%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU819^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 09:37:28 AM UTC 2026
% Result : Theorem 15.74s 3.62s
% Output : Refutation 15.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 21
% Syntax : Number of formulae : 92 ( 18 unt; 0 typ; 9 def)
% Number of atoms : 5823 (1580 equ; 0 cnn)
% Maximal formula atoms : 338 ( 63 avg)
% Number of connectives : 3092 ( 151 ~; 134 |;1055 &; 362 @)
% ( 17 <=>;1373 =>; 0 <=; 0 <~>)
% Maximal formula depth : 343 ( 30 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 603 ( 600 usr; 354 con; 0-6 aty)
% Number of variables : 129 ( 0 ^; 99 !; 30 ?; 129 :)
% 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_378,type,
omegaS: $i > $i ).
thf(func_def_382,type,
peano3: $i > $i > $i > $o ).
thf(func_def_383,type,
peano4: $i > $i > $i > $o ).
thf(func_def_384,type,
peano5: $i > $i > $i > $o ).
thf(func_def_386,type,
peano: $i > $i > $i > $o ).
thf(func_def_387,type,
transitiveset: $i > $o ).
thf(func_def_392,type,
stricttotalorderedByIn: $i > $o ).
thf(func_def_393,type,
wellorderedByIn: $i > $o ).
thf(func_def_394,type,
ordinal: $i > $o ).
thf(func_def_395,type,
limitOrdinal: $i > $o ).
thf(func_def_417,type,
sP3: $i > $i > $i > $o ).
thf(func_def_418,type,
sP4: $i > $i > $i > $o ).
thf(func_def_420,type,
sP6: $i > $i > $o ).
thf(func_def_421,type,
sP7: $i > $o ).
thf(func_def_422,type,
sP8: $i > $i > $o ).
thf(func_def_423,type,
sP9: $i > $i > $o ).
thf(func_def_428,type,
sP14: $i > $i > $i > $i > $o ).
thf(func_def_431,type,
sP17: $i > $i > $i > $o > $o ).
thf(func_def_437,type,
sK23: $i > $i ).
thf(func_def_440,type,
sK26: $i > $i > $o ).
thf(func_def_441,type,
sK27: $i > $i ).
thf(func_def_442,type,
sK28: $i > $i ).
thf(func_def_443,type,
sK29: ( $i > $i > $o ) > $i > $i ).
thf(func_def_444,type,
sK30: ( $i > $i > $o ) > $i > $i ).
thf(func_def_445,type,
sK31: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_450,type,
sK36: $i > $i ).
thf(func_def_453,type,
sK39: $i > ( $i > $i ) > $i > $i ).
thf(func_def_454,type,
sK40: $i > $i > ( $i > $i ) > $i > $i ).
thf(func_def_461,type,
sK47: $i > $i > $i > $i ).
thf(func_def_462,type,
sK48: $i > $i > $i > $i ).
thf(func_def_469,type,
sK55: $i > $i > $i > $i > $i ).
thf(func_def_490,type,
sK76: $i > $i ).
thf(func_def_491,type,
sK77: $i > $o ).
thf(func_def_493,type,
sK79: $i > ( $i > $o ) > $i ).
thf(func_def_495,type,
sK81: $i > $i ).
thf(func_def_496,type,
sK82: $i > $i > $i > $i > $i ).
thf(func_def_501,type,
sK87: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_502,type,
sK88: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_506,type,
sK92: $i > $o ).
thf(func_def_519,type,
sK105: $i > $i > $i > $i > $i > $i ).
thf(func_def_523,type,
sK109: $i > $o ).
thf(func_def_542,type,
sK128: $i > $o ).
thf(func_def_559,type,
sK145: $i > $o ).
thf(func_def_565,type,
sK151: $i > $o ).
thf(func_def_570,type,
sK156: $i > $o ).
thf(func_def_577,type,
sK163: $i > $o ).
thf(func_def_579,type,
sK165: $i > $o ).
thf(func_def_581,type,
sK167: ( $i > $o ) > $i ).
thf(func_def_582,type,
sK168: ( $i > $o ) > $i ).
thf(func_def_583,type,
sK169: ( $i > $o ) > $i > $i > $i ).
thf(func_def_584,type,
sK170: ( $i > $o ) > $i > $i > $i ).
thf(func_def_587,type,
sK173: $i > $o ).
thf(func_def_593,type,
sK179: $i > $o ).
thf(func_def_595,type,
sK181: ( $i > $o ) > $i > $i ).
thf(func_def_605,type,
sK191: $i > ( $i > $o ) > $i ).
thf(func_def_606,type,
sK192: $i > $o ).
thf(func_def_616,type,
sK202: $i > $i ).
thf(func_def_617,type,
sK203: ( $i > $i ) > $i > $i > $i ).
thf(func_def_627,type,
sK213: $i > $i > $i > $i ).
thf(func_def_628,type,
sK214: $i > $i > $i > $i ).
thf(func_def_644,type,
sK230: $i > $i > $o ).
thf(func_def_647,type,
sK233: $i > $i > ( $i > $i ) > $i ).
thf(func_def_648,type,
sK234: $i > $i ).
thf(func_def_713,type,
sK299: $i > $i > $i > $i ).
thf(func_def_714,type,
sK300: $i > $i > $i > $i ).
thf(func_def_715,type,
sK301: $i > $i > $i > $i ).
thf(func_def_716,type,
sK302: $i > $i > $i > $i ).
thf(func_def_720,type,
sK306: $i > $i > $i ).
thf(func_def_725,type,
sK311: $i > $i > $i ).
thf(func_def_731,type,
sK317: $i > $o ).
thf(func_def_732,type,
sK318: $i > $o ).
thf(func_def_733,type,
sK319: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_734,type,
sK320: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_736,type,
sK322: $i > $o ).
thf(func_def_739,type,
sK325: $i > $i > $i ).
thf(func_def_740,type,
sK326: $i > $i > $i ).
thf(func_def_741,type,
sK327: $i > $i > $i ).
thf(func_def_742,type,
sK328: $i > $i > $i ).
thf(func_def_743,type,
sK329: $i > $i > $i ).
thf(func_def_744,type,
sK330: $i > $i > $i > $i ).
thf(func_def_745,type,
sK331: $i > $i ).
thf(func_def_746,type,
sK332: $i > $i ).
thf(func_def_747,type,
sK333: $i > $i ).
thf(func_def_748,type,
sK334: $i > $i ).
thf(func_def_749,type,
sK335: $i > $i > $i > $i ).
thf(func_def_750,type,
sK336: $i > $i > $i > $i ).
thf(func_def_751,type,
sK337: $i > $i > $i ).
thf(func_def_752,type,
sK338: $i > $i > $i ).
thf(func_def_753,type,
sK339: $i > $i > $i ).
thf(func_def_755,type,
sK341: $i > $i ).
thf(func_def_756,type,
sK342: $i > $i ).
thf(func_def_757,type,
sK343: $i > $i ).
thf(func_def_770,type,
sK356: $i > $i ).
thf(func_def_771,type,
sK357: $i > $i > $i > $i ).
thf(func_def_772,type,
sK358: $i > $i > $i > $i ).
thf(func_def_780,type,
sK366: $i > $i > $i ).
thf(func_def_781,type,
sK367: $i > $i > $i ).
thf(func_def_787,type,
sK373: $i > $i > $o ).
thf(func_def_799,type,
sK385: ( $i > $i ) > $i > $i > $i ).
thf(func_def_802,type,
sK388: $i > $i ).
thf(func_def_810,type,
sK396: $i > $o ).
thf(func_def_811,type,
sK397: $i > $i > $i > $i ).
thf(func_def_818,type,
sK404: $i > ( $i > $o ) > $i ).
thf(func_def_819,type,
sK405: $i > $o ).
thf(func_def_829,type,
sK415: $i > $o ).
thf(func_def_848,type,
sK434: $i > $o ).
thf(func_def_851,type,
sK437: $i > $i > ( $i > $o ) > $i ).
thf(func_def_854,type,
sK440: $i > $o ).
thf(func_def_855,type,
sK441: $i > $i ).
thf(func_def_856,type,
sK442: ( $i > $o ) > $i ).
thf(func_def_859,type,
sK445: $i > $o ).
thf(func_def_861,type,
sK447: ( $i > $o ) > $i > $i ).
thf(func_def_862,type,
sK448: ( $i > $o ) > $i > $i ).
thf(func_def_881,type,
sK467: $i > ( $i > $i ) > $i ).
thf(func_def_882,type,
sK468: $i > $i > ( $i > $i ) > $i ).
thf(func_def_883,type,
sK469: $i > $i ).
thf(func_def_885,type,
sK471: $i > $i ).
thf(func_def_886,type,
sK472: $i > $i ).
thf(func_def_904,type,
sK490: $i > $i ).
thf(func_def_915,type,
sK501: $i > $i > $i > $i > $i ).
thf(func_def_917,type,
sK503: $i > $o ).
thf(func_def_918,type,
sK504: $i > $o ).
thf(func_def_921,type,
sK507: $i > ( $i > $o ) > $i ).
thf(func_def_922,type,
sK508: $i > ( $i > $o ) > $i ).
thf(func_def_944,type,
sK530: $i > $i ).
thf(func_def_958,type,
sK544: $i > $i > $o ).
thf(func_def_977,type,
sK563: $i > $i > $i ).
thf(func_def_997,type,
sK583: $i > $o ).
thf(func_def_1018,type,
sK604: $i > $i > $i > $i > $i ).
thf(func_def_1019,type,
sK605: $i > $i > $i > $i > $i ).
thf(func_def_1020,type,
sK606: $i > $i > $i > $i > $i ).
thf(func_def_1021,type,
sK607: $i > $i > $i > $i > $i ).
thf(func_def_1022,type,
sK608: $i > $i > $i ).
thf(func_def_1028,type,
sK614: $i > $i > $o ).
thf(func_def_1031,type,
sK617: $i > $i > $o ).
thf(func_def_1056,type,
sK642: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1058,type,
sK644: $i > $i ).
thf(func_def_1077,type,
sK663: $i > $o ).
thf(func_def_1079,type,
sK665: $i > ( $i > $o ) > $i ).
thf(func_def_1106,type,
sK692: $i > $i > $i > $i > $i ).
thf(func_def_1107,type,
sK693: $i > $i > $i > $i > $i ).
thf(func_def_1109,type,
sK695: $i > $i ).
thf(func_def_1111,type,
sK697: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1113,type,
sK699: $i > $i ).
thf(func_def_1158,type,
sK744: $i > $o ).
thf(func_def_1159,type,
sK745: ( $i > $o ) > $i ).
thf(func_def_1169,type,
sK755: $i > $o ).
thf(func_def_1171,type,
sK757: ( $i > $o ) > $i > $i > $i ).
thf(func_def_1172,type,
sK758: ( $i > $o ) > $i > $i > $i ).
thf(func_def_1173,type,
sK759: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1176,type,
sK762: $i > $i ).
thf(func_def_1178,type,
sK764: $i > $i > $o ).
thf(func_def_1187,type,
sK773: $i > ( $i > $o ) > $i ).
thf(func_def_1188,type,
sK774: $i > $o ).
thf(func_def_1205,type,
sK791: ( $i > $o ) > $i ).
thf(func_def_1206,type,
sK792: $i > $o ).
thf(func_def_1207,type,
sK793: $i > $i ).
thf(func_def_1208,type,
sK794: $i > ( $i > $o ) > $i ).
thf(func_def_1209,type,
sK795: $i > $o ).
thf(func_def_1221,type,
sK807: $i > $i > $i ).
thf(func_def_1264,type,
sK850: $i > $i > $i ).
thf(func_def_1270,type,
sK856: $i > $i > $i ).
thf(func_def_1279,type,
sK865: $i > $i ).
thf(func_def_1292,type,
sK878: $o > $i > $i > $i > $i > $i > $i ).
thf(func_def_1299,type,
sK885: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1300,type,
sK886: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1301,type,
sK887: $i > $o ).
thf(func_def_1302,type,
sK888: $i > $o ).
thf(func_def_1309,type,
sK895: $i > $i > $o ).
thf(func_def_1330,type,
sK916: $i > $i > $i > $i ).
thf(func_def_1355,type,
sK941: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_1357,type,
sK943: $i > $i > $o ).
thf(func_def_1361,type,
sK947: $i > $i ).
thf(func_def_1363,type,
sK949: $i > $i ).
thf(func_def_1366,type,
sK952: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1381,type,
sK967: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1383,type,
sK969: $i > $i ).
thf(func_def_1385,type,
sK971: $i > $o ).
thf(func_def_1400,type,
sK986: $i > $o ).
thf(func_def_1413,type,
sK999: $o > $i > $i > $i ).
thf(func_def_1428,type,
sK1014: $i > $o ).
thf(func_def_1430,type,
sK1016: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_1431,type,
sK1017: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_1440,type,
sK1026: $i > ( $i > $o ) > $i ).
thf(func_def_1441,type,
sK1027: $i > $o ).
thf(func_def_1455,type,
sK1041: $i > $i ).
thf(func_def_1456,type,
sK1042: $i > $i ).
thf(func_def_1461,type,
sK1047: $i > $i > $i ).
thf(func_def_1466,type,
sK1052: $i > ( $i > $o ) > $i ).
thf(func_def_1467,type,
sK1053: $i > $o ).
thf(func_def_1470,type,
sK1056: $i > $i ).
thf(func_def_1474,type,
sK1060: $i > $i > $o ).
thf(func_def_1498,type,
sK1084: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_1499,type,
sK1085: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_1502,type,
sK1088: $i > $o ).
thf(func_def_1503,type,
sK1089: $i > $o ).
thf(func_def_1526,type,
ph1112:
!>[X0: $tType] : X0 ).
thf(f15607,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f7519,f10663,f11507,f12688,f13002,f13137,f13146,f13569,f13589,f15606]) ).
thf(f15606,plain,
( ~ spl1111_498
| ~ spl1111_539
| ~ spl1111_1166
| ~ spl1111_1645
| ~ spl1111_1674 ),
inference(avatar_contradiction_clause,[status(thm)],[f15605]) ).
thf(f15605,plain,
( $false
| ~ spl1111_498
| ~ spl1111_539
| ~ spl1111_1166
| ~ spl1111_1645
| ~ spl1111_1674 ),
inference(subsumption_resolution,[status(thm)],[f15601,f3476]) ).
thf(f3476,plain,
( ( transitiveset @ ( setunion @ sK70 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f1595]) ).
thf(f1595,plain,
( ( setukpairinjR1 = $true )
& ( funcImageSingleton = $true )
& ( eta2 = $true )
& ( breln1unionEcases = $true )
& ( foundation2 = $true )
& ( doubleComplementSub1 = $true )
& ( setukpairinjR12 = $true )
& ( setadjoinIR = $true )
& ( breln1unionprop = $true )
& ( breln1all2 = $true )
& ( complementTE1 = $true )
& ( binintersectSubset1 = $true )
& ( eqimpsubset2 = $true )
& ( inCongP = $true )
& ( emptyI = $true )
& ( surjCantorThm = $true )
& ( disjointsetsI1 = $true )
& ( dsetconstrER = $true )
& ( symdiffIneg1 = $true )
& ( ifp = $true )
& ( singletoninpowunion = $true )
& ( doubleComplementSub2 = $true )
& ( woz1_5 = $true )
& ( quantDeMorgan3 = $true )
& ( setminusELneg = $true )
& ( ex1I = $true )
& ( cartprodsndin = $true )
& ( lamp = $true )
& ( setunion__Cong = $true )
& ( funcGraphProp4 = $true )
& ( eqbreln1 = $true )
& ( exuE2 = $true )
& ( image1I = $true )
& ( setunionsingleton2 = $true )
& ( demorgan2b = $true )
& ( breln1compprop = $true )
& ( app = $true )
& ( subbreln = $true )
& ( peano0notS = $true )
& ( iffalseProp2 = $true )
& ( eta1 = $true )
& ( ubforcartprodlem1 = $true )
& ( breln1unionIR = $true )
& ( doubleComplementI1 = $true )
& ( breln1SetBreln1 = $true )
& ( emptysetAx = $true )
& ( dpsetconstrEL1 = $true )
& ( omega0Ax = $true )
& ( emptyInPowerset = $true )
& ( ex1I2 = $true )
& ( complementTnotintersectT = $true )
& ( emptysetimpfalse = $true )
& ( binintersectRsub = $true )
& ( binunionEcases = $true )
& ( setOfPairsIsBReln1 = $true )
& ( ifSingleton = $true )
& ( setminusERneg = $true )
& ( singletonsubset = $true )
& ( subsetI1 = $true )
& ( woz2Ex = $true )
& ( powerset__Cong = $true )
& ( complementTcontraSubset = $true )
& ( demorgan2b2 = $true )
& ( lam2p = $true )
& ( woz1_1 = $true )
& ( symdiffE = $true )
& ( binintersectEL = $true )
& ( secondinupair = $true )
& ( subsetI2 = $true )
& ( emptysetsubset = $true )
& ( contrasubsetT = $true )
& ( injFuncSetFuncIn = $true )
& ( setunionTransitive = $true )
& ( symdiffI2 = $true )
& ( setukpairinjL2 = $true )
& ( binintersectI = $true )
& ( iftrueProp2 = $true )
& ( image1Equiv = $true )
& ( symdiffI1 = $true )
& ( notinsingleton = $true )
& ( subbreln1 = $true )
& ( exuI2 = $true )
& ( setoftrueEq = $true )
& ( funcGraphProp1 = $true )
& ( setminusT_lem = $true )
& ( binintersectTERcontra = $true )
& ( exuE1 = $true )
& ( beta2 = $true )
& ( iftrueProp1 = $true )
& ( iffalseProp1 = $true )
& ( subsetE = $true )
& ( setminusILneg = $true )
& ( emptyinunitempty = $true )
& ( kfstsingleton = $true )
& ( quantDeMorgan2 = $true )
& ( image1E = $true )
& ( setukpairinjL = $true )
& ( ordinalTransSet = $true )
& ( vacuousDall = $true )
& ( ksndpairEq = $true )
& ( ex1E2 = $true )
& ( demorgan2a2 = $true )
& ( powersetT_lem = $true )
& ( demorgan1 = $true )
& ( woz13rule2 = $true )
& ( cartprodfstpairEq = $true )
& ( omegaSclos = $true )
& ( iffalse = $true )
& ( setbeta = $true )
& ( breln1unionCommutes = $true )
& ( binintersectSubset3 = $true )
& ( singletonsuniq = $true )
& ( cartprodsndpairEq = $true )
& ( replAx = $true )
& ( cartprodpairmemEL = $true )
& ( ap2apEq1 = $true )
& ( surjFuncSetFuncSurj = $true )
& ( setminusIRneg = $true )
& ( doubleComplementE1 = $true )
& ( theeq = $true )
& ( exuEu = $true )
& ( breln1unionI = $true )
& ( setadjoinE = $true )
& ( woz13rule0 = $true )
& ( choice2fnsingleton = $true )
& ( complementImpComplementIntersect = $true )
& ( setminusSubset2 = $true )
& ( contrasubsetT2 = $true )
& ( nonemptyI = $true )
& ( breln1unionIL = $true )
& ( notinemptyset = $true )
& ( in__Cong = $true )
& ( breln1compE = $true )
& ( eqimpsubset1 = $true )
& ( inIntersectImpInUnion = $true )
& ( powersetAx = $true )
& ( powersetE = $true )
& ( powersetsubset = $true )
& ( binunionE = $true )
& ( notinself = $true )
& ( omega__Cong = $true )
& ( notequalI2 = $true )
& ( eqinunit = $true )
& ( setadjoinOr = $true )
& ( funcextLem = $true )
& ( funcext2 = $true )
& ( apProp = $true )
& ( setextsub = $true )
& ( notequalI1 = $true )
& ( setunionE2 = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( descr__Cong = $true )
& ( upairsetIR = $true )
& ( singletonsswitch = $true )
& ( woz13rule4 = $true )
& ( ( transitiveset @ ( setunion @ sK70 ) )
!= $true )
& ! [X1: $i] :
( ( ( ordinal @ X1 )
= $true )
| ( ( in @ X1 @ sK70 )
!= $true ) )
& ( inComplementUnionImpNotIn1 = $true )
& ( dpsetconstrER = $true )
& ( upairsetIL = $true )
& ( ubforcartprodlem2 = $true )
& ( uniqinunit = $true )
& ( binunionLsub = $true )
& ( cartprodmempaircEq = $true )
& ( setextAx = $true )
& ( cartprodpairin = $true )
& ( cartprodmempair = $true )
& ( exuI1 = $true )
& ( setminusI = $true )
& ( theprop = $true )
& ( sepInPowerset = $true )
& ( nonemptyE1 = $true )
& ( injFuncSetFuncInj = $true )
& ( transitivesetOp1 = $true )
& ( dpsetconstrI = $true )
& ( foundationAx = $true )
& ( binintersectSubset2 = $true )
& ( breln1compEex = $true )
& ( upairset2IR = $true )
& ( image1Ex1 = $true )
& ( peanoSinj = $true )
& ( inPowerset = $true )
& ( powersetI = $true )
& ( singletoninpowerset = $true )
& ( breln1unionE = $true )
& ( quantDeMorgan1 = $true )
& ( binunionT_lem = $true )
& ( breln1invE = $true )
& ( setadjoin__Cong = $true )
& ( upairsubunion = $true )
& ( iftrueorfalse = $true )
& ( sepSubset = $true )
& ( nonemptyImpWitness = $true )
& ( exuE3e = $true )
& ( kpairp = $true )
& ( upairsetE = $true )
& ( dpsetconstrSub = $true )
& ( binunionTIRcontra = $true )
& ( binunionIL = $true )
& ( omegaSAx = $true )
& ( ex1E1 = $true )
& ( binunionRsub = $true )
& ( transitivesetOp2 = $true )
& ( iftrue = $true )
& ( ubforcartprodlem3 = $true )
& ( nonemptyI1 = $true )
& ( binunionTE = $true )
& ( cartprodpairsurjEq = $true )
& ( complementUnionInPowersetComplement = $true )
& ( setukpairinjL1 = $true )
& ( kfstpairEq = $true )
& ( notsubsetI = $true )
& ( woz2W = $true )
& ( omegaSp = $true )
& ( kpairiskpair = $true )
& ( kpairsurjEq = $true )
& ( setminusEL = $true )
& ( exu__Cong = $true )
& ( funcGraphProp3 = $true )
& ( setadjoinSub = $true )
& ( cartprodfstin = $true )
& ( binintersectLsub = $true )
& ( injFuncInInjFuncSet = $true )
& ( binintersectER = $true )
& ( emptyset__Cong = $true )
& ( exuE3u = $true )
& ( demorgan1a = $true )
& ( powersetTE1 = $true )
& ( dpsetconstrERa = $true )
& ( funcext = $true )
& ( dsetconstr__Cong = $true )
& ( notdexE = $true )
& ( setminusLsub = $true )
& ( singletonprop = $true )
& ( subPowSU = $true )
& ( infuncsetfunc = $true )
& ( brelnall1 = $true )
& ( wellorderingAx = $true )
& ( notdallE = $true )
& ( powersetTI1 = $true )
& ( complementTI1 = $true )
& ( demorgan2a1 = $true )
& ( setunionE = $true )
& ( ordinalTransSet1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setukpairIR = $true )
& ( subsetTrans = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( binintersectSubset5 = $true )
& ( setukpairinjR = $true )
& ( exuI3 = $true )
& ( setunionI = $true )
& ( subsetTI = $true )
& ( ap2p = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR11 = $true )
& ( eqbreln = $true )
& ( dsetconstrI = $true )
& ( image1Ex = $true )
& ( ap2apEq2 = $true )
& ( subsetRefl = $true )
& ( prop2setI = $true )
& ( subset2powerset = $true )
& ( contrasubsetT1 = $true )
& ( woz2B = $true )
& ( binintersectTELcontra = $true )
& ( upairinpowunion = $true )
& ( setextT = $true )
& ( leftInvIsSurj = $true )
& ( ordinalMinLem1 = $true )
& ( subsetE2 = $true )
& ( setminusER = $true )
& ( symdiffIneg2 = $true )
& ( setunionsingleton1 = $true )
& ( powersetI1 = $true )
& ( lamProp = $true )
& ( woz1_4 = $true )
& ( demorgan1b = $true )
& ( contraSubsetComplement = $true )
& ( brelnall2 = $true )
& ( funcGraphProp2 = $true )
& ( binunionIR = $true )
& ( setadjoinAx = $true )
& ( breln1compI = $true )
& ( upairequniteq = $true )
& ( notinself2 = $true )
& ( setminusSubset1 = $true )
& ( emptysetE = $true )
& ( noeltsimpempty = $true )
& ( prop2setE = $true )
& ( powersetE1 = $true )
& ( beta1 = $true )
& ( binintersectT_lem = $true )
& ( bs114d = $true )
& ( emptyE1 = $true )
& ( doubleComplementEq = $true )
& ( prop2set2propI = $true )
& ( setadjoinIL = $true )
& ( breln1all1 = $true )
& ( descrp = $true )
& ( binintTransitive = $true )
& ( dsetconstrEL = $true )
& ( inIntersectImpInUnion2 = $true )
& ( surjFuncSetFuncIn = $true )
& ( quantDeMorgan4 = $true )
& ( cartprodmempair1 = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( setOfPairsIsBReln = $true )
& ( setukpairinjR2 = $true )
& ( complementSubsetComplementIntersect = $true )
& ( setunionsingleton = $true )
& ( demorgan2 = $true )
& ( contrasubsetT3 = $true )
& ( breln1invI = $true )
& ( woz13rule3 = $true )
& ( woz2A = $true )
& ( demorgan2a = $true )
& ( binintersectSubset4 = $true )
& ( breln1invprop = $true )
& ( omegaIndAx = $true )
& ( woz1_2 = $true )
& ( setunionAx = $true )
& ( upairset2E = $true )
& ( cartprodpairmemER = $true )
& ( funcinfuncset = $true )
& ( lam2lamEq = $true )
& ( binunionTILcontra = $true )
& ( binunionTEcontra = $true )
& ( setukpairIL = $true )
& ( emptyinPowerset = $true )
& ( dpsetconstrEL2 = $true )
& ( woz13rule1 = $true )
& ( setadjoinSub2 = $true )
& ( setext = $true )
& ( woz1_3 = $true )
& ( complementT_lem = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK70])],[f1270,f1594]) ).
thf(f1594,plain,
( ? [X0: $i] :
( ( ( transitiveset @ ( setunion @ X0 ) )
!= $true )
& ! [X1: $i] :
( ( ( ordinal @ X1 )
= $true )
| ( ( in @ X1 @ X0 )
!= $true ) ) )
=> ( ( ( transitiveset @ ( setunion @ sK70 ) )
!= $true )
& ! [X1: $i] :
( ( ( ordinal @ X1 )
= $true )
| ( ( in @ X1 @ sK70 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1270,plain,
( ( setukpairinjR1 = $true )
& ( funcImageSingleton = $true )
& ( eta2 = $true )
& ( breln1unionEcases = $true )
& ( foundation2 = $true )
& ( doubleComplementSub1 = $true )
& ( setukpairinjR12 = $true )
& ( setadjoinIR = $true )
& ( breln1unionprop = $true )
& ( breln1all2 = $true )
& ( complementTE1 = $true )
& ( binintersectSubset1 = $true )
& ( eqimpsubset2 = $true )
& ( inCongP = $true )
& ( emptyI = $true )
& ( surjCantorThm = $true )
& ( disjointsetsI1 = $true )
& ( dsetconstrER = $true )
& ( symdiffIneg1 = $true )
& ( ifp = $true )
& ( singletoninpowunion = $true )
& ( doubleComplementSub2 = $true )
& ( woz1_5 = $true )
& ( quantDeMorgan3 = $true )
& ( setminusELneg = $true )
& ( ex1I = $true )
& ( cartprodsndin = $true )
& ( lamp = $true )
& ( setunion__Cong = $true )
& ( funcGraphProp4 = $true )
& ( eqbreln1 = $true )
& ( exuE2 = $true )
& ( image1I = $true )
& ( setunionsingleton2 = $true )
& ( demorgan2b = $true )
& ( breln1compprop = $true )
& ( app = $true )
& ( subbreln = $true )
& ( peano0notS = $true )
& ( iffalseProp2 = $true )
& ( eta1 = $true )
& ( ubforcartprodlem1 = $true )
& ( breln1unionIR = $true )
& ( doubleComplementI1 = $true )
& ( breln1SetBreln1 = $true )
& ( emptysetAx = $true )
& ( dpsetconstrEL1 = $true )
& ( omega0Ax = $true )
& ( emptyInPowerset = $true )
& ( ex1I2 = $true )
& ( complementTnotintersectT = $true )
& ( emptysetimpfalse = $true )
& ( binintersectRsub = $true )
& ( binunionEcases = $true )
& ( setOfPairsIsBReln1 = $true )
& ( ifSingleton = $true )
& ( setminusERneg = $true )
& ( singletonsubset = $true )
& ( subsetI1 = $true )
& ( woz2Ex = $true )
& ( powerset__Cong = $true )
& ( complementTcontraSubset = $true )
& ( demorgan2b2 = $true )
& ( lam2p = $true )
& ( woz1_1 = $true )
& ( symdiffE = $true )
& ( binintersectEL = $true )
& ( secondinupair = $true )
& ( subsetI2 = $true )
& ( emptysetsubset = $true )
& ( contrasubsetT = $true )
& ( injFuncSetFuncIn = $true )
& ( setunionTransitive = $true )
& ( symdiffI2 = $true )
& ( setukpairinjL2 = $true )
& ( binintersectI = $true )
& ( iftrueProp2 = $true )
& ( image1Equiv = $true )
& ( symdiffI1 = $true )
& ( notinsingleton = $true )
& ( subbreln1 = $true )
& ( exuI2 = $true )
& ( setoftrueEq = $true )
& ( funcGraphProp1 = $true )
& ( setminusT_lem = $true )
& ( binintersectTERcontra = $true )
& ( exuE1 = $true )
& ( beta2 = $true )
& ( iftrueProp1 = $true )
& ( iffalseProp1 = $true )
& ( subsetE = $true )
& ( setminusILneg = $true )
& ( emptyinunitempty = $true )
& ( kfstsingleton = $true )
& ( quantDeMorgan2 = $true )
& ( image1E = $true )
& ( setukpairinjL = $true )
& ( ordinalTransSet = $true )
& ( vacuousDall = $true )
& ( ksndpairEq = $true )
& ( ex1E2 = $true )
& ( demorgan2a2 = $true )
& ( powersetT_lem = $true )
& ( demorgan1 = $true )
& ( woz13rule2 = $true )
& ( cartprodfstpairEq = $true )
& ( omegaSclos = $true )
& ( iffalse = $true )
& ( setbeta = $true )
& ( breln1unionCommutes = $true )
& ( binintersectSubset3 = $true )
& ( singletonsuniq = $true )
& ( cartprodsndpairEq = $true )
& ( replAx = $true )
& ( cartprodpairmemEL = $true )
& ( ap2apEq1 = $true )
& ( surjFuncSetFuncSurj = $true )
& ( setminusIRneg = $true )
& ( doubleComplementE1 = $true )
& ( theeq = $true )
& ( exuEu = $true )
& ( breln1unionI = $true )
& ( setadjoinE = $true )
& ( woz13rule0 = $true )
& ( choice2fnsingleton = $true )
& ( complementImpComplementIntersect = $true )
& ( setminusSubset2 = $true )
& ( contrasubsetT2 = $true )
& ( nonemptyI = $true )
& ( breln1unionIL = $true )
& ( notinemptyset = $true )
& ( in__Cong = $true )
& ( breln1compE = $true )
& ( eqimpsubset1 = $true )
& ( inIntersectImpInUnion = $true )
& ( powersetAx = $true )
& ( powersetE = $true )
& ( powersetsubset = $true )
& ( binunionE = $true )
& ( notinself = $true )
& ( omega__Cong = $true )
& ( notequalI2 = $true )
& ( eqinunit = $true )
& ( setadjoinOr = $true )
& ( funcextLem = $true )
& ( funcext2 = $true )
& ( apProp = $true )
& ( setextsub = $true )
& ( notequalI1 = $true )
& ( setunionE2 = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( descr__Cong = $true )
& ( upairsetIR = $true )
& ( singletonsswitch = $true )
& ( woz13rule4 = $true )
& ? [X0: $i] :
( ( ( transitiveset @ ( setunion @ X0 ) )
!= $true )
& ! [X1: $i] :
( ( ( ordinal @ X1 )
= $true )
| ( ( in @ X1 @ X0 )
!= $true ) ) )
& ( inComplementUnionImpNotIn1 = $true )
& ( dpsetconstrER = $true )
& ( upairsetIL = $true )
& ( ubforcartprodlem2 = $true )
& ( uniqinunit = $true )
& ( binunionLsub = $true )
& ( cartprodmempaircEq = $true )
& ( setextAx = $true )
& ( cartprodpairin = $true )
& ( cartprodmempair = $true )
& ( exuI1 = $true )
& ( setminusI = $true )
& ( theprop = $true )
& ( sepInPowerset = $true )
& ( nonemptyE1 = $true )
& ( injFuncSetFuncInj = $true )
& ( transitivesetOp1 = $true )
& ( dpsetconstrI = $true )
& ( foundationAx = $true )
& ( binintersectSubset2 = $true )
& ( breln1compEex = $true )
& ( upairset2IR = $true )
& ( image1Ex1 = $true )
& ( peanoSinj = $true )
& ( inPowerset = $true )
& ( powersetI = $true )
& ( singletoninpowerset = $true )
& ( breln1unionE = $true )
& ( quantDeMorgan1 = $true )
& ( binunionT_lem = $true )
& ( breln1invE = $true )
& ( setadjoin__Cong = $true )
& ( upairsubunion = $true )
& ( iftrueorfalse = $true )
& ( sepSubset = $true )
& ( nonemptyImpWitness = $true )
& ( exuE3e = $true )
& ( kpairp = $true )
& ( upairsetE = $true )
& ( dpsetconstrSub = $true )
& ( binunionTIRcontra = $true )
& ( binunionIL = $true )
& ( omegaSAx = $true )
& ( ex1E1 = $true )
& ( binunionRsub = $true )
& ( transitivesetOp2 = $true )
& ( iftrue = $true )
& ( ubforcartprodlem3 = $true )
& ( nonemptyI1 = $true )
& ( binunionTE = $true )
& ( cartprodpairsurjEq = $true )
& ( complementUnionInPowersetComplement = $true )
& ( setukpairinjL1 = $true )
& ( kfstpairEq = $true )
& ( notsubsetI = $true )
& ( woz2W = $true )
& ( omegaSp = $true )
& ( kpairiskpair = $true )
& ( kpairsurjEq = $true )
& ( setminusEL = $true )
& ( exu__Cong = $true )
& ( funcGraphProp3 = $true )
& ( setadjoinSub = $true )
& ( cartprodfstin = $true )
& ( binintersectLsub = $true )
& ( injFuncInInjFuncSet = $true )
& ( binintersectER = $true )
& ( emptyset__Cong = $true )
& ( exuE3u = $true )
& ( demorgan1a = $true )
& ( powersetTE1 = $true )
& ( dpsetconstrERa = $true )
& ( funcext = $true )
& ( dsetconstr__Cong = $true )
& ( notdexE = $true )
& ( setminusLsub = $true )
& ( singletonprop = $true )
& ( subPowSU = $true )
& ( infuncsetfunc = $true )
& ( brelnall1 = $true )
& ( wellorderingAx = $true )
& ( notdallE = $true )
& ( powersetTI1 = $true )
& ( complementTI1 = $true )
& ( demorgan2a1 = $true )
& ( setunionE = $true )
& ( ordinalTransSet1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setukpairIR = $true )
& ( subsetTrans = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( binintersectSubset5 = $true )
& ( setukpairinjR = $true )
& ( exuI3 = $true )
& ( setunionI = $true )
& ( subsetTI = $true )
& ( ap2p = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR11 = $true )
& ( eqbreln = $true )
& ( dsetconstrI = $true )
& ( image1Ex = $true )
& ( ap2apEq2 = $true )
& ( subsetRefl = $true )
& ( prop2setI = $true )
& ( subset2powerset = $true )
& ( contrasubsetT1 = $true )
& ( woz2B = $true )
& ( binintersectTELcontra = $true )
& ( upairinpowunion = $true )
& ( setextT = $true )
& ( leftInvIsSurj = $true )
& ( ordinalMinLem1 = $true )
& ( subsetE2 = $true )
& ( setminusER = $true )
& ( symdiffIneg2 = $true )
& ( setunionsingleton1 = $true )
& ( powersetI1 = $true )
& ( lamProp = $true )
& ( woz1_4 = $true )
& ( demorgan1b = $true )
& ( contraSubsetComplement = $true )
& ( brelnall2 = $true )
& ( funcGraphProp2 = $true )
& ( binunionIR = $true )
& ( setadjoinAx = $true )
& ( breln1compI = $true )
& ( upairequniteq = $true )
& ( notinself2 = $true )
& ( setminusSubset1 = $true )
& ( emptysetE = $true )
& ( noeltsimpempty = $true )
& ( prop2setE = $true )
& ( powersetE1 = $true )
& ( beta1 = $true )
& ( binintersectT_lem = $true )
& ( bs114d = $true )
& ( emptyE1 = $true )
& ( doubleComplementEq = $true )
& ( prop2set2propI = $true )
& ( setadjoinIL = $true )
& ( breln1all1 = $true )
& ( descrp = $true )
& ( binintTransitive = $true )
& ( dsetconstrEL = $true )
& ( inIntersectImpInUnion2 = $true )
& ( surjFuncSetFuncIn = $true )
& ( quantDeMorgan4 = $true )
& ( cartprodmempair1 = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( setOfPairsIsBReln = $true )
& ( setukpairinjR2 = $true )
& ( complementSubsetComplementIntersect = $true )
& ( setunionsingleton = $true )
& ( demorgan2 = $true )
& ( contrasubsetT3 = $true )
& ( breln1invI = $true )
& ( woz13rule3 = $true )
& ( woz2A = $true )
& ( demorgan2a = $true )
& ( binintersectSubset4 = $true )
& ( breln1invprop = $true )
& ( omegaIndAx = $true )
& ( woz1_2 = $true )
& ( setunionAx = $true )
& ( upairset2E = $true )
& ( cartprodpairmemER = $true )
& ( funcinfuncset = $true )
& ( lam2lamEq = $true )
& ( binunionTILcontra = $true )
& ( binunionTEcontra = $true )
& ( setukpairIL = $true )
& ( emptyinPowerset = $true )
& ( dpsetconstrEL2 = $true )
& ( woz13rule1 = $true )
& ( setadjoinSub2 = $true )
& ( setext = $true )
& ( woz1_3 = $true )
& ( complementT_lem = $true ) ),
inference(flattening,[status(thm)],[f1269]) ).
thf(f1269,plain,
( ? [X0: $i] :
( ( ( transitiveset @ ( setunion @ X0 ) )
!= $true )
& ! [X1: $i] :
( ( ( ordinal @ X1 )
= $true )
| ( ( in @ X1 @ X0 )
!= $true ) ) )
& ( ordinalTransSet1 = $true )
& ( ordinalTransSet = $true )
& ( ordinalMinLem1 = $true )
& ( setunionTransitive = $true )
& ( transitivesetOp2 = $true )
& ( binintTransitive = $true )
& ( transitivesetOp1 = $true )
& ( peanoSinj = $true )
& ( peano0notS = $true )
& ( omegaSclos = $true )
& ( omegaSp = $true )
& ( notinself2 = $true )
& ( notinself = $true )
& ( 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)],[f665]) ).
thf(f665,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 )
=> ( ( notinself = $true )
=> ( ( notinself2 = $true )
=> ( ( omegaSp = $true )
=> ( ( omegaSclos = $true )
=> ( ( peano0notS = $true )
=> ( ( peanoSinj = $true )
=> ( ( transitivesetOp1 = $true )
=> ( ( binintTransitive = $true )
=> ( ( transitivesetOp2 = $true )
=> ( ( setunionTransitive = $true )
=> ( ( ordinalMinLem1 = $true )
=> ( ( ordinalTransSet = $true )
=> ( ( ordinalTransSet1 = $true )
=> ! [X0: $i] :
( ! [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( ordinal @ X1 )
= $true ) )
=> ( ( transitiveset @ ( setunion @ X0 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f664]) ).
thf(f664,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
=> ( notinself
=> ( notinself2
=> ( omegaSp
=> ( omegaSclos
=> ( peano0notS
=> ( peanoSinj
=> ( transitivesetOp1
=> ( binintTransitive
=> ( transitivesetOp2
=> ( setunionTransitive
=> ( ordinalMinLem1
=> ( ordinalTransSet
=> ( ordinalTransSet1
=> ! [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( ordinal @ X1 ) )
=> ( transitiveset @ ( setunion @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f343]) ).
thf(f343,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
=> ( notinself
=> ( notinself2
=> ( omegaSp
=> ( omegaSclos
=> ( peano0notS
=> ( peanoSinj
=> ( transitivesetOp1
=> ( binintTransitive
=> ( transitivesetOp2
=> ( setunionTransitive
=> ( ordinalMinLem1
=> ( ordinalTransSet
=> ( ordinalTransSet1
=> ! [X11: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X11 )
=> ( ordinal @ X1 ) )
=> ( transitiveset @ ( setunion @ X11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f342]) ).
thf(f342,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
=> ( notinself
=> ( notinself2
=> ( omegaSp
=> ( omegaSclos
=> ( peano0notS
=> ( peanoSinj
=> ( transitivesetOp1
=> ( binintTransitive
=> ( transitivesetOp2
=> ( setunionTransitive
=> ( ordinalMinLem1
=> ( ordinalTransSet
=> ( ordinalTransSet1
=> ! [X11: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X11 )
=> ( ordinal @ X1 ) )
=> ( transitiveset @ ( setunion @ X11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.d0DxC7kphv/DTF2THF_20722.p',setunionOrdinalLem1) ).
thf(f15601,plain,
( ( ( transitiveset @ ( setunion @ sK70 ) )
= $true )
| ~ spl1111_498
| ~ spl1111_539
| ~ spl1111_1166
| ~ spl1111_1645
| ~ spl1111_1674 ),
inference(trivial_inequality_removal,[status(thm)],[f15597]) ).
thf(f15597,plain,
( ( $true != $true )
| ( ( transitiveset @ ( setunion @ sK70 ) )
= $true )
| ~ spl1111_498
| ~ spl1111_539
| ~ spl1111_1166
| ~ spl1111_1645
| ~ spl1111_1674 ),
inference(superposition,[status(thm)],[f10662,f15546]) ).
thf(f15546,plain,
( ( ( transitiveset @ ( sK81 @ sK70 ) )
= $true )
| ~ spl1111_498
| ~ spl1111_539
| ~ spl1111_1645
| ~ spl1111_1674 ),
inference(forward_demodulation,[status(thm)],[f15545,f14001]) ).
thf(f14001,plain,
( ! [X0: $i] :
( ( binintersect @ X0 @ X0 )
= X0 )
| ~ spl1111_498
| ~ spl1111_539 ),
inference(trivial_inequality_removal,[status(thm)],[f13984]) ).
thf(f13984,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( binintersect @ X0 @ X0 )
= X0 ) )
| ~ spl1111_498
| ~ spl1111_539 ),
inference(superposition,[status(thm)],[f7514,f7701]) ).
thf(f7701,plain,
( ! [X0: $i] :
( ( subset @ X0 @ X0 )
= $true )
| ~ spl1111_539 ),
inference(avatar_component_clause,[status(thm)],[f7700]) ).
thf(f7700,definition,
( spl1111_539
<=> ! [X0: $i] :
( ( subset @ X0 @ X0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1111_539])],[avatar_definition]) ).
thf(f7514,plain,
( ! [X2: $i,X3: $i] :
( ( ( subset @ X2 @ X3 )
!= $true )
| ( ( binintersect @ X3 @ X2 )
= X2 ) )
| ~ spl1111_498 ),
inference(avatar_component_clause,[status(thm)],[f7513]) ).
thf(f7513,definition,
( spl1111_498
<=> ! [X2: $i,X3: $i] :
( ( ( subset @ X2 @ X3 )
!= $true )
| ( ( binintersect @ X3 @ X2 )
= X2 ) ) ),
introduced(definition,[new_symbols(naming,[spl1111_498])],[avatar_definition]) ).
thf(f15545,plain,
( ( ( transitiveset @ ( binintersect @ ( sK81 @ sK70 ) @ ( sK81 @ sK70 ) ) )
= $true )
| ~ spl1111_1645
| ~ spl1111_1674 ),
inference(trivial_inequality_removal,[status(thm)],[f15536]) ).
thf(f15536,plain,
( ( ( transitiveset @ ( binintersect @ ( sK81 @ sK70 ) @ ( sK81 @ sK70 ) ) )
= $true )
| ( $true != $true )
| ~ spl1111_1645
| ~ spl1111_1674 ),
inference(superposition,[status(thm)],[f15214,f14351]) ).
thf(f14351,plain,
( ( ( ordinal @ ( sK81 @ sK70 ) )
= $true )
| ~ spl1111_1645 ),
inference(subsumption_resolution,[status(thm)],[f14347,f3476]) ).
thf(f14347,plain,
( ( ( ordinal @ ( sK81 @ sK70 ) )
= $true )
| ( ( transitiveset @ ( setunion @ sK70 ) )
= $true )
| ~ spl1111_1645 ),
inference(trivial_inequality_removal,[status(thm)],[f14345]) ).
thf(f14345,plain,
( ( $true != $true )
| ( ( ordinal @ ( sK81 @ sK70 ) )
= $true )
| ( ( transitiveset @ ( setunion @ sK70 ) )
= $true )
| ~ spl1111_1645 ),
inference(superposition,[status(thm)],[f3475,f13001]) ).
thf(f13001,plain,
( ! [X2: $i] :
( ( ( in @ ( sK81 @ X2 ) @ X2 )
= $true )
| ( ( transitiveset @ ( setunion @ X2 ) )
= $true ) )
| ~ spl1111_1645 ),
inference(avatar_component_clause,[status(thm)],[f13000]) ).
thf(f13000,definition,
( spl1111_1645
<=> ! [X2: $i] :
( ( ( transitiveset @ ( setunion @ X2 ) )
= $true )
| ( ( in @ ( sK81 @ X2 ) @ X2 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl1111_1645])],[avatar_definition]) ).
thf(f3475,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK70 )
!= $true )
| ( ( ordinal @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f1595]) ).
thf(f15214,plain,
( ! [X0: $i] :
( ( ( ordinal @ X0 )
!= $true )
| ( ( transitiveset @ ( binintersect @ X0 @ ( sK81 @ sK70 ) ) )
= $true ) )
| ~ spl1111_1645
| ~ spl1111_1674 ),
inference(trivial_inequality_removal,[status(thm)],[f15209]) ).
thf(f15209,plain,
( ! [X0: $i] :
( ( ( ordinal @ X0 )
!= $true )
| ( ( transitiveset @ ( binintersect @ X0 @ ( sK81 @ sK70 ) ) )
= $true )
| ( $true != $true ) )
| ~ spl1111_1645
| ~ spl1111_1674 ),
inference(superposition,[status(thm)],[f13145,f14351]) ).
thf(f13145,plain,
( ! [X0: $i,X1: $i] :
( ( ( ordinal @ X1 )
!= $true )
| ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( ordinal @ X0 )
!= $true ) )
| ~ spl1111_1674 ),
inference(avatar_component_clause,[status(thm)],[f13144]) ).
thf(f13144,definition,
( spl1111_1674
<=> ! [X0: $i,X1: $i] :
( ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( ordinal @ X1 )
!= $true )
| ( ( ordinal @ X0 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl1111_1674])],[avatar_definition]) ).
thf(f10662,plain,
( ! [X2: $i] :
( ( ( transitiveset @ ( sK81 @ X2 ) )
!= $true )
| ( ( transitiveset @ ( setunion @ X2 ) )
= $true ) )
| ~ spl1111_1166 ),
inference(avatar_component_clause,[status(thm)],[f10661]) ).
thf(f10661,definition,
( spl1111_1166
<=> ! [X2: $i] :
( ( ( transitiveset @ ( sK81 @ X2 ) )
!= $true )
| ( ( transitiveset @ ( setunion @ X2 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl1111_1166])],[avatar_definition]) ).
thf(f13589,plain,
spl1111_731,
inference(avatar_split_clause,[status(thm)],[f3560,f8574]) ).
thf(f8574,definition,
( spl1111_731
<=> ( setunionTransitive = $true ) ),
introduced(definition,[new_symbols(naming,[spl1111_731])],[avatar_definition]) ).
thf(f3560,plain,
setunionTransitive = $true,
inference(cnf_transformation,[status(thm)],[f1595]) ).
thf(f13569,plain,
spl1111_857,
inference(avatar_split_clause,[status(thm)],[f3499,f9170]) ).
thf(f9170,definition,
( spl1111_857
<=> ( eqimpsubset1 = $true ) ),
introduced(definition,[new_symbols(naming,[spl1111_857])],[avatar_definition]) ).
thf(f3499,plain,
eqimpsubset1 = $true,
inference(cnf_transformation,[status(thm)],[f1595]) ).
thf(f13146,plain,
( ~ spl1111_495
| spl1111_1674 ),
inference(avatar_split_clause,[status(thm)],[f3270,f13144,f7497]) ).
thf(f7497,definition,
( spl1111_495
<=> ( ordinalMinLem1 = $true ) ),
introduced(definition,[new_symbols(naming,[spl1111_495])],[avatar_definition]) ).
thf(f3270,plain,
! [X0: $i,X1: $i] :
( ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ordinalMinLem1 != $true )
| ( ( ordinal @ X0 )
!= $true )
| ( ( ordinal @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1575]) ).
thf(f1575,plain,
( ( ! [X0: $i] :
( ( ( ordinal @ X0 )
!= $true )
| ! [X1: $i] :
( ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( ordinal @ X1 )
!= $true ) ) )
| ( ordinalMinLem1 != $true ) )
& ( ( ordinalMinLem1 = $true )
| ( ( ( ordinal @ sK56 )
= $true )
& ( ( transitiveset @ ( binintersect @ sK56 @ sK57 ) )
!= $true )
& ( ( ordinal @ sK57 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK56,sK57])],[f1572,f1574,f1573]) ).
thf(f1573,plain,
( ? [X2: $i] :
( ( ( ordinal @ X2 )
= $true )
& ? [X3: $i] :
( ( ( transitiveset @ ( binintersect @ X2 @ X3 ) )
!= $true )
& ( ( ordinal @ X3 )
= $true ) ) )
=> ( ( ( ordinal @ sK56 )
= $true )
& ? [X3: $i] :
( ( ( transitiveset @ ( binintersect @ sK56 @ X3 ) )
!= $true )
& ( ( ordinal @ X3 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1574,plain,
( ? [X3: $i] :
( ( ( transitiveset @ ( binintersect @ sK56 @ X3 ) )
!= $true )
& ( ( ordinal @ X3 )
= $true ) )
=> ( ( ( transitiveset @ ( binintersect @ sK56 @ sK57 ) )
!= $true )
& ( ( ordinal @ sK57 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1572,plain,
( ( ! [X0: $i] :
( ( ( ordinal @ X0 )
!= $true )
| ! [X1: $i] :
( ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( ordinal @ X1 )
!= $true ) ) )
| ( ordinalMinLem1 != $true ) )
& ( ( ordinalMinLem1 = $true )
| ? [X2: $i] :
( ( ( ordinal @ X2 )
= $true )
& ? [X3: $i] :
( ( ( transitiveset @ ( binintersect @ X2 @ X3 ) )
!= $true )
& ( ( ordinal @ X3 )
= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f1571]) ).
thf(f1571,plain,
( ( ! [X0: $i] :
( ( ( ordinal @ X0 )
!= $true )
| ! [X1: $i] :
( ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( ordinal @ X1 )
!= $true ) ) )
| ( ordinalMinLem1 != $true ) )
& ( ( ordinalMinLem1 = $true )
| ? [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
& ? [X1: $i] :
( ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
!= $true )
& ( ( ordinal @ X1 )
= $true ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f1427]) ).
thf(f1427,plain,
( ! [X0: $i] :
( ( ( ordinal @ X0 )
!= $true )
| ! [X1: $i] :
( ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( ordinal @ X1 )
!= $true ) ) )
<=> ( ordinalMinLem1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f976]) ).
thf(f976,plain,
( ( ordinalMinLem1 = $true )
<=> ! [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
=> ! [X1: $i] :
( ( ( ordinal @ X1 )
= $true )
=> ( ( transitiveset @ ( binintersect @ X0 @ X1 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f975]) ).
thf(f975,plain,
( ordinalMinLem1
= ( ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i] :
( ( ordinal @ X1 )
=> ( transitiveset @ ( binintersect @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f339]) ).
thf(f339,axiom,
( ordinalMinLem1
= ( ! [X11: $i] :
( ( ordinal @ X11 )
=> ! [X16: $i] :
( ( ordinal @ X16 )
=> ( transitiveset @ ( binintersect @ X11 @ X16 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.d0DxC7kphv/DTF2THF_20722.p',ordinalMinLem1) ).
thf(f13137,plain,
( spl1111_539
| ~ spl1111_857 ),
inference(avatar_split_clause,[status(thm)],[f5102,f9170,f7700]) ).
thf(f5102,plain,
! [X1: $i] :
( ( eqimpsubset1 != $true )
| ( ( subset @ X1 @ X1 )
= $true ) ),
inference(equality_resolution,[status(thm)],[f4480]) ).
