30 thf(func_def_637, type, sK247: $i > $i > $o).
% 34.78/6.30 thf(func_def_651, type, sK261: $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_652, type, sK262: $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_663, type, sK273: $i > $i).
% 34.78/6.30 thf(func_def_676, type, sK286: $i > $i > $i).
% 34.78/6.30 thf(func_def_679, type, sK289: $i > $i > $o).
% 34.78/6.30 thf(func_def_708, type, sK318: $i > $i).
% 34.78/6.30 thf(func_def_712, type, sK322: $i > $i > ($i > $i) > $i).
% 34.78/6.30 thf(func_def_724, type, sK334: $i > $i > $i).
% 34.78/6.30 thf(func_def_739, type, sK349: $i > $i).
% 34.78/6.30 thf(func_def_757, type, sK367: $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_761, type, sK371: $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_762, type, sK372: $i > ($i > $i) > $i > $i).
% 34.78/6.30 thf(func_def_764, type, sK374: $i > $i).
% 34.78/6.30 thf(func_def_770, type, sK380: $i > $i > $o).
% 34.78/6.30 thf(func_def_773, type, sK383: $i > $o).
% 34.78/6.30 thf(func_def_775, type, sK385: ($i > $o) > $i > $i > $i).
% 34.78/6.30 thf(func_def_776, type, sK386: ($i > $o) > $i > $i > $i).
% 34.78/6.30 thf(func_def_784, type, sK394: $i > $o).
% 34.78/6.30 thf(func_def_792, type, sK402: $i > $i).
% 34.78/6.30 thf(func_def_794, type, sK404: ($i > $i) > $i > $i > $i).
% 34.78/6.30 thf(func_def_807, type, sK417: $i > $i > $i).
% 34.78/6.30 thf(func_def_829, type, sK439: $i > $o).
% 34.78/6.30 thf(func_def_832, type, sK442: ($i > $o) > $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_833, type, sK443: ($i > $o) > $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_837, type, sK447: $i > $o).
% 34.78/6.30 thf(func_def_839, type, sK449: $i > $i > $o).
% 34.78/6.30 thf(func_def_842, type, sK452: $i > $i).
% 34.78/6.30 thf(func_def_850, type, sK460: $i > $i > $i).
% 34.78/6.30 thf(func_def_866, type, sK476: $i > $i > $o).
% 34.78/6.30 thf(func_def_869, type, sK479: $i > $o).
% 34.78/6.30 thf(func_def_901, type, sK511: $i > $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_902, type, sK512: $i > $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_908, type, sK518: $i > $o).
% 34.78/6.30 thf(func_def_910, type, sK520: ($i > $o) > $i > $i).
% 34.78/6.30 thf(func_def_919, type, sK529: $i > ($i > $i) > $i > $i).
% 34.78/6.30 thf(func_def_921, type, sK531: $i > $i).
% 34.78/6.30 thf(func_def_936, type, sK546: $i > $i).
% 34.78/6.30 thf(func_def_938, type, sK548: $i > ($i > $i) > $i > $i > $i).
% 34.78/6.30 thf(func_def_939, type, sK549: ($i > $i) > $i > $i > $i).
% 34.78/6.30 thf(func_def_941, type, sK551: $i > $i > $o).
% 34.78/6.30 thf(func_def_955, type, sK565: $i > $i > $i).
% 34.78/6.30 thf(func_def_956, type, sK566: $i > ($i > $i) > $i > $i).
% 34.78/6.30 thf(func_def_958, type, sK568: $i > $i).
% 34.78/6.30 thf(func_def_966, type, sK576: $i > $o).
% 34.78/6.30 thf(func_def_969, type, sK579: $i > ($i > $o) > $i).
% 34.78/6.30 thf(func_def_974, type, sK584: $i > $o).
% 34.78/6.30 thf(func_def_981, type, sK591: $i > $o).
% 34.78/6.30 thf(func_def_997, type, sK607: $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_998, type, sK608: $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_999, type, sK609: $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_1000, type, sK610: $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_1003, type, sK613: ($i > $i) > $i > $i).
% 34.78/6.30 thf(func_def_1004, type, sK614: $i > ($i > $i) > $i > $i).
% 34.78/6.30 thf(func_def_1006, type, sK616: $i > $i).
% 34.78/6.30 thf(func_def_1007, type, sK617: $i > $i).
% 34.78/6.30 thf(func_def_1008, type, sK618: $i > $i).
% 34.78/6.30 thf(func_def_1066, type, sK676: $i > $i > $i).
% 34.78/6.30 thf(func_def_1071, type, sK681: $i > $o).
% 34.78/6.30 thf(func_def_1085, type, sK695: $i > $o).
% 34.78/6.30 thf(func_def_1087, type, sK697: ($i > $o) > $i > $i).
% 34.78/6.30 thf(func_def_1088, type, sK698: ($i > $o) > $i > $i).
% 34.78/6.30 thf(func_def_1095, type, sK705: $i > $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_1120, type, sK730: ($i > $i) > $i > $i > $i).
% 34.78/6.30 thf(func_def_1123, type, sK733: $i > $i).
% 34.78/6.30 thf(func_def_1127, type, sK737: $i > $i).
% 34.78/6.30 thf(func_def_1134, type, sK744: $i > $i).
% 34.78/6.30 thf(func_def_1137, type, sK747: $i > $o).
% 34.78/6.30 thf(func_def_1139, type, sK749: ($i > $o) > $i > $i > $i).
% 34.78/6.30 thf(func_def_1140, type, sK750: ($i > $o) > $i > $i > $i).
% 34.78/6.30 thf(func_def_1172, type, sK782: $i > $i > $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_1178, type, sK788: $i > $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_1181, type, sK791: $i > $i > $o).
% 34.78/6.30 thf(func_def_1186, type, sK796: $o > $i > $i > $i).
% 34.78/6.30 thf(func_def_1190, type, sK800: ($i > $o) > $i).
% 34.78/6.30 thf(func_def_1191, type, sK801: $i > $o).
% 34.78/6.30 thf(func_def_1195, type, sK805: $i > $o).
% 34.78/6.30 thf(func_def_1197, type, sK807: ($i > $o) > $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_1198, type, sK808: ($i > $o) > $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_1208, type, sK818: $i > $o).
% 34.78/6.30 thf(func_def_1212, type, sK822: $i > $i).
% 34.78/6.30 thf(func_def_1213, type, sK823: $i > $i).
% 34.78/6.30 thf(func_def_1214, type, sK824: $i > $o).
% 34.78/6.30 thf(func_def_1216, type, sK826: $i > ($i > $o) > $i).
% 34.78/6.30 thf(func_def_1224, type, sK834: $i > $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_1225, type, sK835: $i > $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_1226, type, sK836: $i > $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_1227, type, sK837: $i > $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_1228, type, sK838: $i > $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_1240, type, sK850: $i > $o).
% 34.78/6.30 thf(func_def_1242, type, sK852: ($i > $o) > $i).
% 34.78/6.30 thf(func_def_1243, type, sK853: ($i > $o) > $i).
% 34.78/6.30 thf(func_def_1250, type, sK860: $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_1270, type, sK880: ($i > $i) > $i > $i > $i).
% 34.78/6.30 thf(func_def_1273, type, sK883: $i > $i).
% 34.78/6.30 thf(func_def_1274, type, sK884: $i > ($i > $o) > $i).
% 34.78/6.30 thf(func_def_1275, type, sK885: $i > $o).
% 34.78/6.30 thf(func_def_1295, type, sK905: $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_1296, type, sK906: $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_1321, type, sK931: $i > $o).
% 34.78/6.30 thf(func_def_1323, type, sK933: $i > ($i > $o) > $i > $i).
% 34.78/6.30 thf(func_def_1328, type, sK938: $i > $o).
% 34.78/6.30 thf(func_def_1333, type, sK943: $i > $i).
% 34.78/6.30 thf(func_def_1337, type, sK947: $i > $i > ($i > $i) > $i).
% 34.78/6.30 thf(func_def_1338, type, sK948: $i > $o).
% 34.78/6.30 thf(func_def_1339, type, sK949: $i > $o).
% 34.78/6.30 thf(func_def_1340, type, sK950: ($i > $o) > ($i > $o) > $i).
% 34.78/6.30 thf(func_def_1341, type, sK951: ($i > $o) > ($i > $o) > $i).
% 34.78/6.30 thf(func_def_1345, type, sK955: $i > $i > $i).
% 34.78/6.30 thf(func_def_1351, type, sK961: $i > $o).
% 34.78/6.30 thf(func_def_1353, type, sK963: ($i > $o) > $i > $i).
% 34.78/6.30 thf(func_def_1355, type, sK965: $i > $o).
% 34.78/6.30 thf(func_def_1357, type, sK967: ($i > $o) > $i > $i).
% 34.78/6.30 thf(func_def_1381, type, sK991: $i > $i > $i).
% 34.78/6.30 thf(func_def_1401, type, sK1011: $i > $i > $i > $i).
% 34.78/6.30 thf(func_def_1410, type, sK1020: $i > $o).
% 34.78/6.30 thf(func_def_1422, type, sK1032: $i > $o).
% 34.78/6.30 thf(func_def_1423, type, sK1033: $i > $i).
% 34.78/6.30 thf(func_def_1424, type, sK1034: ($i > $o) > $i).
% 34.78/6.30 thf(func_def_1425, type, sK1035: $i > $i).
% 34.78/6.30 thf(func_def_1431, type, sK1041: $i > ($i > $o) > $i).
% 34.78/6.30 thf(func_def_1432, type, sK1042: $i > $o).
% 34.78/6.30 thf(func_def_1443, type, sK1053: $i > $o).
% 34.78/6.30 thf(func_def_1468, type, ph1078: !>[X0: $tType]:(X0)).
% 34.78/6.30 thf(f11438,plain,(
% 34.78/6.30 $false),
% 34.78/6.30 inference(trivial_inequality_removal,[status(thm)],[f11435])).
% 34.78/6.30 thf(f11435,plain,(
% 34.78/6.30 ($true != $true)),
% 34.78/6.30 inference(superposition,[status(thm)],[f11333,f3373])).
% 34.78/6.30 thf(f3373,plain,(
% 34.78/6.30 ($true = (in @ sK28 @ sK28))),
% 34.78/6.30 inference(cnf_transformation,[status(thm)],[f1465])).
% 34.78/6.30 thf(f1465,plain,(
% 34.78/6.30 (setunionE2 = $true) & (secondinupair = $true) & (inPowerset = $true) & (complementTI1 = $true) & (subbreln = $true) & (contrasubsetT2 = $true) & (brelnall2 = $true) & (setminusSubset1 = $true) & (emptysetsubset = $true) & (ex1I2 = $true) & (contraSubsetComplement = $true) & (ksndsingleton = $true) & (sepSubset = $true) & (setminusIRneg = $true) & (complementTcontraSubset = $true) & (injFuncSetFuncIn = $true) & (breln1unionprop = $true) & (foundation2 = $true) & (inCongP = $true) & (theeq = $true) & (setextsub = $true) & (quantDeMorgan3 = $true) & (setunionsingleton1 = $true) & (setukpairinjL1 = $true) & (breln1compprop = $true) & (ex1E2 = $true) & (singletonsswitch = $true) & (subsetI1 = $true) & (dsetconstrER = $true) & (exuE1 = $true) & (binunionIR = $true) & ($true = (in @ sK28 @ sK28)) & (woz2B = $true) & (infuncsetfunc = $true) & (image1Ex = $true) & (breln1invE = $true) & (emptyI = $true) & (kpairsurjEq = $true) & (subsetTrans = $true) & (woz13rule0 = $true) & (setminusILneg = $true) & (setukpairinjL = $true) & (setukpairinjR2 = $true) & (inComplementUnionImpInComplement1 = $true) & (upairset2E = $true) & (quantDeMorgan4 = $true) & (singletonsubset = $true) & (setminusELneg = $true) & (ifp = $true) & (ap2apEq2 = $true) & (ifSingleton = $true) & (notequalI1 = $true) & (breln1invprop = $true) & (subsetemptysetimpeq = $true) & (setukpairIL = $true) & (subsetRefl = $true) & (lamp = $true) & (setminusT_lem = $true) & (sepInPowerset = $true) & (upairsubunion = $true) & (ap2p = $true) & (notinemptyset = $true) & (contrasubsetT = $true) & (injFuncSetFuncInj = $true) & (symdiffE = $true) & (setOfPairsIsBReln = $true) & (binintersectSubset1 = $true) & (wellorderingAx = $true) & (binintersectSubset5 = $true) & (choice2fnsingleton = $true) & (binintersectRsub = $true) & (woz1_3 = $true) & (iftrueorfalse = $true) & (eta2 = $true) & (demorgan1b = $true) & (woz2W = $true) & (prop2set2propI = $true) & (prop2setI = $true) & (binintersectER = $true) & (woz2Ex = $true) & (surjFuncSetFuncIn = $true) & (emptyinPowerset = $true) & (complementImpComplementIntersect = $true) & (omegaIndAx = $true) & (demorgan1a = $true) & (binintersectI = $true) & (binintersectSubset2 = $true) & (ex1I = $true) & (singletoninpowunion = $true) & (noeltsimpempty = $true) & (iftrueProp2 = $true) & (binunionT_lem = $true) & (cartprodsndin = $true) & (contrasubsetT3 = $true) & (cartprodmempaircEq = $true) & (subsetE2 = $true) & (dpsetconstrEL1 = $true) & (doubleComplementSub1 = $true) & (emptyset__Cong = $true) & (ksndpairEq = $true) & (upairsetIR = $true) & (leftInvIsSurj = $true) & (dsetconstrEL = $true) & (cartprodmempair = $true) & (powersetE1 = $true) & (cartprodpairmemEL = $true) & (setukpairinjR = $true) & (woz13rule1 = $true) & (setadjoinSub = $true) & (exuI3 = $true) & (upairsetIL = $true) & (cartprodfstpairEq = $true) & (vacuousDall = $true) & (breln1unionEcases = $true) & (exuE3u = $true) & (demorgan2b2 = $true) & (kfstsingleton = $true) & (powersetE = $true) & (app = $true) & (dpsetconstrEL2 = $true) & (woz13rule4 = $true) & (exuI2 = $true) & (emptysetAx = $true) & (subsetTI = $true) & (in__Cong = $true) & (prop2setE = $true) & (setOfPairsIsBReln1 = $true) & (setminusER = $true) & (breln1compI = $true) & (funcextLem = $true) & (setukpairinjR11 = $true) & (dpsetconstrSub = $true) & (setminusEL = $true) & (image1Ex1 = $true) & (image1I = $true) & (image1E = $true) & (setminusERneg = $true) & (demorgan2a1 = $true) & (iffalseProp2 = $true) & (demorgan2a2 = $true) & (symdiffIneg2 = $true) & (dpsetconstrI = $true) & (breln1unionCommutes = $true) & (exu__Cong = $true) & (descr__Cong = $true) & (woz1_5 = $true) & (woz13rule3 = $true) & (cartprodfstin = $true) & (contrasubsetT1 = $true) & (breln1all1 = $true) & (demorgan2a = $true) & (breln1unionI = $true) & (breln1compEex = $true) & (brelnall1 = $true) & (exuI1 = $true) & (setadjoinSub2 = $true) & (subsetI2 = $true) & (inIntersectImpInUnion2 = $true) & (breln1all2 = $true) & (dpsetconstrERa = $true) & (complementTE1 = $true) & (binunionLsub = $true) & (funcGraphProp3 = $true) & (binunionIL = $true) & (eqbreln1 = $true) & (binintersectT_lem = $true) & (setukpairinjR1 = $true) & (ubforcartprodlem2 = $true) & (notequalI2 = $true) & (exuE2 = $true) & (omegaSAx = $true) & (powersetsubset = $true) & (powersetT_lem = $true) & (powersetAx = $true) & (binunionTILcontra = $true) & (symdiffI1 = $true) & (woz1_1 = $true) & (singletoninpowerset = $true) & (eta1 = $true) & (emptysetimpfalse = $true) & (nonemptyI1 = $true) & (doubleComplementE1 = $true) & (cartprodsndpairEq = $true) & (omega0Ax = $true) & (ex1E1 = $true) & (complementTnotintersectT = $true) & (breln1SetBreln1 = $true) & (setminusI = $true) & (cartprodpairin = $true) & (setunionsingleton = $true) & (breln1unionIR = $true) & (demorgan2 = $true) & (bs114d = $true) & (binintersectSubset4 = $true) & (notdexE = $true) & (complementInPowersetComplementIntersect = $true) & (binintersectTELcontra = $true) & (theprop = $true) & (binunionTEcontra = $true) & (notsubsetI = $true) & (ubforcartprodlem3 = $true) & (setoftrueEq = $true) & (eqinunit = $true) & (funcGraphProp2 = $true) & (doubleComplementEq = $true) & (setextAx = $true) & (demorgan2b = $true) & (funcext = $true) & (nonemptyImpWitness = $true) & (lam2lamEq = $true) & (beta2 = $true) & (symdiffIneg1 = $true) & (powersetTI1 = $true) & (setadjoinOr = $true) & (kpairp = $true) & (setadjoinIR = $true) & (funcext2 = $true) & (iffalse = $true) & (eqimpsubset1 = $true) & (lamProp = $true) & (notdallE = $true) & (binintersectEL = $true) & (eqimpsubset2 = $true) & (binintersectLsub = $true) & (complementT_lem = $true) & (upairinpowunion = $true) & (iftrue = $true) & (ubforcartprodlem1 = $true) & (breln1unionE = $true) & (inIntersectImpInIntersectUnions = $true) & (binintersectTERcontra = $true) & (woz1_2 = $true) & (setminusLsub = $true) & (exuEu = $true) & (upairsetE = $true) & (upairequniteq = $true) & (breln1compE = $true) & (replAx = $true) & (cartprodmempair1 = $true) & (setadjoinE = $true) & (singletonsuniq = $true) & (binunionTE = $true) & (descrp = $true) & (funcGraphProp4 = $true) & (nonemptyI = $true) & (setadjoin__Cong = $true) & (eqbreln = $true) & (binunionEcases = $true) & (binunionTIRcontra = $true) & (iffalseProp1 = $true) & (binunionRsub = $true) & (disjointsetsI1 = $true) & (surjFuncSetFuncSurj = $true) & (iftrueProp1 = $true) & (complementSubsetComplementIntersect = $true) & (setminusSubset2 = $true) & (exuE3e = $true) & (setukpairinjR12 = $true) & (emptyE1 = $true) & (woz13rule2 = $true) & (complementUnionInPowersetComplement = $true) & (subsetE = $true) & (funcImageSingleton = $true) & (emptyinunitempty = $true) & (funcGraphProp1 = $true) & (demorgan1 = $true) & (powersetI = $true) & (inComplementUnionImpNotIn1 = $true) & (powersetI1 = $true) & (lam2p = $true) & (surjCantorThm = $true) & (subset2powerset = $true) & (breln1invI = $true) & (image1Equiv = $true) & (upairset2IR = $true) & (setunionAx = $true) & (setunionsingleton2 = $true) & (funcinfuncset = $true) & (doubleComplementSub2 = $true) & (kfstpairEq = $true) & (inIntersectImpInUnion = $true) & (woz1_4 = $true) & (setunionE = $true) & (cartprodpairmemER = $true) & (emptysetE = $true) & (notinsingleton = $true) & (foundationAx = $true) & (woz2A = $true) & (setextT = $true) & (intersectInPowersetIntersectUnions = $true) & (powersetTE1 = $true) & (setunion__Cong = $true) & (cartprodpairsurjEq = $true) & (setukpairinjL2 = $true) & (dsetconstr__Cong = $true) & (setunionI = $true) & (quantDeMorgan1 = $true) & (apProp = $true) & (nonemptyE1 = $true) & (setadjoinIL = $true) & (binintersectSubset3 = $true) & (singletonprop = $true) & (dpsetconstrER = $true) & (kpairiskpair = $true) & (uniqinunit = $true) & (ap2apEq1 = $true) & (emptyInPowerset = $true) & (setext = $true) & (powerset__Cong = $true) & (injFuncInInjFuncSet = $true) & (beta1 = $true) & (setadjoinAx = $true) & (quantDeMorgan2 = $true) & (setbeta = $true) & (symdiffI2 = $true) & (subbreln1 = $true) & (breln1unionIL = $true) & (subPowSU = $true) & (doubleComplementI1 = $true) & (binunionE = $true) & (omega__Cong = $true) & (dsetconstrI = $true) & (setukpairIR = $true)),
% 34.78/6.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f1366,f1464])).