thf(f4480,plain,
! [X0: $i,X1: $i] :
( ( X0 != X1 )
| ( ( subset @ X1 @ X0 )
= $true )
| ( eqimpsubset1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f2548]) ).
thf(f2548,plain,
( ( ! [X0: $i,X1: $i] :
( ( X0 != X1 )
| ( ( subset @ X1 @ X0 )
= $true ) )
| ( eqimpsubset1 != $true ) )
& ( ( eqimpsubset1 = $true )
| ( ( sK667 = sK666 )
& ( ( subset @ sK667 @ sK666 )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK666,sK667])],[f2546,f2547]) ).
thf(f2547,plain,
( ? [X2: $i,X3: $i] :
( ( X2 = X3 )
& ( ( subset @ X3 @ X2 )
!= $true ) )
=> ( ( sK667 = sK666 )
& ( ( subset @ sK667 @ sK666 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2546,plain,
( ( ! [X0: $i,X1: $i] :
( ( X0 != X1 )
| ( ( subset @ X1 @ X0 )
= $true ) )
| ( eqimpsubset1 != $true ) )
& ( ( eqimpsubset1 = $true )
| ? [X2: $i,X3: $i] :
( ( X2 = X3 )
& ( ( subset @ X3 @ X2 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f2545]) ).
thf(f2545,plain,
( ( ! [X0: $i,X1: $i] :
( ( X0 != X1 )
| ( ( subset @ X1 @ X0 )
= $true ) )
| ( eqimpsubset1 != $true ) )
& ( ( eqimpsubset1 = $true )
| ? [X0: $i,X1: $i] :
( ( X0 = X1 )
& ( ( subset @ X1 @ X0 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f1358]) ).
thf(f1358,plain,
( ! [X0: $i,X1: $i] :
( ( X0 != X1 )
| ( ( subset @ X1 @ X0 )
= $true ) )
<=> ( eqimpsubset1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f370]) ).
thf(f370,plain,
( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( ( subset @ X1 @ X0 )
= $true ) )
<=> ( eqimpsubset1 = $true ) ),
inference(fool_elimination,[status(thm)],[f369]) ).
thf(f369,plain,
( eqimpsubset1
= ( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( subset @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f80]) ).
thf(f80,axiom,
( eqimpsubset1
= ( ! [X4: $i,X3: $i] :
( ( X3 = X4 )
=> ( subset @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.d0DxC7kphv/DTF2THF_20722.p',eqimpsubset1) ).
thf(f13002,plain,
( ~ spl1111_731
| spl1111_1645 ),
inference(avatar_split_clause,[status(thm)],[f3648,f13000,f8574]) ).
thf(f3648,plain,
! [X2: $i] :
( ( setunionTransitive != $true )
| ( ( transitiveset @ ( setunion @ X2 ) )
= $true )
| ( ( in @ ( sK81 @ X2 ) @ X2 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f1619]) ).
thf(f1619,plain,
( ( ( setunionTransitive = $true )
| ( ! [X1: $i] :
( ( ( transitiveset @ X1 )
= $true )
| ( ( in @ X1 @ sK80 )
!= $true ) )
& ( ( transitiveset @ ( setunion @ sK80 ) )
!= $true ) ) )
& ( ! [X2: $i] :
( ( ( ( transitiveset @ ( sK81 @ X2 ) )
!= $true )
& ( ( in @ ( sK81 @ X2 ) @ X2 )
= $true ) )
| ( ( transitiveset @ ( setunion @ X2 ) )
= $true ) )
| ( setunionTransitive != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK80,sK81])],[f1616,f1618,f1617]) ).
thf(f1617,plain,
( ? [X0: $i] :
( ! [X1: $i] :
( ( ( transitiveset @ X1 )
= $true )
| ( ( in @ X1 @ X0 )
!= $true ) )
& ( ( transitiveset @ ( setunion @ X0 ) )
!= $true ) )
=> ( ! [X1: $i] :
( ( ( transitiveset @ X1 )
= $true )
| ( ( in @ X1 @ sK80 )
!= $true ) )
& ( ( transitiveset @ ( setunion @ sK80 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1618,plain,
! [X2: $i] :
( ? [X3: $i] :
( ( ( transitiveset @ X3 )
!= $true )
& ( ( in @ X3 @ X2 )
= $true ) )
=> ( ( ( transitiveset @ ( sK81 @ X2 ) )
!= $true )
& ( ( in @ ( sK81 @ X2 ) @ X2 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1616,plain,
( ( ( setunionTransitive = $true )
| ? [X0: $i] :
( ! [X1: $i] :
( ( ( transitiveset @ X1 )
= $true )
| ( ( in @ X1 @ X0 )
!= $true ) )
& ( ( transitiveset @ ( setunion @ X0 ) )
!= $true ) ) )
& ( ! [X2: $i] :
( ? [X3: $i] :
( ( ( transitiveset @ X3 )
!= $true )
& ( ( in @ X3 @ X2 )
= $true ) )
| ( ( transitiveset @ ( setunion @ X2 ) )
= $true ) )
| ( setunionTransitive != $true ) ) ),
inference(rectify,[status(thm)],[f1615]) ).
thf(f1615,plain,
( ( ( setunionTransitive = $true )
| ? [X0: $i] :
( ! [X1: $i] :
( ( ( transitiveset @ X1 )
= $true )
| ( ( in @ X1 @ X0 )
!= $true ) )
& ( ( transitiveset @ ( setunion @ X0 ) )
!= $true ) ) )
& ( ! [X0: $i] :
( ? [X1: $i] :
( ( ( transitiveset @ X1 )
!= $true )
& ( ( in @ X1 @ X0 )
= $true ) )
| ( ( transitiveset @ ( setunion @ X0 ) )
= $true ) )
| ( setunionTransitive != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f1262]) ).
thf(f1262,plain,
( ( setunionTransitive = $true )
<=> ! [X0: $i] :
( ? [X1: $i] :
( ( ( transitiveset @ X1 )
!= $true )
& ( ( in @ X1 @ X0 )
= $true ) )
| ( ( transitiveset @ ( setunion @ X0 ) )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f627]) ).
thf(f627,plain,
( ! [X0: $i] :
( ! [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( transitiveset @ X1 )
= $true ) )
=> ( ( transitiveset @ ( setunion @ X0 ) )
= $true ) )
<=> ( setunionTransitive = $true ) ),
inference(fool_elimination,[status(thm)],[f626]) ).
thf(f626,plain,
! [X0: $i] :
( ( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( transitiveset @ X1 ) )
=> ( transitiveset @ ( setunion @ X0 ) ) )
= setunionTransitive ),
inference(rectify,[status(thm)],[f335]) ).
thf(f335,axiom,
! [X11: $i] :
( ( ! [X1: $i] :
( ( in @ X1 @ X11 )
=> ( transitiveset @ X1 ) )
=> ( transitiveset @ ( setunion @ X11 ) ) )
= setunionTransitive ),
file('/export/starexec/sandbox/tmp/tmp.d0DxC7kphv/DTF2THF_20722.p',setunionTransitive) ).
thf(f12688,plain,
spl1111_495,
inference(avatar_split_clause,[status(thm)],[f3362,f7497]) ).
thf(f3362,plain,
ordinalMinLem1 = $true,
inference(cnf_transformation,[status(thm)],[f1595]) ).
thf(f11507,plain,
spl1111_499,
inference(avatar_split_clause,[status(thm)],[f3314,f7516]) ).
thf(f7516,definition,
( spl1111_499
<=> ( binintersectSubset4 = $true ) ),
introduced(definition,[new_symbols(naming,[spl1111_499])],[avatar_definition]) ).
thf(f3314,plain,
binintersectSubset4 = $true,
inference(cnf_transformation,[status(thm)],[f1595]) ).
thf(f10663,plain,
( spl1111_1166
| ~ spl1111_731 ),
inference(avatar_split_clause,[status(thm)],[f3649,f8574,f10661]) ).
thf(f3649,plain,
! [X2: $i] :
( ( setunionTransitive != $true )
| ( ( transitiveset @ ( sK81 @ X2 ) )
!= $true )
| ( ( transitiveset @ ( setunion @ X2 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f1619]) ).
thf(f7519,plain,
( spl1111_498
| ~ spl1111_499 ),
inference(avatar_split_clause,[status(thm)],[f4735,f7516,f7513]) ).
thf(f4735,plain,
! [X2: $i,X3: $i] :
( ( binintersectSubset4 != $true )
| ( ( subset @ X2 @ X3 )
!= $true )
| ( ( binintersect @ X3 @ X2 )
= X2 ) ),
inference(cnf_transformation,[status(thm)],[f2844]) ).
thf(f2844,plain,
( ( ( binintersectSubset4 = $true )
| ( ( ( binintersect @ sK864 @ sK863 )
!= sK863 )
& ( ( subset @ sK863 @ sK864 )
= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( binintersect @ X3 @ X2 )
= X2 )
| ( ( subset @ X2 @ X3 )
!= $true ) )
| ( binintersectSubset4 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK863,sK864])],[f2842,f2843]) ).
thf(f2843,plain,
( ? [X0: $i,X1: $i] :
( ( ( binintersect @ X1 @ X0 )
!= X0 )
& ( ( subset @ X0 @ X1 )
= $true ) )
=> ( ( ( binintersect @ sK864 @ sK863 )
!= sK863 )
& ( ( subset @ sK863 @ sK864 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2842,plain,
( ( ( binintersectSubset4 = $true )
| ? [X0: $i,X1: $i] :
( ( ( binintersect @ X1 @ X0 )
!= X0 )
& ( ( subset @ X0 @ X1 )
= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( binintersect @ X3 @ X2 )
= X2 )
| ( ( subset @ X2 @ X3 )
!= $true ) )
| ( binintersectSubset4 != $true ) ) ),
inference(rectify,[status(thm)],[f2841]) ).
thf(f2841,plain,
( ( ( binintersectSubset4 = $true )
| ? [X0: $i,X1: $i] :
( ( ( binintersect @ X1 @ X0 )
!= X0 )
& ( ( subset @ X0 @ X1 )
= $true ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( binintersect @ X1 @ X0 )
= X0 )
| ( ( subset @ X0 @ X1 )
!= $true ) )
| ( binintersectSubset4 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f1279]) ).
thf(f1279,plain,
( ( binintersectSubset4 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( binintersect @ X1 @ X0 )
= X0 )
| ( ( subset @ X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f557]) ).
thf(f557,plain,
( ( binintersectSubset4 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
=> ( ( binintersect @ X1 @ X0 )
= X0 ) ) ),
inference(fool_elimination,[status(thm)],[f556]) ).
thf(f556,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( binintersect @ X1 @ X0 )
= X0 ) )
= binintersectSubset4 ),
inference(rectify,[status(thm)],[f117]) ).
thf(f117,axiom,
! [X4: $i,X3: $i] :
( ( ( subset @ X4 @ X3 )
=> ( ( binintersect @ X3 @ X4 )
= X4 ) )
= binintersectSubset4 ),
file('/export/starexec/sandbox/tmp/tmp.d0DxC7kphv/DTF2THF_20722.p',binintersectSubset4) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU819^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n020.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:35:12 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEU819^1 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.46 % Domain : Set Theory
% 0.30/0.46 % Problem : Ordinals
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English : (! X:i.(! x:i.in x X -> ordinal x) -> transitiveset (setunion X))
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.46 % Source : [Bro08]
% 0.30/0.46 % Names : ZFC321g [Bro08]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.27 v7.5.0, 0.43 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.80 v6.2.0, 0.57 v5.5.0, 0.67 v5.4.0, 0.80 v5.2.0, 1.00 v3.7.0
% 0.30/0.46 % Syntax : Number of formulae : 740 ( 341 unt; 398 typ; 341 def)
% 0.30/0.46 % Number of atoms : 2107 ( 488 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 338 ( 6 avg)
% 0.30/0.46 % Number of connectives : 4557 ( 78 ~; 17 |; 60 &;3303 @)
% 0.30/0.46 % ( 17 <=>;1082 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 342 ( 2 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 194 ( 194 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 401 ( 398 usr; 339 con; 0-4 aty)
% 0.30/0.46 % Number of variables : 1183 ( 79 ^;1059 !; 45 ?;1183 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : http://mathgate.info/detsetitem.php?id=515
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(in_type,type,
% 0.30/0.46 in: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(exu_type,type,
% 0.30/0.46 exu: ( $i > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(exu,definition,
% 0.30/0.46 ( exu
% 0.30/0.46 = ( ^ [Xphi: $i > $o] :
% 0.30/0.46 ? [Xx: $i] :
% 0.30/0.46 ( ( Xphi @ Xx )
% 0.30/0.46 & ! [Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setextAx_type,type,
% 0.30/0.46 setextAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setextAx,definition,
% 0.30/0.46 ( setextAx
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 <=> ( in @ Xx @ B ) )
% 0.30/0.46 => ( A = B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyset_type,type,
% 0.30/0.46 emptyset: $i ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetAx_type,type,
% 0.30/0.46 emptysetAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetAx,definition,
% 0.30/0.46 ( emptysetAx
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoin_type,type,
% 0.30/0.46 setadjoin: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinAx_type,type,
% 0.30/0.46 setadjoinAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinAx,definition,
% 0.30/0.46 ( setadjoinAx
% 0.30/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/0.46 <=> ( ( Xy = Xx )
% 0.30/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(powerset_type,type,
% 0.30/0.46 powerset: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(powersetAx_type,type,
% 0.30/0.46 powersetAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(powersetAx,definition,
% 0.30/0.46 ( powersetAx
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.30/0.46 <=> ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setunion_type,type,
% 0.30/0.46 setunion: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(setunionAx_type,type,
% 0.30/0.46 setunionAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setunionAx,definition,
% 0.30/0.46 ( setunionAx
% 0.30/0.46 = ( ! [A: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.30/0.46 <=> ? [B: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(omega_type,type,
% 0.30/0.46 omega: $i ).
% 0.30/0.46
% 0.30/0.46 thf(omega0Ax_type,type,
% 0.30/0.46 omega0Ax: $o ).
% 0.30/0.46
% 0.30/0.46 thf(omega0Ax,definition,
% 0.30/0.46 ( omega0Ax
% 0.30/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(omegaSAx_type,type,
% 0.30/0.46 omegaSAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(omegaSAx,definition,
% 0.30/0.46 ( omegaSAx
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ omega )
% 0.30/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(omegaIndAx_type,type,
% 0.30/0.46 omegaIndAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(omegaIndAx,definition,
% 0.30/0.46 ( omegaIndAx
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ( ( in @ emptyset @ A )
% 0.30/0.46 & ! [Xx: $i] :
% 0.30/0.46 ( ( ( in @ Xx @ omega )
% 0.30/0.46 & ( in @ Xx @ A ) )
% 0.30/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ omega )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(replAx_type,type,
% 0.30/0.46 replAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(replAx,definition,
% 0.30/0.46 ( replAx
% 0.30/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( exu
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.30/0.46 => ? [B: $i] :
% 0.30/0.46 ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 <=> ? [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ A )
% 0.30/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(foundationAx_type,type,
% 0.30/0.46 foundationAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(foundationAx,definition,
% 0.30/0.46 ( foundationAx
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.30/0.46 => ? [B: $i] :
% 0.30/0.46 ( ( in @ B @ A )
% 0.30/0.46 & ~ ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(wellorderingAx_type,type,
% 0.30/0.46 wellorderingAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(wellorderingAx,definition,
% 0.30/0.46 ( wellorderingAx
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ? [B: $i] :
% 0.30/0.46 ( ! [C: $i] :
% 0.30/0.46 ( ( in @ C @ B )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ C )
% 0.30/0.46 => ( in @ Xx @ A ) ) )
% 0.30/0.46 & ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( ( in @ Xx @ A )
% 0.30/0.46 & ( in @ Xy @ A ) )
% 0.30/0.46 => ( ! [C: $i] :
% 0.30/0.46 ( ( in @ C @ B )
% 0.30/0.46 => ( ( in @ Xx @ C )
% 0.30/0.46 <=> ( in @ Xy @ C ) ) )
% 0.30/0.46 => ( Xx = Xy ) ) )
% 0.30/0.46 & ! [C: $i,D: $i] :
% 0.30/0.46 ( ( ( in @ C @ B )
% 0.30/0.46 & ( in @ D @ B ) )
% 0.30/0.46 => ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ C )
% 0.30/0.46 => ( in @ Xx @ D ) )
% 0.30/0.46 | ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ D )
% 0.30/0.46 => ( in @ Xx @ C ) ) ) )
% 0.30/0.46 & ! [C: $i] :
% 0.30/0.46 ( ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ C )
% 0.30/0.46 => ( in @ Xx @ A ) )
% 0.30/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.30/0.46 => ? [D: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ D @ B )
% 0.30/0.46 & ( in @ Xx @ C )
% 0.30/0.46 & ~ ? [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ D )
% 0.30/0.46 & ( in @ Xy @ C ) )
% 0.30/0.46 & ! [E: $i] :
% 0.30/0.46 ( ( in @ E @ B )
% 0.30/0.46 => ( ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ E )
% 0.30/0.46 => ( in @ Xy @ D ) )
% 0.30/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(descr_type,type,
% 0.30/0.46 descr: ( $i > $o ) > $i ).
% 0.30/0.46
% 0.30/0.46 thf(descrp_type,type,
% 0.30/0.46 descrp: $o ).
% 0.30/0.46
% 0.30/0.46 thf(descrp,definition,
% 0.30/0.46 ( descrp
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ( Xphi
% 0.30/0.46 @ ( descr
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstr_type,type,
% 0.30/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrI_type,type,
% 0.30/0.46 dsetconstrI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrI,definition,
% 0.30/0.46 ( dsetconstrI
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( Xphi @ Xx )
% 0.30/0.46 => ( in @ Xx
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrEL_type,type,
% 0.30/0.46 dsetconstrEL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrEL,definition,
% 0.30/0.46 ( dsetconstrEL
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrER_type,type,
% 0.30/0.46 dsetconstrER: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrER,definition,
% 0.30/0.46 ( dsetconstrER
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuE1_type,type,
% 0.30/0.46 exuE1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuE1,definition,
% 0.30/0.46 ( exuE1
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ? [Xx: $i] :
% 0.30/0.46 ( ( Xphi @ Xx )
% 0.30/0.46 & ! [Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(prop2set_type,type,
% 0.30/0.46 prop2set: $o > $i ).
% 0.30/0.46
% 0.30/0.46 thf(prop2setE_type,type,
% 0.30/0.46 prop2setE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(prop2setE,definition,
% 0.30/0.46 ( prop2setE
% 0.30/0.46 = ( ! [Xphi: $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.30/0.46 => Xphi ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetE_type,type,
% 0.30/0.46 emptysetE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetE,definition,
% 0.30/0.46 ( emptysetE
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ emptyset )
% 0.30/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetimpfalse_type,type,
% 0.30/0.46 emptysetimpfalse: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetimpfalse,definition,
% 0.30/0.46 ( emptysetimpfalse
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ emptyset )
% 0.30/0.46 => $false ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(notinemptyset_type,type,
% 0.30/0.46 notinemptyset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(notinemptyset,definition,
% 0.30/0.46 ( notinemptyset
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuE3e_type,type,
% 0.30/0.46 exuE3e: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuE3e,definition,
% 0.30/0.46 ( exuE3e
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setext_type,type,
% 0.30/0.46 setext: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setext,definition,
% 0.30/0.46 ( setext
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ B ) )
% 0.30/0.46 => ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ A ) )
% 0.30/0.46 => ( A = B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyI_type,type,
% 0.30/0.46 emptyI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyI,definition,
% 0.30/0.46 ( emptyI
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ~ ( in @ Xx @ A )
% 0.30/0.46 => ( A = emptyset ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(noeltsimpempty_type,type,
% 0.30/0.46 noeltsimpempty: $o ).
% 0.30/0.46
% 0.30/0.46 thf(noeltsimpempty,definition,
% 0.30/0.46 ( noeltsimpempty
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ~ ( in @ Xx @ A )
% 0.30/0.46 => ( A = emptyset ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setbeta_type,type,
% 0.30/0.46 setbeta: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setbeta,definition,
% 0.30/0.46 ( setbeta
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( in @ Xx
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(nonempty_type,type,
% 0.30/0.46 nonempty: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(nonempty,definition,
% 0.30/0.46 ( nonempty
% 0.30/0.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyE1_type,type,
% 0.30/0.46 nonemptyE1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyE1,definition,
% 0.30/0.46 ( nonemptyE1
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ( nonempty @ A )
% 0.30/0.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyI_type,type,
% 0.30/0.46 nonemptyI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyI,definition,
% 0.30/0.46 ( nonemptyI
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( Xphi @ Xx )
% 0.30/0.46 => ( nonempty
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyI1_type,type,
% 0.30/0.46 nonemptyI1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyI1,definition,
% 0.30/0.46 ( nonemptyI1
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.30/0.46 => ( nonempty @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinIL_type,type,
% 0.30/0.46 setadjoinIL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinIL,definition,
% 0.30/0.46 ( setadjoinIL
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyinunitempty_type,type,
% 0.30/0.46 emptyinunitempty: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyinunitempty,definition,
% 0.30/0.46 ( emptyinunitempty
% 0.30/0.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinIR_type,type,
% 0.30/0.46 setadjoinIR: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinIR,definition,
% 0.30/0.46 ( setadjoinIR
% 0.30/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ A )
% 0.30/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinE_type,type,
% 0.30/0.46 setadjoinE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinE,definition,
% 0.30/0.46 ( setadjoinE
% 0.30/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/0.46 => ! [Xphi: $o] :
% 0.30/0.46 ( ( ( Xy = Xx )
% 0.30/0.46 => Xphi )
% 0.30/0.46 => ( ( ( in @ Xy @ A )
% 0.30/0.46 => Xphi )
% 0.30/0.46 => Xphi ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinOr_type,type,
% 0.30/0.46 setadjoinOr: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinOr,definition,
% 0.30/0.46 ( setadjoinOr
% 0.30/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/0.46 => ( ( Xy = Xx )
% 0.30/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setoftrueEq_type,type,
% 0.30/0.46 setoftrueEq: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setoftrueEq,definition,
% 0.30/0.46 ( setoftrueEq
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xx: $i] : $true )
% 0.30/0.46 = A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(powersetI_type,type,
% 0.30/0.46 powersetI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(powersetI,definition,
% 0.30/0.46 ( powersetI
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ A ) )
% 0.30/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyinPowerset_type,type,
% 0.30/0.46 emptyinPowerset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyinPowerset,definition,
% 0.30/0.46 ( emptyinPowerset
% 0.30/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyInPowerset_type,type,
% 0.30/0.46 emptyInPowerset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyInPowerset,definition,
% 0.30/0.46 ( emptyInPowerset
% 0.30/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(powersetE_type,type,
% 0.30/0.46 powersetE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(powersetE,definition,
% 0.30/0.46 ( powersetE
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.30/0.46 => ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setunionI_type,type,
% 0.30/0.46 setunionI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setunionI,definition,
% 0.30/0.46 ( setunionI
% 0.30/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ( ( in @ B @ A )
% 0.30/0.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setunionE_type,type,
% 0.30/0.46 setunionE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setunionE,definition,
% 0.30/0.46 ( setunionE
% 0.30/0.46 = ( ! [A: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.30/0.46 => ! [Xphi: $o] :
% 0.30/0.46 ( ! [B: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ( ( in @ B @ A )
% 0.30/0.46 => Xphi ) )
% 0.30/0.46 => Xphi ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subPowSU_type,type,
% 0.30/0.46 subPowSU: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subPowSU,definition,
% 0.30/0.46 ( subPowSU
% 0.30/0.46 = ( ! [A: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuE2_type,type,
% 0.30/0.46 exuE2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuE2,definition,
% 0.30/0.46 ( exuE2
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ? [Xx: $i] :
% 0.30/0.46 ! [Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xy )
% 0.30/0.46 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyImpWitness_type,type,
% 0.30/0.46 nonemptyImpWitness: $o ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyImpWitness,definition,
% 0.30/0.46 ( nonemptyImpWitness
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ( nonempty @ A )
% 0.30/0.46 => ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & $true ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(uniqinunit_type,type,
% 0.30/0.46 uniqinunit: $o ).
% 0.30/0.46
% 0.30/0.46 thf(uniqinunit,definition,
% 0.30/0.46 ( uniqinunit
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(notinsingleton_type,type,
% 0.30/0.46 notinsingleton: $o ).
% 0.30/0.46
% 0.30/0.46 thf(notinsingleton,definition,
% 0.30/0.46 ( notinsingleton
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx != Xy )
% 0.30/0.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(eqinunit_type,type,
% 0.30/0.46 eqinunit: $o ).
% 0.30/0.46
% 0.30/0.46 thf(eqinunit,definition,
% 0.30/0.46 ( eqinunit
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx = Xy )
% 0.30/0.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(singletonsswitch_type,type,
% 0.30/0.46 singletonsswitch: $o ).
% 0.30/0.46
% 0.30/0.46 thf(singletonsswitch,definition,
% 0.30/0.46 ( singletonsswitch
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.30/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(upairsetE_type,type,
% 0.30/0.46 upairsetE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(upairsetE,definition,
% 0.30/0.46 ( upairsetE
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.30/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.30/0.46 => ( ( Xz = Xx )
% 0.30/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(upairsetIL_type,type,
% 0.30/0.46 upairsetIL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(upairsetIL,definition,
% 0.30/0.46 ( upairsetIL
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(upairsetIR_type,type,
% 0.30/0.46 upairsetIR: $o ).
% 0.30/0.46
% 0.30/0.46 thf(upairsetIR,definition,
% 0.30/0.46 ( upairsetIR
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyE1_type,type,
% 0.30/0.46 emptyE1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyE1,definition,
% 0.30/0.46 ( emptyE1
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ( Xphi @ Xx ) )
% 0.30/0.46 => ( ( ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 = emptyset )
% 0.30/0.46 => $false ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(vacuousDall_type,type,
% 0.30/0.46 vacuousDall: $o ).
% 0.30/0.46
% 0.30/0.46 thf(vacuousDall,definition,
% 0.30/0.46 ( vacuousDall
% 0.30/0.46 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ emptyset )
% 0.30/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan1_type,type,
% 0.30/0.46 quantDeMorgan1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan1,definition,
% 0.30/0.46 ( quantDeMorgan1
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ~ ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( Xphi @ Xx ) )
% 0.30/0.46 => ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan2_type,type,
% 0.30/0.46 quantDeMorgan2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan2,definition,
% 0.30/0.46 ( quantDeMorgan2
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ~ ( Xphi @ Xx ) )
% 0.30/0.46 => ~ ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan3_type,type,
% 0.30/0.46 quantDeMorgan3: $o ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan3,definition,
% 0.30/0.46 ( quantDeMorgan3
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ~ ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ( Xphi @ Xx ) )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan4_type,type,
% 0.30/0.46 quantDeMorgan4: $o ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan4,definition,
% 0.30/0.46 ( quantDeMorgan4
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ~ ( Xphi @ Xx ) )
% 0.30/0.46 => ~ ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(prop2setI_type,type,
% 0.30/0.46 prop2setI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(prop2setI,definition,
% 0.30/0.46 ( prop2setI
% 0.30/0.46 = ( ! [Xphi: $o] :
% 0.30/0.46 ( Xphi
% 0.30/0.46 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(set2prop_type,type,
% 0.30/0.46 set2prop: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(prop2set2propI_type,type,
% 0.30/0.46 prop2set2propI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(prop2set2propI,definition,
% 0.30/0.46 ( prop2set2propI
% 0.30/0.46 = ( ! [Xphi: $o] :
% 0.30/0.46 ( Xphi
% 0.30/0.46 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(notdexE_type,type,
% 0.30/0.46 notdexE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(notdexE,definition,
% 0.30/0.46 ( notdexE
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ~ ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ( Xphi @ Xx ) )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(notdallE_type,type,
% 0.30/0.46 notdallE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(notdallE,definition,
% 0.30/0.46 ( notdallE
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ~ ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( Xphi @ Xx ) )
% 0.30/0.46 => ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuI1_type,type,
% 0.30/0.46 exuI1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuI1,definition,
% 0.30/0.46 ( exuI1
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ? [Xx: $i] :
% 0.30/0.46 ( ( Xphi @ Xx )
% 0.30/0.46 & ! [Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) )
% 0.30/0.46 => ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuI3_type,type,
% 0.30/0.46 exuI3: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuI3,definition,
% 0.30/0.46 ( exuI3
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.30/0.46 => ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xx )
% 0.30/0.46 => ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) )
% 0.30/0.46 => ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuI2_type,type,
% 0.30/0.46 exuI2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuI2,definition,
% 0.30/0.46 ( exuI2
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ? [Xx: $i] :
% 0.30/0.46 ! [Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xy )
% 0.30/0.46 <=> ( Xy = Xx ) )
% 0.30/0.46 => ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(inCongP_type,type,
% 0.30/0.46 inCongP: $o ).
% 0.30/0.46
% 0.30/0.46 thf(inCongP,definition,
% 0.30/0.46 ( inCongP
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx = Xy )
% 0.30/0.46 => ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(in__Cong_type,type,
% 0.30/0.46 in__Cong: $o ).
% 0.30/0.46
% 0.30/0.46 thf(in__Cong,definition,
% 0.30/0.46 ( in__Cong
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx = Xy )
% 0.30/0.46 => ( ( in @ Xx @ A )
% 0.30/0.46 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuE3u_type,type,
% 0.30/0.46 exuE3u: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuE3u,definition,
% 0.30/0.46 ( exuE3u
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xx )
% 0.30/0.46 => ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exu__Cong_type,type,
% 0.30/0.46 exu__Cong: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exu__Cong,definition,
% 0.30/0.46 ( exu__Cong
% 0.30/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.30/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx = Xy )
% 0.30/0.46 => ( ( Xphi @ Xx )
% 0.30/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.30/0.46 => ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 <=> ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyset__Cong_type,type,
% 0.30/0.46 emptyset__Cong: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyset__Cong,definition,
% 0.30/0.46 ( emptyset__Cong
% 0.30/0.46 = ( emptyset = emptyset ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoin__Cong_type,type,
% 0.30/0.46 setadjoin__Cong: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoin__Cong,definition,
% 0.30/0.46 ( setadjoin__Cong
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx = Xy )
% 0.30/0.46 => ! [Xz: $i,Xu: $i] :
% 0.30/0.46 ( ( Xz = Xu )
% 0.30/0.46 => ( ( setadjoin @ Xx @ Xz )
% 0.30/0.46 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(powerset__Cong_type,type,
% 0.30/0.46 powerset__Cong: $o ).
% 0.30/0.46
% 0.30/0.46 thf(powerset__Cong,definition,
% 0.30/0.46 ( powerset__Cong
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ( ( powerset @ A )
% 0.30/0.46 = ( powerset @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setunion__Cong_type,type,
% 0.30/0.46 setunion__Cong: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setunion__Cong,definition,
% 0.30/0.46 ( setunion__Cong
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ( ( setunion @ A )
% 0.30/0.46 = ( setunion @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(omega__Cong_type,type,
% 0.30/0.46 omega__Cong: $o ).
% 0.30/0.46
% 0.30/0.46 thf(omega__Cong,definition,
% 0.30/0.46 ( omega__Cong
% 0.30/0.46 = ( omega = omega ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuEu_type,type,
% 0.30/0.46 exuEu: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuEu,definition,
% 0.30/0.46 ( exuEu
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xx )
% 0.30/0.46 => ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(descr__Cong_type,type,
% 0.30/0.46 descr__Cong: $o ).
% 0.30/0.46
% 0.30/0.46 thf(descr__Cong,definition,
% 0.30/0.46 ( descr__Cong
% 0.30/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.30/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx = Xy )
% 0.30/0.46 => ( ( Xphi @ Xx )
% 0.30/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.30/0.46 => ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.30/0.46 => ( ( descr
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 = ( descr
% 0.30/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstr__Cong_type,type,
% 0.30/0.46 dsetconstr__Cong: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstr__Cong,definition,
% 0.30/0.46 ( dsetconstr__Cong
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( ( Xx = Xy )
% 0.30/0.46 => ( ( Xphi @ Xx )
% 0.30/0.46 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.30/0.46 => ( ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 = ( dsetconstr @ B
% 0.30/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subset_type,type,
% 0.30/0.46 subset: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(disjoint_type,type,
% 0.30/0.46 disjoint: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(setsmeet_type,type,
% 0.30/0.46 setsmeet: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetI1_type,type,
% 0.30/0.46 subsetI1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetI1,definition,
% 0.30/0.46 ( subsetI1
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ B ) )
% 0.30/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(eqimpsubset2_type,type,
% 0.30/0.46 eqimpsubset2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(eqimpsubset2,definition,
% 0.30/0.46 ( eqimpsubset2
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(eqimpsubset1_type,type,
% 0.30/0.46 eqimpsubset1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(eqimpsubset1,definition,
% 0.30/0.46 ( eqimpsubset1
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subsetI2_type,type,
% 0.30/0.46 subsetI2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetI2,definition,
% 0.30/0.46 ( subsetI2
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ B ) )
% 0.30/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetsubset_type,type,
% 0.30/0.46 emptysetsubset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetsubset,definition,
% 0.30/0.46 ( emptysetsubset
% 0.30/0.46 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subsetE_type,type,
% 0.30/0.46 subsetE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetE,definition,
% 0.30/0.46 ( subsetE
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subsetE2_type,type,
% 0.30/0.46 subsetE2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetE2,definition,
% 0.30/0.46 ( subsetE2
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( ~ ( in @ Xx @ B )
% 0.30/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(notsubsetI_type,type,
% 0.30/0.46 notsubsetI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(notsubsetI,definition,
% 0.30/0.46 ( notsubsetI
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ~ ( in @ Xx @ B )
% 0.30/0.46 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(notequalI1_type,type,
% 0.30/0.46 notequalI1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(notequalI1,definition,
% 0.30/0.46 ( notequalI1
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ~ ( subset @ A @ B )
% 0.30/0.46 => ( A != B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(notequalI2_type,type,
% 0.30/0.46 notequalI2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(notequalI2,definition,
% 0.30/0.46 ( notequalI2
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ~ ( in @ Xx @ B )
% 0.30/0.46 => ( A != B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subsetRefl_type,type,
% 0.30/0.46 subsetRefl: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetRefl,definition,
% 0.30/0.46 ( subsetRefl
% 0.30/0.46 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subsetTrans_type,type,
% 0.30/0.46 subsetTrans: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetTrans,definition,
% 0.30/0.46 ( subsetTrans
% 0.30/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( ( subset @ B @ C )
% 0.30/0.46 => ( subset @ A @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinSub_type,type,
% 0.30/0.46 setadjoinSub: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinSub,definition,
% 0.30/0.46 ( setadjoinSub
% 0.30/0.46 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinSub2_type,type,
% 0.30/0.46 setadjoinSub2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinSub2,definition,
% 0.30/0.46 ( setadjoinSub2
% 0.30/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subset2powerset_type,type,
% 0.30/0.46 subset2powerset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subset2powerset,definition,
% 0.30/0.46 ( subset2powerset
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setextsub_type,type,
% 0.30/0.46 setextsub: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setextsub,definition,
% 0.30/0.46 ( setextsub
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( ( subset @ B @ A )
% 0.30/0.46 => ( A = B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subsetemptysetimpeq_type,type,
% 0.30/0.46 subsetemptysetimpeq: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetemptysetimpeq,definition,
% 0.30/0.46 ( subsetemptysetimpeq
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ( subset @ A @ emptyset )
% 0.30/0.46 => ( A = emptyset ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(powersetI1_type,type,
% 0.30/0.46 powersetI1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(powersetI1,definition,
% 0.30/0.46 ( powersetI1
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( subset @ B @ A )
% 0.30/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(powersetE1_type,type,
% 0.30/0.46 powersetE1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(powersetE1,definition,
% 0.30/0.46 ( powersetE1
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.30/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(inPowerset_type,type,
% 0.30/0.46 inPowerset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(inPowerset,definition,
% 0.30/0.46 ( inPowerset
% 0.30/0.46 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(powersetsubset_type,type,
% 0.30/0.46 powersetsubset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(powersetsubset,definition,
% 0.30/0.46 ( powersetsubset
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sepInPowerset_type,type,
% 0.30/0.46 sepInPowerset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(sepInPowerset,definition,
% 0.30/0.46 ( sepInPowerset
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( in
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 @ ( powerset @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sepSubset_type,type,
% 0.30/0.46 sepSubset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(sepSubset,definition,
% 0.30/0.46 ( sepSubset
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( subset
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binunion_type,type,
% 0.30/0.46 binunion: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(binunionIL_type,type,
% 0.30/0.46 binunionIL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binunionIL,definition,
% 0.30/0.46 ( binunionIL
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(upairset2IR_type,type,
% 0.30/0.46 upairset2IR: $o ).
% 0.30/0.46
% 0.30/0.46 thf(upairset2IR,definition,
% 0.30/0.46 ( upairset2IR
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binunionIR_type,type,
% 0.30/0.46 binunionIR: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binunionIR,definition,
% 0.30/0.46 ( binunionIR
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binunionEcases_type,type,
% 0.30/0.46 binunionEcases: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binunionEcases,definition,
% 0.30/0.46 ( binunionEcases
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.30/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.30/0.46 => ( ( ( in @ Xx @ A )
% 0.30/0.46 => Xphi )
% 0.30/0.46 => ( ( ( in @ Xx @ B )
% 0.30/0.46 => Xphi )
% 0.30/0.46 => Xphi ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binunionE_type,type,
% 0.30/0.46 binunionE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binunionE,definition,
% 0.30/0.46 ( binunionE
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.30/0.46 => ( ( in @ Xx @ A )
% 0.30/0.46 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binunionLsub_type,type,
% 0.30/0.46 binunionLsub: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binunionLsub,definition,
% 0.30/0.46 ( binunionLsub
% 0.30/0.46 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binunionRsub_type,type,
% 0.30/0.46 binunionRsub: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binunionRsub,definition,
% 0.30/0.46 ( binunionRsub
% 0.30/0.46 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersect_type,type,
% 0.30/0.46 binintersect: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectI_type,type,
% 0.30/0.46 binintersectI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectI,definition,
% 0.30/0.46 ( binintersectI
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset5_type,type,
% 0.30/0.46 binintersectSubset5: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset5,definition,
% 0.30/0.46 ( binintersectSubset5
% 0.30/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.30/0.46 ( ( subset @ C @ A )
% 0.30/0.46 => ( ( subset @ C @ B )
% 0.30/0.46 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectEL_type,type,
% 0.30/0.46 binintersectEL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectEL,definition,
% 0.30/0.46 ( binintersectEL
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectLsub_type,type,
% 0.30/0.46 binintersectLsub: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectLsub,definition,
% 0.30/0.46 ( binintersectLsub
% 0.30/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset2_type,type,
% 0.30/0.46 binintersectSubset2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset2,definition,
% 0.30/0.46 ( binintersectSubset2
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( ( binintersect @ A @ B )
% 0.30/0.46 = A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset3_type,type,
% 0.30/0.46 binintersectSubset3: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset3,definition,
% 0.30/0.46 ( binintersectSubset3
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( ( binintersect @ A @ B )
% 0.30/0.46 = B )
% 0.30/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectER_type,type,
% 0.30/0.46 binintersectER: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectER,definition,
% 0.30/0.46 ( binintersectER
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.30/0.46 => ( in @ Xx @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(disjointsetsI1_type,type,
% 0.30/0.46 disjointsetsI1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(disjointsetsI1,definition,
% 0.30/0.46 ( disjointsetsI1
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ~ ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ( in @ Xx @ B ) )
% 0.30/0.46 => ( ( binintersect @ A @ B )
% 0.30/0.46 = emptyset ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectRsub_type,type,
% 0.30/0.46 binintersectRsub: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectRsub,definition,
% 0.30/0.46 ( binintersectRsub
% 0.30/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset4_type,type,
% 0.30/0.46 binintersectSubset4: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset4,definition,
% 0.30/0.46 ( binintersectSubset4
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( subset @ B @ A )
% 0.30/0.46 => ( ( binintersect @ A @ B )
% 0.30/0.46 = B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset1_type,type,
% 0.30/0.46 binintersectSubset1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset1,definition,
% 0.30/0.46 ( binintersectSubset1
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( ( binintersect @ A @ B )
% 0.30/0.46 = A )
% 0.30/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(bs114d_type,type,
% 0.30/0.46 bs114d: $o ).
% 0.30/0.46
% 0.30/0.46 thf(bs114d,definition,
% 0.30/0.46 ( bs114d
% 0.30/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.30/0.46 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.30/0.46 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(regular_type,type,
% 0.30/0.46 regular: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminus_type,type,
% 0.30/0.46 setminus: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(setminusI_type,type,
% 0.30/0.46 setminusI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusI,definition,
% 0.30/0.46 ( setminusI
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ~ ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminusEL_type,type,
% 0.30/0.46 setminusEL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusEL,definition,
% 0.30/0.46 ( setminusEL
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminusER_type,type,
% 0.30/0.46 setminusER: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusER,definition,
% 0.30/0.46 ( setminusER
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.30/0.46 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminusSubset2_type,type,
% 0.30/0.46 setminusSubset2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusSubset2,definition,
% 0.30/0.46 ( setminusSubset2
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( ( setminus @ A @ B )
% 0.30/0.46 = emptyset ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminusERneg_type,type,
% 0.30/0.46 setminusERneg: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusERneg,definition,
% 0.30/0.46 ( setminusERneg
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.30/0.46 => ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminusELneg_type,type,
% 0.30/0.46 setminusELneg: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusELneg,definition,
% 0.30/0.46 ( setminusELneg
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.30/0.46 => ( ~ ( in @ Xx @ B )
% 0.30/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminusILneg_type,type,
% 0.30/0.46 setminusILneg: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusILneg,definition,
% 0.30/0.46 ( setminusILneg
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ~ ( in @ Xx @ A )
% 0.30/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminusIRneg_type,type,
% 0.30/0.46 setminusIRneg: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusIRneg,definition,
% 0.30/0.46 ( setminusIRneg
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminusLsub_type,type,
% 0.30/0.46 setminusLsub: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusLsub,definition,
% 0.30/0.46 ( setminusLsub
% 0.30/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminusSubset1_type,type,
% 0.30/0.46 setminusSubset1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusSubset1,definition,
% 0.30/0.46 ( setminusSubset1
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( ( setminus @ A @ B )
% 0.30/0.46 = emptyset )
% 0.30/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(symdiff_type,type,
% 0.30/0.46 symdiff: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(symdiffE_type,type,
% 0.30/0.46 symdiffE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(symdiffE,definition,
% 0.30/0.46 ( symdiffE
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.30/0.46 => ! [Xphi: $o] :
% 0.30/0.46 ( ( ( in @ Xx @ A )
% 0.30/0.46 => ( ~ ( in @ Xx @ B )
% 0.30/0.46 => Xphi ) )
% 0.30/0.46 => ( ( ~ ( in @ Xx @ A )
% 0.30/0.46 => ( ( in @ Xx @ B )
% 0.30/0.46 => Xphi ) )
% 0.30/0.46 => Xphi ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(symdiffI1_type,type,
% 0.30/0.46 symdiffI1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(symdiffI1,definition,
% 0.30/0.46 ( symdiffI1
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ~ ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(symdiffI2_type,type,
% 0.30/0.46 symdiffI2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(symdiffI2,definition,
% 0.30/0.46 ( symdiffI2
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ~ ( in @ Xx @ A )
% 0.30/0.46 => ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(symdiffIneg1_type,type,
% 0.30/0.46 symdiffIneg1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(symdiffIneg1,definition,
% 0.30/0.46 ( symdiffIneg1
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( in @ Xx @ B )
% 0.30/0.46 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(symdiffIneg2_type,type,
% 0.30/0.46 symdiffIneg2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(symdiffIneg2,definition,
% 0.30/0.46 ( symdiffIneg2
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ~ ( in @ Xx @ A )
% 0.30/0.46 => ( ~ ( in @ Xx @ B )
% 0.30/0.46 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(iskpair_type,type,
% 0.30/0.46 iskpair: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(secondinupair_type,type,
% 0.30/0.46 secondinupair: $o ).
% 0.30/0.46
% 0.30/0.46 thf(secondinupair,definition,
% 0.30/0.46 ( secondinupair
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairIL_type,type,
% 0.30/0.46 setukpairIL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairIL,definition,
% 0.30/0.46 ( setukpairIL
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairIR_type,type,
% 0.30/0.46 setukpairIR: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairIR,definition,
% 0.30/0.46 ( setukpairIR
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(kpairiskpair_type,type,
% 0.30/0.46 kpairiskpair: $o ).
% 0.30/0.46
% 0.30/0.46 thf(kpairiskpair,definition,
% 0.30/0.46 ( kpairiskpair
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(kpair_type,type,
% 0.30/0.46 kpair: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(kpairp_type,type,
% 0.30/0.46 kpairp: $o ).
% 0.30/0.46
% 0.30/0.46 thf(kpairp,definition,
% 0.30/0.46 ( kpairp
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(cartprod_type,type,
% 0.30/0.46 cartprod: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(singletonsubset_type,type,
% 0.30/0.46 singletonsubset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(singletonsubset,definition,
% 0.30/0.46 ( singletonsubset
% 0.30/0.46 = ( ! [A: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(singletoninpowerset_type,type,
% 0.30/0.46 singletoninpowerset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(singletoninpowerset,definition,
% 0.30/0.46 ( singletoninpowerset
% 0.30/0.46 = ( ! [A: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(singletoninpowunion_type,type,
% 0.30/0.46 singletoninpowunion: $o ).
% 0.30/0.46
% 0.30/0.46 thf(singletoninpowunion,definition,
% 0.30/0.46 ( singletoninpowunion
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(upairset2E_type,type,
% 0.30/0.46 upairset2E: $o ).
% 0.30/0.46
% 0.30/0.46 thf(upairset2E,definition,
% 0.30/0.46 ( upairset2E
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.30/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.30/0.46 => ( ( Xz = Xx )
% 0.30/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(upairsubunion_type,type,
% 0.30/0.46 upairsubunion: $o ).
% 0.30/0.46
% 0.30/0.46 thf(upairsubunion,definition,
% 0.30/0.46 ( upairsubunion
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(upairinpowunion_type,type,
% 0.30/0.46 upairinpowunion: $o ).
% 0.30/0.46
% 0.30/0.46 thf(upairinpowunion,definition,
% 0.30/0.46 ( upairinpowunion
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(ubforcartprodlem1_type,type,
% 0.30/0.46 ubforcartprodlem1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(ubforcartprodlem1,definition,
% 0.30/0.46 ( ubforcartprodlem1
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(ubforcartprodlem2_type,type,
% 0.30/0.46 ubforcartprodlem2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(ubforcartprodlem2,definition,
% 0.30/0.46 ( ubforcartprodlem2
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(ubforcartprodlem3_type,type,
% 0.30/0.46 ubforcartprodlem3: $o ).
% 0.30/0.46
% 0.30/0.46 thf(ubforcartprodlem3,definition,
% 0.30/0.46 ( ubforcartprodlem3
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodpairin_type,type,
% 0.30/0.46 cartprodpairin: $o ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodpairin,definition,
% 0.30/0.46 ( cartprodpairin
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodmempair1_type,type,
% 0.30/0.46 cartprodmempair1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodmempair1,definition,
% 0.30/0.46 ( cartprodmempair1
% 0.30/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.30/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.30/0.46 => ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ? [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 & ( Xu
% 0.30/0.46 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodmempair_type,type,
% 0.30/0.46 cartprodmempair: $o ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodmempair,definition,
% 0.30/0.46 ( cartprodmempair
% 0.30/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.30/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.30/0.46 => ( iskpair @ Xu ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setunionE2_type,type,
% 0.30/0.46 setunionE2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setunionE2,definition,
% 0.30/0.46 ( setunionE2
% 0.30/0.46 = ( ! [A: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.30/0.46 => ? [X: $i] :
% 0.30/0.46 ( ( in @ X @ A )
% 0.30/0.46 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setunionsingleton1_type,type,
% 0.30/0.46 setunionsingleton1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setunionsingleton1,definition,
% 0.30/0.46 ( setunionsingleton1
% 0.30/0.46 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setunionsingleton2_type,type,
% 0.30/0.46 setunionsingleton2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setunionsingleton2,definition,
% 0.30/0.46 ( setunionsingleton2
% 0.30/0.46 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setunionsingleton_type,type,
% 0.30/0.46 setunionsingleton: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setunionsingleton,definition,
% 0.30/0.46 ( setunionsingleton
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.30/0.46 = Xx ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(singleton_type,type,
% 0.30/0.46 singleton: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(singletonprop_type,type,
% 0.30/0.46 singletonprop: $o ).
% 0.30/0.46
% 0.30/0.46 thf(singletonprop,definition,
% 0.30/0.46 ( singletonprop
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ A )
% 0.30/0.46 => ( ( Xphi @ Xx )
% 0.30/0.46 => ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) )
% 0.30/0.46 => ( ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ( Xphi @ Xx ) )
% 0.30/0.46 => ( singleton
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(ex1_type,type,
% 0.30/0.46 ex1: $i > ( $i > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(ex1E1_type,type,
% 0.30/0.46 ex1E1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(ex1E1,definition,
% 0.30/0.46 ( ex1E1
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ( ex1 @ A
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(ex1I_type,type,
% 0.30/0.46 ex1I: $o ).
% 0.30/0.46
% 0.30/0.46 thf(ex1I,definition,
% 0.30/0.46 ( ex1I
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( Xphi @ Xx )
% 0.30/0.46 => ( ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ A )
% 0.30/0.46 => ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xy = Xx ) ) )
% 0.30/0.46 => ( ex1 @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(ex1I2_type,type,
% 0.30/0.46 ex1I2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(ex1I2,definition,
% 0.30/0.46 ( ex1I2
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ A )
% 0.30/0.46 => ( ( Xphi @ Xx )
% 0.30/0.46 => ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) )
% 0.30/0.46 => ( ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ( Xphi @ Xx ) )
% 0.30/0.46 => ( ex1 @ A
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(singletonsuniq_type,type,
% 0.30/0.46 singletonsuniq: $o ).
% 0.30/0.46
% 0.30/0.46 thf(singletonsuniq,definition,
% 0.30/0.46 ( singletonsuniq
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( ( setadjoin @ Xx @ emptyset )
% 0.30/0.46 = ( setadjoin @ Xy @ emptyset ) )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(atmost1p_type,type,
% 0.30/0.46 atmost1p: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(atleast2p_type,type,
% 0.30/0.46 atleast2p: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(atmost2p_type,type,
% 0.30/0.46 atmost2p: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(upairsetp_type,type,
% 0.30/0.46 upairsetp: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjL1_type,type,
% 0.30/0.46 setukpairinjL1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjL1,definition,
% 0.30/0.46 ( setukpairinjL1
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.30/0.46 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.30/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(kfstsingleton_type,type,
% 0.30/0.46 kfstsingleton: $o ).
% 0.30/0.46
% 0.30/0.46 thf(kfstsingleton,definition,
% 0.30/0.46 ( kfstsingleton
% 0.30/0.46 = ( ! [Xu: $i] :
% 0.30/0.46 ( ( iskpair @ Xu )
% 0.30/0.46 => ( singleton
% 0.30/0.46 @ ( dsetconstr @ ( setunion @ Xu )
% 0.30/0.46 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(theprop_type,type,
% 0.30/0.46 theprop: $o ).
% 0.30/0.46
% 0.30/0.46 thf(theprop,definition,
% 0.30/0.46 ( theprop
% 0.30/0.46 = ( ! [X: $i] :
% 0.30/0.46 ( ( singleton @ X )
% 0.30/0.46 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(kfst_type,type,
% 0.30/0.46 kfst: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(kfstpairEq_type,type,
% 0.30/0.46 kfstpairEq: $o ).
% 0.30/0.46
% 0.30/0.46 thf(kfstpairEq,definition,
% 0.30/0.46 ( kfstpairEq
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.30/0.46 = Xx ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodfstin_type,type,
% 0.30/0.46 cartprodfstin: $o ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodfstin,definition,
% 0.30/0.46 ( cartprodfstin
% 0.30/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.30/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.30/0.46 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjL2_type,type,
% 0.30/0.46 setukpairinjL2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjL2,definition,
% 0.30/0.46 ( setukpairinjL2
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.30/0.46 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.30/0.46 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.30/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjL_type,type,
% 0.30/0.46 setukpairinjL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjL,definition,
% 0.30/0.46 ( setukpairinjL
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.30/0.46 ( ( ( kpair @ Xx @ Xy )
% 0.30/0.46 = ( kpair @ Xz @ Xu ) )
% 0.30/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjR11_type,type,
% 0.30/0.46 setukpairinjR11: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjR11,definition,
% 0.30/0.46 ( setukpairinjR11
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx = Xy )
% 0.30/0.46 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.30/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjR12_type,type,
% 0.30/0.46 setukpairinjR12: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjR12,definition,
% 0.30/0.46 ( setukpairinjR12
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx = Xy )
% 0.30/0.46 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.30/0.46 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjR1_type,type,
% 0.30/0.46 setukpairinjR1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjR1,definition,
% 0.30/0.46 ( setukpairinjR1
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.30/0.46 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.30/0.46 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.30/0.46 => ( ( Xz = Xu )
% 0.30/0.46 => ( Xy = Xu ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(upairequniteq_type,type,
% 0.30/0.46 upairequniteq: $o ).
% 0.30/0.46
% 0.30/0.46 thf(upairequniteq,definition,
% 0.30/0.46 ( upairequniteq
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.30/0.46 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.30/0.46 = ( setadjoin @ Xz @ emptyset ) )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjR2_type,type,
% 0.30/0.46 setukpairinjR2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjR2,definition,
% 0.30/0.46 ( setukpairinjR2
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.30/0.46 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.30/0.46 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.30/0.46 => ( Xy = Xu ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjR_type,type,
% 0.30/0.46 setukpairinjR: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjR,definition,
% 0.30/0.46 ( setukpairinjR
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.30/0.46 ( ( ( kpair @ Xx @ Xy )
% 0.30/0.46 = ( kpair @ Xz @ Xu ) )
% 0.30/0.46 => ( Xy = Xu ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(ksndsingleton_type,type,
% 0.30/0.46 ksndsingleton: $o ).