% 34.78/6.30 thf(f1464,plain,(
% 34.78/6.30 ? [X0 : $i] : ($true = (in @ X0 @ X0)) => ($true = (in @ sK28 @ sK28))),
% 34.78/6.30 introduced(definition,[],[choice_axiom])).
% 34.78/6.30 thf(f1366,plain,(
% 34.78/6.30 (setunionE2 = $true) & (secondinupair = $true) & (inPowerset = $true) & (complementTI1 = $true) & (subbreln = $true) & (contrasubsetT2 = $true) & (brelnall2 = $true) & (setminusSubset1 = $true) & (emptysetsubset = $true) & (ex1I2 = $true) & (contraSubsetComplement = $true) & (ksndsingleton = $true) & (sepSubset = $true) & (setminusIRneg = $true) & (complementTcontraSubset = $true) & (injFuncSetFuncIn = $true) & (breln1unionprop = $true) & (foundation2 = $true) & (inCongP = $true) & (theeq = $true) & (setextsub = $true) & (quantDeMorgan3 = $true) & (setunionsingleton1 = $true) & (setukpairinjL1 = $true) & (breln1compprop = $true) & (ex1E2 = $true) & (singletonsswitch = $true) & (subsetI1 = $true) & (dsetconstrER = $true) & (exuE1 = $true) & (binunionIR = $true) & ? [X0 : $i] : ($true = (in @ X0 @ X0)) & (woz2B = $true) & (infuncsetfunc = $true) & (image1Ex = $true) & (breln1invE = $true) & (emptyI = $true) & (kpairsurjEq = $true) & (subsetTrans = $true) & (woz13rule0 = $true) & (setminusILneg = $true) & (setukpairinjL = $true) & (setukpairinjR2 = $true) & (inComplementUnionImpInComplement1 = $true) & (upairset2E = $true) & (quantDeMorgan4 = $true) & (singletonsubset = $true) & (setminusELneg = $true) & (ifp = $true) & (ap2apEq2 = $true) & (ifSingleton = $true) & (notequalI1 = $true) & (breln1invprop = $true) & (subsetemptysetimpeq = $true) & (setukpairIL = $true) & (subsetRefl = $true) & (lamp = $true) & (setminusT_lem = $true) & (sepInPowerset = $true) & (upairsubunion = $true) & (ap2p = $true) & (notinemptyset = $true) & (contrasubsetT = $true) & (injFuncSetFuncInj = $true) & (symdiffE = $true) & (setOfPairsIsBReln = $true) & (binintersectSubset1 = $true) & (wellorderingAx = $true) & (binintersectSubset5 = $true) & (choice2fnsingleton = $true) & (binintersectRsub = $true) & (woz1_3 = $true) & (iftrueorfalse = $true) & (eta2 = $true) & (demorgan1b = $true) & (woz2W = $true) & (prop2set2propI = $true) & (prop2setI = $true) & (binintersectER = $true) & (woz2Ex = $true) & (surjFuncSetFuncIn = $true) & (emptyinPowerset = $true) & (complementImpComplementIntersect = $true) & (omegaIndAx = $true) & (demorgan1a = $true) & (binintersectI = $true) & (binintersectSubset2 = $true) & (ex1I = $true) & (singletoninpowunion = $true) & (noeltsimpempty = $true) & (iftrueProp2 = $true) & (binunionT_lem = $true) & (cartprodsndin = $true) & (contrasubsetT3 = $true) & (cartprodmempaircEq = $true) & (subsetE2 = $true) & (dpsetconstrEL1 = $true) & (doubleComplementSub1 = $true) & (emptyset__Cong = $true) & (ksndpairEq = $true) & (upairsetIR = $true) & (leftInvIsSurj = $true) & (dsetconstrEL = $true) & (cartprodmempair = $true) & (powersetE1 = $true) & (cartprodpairmemEL = $true) & (setukpairinjR = $true) & (woz13rule1 = $true) & (setadjoinSub = $true) & (exuI3 = $true) & (upairsetIL = $true) & (cartprodfstpairEq = $true) & (vacuousDall = $true) & (breln1unionEcases = $true) & (exuE3u = $true) & (demorgan2b2 = $true) & (kfstsingleton = $true) & (powersetE = $true) & (app = $true) & (dpsetconstrEL2 = $true) & (woz13rule4 = $true) & (exuI2 = $true) & (emptysetAx = $true) & (subsetTI = $true) & (in__Cong = $true) & (prop2setE = $true) & (setOfPairsIsBReln1 = $true) & (setminusER = $true) & (breln1compI = $true) & (funcextLem = $true) & (setukpairinjR11 = $true) & (dpsetconstrSub = $true) & (setminusEL = $true) & (image1Ex1 = $true) & (image1I = $true) & (image1E = $true) & (setminusERneg = $true) & (demorgan2a1 = $true) & (iffalseProp2 = $true) & (demorgan2a2 = $true) & (symdiffIneg2 = $true) & (dpsetconstrI = $true) & (breln1unionCommutes = $true) & (exu__Cong = $true) & (descr__Cong = $true) & (woz1_5 = $true) & (woz13rule3 = $true) & (cartprodfstin = $true) & (contrasubsetT1 = $true) & (breln1all1 = $true) & (demorgan2a = $true) & (breln1unionI = $true) & (breln1compEex = $true) & (brelnall1 = $true) & (exuI1 = $true) & (setadjoinSub2 = $true) & (subsetI2 = $true) & (inIntersectImpInUnion2 = $true) & (breln1all2 = $true) & (dpsetconstrERa = $true) & (complementTE1 = $true) & (binunionLsub = $true) & (funcGraphProp3 = $true) & (binunionIL = $true) & (eqbreln1 = $true) & (binintersectT_lem = $true) & (setukpairinjR1 = $true) & (ubforcartprodlem2 = $true) & (notequalI2 = $true) & (exuE2 = $true) & (omegaSAx = $true) & (powersetsubset = $true) & (powersetT_lem = $true) & (powersetAx = $true) & (binunionTILcontra = $true) & (symdiffI1 = $true) & (woz1_1 = $true) & (singletoninpowerset = $true) & (eta1 = $true) & (emptysetimpfalse = $true) & (nonemptyI1 = $true) & (doubleComplementE1 = $true) & (cartprodsndpairEq = $true) & (omega0Ax = $true) & (ex1E1 = $true) & (complementTnotintersectT = $true) & (breln1SetBreln1 = $true) & (setminusI = $true) & (cartprodpairin = $true) & (setunionsingleton = $true) & (breln1unionIR = $true) & (demorgan2 = $true) & (bs114d = $true) & (binintersectSubset4 = $true) & (notdexE = $true) & (complementInPowersetComplementIntersect = $true) & (binintersectTELcontra = $true) & (theprop = $true) & (binunionTEcontra = $true) & (notsubsetI = $true) & (ubforcartprodlem3 = $true) & (setoftrueEq = $true) & (eqinunit = $true) & (funcGraphProp2 = $true) & (doubleComplementEq = $true) & (setextAx = $true) & (demorgan2b = $true) & (funcext = $true) & (nonemptyImpWitness = $true) & (lam2lamEq = $true) & (beta2 = $true) & (symdiffIneg1 = $true) & (powersetTI1 = $true) & (setadjoinOr = $true) & (kpairp = $true) & (setadjoinIR = $true) & (funcext2 = $true) & (iffalse = $true) & (eqimpsubset1 = $true) & (lamProp = $true) & (notdallE = $true) & (binintersectEL = $true) & (eqimpsubset2 = $true) & (binintersectLsub = $true) & (complementT_lem = $true) & (upairinpowunion = $true) & (iftrue = $true) & (ubforcartprodlem1 = $true) & (breln1unionE = $true) & (inIntersectImpInIntersectUnions = $true) & (binintersectTERcontra = $true) & (woz1_2 = $true) & (setminusLsub = $true) & (exuEu = $true) & (upairsetE = $true) & (upairequniteq = $true) & (breln1compE = $true) & (replAx = $true) & (cartprodmempair1 = $true) & (setadjoinE = $true) & (singletonsuniq = $true) & (binunionTE = $true) & (descrp = $true) & (funcGraphProp4 = $true) & (nonemptyI = $true) & (setadjoin__Cong = $true) & (eqbreln = $true) & (binunionEcases = $true) & (binunionTIRcontra = $true) & (iffalseProp1 = $true) & (binunionRsub = $true) & (disjointsetsI1 = $true) & (surjFuncSetFuncSurj = $true) & (iftrueProp1 = $true) & (complementSubsetComplementIntersect = $true) & (setminusSubset2 = $true) & (exuE3e = $true) & (setukpairinjR12 = $true) & (emptyE1 = $true) & (woz13rule2 = $true) & (complementUnionInPowersetComplement = $true) & (subsetE = $true) & (funcImageSingleton = $true) & (emptyinunitempty = $true) & (funcGraphProp1 = $true) & (demorgan1 = $true) & (powersetI = $true) & (inComplementUnionImpNotIn1 = $true) & (powersetI1 = $true) & (lam2p = $true) & (surjCantorThm = $true) & (subset2powerset = $true) & (breln1invI = $true) & (image1Equiv = $true) & (upairset2IR = $true) & (setunionAx = $true) & (setunionsingleton2 = $true) & (funcinfuncset = $true) & (doubleComplementSub2 = $true) & (kfstpairEq = $true) & (inIntersectImpInUnion = $true) & (woz1_4 = $true) & (setunionE = $true) & (cartprodpairmemER = $true) & (emptysetE = $true) & (notinsingleton = $true) & (foundationAx = $true) & (woz2A = $true) & (setextT = $true) & (intersectInPowersetIntersectUnions = $true) & (powersetTE1 = $true) & (setunion__Cong = $true) & (cartprodpairsurjEq = $true) & (setukpairinjL2 = $true) & (dsetconstr__Cong = $true) & (setunionI = $true) & (quantDeMorgan1 = $true) & (apProp = $true) & (nonemptyE1 = $true) & (setadjoinIL = $true) & (binintersectSubset3 = $true) & (singletonprop = $true) & (dpsetconstrER = $true) & (kpairiskpair = $true) & (uniqinunit = $true) & (ap2apEq1 = $true) & (emptyInPowerset = $true) & (setext = $true) & (powerset__Cong = $true) & (injFuncInInjFuncSet = $true) & (beta1 = $true) & (setadjoinAx = $true) & (quantDeMorgan2 = $true) & (setbeta = $true) & (symdiffI2 = $true) & (subbreln1 = $true) & (breln1unionIL = $true) & (subPowSU = $true) & (doubleComplementI1 = $true) & (binunionE = $true) & (omega__Cong = $true) & (dsetconstrI = $true) & (setukpairIR = $true)),
% 34.78/6.30 inference(flattening,[status(thm)],[f1365])).
% 34.78/6.30 thf(f1365,plain,(
% 34.78/6.30 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i] : ($true = (in @ X0 @ X0)) & (foundation2 = $true)) & (surjCantorThm = $true)) & (leftInvIsSurj = $true)) & (surjFuncSetFuncSurj = $true)) & (surjFuncSetFuncIn = $true)) & (injFuncSetFuncInj = $true)) & (injFuncSetFuncIn = $true)) & (injFuncInInjFuncSet = $true)) & (image1I = $true)) & (image1E = $true)) & (image1Equiv = $true)) & (image1Ex1 = $true)) & (image1Ex = $true)) & (woz2B = $true)) & (woz2A = $true)) & (woz2W = $true)) & (woz2Ex = $true)) & (breln1unionCommutes = $true)) & (breln1unionEcases = $true)) & (breln1unionE = $true)) & (breln1unionI = $true)) & (breln1unionIR = $true)) & (breln1unionIL = $true)) & (breln1unionprop = $true)) & (breln1compEex = $true)) & (breln1compE = $true)) & (breln1compI = $true)) & (breln1compprop = $true)) & (breln1invE = $true)) & (breln1invI = $true)) & (breln1invprop = $true)) & (eqbreln1 = $true)) & (subbreln1 = $true)) & (breln1all1 = $true)) & (setOfPairsIsBReln1 = $true)) & (choice2fnsingleton = $true)) & (breln1SetBreln1 = $true)) & (breln1all2 = $true)) & (woz1_5 = $true)) & (woz1_4 = $true)) & (woz1_3 = $true)) & (woz1_2 = $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)),
% 34.78/6.30 inference(ennf_transformation,[status(thm)],[f972])).
% 34.78/6.30 thf(f972,plain,(
% 34.78/6.30 ~((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) => ((woz1_2 = $true) => ((woz1_3 = $true) => ((woz1_4 = $true) => ((woz1_5 = $true) => ((breln1all2 = $true) => ((breln1SetBreln1 = $true) => ((choice2fnsingleton = $true) => ((setOfPairsIsBReln1 = $true) => ((breln1all1 = $true) => ((subbreln1 = $true) => ((eqbreln1 = $true) => ((breln1invprop = $true) => ((breln1invI = $true) => ((breln1invE = $true) => ((breln1compprop = $true) => ((breln1compI = $true) => ((breln1compE = $true) => ((breln1compEex = $true) => ((breln1unionprop = $true) => ((breln1unionIL = $true) => ((breln1unionIR = $true) => ((breln1unionI = $true) => ((breln1unionE = $true) => ((breln1unionEcases = $true) => ((breln1unionCommutes = $true) => ((woz2Ex = $true) => ((woz2W = $true) => ((woz2A = $true) => ((woz2B = $true) => ((image1Ex = $true) => ((image1Ex1 = $true) => ((image1Equiv = $true) => ((image1E = $true) => ((image1I = $true) => ((injFuncInInjFuncSet = $true) => ((injFuncSetFuncIn = $true) => ((injFuncSetFuncInj = $true) => ((surjFuncSetFuncIn = $true) => ((surjFuncSetFuncSurj = $true) => ((leftInvIsSurj = $true) => ((surjCantorThm = $true) => ((foundation2 = $true) => ! [X0 : $i] : ($true != (in @ X0 @ X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 34.78/6.30 inference(flattening,[status(thm)],[f913])).
% 34.78/6.30 thf(f913,plain,(
% 34.78/6.30 ~((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) => ((woz1_2 = $true) => ((woz1_3 = $true) => ((woz1_4 = $true) => ((woz1_5 = $true) => ((breln1all2 = $true) => ((breln1SetBreln1 = $true) => ((choice2fnsingleton = $true) => ((setOfPairsIsBReln1 = $true) => ((breln1all1 = $true) => ((subbreln1 = $true) => ((eqbreln1 = $true) => ((breln1invprop = $true) => ((breln1invI = $true) => ((breln1invE = $true) => ((breln1compprop = $true) => ((breln1compI = $true) => ((breln1compE = $true) => ((breln1compEex = $true) => ((breln1unionprop = $true) => ((breln1unionIL = $true) => ((breln1unionIR = $true) => ((breln1unionI = $true) => ((breln1unionE = $true) => ((breln1unionEcases = $true) => ((breln1unionCommutes = $true) => ((woz2Ex = $true) => ((woz2W = $true) => ((woz2A = $true) => ((woz2B = $true) => ((image1Ex = $true) => ((image1Ex1 = $true) => ((image1Equiv = $true) => ((image1E = $true) => ((image1I = $true) => ((injFuncInInjFuncSet = $true) => ((injFuncSetFuncIn = $true) => ((injFuncSetFuncInj = $true) => ((surjFuncSetFuncIn = $true) => ((surjFuncSetFuncSurj = $true) => ((leftInvIsSurj = $true) => ((surjCantorThm = $true) => ((foundation2 = $true) => ! [X0 : $i] : ~($true = (in @ X0 @ X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 34.78/6.30 inference(fool_elimination,[status(thm)],[f912])).
% 34.78/6.30 thf(f912,plain,(
% 34.78/6.30 ~(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 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (eqbreln1 => (breln1invprop => (breln1invI => (breln1invE => (breln1compprop => (breln1compI => (breln1compE => (breln1compEex => (breln1unionprop => (breln1unionIL => (breln1unionIR => (breln1unionI => (breln1unionE => (breln1unionEcases => (breln1unionCommutes => (woz2Ex => (woz2W => (woz2A => (woz2B => (image1Ex => (image1Ex1 => (image1Equiv => (image1E => (image1I => (injFuncInInjFuncSet => (injFuncSetFuncIn => (injFuncSetFuncInj => (surjFuncSetFuncIn => (surjFuncSetFuncSurj => (leftInvIsSurj => (surjCantorThm => (foundation2 => ! [X0 : $i] : ~(in @ X0 @ X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 34.78/6.30 inference(rectify,[status(thm)],[f326])).
% 34.78/6.30 thf(f326,negated_conjecture,(
% 34.78/6.30 ~(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 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (eqbreln1 => (breln1invprop => (breln1invI => (breln1invE => (breln1compprop => (breln1compI => (breln1compE => (breln1compEex => (breln1unionprop => (breln1unionIL => (breln1unionIR => (breln1unionI => (breln1unionE => (breln1unionEcases => (breln1unionCommutes => (woz2Ex => (woz2W => (woz2A => (woz2B => (image1Ex => (image1Ex1 => (image1Equiv => (image1E => (image1I => (injFuncInInjFuncSet => (injFuncSetFuncIn => (injFuncSetFuncInj => (surjFuncSetFuncIn => (surjFuncSetFuncSurj => (leftInvIsSurj => (surjCantorThm => (foundation2 => ! [X3 : $i] : ~(in @ X3 @ X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 34.78/6.30 inference(negated_conjecture,[status(cth)],[f325])).
% 34.78/6.30 thf(f325,conjecture,(
% 34.78/6.30 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 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (eqbreln1 => (breln1invprop => (breln1invI => (breln1invE => (breln1compprop => (breln1compI => (breln1compE => (breln1compEex => (breln1unionprop => (breln1unionIL => (breln1unionIR => (breln1unionI => (breln1unionE => (breln1unionEcases => (breln1unionCommutes => (woz2Ex => (woz2W => (woz2A => (woz2B => (image1Ex => (image1Ex1 => (image1Equiv => (image1E => (image1I => (injFuncInInjFuncSet => (injFuncSetFuncIn => (injFuncSetFuncInj => (surjFuncSetFuncIn => (surjFuncSetFuncSurj => (leftInvIsSurj => (surjCantorThm => (foundation2 => ! [X3 : $i] : ~(in @ X3 @ X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 34.78/6.30 file('/export/starexec/sandbox2/tmp/tmp.yv4wus1g2e/DTF2THF_4600.p',notinself)).