% 0.30/0.46
% 0.30/0.46 thf(ksndsingleton,definition,
% 0.30/0.46 ( ksndsingleton
% 0.30/0.46 = ( ! [Xu: $i] :
% 0.30/0.46 ( ( iskpair @ Xu )
% 0.30/0.46 => ( singleton
% 0.30/0.46 @ ( dsetconstr @ ( setunion @ Xu )
% 0.30/0.46 @ ^ [Xx: $i] :
% 0.30/0.46 ( Xu
% 0.30/0.46 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(ksnd_type,type,
% 0.30/0.46 ksnd: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(ksndpairEq_type,type,
% 0.30/0.46 ksndpairEq: $o ).
% 0.30/0.46
% 0.30/0.46 thf(ksndpairEq,definition,
% 0.30/0.46 ( ksndpairEq
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.30/0.46 = Xy ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(kpairsurjEq_type,type,
% 0.30/0.46 kpairsurjEq: $o ).
% 0.30/0.46
% 0.30/0.46 thf(kpairsurjEq,definition,
% 0.30/0.46 ( kpairsurjEq
% 0.30/0.46 = ( ! [Xu: $i] :
% 0.30/0.46 ( ( iskpair @ Xu )
% 0.30/0.46 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.30/0.46 = Xu ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodsndin_type,type,
% 0.30/0.46 cartprodsndin: $o ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodsndin,definition,
% 0.30/0.46 ( cartprodsndin
% 0.30/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.30/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.30/0.46 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodpairmemEL_type,type,
% 0.30/0.46 cartprodpairmemEL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodpairmemEL,definition,
% 0.30/0.46 ( cartprodpairmemEL
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodpairmemER_type,type,
% 0.30/0.46 cartprodpairmemER: $o ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodpairmemER,definition,
% 0.30/0.46 ( cartprodpairmemER
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.30/0.46 => ( in @ Xy @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodmempaircEq_type,type,
% 0.30/0.46 cartprodmempaircEq: $o ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodmempaircEq,definition,
% 0.30/0.46 ( cartprodmempaircEq
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( ( kpair @ Xx @ Xy )
% 0.30/0.46 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodfstpairEq_type,type,
% 0.30/0.46 cartprodfstpairEq: $o ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodfstpairEq,definition,
% 0.30/0.46 ( cartprodfstpairEq
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.30/0.46 = Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodsndpairEq_type,type,
% 0.30/0.46 cartprodsndpairEq: $o ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodsndpairEq,definition,
% 0.30/0.46 ( cartprodsndpairEq
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.30/0.46 = Xy ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodpairsurjEq_type,type,
% 0.30/0.46 cartprodpairsurjEq: $o ).
% 0.30/0.46
% 0.30/0.46 thf(cartprodpairsurjEq,definition,
% 0.30/0.46 ( cartprodpairsurjEq
% 0.30/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.30/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.30/0.46 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.30/0.46 = Xu ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(breln_type,type,
% 0.30/0.46 breln: $i > $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(dpsetconstr_type,type,
% 0.30/0.46 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.30/0.46
% 0.30/0.46 thf(dpsetconstrI_type,type,
% 0.30/0.46 dpsetconstrI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dpsetconstrI,definition,
% 0.30/0.46 ( dpsetconstrI
% 0.30/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( ( Xphi @ Xx @ Xy )
% 0.30/0.46 => ( in @ ( kpair @ Xx @ Xy )
% 0.30/0.46 @ ( dpsetconstr @ A @ B
% 0.30/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dpsetconstrSub_type,type,
% 0.30/0.46 dpsetconstrSub: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dpsetconstrSub,definition,
% 0.30/0.46 ( dpsetconstrSub
% 0.30/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.30/0.46 ( subset
% 0.30/0.46 @ ( dpsetconstr @ A @ B
% 0.30/0.46 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.30/0.46 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setOfPairsIsBReln_type,type,
% 0.30/0.46 setOfPairsIsBReln: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setOfPairsIsBReln,definition,
% 0.30/0.46 ( setOfPairsIsBReln
% 0.30/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.30/0.46 ( breln @ A @ B
% 0.30/0.46 @ ( dpsetconstr @ A @ B
% 0.30/0.46 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dpsetconstrERa_type,type,
% 0.30/0.46 dpsetconstrERa: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dpsetconstrERa,definition,
% 0.30/0.46 ( dpsetconstrERa
% 0.30/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.30/0.46 @ ( dpsetconstr @ A @ B
% 0.30/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.30/0.46 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dpsetconstrEL1_type,type,
% 0.30/0.46 dpsetconstrEL1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dpsetconstrEL1,definition,
% 0.30/0.46 ( dpsetconstrEL1
% 0.30/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ ( kpair @ Xx @ Xy )
% 0.30/0.46 @ ( dpsetconstr @ A @ B
% 0.30/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dpsetconstrEL2_type,type,
% 0.30/0.46 dpsetconstrEL2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dpsetconstrEL2,definition,
% 0.30/0.46 ( dpsetconstrEL2
% 0.30/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ ( kpair @ Xx @ Xy )
% 0.30/0.46 @ ( dpsetconstr @ A @ B
% 0.30/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.30/0.46 => ( in @ Xy @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dpsetconstrER_type,type,
% 0.30/0.46 dpsetconstrER: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dpsetconstrER,definition,
% 0.30/0.46 ( dpsetconstrER
% 0.30/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ ( kpair @ Xx @ Xy )
% 0.30/0.46 @ ( dpsetconstr @ A @ B
% 0.30/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.30/0.46 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(func_type,type,
% 0.30/0.46 func: $i > $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(funcSet_type,type,
% 0.30/0.46 funcSet: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(funcImageSingleton_type,type,
% 0.30/0.46 funcImageSingleton: $o ).
% 0.30/0.46
% 0.30/0.46 thf(funcImageSingleton,definition,
% 0.30/0.46 ( funcImageSingleton
% 0.30/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.46 ( ( func @ A @ B @ Xf )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( singleton
% 0.30/0.46 @ ( dsetconstr @ B
% 0.30/0.46 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(apProp_type,type,
% 0.30/0.46 apProp: $o ).
% 0.30/0.46
% 0.30/0.46 thf(apProp,definition,
% 0.30/0.46 ( apProp
% 0.30/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.46 ( ( func @ A @ B @ Xf )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in
% 0.30/0.46 @ ( setunion
% 0.30/0.46 @ ( dsetconstr @ B
% 0.30/0.46 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.30/0.46 @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(ap_type,type,
% 0.30/0.46 ap: $i > $i > $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(app_type,type,
% 0.30/0.46 app: $o ).
% 0.30/0.46
% 0.30/0.46 thf(app,definition,
% 0.30/0.46 ( app
% 0.30/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.46 ( ( func @ A @ B @ Xf )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(infuncsetfunc_type,type,
% 0.30/0.46 infuncsetfunc: $o ).
% 0.30/0.46
% 0.30/0.46 thf(infuncsetfunc,definition,
% 0.30/0.46 ( infuncsetfunc
% 0.30/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.30/0.46 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(ap2p_type,type,
% 0.30/0.46 ap2p: $o ).
% 0.30/0.46
% 0.30/0.46 thf(ap2p,definition,
% 0.30/0.46 ( ap2p
% 0.30/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(funcinfuncset_type,type,
% 0.30/0.46 funcinfuncset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(funcinfuncset,definition,
% 0.30/0.46 ( funcinfuncset
% 0.30/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.46 ( ( func @ A @ B @ Xf )
% 0.30/0.46 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(lamProp_type,type,
% 0.30/0.46 lamProp: $o ).
% 0.30/0.46
% 0.30/0.46 thf(lamProp,definition,
% 0.30/0.46 ( lamProp
% 0.30/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.30/0.46 => ( func @ A @ B
% 0.30/0.46 @ ( dpsetconstr @ A @ B
% 0.30/0.46 @ ^ [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xf @ Xx )
% 0.30/0.46 = Xy ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(lam_type,type,
% 0.30/0.46 lam: $i > $i > ( $i > $i ) > $i ).
% 0.30/0.46
% 0.30/0.46 thf(lamp_type,type,
% 0.30/0.46 lamp: $o ).
% 0.30/0.46
% 0.30/0.46 thf(lamp,definition,
% 0.30/0.46 ( lamp
% 0.30/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.30/0.46 => ( func @ A @ B
% 0.30/0.46 @ ( lam @ A @ B
% 0.30/0.46 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(lam2p_type,type,
% 0.30/0.46 lam2p: $o ).
% 0.30/0.46
% 0.30/0.46 thf(lam2p,definition,
% 0.30/0.46 ( lam2p
% 0.30/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.30/0.46 => ( in
% 0.30/0.46 @ ( lam @ A @ B
% 0.30/0.46 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.30/0.46 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(brelnall1_type,type,
% 0.30/0.46 brelnall1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(brelnall1,definition,
% 0.30/0.46 ( brelnall1
% 0.30/0.46 = ( ! [A: $i,B: $i,R: $i] :
% 0.30/0.46 ( ( breln @ A @ B @ R )
% 0.30/0.46 => ! [Xphi: $i > $o] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.30/0.46 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ R )
% 0.30/0.46 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(brelnall2_type,type,
% 0.30/0.46 brelnall2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(brelnall2,definition,
% 0.30/0.46 ( brelnall2
% 0.30/0.46 = ( ! [A: $i,B: $i,R: $i] :
% 0.30/0.46 ( ( breln @ A @ B @ R )
% 0.30/0.46 => ! [Xphi: $i > $o] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.30/0.46 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ R )
% 0.30/0.46 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(ex1E2_type,type,
% 0.30/0.46 ex1E2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(ex1E2,definition,
% 0.30/0.46 ( ex1E2
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ( ex1 @ A
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ A )
% 0.30/0.46 => ( ( Xphi @ Xx )
% 0.30/0.46 => ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(funcGraphProp1_type,type,
% 0.30/0.46 funcGraphProp1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(funcGraphProp1,definition,
% 0.30/0.46 ( funcGraphProp1
% 0.30/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.46 ( ( func @ A @ B @ Xf )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(funcGraphProp3_type,type,
% 0.30/0.46 funcGraphProp3: $o ).
% 0.30/0.46
% 0.30/0.46 thf(funcGraphProp3,definition,
% 0.30/0.46 ( funcGraphProp3
% 0.30/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(funcGraphProp2_type,type,
% 0.30/0.46 funcGraphProp2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(funcGraphProp2,definition,
% 0.30/0.46 ( funcGraphProp2
% 0.30/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.46 ( ( func @ A @ B @ Xf )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.30/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.30/0.46 = Xy ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(funcextLem_type,type,
% 0.30/0.46 funcextLem: $o ).
% 0.30/0.46
% 0.30/0.46 thf(funcextLem,definition,
% 0.30/0.46 ( funcextLem
% 0.30/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.46 ( ( func @ A @ B @ Xf )
% 0.30/0.46 => ! [Xg: $i] :
% 0.30/0.46 ( ( func @ A @ B @ Xg )
% 0.30/0.46 => ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.30/0.46 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 0.30/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(funcGraphProp4_type,type,
% 0.30/0.46 funcGraphProp4: $o ).
% 0.30/0.46
% 0.30/0.46 thf(funcGraphProp4,definition,
% 0.30/0.46 ( funcGraphProp4
% 0.30/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.30/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.30/0.46 = Xy ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subbreln_type,type,
% 0.30/0.46 subbreln: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subbreln,definition,
% 0.30/0.46 ( subbreln
% 0.30/0.46 = ( ! [A: $i,B: $i,R: $i] :
% 0.30/0.46 ( ( breln @ A @ B @ R )
% 0.30/0.46 => ! [S: $i] :
% 0.30/0.46 ( ( breln @ A @ B @ S )
% 0.30/0.46 => ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.30/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.30/0.46 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(eqbreln_type,type,
% 0.30/0.46 eqbreln: $o ).
% 0.30/0.46
% 0.30/0.46 thf(eqbreln,definition,
% 0.30/0.46 ( eqbreln
% 0.30/0.46 = ( ! [A: $i,B: $i,R: $i] :
% 0.30/0.46 ( ( breln @ A @ B @ R )
% 0.30/0.46 => ! [S: $i] :
% 0.30/0.46 ( ( breln @ A @ B @ S )
% 0.30/0.46 => ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.30/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.30/0.46 => ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.30/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.30/0.47 => ( R = S ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(funcext_type,type,
% 0.30/0.47 funcext: $o ).
% 0.30/0.47
% 0.30/0.47 thf(funcext,definition,
% 0.30/0.47 ( funcext
% 0.30/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.47 ( ( func @ A @ B @ Xf )
% 0.30/0.47 => ! [Xg: $i] :
% 0.30/0.47 ( ( func @ A @ B @ Xg )
% 0.30/0.47 => ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.30/0.47 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.30/0.47 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(funcext2_type,type,
% 0.30/0.47 funcext2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(funcext2,definition,
% 0.30/0.47 ( funcext2
% 0.30/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.30/0.47 => ! [Xg: $i] :
% 0.30/0.47 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 0.30/0.47 => ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.30/0.47 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.30/0.47 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(ap2apEq1_type,type,
% 0.30/0.47 ap2apEq1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(ap2apEq1,definition,
% 0.30/0.47 ( ap2apEq1
% 0.30/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.30/0.47 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(ap2apEq2_type,type,
% 0.30/0.47 ap2apEq2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(ap2apEq2,definition,
% 0.30/0.47 ( ap2apEq2
% 0.30/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.47 ( ( func @ A @ B @ Xf )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.30/0.47 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(beta1_type,type,
% 0.30/0.47 beta1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(beta1,definition,
% 0.30/0.47 ( beta1
% 0.30/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( ap @ A @ B
% 0.30/0.47 @ ( lam @ A @ B
% 0.30/0.47 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.30/0.47 @ Xx )
% 0.30/0.47 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(eta1_type,type,
% 0.30/0.47 eta1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(eta1,definition,
% 0.30/0.47 ( eta1
% 0.30/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.47 ( ( func @ A @ B @ Xf )
% 0.30/0.47 => ( ( lam @ A @ B
% 0.30/0.47 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.30/0.47 = Xf ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(lam2lamEq_type,type,
% 0.30/0.47 lam2lamEq: $o ).
% 0.30/0.47
% 0.30/0.47 thf(lam2lamEq,definition,
% 0.30/0.47 ( lam2lamEq
% 0.30/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.30/0.47 => ( ( lam @ A @ B
% 0.30/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.30/0.47 = ( lam @ A @ B
% 0.30/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(beta2_type,type,
% 0.30/0.47 beta2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(beta2,definition,
% 0.30/0.47 ( beta2
% 0.30/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( ap @ A @ B
% 0.30/0.47 @ ( lam @ A @ B
% 0.30/0.47 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.30/0.47 @ Xx )
% 0.30/0.47 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(eta2_type,type,
% 0.30/0.47 eta2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(eta2,definition,
% 0.30/0.47 ( eta2
% 0.30/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.30/0.47 => ( ( lam @ A @ B
% 0.30/0.47 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.30/0.47 = Xf ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(iffalseProp1_type,type,
% 0.30/0.47 iffalseProp1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(iffalseProp1,definition,
% 0.30/0.47 ( iffalseProp1
% 0.30/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( ~ Xphi
% 0.30/0.47 => ( in @ Xy
% 0.30/0.47 @ ( dsetconstr @ A
% 0.30/0.47 @ ^ [Xz: $i] :
% 0.30/0.47 ( ( Xphi
% 0.30/0.47 & ( Xz = Xx ) )
% 0.30/0.47 | ( ~ Xphi
% 0.30/0.47 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(iffalseProp2_type,type,
% 0.30/0.47 iffalseProp2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(iffalseProp2,definition,
% 0.30/0.47 ( iffalseProp2
% 0.30/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( ~ Xphi
% 0.30/0.47 => ( ( dsetconstr @ A
% 0.30/0.47 @ ^ [Xz: $i] :
% 0.30/0.47 ( ( Xphi
% 0.30/0.47 & ( Xz = Xx ) )
% 0.30/0.47 | ( ~ Xphi
% 0.30/0.47 & ( Xz = Xy ) ) ) )
% 0.30/0.47 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(iftrueProp1_type,type,
% 0.30/0.47 iftrueProp1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(iftrueProp1,definition,
% 0.30/0.47 ( iftrueProp1
% 0.30/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( Xphi
% 0.30/0.47 => ( in @ Xx
% 0.30/0.47 @ ( dsetconstr @ A
% 0.30/0.47 @ ^ [Xz: $i] :
% 0.30/0.47 ( ( Xphi
% 0.30/0.47 & ( Xz = Xx ) )
% 0.30/0.47 | ( ~ Xphi
% 0.30/0.47 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(iftrueProp2_type,type,
% 0.30/0.47 iftrueProp2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(iftrueProp2,definition,
% 0.30/0.47 ( iftrueProp2
% 0.30/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( Xphi
% 0.30/0.47 => ( ( dsetconstr @ A
% 0.30/0.47 @ ^ [Xz: $i] :
% 0.30/0.47 ( ( Xphi
% 0.30/0.47 & ( Xz = Xx ) )
% 0.30/0.47 | ( ~ Xphi
% 0.30/0.47 & ( Xz = Xy ) ) ) )
% 0.30/0.47 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(ifSingleton_type,type,
% 0.30/0.47 ifSingleton: $o ).
% 0.30/0.47
% 0.30/0.47 thf(ifSingleton,definition,
% 0.30/0.47 ( ifSingleton
% 0.30/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( singleton
% 0.30/0.47 @ ( dsetconstr @ A
% 0.30/0.47 @ ^ [Xz: $i] :
% 0.30/0.47 ( ( Xphi
% 0.30/0.47 & ( Xz = Xx ) )
% 0.30/0.47 | ( ~ Xphi
% 0.30/0.47 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(if_type,type,
% 0.30/0.47 if: $i > $o > $i > $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(ifp_type,type,
% 0.30/0.47 ifp: $o ).
% 0.30/0.47
% 0.30/0.47 thf(ifp,definition,
% 0.30/0.47 ( ifp
% 0.30/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(theeq_type,type,
% 0.30/0.47 theeq: $o ).
% 0.30/0.47
% 0.30/0.47 thf(theeq,definition,
% 0.30/0.47 ( theeq
% 0.30/0.47 = ( ! [X: $i] :
% 0.30/0.47 ( ( singleton @ X )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ X )
% 0.30/0.47 => ( ( setunion @ X )
% 0.30/0.47 = Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(iftrue_type,type,
% 0.30/0.47 iftrue: $o ).
% 0.30/0.47
% 0.30/0.47 thf(iftrue,definition,
% 0.30/0.47 ( iftrue
% 0.30/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( Xphi
% 0.30/0.47 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.30/0.47 = Xx ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(iffalse_type,type,
% 0.30/0.47 iffalse: $o ).
% 0.30/0.47
% 0.30/0.47 thf(iffalse,definition,
% 0.30/0.47 ( iffalse
% 0.30/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( ~ Xphi
% 0.30/0.47 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.30/0.47 = Xy ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(iftrueorfalse_type,type,
% 0.30/0.47 iftrueorfalse: $o ).
% 0.30/0.47
% 0.30/0.47 thf(iftrueorfalse,definition,
% 0.30/0.47 ( iftrueorfalse
% 0.30/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(binintersectT_lem_type,type,
% 0.30/0.47 binintersectT_lem: $o ).
% 0.30/0.47
% 0.30/0.47 thf(binintersectT_lem,definition,
% 0.30/0.47 ( binintersectT_lem
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(binunionT_lem_type,type,
% 0.30/0.47 binunionT_lem: $o ).
% 0.30/0.47
% 0.30/0.47 thf(binunionT_lem,definition,
% 0.30/0.47 ( binunionT_lem
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(powersetT_lem_type,type,
% 0.30/0.47 powersetT_lem: $o ).
% 0.30/0.47
% 0.30/0.47 thf(powersetT_lem,definition,
% 0.30/0.47 ( powersetT_lem
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setminusT_lem_type,type,
% 0.30/0.47 setminusT_lem: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setminusT_lem,definition,
% 0.30/0.47 ( setminusT_lem
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(complementT_lem_type,type,
% 0.30/0.47 complementT_lem: $o ).
% 0.30/0.47
% 0.30/0.47 thf(complementT_lem,definition,
% 0.30/0.47 ( complementT_lem
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setextT_type,type,
% 0.30/0.47 setextT: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setextT,definition,
% 0.30/0.47 ( setextT
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx @ X )
% 0.30/0.47 => ( in @ Xx @ Y ) ) )
% 0.30/0.47 => ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx @ Y )
% 0.30/0.47 => ( in @ Xx @ X ) ) )
% 0.30/0.47 => ( X = Y ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(subsetTI_type,type,
% 0.30/0.47 subsetTI: $o ).
% 0.30/0.47
% 0.30/0.47 thf(subsetTI,definition,
% 0.30/0.47 ( subsetTI
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx @ X )
% 0.30/0.47 => ( in @ Xx @ Y ) ) )
% 0.30/0.47 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(powersetTI1_type,type,
% 0.30/0.47 powersetTI1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(powersetTI1,definition,
% 0.30/0.47 ( powersetTI1
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx @ X )
% 0.30/0.47 => ( in @ Xx @ Y ) ) )
% 0.30/0.47 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(powersetTE1_type,type,
% 0.30/0.47 powersetTE1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(powersetTE1,definition,
% 0.30/0.47 ( powersetTE1
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ X @ ( powerset @ Y ) )
% 0.30/0.47 => ( ( in @ Xx @ X )
% 0.30/0.47 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(complementTI1_type,type,
% 0.30/0.47 complementTI1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(complementTI1,definition,
% 0.30/0.47 ( complementTI1
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx @ X )
% 0.30/0.47 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(complementTE1_type,type,
% 0.30/0.47 complementTE1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(complementTE1,definition,
% 0.30/0.47 ( complementTE1
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 0.30/0.47 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(binintersectTELcontra_type,type,
% 0.30/0.47 binintersectTELcontra: $o ).
% 0.30/0.47
% 0.30/0.47 thf(binintersectTELcontra,definition,
% 0.30/0.47 ( binintersectTELcontra
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ~ ( in @ Xx @ X )
% 0.30/0.47 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(binintersectTERcontra_type,type,
% 0.30/0.47 binintersectTERcontra: $o ).
% 0.30/0.47
% 0.30/0.47 thf(binintersectTERcontra,definition,
% 0.30/0.47 ( binintersectTERcontra
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ~ ( in @ Xx @ Y )
% 0.30/0.47 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(contrasubsetT_type,type,
% 0.30/0.47 contrasubsetT: $o ).
% 0.30/0.47
% 0.30/0.47 thf(contrasubsetT,definition,
% 0.30/0.47 ( contrasubsetT
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.30/0.47 => ( ( in @ Xx @ Y )
% 0.30/0.47 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(contrasubsetT1_type,type,
% 0.30/0.47 contrasubsetT1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(contrasubsetT1,definition,
% 0.30/0.47 ( contrasubsetT1
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( subset @ X @ Y )
% 0.30/0.47 => ( ~ ( in @ Xx @ Y )
% 0.30/0.47 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(contrasubsetT2_type,type,
% 0.30/0.47 contrasubsetT2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(contrasubsetT2,definition,
% 0.30/0.47 ( contrasubsetT2
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ( ( subset @ X @ Y )
% 0.30/0.47 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(contrasubsetT3_type,type,
% 0.30/0.47 contrasubsetT3: $o ).
% 0.30/0.47
% 0.30/0.47 thf(contrasubsetT3,definition,
% 0.30/0.47 ( contrasubsetT3
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 0.30/0.47 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(doubleComplementI1_type,type,
% 0.30/0.47 doubleComplementI1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(doubleComplementI1,definition,
% 0.30/0.47 ( doubleComplementI1
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx @ X )
% 0.30/0.47 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(doubleComplementE1_type,type,
% 0.30/0.47 doubleComplementE1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(doubleComplementE1,definition,
% 0.30/0.47 ( doubleComplementE1
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 0.30/0.47 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(doubleComplementSub1_type,type,
% 0.30/0.47 doubleComplementSub1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(doubleComplementSub1,definition,
% 0.30/0.47 ( doubleComplementSub1
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(doubleComplementSub2_type,type,
% 0.30/0.47 doubleComplementSub2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(doubleComplementSub2,definition,
% 0.30/0.47 ( doubleComplementSub2
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(doubleComplementEq_type,type,
% 0.30/0.47 doubleComplementEq: $o ).
% 0.30/0.47
% 0.30/0.47 thf(doubleComplementEq,definition,
% 0.30/0.47 ( doubleComplementEq
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ( X
% 0.30/0.47 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(complementTnotintersectT_type,type,
% 0.30/0.47 complementTnotintersectT: $o ).
% 0.30/0.47
% 0.30/0.47 thf(complementTnotintersectT,definition,
% 0.30/0.47 ( complementTnotintersectT
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.30/0.47 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(complementImpComplementIntersect_type,type,
% 0.30/0.47 complementImpComplementIntersect: $o ).
% 0.30/0.47
% 0.30/0.47 thf(complementImpComplementIntersect,definition,
% 0.30/0.47 ( complementImpComplementIntersect
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.30/0.47 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(complementSubsetComplementIntersect_type,type,
% 0.30/0.47 complementSubsetComplementIntersect: $o ).
% 0.30/0.47
% 0.30/0.47 thf(complementSubsetComplementIntersect,definition,
% 0.30/0.47 ( complementSubsetComplementIntersect
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(complementInPowersetComplementIntersect_type,type,
% 0.30/0.47 complementInPowersetComplementIntersect: $o ).
% 0.30/0.47
% 0.30/0.47 thf(complementInPowersetComplementIntersect,definition,
% 0.30/0.47 ( complementInPowersetComplementIntersect
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(contraSubsetComplement_type,type,
% 0.30/0.47 contraSubsetComplement: $o ).
% 0.30/0.47
% 0.30/0.47 thf(contraSubsetComplement,definition,
% 0.30/0.47 ( contraSubsetComplement
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx @ Y )
% 0.30/0.47 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(complementTcontraSubset_type,type,
% 0.30/0.47 complementTcontraSubset: $o ).
% 0.30/0.47
% 0.30/0.47 thf(complementTcontraSubset,definition,
% 0.30/0.47 ( complementTcontraSubset
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.30/0.47 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(binunionTILcontra_type,type,
% 0.30/0.47 binunionTILcontra: $o ).
% 0.30/0.47
% 0.30/0.47 thf(binunionTILcontra,definition,
% 0.30/0.47 ( binunionTILcontra
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.30/0.47 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(binunionTIRcontra_type,type,
% 0.30/0.47 binunionTIRcontra: $o ).
% 0.30/0.47
% 0.30/0.47 thf(binunionTIRcontra,definition,
% 0.30/0.47 ( binunionTIRcontra
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.30/0.47 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(inIntersectImpInUnion_type,type,
% 0.30/0.47 inIntersectImpInUnion: $o ).
% 0.30/0.47
% 0.30/0.47 thf(inIntersectImpInUnion,definition,
% 0.30/0.47 ( inIntersectImpInUnion
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Z: $i] :
% 0.30/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.30/0.47 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(inIntersectImpInUnion2_type,type,
% 0.30/0.47 inIntersectImpInUnion2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(inIntersectImpInUnion2,definition,
% 0.30/0.47 ( inIntersectImpInUnion2
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Z: $i] :
% 0.30/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.30/0.47 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(inIntersectImpInIntersectUnions_type,type,
% 0.30/0.47 inIntersectImpInIntersectUnions: $o ).
% 0.30/0.47
% 0.30/0.47 thf(inIntersectImpInIntersectUnions,definition,
% 0.30/0.47 ( inIntersectImpInIntersectUnions
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Z: $i] :
% 0.30/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.30/0.47 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(intersectInPowersetIntersectUnions_type,type,
% 0.30/0.47 intersectInPowersetIntersectUnions: $o ).
% 0.30/0.47
% 0.30/0.47 thf(intersectInPowersetIntersectUnions,definition,
% 0.30/0.47 ( intersectInPowersetIntersectUnions
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Z: $i] :
% 0.30/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.30/0.47 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(inComplementUnionImpNotIn1_type,type,
% 0.30/0.47 inComplementUnionImpNotIn1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(inComplementUnionImpNotIn1,definition,
% 0.30/0.47 ( inComplementUnionImpNotIn1
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.30/0.47 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(inComplementUnionImpInComplement1_type,type,
% 0.30/0.47 inComplementUnionImpInComplement1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(inComplementUnionImpInComplement1,definition,
% 0.30/0.47 ( inComplementUnionImpInComplement1
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.30/0.47 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(binunionTE_type,type,
% 0.30/0.47 binunionTE: $o ).
% 0.30/0.47
% 0.30/0.47 thf(binunionTE,definition,
% 0.30/0.47 ( binunionTE
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Xphi: $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.30/0.47 => ( ( ( in @ Xx @ X )
% 0.30/0.47 => Xphi )
% 0.30/0.47 => ( ( ( in @ Xx @ Y )
% 0.30/0.47 => Xphi )
% 0.30/0.47 => Xphi ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(binunionTEcontra_type,type,
% 0.30/0.47 binunionTEcontra: $o ).
% 0.30/0.47
% 0.30/0.47 thf(binunionTEcontra,definition,
% 0.30/0.47 ( binunionTEcontra
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ~ ( in @ Xx @ X )
% 0.30/0.47 => ( ~ ( in @ Xx @ Y )
% 0.30/0.47 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(demorgan2a1_type,type,
% 0.30/0.47 demorgan2a1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(demorgan2a1,definition,
% 0.30/0.47 ( demorgan2a1
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.30/0.47 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(complementUnionInPowersetComplement_type,type,
% 0.30/0.47 complementUnionInPowersetComplement: $o ).
% 0.30/0.47
% 0.30/0.47 thf(complementUnionInPowersetComplement,definition,
% 0.30/0.47 ( complementUnionInPowersetComplement
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(demorgan2a2_type,type,
% 0.30/0.47 demorgan2a2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(demorgan2a2,definition,
% 0.30/0.47 ( demorgan2a2
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.30/0.47 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(demorgan1a_type,type,
% 0.30/0.47 demorgan1a: $o ).
% 0.30/0.47
% 0.30/0.47 thf(demorgan1a,definition,
% 0.30/0.47 ( demorgan1a
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 0.30/0.47 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(demorgan1b_type,type,
% 0.30/0.47 demorgan1b: $o ).
% 0.30/0.47
% 0.30/0.47 thf(demorgan1b,definition,
% 0.30/0.47 ( demorgan1b
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.30/0.47 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(demorgan1_type,type,
% 0.30/0.47 demorgan1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(demorgan1,definition,
% 0.30/0.47 ( demorgan1
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 0.30/0.47 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(demorgan2a_type,type,
% 0.30/0.47 demorgan2a: $o ).
% 0.30/0.47
% 0.30/0.47 thf(demorgan2a,definition,
% 0.30/0.47 ( demorgan2a
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.30/0.47 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(demorgan2b2_type,type,
% 0.30/0.47 demorgan2b2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(demorgan2b2,definition,
% 0.30/0.47 ( demorgan2b2
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.30/0.47 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 0.30/0.47 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(demorgan2b_type,type,
% 0.30/0.47 demorgan2b: $o ).
% 0.30/0.47
% 0.30/0.47 thf(demorgan2b,definition,
% 0.30/0.47 ( demorgan2b
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.30/0.47 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(demorgan2_type,type,
% 0.30/0.47 demorgan2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(demorgan2,definition,
% 0.30/0.47 ( demorgan2
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 0.30/0.47 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(woz13rule0_type,type,
% 0.30/0.47 woz13rule0: $o ).
% 0.30/0.47
% 0.30/0.47 thf(woz13rule0,definition,
% 0.30/0.47 ( woz13rule0
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.30/0.47 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(woz13rule1_type,type,
% 0.30/0.47 woz13rule1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(woz13rule1,definition,
% 0.30/0.47 ( woz13rule1
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Z: $i] :
% 0.30/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.30/0.47 => ( ( subset @ X @ Z )
% 0.30/0.47 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(woz13rule2_type,type,
% 0.30/0.47 woz13rule2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(woz13rule2,definition,
% 0.30/0.47 ( woz13rule2
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Z: $i] :
% 0.30/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.30/0.47 => ( ( subset @ Y @ Z )
% 0.30/0.47 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(woz13rule3_type,type,
% 0.30/0.47 woz13rule3: $o ).
% 0.30/0.47
% 0.30/0.47 thf(woz13rule3,definition,
% 0.30/0.47 ( woz13rule3
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Z: $i] :
% 0.30/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.30/0.47 => ( ( subset @ X @ Y )
% 0.30/0.47 => ( ( subset @ X @ Z )
% 0.30/0.47 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(woz13rule4_type,type,
% 0.30/0.47 woz13rule4: $o ).
% 0.30/0.47
% 0.30/0.47 thf(woz13rule4,definition,
% 0.30/0.47 ( woz13rule4
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Z: $i] :
% 0.30/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.30/0.47 => ! [W: $i] :
% 0.30/0.47 ( ( in @ W @ ( powerset @ A ) )
% 0.30/0.47 => ( ( subset @ X @ Z )
% 0.30/0.47 => ( ( subset @ Y @ W )
% 0.30/0.47 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(woz1_1_type,type,
% 0.30/0.47 woz1_1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(woz1_1,definition,
% 0.30/0.47 ( woz1_1
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(woz1_2_type,type,
% 0.30/0.47 woz1_2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(woz1_2,definition,
% 0.30/0.47 ( woz1_2
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Z: $i] :
% 0.30/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.30/0.47 => ! [W: $i] :
% 0.30/0.47 ( ( in @ W @ ( powerset @ A ) )
% 0.30/0.47 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 0.30/0.47 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(woz1_3_type,type,
% 0.30/0.47 woz1_3: $o ).
% 0.30/0.47
% 0.30/0.47 thf(woz1_3,definition,
% 0.30/0.47 ( woz1_3
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ! [Z: $i] :
% 0.30/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.30/0.47 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(woz1_4_type,type,
% 0.30/0.47 woz1_4: $o ).
% 0.30/0.47
% 0.30/0.47 thf(woz1_4,definition,
% 0.30/0.47 ( woz1_4
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.30/0.47 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(woz1_5_type,type,
% 0.30/0.47 woz1_5: $o ).
% 0.30/0.47
% 0.30/0.47 thf(woz1_5,definition,
% 0.30/0.47 ( woz1_5
% 0.30/0.47 = ( ! [A: $i,X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.47 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(breln1_type,type,
% 0.30/0.47 breln1: $i > $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(breln1all2_type,type,
% 0.30/0.47 breln1all2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(breln1all2,definition,
% 0.30/0.47 ( breln1all2
% 0.30/0.47 = ( ! [A: $i,R: $i] :
% 0.30/0.47 ( ( breln1 @ A @ R )
% 0.30/0.47 => ! [Xphi: $i > $o] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.30/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ R )
% 0.30/0.47 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(breln1Set_type,type,
% 0.30/0.47 breln1Set: $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(breln1SetBreln1_type,type,
% 0.30/0.47 breln1SetBreln1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(breln1SetBreln1,definition,
% 0.30/0.47 ( breln1SetBreln1
% 0.30/0.47 = ( ! [A: $i,R: $i] :
% 0.30/0.47 ( ( in @ R @ ( breln1Set @ A ) )
% 0.30/0.47 => ( breln1 @ A @ R ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(transitive_type,type,
% 0.30/0.47 transitive: $i > $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(antisymmetric_type,type,
% 0.30/0.47 antisymmetric: $i > $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(reflexive_type,type,
% 0.30/0.47 reflexive: $i > $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(refltransitive_type,type,
% 0.30/0.47 refltransitive: $i > $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(refllinearorder_type,type,
% 0.30/0.47 refllinearorder: $i > $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(reflwellordering_type,type,
% 0.30/0.47 reflwellordering: $i > $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(choice2fnsingleton_type,type,
% 0.30/0.47 choice2fnsingleton: $o ).
% 0.30/0.47
% 0.30/0.47 thf(choice2fnsingleton,definition,
% 0.30/0.47 ( choice2fnsingleton
% 0.30/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ? [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ B )
% 0.30/0.47 & ( Xphi @ Xx @ Xy ) ) )
% 0.30/0.47 => ! [R: $i] :
% 0.30/0.47 ( ( in @ R @ ( breln1Set @ B ) )
% 0.30/0.47 => ( ( reflwellordering @ B @ R )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( singleton
% 0.30/0.47 @ ( dsetconstr @ B
% 0.30/0.47 @ ^ [Xy: $i] :
% 0.30/0.47 ( ( Xphi @ Xx @ Xy )
% 0.30/0.47 & ! [Xz: $i] :
% 0.30/0.47 ( ( in @ Xz @ B )
% 0.30/0.47 => ( ( Xphi @ Xx @ Xz )
% 0.30/0.47 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setOfPairsIsBReln1_type,type,
% 0.30/0.47 setOfPairsIsBReln1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setOfPairsIsBReln1,definition,
% 0.30/0.47 ( setOfPairsIsBReln1
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 0.30/0.47 ( breln1 @ A
% 0.30/0.47 @ ( dpsetconstr @ A @ A
% 0.30/0.47 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(breln1all1_type,type,
% 0.30/0.47 breln1all1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(breln1all1,definition,
% 0.30/0.47 ( breln1all1
% 0.30/0.47 = ( ! [A: $i,R: $i] :
% 0.30/0.47 ( ( breln1 @ A @ R )
% 0.30/0.47 => ! [Xphi: $i > $o] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.30/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ R )
% 0.30/0.47 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(subbreln1_type,type,
% 0.30/0.47 subbreln1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(subbreln1,definition,
% 0.30/0.47 ( subbreln1
% 0.30/0.47 = ( ! [A: $i,R: $i] :
% 0.30/0.47 ( ( breln1 @ A @ R )
% 0.30/0.47 => ! [S: $i] :
% 0.30/0.47 ( ( breln1 @ A @ S )
% 0.30/0.47 => ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.30/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.30/0.47 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(eqbreln1_type,type,
% 0.30/0.47 eqbreln1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(eqbreln1,definition,
% 0.30/0.47 ( eqbreln1
% 0.30/0.47 = ( ! [A: $i,R: $i] :
% 0.30/0.47 ( ( breln1 @ A @ R )
% 0.30/0.47 => ! [S: $i] :
% 0.30/0.47 ( ( breln1 @ A @ S )
% 0.30/0.47 => ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.30/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.30/0.47 => ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.30/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.30/0.47 => ( R = S ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(breln1invset_type,type,
% 0.30/0.47 breln1invset: $i > $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(breln1invprop_type,type,
% 0.30/0.47 breln1invprop: $o ).
% 0.30/0.47
% 0.30/0.47 thf(breln1invprop,definition,
% 0.30/0.47 ( breln1invprop
% 0.30/0.47 = ( ! [A: $i,R: $i] :
% 0.30/0.47 ( ( breln1 @ A @ R )
% 0.30/0.47 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(breln1invI_type,type,
% 0.30/0.47 breln1invI: $o ).
% 0.30/0.47
% 0.30/0.47 thf(breln1invI,definition,
% 0.30/0.47 ( breln1invI
% 0.30/0.47 = ( ! [A: $i,R: $i] :
% 0.30/0.47 ( ( breln1 @ A @ R )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.30/0.47 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(breln1invE_type,type,
% 0.30/0.47 breln1invE: $o ).
% 0.30/0.47
% 0.30/0.47 thf(breln1invE,definition,
% 0.30/0.47 ( breln1invE
% 0.30/0.47 = ( ! [A: $i,R: $i] :
% 0.30/0.47 ( ( breln1 @ A @ R )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 0.30/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(breln1compset_type,type,
% 0.30/0.47 breln1compset: $i > $i > $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(breln1compprop_type,type,
% 0.30/0.47 breln1compprop: $o ).
% 0.30/0.47
% 0.30/0.47 thf(breln1compprop,definition,
% 0.30/0.47 ( breln1compprop
% 0.30/0.47 = ( ! [A: $i,R: $i] :
% 0.30/0.47 ( ( breln1 @ A @ R )
% 0.30/0.47 => ! [S: $i] :
% 0.30/0.47 ( ( breln1 @ A @ S )
% 0.30/0.47 => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(breln1compI_type,type,
% 0.30/0.47 breln1compI: $o ).
% 0.30/0.47
% 0.30/0.47 thf(breln1compI,definition,
% 0.30/0.47 ( breln1compI
% 0.30/0.47 = ( ! [A: $i,R: $i] :
% 0.30/0.47 ( ( breln1 @ A @ R )
% 0.30/0.47 => ! [S: $i] :
% 0.30/0.47 ( ( breln1 @ A @ S )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ! [Xz: $i] :
% 0.30/0.47 ( ( in @ Xz @ A )
% 0.30/0.47 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.30/0.47 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 0.30/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(breln1compE_type,type,
% 0.30/0.47 breln1compE: $o ).
% 0.30/0.47
% 0.30/0.47 thf(breln1compE,definition,
% 0.30/0.47 ( breln1compE
% 0.30/0.47 = ( ! [A: $i,R: $i] :
% 0.30/0.47 ( ( breln1 @ A @ R )
% 0.30/0.47 => ! [S: $i] :
% 0.30/0.47 ( ( breln1 @ A @ S )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 0.30/0.47 => ? [Xz: $i] :
% 0.30/0.47 ( ( in @ Xz @ A )
% 0.30/0.47 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.30/0.47 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(breln1compEex_type,type,
% 0.30/0.47 breln1compEex: $o ).
% 0.30/0.47
% 0.30/0.47 thf(breln1compEex,definition,
% 0.30/0.47 ( breln1compEex
% 0.30/0.47 = ( ! [A: $i,R: $i] :
% 0.30/0.47 ( ( breln1 @ A @ R )
% 0.30/0.47 => ! [S: $i] :
% 0.30/0.47 ( ( breln1 @ A @ S )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 0.30/0.47 => ! [Xphi: $o] :
% 0.30/0.47 ( ! [Xz: $i] :
% 0.30/0.47 ( ( in @ Xz @ A )
% 0.30/0.47 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.30/0.47 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 0.30/0.47 => Xphi ) ) )
% 0.30/0.47 => Xphi ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(breln1unionprop_type,type,
% 0.30/0.47 breln1unionprop: $o ).
% 0.30/0.47
% 0.30/0.47 thf(breln1unionprop,definition,
% 0.30/0.47 ( breln1unionprop
% 0.30/0.47 = ( ! [A: $i,R: $i] :
% 0.30/0.47 ( ( breln1 @ A @ R )
% 0.30/0.47 => ! [S: $i] :
% 0.30/0.47 ( ( breln1 @ A @ S )
% 0.30/0.47 => ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(breln1unionIL_type,type,
% 0.30/0.47 breln1unionIL: $o ).
% 0.30/0.47
% 0.30/0.47 thf(breln1unionIL,definition,
% 0.30/0.47 ( breln1unionIL
% 0.30/0.47 = ( ! [A: $i,R: $i] :
% 0.30/0.47 ( ( breln1 @ A @ R )
% 0.30/0.47 => ! [S: $i] :
% 0.30/0.47 ( ( breln1 @ A @ S )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.30/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(breln1unionIR_type,type,
% 0.30/0.47 breln1unionIR: $o ).
% 0.30/0.47
% 0.30/0.47 thf(breln1unionIR,definition,
% 0.30/0.47 ( breln1unionIR
% 0.30/0.47 = ( ! [A: $i,R: $i] :
% 0.30/0.47 ( ( breln1 @ A @ R )
% 0.30/0.47 => ! [S: $i] :
% 0.30/0.47 ( ( breln1 @ A @ S )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.30/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(breln1unionI_type,type,
% 0.30/0.47 breln1unionI: $o ).
% 0.30/0.47
% 0.30/0.47 thf(breln1unionI,definition,
% 0.30/0.47 ( breln1unionI
% 0.30/0.47 = ( ! [A: $i,R: $i] :
% 0.30/0.47 ( ( breln1 @ A @ R )
% 0.30/0.47 => ! [S: $i] :
% 0.30/0.47 ( ( breln1 @ A @ S )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.30/0.47 | ( in @ ( kpair @ Xx @ Xy ) @ S ) )
% 0.30/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(breln1unionE_type,type,
% 0.30/0.47 breln1unionE: $o ).
% 0.30/0.47
% 0.30/0.47 thf(breln1unionE,definition,
% 0.30/0.47 ( breln1unionE
% 0.30/0.47 = ( ! [A: $i,R: $i] :
% 0.30/0.47 ( ( breln1 @ A @ R )
% 0.30/0.47 => ! [S: $i] :
% 0.30/0.47 ( ( breln1 @ A @ S )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 0.30/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.30/0.47 | ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(breln1unionEcases_type,type,
% 0.30/0.47 breln1unionEcases: $o ).
% 0.30/0.47
% 0.30/0.47 thf(breln1unionEcases,definition,
% 0.30/0.47 ( breln1unionEcases
% 0.30/0.47 = ( ! [A: $i,R: $i] :
% 0.30/0.47 ( ( breln1 @ A @ R )
% 0.30/0.47 => ! [S: $i] :
% 0.30/0.47 ( ( breln1 @ A @ S )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 0.30/0.47 => ! [Xphi: $o] :
% 0.30/0.47 ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.30/0.47 => Xphi )
% 0.30/0.47 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.30/0.47 => Xphi )
% 0.30/0.47 => Xphi ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(breln1unionCommutes_type,type,
% 0.30/0.47 breln1unionCommutes: $o ).
% 0.30/0.47
% 0.30/0.47 thf(breln1unionCommutes,definition,
% 0.30/0.47 ( breln1unionCommutes
% 0.30/0.47 = ( ! [A: $i,R: $i] :
% 0.30/0.47 ( ( breln1 @ A @ R )
% 0.30/0.47 => ! [S: $i] :
% 0.30/0.47 ( ( breln1 @ A @ S )
% 0.30/0.47 => ( ( binunion @ R @ S )
% 0.30/0.47 = ( binunion @ S @ R ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(woz2Ex_type,type,
% 0.30/0.47 woz2Ex: $o ).
% 0.30/0.47
% 0.30/0.47 thf(woz2Ex,definition,
% 0.30/0.47 ( woz2Ex
% 0.30/0.47 = ( ! [A: $i,R: $i] :
% 0.30/0.47 ( ( breln1 @ A @ R )
% 0.30/0.47 => ( R
% 0.30/0.47 = ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(woz2W_type,type,
% 0.30/0.47 woz2W: $o ).
% 0.30/0.47
% 0.30/0.47 thf(woz2W,definition,
% 0.30/0.47 ( woz2W
% 0.30/0.47 = ( ! [A: $i,R: $i] :
% 0.30/0.47 ( ( breln1 @ A @ R )
% 0.30/0.47 => ! [S: $i] :
% 0.30/0.47 ( ( breln1 @ A @ S )
% 0.30/0.47 => ( ( breln1invset @ A @ ( breln1compset @ A @ R @ S ) )
% 0.30/0.47 = ( breln1compset @ A @ ( breln1invset @ A @ S ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(woz2A_type,type,
% 0.30/0.47 woz2A: $o ).
% 0.30/0.47
% 0.30/0.47 thf(woz2A,definition,
% 0.30/0.47 ( woz2A
% 0.30/0.47 = ( ! [A: $i,R: $i] :
% 0.30/0.47 ( ( breln1 @ A @ R )
% 0.30/0.47 => ! [S: $i] :
% 0.30/0.47 ( ( breln1 @ A @ S )
% 0.30/0.47 => ! [T: $i] :
% 0.30/0.47 ( ( breln1 @ A @ T )
% 0.30/0.47 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 0.30/0.47 = ( binunion @ ( breln1compset @ A @ R @ T ) @ ( breln1compset @ A @ S @ T ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(woz2B_type,type,
% 0.30/0.47 woz2B: $o ).
% 0.30/0.47
% 0.30/0.47 thf(woz2B,definition,
% 0.30/0.47 ( woz2B
% 0.30/0.47 = ( ! [A: $i,R: $i] :
% 0.30/0.47 ( ( breln1 @ A @ R )
% 0.30/0.47 => ! [S: $i] :
% 0.30/0.47 ( ( breln1 @ A @ S )
% 0.30/0.47 => ! [T: $i] :
% 0.30/0.47 ( ( breln1 @ A @ T )
% 0.30/0.47 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 0.30/0.47 = ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ S ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(image1Ex_type,type,
% 0.30/0.47 image1Ex: $o ).
% 0.30/0.47
% 0.30/0.47 thf(image1Ex,definition,
% 0.30/0.47 ( image1Ex
% 0.30/0.47 = ( ! [A: $i,Xf: $i > $i] :
% 0.30/0.47 ? [B: $i] :
% 0.30/0.47 ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ B )
% 0.30/0.47 <=> ? [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 & ( Xx
% 0.30/0.47 = ( Xf @ Xy ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(image1Ex1_type,type,
% 0.30/0.47 image1Ex1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(image1Ex1,definition,
% 0.30/0.47 ( image1Ex1
% 0.30/0.47 = ( ! [A: $i,Xf: $i > $i] :
% 0.30/0.47 ( exu
% 0.30/0.47 @ ^ [B: $i] :
% 0.30/0.47 ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ B )
% 0.30/0.47 <=> ? [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 & ( Xx
% 0.30/0.47 = ( Xf @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(image1_type,type,
% 0.30/0.47 image1: $i > ( $i > $i ) > $i ).
% 0.30/0.47
% 0.30/0.47 thf(image1Equiv_type,type,
% 0.30/0.47 image1Equiv: $o ).
% 0.30/0.47
% 0.30/0.47 thf(image1Equiv,definition,
% 0.30/0.47 ( image1Equiv
% 0.30/0.47 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx
% 0.30/0.47 @ ( image1 @ A
% 0.30/0.47 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 0.30/0.47 <=> ? [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 & ( Xx
% 0.30/0.47 = ( Xf @ Xy ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(image1E_type,type,
% 0.30/0.47 image1E: $o ).
% 0.30/0.47
% 0.30/0.47 thf(image1E,definition,
% 0.30/0.47 ( image1E
% 0.30/0.47 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx
% 0.30/0.47 @ ( image1 @ A
% 0.30/0.47 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 0.30/0.47 => ? [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 & ( Xx
% 0.30/0.47 = ( Xf @ Xy ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(image1I_type,type,
% 0.30/0.47 image1I: $o ).
% 0.30/0.47
% 0.30/0.47 thf(image1I,definition,
% 0.30/0.47 ( image1I
% 0.30/0.47 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 0.30/0.47 ( ? [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 & ( Xx
% 0.30/0.47 = ( Xf @ Xy ) ) )
% 0.30/0.47 => ( in @ Xx
% 0.30/0.47 @ ( image1 @ A
% 0.30/0.47 @ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(injective_type,type,
% 0.30/0.47 injective: $i > $i > $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(injFuncSet_type,type,
% 0.30/0.47 injFuncSet: $i > $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(injFuncInInjFuncSet_type,type,
% 0.30/0.47 injFuncInInjFuncSet: $o ).
% 0.30/0.47
% 0.30/0.47 thf(injFuncInInjFuncSet,definition,
% 0.30/0.47 ( injFuncInInjFuncSet
% 0.30/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.30/0.47 => ( ( injective @ A @ B @ Xf )
% 0.30/0.47 => ( in @ Xf @ ( injFuncSet @ A @ B ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(injFuncSetFuncIn_type,type,
% 0.30/0.47 injFuncSetFuncIn: $o ).
% 0.30/0.47
% 0.30/0.47 thf(injFuncSetFuncIn,definition,
% 0.30/0.47 ( injFuncSetFuncIn
% 0.30/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.47 ( ( in @ Xf @ ( injFuncSet @ A @ B ) )
% 0.30/0.47 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(injFuncSetFuncInj_type,type,
% 0.30/0.47 injFuncSetFuncInj: $o ).
% 0.30/0.47
% 0.30/0.47 thf(injFuncSetFuncInj,definition,
% 0.30/0.47 ( injFuncSetFuncInj
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i,Xf: $i] :
% 0.30/0.47 ( ( in @ Xf @ ( injFuncSet @ Xx @ Xy ) )
% 0.30/0.47 => ( injective @ Xx @ Xy @ Xf ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(surjective_type,type,
% 0.30/0.47 surjective: $i > $i > $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(surjFuncSet_type,type,
% 0.30/0.47 surjFuncSet: $i > $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(surjFuncSetFuncIn_type,type,
% 0.30/0.47 surjFuncSetFuncIn: $o ).
% 0.30/0.47
% 0.30/0.47 thf(surjFuncSetFuncIn,definition,
% 0.30/0.47 ( surjFuncSetFuncIn
% 0.30/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.47 ( ( in @ Xf @ ( surjFuncSet @ A @ B ) )
% 0.30/0.47 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(surjFuncSetFuncSurj_type,type,
% 0.30/0.47 surjFuncSetFuncSurj: $o ).
% 0.30/0.47
% 0.30/0.47 thf(surjFuncSetFuncSurj,definition,
% 0.30/0.47 ( surjFuncSetFuncSurj
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i,Xf: $i] :
% 0.30/0.47 ( ( in @ Xf @ ( surjFuncSet @ Xx @ Xy ) )
% 0.30/0.47 => ( surjective @ Xx @ Xy @ Xf ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(leftInvIsSurj_type,type,
% 0.30/0.47 leftInvIsSurj: $o ).