% 34.78/6.30 thf(f11333,plain,(
% 34.78/6.30 ( ! [X0 : $i] : (($true != (in @ X0 @ X0))) )),
% 34.78/6.30 inference(forward_demodulation,[status(thm)],[f11332,f7832])).
% 34.78/6.30 thf(f7832,plain,(
% 34.78/6.30 ( ! [X0 : $i] : (((sK273 @ (setadjoin @ X0 @ emptyset)) = X0)) )),
% 34.78/6.30 inference(subsumption_resolution,[status(thm)],[f7774,f7577])).
% 34.78/6.30 thf(f7577,plain,(
% 34.78/6.30 ( ! [X0 : $i,X1 : $i] : ((emptyset != (setadjoin @ X0 @ X1))) )),
% 34.78/6.30 inference(trivial_inequality_removal,[status(thm)],[f7575])).
% 34.78/6.30 thf(f7575,plain,(
% 34.78/6.30 ( ! [X0 : $i,X1 : $i] : ((emptyset != (setadjoin @ X0 @ X1)) | ($true != $true)) )),
% 34.78/6.30 inference(superposition,[status(thm)],[f6333,f6499])).
% 34.78/6.30 thf(f6499,plain,(
% 34.78/6.30 ( ! [X4 : $i,X5 : $i] : (($true = (in @ X4 @ (setadjoin @ X4 @ X5)))) )),
% 34.78/6.30 inference(trivial_inequality_removal,[status(thm)],[f6178])).
% 34.78/6.30 thf(f6178,plain,(
% 34.78/6.30 ( ! [X4 : $i,X5 : $i] : (($true != $true) | ($true = (in @ X4 @ (setadjoin @ X4 @ X5)))) )),
% 34.78/6.30 inference(equality_resolution,[status(thm)],[f5441])).
% 34.78/6.30 thf(f5441,plain,(
% 34.78/6.30 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (setadjoin @ X3 @ X5)) = $true) | (X3 != X4) | ($true != $true)) )),
% 34.78/6.30 inference(definition_unfolding,[status(thm)],[f4048,f3093])).
% 34.78/6.30 thf(f3093,plain,(
% 34.78/6.30 (setadjoinAx = $true)),
% 34.78/6.30 inference(cnf_transformation,[status(thm)],[f1465])).
% 34.78/6.30 thf(f4048,plain,(
% 34.78/6.30 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (setadjoin @ X3 @ X5)) = $true) | (X3 != X4) | (setadjoinAx != $true)) )),
% 34.78/6.30 inference(cnf_transformation,[status(thm)],[f2189])).
% 34.78/6.30 thf(f2189,plain,(
% 34.78/6.30 ((setadjoinAx = $true) | ((($true != (in @ sK507 @ (setadjoin @ sK506 @ sK508))) | ((sK506 != sK507) & ($true != (in @ sK507 @ sK508)))) & (($true = (in @ sK507 @ (setadjoin @ sK506 @ sK508))) | (sK506 = sK507) | ($true = (in @ sK507 @ sK508))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((X3 = X4) | ($true = (in @ X4 @ X5)) | ((in @ X4 @ (setadjoin @ X3 @ X5)) != $true)) & (((in @ X4 @ (setadjoin @ X3 @ X5)) = $true) | ((X3 != X4) & ($true != (in @ X4 @ X5))))) | (setadjoinAx != $true))),
% 34.78/6.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK506,sK507,sK508])],[f2187,f2188])).
% 34.78/6.30 thf(f2188,plain,(
% 34.78/6.30 ? [X0 : $i,X1 : $i,X2 : $i] : ((($true != (in @ X1 @ (setadjoin @ X0 @ X2))) | ((X0 != X1) & ($true != (in @ X1 @ X2)))) & (($true = (in @ X1 @ (setadjoin @ X0 @ X2))) | (X0 = X1) | ($true = (in @ X1 @ X2)))) => ((($true != (in @ sK507 @ (setadjoin @ sK506 @ sK508))) | ((sK506 != sK507) & ($true != (in @ sK507 @ sK508)))) & (($true = (in @ sK507 @ (setadjoin @ sK506 @ sK508))) | (sK506 = sK507) | ($true = (in @ sK507 @ sK508))))),
% 34.78/6.30 introduced(definition,[],[choice_axiom])).
% 34.78/6.30 thf(f2187,plain,(
% 34.78/6.30 ((setadjoinAx = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((($true != (in @ X1 @ (setadjoin @ X0 @ X2))) | ((X0 != X1) & ($true != (in @ X1 @ X2)))) & (($true = (in @ X1 @ (setadjoin @ X0 @ X2))) | (X0 = X1) | ($true = (in @ X1 @ X2))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((X3 = X4) | ($true = (in @ X4 @ X5)) | ((in @ X4 @ (setadjoin @ X3 @ X5)) != $true)) & (((in @ X4 @ (setadjoin @ X3 @ X5)) = $true) | ((X3 != X4) & ($true != (in @ X4 @ X5))))) | (setadjoinAx != $true))),
% 34.78/6.30 inference(rectify,[status(thm)],[f2186])).
% 34.78/6.30 thf(f2186,plain,(
% 34.78/6.30 ((setadjoinAx = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((($true != (in @ X1 @ (setadjoin @ X0 @ X2))) | ((X0 != X1) & ($true != (in @ X1 @ X2)))) & (($true = (in @ X1 @ (setadjoin @ X0 @ X2))) | (X0 = X1) | ($true = (in @ X1 @ X2))))) & (! [X0 : $i,X1 : $i,X2 : $i] : (((X0 = X1) | ($true = (in @ X1 @ X2)) | ($true != (in @ X1 @ (setadjoin @ X0 @ X2)))) & (($true = (in @ X1 @ (setadjoin @ X0 @ X2))) | ((X0 != X1) & ($true != (in @ X1 @ X2))))) | (setadjoinAx != $true))),
% 34.78/6.30 inference(flattening,[status(thm)],[f2185])).
% 34.78/6.30 thf(f2185,plain,(
% 34.78/6.30 ((setadjoinAx = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((($true != (in @ X1 @ (setadjoin @ X0 @ X2))) | ((X0 != X1) & ($true != (in @ X1 @ X2)))) & (($true = (in @ X1 @ (setadjoin @ X0 @ X2))) | ((X0 = X1) | ($true = (in @ X1 @ X2)))))) & (! [X0 : $i,X1 : $i,X2 : $i] : ((((X0 = X1) | ($true = (in @ X1 @ X2))) | ($true != (in @ X1 @ (setadjoin @ X0 @ X2)))) & (($true = (in @ X1 @ (setadjoin @ X0 @ X2))) | ((X0 != X1) & ($true != (in @ X1 @ X2))))) | (setadjoinAx != $true))),
% 34.78/6.30 inference(nnf_transformation,[status(thm)],[f933])).
% 34.78/6.30 thf(f933,plain,(
% 34.78/6.30 (setadjoinAx = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((X0 = X1) | ($true = (in @ X1 @ X2))) <=> ($true = (in @ X1 @ (setadjoin @ X0 @ X2))))),
% 34.78/6.30 inference(fool_elimination,[status(thm)],[f932])).
% 34.78/6.30 thf(f932,plain,(
% 34.78/6.30 (! [X0 : $i,X1 : $i,X2 : $i] : (((X0 = X1) | (in @ X1 @ X2)) <=> (in @ X1 @ (setadjoin @ X0 @ X2))) = setadjoinAx)),
% 34.78/6.30 inference(rectify,[status(thm)],[f4])).
% 34.78/6.30 thf(f4,axiom,(
% 34.78/6.30 (! [X1 : $i,X2 : $i,X3 : $i] : (((X1 = X2) | (in @ X2 @ X3)) <=> (in @ X2 @ (setadjoin @ X1 @ X3))) = setadjoinAx)),
% 34.78/6.30 file('/export/starexec/sandbox2/tmp/tmp.yv4wus1g2e/DTF2THF_4600.p',setadjoinAx)).
% 34.78/6.30 thf(f6333,plain,(
% 34.78/6.30 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ X0)) | (emptyset != X0)) )),
% 34.78/6.30 inference(equality_proxy_clausification,[status(thm)],[f6332])).
% 34.78/6.30 thf(f6332,plain,(
% 34.78/6.30 ( ! [X0 : $i,X1 : $i] : (($false = (emptyset = X0)) | ($true != (in @ X1 @ X0))) )),
% 34.78/6.30 inference(not_proxy_clausification,[status(thm)],[f6331])).
% 34.78/6.30 thf(f6331,plain,(
% 34.78/6.30 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ X0)) | ((~ (emptyset = X0)) = $true)) )),
% 34.78/6.30 inference(beta_eta_normalization,[status(thm)],[f6330])).
% 34.78/6.30 thf(f6330,plain,(
% 34.78/6.30 ( ! [X0 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (~ (emptyset = Y0))) @ X0)) | ($true != (in @ X1 @ X0))) )),
% 34.78/6.30 inference(trivial_inequality_removal,[status(thm)],[f5706])).
% 34.78/6.30 thf(f5706,plain,(
% 34.78/6.30 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true != (in @ X1 @ X0)) | ($true = ((^[Y0 : $i]: (~ (emptyset = Y0))) @ X0))) )),
% 34.78/6.30 inference(definition_unfolding,[status(thm)],[f4365,f3477,f3224])).
% 34.78/6.30 thf(f3224,plain,(
% 34.78/6.30 (nonemptyI1 = $true)),
% 34.78/6.30 inference(cnf_transformation,[status(thm)],[f1465])).
% 34.78/6.30 thf(f3477,plain,(
% 34.78/6.30 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 34.78/6.30 inference(cnf_transformation,[status(thm)],[f705])).
% 34.78/6.30 thf(f705,plain,(
% 34.78/6.30 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 34.78/6.30 inference(fool_elimination,[status(thm)],[f704])).
% 34.78/6.30 thf(f704,plain,(
% 34.78/6.30 ((^[X0 : $i] : ((emptyset != X0))) = nonempty)),
% 34.78/6.30 inference(rectify,[status(thm)],[f27])).
% 34.78/6.30 thf(f27,axiom,(
% 34.78/6.30 ((^[X1 : $i] : ((emptyset != X1))) = nonempty)),
% 34.78/6.30 file('/export/starexec/sandbox2/tmp/tmp.yv4wus1g2e/DTF2THF_4600.p',nonempty)).
% 34.78/6.30 thf(f4365,plain,(
% 34.78/6.30 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ X0)) | ((nonempty @ X0) = $true) | (nonemptyI1 != $true)) )),
% 34.78/6.30 inference(cnf_transformation,[status(thm)],[f2536])).
% 34.78/6.30 thf(f2536,plain,(
% 34.78/6.30 (! [X0 : $i] : (! [X1 : $i] : ($true != (in @ X1 @ X0)) | ((nonempty @ X0) = $true)) | (nonemptyI1 != $true)) & ((nonemptyI1 = $true) | (($true = (in @ sK735 @ sK734)) & ($true != (nonempty @ sK734))))),
% 34.78/6.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK734,sK735])],[f2533,f2535,f2534])).
% 34.78/6.30 thf(f2534,plain,(
% 34.78/6.30 ? [X2 : $i] : (? [X3 : $i] : ($true = (in @ X3 @ X2)) & ($true != (nonempty @ X2))) => (? [X3 : $i] : ($true = (in @ X3 @ sK734)) & ($true != (nonempty @ sK734)))),
% 34.78/6.30 introduced(definition,[],[choice_axiom])).
% 34.78/6.30 thf(f2535,plain,(
% 34.78/6.30 ? [X3 : $i] : ($true = (in @ X3 @ sK734)) => ($true = (in @ sK735 @ sK734))),
% 34.78/6.30 introduced(definition,[],[choice_axiom])).
% 34.78/6.30 thf(f2533,plain,(
% 34.78/6.30 (! [X0 : $i] : (! [X1 : $i] : ($true != (in @ X1 @ X0)) | ((nonempty @ X0) = $true)) | (nonemptyI1 != $true)) & ((nonemptyI1 = $true) | ? [X2 : $i] : (? [X3 : $i] : ($true = (in @ X3 @ X2)) & ($true != (nonempty @ X2))))),
% 34.78/6.30 inference(rectify,[status(thm)],[f2532])).
% 34.78/6.30 thf(f2532,plain,(
% 34.78/6.30 (! [X0 : $i] : (! [X1 : $i] : ($true != (in @ X1 @ X0)) | ((nonempty @ X0) = $true)) | (nonemptyI1 != $true)) & ((nonemptyI1 = $true) | ? [X0 : $i] : (? [X1 : $i] : ($true = (in @ X1 @ X0)) & ((nonempty @ X0) != $true)))),
% 34.78/6.30 inference(nnf_transformation,[status(thm)],[f1318])).
% 34.78/6.30 thf(f1318,plain,(
% 34.78/6.30 ! [X0 : $i] : (! [X1 : $i] : ($true != (in @ X1 @ X0)) | ((nonempty @ X0) = $true)) <=> (nonemptyI1 = $true)),
% 34.78/6.30 inference(ennf_transformation,[status(thm)],[f587])).
% 34.78/6.30 thf(f587,plain,(
% 34.78/6.30 (nonemptyI1 = $true) <=> ! [X0 : $i] : (? [X1 : $i] : ($true = (in @ X1 @ X0)) => ((nonempty @ X0) = $true))),
% 34.78/6.30 inference(fool_elimination,[status(thm)],[f586])).
% 34.78/6.30 thf(f586,plain,(
% 34.78/6.30 (nonemptyI1 = ! [X0 : $i] : (? [X1 : $i] : (in @ X1 @ X0) => (nonempty @ X0)))),
% 34.78/6.30 inference(rectify,[status(thm)],[f30])).
% 34.78/6.30 thf(f30,axiom,(
% 34.78/6.30 (nonemptyI1 = ! [X3 : $i] : (? [X1 : $i] : (in @ X1 @ X3) => (nonempty @ X3)))),
% 34.78/6.30 file('/export/starexec/sandbox2/tmp/tmp.yv4wus1g2e/DTF2THF_4600.p',nonemptyI1)).
% 34.78/6.30 thf(f7774,plain,(
% 34.78/6.30 ( ! [X0 : $i] : (((sK273 @ (setadjoin @ X0 @ emptyset)) = X0) | (emptyset = (setadjoin @ X0 @ emptyset))) )),
% 34.78/6.30 inference(trivial_inequality_removal,[status(thm)],[f7753])).
% 34.78/6.30 thf(f7753,plain,(
% 34.78/6.30 ( ! [X0 : $i] : (((sK273 @ (setadjoin @ X0 @ emptyset)) = X0) | (emptyset = (setadjoin @ X0 @ emptyset)) | ($true != $true)) )),
% 34.78/6.30 inference(superposition,[status(thm)],[f6486,f6416])).
% 34.78/6.30 thf(f6416,plain,(
% 34.78/6.30 ( ! [X2 : $i] : (((in @ (sK273 @ X2) @ X2) = $true) | (emptyset = X2)) )),
% 34.78/6.30 inference(equality_proxy_clausification,[status(thm)],[f6415])).
% 34.78/6.30 thf(f6415,plain,(
% 34.78/6.30 ( ! [X2 : $i] : (($true = (emptyset = X2)) | ((in @ (sK273 @ X2) @ X2) = $true)) )),
% 34.78/6.30 inference(not_proxy_clausification,[status(thm)],[f6414])).
% 34.78/6.30 thf(f6414,plain,(
% 34.78/6.30 ( ! [X2 : $i] : (((in @ (sK273 @ X2) @ X2) = $true) | ($true != (~ (emptyset = X2)))) )),
% 34.78/6.30 inference(beta_eta_normalization,[status(thm)],[f6413])).
% 34.78/6.30 thf(f6413,plain,(
% 34.78/6.30 ( ! [X2 : $i] : (((in @ (sK273 @ X2) @ X2) = $true) | ($true != ((^[Y0 : $i]: (~ (emptyset = Y0))) @ X2))) )),
% 34.78/6.30 inference(trivial_inequality_removal,[status(thm)],[f5145])).
% 34.78/6.30 thf(f5145,plain,(
% 34.78/6.30 ( ! [X2 : $i] : (($true != $true) | ($true != ((^[Y0 : $i]: (~ (emptyset = Y0))) @ X2)) | ((in @ (sK273 @ X2) @ X2) = $true)) )),
% 34.78/6.30 inference(definition_unfolding,[status(thm)],[f3748,f3477,f3387])).
% 34.78/6.30 thf(f3387,plain,(
% 34.78/6.30 (foundation2 = $true)),
% 34.78/6.30 inference(cnf_transformation,[status(thm)],[f1465])).
% 34.78/6.30 thf(f3748,plain,(
% 34.78/6.30 ( ! [X2 : $i] : (((in @ (sK273 @ X2) @ X2) = $true) | ($true != (nonempty @ X2)) | (foundation2 != $true)) )),
% 34.78/6.30 inference(cnf_transformation,[status(thm)],[f1840])).
% 34.78/6.30 thf(f1840,plain,(
% 34.78/6.30 ((foundation2 = $true) | (! [X1 : $i] : ((emptyset != (binintersect @ X1 @ sK272)) | ((in @ X1 @ sK272) != $true)) & ($true = (nonempty @ sK272)))) & (! [X2 : $i] : (((emptyset = (binintersect @ (sK273 @ X2) @ X2)) & ((in @ (sK273 @ X2) @ X2) = $true)) | ($true != (nonempty @ X2))) | (foundation2 != $true))),
% 34.78/6.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK272,sK273])],[f1837,f1839,f1838])).
% 34.78/6.30 thf(f1838,plain,(
% 34.78/6.30 ? [X0 : $i] : (! [X1 : $i] : ((emptyset != (binintersect @ X1 @ X0)) | ($true != (in @ X1 @ X0))) & ((nonempty @ X0) = $true)) => (! [X1 : $i] : ((emptyset != (binintersect @ X1 @ sK272)) | ((in @ X1 @ sK272) != $true)) & ($true = (nonempty @ sK272)))),
% 34.78/6.30 introduced(definition,[],[choice_axiom])).
% 34.78/6.30 thf(f1839,plain,(
% 34.78/6.30 ! [X2 : $i] : (? [X3 : $i] : ((emptyset = (binintersect @ X3 @ X2)) & ($true = (in @ X3 @ X2))) => ((emptyset = (binintersect @ (sK273 @ X2) @ X2)) & ((in @ (sK273 @ X2) @ X2) = $true)))),
% 34.78/6.30 introduced(definition,[],[choice_axiom])).
% 34.78/6.30 thf(f1837,plain,(
% 34.78/6.30 ((foundation2 = $true) | ? [X0 : $i] : (! [X1 : $i] : ((emptyset != (binintersect @ X1 @ X0)) | ($true != (in @ X1 @ X0))) & ((nonempty @ X0) = $true))) & (! [X2 : $i] : (? [X3 : $i] : ((emptyset = (binintersect @ X3 @ X2)) & ($true = (in @ X3 @ X2))) | ($true != (nonempty @ X2))) | (foundation2 != $true))),
% 34.78/6.30 inference(rectify,[status(thm)],[f1836])).
% 34.78/6.30 thf(f1836,plain,(
% 34.78/6.30 ((foundation2 = $true) | ? [X0 : $i] : (! [X1 : $i] : ((emptyset != (binintersect @ X1 @ X0)) | ($true != (in @ X1 @ X0))) & ((nonempty @ X0) = $true))) & (! [X0 : $i] : (? [X1 : $i] : ((emptyset = (binintersect @ X1 @ X0)) & ($true = (in @ X1 @ X0))) | ((nonempty @ X0) != $true)) | (foundation2 != $true))),
% 34.78/6.30 inference(nnf_transformation,[status(thm)],[f1353])).