% 0.30/0.47
% 0.30/0.47 thf(leftInvIsSurj,definition,
% 0.30/0.47 ( leftInvIsSurj
% 0.30/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.30/0.47 => ! [Xg: $i] :
% 0.30/0.47 ( ( in @ Xg @ ( funcSet @ B @ A ) )
% 0.30/0.47 => ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( ap @ B @ A @ Xg @ ( Xf @ Xx ) )
% 0.30/0.47 = Xx ) )
% 0.30/0.47 => ( surjective @ B @ A @ Xg ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(surjCantorThm_type,type,
% 0.30/0.47 surjCantorThm: $o ).
% 0.30/0.47
% 0.30/0.47 thf(surjCantorThm,definition,
% 0.30/0.47 ( surjCantorThm
% 0.30/0.47 = ( ! [A: $i,Xf: $i] :
% 0.30/0.47 ( ( in @ Xf @ ( funcSet @ A @ ( powerset @ A ) ) )
% 0.30/0.47 => ~ ( surjective @ A @ ( powerset @ A ) @ Xf ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(foundation2_type,type,
% 0.30/0.47 foundation2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(foundation2,definition,
% 0.30/0.47 ( foundation2
% 0.30/0.47 = ( ! [A: $i] :
% 0.30/0.47 ( ( nonempty @ A )
% 0.30/0.47 => ? [X: $i] :
% 0.30/0.47 ( ( in @ X @ A )
% 0.30/0.47 & ( ( binintersect @ X @ A )
% 0.30/0.47 = emptyset ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(notinself_type,type,
% 0.30/0.47 notinself: $o ).
% 0.30/0.47
% 0.30/0.47 thf(notinself,definition,
% 0.30/0.47 ( notinself
% 0.30/0.47 = ( ! [A: $i] :
% 0.30/0.47 ~ ( in @ A @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(notinself2_type,type,
% 0.30/0.47 notinself2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(notinself2,definition,
% 0.30/0.47 ( notinself2
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ( in @ A @ B )
% 0.30/0.47 => ~ ( in @ B @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(omegaS_type,type,
% 0.30/0.47 omegaS: $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(omegaSp_type,type,
% 0.30/0.47 omegaSp: $o ).
% 0.30/0.47
% 0.30/0.47 thf(omegaSp,definition,
% 0.30/0.47 ( omegaSp
% 0.30/0.47 = ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ omega )
% 0.30/0.47 => ( in @ ( omegaS @ Xx ) @ omega ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(omegaSclos_type,type,
% 0.30/0.47 omegaSclos: $o ).
% 0.30/0.47
% 0.30/0.47 thf(omegaSclos,definition,
% 0.30/0.47 ( omegaSclos
% 0.30/0.47 = ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ omega )
% 0.30/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(peano0notS_type,type,
% 0.30/0.47 peano0notS: $o ).
% 0.30/0.47
% 0.30/0.47 thf(peano0notS,definition,
% 0.30/0.47 ( peano0notS
% 0.30/0.47 = ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ omega )
% 0.30/0.47 => ( ( omegaS @ Xx )
% 0.30/0.47 != emptyset ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(peano3_type,type,
% 0.30/0.47 peano3: $i > $i > $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(peano4_type,type,
% 0.30/0.47 peano4: $i > $i > $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(peano5_type,type,
% 0.30/0.47 peano5: $i > $i > $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(peanoSinj_type,type,
% 0.30/0.47 peanoSinj: $o ).
% 0.30/0.47
% 0.30/0.47 thf(peanoSinj,definition,
% 0.30/0.47 ( peanoSinj
% 0.30/0.47 = ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ omega )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ omega )
% 0.30/0.47 => ( ( ( omegaS @ Xx )
% 0.30/0.47 = ( omegaS @ Xy ) )
% 0.30/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(peano_type,type,
% 0.30/0.47 peano: $i > $i > $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(transitiveset_type,type,
% 0.30/0.47 transitiveset: $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(transitiveset,definition,
% 0.30/0.47 ( transitiveset
% 0.30/0.47 = ( ^ [A: $i] :
% 0.30/0.47 ! [X: $i] :
% 0.30/0.47 ( ( in @ X @ A )
% 0.30/0.47 => ( subset @ X @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(transitivesetOp1_type,type,
% 0.30/0.47 transitivesetOp1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(transitivesetOp1,definition,
% 0.30/0.47 ( transitivesetOp1
% 0.30/0.47 = ( ! [X: $i] :
% 0.30/0.47 ( ( transitiveset @ X )
% 0.30/0.47 => ! [A: $i] :
% 0.30/0.47 ( ( in @ A @ X )
% 0.30/0.47 => ( subset @ A @ X ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(binintTransitive_type,type,
% 0.30/0.47 binintTransitive: $o ).
% 0.30/0.47
% 0.30/0.47 thf(binintTransitive,definition,
% 0.30/0.47 ( binintTransitive
% 0.30/0.47 = ( ! [X: $i] :
% 0.30/0.47 ( ( transitiveset @ X )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( transitiveset @ Y )
% 0.30/0.47 => ( transitiveset @ ( binintersect @ X @ Y ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(transitivesetOp2_type,type,
% 0.30/0.47 transitivesetOp2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(transitivesetOp2,definition,
% 0.30/0.47 ( transitivesetOp2
% 0.30/0.47 = ( ! [X: $i] :
% 0.30/0.47 ( ( transitiveset @ X )
% 0.30/0.47 => ! [A: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ A @ X )
% 0.30/0.47 => ( ( in @ Xx @ A )
% 0.30/0.47 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setunionTransitive_type,type,
% 0.30/0.47 setunionTransitive: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setunionTransitive,definition,
% 0.30/0.47 ( setunionTransitive
% 0.30/0.47 = ( ! [X: $i] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ X )
% 0.30/0.47 => ( transitiveset @ Xx ) )
% 0.30/0.47 => ( transitiveset @ ( setunion @ X ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(stricttotalorderedByIn_type,type,
% 0.30/0.47 stricttotalorderedByIn: $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(stricttotalorderedByIn,definition,
% 0.30/0.47 ( stricttotalorderedByIn
% 0.30/0.47 = ( ^ [A: $i] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [X: $i] :
% 0.30/0.47 ( ( in @ X @ A )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ A )
% 0.30/0.47 => ( ( ( in @ Xx @ X )
% 0.30/0.47 & ( in @ X @ Y ) )
% 0.30/0.47 => ( in @ Xx @ Y ) ) ) ) )
% 0.30/0.47 & ! [X: $i] :
% 0.30/0.47 ( ( in @ X @ A )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ A )
% 0.30/0.47 => ( ( X = Y )
% 0.30/0.47 | ( in @ X @ Y )
% 0.30/0.47 | ( in @ Y @ X ) ) ) )
% 0.30/0.47 & ! [X: $i] :
% 0.30/0.47 ( ( in @ X @ A )
% 0.30/0.47 => ~ ( in @ X @ X ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(wellorderedByIn_type,type,
% 0.30/0.47 wellorderedByIn: $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(wellorderedByIn,definition,
% 0.30/0.47 ( wellorderedByIn
% 0.30/0.47 = ( ^ [A: $i] :
% 0.30/0.47 ( ( stricttotalorderedByIn @ A )
% 0.30/0.47 & ! [X: $i] :
% 0.30/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.47 => ( ( nonempty @ X )
% 0.30/0.47 => ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ X )
% 0.30/0.47 & ! [Y: $i] :
% 0.30/0.47 ( ( in @ Y @ X )
% 0.30/0.47 => ( ( Xx = Y )
% 0.30/0.47 | ( in @ Xx @ Y ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(ordinal_type,type,
% 0.30/0.47 ordinal: $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(ordinal,definition,
% 0.30/0.47 ( ordinal
% 0.30/0.47 = ( ^ [Xx: $i] :
% 0.30/0.47 ( ( transitiveset @ Xx )
% 0.30/0.47 & ( wellorderedByIn @ Xx ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(limitOrdinal_type,type,
% 0.30/0.47 limitOrdinal: $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(ordinalMinLem1_type,type,
% 0.30/0.47 ordinalMinLem1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(ordinalMinLem1,definition,
% 0.30/0.47 ( ordinalMinLem1
% 0.30/0.47 = ( ! [X: $i] :
% 0.30/0.47 ( ( ordinal @ X )
% 0.30/0.47 => ! [Y: $i] :
% 0.30/0.47 ( ( ordinal @ Y )
% 0.30/0.47 => ( transitiveset @ ( binintersect @ X @ Y ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(ordinalTransSet_type,type,
% 0.30/0.47 ordinalTransSet: $o ).
% 0.30/0.47
% 0.30/0.47 thf(ordinalTransSet,definition,
% 0.30/0.47 ( ordinalTransSet
% 0.30/0.47 = ( ! [X: $i] :
% 0.30/0.47 ( ( ordinal @ X )
% 0.30/0.47 => ! [Xx: $i,A: $i] :
% 0.30/0.47 ( ( in @ A @ X )
% 0.30/0.47 => ( ( in @ Xx @ A )
% 0.30/0.47 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(ordinalTransSet1_type,type,
% 0.30/0.47 ordinalTransSet1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(ordinalTransSet1,definition,
% 0.30/0.47 ( ordinalTransSet1
% 0.30/0.47 = ( ! [X: $i] :
% 0.30/0.47 ( ( ordinal @ X )
% 0.30/0.47 => ! [A: $i] :
% 0.30/0.47 ( ( in @ A @ X )
% 0.30/0.47 => ( subset @ A @ X ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setunionOrdinalLem1,conjecture,
% 0.30/0.47 ( setextAx
% 0.30/0.47 => ( emptysetAx
% 0.30/0.47 => ( setadjoinAx
% 0.30/0.47 => ( powersetAx
% 0.30/0.47 => ( setunionAx
% 0.30/0.47 => ( omega0Ax
% 0.30/0.47 => ( omegaSAx
% 0.30/0.47 => ( omegaIndAx
% 0.30/0.47 => ( replAx
% 0.30/0.47 => ( foundationAx
% 0.30/0.47 => ( wellorderingAx
% 0.30/0.47 => ( descrp
% 0.30/0.47 => ( dsetconstrI
% 0.30/0.47 => ( dsetconstrEL
% 0.30/0.47 => ( dsetconstrER
% 0.30/0.47 => ( exuE1
% 0.30/0.47 => ( prop2setE
% 0.30/0.47 => ( emptysetE
% 0.30/0.47 => ( emptysetimpfalse
% 0.30/0.47 => ( notinemptyset
% 0.30/0.47 => ( exuE3e
% 0.30/0.47 => ( setext
% 0.30/0.47 => ( emptyI
% 0.30/0.47 => ( noeltsimpempty
% 0.30/0.47 => ( setbeta
% 0.30/0.47 => ( nonemptyE1
% 0.30/0.47 => ( nonemptyI
% 0.30/0.47 => ( nonemptyI1
% 0.30/0.47 => ( setadjoinIL
% 0.30/0.47 => ( emptyinunitempty
% 0.30/0.47 => ( setadjoinIR
% 0.30/0.47 => ( setadjoinE
% 0.30/0.47 => ( setadjoinOr
% 0.30/0.47 => ( setoftrueEq
% 0.30/0.47 => ( powersetI
% 0.30/0.47 => ( emptyinPowerset
% 0.30/0.47 => ( emptyInPowerset
% 0.30/0.47 => ( powersetE
% 0.30/0.47 => ( setunionI
% 0.30/0.47 => ( setunionE
% 0.30/0.47 => ( subPowSU
% 0.30/0.47 => ( exuE2
% 0.30/0.47 => ( nonemptyImpWitness
% 0.30/0.47 => ( uniqinunit
% 0.30/0.47 => ( notinsingleton
% 0.30/0.47 => ( eqinunit
% 0.30/0.47 => ( singletonsswitch
% 0.30/0.47 => ( upairsetE
% 0.30/0.47 => ( upairsetIL
% 0.30/0.47 => ( upairsetIR
% 0.30/0.47 => ( emptyE1
% 0.30/0.47 => ( vacuousDall
% 0.30/0.47 => ( quantDeMorgan1
% 0.30/0.47 => ( quantDeMorgan2
% 0.30/0.47 => ( quantDeMorgan3
% 0.30/0.47 => ( quantDeMorgan4
% 0.30/0.47 => ( prop2setI
% 0.30/0.47 => ( prop2set2propI
% 0.30/0.47 => ( notdexE
% 0.30/0.47 => ( notdallE
% 0.30/0.47 => ( exuI1
% 0.30/0.47 => ( exuI3
% 0.30/0.47 => ( exuI2
% 0.30/0.47 => ( inCongP
% 0.30/0.47 => ( in__Cong
% 0.30/0.47 => ( exuE3u
% 0.30/0.47 => ( exu__Cong
% 0.30/0.47 => ( emptyset__Cong
% 0.30/0.47 => ( setadjoin__Cong
% 0.30/0.47 => ( powerset__Cong
% 0.30/0.47 => ( setunion__Cong
% 0.30/0.47 => ( omega__Cong
% 0.30/0.47 => ( exuEu
% 0.30/0.47 => ( descr__Cong
% 0.30/0.47 => ( dsetconstr__Cong
% 0.30/0.47 => ( subsetI1
% 0.30/0.47 => ( eqimpsubset2
% 0.30/0.47 => ( eqimpsubset1
% 0.30/0.47 => ( subsetI2
% 0.30/0.47 => ( emptysetsubset
% 0.30/0.47 => ( subsetE
% 0.30/0.47 => ( subsetE2
% 0.30/0.47 => ( notsubsetI
% 0.30/0.47 => ( notequalI1
% 0.30/0.47 => ( notequalI2
% 0.30/0.47 => ( subsetRefl
% 0.30/0.47 => ( subsetTrans
% 0.30/0.47 => ( setadjoinSub
% 0.30/0.47 => ( setadjoinSub2
% 0.30/0.47 => ( subset2powerset
% 0.30/0.47 => ( setextsub
% 0.30/0.47 => ( subsetemptysetimpeq
% 0.30/0.47 => ( powersetI1
% 0.30/0.47 => ( powersetE1
% 0.30/0.47 => ( inPowerset
% 0.30/0.47 => ( powersetsubset
% 0.30/0.47 => ( sepInPowerset
% 0.30/0.47 => ( sepSubset
% 0.30/0.47 => ( binunionIL
% 0.30/0.47 => ( upairset2IR
% 0.30/0.47 => ( binunionIR
% 0.30/0.47 => ( binunionEcases
% 0.30/0.47 => ( binunionE
% 0.30/0.47 => ( binunionLsub
% 0.30/0.47 => ( binunionRsub
% 0.30/0.47 => ( binintersectI
% 0.30/0.47 => ( binintersectSubset5
% 0.30/0.47 => ( binintersectEL
% 0.30/0.47 => ( binintersectLsub
% 0.30/0.47 => ( binintersectSubset2
% 0.30/0.47 => ( binintersectSubset3
% 0.30/0.47 => ( binintersectER
% 0.30/0.47 => ( disjointsetsI1
% 0.30/0.47 => ( binintersectRsub
% 0.30/0.47 => ( binintersectSubset4
% 0.30/0.47 => ( binintersectSubset1
% 0.30/0.47 => ( bs114d
% 0.30/0.47 => ( setminusI
% 0.30/0.47 => ( setminusEL
% 0.30/0.47 => ( setminusER
% 0.30/0.47 => ( setminusSubset2
% 0.30/0.47 => ( setminusERneg
% 0.30/0.47 => ( setminusELneg
% 0.30/0.47 => ( setminusILneg
% 0.30/0.47 => ( setminusIRneg
% 0.30/0.47 => ( setminusLsub
% 0.30/0.47 => ( setminusSubset1
% 0.30/0.47 => ( symdiffE
% 0.30/0.47 => ( symdiffI1
% 0.30/0.47 => ( symdiffI2
% 0.30/0.47 => ( symdiffIneg1
% 0.30/0.47 => ( symdiffIneg2
% 0.30/0.47 => ( secondinupair
% 0.30/0.47 => ( setukpairIL
% 0.30/0.47 => ( setukpairIR
% 0.30/0.47 => ( kpairiskpair
% 0.30/0.47 => ( kpairp
% 0.30/0.47 => ( singletonsubset
% 0.30/0.47 => ( singletoninpowerset
% 0.30/0.47 => ( singletoninpowunion
% 0.30/0.47 => ( upairset2E
% 0.30/0.47 => ( upairsubunion
% 0.30/0.47 => ( upairinpowunion
% 0.30/0.47 => ( ubforcartprodlem1
% 0.30/0.47 => ( ubforcartprodlem2
% 0.30/0.47 => ( ubforcartprodlem3
% 0.30/0.47 => ( cartprodpairin
% 0.30/0.47 => ( cartprodmempair1
% 0.30/0.47 => ( cartprodmempair
% 0.30/0.47 => ( setunionE2
% 0.30/0.47 => ( setunionsingleton1
% 0.30/0.47 => ( setunionsingleton2
% 0.30/0.47 => ( setunionsingleton
% 0.30/0.47 => ( singletonprop
% 0.30/0.47 => ( ex1E1
% 0.30/0.47 => ( ex1I
% 0.30/0.47 => ( ex1I2
% 0.30/0.47 => ( singletonsuniq
% 0.30/0.47 => ( setukpairinjL1
% 0.30/0.47 => ( kfstsingleton
% 0.30/0.47 => ( theprop
% 0.30/0.47 => ( kfstpairEq
% 0.30/0.47 => ( cartprodfstin
% 0.30/0.47 => ( setukpairinjL2
% 0.30/0.47 => ( setukpairinjL
% 0.30/0.47 => ( setukpairinjR11
% 0.30/0.47 => ( setukpairinjR12
% 0.30/0.47 => ( setukpairinjR1
% 0.30/0.47 => ( upairequniteq
% 0.30/0.47 => ( setukpairinjR2
% 0.30/0.47 => ( setukpairinjR
% 0.30/0.47 => ( ksndsingleton
% 0.30/0.47 => ( ksndpairEq
% 0.30/0.47 => ( kpairsurjEq
% 0.30/0.47 => ( cartprodsndin
% 0.30/0.47 => ( cartprodpairmemEL
% 0.30/0.47 => ( cartprodpairmemER
% 0.30/0.47 => ( cartprodmempaircEq
% 0.30/0.47 => ( cartprodfstpairEq
% 0.30/0.47 => ( cartprodsndpairEq
% 0.30/0.47 => ( cartprodpairsurjEq
% 0.30/0.47 => ( dpsetconstrI
% 0.30/0.47 => ( dpsetconstrSub
% 0.30/0.47 => ( setOfPairsIsBReln
% 0.30/0.47 => ( dpsetconstrERa
% 0.30/0.47 => ( dpsetconstrEL1
% 0.30/0.47 => ( dpsetconstrEL2
% 0.30/0.47 => ( dpsetconstrER
% 0.30/0.47 => ( funcImageSingleton
% 0.30/0.47 => ( apProp
% 0.30/0.47 => ( app
% 0.30/0.47 => ( infuncsetfunc
% 0.30/0.47 => ( ap2p
% 0.30/0.47 => ( funcinfuncset
% 0.30/0.47 => ( lamProp
% 0.30/0.47 => ( lamp
% 0.30/0.47 => ( lam2p
% 0.30/0.47 => ( brelnall1
% 0.30/0.47 => ( brelnall2
% 0.30/0.47 => ( ex1E2
% 0.30/0.47 => ( funcGraphProp1
% 0.30/0.47 => ( funcGraphProp3
% 0.30/0.47 => ( funcGraphProp2
% 0.30/0.47 => ( funcextLem
% 0.30/0.47 => ( funcGraphProp4
% 0.30/0.47 => ( subbreln
% 0.30/0.47 => ( eqbreln
% 0.30/0.47 => ( funcext
% 0.30/0.47 => ( funcext2
% 0.30/0.47 => ( ap2apEq1
% 0.30/0.47 => ( ap2apEq2
% 0.30/0.47 => ( beta1
% 0.30/0.47 => ( eta1
% 0.30/0.47 => ( lam2lamEq
% 0.30/0.47 => ( beta2
% 0.30/0.47 => ( eta2
% 0.30/0.47 => ( iffalseProp1
% 0.30/0.47 => ( iffalseProp2
% 0.30/0.47 => ( iftrueProp1
% 0.30/0.47 => ( iftrueProp2
% 0.30/0.47 => ( ifSingleton
% 0.30/0.47 => ( ifp
% 0.30/0.47 => ( theeq
% 0.30/0.47 => ( iftrue
% 0.30/0.47 => ( iffalse
% 0.30/0.47 => ( iftrueorfalse
% 0.30/0.47 => ( binintersectT_lem
% 0.30/0.47 => ( binunionT_lem
% 0.30/0.47 => ( powersetT_lem
% 0.30/0.47 => ( setminusT_lem
% 0.30/0.47 => ( complementT_lem
% 0.30/0.47 => ( setextT
% 0.30/0.47 => ( subsetTI
% 0.30/0.47 => ( powersetTI1
% 0.30/0.47 => ( powersetTE1
% 0.30/0.47 => ( complementTI1
% 0.30/0.47 => ( complementTE1
% 0.30/0.47 => ( binintersectTELcontra
% 0.30/0.47 => ( binintersectTERcontra
% 0.30/0.47 => ( contrasubsetT
% 0.30/0.47 => ( contrasubsetT1
% 0.30/0.47 => ( contrasubsetT2
% 0.30/0.47 => ( contrasubsetT3
% 0.30/0.47 => ( doubleComplementI1
% 0.30/0.47 => ( doubleComplementE1
% 0.30/0.47 => ( doubleComplementSub1
% 0.30/0.47 => ( doubleComplementSub2
% 0.30/0.47 => ( doubleComplementEq
% 0.30/0.47 => ( complementTnotintersectT
% 0.30/0.47 => ( complementImpComplementIntersect
% 0.30/0.47 => ( complementSubsetComplementIntersect
% 0.30/0.47 => ( complementInPowersetComplementIntersect
% 0.30/0.47 => ( contraSubsetComplement
% 0.30/0.47 => ( complementTcontraSubset
% 0.30/0.47 => ( binunionTILcontra
% 0.30/0.47 => ( binunionTIRcontra
% 0.30/0.47 => ( inIntersectImpInUnion
% 0.30/0.47 => ( inIntersectImpInUnion2
% 0.30/0.47 => ( inIntersectImpInIntersectUnions
% 0.30/0.47 => ( intersectInPowersetIntersectUnions
% 0.30/0.47 => ( inComplementUnionImpNotIn1
% 0.30/0.47 => ( inComplementUnionImpInComplement1
% 0.30/0.47 => ( binunionTE
% 0.30/0.47 => ( binunionTEcontra
% 0.30/0.47 => ( demorgan2a1
% 0.30/0.47 => ( complementUnionInPowersetComplement
% 0.30/0.47 => ( demorgan2a2
% 0.30/0.47 => ( demorgan1a
% 0.30/0.47 => ( demorgan1b
% 0.30/0.47 => ( demorgan1
% 0.30/0.47 => ( demorgan2a
% 0.30/0.47 => ( demorgan2b2
% 0.30/0.47 => ( demorgan2b
% 0.30/0.47 => ( demorgan2
% 0.30/0.47 => ( woz13rule0
% 0.30/0.47 => ( woz13rule1
% 0.30/0.47 => ( woz13rule2
% 0.30/0.47 => ( woz13rule3
% 0.30/0.47 => ( woz13rule4
% 0.30/0.47 => ( woz1_1
% 0.30/0.47 => ( woz1_2
% 0.30/0.47 => ( woz1_3
% 0.30/0.47 => ( woz1_4
% 0.30/0.47 => ( woz1_5
% 0.30/0.47 => ( breln1all2
% 0.30/0.47 => ( breln1SetBreln1
% 0.30/0.47 => ( choice2fnsingleton
% 0.30/0.47 => ( setOfPairsIsBReln1
% 0.30/0.47 => ( breln1all1
% 0.30/0.47 => ( subbreln1
% 0.30/0.47 => ( eqbreln1
% 0.30/0.47 => ( breln1invprop
% 0.30/0.47 => ( breln1invI
% 0.30/0.47 => ( breln1invE
% 0.30/0.47 => ( breln1compprop
% 0.30/0.47 => ( breln1compI
% 0.30/0.47 => ( breln1compE
% 0.30/0.47 => ( breln1compEex
% 0.30/0.47 => ( breln1unionprop
% 0.30/0.47 => ( breln1unionIL
% 0.30/0.47 => ( breln1unionIR
% 0.30/0.47 => ( breln1unionI
% 0.30/0.47 => ( breln1unionE
% 0.30/0.47 => ( breln1unionEcases
% 0.30/0.47 => ( breln1unionCommutes
% 0.30/0.47 => ( woz2Ex
% 0.30/0.47 => ( woz2W
% 0.30/0.47 => ( woz2A
% 0.30/0.47 => ( woz2B
% 0.30/0.47 => ( image1Ex
% 0.30/0.47 => ( image1Ex1
% 0.30/0.47 => ( image1Equiv
% 0.30/0.47 => ( image1E
% 0.30/0.47 => ( image1I
% 0.30/0.47 => ( injFuncInInjFuncSet
% 0.30/0.47 => ( injFuncSetFuncIn
% 0.30/0.47 => ( injFuncSetFuncInj
% 0.30/0.47 => ( surjFuncSetFuncIn
% 0.30/0.47 => ( surjFuncSetFuncSurj
% 0.30/0.47 => ( leftInvIsSurj
% 0.30/0.47 => ( surjCantorThm
% 0.30/0.47 => ( foundation2
% 0.30/0.47 => ( notinself
% 0.30/0.47 => ( notinself2
% 0.30/0.47 => ( omegaSp
% 0.30/0.47 => ( omegaSclos
% 0.30/0.47 => ( peano0notS
% 0.30/0.47 => ( peanoSinj
% 0.30/0.47 => ( transitivesetOp1
% 0.30/0.47 => ( binintTransitive
% 0.30/0.47 => ( transitivesetOp2
% 0.30/0.47 => ( setunionTransitive
% 0.30/0.47 => ( ordinalMinLem1
% 0.30/0.47 => ( ordinalTransSet
% 0.30/0.47 => ( ordinalTransSet1
% 0.30/0.47 => ! [X: $i] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ X )
% 0.30/0.47 => ( ordinal @ Xx ) )
% 0.30/0.47 => ( transitiveset @ ( setunion @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 2.92/1.58 ---- Embedded in THF ---
% 2.92/1.58 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.92/1.58 %%% Generated on Tue Feb 24 12:35:13 EST 2026
% 2.92/1.58 %%% using '$$dhol' embedding, version 1.3.0.
% 2.92/1.58 %%% Logic specification used:
% 2.92/1.58 %%% thf(spec, logic, $$dhol).
% 2.92/1.58
% 2.92/1.58 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.d0DxC7kphv/DTF2DTF20722.p
% See solution above
% 2.92/1.59 ------------------------
% 3.24/1.62 ---- Cleaned THF ---
% 3.24/1.62 thf(in_type,type,
% 3.24/1.62 in: $i > $i > $o ).
% 3.24/1.62
% 3.24/1.62 thf(exu_type,type,
% 3.24/1.62 exu: ( $i > $o ) > $o ).
% 3.24/1.62
% 3.24/1.62 thf(exu,definition,
% 3.24/1.62 ( exu
% 3.24/1.62 = ( ^ [Xphi: $i > $o] :
% 3.24/1.62 ? [Xx: $i] :
% 3.24/1.62 ( ( Xphi @ Xx )
% 3.24/1.62 & ! [Xy: $i] :
% 3.24/1.62 ( ( Xphi @ Xy )
% 3.24/1.62 => ( Xx = Xy ) ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(setextAx_type,type,
% 3.24/1.62 setextAx: $o ).
% 3.24/1.62
% 3.24/1.62 thf(setextAx,definition,
% 3.24/1.62 ( setextAx
% 3.24/1.62 = ( ! [A: $i,B: $i] :
% 3.24/1.62 ( ! [Xx: $i] :
% 3.24/1.62 ( ( in @ Xx @ A )
% 3.24/1.62 <=> ( in @ Xx @ B ) )
% 3.24/1.62 => ( A = B ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(emptyset_type,type,
% 3.24/1.62 emptyset: $i ).
% 3.24/1.62
% 3.24/1.62 thf(emptysetAx_type,type,
% 3.24/1.62 emptysetAx: $o ).
% 3.24/1.62
% 3.24/1.62 thf(emptysetAx,definition,
% 3.24/1.62 ( emptysetAx
% 3.24/1.62 = ( ! [Xx: $i] :
% 3.24/1.62 ~ ( in @ Xx @ emptyset ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(setadjoin_type,type,
% 3.24/1.62 setadjoin: $i > $i > $i ).
% 3.24/1.62
% 3.24/1.62 thf(setadjoinAx_type,type,
% 3.24/1.62 setadjoinAx: $o ).
% 3.24/1.62
% 3.24/1.62 thf(setadjoinAx,definition,
% 3.24/1.62 ( setadjoinAx
% 3.24/1.62 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.24/1.62 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.24/1.62 <=> ( ( Xy = Xx )
% 3.24/1.62 | ( in @ Xy @ A ) ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(powerset_type,type,
% 3.24/1.62 powerset: $i > $i ).
% 3.24/1.62
% 3.24/1.62 thf(powersetAx_type,type,
% 3.24/1.62 powersetAx: $o ).
% 3.24/1.62
% 3.24/1.62 thf(powersetAx,definition,
% 3.24/1.62 ( powersetAx
% 3.24/1.62 = ( ! [A: $i,B: $i] :
% 3.24/1.62 ( ( in @ B @ ( powerset @ A ) )
% 3.24/1.62 <=> ! [Xx: $i] :
% 3.24/1.62 ( ( in @ Xx @ B )
% 3.24/1.62 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(setunion_type,type,
% 3.24/1.62 setunion: $i > $i ).
% 3.24/1.62
% 3.24/1.62 thf(setunionAx_type,type,
% 3.24/1.62 setunionAx: $o ).
% 3.24/1.62
% 3.24/1.62 thf(setunionAx,definition,
% 3.24/1.62 ( setunionAx
% 3.24/1.62 = ( ! [A: $i,Xx: $i] :
% 3.24/1.62 ( ( in @ Xx @ ( setunion @ A ) )
% 3.24/1.62 <=> ? [B: $i] :
% 3.24/1.62 ( ( in @ Xx @ B )
% 3.24/1.62 & ( in @ B @ A ) ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(omega_type,type,
% 3.24/1.62 omega: $i ).
% 3.24/1.62
% 3.24/1.62 thf(omega0Ax_type,type,
% 3.24/1.62 omega0Ax: $o ).
% 3.24/1.62
% 3.24/1.62 thf(omega0Ax,definition,
% 3.24/1.62 ( omega0Ax
% 3.24/1.62 = ( in @ emptyset @ omega ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(omegaSAx_type,type,
% 3.24/1.62 omegaSAx: $o ).
% 3.24/1.62
% 3.24/1.62 thf(omegaSAx,definition,
% 3.24/1.62 ( omegaSAx
% 3.24/1.62 = ( ! [Xx: $i] :
% 3.24/1.62 ( ( in @ Xx @ omega )
% 3.24/1.62 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(omegaIndAx_type,type,
% 3.24/1.62 omegaIndAx: $o ).
% 3.24/1.62
% 3.24/1.62 thf(omegaIndAx,definition,
% 3.24/1.62 ( omegaIndAx
% 3.24/1.62 = ( ! [A: $i] :
% 3.24/1.62 ( ( ( in @ emptyset @ A )
% 3.24/1.62 & ! [Xx: $i] :
% 3.24/1.62 ( ( ( in @ Xx @ omega )
% 3.24/1.62 & ( in @ Xx @ A ) )
% 3.24/1.62 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 3.24/1.62 => ! [Xx: $i] :
% 3.24/1.62 ( ( in @ Xx @ omega )
% 3.24/1.62 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(replAx_type,type,
% 3.24/1.62 replAx: $o ).
% 3.24/1.62
% 3.24/1.62 thf(replAx,definition,
% 3.24/1.62 ( replAx
% 3.24/1.62 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 3.24/1.62 ( ! [Xx: $i] :
% 3.24/1.62 ( ( in @ Xx @ A )
% 3.24/1.62 => ( exu
% 3.24/1.62 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 3.24/1.62 => ? [B: $i] :
% 3.24/1.62 ! [Xx: $i] :
% 3.24/1.62 ( ( in @ Xx @ B )
% 3.24/1.62 <=> ? [Xy: $i] :
% 3.24/1.62 ( ( in @ Xy @ A )
% 3.24/1.62 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(foundationAx_type,type,
% 3.24/1.62 foundationAx: $o ).
% 3.24/1.62
% 3.24/1.62 thf(foundationAx,definition,
% 3.24/1.62 ( foundationAx
% 3.24/1.62 = ( ! [A: $i] :
% 3.24/1.62 ( ? [Xx: $i] : ( in @ Xx @ A )
% 3.24/1.62 => ? [B: $i] :
% 3.24/1.62 ( ( in @ B @ A )
% 3.24/1.62 & ~ ? [Xx: $i] :
% 3.24/1.62 ( ( in @ Xx @ B )
% 3.24/1.62 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(wellorderingAx_type,type,
% 3.24/1.62 wellorderingAx: $o ).
% 3.24/1.62
% 3.24/1.62 thf(wellorderingAx,definition,
% 3.24/1.62 ( wellorderingAx
% 3.24/1.62 = ( ! [A: $i] :
% 3.24/1.62 ? [B: $i] :
% 3.24/1.62 ( ! [C: $i] :
% 3.24/1.62 ( ( in @ C @ B )
% 3.24/1.62 => ! [Xx: $i] :
% 3.24/1.62 ( ( in @ Xx @ C )
% 3.24/1.62 => ( in @ Xx @ A ) ) )
% 3.24/1.62 & ! [Xx: $i,Xy: $i] :
% 3.24/1.62 ( ( ( in @ Xx @ A )
% 3.24/1.62 & ( in @ Xy @ A ) )
% 3.24/1.62 => ( ! [C: $i] :
% 3.24/1.62 ( ( in @ C @ B )
% 3.24/1.62 => ( ( in @ Xx @ C )
% 3.24/1.62 <=> ( in @ Xy @ C ) ) )
% 3.24/1.62 => ( Xx = Xy ) ) )
% 3.24/1.62 & ! [C: $i,D: $i] :
% 3.24/1.62 ( ( ( in @ C @ B )
% 3.24/1.62 & ( in @ D @ B ) )
% 3.24/1.62 => ( ! [Xx: $i] :
% 3.24/1.62 ( ( in @ Xx @ C )
% 3.24/1.62 => ( in @ Xx @ D ) )
% 3.24/1.62 | ! [Xx: $i] :
% 3.24/1.62 ( ( in @ Xx @ D )
% 3.24/1.62 => ( in @ Xx @ C ) ) ) )
% 3.24/1.62 & ! [C: $i] :
% 3.24/1.62 ( ( ! [Xx: $i] :
% 3.24/1.62 ( ( in @ Xx @ C )
% 3.24/1.62 => ( in @ Xx @ A ) )
% 3.24/1.62 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 3.24/1.62 => ? [D: $i,Xx: $i] :
% 3.24/1.62 ( ( in @ D @ B )
% 3.24/1.62 & ( in @ Xx @ C )
% 3.24/1.62 & ~ ? [Xy: $i] :
% 3.24/1.62 ( ( in @ Xy @ D )
% 3.24/1.62 & ( in @ Xy @ C ) )
% 3.24/1.62 & ! [E: $i] :
% 3.24/1.62 ( ( in @ E @ B )
% 3.24/1.62 => ( ! [Xy: $i] :
% 3.24/1.62 ( ( in @ Xy @ E )
% 3.24/1.62 => ( in @ Xy @ D ) )
% 3.24/1.62 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(descr_type,type,
% 3.24/1.62 descr: ( $i > $o ) > $i ).
% 3.24/1.62
% 3.24/1.62 thf(descrp_type,type,
% 3.24/1.62 descrp: $o ).
% 3.24/1.62
% 3.24/1.62 thf(descrp,definition,
% 3.24/1.62 ( descrp
% 3.24/1.62 = ( ! [Xphi: $i > $o] :
% 3.24/1.62 ( ( exu
% 3.24/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.24/1.62 => ( Xphi
% 3.24/1.62 @ ( descr
% 3.24/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(dsetconstr_type,type,
% 3.24/1.62 dsetconstr: $i > ( $i > $o ) > $i ).
% 3.24/1.62
% 3.24/1.62 thf(dsetconstrI_type,type,
% 3.24/1.62 dsetconstrI: $o ).
% 3.24/1.62
% 3.24/1.62 thf(dsetconstrI,definition,
% 3.24/1.62 ( dsetconstrI
% 3.24/1.62 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.24/1.62 ( ( in @ Xx @ A )
% 3.24/1.62 => ( ( Xphi @ Xx )
% 3.24/1.62 => ( in @ Xx
% 3.24/1.62 @ ( dsetconstr @ A
% 3.24/1.62 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(dsetconstrEL_type,type,
% 3.24/1.62 dsetconstrEL: $o ).
% 3.24/1.62
% 3.24/1.62 thf(dsetconstrEL,definition,
% 3.24/1.62 ( dsetconstrEL
% 3.24/1.62 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.24/1.62 ( ( in @ Xx
% 3.24/1.62 @ ( dsetconstr @ A
% 3.24/1.62 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.24/1.62 => ( in @ Xx @ A ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(dsetconstrER_type,type,
% 3.24/1.62 dsetconstrER: $o ).
% 3.24/1.62
% 3.24/1.62 thf(dsetconstrER,definition,
% 3.24/1.62 ( dsetconstrER
% 3.24/1.62 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.24/1.62 ( ( in @ Xx
% 3.24/1.62 @ ( dsetconstr @ A
% 3.24/1.62 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.24/1.62 => ( Xphi @ Xx ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(exuE1_type,type,
% 3.24/1.62 exuE1: $o ).
% 3.24/1.62
% 3.24/1.62 thf(exuE1,definition,
% 3.24/1.62 ( exuE1
% 3.24/1.62 = ( ! [Xphi: $i > $o] :
% 3.24/1.62 ( ( exu
% 3.24/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.24/1.62 => ? [Xx: $i] :
% 3.24/1.62 ( ( Xphi @ Xx )
% 3.24/1.62 & ! [Xy: $i] :
% 3.24/1.62 ( ( Xphi @ Xy )
% 3.24/1.62 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(prop2set_type,type,
% 3.24/1.62 prop2set: $o > $i ).
% 3.24/1.62
% 3.24/1.62 thf(prop2setE_type,type,
% 3.24/1.62 prop2setE: $o ).
% 3.24/1.62
% 3.24/1.62 thf(prop2setE,definition,
% 3.24/1.62 ( prop2setE
% 3.24/1.62 = ( ! [Xphi: $o,Xx: $i] :
% 3.24/1.62 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 3.24/1.62 => Xphi ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(emptysetE_type,type,
% 3.24/1.62 emptysetE: $o ).
% 3.24/1.62
% 3.24/1.62 thf(emptysetE,definition,
% 3.24/1.62 ( emptysetE
% 3.24/1.62 = ( ! [Xx: $i] :
% 3.24/1.62 ( ( in @ Xx @ emptyset )
% 3.24/1.62 => ! [Xphi: $o] : Xphi ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(emptysetimpfalse_type,type,
% 3.24/1.62 emptysetimpfalse: $o ).
% 3.24/1.62
% 3.24/1.62 thf(emptysetimpfalse,definition,
% 3.24/1.62 ( emptysetimpfalse
% 3.24/1.62 = ( ! [Xx: $i] :
% 3.24/1.62 ( ( in @ Xx @ emptyset )
% 3.24/1.62 => $false ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(notinemptyset_type,type,
% 3.24/1.62 notinemptyset: $o ).
% 3.24/1.62
% 3.24/1.62 thf(notinemptyset,definition,
% 3.24/1.62 ( notinemptyset
% 3.24/1.62 = ( ! [Xx: $i] :
% 3.24/1.62 ~ ( in @ Xx @ emptyset ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(exuE3e_type,type,
% 3.24/1.62 exuE3e: $o ).
% 3.24/1.62
% 3.24/1.62 thf(exuE3e,definition,
% 3.24/1.62 ( exuE3e
% 3.24/1.62 = ( ! [Xphi: $i > $o] :
% 3.24/1.62 ( ( exu
% 3.24/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.24/1.62 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(setext_type,type,
% 3.24/1.62 setext: $o ).
% 3.24/1.62
% 3.24/1.62 thf(setext,definition,
% 3.24/1.62 ( setext
% 3.24/1.62 = ( ! [A: $i,B: $i] :
% 3.24/1.62 ( ! [Xx: $i] :
% 3.24/1.62 ( ( in @ Xx @ A )
% 3.24/1.62 => ( in @ Xx @ B ) )
% 3.24/1.62 => ( ! [Xx: $i] :
% 3.24/1.62 ( ( in @ Xx @ B )
% 3.24/1.62 => ( in @ Xx @ A ) )
% 3.24/1.62 => ( A = B ) ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(emptyI_type,type,
% 3.24/1.62 emptyI: $o ).
% 3.24/1.62
% 3.24/1.62 thf(emptyI,definition,
% 3.24/1.62 ( emptyI
% 3.24/1.62 = ( ! [A: $i] :
% 3.24/1.62 ( ! [Xx: $i] :
% 3.24/1.62 ~ ( in @ Xx @ A )
% 3.24/1.62 => ( A = emptyset ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(noeltsimpempty_type,type,
% 3.24/1.62 noeltsimpempty: $o ).
% 3.24/1.62
% 3.24/1.62 thf(noeltsimpempty,definition,
% 3.24/1.62 ( noeltsimpempty
% 3.24/1.62 = ( ! [A: $i] :
% 3.24/1.62 ( ! [Xx: $i] :
% 3.24/1.62 ~ ( in @ Xx @ A )
% 3.24/1.62 => ( A = emptyset ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(setbeta_type,type,
% 3.24/1.62 setbeta: $o ).
% 3.24/1.62
% 3.24/1.62 thf(setbeta,definition,
% 3.24/1.62 ( setbeta
% 3.24/1.62 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.24/1.62 ( ( in @ Xx @ A )
% 3.24/1.62 => ( ( in @ Xx
% 3.24/1.62 @ ( dsetconstr @ A
% 3.24/1.62 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.24/1.62 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(nonempty_type,type,
% 3.24/1.62 nonempty: $i > $o ).
% 3.24/1.62
% 3.24/1.62 thf(nonempty,definition,
% 3.24/1.62 ( nonempty
% 3.24/1.62 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(nonemptyE1_type,type,
% 3.24/1.62 nonemptyE1: $o ).
% 3.24/1.62
% 3.24/1.62 thf(nonemptyE1,definition,
% 3.24/1.62 ( nonemptyE1
% 3.24/1.62 = ( ! [A: $i] :
% 3.24/1.62 ( ( nonempty @ A )
% 3.24/1.62 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(nonemptyI_type,type,
% 3.24/1.62 nonemptyI: $o ).
% 3.24/1.62
% 3.24/1.62 thf(nonemptyI,definition,
% 3.24/1.62 ( nonemptyI
% 3.24/1.62 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.24/1.62 ( ( in @ Xx @ A )
% 3.24/1.62 => ( ( Xphi @ Xx )
% 3.24/1.62 => ( nonempty
% 3.24/1.62 @ ( dsetconstr @ A
% 3.24/1.62 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(nonemptyI1_type,type,
% 3.24/1.62 nonemptyI1: $o ).
% 3.24/1.62
% 3.24/1.62 thf(nonemptyI1,definition,
% 3.24/1.62 ( nonemptyI1
% 3.24/1.62 = ( ! [A: $i] :
% 3.24/1.62 ( ? [Xx: $i] : ( in @ Xx @ A )
% 3.24/1.62 => ( nonempty @ A ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(setadjoinIL_type,type,
% 3.24/1.62 setadjoinIL: $o ).
% 3.24/1.62
% 3.24/1.62 thf(setadjoinIL,definition,
% 3.24/1.62 ( setadjoinIL
% 3.24/1.62 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(emptyinunitempty_type,type,
% 3.24/1.62 emptyinunitempty: $o ).
% 3.24/1.62
% 3.24/1.62 thf(emptyinunitempty,definition,
% 3.24/1.62 ( emptyinunitempty
% 3.24/1.62 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(setadjoinIR_type,type,
% 3.24/1.62 setadjoinIR: $o ).
% 3.24/1.62
% 3.24/1.62 thf(setadjoinIR,definition,
% 3.24/1.62 ( setadjoinIR
% 3.24/1.62 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.24/1.62 ( ( in @ Xy @ A )
% 3.24/1.62 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(setadjoinE_type,type,
% 3.24/1.62 setadjoinE: $o ).
% 3.24/1.62
% 3.24/1.62 thf(setadjoinE,definition,
% 3.24/1.62 ( setadjoinE
% 3.24/1.62 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.24/1.62 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.24/1.62 => ! [Xphi: $o] :
% 3.24/1.62 ( ( ( Xy = Xx )
% 3.24/1.62 => Xphi )
% 3.24/1.62 => ( ( ( in @ Xy @ A )
% 3.24/1.62 => Xphi )
% 3.24/1.62 => Xphi ) ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(setadjoinOr_type,type,
% 3.24/1.62 setadjoinOr: $o ).
% 3.24/1.62
% 3.24/1.62 thf(setadjoinOr,definition,
% 3.24/1.62 ( setadjoinOr
% 3.24/1.62 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.24/1.62 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.24/1.62 => ( ( Xy = Xx )
% 3.24/1.62 | ( in @ Xy @ A ) ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(setoftrueEq_type,type,
% 3.24/1.62 setoftrueEq: $o ).
% 3.24/1.62
% 3.24/1.62 thf(setoftrueEq,definition,
% 3.24/1.62 ( setoftrueEq
% 3.24/1.62 = ( ! [A: $i] :
% 3.24/1.62 ( ( dsetconstr @ A
% 3.24/1.62 @ ^ [Xx: $i] : $true )
% 3.24/1.62 = A ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(powersetI_type,type,
% 3.24/1.62 powersetI: $o ).
% 3.24/1.62
% 3.24/1.62 thf(powersetI,definition,
% 3.24/1.62 ( powersetI
% 3.24/1.62 = ( ! [A: $i,B: $i] :
% 3.24/1.62 ( ! [Xx: $i] :
% 3.24/1.62 ( ( in @ Xx @ B )
% 3.24/1.62 => ( in @ Xx @ A ) )
% 3.24/1.62 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(emptyinPowerset_type,type,
% 3.24/1.62 emptyinPowerset: $o ).
% 3.24/1.62
% 3.24/1.62 thf(emptyinPowerset,definition,
% 3.24/1.62 ( emptyinPowerset
% 3.24/1.62 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(emptyInPowerset_type,type,
% 3.24/1.62 emptyInPowerset: $o ).
% 3.24/1.62
% 3.24/1.62 thf(emptyInPowerset,definition,
% 3.24/1.62 ( emptyInPowerset
% 3.24/1.62 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(powersetE_type,type,
% 3.24/1.62 powersetE: $o ).
% 3.24/1.62
% 3.24/1.62 thf(powersetE,definition,
% 3.24/1.62 ( powersetE
% 3.24/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.62 ( ( in @ B @ ( powerset @ A ) )
% 3.24/1.62 => ( ( in @ Xx @ B )
% 3.24/1.62 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(setunionI_type,type,
% 3.24/1.62 setunionI: $o ).
% 3.24/1.62
% 3.24/1.62 thf(setunionI,definition,
% 3.24/1.62 ( setunionI
% 3.24/1.62 = ( ! [A: $i,Xx: $i,B: $i] :
% 3.24/1.62 ( ( in @ Xx @ B )
% 3.24/1.62 => ( ( in @ B @ A )
% 3.24/1.62 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(setunionE_type,type,
% 3.24/1.62 setunionE: $o ).
% 3.24/1.62
% 3.24/1.62 thf(setunionE,definition,
% 3.24/1.62 ( setunionE
% 3.24/1.62 = ( ! [A: $i,Xx: $i] :
% 3.24/1.62 ( ( in @ Xx @ ( setunion @ A ) )
% 3.24/1.62 => ! [Xphi: $o] :
% 3.24/1.62 ( ! [B: $i] :
% 3.24/1.62 ( ( in @ Xx @ B )
% 3.24/1.62 => ( ( in @ B @ A )
% 3.24/1.62 => Xphi ) )
% 3.24/1.62 => Xphi ) ) ) ) ).
% 3.24/1.62
% 3.24/1.62 thf(subPowSU_type,type,
% 3.24/1.62 subPowSU: $o ).
% 3.24/1.62
% 3.24/1.62 thf(subPowSU,definition,
% 3.24/1.62 ( subPowSU
% 3.24/1.62 = ( ! [A: $i,Xx: $i] :
% 3.24/1.62 ( ( in @ Xx @ A )
% 3.24/1.62 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(exuE2_type,type,
% 3.24/1.63 exuE2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(exuE2,definition,
% 3.24/1.63 ( exuE2
% 3.24/1.63 = ( ! [Xphi: $i > $o] :
% 3.24/1.63 ( ( exu
% 3.24/1.63 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.24/1.63 => ? [Xx: $i] :
% 3.24/1.63 ! [Xy: $i] :
% 3.24/1.63 ( ( Xphi @ Xy )
% 3.24/1.63 <=> ( Xy = Xx ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(nonemptyImpWitness_type,type,
% 3.24/1.63 nonemptyImpWitness: $o ).
% 3.24/1.63
% 3.24/1.63 thf(nonemptyImpWitness,definition,
% 3.24/1.63 ( nonemptyImpWitness
% 3.24/1.63 = ( ! [A: $i] :
% 3.24/1.63 ( ( nonempty @ A )
% 3.24/1.63 => ? [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 & $true ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(uniqinunit_type,type,
% 3.24/1.63 uniqinunit: $o ).
% 3.24/1.63
% 3.24/1.63 thf(uniqinunit,definition,
% 3.24/1.63 ( uniqinunit
% 3.24/1.63 = ( ! [Xx: $i,Xy: $i] :
% 3.24/1.63 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.24/1.63 => ( Xx = Xy ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(notinsingleton_type,type,
% 3.24/1.63 notinsingleton: $o ).
% 3.24/1.63
% 3.24/1.63 thf(notinsingleton,definition,
% 3.24/1.63 ( notinsingleton
% 3.24/1.63 = ( ! [Xx: $i,Xy: $i] :
% 3.24/1.63 ( ( Xx != Xy )
% 3.24/1.63 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(eqinunit_type,type,
% 3.24/1.63 eqinunit: $o ).
% 3.24/1.63
% 3.24/1.63 thf(eqinunit,definition,
% 3.24/1.63 ( eqinunit
% 3.24/1.63 = ( ! [Xx: $i,Xy: $i] :
% 3.24/1.63 ( ( Xx = Xy )
% 3.24/1.63 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(singletonsswitch_type,type,
% 3.24/1.63 singletonsswitch: $o ).
% 3.24/1.63
% 3.24/1.63 thf(singletonsswitch,definition,
% 3.24/1.63 ( singletonsswitch
% 3.24/1.63 = ( ! [Xx: $i,Xy: $i] :
% 3.24/1.63 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.24/1.63 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(upairsetE_type,type,
% 3.24/1.63 upairsetE: $o ).
% 3.24/1.63
% 3.24/1.63 thf(upairsetE,definition,
% 3.24/1.63 ( upairsetE
% 3.24/1.63 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.24/1.63 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 3.24/1.63 => ( ( Xz = Xx )
% 3.24/1.63 | ( Xz = Xy ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(upairsetIL_type,type,
% 3.24/1.63 upairsetIL: $o ).
% 3.24/1.63
% 3.24/1.63 thf(upairsetIL,definition,
% 3.24/1.63 ( upairsetIL
% 3.24/1.63 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(upairsetIR_type,type,
% 3.24/1.63 upairsetIR: $o ).
% 3.24/1.63
% 3.24/1.63 thf(upairsetIR,definition,
% 3.24/1.63 ( upairsetIR
% 3.24/1.63 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(emptyE1_type,type,
% 3.24/1.63 emptyE1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(emptyE1,definition,
% 3.24/1.63 ( emptyE1
% 3.24/1.63 = ( ! [A: $i,Xphi: $i > $o] :
% 3.24/1.63 ( ? [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 & ( Xphi @ Xx ) )
% 3.24/1.63 => ( ( ( dsetconstr @ A
% 3.24/1.63 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.24/1.63 = emptyset )
% 3.24/1.63 => $false ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(vacuousDall_type,type,
% 3.24/1.63 vacuousDall: $o ).
% 3.24/1.63
% 3.24/1.63 thf(vacuousDall,definition,
% 3.24/1.63 ( vacuousDall
% 3.24/1.63 = ( ! [Xphi: $i > $o,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ emptyset )
% 3.24/1.63 => ( Xphi @ Xx ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(quantDeMorgan1_type,type,
% 3.24/1.63 quantDeMorgan1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(quantDeMorgan1,definition,
% 3.24/1.63 ( quantDeMorgan1
% 3.24/1.63 = ( ! [A: $i,Xphi: $i > $o] :
% 3.24/1.63 ( ~ ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( Xphi @ Xx ) )
% 3.24/1.63 => ? [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(quantDeMorgan2_type,type,
% 3.24/1.63 quantDeMorgan2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(quantDeMorgan2,definition,
% 3.24/1.63 ( quantDeMorgan2
% 3.24/1.63 = ( ! [A: $i,Xphi: $i > $o] :
% 3.24/1.63 ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ~ ( Xphi @ Xx ) )
% 3.24/1.63 => ~ ? [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 & ( Xphi @ Xx ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(quantDeMorgan3_type,type,
% 3.24/1.63 quantDeMorgan3: $o ).