% 34.78/6.30 thf(f1353,plain,(
% 34.78/6.30 (foundation2 = $true) <=> ! [X0 : $i] : (? [X1 : $i] : ((emptyset = (binintersect @ X1 @ X0)) & ($true = (in @ X1 @ X0))) | ((nonempty @ X0) != $true))),
% 34.78/6.30 inference(ennf_transformation,[status(thm)],[f373])).
% 34.78/6.30 thf(f373,plain,(
% 34.78/6.30 (foundation2 = $true) <=> ! [X0 : $i] : (((nonempty @ X0) = $true) => ? [X1 : $i] : ((emptyset = (binintersect @ X1 @ X0)) & ($true = (in @ X1 @ X0))))),
% 34.78/6.30 inference(fool_elimination,[status(thm)],[f372])).
% 34.78/6.30 thf(f372,plain,(
% 34.78/6.30 (! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : ((emptyset = (binintersect @ X1 @ X0)) & (in @ X1 @ X0))) = foundation2)),
% 34.78/6.30 inference(rectify,[status(thm)],[f324])).
% 34.78/6.30 thf(f324,axiom,(
% 34.78/6.30 (! [X3 : $i] : ((nonempty @ X3) => ? [X11 : $i] : ((emptyset = (binintersect @ X11 @ X3)) & (in @ X11 @ X3))) = foundation2)),
% 34.78/6.30 file('/export/starexec/sandbox2/tmp/tmp.yv4wus1g2e/DTF2THF_4600.p',foundation2)).
% 34.78/6.30 thf(f6486,plain,(
% 34.78/6.30 ( ! [X2 : $i,X3 : $i] : (($true != (in @ X2 @ (setadjoin @ X3 @ emptyset))) | (X2 = X3)) )),
% 34.78/6.30 inference(trivial_inequality_removal,[status(thm)],[f5885])).
% 34.78/6.30 thf(f5885,plain,(
% 34.78/6.30 ( ! [X2 : $i,X3 : $i] : (($true != $true) | (X2 = X3) | ($true != (in @ X2 @ (setadjoin @ X3 @ emptyset)))) )),
% 34.78/6.30 inference(definition_unfolding,[status(thm)],[f4575,f3119])).
% 34.78/6.30 thf(f3119,plain,(
% 34.78/6.30 (notinsingleton = $true)),
% 34.78/6.30 inference(cnf_transformation,[status(thm)],[f1465])).
% 34.78/6.30 thf(f4575,plain,(
% 34.78/6.30 ( ! [X2 : $i,X3 : $i] : ((X2 = X3) | ($true != (in @ X2 @ (setadjoin @ X3 @ emptyset))) | (notinsingleton != $true)) )),
% 34.78/6.30 inference(cnf_transformation,[status(thm)],[f2767])).
% 34.78/6.30 thf(f2767,plain,(
% 34.78/6.30 ((notinsingleton = $true) | ((sK879 != sK878) & ((in @ sK878 @ (setadjoin @ sK879 @ emptyset)) = $true))) & (! [X2 : $i,X3 : $i] : ((X2 = X3) | ($true != (in @ X2 @ (setadjoin @ X3 @ emptyset)))) | (notinsingleton != $true))),
% 34.78/6.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK878,sK879])],[f2765,f2766])).
% 34.78/6.30 thf(f2766,plain,(
% 34.78/6.30 ? [X0 : $i,X1 : $i] : ((X0 != X1) & ((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true)) => ((sK879 != sK878) & ((in @ sK878 @ (setadjoin @ sK879 @ emptyset)) = $true))),
% 34.78/6.30 introduced(definition,[],[choice_axiom])).
% 34.78/6.30 thf(f2765,plain,(
% 34.78/6.30 ((notinsingleton = $true) | ? [X0 : $i,X1 : $i] : ((X0 != X1) & ((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true))) & (! [X2 : $i,X3 : $i] : ((X2 = X3) | ($true != (in @ X2 @ (setadjoin @ X3 @ emptyset)))) | (notinsingleton != $true))),
% 34.78/6.30 inference(rectify,[status(thm)],[f2764])).
% 34.78/6.30 thf(f2764,plain,(
% 34.78/6.30 ((notinsingleton = $true) | ? [X0 : $i,X1 : $i] : ((X0 != X1) & ((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true))) & (! [X0 : $i,X1 : $i] : ((X0 = X1) | ((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true)) | (notinsingleton != $true))),
% 34.78/6.30 inference(nnf_transformation,[status(thm)],[f1389])).
% 34.78/6.30 thf(f1389,plain,(
% 34.78/6.30 (notinsingleton = $true) <=> ! [X0 : $i,X1 : $i] : ((X0 = X1) | ((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true))),
% 34.78/6.30 inference(ennf_transformation,[status(thm)],[f984])).
% 34.78/6.30 thf(f984,plain,(
% 34.78/6.30 ! [X0 : $i,X1 : $i] : ((X0 != X1) => ((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true)) <=> (notinsingleton = $true)),
% 34.78/6.30 inference(flattening,[status(thm)],[f355])).
% 34.78/6.30 thf(f355,plain,(
% 34.78/6.30 ! [X0 : $i,X1 : $i] : ((X0 != X1) => ~((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true)) <=> (notinsingleton = $true)),
% 34.78/6.30 inference(fool_elimination,[status(thm)],[f354])).
% 34.78/6.30 thf(f354,plain,(
% 34.78/6.30 (! [X0 : $i,X1 : $i] : ((X0 != X1) => ~(in @ X0 @ (setadjoin @ X1 @ emptyset))) = notinsingleton)),
% 34.78/6.30 inference(rectify,[status(thm)],[f47])).
% 34.78/6.30 thf(f47,axiom,(
% 34.78/6.30 (! [X2 : $i,X1 : $i] : ((X1 != X2) => ~(in @ X2 @ (setadjoin @ X1 @ emptyset))) = notinsingleton)),
% 34.78/6.30 file('/export/starexec/sandbox2/tmp/tmp.yv4wus1g2e/DTF2THF_4600.p',notinsingleton)).
% 34.78/6.30 thf(f11332,plain,(
% 34.78/6.30 ( ! [X0 : $i] : (($true != (in @ X0 @ (sK273 @ (setadjoin @ X0 @ emptyset))))) )),
% 34.78/6.30 inference(subsumption_resolution,[status(thm)],[f11326,f7577])).
% 34.78/6.30 thf(f11326,plain,(
% 34.78/6.30 ( ! [X0 : $i] : ((emptyset = (setadjoin @ X0 @ emptyset)) | ($true != (in @ X0 @ (sK273 @ (setadjoin @ X0 @ emptyset))))) )),
% 34.78/6.30 inference(trivial_inequality_removal,[status(thm)],[f11323])).
% 34.78/6.30 thf(f11323,plain,(
% 34.78/6.30 ( ! [X0 : $i] : ((emptyset = (setadjoin @ X0 @ emptyset)) | ($true != (in @ X0 @ (sK273 @ (setadjoin @ X0 @ emptyset)))) | ($true != $true)) )),
% 34.78/6.30 inference(superposition,[status(thm)],[f7666,f6597])).
% 34.78/6.30 thf(f6597,plain,(
% 34.78/6.30 ( ! [X0 : $i,X1 : $i] : (((subset @ (setadjoin @ X1 @ emptyset) @ X0) = $true) | ($true != (in @ X1 @ X0))) )),
% 34.78/6.30 inference(trivial_inequality_removal,[status(thm)],[f5874])).
% 34.78/6.30 thf(f5874,plain,(
% 34.78/6.30 ( ! [X0 : $i,X1 : $i] : (((subset @ (setadjoin @ X1 @ emptyset) @ X0) = $true) | ($true != $true) | ($true != (in @ X1 @ X0))) )),
% 34.78/6.30 inference(definition_unfolding,[status(thm)],[f4568,f3358])).
% 34.78/6.30 thf(f3358,plain,(
% 34.78/6.30 (singletonsubset = $true)),
% 34.78/6.30 inference(cnf_transformation,[status(thm)],[f1465])).
% 34.78/6.30 thf(f4568,plain,(
% 34.78/6.30 ( ! [X0 : $i,X1 : $i] : (((subset @ (setadjoin @ X1 @ emptyset) @ X0) = $true) | ($true != (in @ X1 @ X0)) | (singletonsubset != $true)) )),
% 34.78/6.30 inference(cnf_transformation,[status(thm)],[f2758])).
% 34.78/6.30 thf(f2758,plain,(
% 34.78/6.30 (! [X0 : $i,X1 : $i] : (((subset @ (setadjoin @ X1 @ emptyset) @ X0) = $true) | ($true != (in @ X1 @ X0))) | (singletonsubset != $true)) & ((singletonsubset = $true) | (((subset @ (setadjoin @ sK875 @ emptyset) @ sK874) != $true) & ((in @ sK875 @ sK874) = $true)))),
% 34.78/6.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK874,sK875])],[f2756,f2757])).
% 34.78/6.30 thf(f2757,plain,(
% 34.78/6.30 ? [X2 : $i,X3 : $i] : (($true != (subset @ (setadjoin @ X3 @ emptyset) @ X2)) & ($true = (in @ X3 @ X2))) => (((subset @ (setadjoin @ sK875 @ emptyset) @ sK874) != $true) & ((in @ sK875 @ sK874) = $true))),
% 34.78/6.30 introduced(definition,[],[choice_axiom])).
% 34.78/6.30 thf(f2756,plain,(
% 34.78/6.30 (! [X0 : $i,X1 : $i] : (((subset @ (setadjoin @ X1 @ emptyset) @ X0) = $true) | ($true != (in @ X1 @ X0))) | (singletonsubset != $true)) & ((singletonsubset = $true) | ? [X2 : $i,X3 : $i] : (($true != (subset @ (setadjoin @ X3 @ emptyset) @ X2)) & ($true = (in @ X3 @ X2))))),
% 34.78/6.30 inference(rectify,[status(thm)],[f2755])).