% 3.24/1.63
% 3.24/1.63 thf(quantDeMorgan3,definition,
% 3.24/1.63 ( quantDeMorgan3
% 3.24/1.63 = ( ! [A: $i,Xphi: $i > $o] :
% 3.24/1.63 ( ~ ? [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 & ( Xphi @ Xx ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(quantDeMorgan4_type,type,
% 3.24/1.63 quantDeMorgan4: $o ).
% 3.24/1.63
% 3.24/1.63 thf(quantDeMorgan4,definition,
% 3.24/1.63 ( quantDeMorgan4
% 3.24/1.63 = ( ! [A: $i,Xphi: $i > $o] :
% 3.24/1.63 ( ? [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 & ~ ( Xphi @ Xx ) )
% 3.24/1.63 => ~ ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( Xphi @ Xx ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(prop2setI_type,type,
% 3.24/1.63 prop2setI: $o ).
% 3.24/1.63
% 3.24/1.63 thf(prop2setI,definition,
% 3.24/1.63 ( prop2setI
% 3.24/1.63 = ( ! [Xphi: $o] :
% 3.24/1.63 ( Xphi
% 3.24/1.63 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(set2prop_type,type,
% 3.24/1.63 set2prop: $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(prop2set2propI_type,type,
% 3.24/1.63 prop2set2propI: $o ).
% 3.24/1.63
% 3.24/1.63 thf(prop2set2propI,definition,
% 3.24/1.63 ( prop2set2propI
% 3.24/1.63 = ( ! [Xphi: $o] :
% 3.24/1.63 ( Xphi
% 3.24/1.63 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(notdexE_type,type,
% 3.24/1.63 notdexE: $o ).
% 3.24/1.63
% 3.24/1.63 thf(notdexE,definition,
% 3.24/1.63 ( notdexE
% 3.24/1.63 = ( ! [A: $i,Xphi: $i > $o] :
% 3.24/1.63 ( ~ ? [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 & ( Xphi @ Xx ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(notdallE_type,type,
% 3.24/1.63 notdallE: $o ).
% 3.24/1.63
% 3.24/1.63 thf(notdallE,definition,
% 3.24/1.63 ( notdallE
% 3.24/1.63 = ( ! [A: $i,Xphi: $i > $o] :
% 3.24/1.63 ( ~ ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( Xphi @ Xx ) )
% 3.24/1.63 => ? [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(exuI1_type,type,
% 3.24/1.63 exuI1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(exuI1,definition,
% 3.24/1.63 ( exuI1
% 3.24/1.63 = ( ! [Xphi: $i > $o] :
% 3.24/1.63 ( ? [Xx: $i] :
% 3.24/1.63 ( ( Xphi @ Xx )
% 3.24/1.63 & ! [Xy: $i] :
% 3.24/1.63 ( ( Xphi @ Xy )
% 3.24/1.63 => ( Xx = Xy ) ) )
% 3.24/1.63 => ( exu
% 3.24/1.63 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(exuI3_type,type,
% 3.24/1.63 exuI3: $o ).
% 3.24/1.63
% 3.24/1.63 thf(exuI3,definition,
% 3.24/1.63 ( exuI3
% 3.24/1.63 = ( ! [Xphi: $i > $o] :
% 3.24/1.63 ( ? [Xx: $i] : ( Xphi @ Xx )
% 3.24/1.63 => ( ! [Xx: $i,Xy: $i] :
% 3.24/1.63 ( ( Xphi @ Xx )
% 3.24/1.63 => ( ( Xphi @ Xy )
% 3.24/1.63 => ( Xx = Xy ) ) )
% 3.24/1.63 => ( exu
% 3.24/1.63 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(exuI2_type,type,
% 3.24/1.63 exuI2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(exuI2,definition,
% 3.24/1.63 ( exuI2
% 3.24/1.63 = ( ! [Xphi: $i > $o] :
% 3.24/1.63 ( ? [Xx: $i] :
% 3.24/1.63 ! [Xy: $i] :
% 3.24/1.63 ( ( Xphi @ Xy )
% 3.24/1.63 <=> ( Xy = Xx ) )
% 3.24/1.63 => ( exu
% 3.24/1.63 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(inCongP_type,type,
% 3.24/1.63 inCongP: $o ).
% 3.24/1.63
% 3.24/1.63 thf(inCongP,definition,
% 3.24/1.63 ( inCongP
% 3.24/1.63 = ( ! [A: $i,B: $i] :
% 3.24/1.63 ( ( A = B )
% 3.24/1.63 => ! [Xx: $i,Xy: $i] :
% 3.24/1.63 ( ( Xx = Xy )
% 3.24/1.63 => ( ( in @ Xx @ A )
% 3.24/1.63 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(in__Cong_type,type,
% 3.24/1.63 in__Cong: $o ).
% 3.24/1.63
% 3.24/1.63 thf(in__Cong,definition,
% 3.24/1.63 ( in__Cong
% 3.24/1.63 = ( ! [A: $i,B: $i] :
% 3.24/1.63 ( ( A = B )
% 3.24/1.63 => ! [Xx: $i,Xy: $i] :
% 3.24/1.63 ( ( Xx = Xy )
% 3.24/1.63 => ( ( in @ Xx @ A )
% 3.24/1.63 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(exuE3u_type,type,
% 3.24/1.63 exuE3u: $o ).
% 3.24/1.63
% 3.24/1.63 thf(exuE3u,definition,
% 3.24/1.63 ( exuE3u
% 3.24/1.63 = ( ! [Xphi: $i > $o] :
% 3.24/1.63 ( ( exu
% 3.24/1.63 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.24/1.63 => ! [Xx: $i,Xy: $i] :
% 3.24/1.63 ( ( Xphi @ Xx )
% 3.24/1.63 => ( ( Xphi @ Xy )
% 3.24/1.63 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(exu__Cong_type,type,
% 3.24/1.63 exu__Cong: $o ).
% 3.24/1.63
% 3.24/1.63 thf(exu__Cong,definition,
% 3.24/1.63 ( exu__Cong
% 3.24/1.63 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.24/1.63 ( ! [Xx: $i,Xy: $i] :
% 3.24/1.63 ( ( Xx = Xy )
% 3.24/1.63 => ( ( Xphi @ Xx )
% 3.24/1.63 <=> ( Xpsi @ Xy ) ) )
% 3.24/1.63 => ( ( exu
% 3.24/1.63 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.24/1.63 <=> ( exu
% 3.24/1.63 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(emptyset__Cong_type,type,
% 3.24/1.63 emptyset__Cong: $o ).
% 3.24/1.63
% 3.24/1.63 thf(emptyset__Cong,definition,
% 3.24/1.63 ( emptyset__Cong
% 3.24/1.63 = ( emptyset = emptyset ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setadjoin__Cong_type,type,
% 3.24/1.63 setadjoin__Cong: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setadjoin__Cong,definition,
% 3.24/1.63 ( setadjoin__Cong
% 3.24/1.63 = ( ! [Xx: $i,Xy: $i] :
% 3.24/1.63 ( ( Xx = Xy )
% 3.24/1.63 => ! [Xz: $i,Xu: $i] :
% 3.24/1.63 ( ( Xz = Xu )
% 3.24/1.63 => ( ( setadjoin @ Xx @ Xz )
% 3.24/1.63 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(powerset__Cong_type,type,
% 3.24/1.63 powerset__Cong: $o ).
% 3.24/1.63
% 3.24/1.63 thf(powerset__Cong,definition,
% 3.24/1.63 ( powerset__Cong
% 3.24/1.63 = ( ! [A: $i,B: $i] :
% 3.24/1.63 ( ( A = B )
% 3.24/1.63 => ( ( powerset @ A )
% 3.24/1.63 = ( powerset @ B ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setunion__Cong_type,type,
% 3.24/1.63 setunion__Cong: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setunion__Cong,definition,
% 3.24/1.63 ( setunion__Cong
% 3.24/1.63 = ( ! [A: $i,B: $i] :
% 3.24/1.63 ( ( A = B )
% 3.24/1.63 => ( ( setunion @ A )
% 3.24/1.63 = ( setunion @ B ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(omega__Cong_type,type,
% 3.24/1.63 omega__Cong: $o ).
% 3.24/1.63
% 3.24/1.63 thf(omega__Cong,definition,
% 3.24/1.63 ( omega__Cong
% 3.24/1.63 = ( omega = omega ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(exuEu_type,type,
% 3.24/1.63 exuEu: $o ).
% 3.24/1.63
% 3.24/1.63 thf(exuEu,definition,
% 3.24/1.63 ( exuEu
% 3.24/1.63 = ( ! [Xphi: $i > $o] :
% 3.24/1.63 ( ( exu
% 3.24/1.63 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.24/1.63 => ! [Xx: $i,Xy: $i] :
% 3.24/1.63 ( ( Xphi @ Xx )
% 3.24/1.63 => ( ( Xphi @ Xy )
% 3.24/1.63 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(descr__Cong_type,type,
% 3.24/1.63 descr__Cong: $o ).
% 3.24/1.63
% 3.24/1.63 thf(descr__Cong,definition,
% 3.24/1.63 ( descr__Cong
% 3.24/1.63 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.24/1.63 ( ! [Xx: $i,Xy: $i] :
% 3.24/1.63 ( ( Xx = Xy )
% 3.24/1.63 => ( ( Xphi @ Xx )
% 3.24/1.63 <=> ( Xpsi @ Xy ) ) )
% 3.24/1.63 => ( ( exu
% 3.24/1.63 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.24/1.63 => ( ( exu
% 3.24/1.63 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 3.24/1.63 => ( ( descr
% 3.24/1.63 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.24/1.63 = ( descr
% 3.24/1.63 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(dsetconstr__Cong_type,type,
% 3.24/1.63 dsetconstr__Cong: $o ).
% 3.24/1.63
% 3.24/1.63 thf(dsetconstr__Cong,definition,
% 3.24/1.63 ( dsetconstr__Cong
% 3.24/1.63 = ( ! [A: $i,B: $i] :
% 3.24/1.63 ( ( A = B )
% 3.24/1.63 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.24/1.63 ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ B )
% 3.24/1.63 => ( ( Xx = Xy )
% 3.24/1.63 => ( ( Xphi @ Xx )
% 3.24/1.63 <=> ( Xpsi @ Xy ) ) ) ) )
% 3.24/1.63 => ( ( dsetconstr @ A
% 3.24/1.63 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.24/1.63 = ( dsetconstr @ B
% 3.24/1.63 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(subset_type,type,
% 3.24/1.63 subset: $i > $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(disjoint_type,type,
% 3.24/1.63 disjoint: $i > $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(setsmeet_type,type,
% 3.24/1.63 setsmeet: $i > $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(subsetI1_type,type,
% 3.24/1.63 subsetI1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(subsetI1,definition,
% 3.24/1.63 ( subsetI1
% 3.24/1.63 = ( ! [A: $i,B: $i] :
% 3.24/1.63 ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( in @ Xx @ B ) )
% 3.24/1.63 => ( subset @ A @ B ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(eqimpsubset2_type,type,
% 3.24/1.63 eqimpsubset2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(eqimpsubset2,definition,
% 3.24/1.63 ( eqimpsubset2
% 3.24/1.63 = ( ! [A: $i,B: $i] :
% 3.24/1.63 ( ( A = B )
% 3.24/1.63 => ( subset @ B @ A ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(eqimpsubset1_type,type,
% 3.24/1.63 eqimpsubset1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(eqimpsubset1,definition,
% 3.24/1.63 ( eqimpsubset1
% 3.24/1.63 = ( ! [A: $i,B: $i] :
% 3.24/1.63 ( ( A = B )
% 3.24/1.63 => ( subset @ A @ B ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(subsetI2_type,type,
% 3.24/1.63 subsetI2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(subsetI2,definition,
% 3.24/1.63 ( subsetI2
% 3.24/1.63 = ( ! [A: $i,B: $i] :
% 3.24/1.63 ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( in @ Xx @ B ) )
% 3.24/1.63 => ( subset @ A @ B ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(emptysetsubset_type,type,
% 3.24/1.63 emptysetsubset: $o ).
% 3.24/1.63
% 3.24/1.63 thf(emptysetsubset,definition,
% 3.24/1.63 ( emptysetsubset
% 3.24/1.63 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(subsetE_type,type,
% 3.24/1.63 subsetE: $o ).
% 3.24/1.63
% 3.24/1.63 thf(subsetE,definition,
% 3.24/1.63 ( subsetE
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ( subset @ A @ B )
% 3.24/1.63 => ( ( in @ Xx @ A )
% 3.24/1.63 => ( in @ Xx @ B ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(subsetE2_type,type,
% 3.24/1.63 subsetE2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(subsetE2,definition,
% 3.24/1.63 ( subsetE2
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ( subset @ A @ B )
% 3.24/1.63 => ( ~ ( in @ Xx @ B )
% 3.24/1.63 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(notsubsetI_type,type,
% 3.24/1.63 notsubsetI: $o ).
% 3.24/1.63
% 3.24/1.63 thf(notsubsetI,definition,
% 3.24/1.63 ( notsubsetI
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ~ ( in @ Xx @ B )
% 3.24/1.63 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(notequalI1_type,type,
% 3.24/1.63 notequalI1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(notequalI1,definition,
% 3.24/1.63 ( notequalI1
% 3.24/1.63 = ( ! [A: $i,B: $i] :
% 3.24/1.63 ( ~ ( subset @ A @ B )
% 3.24/1.63 => ( A != B ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(notequalI2_type,type,
% 3.24/1.63 notequalI2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(notequalI2,definition,
% 3.24/1.63 ( notequalI2
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ~ ( in @ Xx @ B )
% 3.24/1.63 => ( A != B ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(subsetRefl_type,type,
% 3.24/1.63 subsetRefl: $o ).
% 3.24/1.63
% 3.24/1.63 thf(subsetRefl,definition,
% 3.24/1.63 ( subsetRefl
% 3.24/1.63 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(subsetTrans_type,type,
% 3.24/1.63 subsetTrans: $o ).
% 3.24/1.63
% 3.24/1.63 thf(subsetTrans,definition,
% 3.24/1.63 ( subsetTrans
% 3.24/1.63 = ( ! [A: $i,B: $i,C: $i] :
% 3.24/1.63 ( ( subset @ A @ B )
% 3.24/1.63 => ( ( subset @ B @ C )
% 3.24/1.63 => ( subset @ A @ C ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setadjoinSub_type,type,
% 3.24/1.63 setadjoinSub: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setadjoinSub,definition,
% 3.24/1.63 ( setadjoinSub
% 3.24/1.63 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setadjoinSub2_type,type,
% 3.24/1.63 setadjoinSub2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setadjoinSub2,definition,
% 3.24/1.63 ( setadjoinSub2
% 3.24/1.63 = ( ! [A: $i,Xx: $i,B: $i] :
% 3.24/1.63 ( ( subset @ A @ B )
% 3.24/1.63 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(subset2powerset_type,type,
% 3.24/1.63 subset2powerset: $o ).
% 3.24/1.63
% 3.24/1.63 thf(subset2powerset,definition,
% 3.24/1.63 ( subset2powerset
% 3.24/1.63 = ( ! [A: $i,B: $i] :
% 3.24/1.63 ( ( subset @ A @ B )
% 3.24/1.63 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setextsub_type,type,
% 3.24/1.63 setextsub: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setextsub,definition,
% 3.24/1.63 ( setextsub
% 3.24/1.63 = ( ! [A: $i,B: $i] :
% 3.24/1.63 ( ( subset @ A @ B )
% 3.24/1.63 => ( ( subset @ B @ A )
% 3.24/1.63 => ( A = B ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(subsetemptysetimpeq_type,type,
% 3.24/1.63 subsetemptysetimpeq: $o ).
% 3.24/1.63
% 3.24/1.63 thf(subsetemptysetimpeq,definition,
% 3.24/1.63 ( subsetemptysetimpeq
% 3.24/1.63 = ( ! [A: $i] :
% 3.24/1.63 ( ( subset @ A @ emptyset )
% 3.24/1.63 => ( A = emptyset ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(powersetI1_type,type,
% 3.24/1.63 powersetI1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(powersetI1,definition,
% 3.24/1.63 ( powersetI1
% 3.24/1.63 = ( ! [A: $i,B: $i] :
% 3.24/1.63 ( ( subset @ B @ A )
% 3.24/1.63 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(powersetE1_type,type,
% 3.24/1.63 powersetE1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(powersetE1,definition,
% 3.24/1.63 ( powersetE1
% 3.24/1.63 = ( ! [A: $i,B: $i] :
% 3.24/1.63 ( ( in @ B @ ( powerset @ A ) )
% 3.24/1.63 => ( subset @ B @ A ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(inPowerset_type,type,
% 3.24/1.63 inPowerset: $o ).
% 3.24/1.63
% 3.24/1.63 thf(inPowerset,definition,
% 3.24/1.63 ( inPowerset
% 3.24/1.63 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(powersetsubset_type,type,
% 3.24/1.63 powersetsubset: $o ).
% 3.24/1.63
% 3.24/1.63 thf(powersetsubset,definition,
% 3.24/1.63 ( powersetsubset
% 3.24/1.63 = ( ! [A: $i,B: $i] :
% 3.24/1.63 ( ( subset @ A @ B )
% 3.24/1.63 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(sepInPowerset_type,type,
% 3.24/1.63 sepInPowerset: $o ).
% 3.24/1.63
% 3.24/1.63 thf(sepInPowerset,definition,
% 3.24/1.63 ( sepInPowerset
% 3.24/1.63 = ( ! [A: $i,Xphi: $i > $o] :
% 3.24/1.63 ( in
% 3.24/1.63 @ ( dsetconstr @ A
% 3.24/1.63 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.24/1.63 @ ( powerset @ A ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(sepSubset_type,type,
% 3.24/1.63 sepSubset: $o ).
% 3.24/1.63
% 3.24/1.63 thf(sepSubset,definition,
% 3.24/1.63 ( sepSubset
% 3.24/1.63 = ( ! [A: $i,Xphi: $i > $o] :
% 3.24/1.63 ( subset
% 3.24/1.63 @ ( dsetconstr @ A
% 3.24/1.63 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.24/1.63 @ A ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(binunion_type,type,
% 3.24/1.63 binunion: $i > $i > $i ).
% 3.24/1.63
% 3.24/1.63 thf(binunionIL_type,type,
% 3.24/1.63 binunionIL: $o ).
% 3.24/1.63
% 3.24/1.63 thf(binunionIL,definition,
% 3.24/1.63 ( binunionIL
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(upairset2IR_type,type,
% 3.24/1.63 upairset2IR: $o ).
% 3.24/1.63
% 3.24/1.63 thf(upairset2IR,definition,
% 3.24/1.63 ( upairset2IR
% 3.24/1.63 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(binunionIR_type,type,
% 3.24/1.63 binunionIR: $o ).
% 3.24/1.63
% 3.24/1.63 thf(binunionIR,definition,
% 3.24/1.63 ( binunionIR
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ B )
% 3.24/1.63 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(binunionEcases_type,type,
% 3.24/1.63 binunionEcases: $o ).
% 3.24/1.63
% 3.24/1.63 thf(binunionEcases,definition,
% 3.24/1.63 ( binunionEcases
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 3.24/1.63 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 3.24/1.63 => ( ( ( in @ Xx @ A )
% 3.24/1.63 => Xphi )
% 3.24/1.63 => ( ( ( in @ Xx @ B )
% 3.24/1.63 => Xphi )
% 3.24/1.63 => Xphi ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(binunionE_type,type,
% 3.24/1.63 binunionE: $o ).
% 3.24/1.63
% 3.24/1.63 thf(binunionE,definition,
% 3.24/1.63 ( binunionE
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 3.24/1.63 => ( ( in @ Xx @ A )
% 3.24/1.63 | ( in @ Xx @ B ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(binunionLsub_type,type,
% 3.24/1.63 binunionLsub: $o ).
% 3.24/1.63
% 3.24/1.63 thf(binunionLsub,definition,
% 3.24/1.63 ( binunionLsub
% 3.24/1.63 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(binunionRsub_type,type,
% 3.24/1.63 binunionRsub: $o ).
% 3.24/1.63
% 3.24/1.63 thf(binunionRsub,definition,
% 3.24/1.63 ( binunionRsub
% 3.24/1.63 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(binintersect_type,type,
% 3.24/1.63 binintersect: $i > $i > $i ).
% 3.24/1.63
% 3.24/1.63 thf(binintersectI_type,type,
% 3.24/1.63 binintersectI: $o ).
% 3.24/1.63
% 3.24/1.63 thf(binintersectI,definition,
% 3.24/1.63 ( binintersectI
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( in @ Xx @ B )
% 3.24/1.63 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(binintersectSubset5_type,type,
% 3.24/1.63 binintersectSubset5: $o ).
% 3.24/1.63
% 3.24/1.63 thf(binintersectSubset5,definition,
% 3.24/1.63 ( binintersectSubset5
% 3.24/1.63 = ( ! [A: $i,B: $i,C: $i] :
% 3.24/1.63 ( ( subset @ C @ A )
% 3.24/1.63 => ( ( subset @ C @ B )
% 3.24/1.63 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(binintersectEL_type,type,
% 3.24/1.63 binintersectEL: $o ).
% 3.24/1.63
% 3.24/1.63 thf(binintersectEL,definition,
% 3.24/1.63 ( binintersectEL
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 3.24/1.63 => ( in @ Xx @ A ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(binintersectLsub_type,type,
% 3.24/1.63 binintersectLsub: $o ).
% 3.24/1.63
% 3.24/1.63 thf(binintersectLsub,definition,
% 3.24/1.63 ( binintersectLsub
% 3.24/1.63 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(binintersectSubset2_type,type,
% 3.24/1.63 binintersectSubset2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(binintersectSubset2,definition,
% 3.24/1.63 ( binintersectSubset2
% 3.24/1.63 = ( ! [A: $i,B: $i] :
% 3.24/1.63 ( ( subset @ A @ B )
% 3.24/1.63 => ( ( binintersect @ A @ B )
% 3.24/1.63 = A ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(binintersectSubset3_type,type,
% 3.24/1.63 binintersectSubset3: $o ).
% 3.24/1.63
% 3.24/1.63 thf(binintersectSubset3,definition,
% 3.24/1.63 ( binintersectSubset3
% 3.24/1.63 = ( ! [A: $i,B: $i] :
% 3.24/1.63 ( ( ( binintersect @ A @ B )
% 3.24/1.63 = B )
% 3.24/1.63 => ( subset @ B @ A ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(binintersectER_type,type,
% 3.24/1.63 binintersectER: $o ).
% 3.24/1.63
% 3.24/1.63 thf(binintersectER,definition,
% 3.24/1.63 ( binintersectER
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 3.24/1.63 => ( in @ Xx @ B ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(disjointsetsI1_type,type,
% 3.24/1.63 disjointsetsI1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(disjointsetsI1,definition,
% 3.24/1.63 ( disjointsetsI1
% 3.24/1.63 = ( ! [A: $i,B: $i] :
% 3.24/1.63 ( ~ ? [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 & ( in @ Xx @ B ) )
% 3.24/1.63 => ( ( binintersect @ A @ B )
% 3.24/1.63 = emptyset ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(binintersectRsub_type,type,
% 3.24/1.63 binintersectRsub: $o ).
% 3.24/1.63
% 3.24/1.63 thf(binintersectRsub,definition,
% 3.24/1.63 ( binintersectRsub
% 3.24/1.63 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(binintersectSubset4_type,type,
% 3.24/1.63 binintersectSubset4: $o ).
% 3.24/1.63
% 3.24/1.63 thf(binintersectSubset4,definition,
% 3.24/1.63 ( binintersectSubset4
% 3.24/1.63 = ( ! [A: $i,B: $i] :
% 3.24/1.63 ( ( subset @ B @ A )
% 3.24/1.63 => ( ( binintersect @ A @ B )
% 3.24/1.63 = B ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(binintersectSubset1_type,type,
% 3.24/1.63 binintersectSubset1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(binintersectSubset1,definition,
% 3.24/1.63 ( binintersectSubset1
% 3.24/1.63 = ( ! [A: $i,B: $i] :
% 3.24/1.63 ( ( ( binintersect @ A @ B )
% 3.24/1.63 = A )
% 3.24/1.63 => ( subset @ A @ B ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(bs114d_type,type,
% 3.24/1.63 bs114d: $o ).
% 3.24/1.63
% 3.24/1.63 thf(bs114d,definition,
% 3.24/1.63 ( bs114d
% 3.24/1.63 = ( ! [A: $i,B: $i,C: $i] :
% 3.24/1.63 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 3.24/1.63 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(regular_type,type,
% 3.24/1.63 regular: $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(setminus_type,type,
% 3.24/1.63 setminus: $i > $i > $i ).
% 3.24/1.63
% 3.24/1.63 thf(setminusI_type,type,
% 3.24/1.63 setminusI: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setminusI,definition,
% 3.24/1.63 ( setminusI
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ~ ( in @ Xx @ B )
% 3.24/1.63 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setminusEL_type,type,
% 3.24/1.63 setminusEL: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setminusEL,definition,
% 3.24/1.63 ( setminusEL
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 3.24/1.63 => ( in @ Xx @ A ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setminusER_type,type,
% 3.24/1.63 setminusER: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setminusER,definition,
% 3.24/1.63 ( setminusER
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 3.24/1.63 => ~ ( in @ Xx @ B ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setminusSubset2_type,type,
% 3.24/1.63 setminusSubset2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setminusSubset2,definition,
% 3.24/1.63 ( setminusSubset2
% 3.24/1.63 = ( ! [A: $i,B: $i] :
% 3.24/1.63 ( ( subset @ A @ B )
% 3.24/1.63 => ( ( setminus @ A @ B )
% 3.24/1.63 = emptyset ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setminusERneg_type,type,
% 3.24/1.63 setminusERneg: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setminusERneg,definition,
% 3.24/1.63 ( setminusERneg
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 3.24/1.63 => ( ( in @ Xx @ A )
% 3.24/1.63 => ( in @ Xx @ B ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setminusELneg_type,type,
% 3.24/1.63 setminusELneg: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setminusELneg,definition,
% 3.24/1.63 ( setminusELneg
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 3.24/1.63 => ( ~ ( in @ Xx @ B )
% 3.24/1.63 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setminusILneg_type,type,
% 3.24/1.63 setminusILneg: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setminusILneg,definition,
% 3.24/1.63 ( setminusILneg
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ~ ( in @ Xx @ A )
% 3.24/1.63 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setminusIRneg_type,type,
% 3.24/1.63 setminusIRneg: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setminusIRneg,definition,
% 3.24/1.63 ( setminusIRneg
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ B )
% 3.24/1.63 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setminusLsub_type,type,
% 3.24/1.63 setminusLsub: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setminusLsub,definition,
% 3.24/1.63 ( setminusLsub
% 3.24/1.63 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setminusSubset1_type,type,
% 3.24/1.63 setminusSubset1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setminusSubset1,definition,
% 3.24/1.63 ( setminusSubset1
% 3.24/1.63 = ( ! [A: $i,B: $i] :
% 3.24/1.63 ( ( ( setminus @ A @ B )
% 3.24/1.63 = emptyset )
% 3.24/1.63 => ( subset @ A @ B ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(symdiff_type,type,
% 3.24/1.63 symdiff: $i > $i > $i ).
% 3.24/1.63
% 3.24/1.63 thf(symdiffE_type,type,
% 3.24/1.63 symdiffE: $o ).
% 3.24/1.63
% 3.24/1.63 thf(symdiffE,definition,
% 3.24/1.63 ( symdiffE
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 3.24/1.63 => ! [Xphi: $o] :
% 3.24/1.63 ( ( ( in @ Xx @ A )
% 3.24/1.63 => ( ~ ( in @ Xx @ B )
% 3.24/1.63 => Xphi ) )
% 3.24/1.63 => ( ( ~ ( in @ Xx @ A )
% 3.24/1.63 => ( ( in @ Xx @ B )
% 3.24/1.63 => Xphi ) )
% 3.24/1.63 => Xphi ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(symdiffI1_type,type,
% 3.24/1.63 symdiffI1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(symdiffI1,definition,
% 3.24/1.63 ( symdiffI1
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ~ ( in @ Xx @ B )
% 3.24/1.63 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(symdiffI2_type,type,
% 3.24/1.63 symdiffI2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(symdiffI2,definition,
% 3.24/1.63 ( symdiffI2
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ~ ( in @ Xx @ A )
% 3.24/1.63 => ( ( in @ Xx @ B )
% 3.24/1.63 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(symdiffIneg1_type,type,
% 3.24/1.63 symdiffIneg1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(symdiffIneg1,definition,
% 3.24/1.63 ( symdiffIneg1
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( in @ Xx @ B )
% 3.24/1.63 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(symdiffIneg2_type,type,
% 3.24/1.63 symdiffIneg2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(symdiffIneg2,definition,
% 3.24/1.63 ( symdiffIneg2
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ~ ( in @ Xx @ A )
% 3.24/1.63 => ( ~ ( in @ Xx @ B )
% 3.24/1.63 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(iskpair_type,type,
% 3.24/1.63 iskpair: $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(secondinupair_type,type,
% 3.24/1.63 secondinupair: $o ).
% 3.24/1.63
% 3.24/1.63 thf(secondinupair,definition,
% 3.24/1.63 ( secondinupair
% 3.24/1.63 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setukpairIL_type,type,
% 3.24/1.63 setukpairIL: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setukpairIL,definition,
% 3.24/1.63 ( setukpairIL
% 3.24/1.63 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setukpairIR_type,type,
% 3.24/1.63 setukpairIR: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setukpairIR,definition,
% 3.24/1.63 ( setukpairIR
% 3.24/1.63 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(kpairiskpair_type,type,
% 3.24/1.63 kpairiskpair: $o ).
% 3.24/1.63
% 3.24/1.63 thf(kpairiskpair,definition,
% 3.24/1.63 ( kpairiskpair
% 3.24/1.63 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(kpair_type,type,
% 3.24/1.63 kpair: $i > $i > $i ).
% 3.24/1.63
% 3.24/1.63 thf(kpairp_type,type,
% 3.24/1.63 kpairp: $o ).
% 3.24/1.63
% 3.24/1.63 thf(kpairp,definition,
% 3.24/1.63 ( kpairp
% 3.24/1.63 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(cartprod_type,type,
% 3.24/1.63 cartprod: $i > $i > $i ).
% 3.24/1.63
% 3.24/1.63 thf(singletonsubset_type,type,
% 3.24/1.63 singletonsubset: $o ).
% 3.24/1.63
% 3.24/1.63 thf(singletonsubset,definition,
% 3.24/1.63 ( singletonsubset
% 3.24/1.63 = ( ! [A: $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(singletoninpowerset_type,type,
% 3.24/1.63 singletoninpowerset: $o ).
% 3.24/1.63
% 3.24/1.63 thf(singletoninpowerset,definition,
% 3.24/1.63 ( singletoninpowerset
% 3.24/1.63 = ( ! [A: $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(singletoninpowunion_type,type,
% 3.24/1.63 singletoninpowunion: $o ).
% 3.24/1.63
% 3.24/1.63 thf(singletoninpowunion,definition,
% 3.24/1.63 ( singletoninpowunion
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(upairset2E_type,type,
% 3.24/1.63 upairset2E: $o ).
% 3.24/1.63
% 3.24/1.63 thf(upairset2E,definition,
% 3.24/1.63 ( upairset2E
% 3.24/1.63 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.24/1.63 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 3.24/1.63 => ( ( Xz = Xx )
% 3.24/1.63 | ( Xz = Xy ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(upairsubunion_type,type,
% 3.24/1.63 upairsubunion: $o ).
% 3.24/1.63
% 3.24/1.63 thf(upairsubunion,definition,
% 3.24/1.63 ( upairsubunion
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ B )
% 3.24/1.63 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(upairinpowunion_type,type,
% 3.24/1.63 upairinpowunion: $o ).
% 3.24/1.63
% 3.24/1.63 thf(upairinpowunion,definition,
% 3.24/1.63 ( upairinpowunion
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ B )
% 3.24/1.63 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(ubforcartprodlem1_type,type,
% 3.24/1.63 ubforcartprodlem1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(ubforcartprodlem1,definition,
% 3.24/1.63 ( ubforcartprodlem1
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ B )
% 3.24/1.63 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(ubforcartprodlem2_type,type,
% 3.24/1.63 ubforcartprodlem2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(ubforcartprodlem2,definition,
% 3.24/1.63 ( ubforcartprodlem2
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ B )
% 3.24/1.63 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(ubforcartprodlem3_type,type,
% 3.24/1.63 ubforcartprodlem3: $o ).
% 3.24/1.63
% 3.24/1.63 thf(ubforcartprodlem3,definition,
% 3.24/1.63 ( ubforcartprodlem3
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ B )
% 3.24/1.63 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(cartprodpairin_type,type,
% 3.24/1.63 cartprodpairin: $o ).
% 3.24/1.63
% 3.24/1.63 thf(cartprodpairin,definition,
% 3.24/1.63 ( cartprodpairin
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ B )
% 3.24/1.63 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(cartprodmempair1_type,type,
% 3.24/1.63 cartprodmempair1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(cartprodmempair1,definition,
% 3.24/1.63 ( cartprodmempair1
% 3.24/1.63 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.24/1.63 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.24/1.63 => ? [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 & ? [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ B )
% 3.24/1.63 & ( Xu
% 3.24/1.63 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(cartprodmempair_type,type,
% 3.24/1.63 cartprodmempair: $o ).
% 3.24/1.63
% 3.24/1.63 thf(cartprodmempair,definition,
% 3.24/1.63 ( cartprodmempair
% 3.24/1.63 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.24/1.63 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.24/1.63 => ( iskpair @ Xu ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setunionE2_type,type,
% 3.24/1.63 setunionE2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setunionE2,definition,
% 3.24/1.63 ( setunionE2
% 3.24/1.63 = ( ! [A: $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ ( setunion @ A ) )
% 3.24/1.63 => ? [X: $i] :
% 3.24/1.63 ( ( in @ X @ A )
% 3.24/1.63 & ( in @ Xx @ X ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setunionsingleton1_type,type,
% 3.24/1.63 setunionsingleton1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setunionsingleton1,definition,
% 3.24/1.63 ( setunionsingleton1
% 3.24/1.63 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setunionsingleton2_type,type,
% 3.24/1.63 setunionsingleton2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setunionsingleton2,definition,
% 3.24/1.63 ( setunionsingleton2
% 3.24/1.63 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setunionsingleton_type,type,
% 3.24/1.63 setunionsingleton: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setunionsingleton,definition,
% 3.24/1.63 ( setunionsingleton
% 3.24/1.63 = ( ! [Xx: $i] :
% 3.24/1.63 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 3.24/1.63 = Xx ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(singleton_type,type,
% 3.24/1.63 singleton: $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(singletonprop_type,type,
% 3.24/1.63 singletonprop: $o ).
% 3.24/1.63
% 3.24/1.63 thf(singletonprop,definition,
% 3.24/1.63 ( singletonprop
% 3.24/1.63 = ( ! [A: $i,Xphi: $i > $o] :
% 3.24/1.63 ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 => ( ( Xphi @ Xx )
% 3.24/1.63 => ( ( Xphi @ Xy )
% 3.24/1.63 => ( Xx = Xy ) ) ) ) )
% 3.24/1.63 => ( ? [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 & ( Xphi @ Xx ) )
% 3.24/1.63 => ( singleton
% 3.24/1.63 @ ( dsetconstr @ A
% 3.24/1.63 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(ex1_type,type,
% 3.24/1.63 ex1: $i > ( $i > $o ) > $o ).
% 3.24/1.63
% 3.24/1.63 thf(ex1E1_type,type,
% 3.24/1.63 ex1E1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(ex1E1,definition,
% 3.24/1.63 ( ex1E1
% 3.24/1.63 = ( ! [A: $i,Xphi: $i > $o] :
% 3.24/1.63 ( ( ex1 @ A
% 3.24/1.63 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.24/1.63 => ? [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 & ( Xphi @ Xx ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(ex1I_type,type,
% 3.24/1.63 ex1I: $o ).
% 3.24/1.63
% 3.24/1.63 thf(ex1I,definition,
% 3.24/1.63 ( ex1I
% 3.24/1.63 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( Xphi @ Xx )
% 3.24/1.63 => ( ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 => ( ( Xphi @ Xy )
% 3.24/1.63 => ( Xy = Xx ) ) )
% 3.24/1.63 => ( ex1 @ A
% 3.24/1.63 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(ex1I2_type,type,
% 3.24/1.63 ex1I2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(ex1I2,definition,
% 3.24/1.63 ( ex1I2
% 3.24/1.63 = ( ! [A: $i,Xphi: $i > $o] :
% 3.24/1.63 ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 => ( ( Xphi @ Xx )
% 3.24/1.63 => ( ( Xphi @ Xy )
% 3.24/1.63 => ( Xx = Xy ) ) ) ) )
% 3.24/1.63 => ( ? [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 & ( Xphi @ Xx ) )
% 3.24/1.63 => ( ex1 @ A
% 3.24/1.63 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(singletonsuniq_type,type,
% 3.24/1.63 singletonsuniq: $o ).
% 3.24/1.63
% 3.24/1.63 thf(singletonsuniq,definition,
% 3.24/1.63 ( singletonsuniq
% 3.24/1.63 = ( ! [Xx: $i,Xy: $i] :
% 3.24/1.63 ( ( ( setadjoin @ Xx @ emptyset )
% 3.24/1.63 = ( setadjoin @ Xy @ emptyset ) )
% 3.24/1.63 => ( Xx = Xy ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(atmost1p_type,type,
% 3.24/1.63 atmost1p: $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(atleast2p_type,type,
% 3.24/1.63 atleast2p: $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(atmost2p_type,type,
% 3.24/1.63 atmost2p: $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(upairsetp_type,type,
% 3.24/1.63 upairsetp: $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(setukpairinjL1_type,type,
% 3.24/1.63 setukpairinjL1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setukpairinjL1,definition,
% 3.24/1.63 ( setukpairinjL1
% 3.24/1.63 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.24/1.63 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 3.24/1.63 => ( Xx = Xz ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(kfstsingleton_type,type,
% 3.24/1.63 kfstsingleton: $o ).
% 3.24/1.63
% 3.24/1.63 thf(kfstsingleton,definition,
% 3.24/1.63 ( kfstsingleton
% 3.24/1.63 = ( ! [Xu: $i] :
% 3.24/1.63 ( ( iskpair @ Xu )
% 3.24/1.63 => ( singleton
% 3.24/1.63 @ ( dsetconstr @ ( setunion @ Xu )
% 3.24/1.63 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(theprop_type,type,
% 3.24/1.63 theprop: $o ).
% 3.24/1.63
% 3.24/1.63 thf(theprop,definition,
% 3.24/1.63 ( theprop
% 3.24/1.63 = ( ! [X: $i] :
% 3.24/1.63 ( ( singleton @ X )
% 3.24/1.63 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(kfst_type,type,
% 3.24/1.63 kfst: $i > $i ).
% 3.24/1.63
% 3.24/1.63 thf(kfstpairEq_type,type,
% 3.24/1.63 kfstpairEq: $o ).
% 3.24/1.63
% 3.24/1.63 thf(kfstpairEq,definition,
% 3.24/1.63 ( kfstpairEq
% 3.24/1.63 = ( ! [Xx: $i,Xy: $i] :
% 3.24/1.63 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 3.24/1.63 = Xx ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(cartprodfstin_type,type,
% 3.24/1.63 cartprodfstin: $o ).
% 3.24/1.63
% 3.24/1.63 thf(cartprodfstin,definition,
% 3.24/1.63 ( cartprodfstin
% 3.24/1.63 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.24/1.63 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.24/1.63 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setukpairinjL2_type,type,
% 3.24/1.63 setukpairinjL2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setukpairinjL2,definition,
% 3.24/1.63 ( setukpairinjL2
% 3.24/1.63 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.24/1.63 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.24/1.63 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.24/1.63 => ( Xx = Xz ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setukpairinjL_type,type,
% 3.24/1.63 setukpairinjL: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setukpairinjL,definition,
% 3.24/1.63 ( setukpairinjL
% 3.24/1.63 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.24/1.63 ( ( ( kpair @ Xx @ Xy )
% 3.24/1.63 = ( kpair @ Xz @ Xu ) )
% 3.24/1.63 => ( Xx = Xz ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setukpairinjR11_type,type,
% 3.24/1.63 setukpairinjR11: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setukpairinjR11,definition,
% 3.24/1.63 ( setukpairinjR11
% 3.24/1.63 = ( ! [Xx: $i,Xy: $i] :
% 3.24/1.63 ( ( Xx = Xy )
% 3.24/1.63 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.24/1.63 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setukpairinjR12_type,type,
% 3.24/1.63 setukpairinjR12: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setukpairinjR12,definition,
% 3.24/1.63 ( setukpairinjR12
% 3.24/1.63 = ( ! [Xx: $i,Xy: $i] :
% 3.24/1.63 ( ( Xx = Xy )
% 3.24/1.63 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.24/1.63 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setukpairinjR1_type,type,
% 3.24/1.63 setukpairinjR1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setukpairinjR1,definition,
% 3.24/1.63 ( setukpairinjR1
% 3.24/1.63 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.24/1.63 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.24/1.63 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.24/1.63 => ( ( Xz = Xu )
% 3.24/1.63 => ( Xy = Xu ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(upairequniteq_type,type,
% 3.24/1.63 upairequniteq: $o ).
% 3.24/1.63
% 3.24/1.63 thf(upairequniteq,definition,
% 3.24/1.63 ( upairequniteq
% 3.24/1.63 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.24/1.63 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.24/1.63 = ( setadjoin @ Xz @ emptyset ) )
% 3.24/1.63 => ( Xx = Xy ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setukpairinjR2_type,type,
% 3.24/1.63 setukpairinjR2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setukpairinjR2,definition,
% 3.24/1.63 ( setukpairinjR2
% 3.24/1.63 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.24/1.63 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.24/1.63 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.24/1.63 => ( Xy = Xu ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setukpairinjR_type,type,
% 3.24/1.63 setukpairinjR: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setukpairinjR,definition,
% 3.24/1.63 ( setukpairinjR
% 3.24/1.63 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.24/1.63 ( ( ( kpair @ Xx @ Xy )
% 3.24/1.63 = ( kpair @ Xz @ Xu ) )
% 3.24/1.63 => ( Xy = Xu ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(ksndsingleton_type,type,
% 3.24/1.63 ksndsingleton: $o ).
% 3.24/1.63
% 3.24/1.63 thf(ksndsingleton,definition,
% 3.24/1.63 ( ksndsingleton
% 3.24/1.63 = ( ! [Xu: $i] :
% 3.24/1.63 ( ( iskpair @ Xu )
% 3.24/1.63 => ( singleton
% 3.24/1.63 @ ( dsetconstr @ ( setunion @ Xu )
% 3.24/1.63 @ ^ [Xx: $i] :
% 3.24/1.63 ( Xu
% 3.24/1.63 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(ksnd_type,type,
% 3.24/1.63 ksnd: $i > $i ).
% 3.24/1.63
% 3.24/1.63 thf(ksndpairEq_type,type,
% 3.24/1.63 ksndpairEq: $o ).
% 3.24/1.63
% 3.24/1.63 thf(ksndpairEq,definition,
% 3.24/1.63 ( ksndpairEq
% 3.24/1.63 = ( ! [Xx: $i,Xy: $i] :
% 3.24/1.63 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 3.24/1.63 = Xy ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(kpairsurjEq_type,type,
% 3.24/1.63 kpairsurjEq: $o ).
% 3.24/1.63
% 3.24/1.63 thf(kpairsurjEq,definition,
% 3.24/1.63 ( kpairsurjEq
% 3.24/1.63 = ( ! [Xu: $i] :
% 3.24/1.63 ( ( iskpair @ Xu )
% 3.24/1.63 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 3.24/1.63 = Xu ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(cartprodsndin_type,type,
% 3.24/1.63 cartprodsndin: $o ).
% 3.24/1.63
% 3.24/1.63 thf(cartprodsndin,definition,
% 3.24/1.63 ( cartprodsndin
% 3.24/1.63 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.24/1.63 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.24/1.63 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(cartprodpairmemEL_type,type,
% 3.24/1.63 cartprodpairmemEL: $o ).
% 3.24/1.63
% 3.24/1.63 thf(cartprodpairmemEL,definition,
% 3.24/1.63 ( cartprodpairmemEL
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 3.24/1.63 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 3.24/1.63 => ( in @ Xx @ A ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(cartprodpairmemER_type,type,
% 3.24/1.63 cartprodpairmemER: $o ).
% 3.24/1.63
% 3.24/1.63 thf(cartprodpairmemER,definition,
% 3.24/1.63 ( cartprodpairmemER
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 3.24/1.63 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 3.24/1.63 => ( in @ Xy @ B ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(cartprodmempaircEq_type,type,
% 3.24/1.63 cartprodmempaircEq: $o ).
% 3.24/1.63
% 3.24/1.63 thf(cartprodmempaircEq,definition,
% 3.24/1.63 ( cartprodmempaircEq
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ B )
% 3.24/1.63 => ( ( kpair @ Xx @ Xy )
% 3.24/1.63 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(cartprodfstpairEq_type,type,
% 3.24/1.63 cartprodfstpairEq: $o ).
% 3.24/1.63
% 3.24/1.63 thf(cartprodfstpairEq,definition,
% 3.24/1.63 ( cartprodfstpairEq
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ B )
% 3.24/1.63 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 3.24/1.63 = Xx ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(cartprodsndpairEq_type,type,
% 3.24/1.63 cartprodsndpairEq: $o ).
% 3.24/1.63
% 3.24/1.63 thf(cartprodsndpairEq,definition,
% 3.24/1.63 ( cartprodsndpairEq
% 3.24/1.63 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ B )
% 3.24/1.63 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 3.24/1.63 = Xy ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(cartprodpairsurjEq_type,type,
% 3.24/1.63 cartprodpairsurjEq: $o ).
% 3.24/1.63
% 3.24/1.63 thf(cartprodpairsurjEq,definition,
% 3.24/1.63 ( cartprodpairsurjEq
% 3.24/1.63 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.24/1.63 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.24/1.63 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 3.24/1.63 = Xu ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(breln_type,type,
% 3.24/1.63 breln: $i > $i > $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(dpsetconstr_type,type,
% 3.24/1.63 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 3.24/1.63
% 3.24/1.63 thf(dpsetconstrI_type,type,
% 3.24/1.63 dpsetconstrI: $o ).
% 3.24/1.63
% 3.24/1.63 thf(dpsetconstrI,definition,
% 3.24/1.63 ( dpsetconstrI
% 3.24/1.63 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ B )
% 3.24/1.63 => ( ( Xphi @ Xx @ Xy )
% 3.24/1.63 => ( in @ ( kpair @ Xx @ Xy )
% 3.24/1.63 @ ( dpsetconstr @ A @ B
% 3.24/1.63 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(dpsetconstrSub_type,type,
% 3.24/1.63 dpsetconstrSub: $o ).
% 3.24/1.63
% 3.24/1.63 thf(dpsetconstrSub,definition,
% 3.24/1.63 ( dpsetconstrSub
% 3.24/1.63 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.24/1.63 ( subset
% 3.24/1.63 @ ( dpsetconstr @ A @ B
% 3.24/1.63 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 3.24/1.63 @ ( cartprod @ A @ B ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setOfPairsIsBReln_type,type,
% 3.24/1.63 setOfPairsIsBReln: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setOfPairsIsBReln,definition,
% 3.24/1.63 ( setOfPairsIsBReln
% 3.24/1.63 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.24/1.63 ( breln @ A @ B
% 3.24/1.63 @ ( dpsetconstr @ A @ B
% 3.24/1.63 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(dpsetconstrERa_type,type,
% 3.24/1.63 dpsetconstrERa: $o ).
% 3.24/1.63
% 3.24/1.63 thf(dpsetconstrERa,definition,
% 3.24/1.63 ( dpsetconstrERa
% 3.24/1.63 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ B )
% 3.24/1.63 => ( ( in @ ( kpair @ Xx @ Xy )
% 3.24/1.63 @ ( dpsetconstr @ A @ B
% 3.24/1.63 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.24/1.63 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(dpsetconstrEL1_type,type,
% 3.24/1.63 dpsetconstrEL1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(dpsetconstrEL1,definition,
% 3.24/1.63 ( dpsetconstrEL1
% 3.24/1.63 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.24/1.63 ( ( in @ ( kpair @ Xx @ Xy )
% 3.24/1.63 @ ( dpsetconstr @ A @ B
% 3.24/1.63 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.24/1.63 => ( in @ Xx @ A ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(dpsetconstrEL2_type,type,
% 3.24/1.63 dpsetconstrEL2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(dpsetconstrEL2,definition,
% 3.24/1.63 ( dpsetconstrEL2
% 3.24/1.63 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.24/1.63 ( ( in @ ( kpair @ Xx @ Xy )
% 3.24/1.63 @ ( dpsetconstr @ A @ B
% 3.24/1.63 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.24/1.63 => ( in @ Xy @ B ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(dpsetconstrER_type,type,
% 3.24/1.63 dpsetconstrER: $o ).
% 3.24/1.63
% 3.24/1.63 thf(dpsetconstrER,definition,
% 3.24/1.63 ( dpsetconstrER
% 3.24/1.63 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.24/1.63 ( ( in @ ( kpair @ Xx @ Xy )
% 3.24/1.63 @ ( dpsetconstr @ A @ B
% 3.24/1.63 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.24/1.63 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(func_type,type,
% 3.24/1.63 func: $i > $i > $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(funcSet_type,type,
% 3.24/1.63 funcSet: $i > $i > $i ).
% 3.24/1.63
% 3.24/1.63 thf(funcImageSingleton_type,type,
% 3.24/1.63 funcImageSingleton: $o ).
% 3.24/1.63
% 3.24/1.63 thf(funcImageSingleton,definition,
% 3.24/1.63 ( funcImageSingleton
% 3.24/1.63 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.24/1.63 ( ( func @ A @ B @ Xf )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( singleton
% 3.24/1.63 @ ( dsetconstr @ B
% 3.24/1.63 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(apProp_type,type,
% 3.24/1.63 apProp: $o ).
% 3.24/1.63
% 3.24/1.63 thf(apProp,definition,
% 3.24/1.63 ( apProp
% 3.24/1.63 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.24/1.63 ( ( func @ A @ B @ Xf )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( in
% 3.24/1.63 @ ( setunion
% 3.24/1.63 @ ( dsetconstr @ B
% 3.24/1.63 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 3.24/1.63 @ B ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(ap_type,type,
% 3.24/1.63 ap: $i > $i > $i > $i > $i ).
% 3.24/1.63
% 3.24/1.63 thf(app_type,type,
% 3.24/1.63 app: $o ).
% 3.24/1.63
% 3.24/1.63 thf(app,definition,
% 3.24/1.63 ( app
% 3.24/1.63 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.24/1.63 ( ( func @ A @ B @ Xf )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(infuncsetfunc_type,type,
% 3.24/1.63 infuncsetfunc: $o ).
% 3.24/1.63
% 3.24/1.63 thf(infuncsetfunc,definition,
% 3.24/1.63 ( infuncsetfunc
% 3.24/1.63 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.24/1.63 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.24/1.63 => ( func @ A @ B @ Xf ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(ap2p_type,type,
% 3.24/1.63 ap2p: $o ).
% 3.24/1.63
% 3.24/1.63 thf(ap2p,definition,
% 3.24/1.63 ( ap2p
% 3.24/1.63 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.24/1.63 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(funcinfuncset_type,type,
% 3.24/1.63 funcinfuncset: $o ).
% 3.24/1.63
% 3.24/1.63 thf(funcinfuncset,definition,
% 3.24/1.63 ( funcinfuncset
% 3.24/1.63 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.24/1.63 ( ( func @ A @ B @ Xf )
% 3.24/1.63 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(lamProp_type,type,
% 3.24/1.63 lamProp: $o ).
% 3.24/1.63
% 3.24/1.63 thf(lamProp,definition,
% 3.24/1.63 ( lamProp
% 3.24/1.63 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.24/1.63 ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.24/1.63 => ( func @ A @ B
% 3.24/1.63 @ ( dpsetconstr @ A @ B
% 3.24/1.63 @ ^ [Xx: $i,Xy: $i] :
% 3.24/1.63 ( ( Xf @ Xx )
% 3.24/1.63 = Xy ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(lam_type,type,
% 3.24/1.63 lam: $i > $i > ( $i > $i ) > $i ).
% 3.24/1.63
% 3.24/1.63 thf(lamp_type,type,
% 3.24/1.63 lamp: $o ).
% 3.24/1.63
% 3.24/1.63 thf(lamp,definition,
% 3.24/1.63 ( lamp
% 3.24/1.63 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.24/1.63 ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.24/1.63 => ( func @ A @ B
% 3.24/1.63 @ ( lam @ A @ B
% 3.24/1.63 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(lam2p_type,type,
% 3.24/1.63 lam2p: $o ).
% 3.24/1.63
% 3.24/1.63 thf(lam2p,definition,
% 3.24/1.63 ( lam2p
% 3.24/1.63 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.24/1.63 ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.24/1.63 => ( in
% 3.24/1.63 @ ( lam @ A @ B
% 3.24/1.63 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 3.24/1.63 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(brelnall1_type,type,
% 3.24/1.63 brelnall1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(brelnall1,definition,
% 3.24/1.63 ( brelnall1
% 3.24/1.63 = ( ! [A: $i,B: $i,R: $i] :
% 3.24/1.63 ( ( breln @ A @ B @ R )
% 3.24/1.63 => ! [Xphi: $i > $o] :
% 3.24/1.63 ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ B )
% 3.24/1.63 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.24/1.63 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ R )
% 3.24/1.63 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(brelnall2_type,type,
% 3.24/1.63 brelnall2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(brelnall2,definition,
% 3.24/1.63 ( brelnall2
% 3.24/1.63 = ( ! [A: $i,B: $i,R: $i] :
% 3.24/1.63 ( ( breln @ A @ B @ R )
% 3.24/1.63 => ! [Xphi: $i > $o] :
% 3.24/1.63 ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ B )
% 3.24/1.63 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.24/1.63 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ R )
% 3.24/1.63 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(ex1E2_type,type,
% 3.24/1.63 ex1E2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(ex1E2,definition,
% 3.24/1.63 ( ex1E2
% 3.24/1.63 = ( ! [A: $i,Xphi: $i > $o] :
% 3.24/1.63 ( ( ex1 @ A
% 3.24/1.63 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 => ( ( Xphi @ Xx )
% 3.24/1.63 => ( ( Xphi @ Xy )
% 3.24/1.63 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(funcGraphProp1_type,type,
% 3.24/1.63 funcGraphProp1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(funcGraphProp1,definition,
% 3.24/1.63 ( funcGraphProp1
% 3.24/1.63 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.24/1.63 ( ( func @ A @ B @ Xf )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(funcGraphProp3_type,type,
% 3.24/1.63 funcGraphProp3: $o ).
% 3.24/1.63
% 3.24/1.63 thf(funcGraphProp3,definition,
% 3.24/1.63 ( funcGraphProp3
% 3.24/1.63 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.24/1.63 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(funcGraphProp2_type,type,
% 3.24/1.63 funcGraphProp2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(funcGraphProp2,definition,
% 3.24/1.63 ( funcGraphProp2
% 3.24/1.63 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.24/1.63 ( ( func @ A @ B @ Xf )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ B )
% 3.24/1.63 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 3.24/1.63 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.24/1.63 = Xy ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(funcextLem_type,type,
% 3.24/1.63 funcextLem: $o ).
% 3.24/1.63
% 3.24/1.63 thf(funcextLem,definition,
% 3.24/1.63 ( funcextLem
% 3.24/1.63 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.24/1.63 ( ( func @ A @ B @ Xf )
% 3.24/1.63 => ! [Xg: $i] :
% 3.24/1.63 ( ( func @ A @ B @ Xg )
% 3.24/1.63 => ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.24/1.63 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ B )
% 3.24/1.63 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 3.24/1.63 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(funcGraphProp4_type,type,
% 3.24/1.63 funcGraphProp4: $o ).
% 3.24/1.63
% 3.24/1.63 thf(funcGraphProp4,definition,
% 3.24/1.63 ( funcGraphProp4
% 3.24/1.63 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.24/1.63 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ B )
% 3.24/1.63 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 3.24/1.63 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.24/1.63 = Xy ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(subbreln_type,type,
% 3.24/1.63 subbreln: $o ).
% 3.24/1.63
% 3.24/1.63 thf(subbreln,definition,
% 3.24/1.63 ( subbreln
% 3.24/1.63 = ( ! [A: $i,B: $i,R: $i] :
% 3.24/1.63 ( ( breln @ A @ B @ R )
% 3.24/1.63 => ! [S: $i] :
% 3.24/1.63 ( ( breln @ A @ B @ S )
% 3.24/1.63 => ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ B )
% 3.24/1.63 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.24/1.63 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.24/1.63 => ( subset @ R @ S ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(eqbreln_type,type,
% 3.24/1.63 eqbreln: $o ).
% 3.24/1.63
% 3.24/1.63 thf(eqbreln,definition,
% 3.24/1.63 ( eqbreln
% 3.24/1.63 = ( ! [A: $i,B: $i,R: $i] :
% 3.24/1.63 ( ( breln @ A @ B @ R )
% 3.24/1.63 => ! [S: $i] :
% 3.24/1.63 ( ( breln @ A @ B @ S )
% 3.24/1.63 => ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ B )
% 3.24/1.63 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.24/1.63 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.24/1.63 => ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ B )
% 3.24/1.63 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.24/1.63 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 3.24/1.63 => ( R = S ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(funcext_type,type,
% 3.24/1.63 funcext: $o ).
% 3.24/1.63
% 3.24/1.63 thf(funcext,definition,
% 3.24/1.63 ( funcext
% 3.24/1.63 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.24/1.63 ( ( func @ A @ B @ Xf )
% 3.24/1.63 => ! [Xg: $i] :
% 3.24/1.63 ( ( func @ A @ B @ Xg )
% 3.24/1.63 => ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.24/1.63 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.24/1.63 => ( Xf = Xg ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(funcext2_type,type,
% 3.24/1.63 funcext2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(funcext2,definition,
% 3.24/1.63 ( funcext2
% 3.24/1.63 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.24/1.63 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.24/1.63 => ! [Xg: $i] :
% 3.24/1.63 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 3.24/1.63 => ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.24/1.63 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.24/1.63 => ( Xf = Xg ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(ap2apEq1_type,type,
% 3.24/1.63 ap2apEq1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(ap2apEq1,definition,
% 3.24/1.63 ( ap2apEq1
% 3.24/1.63 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.24/1.63 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.24/1.63 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(ap2apEq2_type,type,
% 3.24/1.63 ap2apEq2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(ap2apEq2,definition,
% 3.24/1.63 ( ap2apEq2
% 3.24/1.63 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.24/1.63 ( ( func @ A @ B @ Xf )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.24/1.63 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(beta1_type,type,
% 3.24/1.63 beta1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(beta1,definition,
% 3.24/1.63 ( beta1
% 3.24/1.63 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.24/1.63 ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( ap @ A @ B
% 3.24/1.63 @ ( lam @ A @ B
% 3.24/1.63 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 3.24/1.63 @ Xx )
% 3.24/1.63 = ( Xf @ Xx ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(eta1_type,type,
% 3.24/1.63 eta1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(eta1,definition,
% 3.24/1.63 ( eta1
% 3.24/1.63 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.24/1.63 ( ( func @ A @ B @ Xf )
% 3.24/1.63 => ( ( lam @ A @ B
% 3.24/1.63 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 3.24/1.63 = Xf ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(lam2lamEq_type,type,
% 3.24/1.63 lam2lamEq: $o ).
% 3.24/1.63
% 3.24/1.63 thf(lam2lamEq,definition,
% 3.24/1.63 ( lam2lamEq
% 3.24/1.63 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.24/1.63 ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.24/1.63 => ( ( lam @ A @ B
% 3.24/1.63 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 3.24/1.63 = ( lam @ A @ B
% 3.24/1.63 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(beta2_type,type,
% 3.24/1.63 beta2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(beta2,definition,
% 3.24/1.63 ( beta2
% 3.24/1.63 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.24/1.63 ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( ap @ A @ B
% 3.24/1.63 @ ( lam @ A @ B
% 3.24/1.63 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 3.24/1.63 @ Xx )
% 3.24/1.63 = ( Xf @ Xx ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(eta2_type,type,
% 3.24/1.63 eta2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(eta2,definition,
% 3.24/1.63 ( eta2
% 3.24/1.63 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.24/1.63 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.24/1.63 => ( ( lam @ A @ B
% 3.24/1.63 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 3.24/1.63 = Xf ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(iffalseProp1_type,type,
% 3.24/1.63 iffalseProp1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(iffalseProp1,definition,
% 3.24/1.63 ( iffalseProp1
% 3.24/1.63 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 => ( ~ Xphi
% 3.24/1.63 => ( in @ Xy
% 3.24/1.63 @ ( dsetconstr @ A
% 3.24/1.63 @ ^ [Xz: $i] :
% 3.24/1.63 ( ( Xphi
% 3.24/1.63 & ( Xz = Xx ) )
% 3.24/1.63 | ( ~ Xphi
% 3.24/1.63 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(iffalseProp2_type,type,
% 3.24/1.63 iffalseProp2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(iffalseProp2,definition,
% 3.24/1.63 ( iffalseProp2
% 3.24/1.63 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 => ( ~ Xphi
% 3.24/1.63 => ( ( dsetconstr @ A
% 3.24/1.63 @ ^ [Xz: $i] :
% 3.24/1.63 ( ( Xphi
% 3.24/1.63 & ( Xz = Xx ) )
% 3.24/1.63 | ( ~ Xphi
% 3.24/1.63 & ( Xz = Xy ) ) ) )
% 3.24/1.63 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(iftrueProp1_type,type,
% 3.24/1.63 iftrueProp1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(iftrueProp1,definition,
% 3.24/1.63 ( iftrueProp1
% 3.24/1.63 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 => ( Xphi
% 3.24/1.63 => ( in @ Xx
% 3.24/1.63 @ ( dsetconstr @ A
% 3.24/1.63 @ ^ [Xz: $i] :
% 3.24/1.63 ( ( Xphi
% 3.24/1.63 & ( Xz = Xx ) )
% 3.24/1.63 | ( ~ Xphi
% 3.24/1.63 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(iftrueProp2_type,type,
% 3.24/1.63 iftrueProp2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(iftrueProp2,definition,
% 3.24/1.63 ( iftrueProp2
% 3.24/1.63 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 => ( Xphi
% 3.24/1.63 => ( ( dsetconstr @ A
% 3.24/1.63 @ ^ [Xz: $i] :
% 3.24/1.63 ( ( Xphi
% 3.24/1.63 & ( Xz = Xx ) )
% 3.24/1.63 | ( ~ Xphi
% 3.24/1.63 & ( Xz = Xy ) ) ) )
% 3.24/1.63 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(ifSingleton_type,type,
% 3.24/1.63 ifSingleton: $o ).
% 3.24/1.63
% 3.24/1.63 thf(ifSingleton,definition,
% 3.24/1.63 ( ifSingleton
% 3.24/1.63 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 => ( singleton
% 3.24/1.63 @ ( dsetconstr @ A
% 3.24/1.63 @ ^ [Xz: $i] :
% 3.24/1.63 ( ( Xphi
% 3.24/1.63 & ( Xz = Xx ) )
% 3.24/1.63 | ( ~ Xphi
% 3.24/1.63 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(if_type,type,
% 3.24/1.63 if: $i > $o > $i > $i > $i ).
% 3.24/1.63
% 3.24/1.63 thf(ifp_type,type,
% 3.24/1.63 ifp: $o ).
% 3.24/1.63
% 3.24/1.63 thf(ifp,definition,
% 3.24/1.63 ( ifp
% 3.24/1.63 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(theeq_type,type,
% 3.24/1.63 theeq: $o ).
% 3.24/1.63
% 3.24/1.63 thf(theeq,definition,
% 3.24/1.63 ( theeq
% 3.24/1.63 = ( ! [X: $i] :
% 3.24/1.63 ( ( singleton @ X )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ X )
% 3.24/1.63 => ( ( setunion @ X )
% 3.24/1.63 = Xx ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(iftrue_type,type,
% 3.24/1.63 iftrue: $o ).
% 3.24/1.63
% 3.24/1.63 thf(iftrue,definition,
% 3.24/1.63 ( iftrue
% 3.24/1.63 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 => ( Xphi
% 3.24/1.63 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 3.24/1.63 = Xx ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(iffalse_type,type,
% 3.24/1.63 iffalse: $o ).
% 3.24/1.63
% 3.24/1.63 thf(iffalse,definition,
% 3.24/1.63 ( iffalse
% 3.24/1.63 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 => ( ~ Xphi
% 3.24/1.63 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 3.24/1.63 = Xy ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(iftrueorfalse_type,type,
% 3.24/1.63 iftrueorfalse: $o ).
% 3.24/1.63
% 3.24/1.63 thf(iftrueorfalse,definition,
% 3.24/1.63 ( iftrueorfalse
% 3.24/1.63 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(binintersectT_lem_type,type,
% 3.24/1.63 binintersectT_lem: $o ).
% 3.24/1.63
% 3.24/1.63 thf(binintersectT_lem,definition,
% 3.24/1.63 ( binintersectT_lem
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(binunionT_lem_type,type,
% 3.24/1.63 binunionT_lem: $o ).
% 3.24/1.63
% 3.24/1.63 thf(binunionT_lem,definition,
% 3.24/1.63 ( binunionT_lem
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(powersetT_lem_type,type,
% 3.24/1.63 powersetT_lem: $o ).
% 3.24/1.63
% 3.24/1.63 thf(powersetT_lem,definition,
% 3.24/1.63 ( powersetT_lem
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setminusT_lem_type,type,
% 3.24/1.63 setminusT_lem: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setminusT_lem,definition,
% 3.24/1.63 ( setminusT_lem
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(complementT_lem_type,type,
% 3.24/1.63 complementT_lem: $o ).
% 3.24/1.63
% 3.24/1.63 thf(complementT_lem,definition,
% 3.24/1.63 ( complementT_lem
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setextT_type,type,
% 3.24/1.63 setextT: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setextT,definition,
% 3.24/1.63 ( setextT
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( in @ Xx @ X )
% 3.24/1.63 => ( in @ Xx @ Y ) ) )
% 3.24/1.63 => ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( in @ Xx @ Y )
% 3.24/1.63 => ( in @ Xx @ X ) ) )
% 3.24/1.63 => ( X = Y ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(subsetTI_type,type,
% 3.24/1.63 subsetTI: $o ).
% 3.24/1.63
% 3.24/1.63 thf(subsetTI,definition,
% 3.24/1.63 ( subsetTI
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( in @ Xx @ X )
% 3.24/1.63 => ( in @ Xx @ Y ) ) )
% 3.24/1.63 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(powersetTI1_type,type,
% 3.24/1.63 powersetTI1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(powersetTI1,definition,
% 3.24/1.63 ( powersetTI1
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( in @ Xx @ X )
% 3.24/1.63 => ( in @ Xx @ Y ) ) )
% 3.24/1.63 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(powersetTE1_type,type,
% 3.24/1.63 powersetTE1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(powersetTE1,definition,
% 3.24/1.63 ( powersetTE1
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( in @ X @ ( powerset @ Y ) )
% 3.24/1.63 => ( ( in @ Xx @ X )
% 3.24/1.63 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(complementTI1_type,type,
% 3.24/1.63 complementTI1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(complementTI1,definition,
% 3.24/1.63 ( complementTI1
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( in @ Xx @ X )
% 3.24/1.63 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(complementTE1_type,type,
% 3.24/1.63 complementTE1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(complementTE1,definition,
% 3.24/1.63 ( complementTE1
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 3.24/1.63 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(binintersectTELcontra_type,type,
% 3.24/1.63 binintersectTELcontra: $o ).
% 3.24/1.63
% 3.24/1.63 thf(binintersectTELcontra,definition,
% 3.24/1.63 ( binintersectTELcontra
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ~ ( in @ Xx @ X )
% 3.24/1.63 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(binintersectTERcontra_type,type,
% 3.24/1.63 binintersectTERcontra: $o ).
% 3.24/1.63
% 3.24/1.63 thf(binintersectTERcontra,definition,
% 3.24/1.63 ( binintersectTERcontra
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ~ ( in @ Xx @ Y )
% 3.24/1.63 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(contrasubsetT_type,type,
% 3.24/1.63 contrasubsetT: $o ).
% 3.24/1.63
% 3.24/1.63 thf(contrasubsetT,definition,
% 3.24/1.63 ( contrasubsetT
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.24/1.63 => ( ( in @ Xx @ Y )
% 3.24/1.63 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(contrasubsetT1_type,type,
% 3.24/1.63 contrasubsetT1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(contrasubsetT1,definition,
% 3.24/1.63 ( contrasubsetT1
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( subset @ X @ Y )
% 3.24/1.63 => ( ~ ( in @ Xx @ Y )
% 3.24/1.63 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(contrasubsetT2_type,type,
% 3.24/1.63 contrasubsetT2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(contrasubsetT2,definition,
% 3.24/1.63 ( contrasubsetT2
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ( ( subset @ X @ Y )
% 3.24/1.63 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(contrasubsetT3_type,type,
% 3.24/1.63 contrasubsetT3: $o ).
% 3.24/1.63
% 3.24/1.63 thf(contrasubsetT3,definition,
% 3.24/1.63 ( contrasubsetT3
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 3.24/1.63 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(doubleComplementI1_type,type,
% 3.24/1.63 doubleComplementI1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(doubleComplementI1,definition,
% 3.24/1.63 ( doubleComplementI1
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( in @ Xx @ X )
% 3.24/1.63 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(doubleComplementE1_type,type,
% 3.24/1.63 doubleComplementE1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(doubleComplementE1,definition,
% 3.24/1.63 ( doubleComplementE1
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 3.24/1.63 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(doubleComplementSub1_type,type,
% 3.24/1.63 doubleComplementSub1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(doubleComplementSub1,definition,
% 3.24/1.63 ( doubleComplementSub1
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(doubleComplementSub2_type,type,
% 3.24/1.63 doubleComplementSub2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(doubleComplementSub2,definition,
% 3.24/1.63 ( doubleComplementSub2
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(doubleComplementEq_type,type,
% 3.24/1.63 doubleComplementEq: $o ).
% 3.24/1.63
% 3.24/1.63 thf(doubleComplementEq,definition,
% 3.24/1.63 ( doubleComplementEq
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ( X
% 3.24/1.63 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(complementTnotintersectT_type,type,
% 3.24/1.63 complementTnotintersectT: $o ).
% 3.24/1.63
% 3.24/1.63 thf(complementTnotintersectT,definition,
% 3.24/1.63 ( complementTnotintersectT
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.24/1.63 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(complementImpComplementIntersect_type,type,
% 3.24/1.63 complementImpComplementIntersect: $o ).
% 3.24/1.63
% 3.24/1.63 thf(complementImpComplementIntersect,definition,
% 3.24/1.63 ( complementImpComplementIntersect
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.24/1.63 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(complementSubsetComplementIntersect_type,type,
% 3.24/1.63 complementSubsetComplementIntersect: $o ).
% 3.24/1.63
% 3.24/1.63 thf(complementSubsetComplementIntersect,definition,
% 3.24/1.63 ( complementSubsetComplementIntersect
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(complementInPowersetComplementIntersect_type,type,
% 3.24/1.63 complementInPowersetComplementIntersect: $o ).
% 3.24/1.63
% 3.24/1.63 thf(complementInPowersetComplementIntersect,definition,
% 3.24/1.63 ( complementInPowersetComplementIntersect
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(contraSubsetComplement_type,type,
% 3.24/1.63 contraSubsetComplement: $o ).
% 3.24/1.63
% 3.24/1.63 thf(contraSubsetComplement,definition,
% 3.24/1.63 ( contraSubsetComplement
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( in @ Xx @ Y )
% 3.24/1.63 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(complementTcontraSubset_type,type,
% 3.24/1.63 complementTcontraSubset: $o ).
% 3.24/1.63
% 3.24/1.63 thf(complementTcontraSubset,definition,
% 3.24/1.63 ( complementTcontraSubset
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.24/1.63 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(binunionTILcontra_type,type,
% 3.24/1.63 binunionTILcontra: $o ).
% 3.24/1.63
% 3.24/1.63 thf(binunionTILcontra,definition,
% 3.24/1.63 ( binunionTILcontra
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.24/1.63 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(binunionTIRcontra_type,type,
% 3.24/1.63 binunionTIRcontra: $o ).
% 3.24/1.63
% 3.24/1.63 thf(binunionTIRcontra,definition,
% 3.24/1.63 ( binunionTIRcontra
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.24/1.63 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(inIntersectImpInUnion_type,type,
% 3.24/1.63 inIntersectImpInUnion: $o ).
% 3.24/1.63
% 3.24/1.63 thf(inIntersectImpInUnion,definition,
% 3.24/1.63 ( inIntersectImpInUnion
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Z: $i] :
% 3.24/1.63 ( ( in @ Z @ ( powerset @ A ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.24/1.63 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(inIntersectImpInUnion2_type,type,
% 3.24/1.63 inIntersectImpInUnion2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(inIntersectImpInUnion2,definition,
% 3.24/1.63 ( inIntersectImpInUnion2
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Z: $i] :
% 3.24/1.63 ( ( in @ Z @ ( powerset @ A ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.24/1.63 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(inIntersectImpInIntersectUnions_type,type,
% 3.24/1.63 inIntersectImpInIntersectUnions: $o ).
% 3.24/1.63
% 3.24/1.63 thf(inIntersectImpInIntersectUnions,definition,
% 3.24/1.63 ( inIntersectImpInIntersectUnions
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Z: $i] :
% 3.24/1.63 ( ( in @ Z @ ( powerset @ A ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.24/1.63 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(intersectInPowersetIntersectUnions_type,type,
% 3.24/1.63 intersectInPowersetIntersectUnions: $o ).
% 3.24/1.63
% 3.24/1.63 thf(intersectInPowersetIntersectUnions,definition,
% 3.24/1.63 ( intersectInPowersetIntersectUnions
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Z: $i] :
% 3.24/1.63 ( ( in @ Z @ ( powerset @ A ) )
% 3.24/1.63 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(inComplementUnionImpNotIn1_type,type,
% 3.24/1.63 inComplementUnionImpNotIn1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(inComplementUnionImpNotIn1,definition,
% 3.24/1.63 ( inComplementUnionImpNotIn1
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.24/1.63 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(inComplementUnionImpInComplement1_type,type,
% 3.24/1.63 inComplementUnionImpInComplement1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(inComplementUnionImpInComplement1,definition,
% 3.24/1.63 ( inComplementUnionImpInComplement1
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.24/1.63 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(binunionTE_type,type,
% 3.24/1.63 binunionTE: $o ).
% 3.24/1.63
% 3.24/1.63 thf(binunionTE,definition,
% 3.24/1.63 ( binunionTE
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Xphi: $o,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.24/1.63 => ( ( ( in @ Xx @ X )
% 3.24/1.63 => Xphi )
% 3.24/1.63 => ( ( ( in @ Xx @ Y )
% 3.24/1.63 => Xphi )
% 3.24/1.63 => Xphi ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(binunionTEcontra_type,type,
% 3.24/1.63 binunionTEcontra: $o ).
% 3.24/1.63
% 3.24/1.63 thf(binunionTEcontra,definition,
% 3.24/1.63 ( binunionTEcontra
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ~ ( in @ Xx @ X )
% 3.24/1.63 => ( ~ ( in @ Xx @ Y )
% 3.24/1.63 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(demorgan2a1_type,type,
% 3.24/1.63 demorgan2a1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(demorgan2a1,definition,
% 3.24/1.63 ( demorgan2a1
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.24/1.63 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(complementUnionInPowersetComplement_type,type,
% 3.24/1.63 complementUnionInPowersetComplement: $o ).
% 3.24/1.63
% 3.24/1.63 thf(complementUnionInPowersetComplement,definition,
% 3.24/1.63 ( complementUnionInPowersetComplement
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(demorgan2a2_type,type,
% 3.24/1.63 demorgan2a2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(demorgan2a2,definition,
% 3.24/1.63 ( demorgan2a2
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.24/1.63 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(demorgan1a_type,type,
% 3.24/1.63 demorgan1a: $o ).
% 3.24/1.63
% 3.24/1.63 thf(demorgan1a,definition,
% 3.24/1.63 ( demorgan1a
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 3.24/1.63 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(demorgan1b_type,type,
% 3.24/1.63 demorgan1b: $o ).
% 3.24/1.63
% 3.24/1.63 thf(demorgan1b,definition,
% 3.24/1.63 ( demorgan1b
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 3.24/1.63 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(demorgan1_type,type,
% 3.24/1.63 demorgan1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(demorgan1,definition,
% 3.24/1.63 ( demorgan1
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 3.24/1.63 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(demorgan2a_type,type,
% 3.24/1.63 demorgan2a: $o ).
% 3.24/1.63
% 3.24/1.63 thf(demorgan2a,definition,
% 3.24/1.63 ( demorgan2a
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.24/1.63 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(demorgan2b2_type,type,
% 3.24/1.63 demorgan2b2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(demorgan2b2,definition,
% 3.24/1.63 ( demorgan2b2
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.24/1.63 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 3.24/1.63 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(demorgan2b_type,type,
% 3.24/1.63 demorgan2b: $o ).
% 3.24/1.63
% 3.24/1.63 thf(demorgan2b,definition,
% 3.24/1.63 ( demorgan2b
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 3.24/1.63 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(demorgan2_type,type,
% 3.24/1.63 demorgan2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(demorgan2,definition,
% 3.24/1.63 ( demorgan2
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 3.24/1.63 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(woz13rule0_type,type,
% 3.24/1.63 woz13rule0: $o ).
% 3.24/1.63
% 3.24/1.63 thf(woz13rule0,definition,
% 3.24/1.63 ( woz13rule0
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.24/1.63 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(woz13rule1_type,type,
% 3.24/1.63 woz13rule1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(woz13rule1,definition,
% 3.24/1.63 ( woz13rule1
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Z: $i] :
% 3.24/1.63 ( ( in @ Z @ ( powerset @ A ) )
% 3.24/1.63 => ( ( subset @ X @ Z )
% 3.24/1.63 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(woz13rule2_type,type,
% 3.24/1.63 woz13rule2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(woz13rule2,definition,
% 3.24/1.63 ( woz13rule2
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Z: $i] :
% 3.24/1.63 ( ( in @ Z @ ( powerset @ A ) )
% 3.24/1.63 => ( ( subset @ Y @ Z )
% 3.24/1.63 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(woz13rule3_type,type,
% 3.24/1.63 woz13rule3: $o ).
% 3.24/1.63
% 3.24/1.63 thf(woz13rule3,definition,
% 3.24/1.63 ( woz13rule3
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Z: $i] :
% 3.24/1.63 ( ( in @ Z @ ( powerset @ A ) )
% 3.24/1.63 => ( ( subset @ X @ Y )
% 3.24/1.63 => ( ( subset @ X @ Z )
% 3.24/1.63 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(woz13rule4_type,type,
% 3.24/1.63 woz13rule4: $o ).
% 3.24/1.63
% 3.24/1.63 thf(woz13rule4,definition,
% 3.24/1.63 ( woz13rule4
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Z: $i] :
% 3.24/1.63 ( ( in @ Z @ ( powerset @ A ) )
% 3.24/1.63 => ! [W: $i] :
% 3.24/1.63 ( ( in @ W @ ( powerset @ A ) )
% 3.24/1.63 => ( ( subset @ X @ Z )
% 3.24/1.63 => ( ( subset @ Y @ W )
% 3.24/1.63 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(woz1_1_type,type,
% 3.24/1.63 woz1_1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(woz1_1,definition,
% 3.24/1.63 ( woz1_1
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(woz1_2_type,type,
% 3.24/1.63 woz1_2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(woz1_2,definition,
% 3.24/1.63 ( woz1_2
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Z: $i] :
% 3.24/1.63 ( ( in @ Z @ ( powerset @ A ) )
% 3.24/1.63 => ! [W: $i] :
% 3.24/1.63 ( ( in @ W @ ( powerset @ A ) )
% 3.24/1.63 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 3.24/1.63 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(woz1_3_type,type,
% 3.24/1.63 woz1_3: $o ).
% 3.24/1.63
% 3.24/1.63 thf(woz1_3,definition,
% 3.24/1.63 ( woz1_3
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ! [Z: $i] :
% 3.24/1.63 ( ( in @ Z @ ( powerset @ A ) )
% 3.24/1.63 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(woz1_4_type,type,
% 3.24/1.63 woz1_4: $o ).
% 3.24/1.63
% 3.24/1.63 thf(woz1_4,definition,
% 3.24/1.63 ( woz1_4
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.24/1.63 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(woz1_5_type,type,
% 3.24/1.63 woz1_5: $o ).
% 3.24/1.63
% 3.24/1.63 thf(woz1_5,definition,
% 3.24/1.63 ( woz1_5
% 3.24/1.63 = ( ! [A: $i,X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.24/1.63 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(breln1_type,type,
% 3.24/1.63 breln1: $i > $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(breln1all2_type,type,
% 3.24/1.63 breln1all2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(breln1all2,definition,
% 3.24/1.63 ( breln1all2
% 3.24/1.63 = ( ! [A: $i,R: $i] :
% 3.24/1.63 ( ( breln1 @ A @ R )
% 3.24/1.63 => ! [Xphi: $i > $o] :
% 3.24/1.63 ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.24/1.63 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ R )
% 3.24/1.63 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(breln1Set_type,type,
% 3.24/1.63 breln1Set: $i > $i ).
% 3.24/1.63
% 3.24/1.63 thf(breln1SetBreln1_type,type,
% 3.24/1.63 breln1SetBreln1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(breln1SetBreln1,definition,
% 3.24/1.63 ( breln1SetBreln1
% 3.24/1.63 = ( ! [A: $i,R: $i] :
% 3.24/1.63 ( ( in @ R @ ( breln1Set @ A ) )
% 3.24/1.63 => ( breln1 @ A @ R ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(transitive_type,type,
% 3.24/1.63 transitive: $i > $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(antisymmetric_type,type,
% 3.24/1.63 antisymmetric: $i > $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(reflexive_type,type,
% 3.24/1.63 reflexive: $i > $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(refltransitive_type,type,
% 3.24/1.63 refltransitive: $i > $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(refllinearorder_type,type,
% 3.24/1.63 refllinearorder: $i > $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(reflwellordering_type,type,
% 3.24/1.63 reflwellordering: $i > $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(choice2fnsingleton_type,type,
% 3.24/1.63 choice2fnsingleton: $o ).
% 3.24/1.63
% 3.24/1.63 thf(choice2fnsingleton,definition,
% 3.24/1.63 ( choice2fnsingleton
% 3.24/1.63 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.24/1.63 ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ? [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ B )
% 3.24/1.63 & ( Xphi @ Xx @ Xy ) ) )
% 3.24/1.63 => ! [R: $i] :
% 3.24/1.63 ( ( in @ R @ ( breln1Set @ B ) )
% 3.24/1.63 => ( ( reflwellordering @ B @ R )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( singleton
% 3.24/1.63 @ ( dsetconstr @ B
% 3.24/1.63 @ ^ [Xy: $i] :
% 3.24/1.63 ( ( Xphi @ Xx @ Xy )
% 3.24/1.63 & ! [Xz: $i] :
% 3.24/1.63 ( ( in @ Xz @ B )
% 3.24/1.63 => ( ( Xphi @ Xx @ Xz )
% 3.24/1.63 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setOfPairsIsBReln1_type,type,
% 3.24/1.63 setOfPairsIsBReln1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setOfPairsIsBReln1,definition,
% 3.24/1.63 ( setOfPairsIsBReln1
% 3.24/1.63 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 3.24/1.63 ( breln1 @ A
% 3.24/1.63 @ ( dpsetconstr @ A @ A
% 3.24/1.63 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(breln1all1_type,type,
% 3.24/1.63 breln1all1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(breln1all1,definition,
% 3.24/1.63 ( breln1all1
% 3.24/1.63 = ( ! [A: $i,R: $i] :
% 3.24/1.63 ( ( breln1 @ A @ R )
% 3.24/1.63 => ! [Xphi: $i > $o] :
% 3.24/1.63 ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.24/1.63 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ R )
% 3.24/1.63 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(subbreln1_type,type,
% 3.24/1.63 subbreln1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(subbreln1,definition,
% 3.24/1.63 ( subbreln1
% 3.24/1.63 = ( ! [A: $i,R: $i] :
% 3.24/1.63 ( ( breln1 @ A @ R )
% 3.24/1.63 => ! [S: $i] :
% 3.24/1.63 ( ( breln1 @ A @ S )
% 3.24/1.63 => ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.24/1.63 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.24/1.63 => ( subset @ R @ S ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(eqbreln1_type,type,
% 3.24/1.63 eqbreln1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(eqbreln1,definition,
% 3.24/1.63 ( eqbreln1
% 3.24/1.63 = ( ! [A: $i,R: $i] :
% 3.24/1.63 ( ( breln1 @ A @ R )
% 3.24/1.63 => ! [S: $i] :
% 3.24/1.63 ( ( breln1 @ A @ S )
% 3.24/1.63 => ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.24/1.63 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.24/1.63 => ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.24/1.63 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 3.24/1.63 => ( R = S ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(breln1invset_type,type,
% 3.24/1.63 breln1invset: $i > $i > $i ).
% 3.24/1.63
% 3.24/1.63 thf(breln1invprop_type,type,
% 3.24/1.63 breln1invprop: $o ).
% 3.24/1.63
% 3.24/1.63 thf(breln1invprop,definition,
% 3.24/1.63 ( breln1invprop
% 3.24/1.63 = ( ! [A: $i,R: $i] :
% 3.24/1.63 ( ( breln1 @ A @ R )
% 3.24/1.63 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(breln1invI_type,type,
% 3.24/1.63 breln1invI: $o ).
% 3.24/1.63
% 3.24/1.63 thf(breln1invI,definition,
% 3.24/1.63 ( breln1invI
% 3.24/1.63 = ( ! [A: $i,R: $i] :
% 3.24/1.63 ( ( breln1 @ A @ R )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.24/1.63 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(breln1invE_type,type,
% 3.24/1.63 breln1invE: $o ).
% 3.24/1.63
% 3.24/1.63 thf(breln1invE,definition,
% 3.24/1.63 ( breln1invE
% 3.24/1.63 = ( ! [A: $i,R: $i] :
% 3.24/1.63 ( ( breln1 @ A @ R )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 3.24/1.63 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(breln1compset_type,type,
% 3.24/1.63 breln1compset: $i > $i > $i > $i ).
% 3.24/1.63
% 3.24/1.63 thf(breln1compprop_type,type,
% 3.24/1.63 breln1compprop: $o ).
% 3.24/1.63
% 3.24/1.63 thf(breln1compprop,definition,
% 3.24/1.63 ( breln1compprop
% 3.24/1.63 = ( ! [A: $i,R: $i] :
% 3.24/1.63 ( ( breln1 @ A @ R )
% 3.24/1.63 => ! [S: $i] :
% 3.24/1.63 ( ( breln1 @ A @ S )
% 3.24/1.63 => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(breln1compI_type,type,
% 3.24/1.63 breln1compI: $o ).
% 3.24/1.63
% 3.24/1.63 thf(breln1compI,definition,
% 3.24/1.63 ( breln1compI
% 3.24/1.63 = ( ! [A: $i,R: $i] :
% 3.24/1.63 ( ( breln1 @ A @ R )
% 3.24/1.63 => ! [S: $i] :
% 3.24/1.63 ( ( breln1 @ A @ S )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 => ! [Xz: $i] :
% 3.24/1.63 ( ( in @ Xz @ A )
% 3.24/1.63 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 3.24/1.63 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 3.24/1.63 => ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(breln1compE_type,type,
% 3.24/1.63 breln1compE: $o ).
% 3.24/1.63
% 3.24/1.63 thf(breln1compE,definition,
% 3.24/1.63 ( breln1compE
% 3.24/1.63 = ( ! [A: $i,R: $i] :
% 3.24/1.63 ( ( breln1 @ A @ R )
% 3.24/1.63 => ! [S: $i] :
% 3.24/1.63 ( ( breln1 @ A @ S )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 3.24/1.63 => ? [Xz: $i] :
% 3.24/1.63 ( ( in @ Xz @ A )
% 3.24/1.63 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 3.24/1.63 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(breln1compEex_type,type,
% 3.24/1.63 breln1compEex: $o ).
% 3.24/1.63
% 3.24/1.63 thf(breln1compEex,definition,
% 3.24/1.63 ( breln1compEex
% 3.24/1.63 = ( ! [A: $i,R: $i] :
% 3.24/1.63 ( ( breln1 @ A @ R )
% 3.24/1.63 => ! [S: $i] :
% 3.24/1.63 ( ( breln1 @ A @ S )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 3.24/1.63 => ! [Xphi: $o] :
% 3.24/1.63 ( ! [Xz: $i] :
% 3.24/1.63 ( ( in @ Xz @ A )
% 3.24/1.63 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 3.24/1.63 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 3.24/1.63 => Xphi ) ) )
% 3.24/1.63 => Xphi ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(breln1unionprop_type,type,
% 3.24/1.63 breln1unionprop: $o ).
% 3.24/1.63
% 3.24/1.63 thf(breln1unionprop,definition,
% 3.24/1.63 ( breln1unionprop
% 3.24/1.63 = ( ! [A: $i,R: $i] :
% 3.24/1.63 ( ( breln1 @ A @ R )
% 3.24/1.63 => ! [S: $i] :
% 3.24/1.63 ( ( breln1 @ A @ S )
% 3.24/1.63 => ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(breln1unionIL_type,type,
% 3.24/1.63 breln1unionIL: $o ).
% 3.24/1.63
% 3.24/1.63 thf(breln1unionIL,definition,
% 3.24/1.63 ( breln1unionIL
% 3.24/1.63 = ( ! [A: $i,R: $i] :
% 3.24/1.63 ( ( breln1 @ A @ R )
% 3.24/1.63 => ! [S: $i] :
% 3.24/1.63 ( ( breln1 @ A @ S )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.24/1.63 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(breln1unionIR_type,type,
% 3.24/1.63 breln1unionIR: $o ).
% 3.24/1.63
% 3.24/1.63 thf(breln1unionIR,definition,
% 3.24/1.63 ( breln1unionIR
% 3.24/1.63 = ( ! [A: $i,R: $i] :
% 3.24/1.63 ( ( breln1 @ A @ R )
% 3.24/1.63 => ! [S: $i] :
% 3.24/1.63 ( ( breln1 @ A @ S )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.24/1.63 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(breln1unionI_type,type,
% 3.24/1.63 breln1unionI: $o ).
% 3.24/1.63
% 3.24/1.63 thf(breln1unionI,definition,
% 3.24/1.63 ( breln1unionI
% 3.24/1.63 = ( ! [A: $i,R: $i] :
% 3.24/1.63 ( ( breln1 @ A @ R )
% 3.24/1.63 => ! [S: $i] :
% 3.24/1.63 ( ( breln1 @ A @ S )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.24/1.63 | ( in @ ( kpair @ Xx @ Xy ) @ S ) )
% 3.24/1.63 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(breln1unionE_type,type,
% 3.24/1.63 breln1unionE: $o ).
% 3.24/1.63
% 3.24/1.63 thf(breln1unionE,definition,
% 3.24/1.63 ( breln1unionE
% 3.24/1.63 = ( ! [A: $i,R: $i] :
% 3.24/1.63 ( ( breln1 @ A @ R )
% 3.24/1.63 => ! [S: $i] :
% 3.24/1.63 ( ( breln1 @ A @ S )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 3.24/1.63 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.24/1.63 | ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(breln1unionEcases_type,type,
% 3.24/1.63 breln1unionEcases: $o ).
% 3.24/1.63
% 3.24/1.63 thf(breln1unionEcases,definition,
% 3.24/1.63 ( breln1unionEcases
% 3.24/1.63 = ( ! [A: $i,R: $i] :
% 3.24/1.63 ( ( breln1 @ A @ R )
% 3.24/1.63 => ! [S: $i] :
% 3.24/1.63 ( ( breln1 @ A @ S )
% 3.24/1.63 => ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 3.24/1.63 => ! [Xphi: $o] :
% 3.24/1.63 ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.24/1.63 => Xphi )
% 3.24/1.63 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.24/1.63 => Xphi )
% 3.24/1.63 => Xphi ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(breln1unionCommutes_type,type,
% 3.24/1.63 breln1unionCommutes: $o ).
% 3.24/1.63
% 3.24/1.63 thf(breln1unionCommutes,definition,
% 3.24/1.63 ( breln1unionCommutes
% 3.24/1.63 = ( ! [A: $i,R: $i] :
% 3.24/1.63 ( ( breln1 @ A @ R )
% 3.24/1.63 => ! [S: $i] :
% 3.24/1.63 ( ( breln1 @ A @ S )
% 3.24/1.63 => ( ( binunion @ R @ S )
% 3.24/1.63 = ( binunion @ S @ R ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(woz2Ex_type,type,
% 3.24/1.63 woz2Ex: $o ).
% 3.24/1.63
% 3.24/1.63 thf(woz2Ex,definition,
% 3.24/1.63 ( woz2Ex
% 3.24/1.63 = ( ! [A: $i,R: $i] :
% 3.24/1.63 ( ( breln1 @ A @ R )
% 3.24/1.63 => ( R
% 3.24/1.63 = ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(woz2W_type,type,
% 3.24/1.63 woz2W: $o ).
% 3.24/1.63
% 3.24/1.63 thf(woz2W,definition,
% 3.24/1.63 ( woz2W
% 3.24/1.63 = ( ! [A: $i,R: $i] :
% 3.24/1.63 ( ( breln1 @ A @ R )
% 3.24/1.63 => ! [S: $i] :
% 3.24/1.63 ( ( breln1 @ A @ S )
% 3.24/1.63 => ( ( breln1invset @ A @ ( breln1compset @ A @ R @ S ) )
% 3.24/1.63 = ( breln1compset @ A @ ( breln1invset @ A @ S ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(woz2A_type,type,
% 3.24/1.63 woz2A: $o ).
% 3.24/1.63
% 3.24/1.63 thf(woz2A,definition,
% 3.24/1.63 ( woz2A
% 3.24/1.63 = ( ! [A: $i,R: $i] :
% 3.24/1.63 ( ( breln1 @ A @ R )
% 3.24/1.63 => ! [S: $i] :
% 3.24/1.63 ( ( breln1 @ A @ S )
% 3.24/1.63 => ! [T: $i] :
% 3.24/1.63 ( ( breln1 @ A @ T )
% 3.24/1.63 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 3.24/1.63 = ( binunion @ ( breln1compset @ A @ R @ T ) @ ( breln1compset @ A @ S @ T ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(woz2B_type,type,
% 3.24/1.63 woz2B: $o ).
% 3.24/1.63
% 3.24/1.63 thf(woz2B,definition,
% 3.24/1.63 ( woz2B
% 3.24/1.63 = ( ! [A: $i,R: $i] :
% 3.24/1.63 ( ( breln1 @ A @ R )
% 3.24/1.63 => ! [S: $i] :
% 3.24/1.63 ( ( breln1 @ A @ S )
% 3.24/1.63 => ! [T: $i] :
% 3.24/1.63 ( ( breln1 @ A @ T )
% 3.24/1.63 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 3.24/1.63 = ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ S ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(image1Ex_type,type,
% 3.24/1.63 image1Ex: $o ).
% 3.24/1.63
% 3.24/1.63 thf(image1Ex,definition,
% 3.24/1.63 ( image1Ex
% 3.24/1.63 = ( ! [A: $i,Xf: $i > $i] :
% 3.24/1.63 ? [B: $i] :
% 3.24/1.63 ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ B )
% 3.24/1.63 <=> ? [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 & ( Xx
% 3.24/1.63 = ( Xf @ Xy ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(image1Ex1_type,type,
% 3.24/1.63 image1Ex1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(image1Ex1,definition,
% 3.24/1.63 ( image1Ex1
% 3.24/1.63 = ( ! [A: $i,Xf: $i > $i] :
% 3.24/1.63 ( exu
% 3.24/1.63 @ ^ [B: $i] :
% 3.24/1.63 ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ B )
% 3.24/1.63 <=> ? [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 & ( Xx
% 3.24/1.63 = ( Xf @ Xy ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(image1_type,type,
% 3.24/1.63 image1: $i > ( $i > $i ) > $i ).
% 3.24/1.63
% 3.24/1.63 thf(image1Equiv_type,type,
% 3.24/1.63 image1Equiv: $o ).
% 3.24/1.63
% 3.24/1.63 thf(image1Equiv,definition,
% 3.24/1.63 ( image1Equiv
% 3.24/1.63 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx
% 3.24/1.63 @ ( image1 @ A
% 3.24/1.63 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 3.24/1.63 <=> ? [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 & ( Xx
% 3.24/1.63 = ( Xf @ Xy ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(image1E_type,type,
% 3.24/1.63 image1E: $o ).
% 3.24/1.63
% 3.24/1.63 thf(image1E,definition,
% 3.24/1.63 ( image1E
% 3.24/1.63 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 3.24/1.63 ( ( in @ Xx
% 3.24/1.63 @ ( image1 @ A
% 3.24/1.63 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 3.24/1.63 => ? [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 & ( Xx
% 3.24/1.63 = ( Xf @ Xy ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(image1I_type,type,
% 3.24/1.63 image1I: $o ).
% 3.24/1.63
% 3.24/1.63 thf(image1I,definition,
% 3.24/1.63 ( image1I
% 3.24/1.63 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 3.24/1.63 ( ? [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ A )
% 3.24/1.63 & ( Xx
% 3.24/1.63 = ( Xf @ Xy ) ) )
% 3.24/1.63 => ( in @ Xx
% 3.24/1.63 @ ( image1 @ A
% 3.24/1.63 @ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(injective_type,type,
% 3.24/1.63 injective: $i > $i > $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(injFuncSet_type,type,
% 3.24/1.63 injFuncSet: $i > $i > $i ).
% 3.24/1.63
% 3.24/1.63 thf(injFuncInInjFuncSet_type,type,
% 3.24/1.63 injFuncInInjFuncSet: $o ).
% 3.24/1.63
% 3.24/1.63 thf(injFuncInInjFuncSet,definition,
% 3.24/1.63 ( injFuncInInjFuncSet
% 3.24/1.63 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.24/1.63 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.24/1.63 => ( ( injective @ A @ B @ Xf )
% 3.24/1.63 => ( in @ Xf @ ( injFuncSet @ A @ B ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(injFuncSetFuncIn_type,type,
% 3.24/1.63 injFuncSetFuncIn: $o ).
% 3.24/1.63
% 3.24/1.63 thf(injFuncSetFuncIn,definition,
% 3.24/1.63 ( injFuncSetFuncIn
% 3.24/1.63 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.24/1.63 ( ( in @ Xf @ ( injFuncSet @ A @ B ) )
% 3.24/1.63 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(injFuncSetFuncInj_type,type,
% 3.24/1.63 injFuncSetFuncInj: $o ).
% 3.24/1.63
% 3.24/1.63 thf(injFuncSetFuncInj,definition,
% 3.24/1.63 ( injFuncSetFuncInj
% 3.24/1.63 = ( ! [Xx: $i,Xy: $i,Xf: $i] :
% 3.24/1.63 ( ( in @ Xf @ ( injFuncSet @ Xx @ Xy ) )
% 3.24/1.63 => ( injective @ Xx @ Xy @ Xf ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(surjective_type,type,
% 3.24/1.63 surjective: $i > $i > $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(surjFuncSet_type,type,
% 3.24/1.63 surjFuncSet: $i > $i > $i ).
% 3.24/1.63
% 3.24/1.63 thf(surjFuncSetFuncIn_type,type,
% 3.24/1.63 surjFuncSetFuncIn: $o ).
% 3.24/1.63
% 3.24/1.63 thf(surjFuncSetFuncIn,definition,
% 3.24/1.63 ( surjFuncSetFuncIn
% 3.24/1.63 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.24/1.63 ( ( in @ Xf @ ( surjFuncSet @ A @ B ) )
% 3.24/1.63 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(surjFuncSetFuncSurj_type,type,
% 3.24/1.63 surjFuncSetFuncSurj: $o ).
% 3.24/1.63
% 3.24/1.63 thf(surjFuncSetFuncSurj,definition,
% 3.24/1.63 ( surjFuncSetFuncSurj
% 3.24/1.63 = ( ! [Xx: $i,Xy: $i,Xf: $i] :
% 3.24/1.63 ( ( in @ Xf @ ( surjFuncSet @ Xx @ Xy ) )
% 3.24/1.63 => ( surjective @ Xx @ Xy @ Xf ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(leftInvIsSurj_type,type,
% 3.24/1.63 leftInvIsSurj: $o ).
% 3.24/1.63
% 3.24/1.63 thf(leftInvIsSurj,definition,
% 3.24/1.63 ( leftInvIsSurj
% 3.24/1.63 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.24/1.63 ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.24/1.63 => ! [Xg: $i] :
% 3.24/1.63 ( ( in @ Xg @ ( funcSet @ B @ A ) )
% 3.24/1.63 => ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ( ( ap @ B @ A @ Xg @ ( Xf @ Xx ) )
% 3.24/1.63 = Xx ) )
% 3.24/1.63 => ( surjective @ B @ A @ Xg ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(surjCantorThm_type,type,
% 3.24/1.63 surjCantorThm: $o ).
% 3.24/1.63
% 3.24/1.63 thf(surjCantorThm,definition,
% 3.24/1.63 ( surjCantorThm
% 3.24/1.63 = ( ! [A: $i,Xf: $i] :
% 3.24/1.63 ( ( in @ Xf @ ( funcSet @ A @ ( powerset @ A ) ) )
% 3.24/1.63 => ~ ( surjective @ A @ ( powerset @ A ) @ Xf ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(foundation2_type,type,
% 3.24/1.63 foundation2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(foundation2,definition,
% 3.24/1.63 ( foundation2
% 3.24/1.63 = ( ! [A: $i] :
% 3.24/1.63 ( ( nonempty @ A )
% 3.24/1.63 => ? [X: $i] :
% 3.24/1.63 ( ( in @ X @ A )
% 3.24/1.63 & ( ( binintersect @ X @ A )
% 3.24/1.63 = emptyset ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(notinself_type,type,
% 3.24/1.63 notinself: $o ).
% 3.24/1.63
% 3.24/1.63 thf(notinself,definition,
% 3.24/1.63 ( notinself
% 3.24/1.63 = ( ! [A: $i] :
% 3.24/1.63 ~ ( in @ A @ A ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(notinself2_type,type,
% 3.24/1.63 notinself2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(notinself2,definition,
% 3.24/1.63 ( notinself2
% 3.24/1.63 = ( ! [A: $i,B: $i] :
% 3.24/1.63 ( ( in @ A @ B )
% 3.24/1.63 => ~ ( in @ B @ A ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(omegaS_type,type,
% 3.24/1.63 omegaS: $i > $i ).
% 3.24/1.63
% 3.24/1.63 thf(omegaSp_type,type,
% 3.24/1.63 omegaSp: $o ).
% 3.24/1.63
% 3.24/1.63 thf(omegaSp,definition,
% 3.24/1.63 ( omegaSp
% 3.24/1.63 = ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ omega )
% 3.24/1.63 => ( in @ ( omegaS @ Xx ) @ omega ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(omegaSclos_type,type,
% 3.24/1.63 omegaSclos: $o ).
% 3.24/1.63
% 3.24/1.63 thf(omegaSclos,definition,
% 3.24/1.63 ( omegaSclos
% 3.24/1.63 = ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ omega )
% 3.24/1.63 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(peano0notS_type,type,
% 3.24/1.63 peano0notS: $o ).
% 3.24/1.63
% 3.24/1.63 thf(peano0notS,definition,
% 3.24/1.63 ( peano0notS
% 3.24/1.63 = ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ omega )
% 3.24/1.63 => ( ( omegaS @ Xx )
% 3.24/1.63 != emptyset ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(peano3_type,type,
% 3.24/1.63 peano3: $i > $i > $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(peano4_type,type,
% 3.24/1.63 peano4: $i > $i > $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(peano5_type,type,
% 3.24/1.63 peano5: $i > $i > $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(peanoSinj_type,type,
% 3.24/1.63 peanoSinj: $o ).
% 3.24/1.63
% 3.24/1.63 thf(peanoSinj,definition,
% 3.24/1.63 ( peanoSinj
% 3.24/1.63 = ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ omega )
% 3.24/1.63 => ! [Xy: $i] :
% 3.24/1.63 ( ( in @ Xy @ omega )
% 3.24/1.63 => ( ( ( omegaS @ Xx )
% 3.24/1.63 = ( omegaS @ Xy ) )
% 3.24/1.63 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(peano_type,type,
% 3.24/1.63 peano: $i > $i > $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(transitiveset_type,type,
% 3.24/1.63 transitiveset: $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(transitiveset,definition,
% 3.24/1.63 ( transitiveset
% 3.24/1.63 = ( ^ [A: $i] :
% 3.24/1.63 ! [X: $i] :
% 3.24/1.63 ( ( in @ X @ A )
% 3.24/1.63 => ( subset @ X @ A ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(transitivesetOp1_type,type,
% 3.24/1.63 transitivesetOp1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(transitivesetOp1,definition,
% 3.24/1.63 ( transitivesetOp1
% 3.24/1.63 = ( ! [X: $i] :
% 3.24/1.63 ( ( transitiveset @ X )
% 3.24/1.63 => ! [A: $i] :
% 3.24/1.63 ( ( in @ A @ X )
% 3.24/1.63 => ( subset @ A @ X ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(binintTransitive_type,type,
% 3.24/1.63 binintTransitive: $o ).
% 3.24/1.63
% 3.24/1.63 thf(binintTransitive,definition,
% 3.24/1.63 ( binintTransitive
% 3.24/1.63 = ( ! [X: $i] :
% 3.24/1.63 ( ( transitiveset @ X )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( transitiveset @ Y )
% 3.24/1.63 => ( transitiveset @ ( binintersect @ X @ Y ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(transitivesetOp2_type,type,
% 3.24/1.63 transitivesetOp2: $o ).
% 3.24/1.63
% 3.24/1.63 thf(transitivesetOp2,definition,
% 3.24/1.63 ( transitivesetOp2
% 3.24/1.63 = ( ! [X: $i] :
% 3.24/1.63 ( ( transitiveset @ X )
% 3.24/1.63 => ! [A: $i,Xx: $i] :
% 3.24/1.63 ( ( in @ A @ X )
% 3.24/1.63 => ( ( in @ Xx @ A )
% 3.24/1.63 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setunionTransitive_type,type,
% 3.24/1.63 setunionTransitive: $o ).