% 34.78/6.30 thf(f2755,plain,(
% 34.78/6.30 (! [X0 : $i,X1 : $i] : (((subset @ (setadjoin @ X1 @ emptyset) @ X0) = $true) | ($true != (in @ X1 @ X0))) | (singletonsubset != $true)) & ((singletonsubset = $true) | ? [X0 : $i,X1 : $i] : (((subset @ (setadjoin @ X1 @ emptyset) @ X0) != $true) & ($true = (in @ X1 @ X0))))),
% 34.78/6.30 inference(nnf_transformation,[status(thm)],[f1156])).
% 34.78/6.30 thf(f1156,plain,(
% 34.78/6.30 ! [X0 : $i,X1 : $i] : (((subset @ (setadjoin @ X1 @ emptyset) @ X0) = $true) | ($true != (in @ X1 @ X0))) <=> (singletonsubset = $true)),
% 34.78/6.30 inference(ennf_transformation,[status(thm)],[f811])).
% 34.78/6.30 thf(f811,plain,(
% 34.78/6.30 (singletonsubset = $true) <=> ! [X0 : $i,X1 : $i] : (($true = (in @ X1 @ X0)) => ((subset @ (setadjoin @ X1 @ emptyset) @ X0) = $true))),
% 34.78/6.30 inference(fool_elimination,[status(thm)],[f810])).
% 34.78/6.30 thf(f810,plain,(
% 34.78/6.30 (singletonsubset = ! [X0 : $i,X1 : $i] : ((in @ X1 @ X0) => (subset @ (setadjoin @ X1 @ emptyset) @ X0)))),
% 34.78/6.30 inference(rectify,[status(thm)],[f140])).
% 34.78/6.30 thf(f140,axiom,(
% 34.78/6.30 (singletonsubset = ! [X3 : $i,X1 : $i] : ((in @ X1 @ X3) => (subset @ (setadjoin @ X1 @ emptyset) @ X3)))),
% 34.78/6.30 file('/export/starexec/sandbox2/tmp/tmp.yv4wus1g2e/DTF2THF_4600.p',singletonsubset)).
% 34.78/6.30 thf(f7666,plain,(
% 34.78/6.30 ( ! [X0 : $i] : (((subset @ X0 @ (sK273 @ X0)) != $true) | (emptyset = X0)) )),
% 34.78/6.30 inference(duplicate_literal_removal,[status(thm)],[f7661])).
% 34.78/6.30 thf(f7661,plain,(
% 34.78/6.30 ( ! [X0 : $i] : (((subset @ X0 @ (sK273 @ X0)) != $true) | (emptyset = X0) | (emptyset = X0)) )),
% 34.78/6.30 inference(superposition,[status(thm)],[f6613,f6408])).
% 34.78/6.30 thf(f6408,plain,(
% 34.78/6.30 ( ! [X2 : $i,X3 : $i] : (((binintersect @ X2 @ X3) = X3) | ($true != (subset @ X3 @ X2))) )),
% 34.78/6.30 inference(trivial_inequality_removal,[status(thm)],[f5124])).
% 34.78/6.30 thf(f5124,plain,(
% 34.78/6.30 ( ! [X2 : $i,X3 : $i] : (((binintersect @ X2 @ X3) = X3) | ($true != $true) | ($true != (subset @ X3 @ X2))) )),
% 34.78/6.30 inference(definition_unfolding,[status(thm)],[f3728,f3211])).
% 34.78/6.30 thf(f3211,plain,(
% 34.78/6.30 (binintersectSubset4 = $true)),
% 34.78/6.30 inference(cnf_transformation,[status(thm)],[f1465])).
% 34.78/6.30 thf(f3728,plain,(
% 34.78/6.30 ( ! [X2 : $i,X3 : $i] : (($true != (subset @ X3 @ X2)) | ((binintersect @ X2 @ X3) = X3) | (binintersectSubset4 != $true)) )),
% 34.78/6.30 inference(cnf_transformation,[status(thm)],[f1815])).
% 34.78/6.30 thf(f1815,plain,(
% 34.78/6.30 ((binintersectSubset4 = $true) | (($true = (subset @ sK256 @ sK255)) & ((binintersect @ sK255 @ sK256) != sK256))) & (! [X2 : $i,X3 : $i] : (($true != (subset @ X3 @ X2)) | ((binintersect @ X2 @ X3) = X3)) | (binintersectSubset4 != $true))),
% 34.78/6.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK255,sK256])],[f1813,f1814])).
% 34.78/6.30 thf(f1814,plain,(
% 34.78/6.30 ? [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) & ((binintersect @ X0 @ X1) != X1)) => (($true = (subset @ sK256 @ sK255)) & ((binintersect @ sK255 @ sK256) != sK256))),
% 34.78/6.30 introduced(definition,[],[choice_axiom])).
% 34.78/6.30 thf(f1813,plain,(
% 34.78/6.30 ((binintersectSubset4 = $true) | ? [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) & ((binintersect @ X0 @ X1) != X1))) & (! [X2 : $i,X3 : $i] : (($true != (subset @ X3 @ X2)) | ((binintersect @ X2 @ X3) = X3)) | (binintersectSubset4 != $true))),
% 34.78/6.30 inference(rectify,[status(thm)],[f1812])).
% 34.78/6.30 thf(f1812,plain,(
% 34.78/6.30 ((binintersectSubset4 = $true) | ? [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) & ((binintersect @ X0 @ X1) != X1))) & (! [X0 : $i,X1 : $i] : (($true != (subset @ X1 @ X0)) | ((binintersect @ X0 @ X1) = X1)) | (binintersectSubset4 != $true))),
% 34.78/6.30 inference(nnf_transformation,[status(thm)],[f1317])).
% 34.78/6.30 thf(f1317,plain,(
% 34.78/6.30 (binintersectSubset4 = $true) <=> ! [X0 : $i,X1 : $i] : (($true != (subset @ X1 @ X0)) | ((binintersect @ X0 @ X1) = X1))),
% 34.78/6.30 inference(ennf_transformation,[status(thm)],[f935])).
% 34.78/6.30 thf(f935,plain,(
% 34.78/6.30 (binintersectSubset4 = $true) <=> ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) => ((binintersect @ X0 @ X1) = X1))),
% 34.78/6.30 inference(fool_elimination,[status(thm)],[f934])).
% 34.78/6.30 thf(f934,plain,(
% 34.78/6.30 (! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => ((binintersect @ X0 @ X1) = X1)) = binintersectSubset4)),
% 34.78/6.30 inference(rectify,[status(thm)],[f117])).
% 34.78/6.30 thf(f117,axiom,(
% 34.78/6.30 (! [X3 : $i,X4 : $i] : ((subset @ X4 @ X3) => ((binintersect @ X3 @ X4) = X4)) = binintersectSubset4)),
% 34.78/6.30 file('/export/starexec/sandbox2/tmp/tmp.yv4wus1g2e/DTF2THF_4600.p',binintersectSubset4)).
% 34.78/6.30 thf(f6613,plain,(
% 34.78/6.30 ( ! [X2 : $i] : ((emptyset = (binintersect @ (sK273 @ X2) @ X2)) | (emptyset = X2)) )),
% 34.78/6.30 inference(equality_proxy_clausification,[status(thm)],[f6612])).
% 34.78/6.30 thf(f6612,plain,(
% 34.78/6.30 ( ! [X2 : $i] : ((emptyset = (binintersect @ (sK273 @ X2) @ X2)) | ($true = (emptyset = X2))) )),
% 34.78/6.30 inference(not_proxy_clausification,[status(thm)],[f6611])).
% 34.78/6.30 thf(f6611,plain,(
% 34.78/6.30 ( ! [X2 : $i] : (($true != (~ (emptyset = X2))) | (emptyset = (binintersect @ (sK273 @ X2) @ X2))) )),
% 34.78/6.30 inference(beta_eta_normalization,[status(thm)],[f6610])).
% 34.78/6.30 thf(f6610,plain,(
% 34.78/6.30 ( ! [X2 : $i] : ((emptyset = (binintersect @ (sK273 @ X2) @ X2)) | ($true != ((^[Y0 : $i]: (~ (emptyset = Y0))) @ X2))) )),
% 34.78/6.30 inference(trivial_inequality_removal,[status(thm)],[f5144])).
% 34.78/6.30 thf(f5144,plain,(
% 34.78/6.30 ( ! [X2 : $i] : (($true != ((^[Y0 : $i]: (~ (emptyset = Y0))) @ X2)) | (emptyset = (binintersect @ (sK273 @ X2) @ X2)) | ($true != $true)) )),
% 34.78/6.30 inference(definition_unfolding,[status(thm)],[f3749,f3477,f3387])).
% 34.78/6.30 thf(f3749,plain,(
% 34.78/6.30 ( ! [X2 : $i] : ((emptyset = (binintersect @ (sK273 @ X2) @ X2)) | ($true != (nonempty @ X2)) | (foundation2 != $true)) )),
% 34.78/6.30 inference(cnf_transformation,[status(thm)],[f1840])).
% 34.78/6.30 % SZS output end Proof for DTF2THF_4600
% 34.78/6.30 % (4887)------------------------------
% 34.78/6.30 % (4887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.78/6.30 % (4887)Termination reason: Refutation
% 34.78/6.30
% 34.78/6.30 % (4887)Memory used [KB]: 13816
% 34.78/6.30 % (4887)Time elapsed: 0.998 s
% 34.78/6.30 % (4887)Instructions burned: 2283 (million)
% 34.78/6.30 % (4887)------------------------------
% 34.78/6.30 % (4887)------------------------------
% 34.78/6.30 % (4701)Success in time 4.774 s
%------------------------------------------------------------------------------