% 3.24/1.63
% 3.24/1.63 thf(setunionTransitive,definition,
% 3.24/1.63 ( setunionTransitive
% 3.24/1.63 = ( ! [X: $i] :
% 3.24/1.63 ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ X )
% 3.24/1.63 => ( transitiveset @ Xx ) )
% 3.24/1.63 => ( transitiveset @ ( setunion @ X ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(stricttotalorderedByIn_type,type,
% 3.24/1.63 stricttotalorderedByIn: $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(stricttotalorderedByIn,definition,
% 3.24/1.63 ( stricttotalorderedByIn
% 3.24/1.63 = ( ^ [A: $i] :
% 3.24/1.63 ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ A )
% 3.24/1.63 => ! [X: $i] :
% 3.24/1.63 ( ( in @ X @ A )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ A )
% 3.24/1.63 => ( ( ( in @ Xx @ X )
% 3.24/1.63 & ( in @ X @ Y ) )
% 3.24/1.63 => ( in @ Xx @ Y ) ) ) ) )
% 3.24/1.63 & ! [X: $i] :
% 3.24/1.63 ( ( in @ X @ A )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ A )
% 3.24/1.63 => ( ( X = Y )
% 3.24/1.63 | ( in @ X @ Y )
% 3.24/1.63 | ( in @ Y @ X ) ) ) )
% 3.24/1.63 & ! [X: $i] :
% 3.24/1.63 ( ( in @ X @ A )
% 3.24/1.63 => ~ ( in @ X @ X ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(wellorderedByIn_type,type,
% 3.24/1.63 wellorderedByIn: $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(wellorderedByIn,definition,
% 3.24/1.63 ( wellorderedByIn
% 3.24/1.63 = ( ^ [A: $i] :
% 3.24/1.63 ( ( stricttotalorderedByIn @ A )
% 3.24/1.63 & ! [X: $i] :
% 3.24/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.24/1.63 => ( ( nonempty @ X )
% 3.24/1.63 => ? [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ X )
% 3.24/1.63 & ! [Y: $i] :
% 3.24/1.63 ( ( in @ Y @ X )
% 3.24/1.63 => ( ( Xx = Y )
% 3.24/1.63 | ( in @ Xx @ Y ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(ordinal_type,type,
% 3.24/1.63 ordinal: $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(ordinal,definition,
% 3.24/1.63 ( ordinal
% 3.24/1.63 = ( ^ [Xx: $i] :
% 3.24/1.63 ( ( transitiveset @ Xx )
% 3.24/1.63 & ( wellorderedByIn @ Xx ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(limitOrdinal_type,type,
% 3.24/1.63 limitOrdinal: $i > $o ).
% 3.24/1.63
% 3.24/1.63 thf(ordinalMinLem1_type,type,
% 3.24/1.63 ordinalMinLem1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(ordinalMinLem1,definition,
% 3.24/1.63 ( ordinalMinLem1
% 3.24/1.63 = ( ! [X: $i] :
% 3.24/1.63 ( ( ordinal @ X )
% 3.24/1.63 => ! [Y: $i] :
% 3.24/1.63 ( ( ordinal @ Y )
% 3.24/1.63 => ( transitiveset @ ( binintersect @ X @ Y ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(ordinalTransSet_type,type,
% 3.24/1.63 ordinalTransSet: $o ).
% 3.24/1.63
% 3.24/1.63 thf(ordinalTransSet,definition,
% 3.24/1.63 ( ordinalTransSet
% 3.24/1.63 = ( ! [X: $i] :
% 3.24/1.63 ( ( ordinal @ X )
% 3.24/1.63 => ! [Xx: $i,A: $i] :
% 3.24/1.63 ( ( in @ A @ X )
% 3.24/1.63 => ( ( in @ Xx @ A )
% 3.24/1.63 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(ordinalTransSet1_type,type,
% 3.24/1.63 ordinalTransSet1: $o ).
% 3.24/1.63
% 3.24/1.63 thf(ordinalTransSet1,definition,
% 3.24/1.63 ( ordinalTransSet1
% 3.24/1.63 = ( ! [X: $i] :
% 3.24/1.63 ( ( ordinal @ X )
% 3.24/1.63 => ! [A: $i] :
% 3.24/1.63 ( ( in @ A @ X )
% 3.24/1.63 => ( subset @ A @ X ) ) ) ) ) ).
% 3.24/1.63
% 3.24/1.63 thf(setunionOrdinalLem1,conjecture,
% 3.24/1.63 ( setextAx
% 3.24/1.63 => ( emptysetAx
% 3.24/1.63 => ( setadjoinAx
% 3.24/1.63 => ( powersetAx
% 3.24/1.63 => ( setunionAx
% 3.24/1.63 => ( omega0Ax
% 3.24/1.63 => ( omegaSAx
% 3.24/1.63 => ( omegaIndAx
% 3.24/1.63 => ( replAx
% 3.24/1.63 => ( foundationAx
% 3.24/1.63 => ( wellorderingAx
% 3.24/1.63 => ( descrp
% 3.24/1.63 => ( dsetconstrI
% 3.24/1.63 => ( dsetconstrEL
% 3.24/1.63 => ( dsetconstrER
% 3.24/1.63 => ( exuE1
% 3.24/1.63 => ( prop2setE
% 3.24/1.63 => ( emptysetE
% 3.24/1.63 => ( emptysetimpfalse
% 3.24/1.63 => ( notinemptyset
% 3.24/1.63 => ( exuE3e
% 3.24/1.63 => ( setext
% 3.24/1.63 => ( emptyI
% 3.24/1.63 => ( noeltsimpempty
% 3.24/1.63 => ( setbeta
% 3.24/1.63 => ( nonemptyE1
% 3.24/1.63 => ( nonemptyI
% 3.24/1.63 => ( nonemptyI1
% 3.24/1.63 => ( setadjoinIL
% 3.24/1.63 => ( emptyinunitempty
% 3.24/1.63 => ( setadjoinIR
% 3.24/1.63 => ( setadjoinE
% 3.24/1.63 => ( setadjoinOr
% 3.24/1.63 => ( setoftrueEq
% 3.24/1.63 => ( powersetI
% 3.24/1.63 => ( emptyinPowerset
% 3.24/1.63 => ( emptyInPowerset
% 3.24/1.63 => ( powersetE
% 3.24/1.63 => ( setunionI
% 3.24/1.63 => ( setunionE
% 3.24/1.63 => ( subPowSU
% 3.24/1.63 => ( exuE2
% 3.24/1.63 => ( nonemptyImpWitness
% 3.24/1.63 => ( uniqinunit
% 3.24/1.63 => ( notinsingleton
% 3.24/1.63 => ( eqinunit
% 3.24/1.63 => ( singletonsswitch
% 3.24/1.63 => ( upairsetE
% 3.24/1.63 => ( upairsetIL
% 3.24/1.63 => ( upairsetIR
% 3.24/1.63 => ( emptyE1
% 3.24/1.63 => ( vacuousDall
% 3.24/1.63 => ( quantDeMorgan1
% 3.24/1.63 => ( quantDeMorgan2
% 3.24/1.63 => ( quantDeMorgan3
% 3.24/1.63 => ( quantDeMorgan4
% 3.24/1.63 => ( prop2setI
% 3.24/1.63 => ( prop2set2propI
% 3.24/1.63 => ( notdexE
% 3.24/1.63 => ( notdallE
% 3.24/1.63 => ( exuI1
% 3.24/1.63 => ( exuI3
% 3.24/1.63 => ( exuI2
% 3.24/1.63 => ( inCongP
% 3.24/1.63 => ( in__Cong
% 3.24/1.63 => ( exuE3u
% 3.24/1.63 => ( exu__Cong
% 3.24/1.63 => ( emptyset__Cong
% 3.24/1.63 => ( setadjoin__Cong
% 3.24/1.63 => ( powerset__Cong
% 3.24/1.63 => ( setunion__Cong
% 3.24/1.63 => ( omega__Cong
% 3.24/1.63 => ( exuEu
% 3.24/1.63 => ( descr__Cong
% 3.24/1.63 => ( dsetconstr__Cong
% 3.24/1.63 => ( subsetI1
% 3.24/1.63 => ( eqimpsubset2
% 3.24/1.63 => ( eqimpsubset1
% 3.24/1.63 => ( subsetI2
% 3.24/1.63 => ( emptysetsubset
% 3.24/1.63 => ( subsetE
% 3.24/1.63 => ( subsetE2
% 3.24/1.63 => ( notsubsetI
% 3.24/1.63 => ( notequalI1
% 3.24/1.63 => ( notequalI2
% 3.24/1.63 => ( subsetRefl
% 3.24/1.63 => ( subsetTrans
% 3.24/1.63 => ( setadjoinSub
% 3.24/1.63 => ( setadjoinSub2
% 3.24/1.63 => ( subset2powerset
% 3.24/1.63 => ( setextsub
% 3.24/1.63 => ( subsetemptysetimpeq
% 3.24/1.63 => ( powersetI1
% 3.24/1.63 => ( powersetE1
% 3.24/1.63 => ( inPowerset
% 3.24/1.63 => ( powersetsubset
% 3.24/1.63 => ( sepInPowerset
% 3.24/1.63 => ( sepSubset
% 3.24/1.63 => ( binunionIL
% 3.24/1.63 => ( upairset2IR
% 3.24/1.63 => ( binunionIR
% 3.24/1.63 => ( binunionEcases
% 3.24/1.63 => ( binunionE
% 3.24/1.63 => ( binunionLsub
% 3.24/1.63 => ( binunionRsub
% 3.24/1.63 => ( binintersectI
% 3.24/1.63 => ( binintersectSubset5
% 3.24/1.63 => ( binintersectEL
% 3.24/1.63 => ( binintersectLsub
% 3.24/1.63 => ( binintersectSubset2
% 3.24/1.63 => ( binintersectSubset3
% 3.24/1.63 => ( binintersectER
% 3.24/1.63 => ( disjointsetsI1
% 3.24/1.63 => ( binintersectRsub
% 3.24/1.63 => ( binintersectSubset4
% 3.24/1.63 => ( binintersectSubset1
% 3.24/1.63 => ( bs114d
% 3.24/1.63 => ( setminusI
% 3.24/1.63 => ( setminusEL
% 3.24/1.63 => ( setminusER
% 3.24/1.63 => ( setminusSubset2
% 3.24/1.63 => ( setminusERneg
% 3.24/1.63 => ( setminusELneg
% 3.24/1.63 => ( setminusILneg
% 3.24/1.63 => ( setminusIRneg
% 3.24/1.63 => ( setminusLsub
% 3.24/1.63 => ( setminusSubset1
% 3.24/1.63 => ( symdiffE
% 3.24/1.63 => ( symdiffI1
% 3.24/1.63 => ( symdiffI2
% 3.24/1.63 => ( symdiffIneg1
% 3.24/1.63 => ( symdiffIneg2
% 3.24/1.63 => ( secondinupair
% 3.24/1.63 => ( setukpairIL
% 3.24/1.63 => ( setukpairIR
% 3.24/1.63 => ( kpairiskpair
% 3.24/1.63 => ( kpairp
% 3.24/1.63 => ( singletonsubset
% 3.24/1.63 => ( singletoninpowerset
% 3.24/1.63 => ( singletoninpowunion
% 3.24/1.63 => ( upairset2E
% 3.24/1.63 => ( upairsubunion
% 3.24/1.63 => ( upairinpowunion
% 3.24/1.63 => ( ubforcartprodlem1
% 3.24/1.63 => ( ubforcartprodlem2
% 3.24/1.63 => ( ubforcartprodlem3
% 3.24/1.63 => ( cartprodpairin
% 3.24/1.63 => ( cartprodmempair1
% 3.24/1.63 => ( cartprodmempair
% 3.24/1.63 => ( setunionE2
% 3.24/1.63 => ( setunionsingleton1
% 3.24/1.63 => ( setunionsingleton2
% 3.24/1.63 => ( setunionsingleton
% 3.24/1.63 => ( singletonprop
% 3.24/1.63 => ( ex1E1
% 3.24/1.63 => ( ex1I
% 3.24/1.63 => ( ex1I2
% 3.24/1.63 => ( singletonsuniq
% 3.24/1.63 => ( setukpairinjL1
% 3.24/1.63 => ( kfstsingleton
% 3.24/1.63 => ( theprop
% 3.24/1.63 => ( kfstpairEq
% 3.24/1.63 => ( cartprodfstin
% 3.24/1.63 => ( setukpairinjL2
% 3.24/1.63 => ( setukpairinjL
% 3.24/1.63 => ( setukpairinjR11
% 3.24/1.63 => ( setukpairinjR12
% 3.24/1.63 => ( setukpairinjR1
% 3.24/1.63 => ( upairequniteq
% 3.24/1.63 => ( setukpairinjR2
% 3.24/1.63 => ( setukpairinjR
% 3.24/1.63 => ( ksndsingleton
% 3.24/1.63 => ( ksndpairEq
% 3.24/1.63 => ( kpairsurjEq
% 3.24/1.63 => ( cartprodsndin
% 3.24/1.63 => ( cartprodpairmemEL
% 3.24/1.63 => ( cartprodpairmemER
% 3.24/1.63 => ( cartprodmempaircEq
% 3.24/1.63 => ( cartprodfstpairEq
% 3.24/1.63 => ( cartprodsndpairEq
% 3.24/1.63 => ( cartprodpairsurjEq
% 3.24/1.63 => ( dpsetconstrI
% 3.24/1.63 => ( dpsetconstrSub
% 3.24/1.63 => ( setOfPairsIsBReln
% 3.24/1.63 => ( dpsetconstrERa
% 3.24/1.63 => ( dpsetconstrEL1
% 3.24/1.63 => ( dpsetconstrEL2
% 3.24/1.63 => ( dpsetconstrER
% 3.24/1.63 => ( funcImageSingleton
% 3.24/1.63 => ( apProp
% 3.24/1.63 => ( app
% 3.24/1.63 => ( infuncsetfunc
% 3.24/1.63 => ( ap2p
% 3.24/1.63 => ( funcinfuncset
% 3.24/1.63 => ( lamProp
% 3.24/1.63 => ( lamp
% 3.24/1.63 => ( lam2p
% 3.24/1.63 => ( brelnall1
% 3.24/1.63 => ( brelnall2
% 3.24/1.63 => ( ex1E2
% 3.24/1.63 => ( funcGraphProp1
% 3.24/1.63 => ( funcGraphProp3
% 3.24/1.63 => ( funcGraphProp2
% 3.24/1.63 => ( funcextLem
% 3.24/1.63 => ( funcGraphProp4
% 3.24/1.63 => ( subbreln
% 3.24/1.63 => ( eqbreln
% 3.24/1.63 => ( funcext
% 3.24/1.63 => ( funcext2
% 3.24/1.63 => ( ap2apEq1
% 3.24/1.63 => ( ap2apEq2
% 3.24/1.63 => ( beta1
% 3.24/1.63 => ( eta1
% 3.24/1.63 => ( lam2lamEq
% 3.24/1.63 => ( beta2
% 3.24/1.63 => ( eta2
% 3.24/1.63 => ( iffalseProp1
% 3.24/1.63 => ( iffalseProp2
% 3.24/1.63 => ( iftrueProp1
% 3.24/1.63 => ( iftrueProp2
% 3.24/1.63 => ( ifSingleton
% 3.24/1.63 => ( ifp
% 3.24/1.63 => ( theeq
% 3.24/1.63 => ( iftrue
% 3.24/1.63 => ( iffalse
% 3.24/1.63 => ( iftrueorfalse
% 3.24/1.63 => ( binintersectT_lem
% 3.24/1.63 => ( binunionT_lem
% 3.24/1.63 => ( powersetT_lem
% 3.24/1.63 => ( setminusT_lem
% 3.24/1.63 => ( complementT_lem
% 3.24/1.63 => ( setextT
% 3.24/1.63 => ( subsetTI
% 3.24/1.63 => ( powersetTI1
% 3.24/1.63 => ( powersetTE1
% 3.24/1.63 => ( complementTI1
% 3.24/1.63 => ( complementTE1
% 3.24/1.63 => ( binintersectTELcontra
% 3.24/1.63 => ( binintersectTERcontra
% 3.24/1.63 => ( contrasubsetT
% 3.24/1.63 => ( contrasubsetT1
% 3.24/1.63 => ( contrasubsetT2
% 3.24/1.63 => ( contrasubsetT3
% 3.24/1.63 => ( doubleComplementI1
% 3.24/1.63 => ( doubleComplementE1
% 3.24/1.63 => ( doubleComplementSub1
% 3.24/1.63 => ( doubleComplementSub2
% 3.24/1.63 => ( doubleComplementEq
% 3.24/1.63 => ( complementTnotintersectT
% 3.24/1.63 => ( complementImpComplementIntersect
% 3.24/1.63 => ( complementSubsetComplementIntersect
% 3.24/1.63 => ( complementInPowersetComplementIntersect
% 3.24/1.63 => ( contraSubsetComplement
% 3.24/1.63 => ( complementTcontraSubset
% 3.24/1.63 => ( binunionTILcontra
% 3.24/1.63 => ( binunionTIRcontra
% 3.24/1.63 => ( inIntersectImpInUnion
% 3.24/1.63 => ( inIntersectImpInUnion2
% 3.24/1.63 => ( inIntersectImpInIntersectUnions
% 3.24/1.63 => ( intersectInPowersetIntersectUnions
% 3.24/1.63 => ( inComplementUnionImpNotIn1
% 3.24/1.63 => ( inComplementUnionImpInComplement1
% 3.24/1.63 => ( binunionTE
% 3.24/1.63 => ( binunionTEcontra
% 3.24/1.63 => ( demorgan2a1
% 3.24/1.63 => ( complementUnionInPowersetComplement
% 3.24/1.63 => ( demorgan2a2
% 3.24/1.63 => ( demorgan1a
% 3.24/1.63 => ( demorgan1b
% 3.24/1.63 => ( demorgan1
% 3.24/1.63 => ( demorgan2a
% 3.24/1.63 => ( demorgan2b2
% 3.24/1.63 => ( demorgan2b
% 3.24/1.63 => ( demorgan2
% 3.24/1.63 => ( woz13rule0
% 3.24/1.63 => ( woz13rule1
% 3.24/1.63 => ( woz13rule2
% 3.24/1.63 => ( woz13rule3
% 3.24/1.63 => ( woz13rule4
% 3.24/1.63 => ( woz1_1
% 3.24/1.63 => ( woz1_2
% 3.24/1.63 => ( woz1_3
% 3.24/1.63 => ( woz1_4
% 3.24/1.63 => ( woz1_5
% 3.24/1.63 => ( breln1all2
% 3.24/1.63 => ( breln1SetBreln1
% 3.24/1.63 => ( choice2fnsingleton
% 3.24/1.63 => ( setOfPairsIsBReln1
% 3.24/1.63 => ( breln1all1
% 3.24/1.63 => ( subbreln1
% 3.24/1.63 => ( eqbreln1
% 3.24/1.63 => ( breln1invprop
% 3.24/1.63 => ( breln1invI
% 3.24/1.63 => ( breln1invE
% 3.24/1.63 => ( breln1compprop
% 3.24/1.63 => ( breln1compI
% 3.24/1.63 => ( breln1compE
% 3.24/1.63 => ( breln1compEex
% 3.24/1.63 => ( breln1unionprop
% 3.24/1.63 => ( breln1unionIL
% 3.24/1.63 => ( breln1unionIR
% 3.24/1.63 => ( breln1unionI
% 3.24/1.63 => ( breln1unionE
% 3.24/1.63 => ( breln1unionEcases
% 3.24/1.63 => ( breln1unionCommutes
% 3.24/1.63 => ( woz2Ex
% 3.24/1.63 => ( woz2W
% 3.24/1.63 => ( woz2A
% 3.24/1.63 => ( woz2B
% 3.24/1.63 => ( image1Ex
% 3.24/1.63 => ( image1Ex1
% 3.24/1.63 => ( image1Equiv
% 3.24/1.63 => ( image1E
% 3.24/1.63 => ( image1I
% 3.24/1.63 => ( injFuncInInjFuncSet
% 3.24/1.63 => ( injFuncSetFuncIn
% 3.24/1.63 => ( injFuncSetFuncInj
% 3.24/1.63 => ( surjFuncSetFuncIn
% 3.24/1.63 => ( surjFuncSetFuncSurj
% 3.24/1.63 => ( leftInvIsSurj
% 3.24/1.63 => ( surjCantorThm
% 3.24/1.63 => ( foundation2
% 3.24/1.63 => ( notinself
% 3.24/1.63 => ( notinself2
% 3.24/1.63 => ( omegaSp
% 3.24/1.63 => ( omegaSclos
% 3.24/1.63 => ( peano0notS
% 3.24/1.63 => ( peanoSinj
% 3.24/1.63 => ( transitivesetOp1
% 3.24/1.63 => ( binintTransitive
% 3.24/1.63 => ( transitivesetOp2
% 3.24/1.63 => ( setunionTransitive
% 3.24/1.63 => ( ordinalMinLem1
% 3.24/1.63 => ( ordinalTransSet
% 3.24/1.63 => ( ordinalTransSet1
% 3.24/1.63 => ! [X: $i] :
% 3.24/1.63 ( ! [Xx: $i] :
% 3.24/1.63 ( ( in @ Xx @ X )
% 3.24/1.63 => ( ordinal @ Xx ) )
% 3.24/1.63 => ( transitiveset @ ( setunion @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.24/1.63 ------------------------
% 3.24/1.68 % (20990)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_20722 for (2999ds/4Mi)
% 3.24/1.68 % (20992)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20722 for (2999ds/2Mi)
% 3.24/1.68 % (20995)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20722 for (2999ds/18Mi)
% 3.24/1.68 % (20989)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20722 for (2999ds/183Mi)
% 3.24/1.68 % (20993)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_20722 for (2999ds/2Mi)
% 3.24/1.68 % (20990)Instruction limit reached!
% 3.24/1.68 % (20990)------------------------------
% 3.24/1.68 % (20990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.24/1.68 % (20990)Termination reason: Unknown
% 3.24/1.68 % (20990)Termination phase: shuffling
% 3.24/1.68
% 3.24/1.68 % (20990)Memory used [KB]: 1663
% 3.24/1.68 % (20990)Time elapsed: 0.003 s
% 3.24/1.68 % (20990)Instructions burned: 4 (million)
% 3.24/1.68 % (20990)------------------------------
% 3.24/1.68 % (20990)------------------------------
% 3.24/1.68 % (20992)Instruction limit reached!
% 3.24/1.68 % (20992)------------------------------
% 3.24/1.68 % (20992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.24/1.68 % (20992)Termination reason: Unknown
% 3.24/1.68 % (20992)Termination phase: shuffling
% 3.24/1.68
% 3.24/1.68 % (20992)Memory used [KB]: 1663
% 3.24/1.68 % (20992)Time elapsed: 0.003 s
% 3.24/1.68 % (20992)Instructions burned: 4 (million)
% 3.24/1.68 % (20992)------------------------------
% 3.24/1.68 % (20992)------------------------------
% 3.24/1.68 % (20993)Instruction limit reached!
% 3.24/1.68 % (20993)------------------------------
% 3.24/1.68 % (20993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.24/1.68 % (20993)Termination reason: Unknown
% 3.24/1.68 % (20993)Termination phase: shuffling
% 3.24/1.68
% 3.24/1.68 % (20993)Memory used [KB]: 1663
% 3.24/1.68 % (20993)Time elapsed: 0.002 s
% 3.24/1.68 % (20993)Instructions burned: 2 (million)
% 3.24/1.68 % (20993)------------------------------
% 3.24/1.68 % (20993)------------------------------
% 3.24/1.69 % (20995)Instruction limit reached!
% 3.24/1.69 % (20995)------------------------------
% 3.24/1.69 % (20995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.24/1.69 % (20995)Termination reason: Unknown
% 3.24/1.69 % (20995)Termination phase: shuffling
% 3.24/1.69
% 3.24/1.69 % (20995)Memory used [KB]: 2046
% 3.24/1.69 % (20995)Time elapsed: 0.008 s
% 3.24/1.69 % (20995)Instructions burned: 20 (million)
% 3.24/1.69 % (20995)------------------------------
% 3.24/1.69 % (20995)------------------------------
% 3.24/1.69 % (20991)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_20722 for (2999ds/27Mi)
% 3.24/1.69 % (20994)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_20722 for (2999ds/275Mi)
% 3.24/1.69 % (21000)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20722 for (2999ds/3Mi)
% 3.24/1.69 % (21001)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_20722 for (2999ds/37Mi)
% 3.24/1.69 % (21000)Instruction limit reached!
% 3.24/1.69 % (21000)------------------------------
% 3.24/1.69 % (21000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.24/1.69 % (21000)Termination reason: Unknown
% 3.24/1.69 % (21000)Termination phase: shuffling
% 3.24/1.69
% 3.24/1.69 % (21000)Memory used [KB]: 1663
% 3.24/1.69 % (21000)Time elapsed: 0.002 s
% 3.24/1.69 % (21000)Instructions burned: 3 (million)
% 3.24/1.69 % (21000)------------------------------
% 3.24/1.69 % (21000)------------------------------
% 3.24/1.69 % (21002)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_20722 for (2999ds/15Mi)
% 3.24/1.69 % (21008)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_20722 for (2999ds/3Mi)
% 3.24/1.70 % (21008)Instruction limit reached!
% 3.24/1.70 % (21008)------------------------------
% 3.24/1.70 % (21008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.24/1.70 % (21008)Termination reason: Unknown
% 3.24/1.70 % (21008)Termination phase: shuffling
% 3.24/1.70
% 3.24/1.70 % (21008)Memory used [KB]: 1663
% 3.24/1.70 % (21008)Time elapsed: 0.002 s
% 3.24/1.70 % (21008)Instructions burned: 3 (million)
% 3.24/1.70 % (21008)------------------------------
% 3.24/1.70 % (21008)------------------------------
% 3.27/1.70 % (21002)Instruction limit reached!
% 3.27/1.70 % (21002)------------------------------
% 3.27/1.70 % (21002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.70 % (21002)Termination reason: Unknown
% 3.27/1.70 % (21002)Termination phase: shuffling
% 3.27/1.70
% 3.27/1.70 % (21002)Memory used [KB]: 2046
% 3.27/1.70 % (21002)Time elapsed: 0.007 s
% 3.27/1.70 % (21002)Instructions burned: 17 (million)
% 3.27/1.70 % (21002)------------------------------
% 3.27/1.70 % (21002)------------------------------
% 3.27/1.70 % (21001)Instruction limit reached!
% 3.27/1.70 % (21001)------------------------------
% 3.27/1.70 % (21001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.70 % (21001)Termination reason: Unknown
% 3.27/1.70 % (21001)Termination phase: shuffling
% 3.27/1.70
% 3.27/1.70 % (21001)Memory used [KB]: 2430
% 3.27/1.70 % (21001)Time elapsed: 0.011 s
% 3.27/1.70 % (21001)Instructions burned: 37 (million)
% 3.27/1.70 % (21001)------------------------------
% 3.27/1.70 % (21001)------------------------------
% 3.27/1.70 % (21009)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_20722 for (2999ds/1041Mi)
% 3.27/1.70 % (20991)Instruction limit reached!
% 3.27/1.70 % (20991)------------------------------
% 3.27/1.70 % (20991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.70 % (20991)Termination reason: Unknown
% 3.27/1.70 % (20991)Termination phase: shuffling
% 3.27/1.70
% 3.27/1.70 % (20991)Memory used [KB]: 2302
% 3.27/1.70 % (20991)Time elapsed: 0.016 s
% 3.27/1.70 % (20991)Instructions burned: 28 (million)
% 3.27/1.70 % (20991)------------------------------
% 3.27/1.70 % (20991)------------------------------
% 3.27/1.71 % (21010)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_20722 for (2999ds/7Mi)
% 3.27/1.71 % (21011)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_20722 for (2999ds/16Mi)
% 3.27/1.71 % (21010)Instruction limit reached!
% 3.27/1.71 % (21010)------------------------------
% 3.27/1.71 % (21010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.71 % (21010)Termination reason: Unknown
% 3.27/1.71 % (21010)Termination phase: shuffling
% 3.27/1.71
% 3.27/1.71 % (21010)Memory used [KB]: 1791
% 3.27/1.71 % (21010)Time elapsed: 0.003 s
% 3.27/1.71 % (21010)Instructions burned: 7 (million)
% 3.27/1.71 % (21010)------------------------------
% 3.27/1.71 % (21010)------------------------------
% 3.27/1.71 % (21012)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_20722 for (2999ds/3Mi)
% 3.27/1.71 % (21012)Instruction limit reached!
% 3.27/1.71 % (21012)------------------------------
% 3.27/1.71 % (21012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.71 % (21012)Termination reason: Unknown
% 3.27/1.71 % (21012)Termination phase: shuffling
% 3.27/1.71
% 3.27/1.71 % (21012)Memory used [KB]: 1663
% 3.27/1.71 % (21012)Time elapsed: 0.002 s
% 3.27/1.71 % (21012)Instructions burned: 3 (million)
% 3.27/1.71 % (21012)------------------------------
% 3.27/1.71 % (21012)------------------------------
% 3.27/1.71 % (21011)Instruction limit reached!
% 3.27/1.71 % (21011)------------------------------
% 3.27/1.71 % (21011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.71 % (21011)Termination reason: Unknown
% 3.27/1.71 % (21011)Termination phase: shuffling
% 3.27/1.71
% 3.27/1.71 % (21011)Memory used [KB]: 2046
% 3.27/1.71 % (21011)Time elapsed: 0.006 s
% 3.27/1.71 % (21011)Instructions burned: 17 (million)
% 3.27/1.71 % (21011)------------------------------
% 3.27/1.71 % (21011)------------------------------
% 3.27/1.72 % (21022)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_20722 for (2999ds/7Mi)
% 3.27/1.72 % (21013)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_20722 for (2999ds/3Mi)
% 3.27/1.72 % (21022)Instruction limit reached!
% 3.27/1.72 % (21022)------------------------------
% 3.27/1.72 % (21022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.72 % (21022)Termination reason: Unknown
% 3.27/1.72 % (21022)Termination phase: shuffling
% 3.27/1.72
% 3.27/1.72 % (21022)Memory used [KB]: 1918
% 3.27/1.72 % (21022)Time elapsed: 0.004 s
% 3.27/1.72 % (21022)Instructions burned: 10 (million)
% 3.27/1.72 % (21022)------------------------------
% 3.27/1.72 % (21022)------------------------------
% 3.27/1.72 % (21026)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_20722 for (2999ds/3Mi)
% 3.27/1.72 % (21013)Instruction limit reached!
% 3.27/1.72 % (21013)------------------------------
% 3.27/1.72 % (21013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.72 % (21013)Termination reason: Unknown
% 3.27/1.72 % (21013)Termination phase: shuffling
% 3.27/1.72
% 3.27/1.72 % (21013)Memory used [KB]: 1663
% 3.27/1.72 % (21013)Time elapsed: 0.004 s
% 3.27/1.72 % (21013)Instructions burned: 3 (million)
% 3.27/1.72 % (21013)------------------------------
% 3.27/1.72 % (21013)------------------------------
% 3.27/1.72 % (21026)Instruction limit reached!
% 3.27/1.72 % (21026)------------------------------
% 3.27/1.72 % (21026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.72 % (21026)Termination reason: Unknown
% 3.27/1.72 % (21026)Termination phase: shuffling
% 3.27/1.72
% 3.27/1.72 % (21026)Memory used [KB]: 1791
% 3.27/1.72 % (21026)Time elapsed: 0.003 s
% 3.27/1.72 % (21026)Instructions burned: 6 (million)
% 3.27/1.72 % (21026)------------------------------
% 3.27/1.72 % (21026)------------------------------
% 3.27/1.72 % (21028)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_20722 for (2999ds/4Mi)
% 3.27/1.72 % (21028)Instruction limit reached!
% 3.27/1.72 % (21028)------------------------------
% 3.27/1.72 % (21028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.72 % (21028)Termination reason: Unknown
% 3.27/1.72 % (21028)Termination phase: shuffling
% 3.27/1.72
% 3.27/1.72 % (21028)Memory used [KB]: 1791
% 3.27/1.72 % (21028)Time elapsed: 0.003 s
% 3.27/1.72 % (21028)Instructions burned: 7 (million)
% 3.27/1.72 % (21028)------------------------------
% 3.27/1.72 % (21028)------------------------------
% 3.27/1.73 % (21032)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_20722 for (2999ds/18Mi)
% 3.27/1.73 % (20989)Instruction limit reached!
% 3.27/1.73 % (20989)------------------------------
% 3.27/1.73 % (20989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.73 % (20989)Termination reason: Unknown
% 3.27/1.73 % (20989)Termination phase: Property scanning
% 3.27/1.73
% 3.27/1.73 % (20989)Memory used [KB]: 3198
% 3.27/1.73 % (20989)Time elapsed: 0.052 s
% 3.27/1.73 % (20989)Instructions burned: 186 (million)
% 3.27/1.73 % (20989)------------------------------
% 3.27/1.73 % (20989)------------------------------
% 3.27/1.73 % (21035)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_20722 for (2999ds/6Mi)
% 3.27/1.73 % (21035)Instruction limit reached!
% 3.27/1.73 % (21035)------------------------------
% 3.27/1.73 % (21035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.73 % (21035)Termination reason: Unknown
% 3.27/1.73 % (21035)Termination phase: shuffling
% 3.27/1.73
% 3.27/1.73 % (21035)Memory used [KB]: 1791
% 3.27/1.73 % (21035)Time elapsed: 0.003 s
% 3.27/1.73 % (21035)Instructions burned: 7 (million)
% 3.27/1.73 % (21035)------------------------------
% 3.27/1.73 % (21035)------------------------------
% 3.27/1.73 % (21032)Instruction limit reached!
% 3.27/1.73 % (21032)------------------------------
% 3.27/1.73 % (21032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.73 % (21032)Termination reason: Unknown
% 3.27/1.73 % (21032)Termination phase: shuffling
% 3.27/1.73
% 3.27/1.73 % (21032)Memory used [KB]: 2046
% 3.27/1.73 % (21032)Time elapsed: 0.006 s
% 3.27/1.73 % (21032)Instructions burned: 18 (million)
% 3.27/1.73 % (21032)------------------------------
% 3.27/1.73 % (21032)------------------------------
% 3.27/1.73 % (21039)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_20722 for (2999ds/902Mi)
% 3.27/1.74 % (21033)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_20722 for (2999ds/710Mi)
% 3.27/1.74 % (21042)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_20722 for (2999ds/21Mi)
% 3.27/1.74 % (21043)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_20722 for (2999ds/5Mi)
% 3.27/1.74 % (21044)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_20722 for (2999ds/6Mi)
% 3.27/1.74 % (21043)Instruction limit reached!
% 3.27/1.74 % (21043)------------------------------
% 3.27/1.74 % (21043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.74 % (21043)Termination reason: Unknown
% 3.27/1.74 % (21043)Termination phase: shuffling
% 3.27/1.74
% 3.27/1.74 % (21043)Memory used [KB]: 1791
% 3.27/1.74 % (21043)Time elapsed: 0.003 s
% 3.27/1.74 % (21043)Instructions burned: 6 (million)
% 3.27/1.74 % (21043)------------------------------
% 3.27/1.74 % (21043)------------------------------
% 3.27/1.75 % (21044)Instruction limit reached!
% 3.27/1.75 % (21044)------------------------------
% 3.27/1.75 % (21044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.75 % (21044)Termination reason: Unknown
% 3.27/1.75 % (21044)Termination phase: shuffling
% 3.27/1.75
% 3.27/1.75 % (21044)Memory used [KB]: 1918
% 3.27/1.75 % (21044)Time elapsed: 0.004 s
% 3.27/1.75 % (21044)Instructions burned: 9 (million)
% 3.27/1.75 % (21044)------------------------------
% 3.27/1.75 % (21044)------------------------------
% 3.27/1.75 % (21042)Instruction limit reached!
% 3.27/1.75 % (21042)------------------------------
% 3.27/1.75 % (21042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.75 % (21042)Termination reason: Unknown
% 3.27/1.75 % (21042)Termination phase: shuffling
% 3.27/1.75
% 3.27/1.75 % (21042)Memory used [KB]: 2174
% 3.27/1.75 % (21042)Time elapsed: 0.008 s
% 3.27/1.75 % (21042)Instructions burned: 24 (million)
% 3.27/1.75 % (21042)------------------------------
% 3.27/1.75 % (21042)------------------------------
% 3.27/1.75 % (21045)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_20722 for (2999ds/377Mi)
% 3.27/1.76 % (21048)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_20722 for (2999ds/779Mi)
% 3.27/1.76 % (21052)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_20722 for (2998ds/19Mi)
% 3.27/1.76 % (21052)Instruction limit reached!
% 3.27/1.76 % (21052)------------------------------
% 3.27/1.76 % (21052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.76 % (21052)Termination reason: Unknown
% 3.27/1.76 % (21052)Termination phase: shuffling
% 3.27/1.76
% 3.27/1.76 % (21052)Memory used [KB]: 2046
% 3.27/1.76 % (21052)Time elapsed: 0.007 s
% 3.27/1.76 % (21052)Instructions burned: 20 (million)
% 3.27/1.76 % (21052)------------------------------
% 3.27/1.76 % (21052)------------------------------
% 3.27/1.77 % (21064)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_20722 for (2998ds/879Mi)
% 3.27/1.78 % (20994)Instruction limit reached!
% 3.27/1.78 % (20994)------------------------------
% 3.27/1.78 % (20994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.78 % (20994)Termination reason: Unknown
% 3.27/1.78 % (20994)Termination phase: Property scanning
% 3.27/1.78
% 3.27/1.78 % (20994)Memory used [KB]: 6012
% 3.27/1.78 % (20994)Time elapsed: 0.090 s
% 3.27/1.78 % (20994)Instructions burned: 278 (million)
% 3.27/1.78 % (20994)------------------------------
% 3.27/1.78 % (20994)------------------------------
% 3.27/1.79 % (21073)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_20722 for (2998ds/17Mi)
% 3.27/1.79 % (21073)Instruction limit reached!
% 3.27/1.79 % (21073)------------------------------
% 3.27/1.79 % (21073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.79 % (21073)Termination reason: Unknown
% 3.27/1.79 % (21073)Termination phase: shuffling
% 3.27/1.79
% 3.27/1.79 % (21073)Memory used [KB]: 2046
% 3.27/1.79 % (21073)Time elapsed: 0.007 s
% 3.27/1.79 % (21073)Instructions burned: 20 (million)
% 3.27/1.79 % (21073)------------------------------
% 3.27/1.79 % (21073)------------------------------
% 3.27/1.80 % (21075)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_20722 for (2998ds/3Mi)
% 3.27/1.80 % (21075)Instruction limit reached!
% 3.27/1.80 % (21075)------------------------------
% 3.27/1.80 % (21075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.80 % (21075)Termination reason: Unknown
% 3.27/1.80 % (21075)Termination phase: shuffling
% 3.27/1.80
% 3.27/1.80 % (21075)Memory used [KB]: 1663
% 3.27/1.80 % (21075)Time elapsed: 0.002 s
% 3.27/1.80 % (21075)Instructions burned: 3 (million)
% 3.27/1.80 % (21075)------------------------------
% 3.27/1.80 % (21075)------------------------------
% 3.27/1.81 % (21086)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_20722 for (2998ds/30Mi)
% 3.27/1.82 % (21086)Instruction limit reached!
% 3.27/1.82 % (21086)------------------------------
% 3.27/1.82 % (21086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.82 % (21086)Termination reason: Unknown
% 3.27/1.82 % (21086)Termination phase: shuffling
% 3.27/1.82
% 3.27/1.82 % (21086)Memory used [KB]: 2430
% 3.27/1.82 % (21086)Time elapsed: 0.010 s
% 3.27/1.82 % (21086)Instructions burned: 32 (million)
% 3.27/1.82 % (21086)------------------------------
% 3.27/1.82 % (21086)------------------------------
% 3.27/1.83 % (21094)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_20722 for (2998ds/127Mi)
% 3.27/1.85 % (21045)Instruction limit reached!
% 3.27/1.85 % (21045)------------------------------
% 3.27/1.85 % (21045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.85 % (21045)Termination reason: Unknown
% 3.27/1.85 % (21045)Termination phase: Saturation
% 3.27/1.85
% 3.27/1.85 % (21045)Memory used [KB]: 8571
% 3.27/1.85 % (21045)Time elapsed: 0.101 s
% 3.27/1.85 % (21045)Instructions burned: 380 (million)
% 3.27/1.85 % (21045)------------------------------
% 3.27/1.85 % (21045)------------------------------
% 3.27/1.86 % (21094)Instruction limit reached!
% 3.27/1.86 % (21094)------------------------------
% 3.27/1.86 % (21094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.86 % (21094)Termination reason: Unknown
% 3.27/1.86 % (21094)Termination phase: Unused predicate definition removal
% 3.27/1.86
% 3.27/1.86 % (21094)Memory used [KB]: 2942
% 3.27/1.86 % (21094)Time elapsed: 0.035 s
% 3.27/1.86 % (21094)Instructions burned: 128 (million)
% 3.27/1.86 % (21094)------------------------------
% 3.27/1.86 % (21094)------------------------------
% 3.27/1.86 % (21109)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_20722 for (2997ds/100Mi)
% 3.27/1.87 % (21114)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_20722 for (2997ds/3Mi)
% 3.27/1.88 % (21114)Instruction limit reached!
% 3.27/1.88 % (21114)------------------------------
% 3.27/1.88 % (21114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.88 % (21114)Termination reason: Unknown
% 3.27/1.88 % (21114)Termination phase: shuffling
% 3.27/1.88
% 3.27/1.88 % (21114)Memory used [KB]: 1791
% 3.27/1.88 % (21114)Time elapsed: 0.003 s
% 3.27/1.88 % (21114)Instructions burned: 6 (million)
% 3.27/1.88 % (21114)------------------------------
% 3.27/1.88 % (21114)------------------------------
% 3.27/1.88 % (21118)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_20722 for (2997ds/20Mi)
% 3.27/1.89 % (21109)Instruction limit reached!
% 3.27/1.89 % (21109)------------------------------
% 3.27/1.89 % (21109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.89 % (21109)Termination reason: Unknown
% 3.27/1.89 % (21109)Termination phase: Property scanning
% 3.27/1.89
% 3.27/1.89 % (21109)Memory used [KB]: 2814
% 3.27/1.89 % (21109)Time elapsed: 0.028 s
% 3.27/1.89 % (21109)Instructions burned: 102 (million)
% 3.27/1.89 % (21109)------------------------------
% 3.27/1.89 % (21109)------------------------------
% 3.27/1.89 % (21118)Instruction limit reached!
% 3.27/1.89 % (21118)------------------------------
% 3.27/1.89 % (21118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.89 % (21118)Termination reason: Unknown
% 3.27/1.89 % (21118)Termination phase: shuffling
% 3.27/1.89
% 3.27/1.89 % (21118)Memory used [KB]: 2046
% 3.27/1.89 % (21118)Time elapsed: 0.008 s
% 3.27/1.89 % (21118)Instructions burned: 20 (million)
% 3.27/1.89 % (21118)------------------------------
% 3.27/1.89 % (21118)------------------------------
% 3.27/1.90 % (21124)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_20722 for (2997ds/86Mi)
% 3.27/1.90 % (21126)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_20722 for (2997ds/107Mi)
% 3.27/1.92 % (21124)Instruction limit reached!
% 3.27/1.92 % (21124)------------------------------
% 3.27/1.92 % (21124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.92 % (21124)Termination reason: Unknown
% 3.27/1.92 % (21124)Termination phase: Property scanning
% 3.27/1.92
% 3.27/1.92 % (21124)Memory used [KB]: 2942
% 3.27/1.92 % (21124)Time elapsed: 0.024 s
% 3.27/1.92 % (21124)Instructions burned: 87 (million)
% 3.27/1.92 % (21124)------------------------------
% 3.27/1.92 % (21124)------------------------------
% 3.27/1.93 % (21126)Instruction limit reached!
% 3.27/1.93 % (21126)------------------------------
% 3.27/1.93 % (21126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.93 % (21126)Termination reason: Unknown
% 3.27/1.93 % (21126)Termination phase: SInE selection
% 3.27/1.93
% 3.27/1.93 % (21126)Memory used [KB]: 2942
% 3.27/1.93 % (21126)Time elapsed: 0.029 s
% 3.27/1.93 % (21126)Instructions burned: 108 (million)
% 3.27/1.93 % (21126)------------------------------
% 3.27/1.93 % (21126)------------------------------
% 3.27/1.93 % (21139)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_20722 for (2997ds/39Mi)
% 3.27/1.94 % (21141)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_20722 for (2997ds/448Mi)
% 3.27/1.94 % (21139)Instruction limit reached!
% 3.27/1.94 % (21139)------------------------------
% 3.27/1.94 % (21139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.94 % (21139)Termination reason: Unknown
% 3.27/1.94 % (21139)Termination phase: shuffling
% 3.27/1.94
% 3.27/1.94 % (21139)Memory used [KB]: 2430
% 3.27/1.94 % (21139)Time elapsed: 0.012 s
% 3.27/1.94 % (21139)Instructions burned: 39 (million)
% 3.27/1.94 % (21139)------------------------------
% 3.27/1.94 % (21139)------------------------------
% 3.27/1.95 % (21048)Instruction limit reached!
% 3.27/1.95 % (21048)------------------------------
% 3.27/1.95 % (21048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.95 % (21048)Termination reason: Unknown
% 3.27/1.95 % (21048)Termination phase: Saturation
% 3.27/1.95
% 3.27/1.95 % (21048)Memory used [KB]: 8059
% 3.27/1.95 % (21048)Time elapsed: 0.195 s
% 3.27/1.95 % (21048)Instructions burned: 781 (million)
% 3.27/1.95 % (21048)------------------------------
% 3.27/1.95 % (21048)------------------------------
% 3.27/1.95 % (21146)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_20722 for (2997ds/46Mi)
% 3.27/1.96 % (21149)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_20722 for (2997ds/98Mi)
% 3.27/1.96 % (21009)Instruction limit reached!
% 3.27/1.96 % (21009)------------------------------
% 3.27/1.96 % (21009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.96 % (21009)Termination reason: Unknown
% 3.27/1.96 % (21009)Termination phase: Saturation
% 3.27/1.96
% 3.27/1.96 % (21009)Memory used [KB]: 16886
% 3.27/1.96 % (21009)Time elapsed: 0.263 s
% 3.27/1.96 % (21009)Instructions burned: 1044 (million)
% 3.27/1.96 % (21009)------------------------------
% 3.27/1.96 % (21009)------------------------------
% 3.27/1.97 % (21146)Instruction limit reached!
% 3.27/1.97 % (21146)------------------------------
% 3.27/1.97 % (21146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.97 % (21146)Termination reason: Unknown
% 3.27/1.97 % (21146)Termination phase: shuffling
% 3.27/1.97
% 3.27/1.97 % (21146)Memory used [KB]: 2686
% 3.27/1.97 % (21146)Time elapsed: 0.015 s
% 3.27/1.97 % (21146)Instructions burned: 49 (million)
% 3.27/1.97 % (21146)------------------------------
% 3.27/1.97 % (21146)------------------------------
% 3.27/1.97 % (21151)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_20722 for (2996ds/507Mi)
% 3.27/1.98 % (21153)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_20722 for (2996ds/149Mi)
% 3.27/1.99 % (21149)Instruction limit reached!
% 3.27/1.99 % (21149)------------------------------
% 3.27/1.99 % (21149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.99 % (21149)Termination reason: Unknown
% 3.27/1.99 % (21149)Termination phase: Property scanning
% 3.27/1.99
% 3.27/1.99 % (21149)Memory used [KB]: 3070
% 3.27/1.99 % (21149)Time elapsed: 0.027 s
% 3.27/1.99 % (21149)Instructions burned: 98 (million)
% 3.27/1.99 % (21149)------------------------------
% 3.27/1.99 % (21149)------------------------------
% 3.27/1.99 % (21033)Instruction limit reached!
% 3.27/1.99 % (21033)------------------------------
% 3.27/1.99 % (21033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.99 % (21033)Termination reason: Unknown
% 3.27/1.99 % (21033)Termination phase: Saturation
% 3.27/1.99
% 3.27/1.99 % (21033)Memory used [KB]: 11897
% 3.27/1.99 % (21033)Time elapsed: 0.256 s
% 3.27/1.99 % (21033)Instructions burned: 710 (million)
% 3.27/1.99 % (21033)------------------------------
% 3.27/1.99 % (21033)------------------------------
% 3.27/2.00 % (21161)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_20722 for (2996ds/39Mi)
% 3.27/2.00 % (21165)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_20722 for (2996ds/6Mi)
% 3.27/2.01 % (21165)Instruction limit reached!
% 3.27/2.01 % (21165)------------------------------
% 3.27/2.01 % (21165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/2.01 % (21165)Termination reason: Unknown
% 3.27/2.01 % (21165)Termination phase: shuffling
% 3.27/2.01
% 3.27/2.01 % (21165)Memory used [KB]: 1791
% 3.27/2.01 % (21165)Time elapsed: 0.003 s
% 3.27/2.01 % (21165)Instructions burned: 6 (million)
% 3.27/2.01 % (21165)------------------------------
% 3.27/2.01 % (21165)------------------------------
% 3.27/2.01 % (21161)Instruction limit reached!
% 3.27/2.01 % (21161)------------------------------
% 3.27/2.01 % (21161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/2.01 % (21161)Termination reason: Unknown
% 3.27/2.01 % (21161)Termination phase: shuffling
% 3.27/2.01
% 3.27/2.01 % (21161)Memory used [KB]: 2430
% 3.27/2.01 % (21161)Time elapsed: 0.012 s
% 3.27/2.01 % (21161)Instructions burned: 40 (million)
% 3.27/2.01 % (21161)------------------------------
% 3.27/2.01 % (21161)------------------------------
% 3.27/2.02 % (21153)Instruction limit reached!
% 3.27/2.02 % (21153)------------------------------
% 3.27/2.02 % (21153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/2.02 % (21153)Termination reason: Unknown
% 3.27/2.02 % (21153)Termination phase: Function definition elimination
% 3.27/2.02
% 3.27/2.02 % (21153)Memory used [KB]: 3070
% 3.27/2.02 % (21153)Time elapsed: 0.040 s
% 3.27/2.02 % (21153)Instructions burned: 153 (million)
% 3.27/2.02 % (21153)------------------------------
% 3.27/2.02 % (21153)------------------------------
% 3.27/2.02 % (21170)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_20722 for (2996ds/47Mi)
% 3.27/2.02 % (21169)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_20722 for (2996ds/1087Mi)
% 3.27/2.02 % (21039)Instruction limit reached!
% 3.27/2.02 % (21039)------------------------------
% 3.27/2.02 % (21039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/2.02 % (21039)Termination reason: Unknown
% 3.27/2.02 % (21039)Termination phase: Saturation
% 3.27/2.02
% 3.27/2.02 % (21039)Memory used [KB]: 13688
% 3.27/2.02 % (21039)Time elapsed: 0.282 s
% 3.27/2.02 % (21039)Instructions burned: 904 (million)
% 3.27/2.02 % (21039)------------------------------
% 3.27/2.02 % (21039)------------------------------
% 5.69/2.02 % (21174)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_20722 for (2996ds/44Mi)
% 5.69/2.03 % (21175)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_20722 for (2996ds/432Mi)
% 5.69/2.03 % (21170)Instruction limit reached!
% 5.69/2.03 % (21170)------------------------------
% 5.69/2.03 % (21170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.69/2.03 % (21170)Termination reason: Unknown
% 5.69/2.03 % (21170)Termination phase: shuffling
% 5.69/2.03
% 5.69/2.03 % (21170)Memory used [KB]: 2558
% 5.69/2.03 % (21170)Time elapsed: 0.014 s
% 5.69/2.03 % (21170)Instructions burned: 48 (million)
% 5.69/2.03 % (21170)------------------------------
% 5.69/2.03 % (21170)------------------------------
% 5.69/2.03 % (21064)Instruction limit reached!
% 5.69/2.03 % (21064)------------------------------
% 5.69/2.03 % (21064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.69/2.03 % (21064)Termination reason: Unknown
% 5.69/2.03 % (21064)Termination phase: Saturation
% 5.69/2.03
% 5.69/2.03 % (21064)Memory used [KB]: 11001
% 5.69/2.03 % (21064)Time elapsed: 0.258 s
% 5.69/2.03 % (21064)Instructions burned: 881 (million)
% 5.69/2.03 % (21064)------------------------------
% 5.69/2.03 % (21064)------------------------------
% 5.69/2.04 % (21174)Instruction limit reached!
% 5.69/2.04 % (21174)------------------------------
% 5.69/2.04 % (21174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.69/2.04 % (21174)Termination reason: Unknown
% 5.69/2.04 % (21174)Termination phase: shuffling
% 5.69/2.04
% 5.69/2.04 % (21174)Memory used [KB]: 2558
% 5.69/2.04 % (21174)Time elapsed: 0.014 s
% 5.69/2.04 % (21174)Instructions burned: 47 (million)
% 5.69/2.04 % (21174)------------------------------
% 5.69/2.04 % (21174)------------------------------
% 5.69/2.04 % (21178)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_20722 for (2996ds/62Mi)
% 5.69/2.04 % (21181)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_20722 for (2996ds/31Mi)
% 5.69/2.05 % (21186)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_20722 for (2996ds/96Mi)
% 5.69/2.05 % (21181)Instruction limit reached!
% 5.69/2.05 % (21181)------------------------------
% 5.69/2.05 % (21181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.69/2.05 % (21181)Termination reason: Unknown
% 5.69/2.05 % (21181)Termination phase: shuffling
% 5.69/2.05
% 5.69/2.05 % (21181)Memory used [KB]: 2302
% 5.69/2.05 % (21181)Time elapsed: 0.010 s
% 5.69/2.05 % (21181)Instructions burned: 31 (million)
% 5.69/2.05 % (21181)------------------------------
% 5.69/2.05 % (21181)------------------------------
% 5.69/2.05 % (21141)Instruction limit reached!
% 5.69/2.05 % (21141)------------------------------
% 5.69/2.05 % (21141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.69/2.05 % (21141)Termination reason: Unknown
% 5.69/2.05 % (21141)Termination phase: Saturation
% 5.69/2.05
% 5.69/2.05 % (21141)Memory used [KB]: 7931
% 5.69/2.05 % (21141)Time elapsed: 0.113 s
% 5.69/2.05 % (21141)Instructions burned: 449 (million)
% 5.69/2.05 % (21141)------------------------------
% 5.69/2.05 % (21141)------------------------------
% 5.69/2.05 % (21178)Instruction limit reached!
% 5.69/2.05 % (21178)------------------------------
% 5.69/2.05 % (21178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.69/2.05 % (21178)Termination reason: Unknown
% 5.69/2.05 % (21178)Termination phase: shuffling
% 5.69/2.05
% 5.69/2.05 % (21178)Memory used [KB]: 2814
% 5.69/2.05 % (21178)Time elapsed: 0.018 s
% 5.69/2.05 % (21178)Instructions burned: 62 (million)
% 5.69/2.05 % (21178)------------------------------
% 5.69/2.05 % (21178)------------------------------
% 5.69/2.06 % (21193)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_20722 for (2995ds/453Mi)
% 5.69/2.06 % (21195)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_20722 for (2995ds/71Mi)
% 5.69/2.06 % (21198)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_20722 for (2995ds/83Mi)
% 5.69/2.07 % (21186)Instruction limit reached!
% 5.69/2.07 % (21186)------------------------------
% 5.69/2.07 % (21186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.69/2.07 % (21186)Termination reason: Unknown
% 5.69/2.07 % (21186)Termination phase: Property scanning
% 5.69/2.07
% 5.69/2.07 % (21186)Memory used [KB]: 2942
% 5.69/2.07 % (21186)Time elapsed: 0.027 s
% 5.69/2.07 % (21186)Instructions burned: 96 (million)
% 5.69/2.07 % (21186)------------------------------
% 5.69/2.07 % (21186)------------------------------
% 5.69/2.08 % (21195)Instruction limit reached!
% 5.69/2.08 % (21195)------------------------------
% 5.69/2.08 % (21195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.69/2.08 % (21195)Termination reason: Unknown
% 5.69/2.08 % (21195)Termination phase: Property scanning
% 5.69/2.08
% 5.69/2.08 % (21195)Memory used [KB]: 2942
% 5.69/2.08 % (21195)Time elapsed: 0.021 s
% 5.69/2.08 % (21195)Instructions burned: 73 (million)
% 5.69/2.08 % (21195)------------------------------
% 5.69/2.08 % (21195)------------------------------
% 5.69/2.08 % (21209)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_20722 for (2995ds/11Mi)
% 5.69/2.09 % (21209)Instruction limit reached!
% 5.69/2.09 % (21209)------------------------------
% 5.69/2.09 % (21209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.69/2.09 % (21209)Termination reason: Unknown
% 5.69/2.09 % (21209)Termination phase: shuffling
% 5.69/2.09
% 5.69/2.09 % (21209)Memory used [KB]: 1918
% 5.69/2.09 % (21209)Time elapsed: 0.005 s
% 5.69/2.09 % (21209)Instructions burned: 14 (million)
% 5.69/2.09 % (21209)------------------------------
% 5.69/2.09 % (21209)------------------------------
% 5.69/2.09 % (21198)Instruction limit reached!
% 5.69/2.09 % (21198)------------------------------
% 5.69/2.09 % (21198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.69/2.09 % (21198)Termination reason: Unknown
% 5.69/2.09 % (21198)Termination phase: Property scanning
% 5.69/2.09
% 5.69/2.09 % (21198)Memory used [KB]: 2942
% 5.69/2.09 % (21198)Time elapsed: 0.024 s
% 5.69/2.09 % (21198)Instructions burned: 85 (million)
% 5.69/2.09 % (21198)------------------------------
% 5.69/2.09 % (21198)------------------------------
% 5.69/2.09 % (21214)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_20722 for (2995ds/41Mi)
% 5.69/2.10 % (21217)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_20722 for (2995ds/6Mi)
% 5.69/2.10 % (21219)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_20722 for (2995ds/150Mi)
% 5.69/2.10 % (21217)Instruction limit reached!
% 5.69/2.10 % (21217)------------------------------
% 5.69/2.10 % (21217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.69/2.10 % (21217)Termination reason: Unknown
% 5.69/2.10 % (21217)Termination phase: shuffling
% 5.69/2.10
% 5.69/2.10 % (21217)Memory used [KB]: 1791
% 5.69/2.10 % (21217)Time elapsed: 0.003 s
% 5.69/2.10 % (21217)Instructions burned: 6 (million)
% 5.69/2.10 % (21217)------------------------------
% 5.69/2.10 % (21217)------------------------------
% 5.69/2.10 % (21214)Instruction limit reached!
% 5.69/2.10 % (21214)------------------------------
% 5.69/2.10 % (21214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.69/2.10 % (21214)Termination reason: Unknown
% 5.69/2.10 % (21214)Termination phase: shuffling
% 5.69/2.10
% 5.69/2.10 % (21214)Memory used [KB]: 2430
% 5.69/2.10 % (21214)Time elapsed: 0.012 s
% 5.69/2.10 % (21214)Instructions burned: 41 (million)
% 5.69/2.10 % (21214)------------------------------
% 5.69/2.10 % (21214)------------------------------
% 5.69/2.11 % (21221)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_20722 for (2995ds/343Mi)
% 5.69/2.11 % (21222)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_20722 for (2995ds/109Mi)
% 5.69/2.11 % (21151)Instruction limit reached!
% 5.69/2.11 % (21151)------------------------------
% 5.69/2.11 % (21151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.69/2.11 % (21151)Termination reason: Unknown
% 5.69/2.11 % (21151)Termination phase: Saturation
% 5.69/2.11
% 5.69/2.11 % (21151)Memory used [KB]: 8443
% 5.69/2.11 % (21151)Time elapsed: 0.143 s
% 5.69/2.11 % (21151)Instructions burned: 509 (million)
% 5.69/2.11 % (21151)------------------------------
% 5.69/2.11 % (21151)------------------------------
% 6.08/2.12 % (21228)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_20722 for (2995ds/253Mi)
% 6.08/2.13 % (21175)Instruction limit reached!
% 6.08/2.13 % (21175)------------------------------
% 6.08/2.13 % (21175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.13 % (21175)Termination reason: Unknown
% 6.08/2.13 % (21175)Termination phase: Saturation
% 6.08/2.13
% 6.08/2.13 % (21175)Memory used [KB]: 3454
% 6.08/2.13 % (21175)Time elapsed: 0.108 s
% 6.08/2.13 % (21175)Instructions burned: 432 (million)
% 6.08/2.13 % (21175)------------------------------
% 6.08/2.13 % (21175)------------------------------
% 6.08/2.14 % (21222)Instruction limit reached!
% 6.08/2.14 % (21222)------------------------------
% 6.08/2.14 % (21222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.14 % (21222)Termination reason: Unknown
% 6.08/2.14 % (21222)Termination phase: SInE selection
% 6.08/2.14
% 6.08/2.14 % (21222)Memory used [KB]: 2942
% 6.08/2.14 % (21222)Time elapsed: 0.029 s
% 6.08/2.14 % (21222)Instructions burned: 109 (million)
% 6.08/2.14 % (21222)------------------------------
% 6.08/2.14 % (21222)------------------------------
% 6.08/2.14 % (21219)Instruction limit reached!
% 6.08/2.14 % (21219)------------------------------
% 6.08/2.14 % (21219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.14 % (21219)Termination reason: Unknown
% 6.08/2.14 % (21219)Termination phase: Preprocessing 3
% 6.08/2.14
% 6.08/2.14 % (21219)Memory used [KB]: 5245
% 6.08/2.14 % (21219)Time elapsed: 0.045 s
% 6.08/2.14 % (21219)Instructions burned: 151 (million)
% 6.08/2.14 % (21219)------------------------------
% 6.08/2.14 % (21219)------------------------------
% 6.08/2.14 % (21229)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_20722 for (2995ds/140Mi)
% 6.08/2.15 % (21230)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_20722 for (2994ds/614Mi)
% 6.08/2.15 % (21231)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_20722 for (2994ds/202Mi)
% 6.08/2.17 % (21193)Instruction limit reached!
% 6.08/2.17 % (21193)------------------------------
% 6.08/2.17 % (21193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.17 % (21193)Termination reason: Unknown
% 6.08/2.17 % (21193)Termination phase: Saturation
% 6.08/2.17
% 6.08/2.17 % (21193)Memory used [KB]: 7931
% 6.08/2.17 % (21193)Time elapsed: 0.112 s
% 6.08/2.17 % (21193)Instructions burned: 453 (million)
% 6.08/2.17 % (21193)------------------------------
% 6.08/2.17 % (21193)------------------------------
% 6.08/2.18 % (21229)Instruction limit reached!
% 6.08/2.18 % (21229)------------------------------
% 6.08/2.18 % (21229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.18 % (21229)Termination reason: Unknown
% 6.08/2.18 % (21229)Termination phase: Property scanning
% 6.08/2.18
% 6.08/2.18 % (21229)Memory used [KB]: 3070
% 6.08/2.18 % (21229)Time elapsed: 0.037 s
% 6.08/2.18 % (21229)Instructions burned: 142 (million)
% 6.08/2.18 % (21229)------------------------------
% 6.08/2.18 % (21229)------------------------------
% 6.08/2.18 % (21232)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_20722 for (2994ds/339Mi)
% 6.08/2.19 % (21233)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_20722 for (2994ds/283Mi)
% 6.08/2.19 % (21221)Instruction limit reached!
% 6.08/2.19 % (21221)------------------------------
% 6.08/2.19 % (21221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.19 % (21221)Termination reason: Unknown
% 6.08/2.19 % (21221)Termination phase: Saturation
% 6.08/2.19
% 6.08/2.19 % (21221)Memory used [KB]: 8443
% 6.08/2.19 % (21221)Time elapsed: 0.088 s
% 6.08/2.19 % (21221)Instructions burned: 343 (million)
% 6.08/2.19 % (21221)------------------------------
% 6.08/2.19 % (21221)------------------------------
% 6.08/2.19 % (21228)Instruction limit reached!
% 6.08/2.19 % (21228)------------------------------
% 6.08/2.19 % (21228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.19 % (21228)Termination reason: Unknown
% 6.08/2.19 % (21228)Termination phase: Property scanning
% 6.08/2.19
% 6.08/2.19 % (21228)Memory used [KB]: 6012
% 6.08/2.19 % (21228)Time elapsed: 0.072 s
% 6.08/2.19 % (21228)Instructions burned: 255 (million)
% 6.08/2.19 % (21228)------------------------------
% 6.08/2.19 % (21228)------------------------------
% 6.63/2.20 % (21234)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_20722 for (2994ds/134Mi)
% 6.63/2.20 % (21235)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_20722 for (2994ds/298Mi)
% 6.63/2.21 % (21231)Instruction limit reached!
% 6.63/2.21 % (21231)------------------------------
% 6.63/2.21 % (21231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.63/2.21 % (21231)Termination reason: Unknown
% 6.63/2.21 % (21231)Termination phase: Property scanning
% 6.63/2.21
% 6.63/2.21 % (21231)Memory used [KB]: 5756
% 6.63/2.21 % (21231)Time elapsed: 0.059 s
% 6.63/2.21 % (21231)Instructions burned: 203 (million)
% 6.63/2.21 % (21231)------------------------------
% 6.63/2.21 % (21231)------------------------------
% 6.63/2.22 % (21236)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_20722 for (2994ds/192Mi)
% 6.63/2.24 % (21234)Instruction limit reached!
% 6.63/2.24 % (21234)------------------------------
% 6.63/2.24 % (21234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.63/2.24 % (21234)Termination reason: Unknown
% 6.63/2.24 % (21234)Termination phase: Property scanning
% 6.63/2.24
% 6.63/2.24 % (21234)Memory used [KB]: 3070
% 6.63/2.24 % (21234)Time elapsed: 0.036 s
% 6.63/2.24 % (21234)Instructions burned: 135 (million)
% 6.63/2.24 % (21234)------------------------------
% 6.63/2.24 % (21234)------------------------------
% 6.63/2.25 % (21237)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_20722 for (2993ds/258Mi)
% 6.63/2.26 % (21233)Instruction limit reached!
% 6.63/2.26 % (21233)------------------------------
% 6.63/2.26 % (21233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.63/2.26 % (21233)Termination reason: Unknown
% 6.63/2.26 % (21233)Termination phase: Saturation
% 6.63/2.26
% 6.63/2.26 % (21233)Memory used [KB]: 7931
% 6.63/2.26 % (21233)Time elapsed: 0.071 s
% 6.63/2.26 % (21233)Instructions burned: 283 (million)
% 6.63/2.26 % (21233)------------------------------
% 6.63/2.26 % (21233)------------------------------
% 6.63/2.27 % (21236)Instruction limit reached!
% 6.63/2.27 % (21236)------------------------------
% 6.63/2.27 % (21236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.63/2.27 % (21236)Termination reason: Unknown
% 6.63/2.27 % (21236)Termination phase: Property scanning
% 6.63/2.27
% 6.63/2.27 % (21236)Memory used [KB]: 3198
% 6.63/2.27 % (21236)Time elapsed: 0.049 s
% 6.63/2.27 % (21236)Instructions burned: 192 (million)
% 6.63/2.27 % (21236)------------------------------
% 6.63/2.27 % (21236)------------------------------
% 6.63/2.27 % (21238)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_20722 for (2993ds/90Mi)
% 6.63/2.27 % (21232)Instruction limit reached!
% 6.63/2.27 % (21232)------------------------------
% 6.63/2.27 % (21232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.63/2.27 % (21232)Termination reason: Unknown
% 6.63/2.27 % (21232)Termination phase: Saturation
% 6.63/2.27
% 6.63/2.27 % (21232)Memory used [KB]: 8187
% 6.63/2.27 % (21232)Time elapsed: 0.092 s
% 6.63/2.27 % (21232)Instructions burned: 341 (million)
% 6.63/2.27 % (21232)------------------------------
% 6.63/2.27 % (21232)------------------------------
% 6.63/2.28 % (21239)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_20722 for (2993ds/231Mi)
% 6.63/2.28 % (21235)Instruction limit reached!
% 6.63/2.28 % (21235)------------------------------
% 6.63/2.28 % (21235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.63/2.28 % (21235)Termination reason: Unknown
% 6.63/2.28 % (21235)Termination phase: Saturation
% 6.63/2.28
% 6.63/2.28 % (21235)Memory used [KB]: 7931
% 6.63/2.28 % (21235)Time elapsed: 0.075 s
% 6.63/2.28 % (21235)Instructions burned: 301 (million)
% 6.63/2.28 % (21235)------------------------------
% 6.63/2.28 % (21235)------------------------------
% 6.63/2.28 % (21240)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_20722 for (2993ds/458Mi)
% 6.63/2.29 % (21241)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_20722 for (2993ds/31Mi)
% 6.63/2.29 % (21238)Instruction limit reached!
% 6.63/2.29 % (21238)------------------------------
% 6.63/2.29 % (21238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.63/2.29 % (21238)Termination reason: Unknown
% 6.63/2.29 % (21238)Termination phase: Property scanning
% 6.63/2.29
% 6.63/2.29 % (21238)Memory used [KB]: 2942
% 6.63/2.29 % (21238)Time elapsed: 0.026 s
% 6.63/2.29 % (21238)Instructions burned: 93 (million)
% 6.63/2.29 % (21238)------------------------------
% 6.63/2.29 % (21238)------------------------------
% 7.11/2.30 % (21241)Instruction limit reached!
% 7.11/2.30 % (21241)------------------------------
% 7.11/2.30 % (21241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.11/2.30 % (21241)Termination reason: Unknown
% 7.11/2.30 % (21241)Termination phase: shuffling
% 7.11/2.30
% 7.11/2.30 % (21241)Memory used [KB]: 2302
% 7.11/2.30 % (21241)Time elapsed: 0.010 s
% 7.11/2.30 % (21241)Instructions burned: 31 (million)
% 7.11/2.30 % (21241)------------------------------
% 7.11/2.30 % (21241)------------------------------
% 7.11/2.30 % (21230)Instruction limit reached!
% 7.11/2.30 % (21230)------------------------------
% 7.11/2.30 % (21230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.11/2.30 % (21230)Termination reason: Unknown
% 7.11/2.30 % (21230)Termination phase: Saturation
% 7.11/2.30
% 7.11/2.30 % (21230)Memory used [KB]: 8955
% 7.11/2.30 % (21230)Time elapsed: 0.155 s
% 7.11/2.30 % (21230)Instructions burned: 615 (million)
% 7.11/2.30 % (21230)------------------------------
% 7.11/2.30 % (21230)------------------------------
% 7.11/2.30 % (21242)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_20722 for (2993ds/297Mi)
% 7.11/2.31 % (21243)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_20722 for (2993ds/987Mi)
% 7.11/2.31 % (21244)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_20722 for (2993ds/182Mi)
% 7.11/2.31 % (21237)Instruction limit reached!
% 7.11/2.31 % (21237)------------------------------
% 7.11/2.31 % (21237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.11/2.31 % (21237)Termination reason: Unknown
% 7.11/2.31 % (21237)Termination phase: Saturation
% 7.11/2.31
% 7.11/2.31 % (21237)Memory used [KB]: 7931
% 7.11/2.31 % (21237)Time elapsed: 0.067 s
% 7.11/2.31 % (21237)Instructions burned: 260 (million)
% 7.11/2.31 % (21237)------------------------------
% 7.11/2.31 % (21237)------------------------------
% 7.11/2.32 % (21245)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_20722 for (2993ds/182Mi)
% 7.11/2.34 % (21239)Instruction limit reached!
% 7.11/2.34 % (21239)------------------------------
% 7.11/2.34 % (21239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.11/2.34 % (21239)Termination reason: Unknown
% 7.11/2.34 % (21239)Termination phase: Property scanning
% 7.11/2.34
% 7.11/2.34 % (21239)Memory used [KB]: 4477
% 7.11/2.34 % (21239)Time elapsed: 0.062 s
% 7.11/2.34 % (21239)Instructions burned: 234 (million)
% 7.11/2.34 % (21239)------------------------------
% 7.11/2.34 % (21239)------------------------------
% 7.11/2.35 % (21246)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_20722 for (2993ds/154Mi)
% 7.11/2.36 % (21244)Instruction limit reached!
% 7.11/2.36 % (21244)------------------------------
% 7.11/2.36 % (21244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.11/2.36 % (21244)Termination reason: Unknown
% 7.11/2.36 % (21244)Termination phase: Property scanning
% 7.11/2.36
% 7.11/2.36 % (21244)Memory used [KB]: 3198
% 7.11/2.36 % (21244)Time elapsed: 0.048 s
% 7.11/2.36 % (21244)Instructions burned: 183 (million)
% 7.11/2.36 % (21244)------------------------------
% 7.11/2.36 % (21244)------------------------------
% 7.11/2.37 % (21247)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_20722 for (2992ds/79Mi)
% 7.11/2.37 % (21169)Instruction limit reached!
% 7.11/2.37 % (21169)------------------------------
% 7.11/2.37 % (21169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.11/2.37 % (21169)Termination reason: Unknown
% 7.11/2.37 % (21169)Termination phase: Saturation
% 7.11/2.37
% 7.11/2.37 % (21169)Memory used [KB]: 13176
% 7.11/2.37 % (21169)Time elapsed: 0.354 s
% 7.11/2.37 % (21169)Instructions burned: 1089 (million)
% 7.11/2.37 % (21169)------------------------------
% 7.11/2.37 % (21169)------------------------------
% 7.11/2.38 % (21242)Instruction limit reached!
% 7.11/2.38 % (21242)------------------------------
% 7.11/2.38 % (21242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.11/2.38 % (21242)Termination reason: Unknown
% 7.11/2.38 % (21242)Termination phase: Saturation
% 7.11/2.38
% 7.11/2.38 % (21242)Memory used [KB]: 7931
% 7.11/2.38 % (21242)Time elapsed: 0.075 s
% 7.11/2.38 % (21242)Instructions burned: 298 (million)
% 7.11/2.38 % (21242)------------------------------
% 7.11/2.38 % (21242)------------------------------
% 7.11/2.38 % (21245)Instruction limit reached!
% 7.11/2.38 % (21245)------------------------------
% 7.11/2.38 % (21245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.11/2.38 % (21245)Termination reason: Unknown
% 7.11/2.38 % (21245)Termination phase: Property scanning
% 7.11/2.38
% 7.11/2.38 % (21245)Memory used [KB]: 5756
% 7.11/2.38 % (21245)Time elapsed: 0.055 s
% 7.11/2.38 % (21245)Instructions burned: 184 (million)
% 7.11/2.38 % (21245)------------------------------
% 7.11/2.38 % (21245)------------------------------
% 7.11/2.38 % (21248)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_20722 for (2992ds/216Mi)
% 7.11/2.39 % (21246)Instruction limit reached!
% 7.11/2.39 % (21246)------------------------------
% 7.11/2.39 % (21246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.11/2.39 % (21246)Termination reason: Unknown
% 7.11/2.39 % (21246)Termination phase: Function definition elimination
% 7.11/2.39
% 7.11/2.39 % (21246)Memory used [KB]: 3198
% 7.11/2.39 % (21246)Time elapsed: 0.040 s
% 7.11/2.39 % (21246)Instructions burned: 155 (million)
% 7.11/2.39 % (21246)------------------------------
% 7.11/2.39 % (21246)------------------------------
% 7.11/2.39 % (21249)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_20722 for (2992ds/114Mi)
% 7.11/2.39 % (21250)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_20722 for (2992ds/922Mi)
% 7.11/2.39 % (21247)Instruction limit reached!
% 7.11/2.39 % (21247)------------------------------
% 7.11/2.39 % (21247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.11/2.39 % (21247)Termination reason: Unknown
% 7.11/2.39 % (21247)Termination phase: Property scanning
% 7.11/2.39
% 7.11/2.39 % (21247)Memory used [KB]: 2942
% 7.11/2.39 % (21247)Time elapsed: 0.023 s
% 7.11/2.39 % (21247)Instructions burned: 83 (million)
% 7.11/2.39 % (21247)------------------------------
% 7.11/2.39 % (21247)------------------------------
% 7.11/2.40 % (21251)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_20722 for (2992ds/182Mi)
% 8.09/2.40 % (21252)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_20722 for (2992ds/164Mi)
% 8.09/2.40 % (21240)Instruction limit reached!
% 8.09/2.40 % (21240)------------------------------
% 8.09/2.40 % (21240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.09/2.40 % (21240)Termination reason: Unknown
% 8.09/2.40 % (21240)Termination phase: Saturation
% 8.09/2.40
% 8.09/2.40 % (21240)Memory used [KB]: 8571
% 8.09/2.40 % (21240)Time elapsed: 0.122 s
% 8.09/2.40 % (21240)Instructions burned: 460 (million)
% 8.09/2.40 % (21240)------------------------------
% 8.09/2.40 % (21240)------------------------------
% 8.09/2.41 % (21253)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_20722 for (2992ds/50Mi)
% 8.09/2.42 % (21249)Instruction limit reached!
% 8.09/2.42 % (21249)------------------------------
% 8.09/2.42 % (21249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.09/2.42 % (21249)Termination reason: Unknown
% 8.09/2.42 % (21249)Termination phase: Property scanning
% 8.09/2.42
% 8.09/2.42 % (21249)Memory used [KB]: 3070
% 8.09/2.42 % (21249)Time elapsed: 0.031 s
% 8.09/2.42 % (21249)Instructions burned: 114 (million)
% 8.09/2.42 % (21249)------------------------------
% 8.09/2.42 % (21249)------------------------------
% 8.09/2.42 % (21253)Instruction limit reached!
% 8.09/2.42 % (21253)------------------------------
% 8.09/2.42 % (21253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.09/2.42 % (21253)Termination reason: Unknown
% 8.09/2.42 % (21253)Termination phase: shuffling
% 8.09/2.42
% 8.09/2.42 % (21253)Memory used [KB]: 2686
% 8.09/2.42 % (21253)Time elapsed: 0.015 s
% 8.09/2.42 % (21253)Instructions burned: 53 (million)
% 8.09/2.42 % (21253)------------------------------
% 8.09/2.42 % (21253)------------------------------
% 8.09/2.43 % (21254)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_20722 for (2992ds/368Mi)
% 8.09/2.43 % (21248)Instruction limit reached!
% 8.09/2.43 % (21248)------------------------------
% 8.09/2.43 % (21248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.09/2.43 % (21248)Termination reason: Unknown
% 8.09/2.43 % (21248)Termination phase: Function definition elimination
% 8.09/2.43
% 8.09/2.43 % (21248)Memory used [KB]: 3198
% 8.09/2.43 % (21248)Time elapsed: 0.054 s
% 8.09/2.43 % (21248)Instructions burned: 217 (million)
% 8.09/2.43 % (21248)------------------------------
% 8.09/2.43 % (21248)------------------------------
% 8.09/2.43 % (21255)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_20722 for (2992ds/1021Mi)
% 8.09/2.44 % (21251)Instruction limit reached!
% 8.09/2.44 % (21251)------------------------------
% 8.09/2.44 % (21251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.09/2.44 % (21251)Termination reason: Unknown
% 8.09/2.44 % (21251)Termination phase: Property scanning
% 8.09/2.44
% 8.09/2.44 % (21251)Memory used [KB]: 3326
% 8.09/2.44 % (21251)Time elapsed: 0.047 s
% 8.09/2.44 % (21251)Instructions burned: 184 (million)
% 8.09/2.44 % (21251)------------------------------
% 8.09/2.44 % (21251)------------------------------
% 8.09/2.44 % (21252)Instruction limit reached!
% 8.09/2.44 % (21252)------------------------------
% 8.09/2.44 % (21252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.09/2.44 % (21252)Termination reason: Unknown
% 8.09/2.44 % (21252)Termination phase: Property scanning
% 8.09/2.44
% 8.09/2.44 % (21252)Memory used [KB]: 3070
% 8.09/2.44 % (21252)Time elapsed: 0.043 s
% 8.09/2.44 % (21252)Instructions burned: 168 (million)
% 8.09/2.44 % (21252)------------------------------
% 8.09/2.44 % (21252)------------------------------
% 8.09/2.44 % (21256)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_20722 for (2992ds/267Mi)
% 8.09/2.45 % (21257)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_20722 for (2992ds/204Mi)
% 8.09/2.46 % (21258)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_20722 for (2992ds/26Mi)
% 8.09/2.47 % (21258)Instruction limit reached!
% 8.09/2.47 % (21258)------------------------------
% 8.09/2.47 % (21258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.09/2.47 % (21258)Termination reason: Unknown
% 8.09/2.47 % (21258)Termination phase: shuffling
% 8.09/2.47
% 8.09/2.47 % (21258)Memory used [KB]: 2174
% 8.09/2.47 % (21258)Time elapsed: 0.016 s
% 8.09/2.47 % (21258)Instructions burned: 27 (million)
% 8.09/2.47 % (21258)------------------------------
% 8.09/2.47 % (21258)------------------------------
% 8.09/2.49 % (21259)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_20722 for (2991ds/53Mi)
% 8.48/2.50 % (21257)Instruction limit reached!
% 8.48/2.50 % (21257)------------------------------
% 8.48/2.50 % (21257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.48/2.50 % (21257)Termination reason: Unknown
% 8.48/2.50 % (21257)Termination phase: Function definition elimination
% 8.48/2.50
% 8.48/2.50 % (21257)Memory used [KB]: 3198
% 8.48/2.50 % (21257)Time elapsed: 0.052 s
% 8.48/2.50 % (21257)Instructions burned: 206 (million)
% 8.48/2.50 % (21257)------------------------------
% 8.48/2.50 % (21257)------------------------------
% 8.48/2.51 % (21256)Instruction limit reached!
% 8.48/2.51 % (21256)------------------------------
% 8.48/2.51 % (21256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.48/2.51 % (21256)Termination reason: Unknown
% 8.48/2.51 % (21256)Termination phase: Saturation
% 8.48/2.51
% 8.48/2.51 % (21256)Memory used [KB]: 7803
% 8.48/2.51 % (21256)Time elapsed: 0.067 s
% 8.48/2.51 % (21256)Instructions burned: 267 (million)
% 8.48/2.51 % (21256)------------------------------
% 8.48/2.51 % (21256)------------------------------
% 8.48/2.51 % (21260)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_20722 for (2991ds/4436Mi)
% 8.48/2.52 % (21261)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_20722 for (2991ds/1539Mi)
% 8.48/2.52 % (21259)Instruction limit reached!
% 8.48/2.52 % (21259)------------------------------
% 8.48/2.52 % (21259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.48/2.52 % (21259)Termination reason: Unknown
% 8.48/2.52 % (21259)Termination phase: shuffling
% 8.48/2.52
% 8.48/2.52 % (21259)Memory used [KB]: 2686
% 8.48/2.52 % (21259)Time elapsed: 0.030 s
% 8.48/2.52 % (21259)Instructions burned: 54 (million)
% 8.48/2.52 % (21259)------------------------------
% 8.48/2.52 % (21259)------------------------------
% 8.48/2.52 % (21254)Instruction limit reached!
% 8.48/2.52 % (21254)------------------------------
% 8.48/2.52 % (21254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.48/2.52 % (21254)Termination reason: Unknown
% 8.48/2.52 % (21254)Termination phase: Saturation
% 8.48/2.52
% 8.48/2.52 % (21254)Memory used [KB]: 8443
% 8.48/2.52 % (21254)Time elapsed: 0.099 s
% 8.48/2.52 % (21254)Instructions burned: 370 (million)
% 8.48/2.52 % (21254)------------------------------
% 8.48/2.52 % (21254)------------------------------
% 8.48/2.53 % (21263)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_20722 for (2991ds/5205Mi)
% 8.48/2.54 % (21262)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_20722 for (2991ds/408Mi)
% 8.48/2.55 % (21243)Instruction limit reached!
% 8.48/2.55 % (21243)------------------------------
% 8.48/2.55 % (21243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.48/2.55 % (21243)Termination reason: Unknown
% 8.48/2.55 % (21243)Termination phase: Saturation
% 8.48/2.55
% 8.48/2.55 % (21243)Memory used [KB]: 10106
% 8.48/2.55 % (21243)Time elapsed: 0.247 s
% 8.48/2.55 % (21243)Instructions burned: 990 (million)
% 8.48/2.55 % (21243)------------------------------
% 8.48/2.55 % (21243)------------------------------
% 8.48/2.56 % (21264)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_20722 for (2990ds/1913Mi)
% 9.03/2.64 % (21250)Instruction limit reached!
% 9.03/2.64 % (21250)------------------------------
% 9.03/2.64 % (21250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.03/2.64 % (21250)Termination reason: Unknown
% 9.03/2.64 % (21250)Termination phase: Saturation
% 9.03/2.64
% 9.03/2.64 % (21250)Memory used [KB]: 13432
% 9.03/2.64 % (21250)Time elapsed: 0.257 s
% 9.03/2.64 % (21250)Instructions burned: 925 (million)
% 9.03/2.64 % (21250)------------------------------
% 9.03/2.64 % (21250)------------------------------
% 9.03/2.66 % (21265)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_20722 for (2990ds/4350Mi)
% 9.03/2.67 % (21262)Instruction limit reached!
% 9.03/2.67 % (21262)------------------------------
% 9.03/2.67 % (21262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.03/2.67 % (21262)Termination reason: Unknown
% 9.03/2.67 % (21262)Termination phase: Saturation
% 9.03/2.67
% 9.03/2.67 % (21262)Memory used [KB]: 12025
% 9.03/2.67 % (21262)Time elapsed: 0.139 s
% 9.03/2.67 % (21262)Instructions burned: 410 (million)
% 9.03/2.67 % (21262)------------------------------
% 9.03/2.67 % (21262)------------------------------
% 9.03/2.68 % (21266)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_20722 for (2989ds/68Mi)
% 9.45/2.71 % (21266)Instruction limit reached!
% 9.45/2.71 % (21266)------------------------------
% 9.45/2.71 % (21266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.45/2.71 % (21266)Termination reason: Unknown
% 9.45/2.71 % (21266)Termination phase: Property scanning
% 9.45/2.71
% 9.45/2.71 % (21266)Memory used [KB]: 2814
% 9.45/2.71 % (21266)Time elapsed: 0.022 s
% 9.45/2.71 % (21266)Instructions burned: 71 (million)
% 9.45/2.71 % (21266)------------------------------
% 9.45/2.71 % (21266)------------------------------
% 9.45/2.72 % (21267)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_20722 for (2989ds/358Mi)
% 9.45/2.72 % (21255)Instruction limit reached!
% 9.45/2.72 % (21255)------------------------------
% 9.45/2.72 % (21255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.45/2.72 % (21255)Termination reason: Unknown
% 9.45/2.72 % (21255)Termination phase: Saturation
% 9.45/2.72
% 9.45/2.72 % (21255)Memory used [KB]: 13560
% 9.45/2.72 % (21255)Time elapsed: 0.284 s
% 9.45/2.72 % (21255)Instructions burned: 1023 (million)
% 9.45/2.72 % (21255)------------------------------
% 9.45/2.72 % (21255)------------------------------
% 9.45/2.73 % (21268)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_20722 for (2989ds/31Mi)
% 9.45/2.74 % (21268)Instruction limit reached!
% 9.45/2.74 % (21268)------------------------------
% 9.45/2.74 % (21268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.45/2.74 % (21268)Termination reason: Unknown
% 9.45/2.74 % (21268)Termination phase: shuffling
% 9.45/2.74
% 9.45/2.74 % (21268)Memory used [KB]: 2302
% 9.45/2.74 % (21268)Time elapsed: 0.010 s
% 9.45/2.74 % (21268)Instructions burned: 31 (million)
% 9.45/2.74 % (21268)------------------------------
% 9.45/2.74 % (21268)------------------------------
% 9.45/2.75 % (21269)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_20722 for (2989ds/279Mi)
% 9.80/2.81 % (21269)Instruction limit reached!
% 9.80/2.81 % (21269)------------------------------
% 9.80/2.81 % (21269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.80/2.81 % (21269)Termination reason: Unknown
% 9.80/2.81 % (21269)Termination phase: Saturation
% 9.80/2.81
% 9.80/2.81 % (21269)Memory used [KB]: 7931
% 9.80/2.81 % (21269)Time elapsed: 0.069 s
% 9.80/2.81 % (21269)Instructions burned: 279 (million)
% 9.80/2.81 % (21269)------------------------------
% 9.80/2.81 % (21269)------------------------------
% 9.80/2.81 % (21267)Instruction limit reached!
% 9.80/2.81 % (21267)------------------------------
% 9.80/2.81 % (21267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.80/2.81 % (21267)Termination reason: Unknown
% 9.80/2.81 % (21267)Termination phase: Saturation
% 9.80/2.81
% 9.80/2.81 % (21267)Memory used [KB]: 8443
% 9.80/2.81 % (21267)Time elapsed: 0.099 s
% 9.80/2.81 % (21267)Instructions burned: 358 (million)
% 9.80/2.81 % (21267)------------------------------
% 9.80/2.81 % (21267)------------------------------
% 9.80/2.82 % (21270)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_20722 for (2988ds/258Mi)
% 9.80/2.82 % (21271)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_20722 for (2988ds/26Mi)
% 9.80/2.83 % (21271)Instruction limit reached!
% 9.80/2.83 % (21271)------------------------------
% 9.80/2.83 % (21271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.80/2.83 % (21271)Termination reason: Unknown
% 9.80/2.83 % (21271)Termination phase: shuffling
% 9.80/2.83
% 9.80/2.83 % (21271)Memory used [KB]: 2302
% 9.80/2.83 % (21271)Time elapsed: 0.009 s
% 9.80/2.83 % (21271)Instructions burned: 27 (million)
% 9.80/2.83 % (21271)------------------------------
% 9.80/2.83 % (21271)------------------------------
% 9.80/2.84 % (21272)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_20722 for (2988ds/995Mi)
% 9.80/2.89 % (21270)Instruction limit reached!
% 9.80/2.89 % (21270)------------------------------
% 9.80/2.89 % (21270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.80/2.89 % (21270)Termination reason: Unknown
% 9.80/2.89 % (21270)Termination phase: Saturation
% 9.80/2.89
% 9.80/2.89 % (21270)Memory used [KB]: 8443
% 9.80/2.89 % (21270)Time elapsed: 0.068 s
% 9.80/2.89 % (21270)Instructions burned: 258 (million)
% 9.80/2.89 % (21270)------------------------------
% 9.80/2.89 % (21270)------------------------------
% 10.09/2.90 % (21273)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_20722 for (2987ds/373Mi)
% 10.09/2.94 % (21261)Instruction limit reached!
% 10.09/2.94 % (21261)------------------------------
% 10.09/2.94 % (21261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.09/2.94 % (21261)Termination reason: Unknown
% 10.09/2.94 % (21261)Termination phase: Saturation
% 10.09/2.94
% 10.09/2.94 % (21261)Memory used [KB]: 14711
% 10.09/2.94 % (21261)Time elapsed: 0.421 s
% 10.09/2.94 % (21261)Instructions burned: 1539 (million)
% 10.09/2.94 % (21261)------------------------------
% 10.09/2.94 % (21261)------------------------------
% 10.09/2.95 % (21274)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_20722 for (2986ds/253Mi)
% 10.09/3.00 % (21273)Instruction limit reached!
% 10.09/3.00 % (21273)------------------------------
% 10.09/3.00 % (21273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.09/3.00 % (21273)Termination reason: Unknown
% 10.09/3.00 % (21273)Termination phase: Saturation
% 10.09/3.00
% 10.09/3.00 % (21273)Memory used [KB]: 9466
% 10.09/3.00 % (21273)Time elapsed: 0.100 s
% 10.09/3.00 % (21273)Instructions burned: 373 (million)
% 10.09/3.00 % (21273)------------------------------
% 10.09/3.00 % (21273)------------------------------
% 10.09/3.01 % (21275)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_20722 for (2986ds/832Mi)
% 12.63/3.01 % (21274)Instruction limit reached!
% 12.63/3.01 % (21274)------------------------------
% 12.63/3.01 % (21274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.63/3.01 % (21274)Termination reason: Unknown
% 12.63/3.01 % (21274)Termination phase: Saturation
% 12.63/3.01
% 12.63/3.01 % (21274)Memory used [KB]: 7803
% 12.63/3.01 % (21274)Time elapsed: 0.066 s
% 12.63/3.01 % (21274)Instructions burned: 255 (million)
% 12.63/3.01 % (21274)------------------------------
% 12.63/3.01 % (21274)------------------------------
% 12.63/3.02 % (21276)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_20722 for (2986ds/668Mi)
% 13.15/3.14 % (21264)Instruction limit reached!
% 13.15/3.14 % (21264)------------------------------
% 13.15/3.14 % (21264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.15/3.14 % (21264)Termination reason: Unknown
% 13.15/3.14 % (21264)Termination phase: Saturation
% 13.15/3.14
% 13.15/3.14 % (21264)Memory used [KB]: 7036
% 13.15/3.14 % (21264)Time elapsed: 0.598 s
% 13.15/3.14 % (21264)Instructions burned: 1914 (million)
% 13.15/3.14 % (21264)------------------------------
% 13.15/3.14 % (21264)------------------------------
% 13.15/3.15 % (21272)Instruction limit reached!
% 13.15/3.15 % (21272)------------------------------
% 13.15/3.15 % (21272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.15/3.15 % (21272)Termination reason: Unknown
% 13.15/3.15 % (21272)Termination phase: Saturation
% 13.15/3.15
% 13.15/3.15 % (21272)Memory used [KB]: 16758
% 13.15/3.15 % (21272)Time elapsed: 0.300 s
% 13.15/3.15 % (21272)Instructions burned: 995 (million)
% 13.15/3.15 % (21272)------------------------------
% 13.15/3.15 % (21272)------------------------------
% 13.15/3.15 % (21277)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_20722 for (2985ds/40Mi)
% 13.15/3.16 % (21278)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_20722 for (2984ds/294Mi)
% 13.15/3.16 % (21277)Instruction limit reached!
% 13.15/3.16 % (21277)------------------------------
% 13.15/3.16 % (21277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.15/3.16 % (21277)Termination reason: Unknown
% 13.15/3.16 % (21277)Termination phase: shuffling
% 13.15/3.16
% 13.15/3.16 % (21277)Memory used [KB]: 2558
% 13.15/3.16 % (21277)Time elapsed: 0.013 s
% 13.15/3.16 % (21277)Instructions burned: 42 (million)
% 13.15/3.16 % (21277)------------------------------
% 13.15/3.16 % (21277)------------------------------
% 13.15/3.17 % (21279)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_20722 for (2984ds/187Mi)
% 13.15/3.18 % (21276)Instruction limit reached!
% 13.15/3.18 % (21276)------------------------------
% 13.15/3.18 % (21276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.15/3.18 % (21276)Termination reason: Unknown
% 13.15/3.18 % (21276)Termination phase: Saturation
% 13.15/3.18
% 13.15/3.18 % (21276)Memory used [KB]: 12537
% 13.15/3.18 % (21276)Time elapsed: 0.164 s
% 13.15/3.18 % (21276)Instructions burned: 668 (million)
% 13.15/3.18 % (21276)------------------------------
% 13.15/3.18 % (21276)------------------------------
% 13.15/3.19 % (21280)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_20722 for (2984ds/371Mi)
% 13.69/3.22 % (21279)Instruction limit reached!
% 13.69/3.22 % (21279)------------------------------
% 13.69/3.22 % (21279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.69/3.22 % (21279)Termination reason: Unknown
% 13.69/3.22 % (21279)Termination phase: Property scanning
% 13.69/3.22
% 13.69/3.22 % (21279)Memory used [KB]: 3198
% 13.69/3.22 % (21279)Time elapsed: 0.048 s
% 13.69/3.22 % (21279)Instructions burned: 187 (million)
% 13.69/3.22 % (21279)------------------------------
% 13.69/3.22 % (21279)------------------------------
% 13.69/3.23 % (21281)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_20722 for (2984ds/1827Mi)
% 13.69/3.23 % (21278)Instruction limit reached!
% 13.69/3.23 % (21278)------------------------------
% 13.69/3.23 % (21278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.69/3.23 % (21278)Termination reason: Unknown
% 13.69/3.23 % (21278)Termination phase: Saturation
% 13.69/3.23
% 13.69/3.23 % (21278)Memory used [KB]: 7931
% 13.69/3.23 % (21278)Time elapsed: 0.074 s
% 13.69/3.23 % (21278)Instructions burned: 295 (million)
% 13.69/3.23 % (21278)------------------------------
% 13.69/3.23 % (21278)------------------------------
% 13.69/3.24 % (21282)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_20722 for (2984ds/70Mi)
% 13.69/3.26 % (21275)Instruction limit reached!
% 13.69/3.26 % (21275)------------------------------
% 13.69/3.26 % (21275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.69/3.26 % (21275)Termination reason: Unknown
% 13.69/3.26 % (21275)Termination phase: Saturation
% 13.69/3.26
% 13.69/3.26 % (21275)Memory used [KB]: 13176
% 13.69/3.26 % (21275)Time elapsed: 0.248 s
% 13.69/3.26 % (21275)Instructions burned: 834 (million)
% 13.69/3.26 % (21275)------------------------------
% 13.69/3.26 % (21275)------------------------------
% 13.69/3.26 % (21282)Instruction limit reached!
% 13.69/3.26 % (21282)------------------------------
% 13.69/3.26 % (21282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.69/3.26 % (21282)Termination reason: Unknown
% 13.69/3.26 % (21282)Termination phase: Property scanning
% 13.69/3.26
% 13.69/3.26 % (21282)Memory used [KB]: 3070
% 13.69/3.26 % (21282)Time elapsed: 0.020 s
% 13.69/3.26 % (21282)Instructions burned: 72 (million)
% 13.69/3.26 % (21282)------------------------------
% 13.69/3.26 % (21282)------------------------------
% 13.69/3.27 % (21283)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_20722 for (2983ds/316Mi)
% 13.69/3.27 % (21284)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_20722 for (2983ds/932Mi)
% 13.69/3.29 % (21280)Instruction limit reached!
% 13.69/3.29 % (21280)------------------------------
% 13.69/3.29 % (21280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.69/3.29 % (21280)Termination reason: Unknown
% 13.69/3.29 % (21280)Termination phase: Saturation
% 13.69/3.29
% 13.69/3.29 % (21280)Memory used [KB]: 8827
% 13.69/3.29 % (21280)Time elapsed: 0.097 s
% 13.69/3.29 % (21280)Instructions burned: 373 (million)
% 13.69/3.29 % (21280)------------------------------
% 13.69/3.29 % (21280)------------------------------
% 14.51/3.30 % (21285)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_20722 for (2983ds/4714Mi)
% 14.51/3.35 % (21283)Instruction limit reached!
% 14.51/3.35 % (21283)------------------------------
% 14.51/3.35 % (21283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.51/3.35 % (21283)Termination reason: Unknown
% 14.51/3.35 % (21283)Termination phase: Saturation
% 14.51/3.35
% 14.51/3.35 % (21283)Memory used [KB]: 7931
% 14.51/3.35 % (21283)Time elapsed: 0.082 s
% 14.51/3.35 % (21283)Instructions burned: 319 (million)
% 14.51/3.35 % (21283)------------------------------
% 14.51/3.35 % (21283)------------------------------
% 14.51/3.36 % (21286)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_20722 for (2983ds/8250Mi)
% 15.20/3.50 % (21284)Instruction limit reached!
% 15.20/3.50 % (21284)------------------------------
% 15.20/3.50 % (21284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.20/3.50 % (21284)Termination reason: Unknown
% 15.20/3.50 % (21284)Termination phase: Saturation
% 15.20/3.50
% 15.20/3.50 % (21284)Memory used [KB]: 12920
% 15.20/3.50 % (21284)Time elapsed: 0.234 s
% 15.20/3.50 % (21284)Instructions burned: 933 (million)
% 15.20/3.50 % (21284)------------------------------
% 15.20/3.50 % (21284)------------------------------
% 15.20/3.51 % (21287)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_20722 for (2981ds/770Mi)
% 15.74/3.62 % (21286)First to succeed.
% 15.74/3.62 % (21286)Refutation found. Thanks to Tanya!
% 15.74/3.62 % SZS status Theorem for DTF2THF_20722
% 15.74/3.62 % SZS output start Proof for DTF2THF_20722
% 15.74/3.62 thf(func_def_0, type, in: $i > $i > $o).
% 15.74/3.62 thf(func_def_1, type, exu: ($i > $o) > $o).
% 15.74/3.62 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 15.74/3.62 thf(func_def_8, type, powerset: $i > $i).
% 15.74/3.62 thf(func_def_10, type, setunion: $i > $i).
% 15.74/3.62 thf(func_def_19, type, descr: ($i > $o) > $i).
% 15.74/3.62 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 15.74/3.62 thf(func_def_26, type, prop2set: $o > $i).
% 15.74/3.62 thf(func_def_36, type, nonempty: $i > $o).
% 15.74/3.62 thf(func_def_69, type, set2prop: $i > $o).
% 15.74/3.62 thf(func_def_88, type, subset: $i > $i > $o).
% 15.74/3.62 thf(func_def_89, type, disjoint: $i > $i > $o).
% 15.74/3.62 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 15.74/3.62 thf(func_def_114, type, binunion: $i > $i > $i).
% 15.74/3.62 thf(func_def_122, type, binintersect: $i > $i > $i).
% 15.74/3.62 thf(func_def_135, type, regular: $i > $o).
% 15.74/3.62 thf(func_def_136, type, setminus: $i > $i > $i).
% 15.74/3.62 thf(func_def_147, type, symdiff: $i > $i > $i).
% 15.74/3.62 thf(func_def_153, type, iskpair: $i > $o).
% 15.74/3.62 thf(func_def_158, type, kpair: $i > $i > $i).
% 15.74/3.62 thf(func_def_160, type, cartprod: $i > $i > $i).
% 15.74/3.62 thf(func_def_177, type, singleton: $i > $o).
% 15.74/3.62 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 15.74/3.62 thf(func_def_184, type, atmost1p: $i > $o).
% 15.74/3.62 thf(func_def_185, type, atleast2p: $i > $o).
% 15.74/3.62 thf(func_def_186, type, atmost2p: $i > $o).
% 15.74/3.62 thf(func_def_187, type, upairsetp: $i > $o).
% 15.74/3.62 thf(func_def_191, type, kfst: $i > $i).
% 15.74/3.62 thf(func_def_203, type, ksnd: $i > $i).
% 15.74/3.62 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 15.74/3.62 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 15.74/3.62 thf(func_def_222, type, func: $i > $i > $i > $o).
% 15.74/3.62 thf(func_def_223, type, funcSet: $i > $i > $i).
% 15.74/3.62 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 15.74/3.62 thf(func_def_259, type, if: $i > $o > $i > $i > $i).
% 15.74/3.62 thf(func_def_323, type, breln1: $i > $i > $o).
% 15.74/3.62 thf(func_def_325, type, breln1Set: $i > $i).
% 15.74/3.62 thf(func_def_327, type, transitive: $i > $i > $o).
% 15.74/3.62 thf(func_def_328, type, antisymmetric: $i > $i > $o).
% 15.74/3.62 thf(func_def_329, type, reflexive: $i > $i > $o).
% 15.74/3.62 thf(func_def_330, type, refltransitive: $i > $i > $o).
% 15.74/3.62 thf(func_def_331, type, refllinearorder: $i > $i > $o).
% 15.74/3.62 thf(func_def_332, type, reflwellordering: $i > $i > $o).
% 15.74/3.62 thf(func_def_338, type, breln1invset: $i > $i > $i).
% 15.74/3.62 thf(func_def_342, type, breln1compset: $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_360, type, image1: $i > ($i > $i) > $i).
% 15.74/3.62 thf(func_def_364, type, injective: $i > $i > $i > $o).
% 15.74/3.62 thf(func_def_365, type, injFuncSet: $i > $i > $i).
% 15.74/3.62 thf(func_def_369, type, surjective: $i > $i > $i > $o).
% 15.74/3.62 thf(func_def_370, type, surjFuncSet: $i > $i > $i).
% 15.74/3.62 thf(func_def_378, type, omegaS: $i > $i).
% 15.74/3.62 thf(func_def_382, type, peano3: $i > $i > $i > $o).
% 15.74/3.62 thf(func_def_383, type, peano4: $i > $i > $i > $o).
% 15.74/3.62 thf(func_def_384, type, peano5: $i > $i > $i > $o).
% 15.74/3.62 thf(func_def_386, type, peano: $i > $i > $i > $o).
% 15.74/3.62 thf(func_def_387, type, transitiveset: $i > $o).
% 15.74/3.62 thf(func_def_392, type, stricttotalorderedByIn: $i > $o).
% 15.74/3.62 thf(func_def_393, type, wellorderedByIn: $i > $o).
% 15.74/3.62 thf(func_def_394, type, ordinal: $i > $o).
% 15.74/3.62 thf(func_def_395, type, limitOrdinal: $i > $o).
% 15.74/3.62 thf(func_def_417, type, sP3: $i > $i > $i > $o).
% 15.74/3.62 thf(func_def_418, type, sP4: $i > $i > $i > $o).
% 15.74/3.62 thf(func_def_420, type, sP6: $i > $i > $o).
% 15.74/3.62 thf(func_def_421, type, sP7: $i > $o).
% 15.74/3.62 thf(func_def_422, type, sP8: $i > $i > $o).
% 15.74/3.62 thf(func_def_423, type, sP9: $i > $i > $o).
% 15.74/3.62 thf(func_def_428, type, sP14: $i > $i > $i > $i > $o).
% 15.74/3.62 thf(func_def_431, type, sP17: $i > $i > $i > $o > $o).
% 15.74/3.62 thf(func_def_437, type, sK23: $i > $i).
% 15.74/3.62 thf(func_def_440, type, sK26: $i > $i > $o).
% 15.74/3.62 thf(func_def_441, type, sK27: $i > $i).
% 15.74/3.62 thf(func_def_442, type, sK28: $i > $i).
% 15.74/3.62 thf(func_def_443, type, sK29: ($i > $i > $o) > $i > $i).
% 15.74/3.62 thf(func_def_444, type, sK30: ($i > $i > $o) > $i > $i).
% 15.74/3.62 thf(func_def_445, type, sK31: $i > ($i > $i > $o) > $i > $i).
% 15.74/3.62 thf(func_def_450, type, sK36: $i > $i).
% 15.74/3.62 thf(func_def_453, type, sK39: $i > ($i > $i) > $i > $i).
% 15.74/3.62 thf(func_def_454, type, sK40: $i > $i > ($i > $i) > $i > $i).
% 15.74/3.62 thf(func_def_461, type, sK47: $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_462, type, sK48: $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_469, type, sK55: $i > $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_490, type, sK76: $i > $i).
% 15.74/3.62 thf(func_def_491, type, sK77: $i > $o).
% 15.74/3.62 thf(func_def_493, type, sK79: $i > ($i > $o) > $i).
% 15.74/3.62 thf(func_def_495, type, sK81: $i > $i).
% 15.74/3.62 thf(func_def_496, type, sK82: $i > $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_501, type, sK87: ($i > $o) > $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_502, type, sK88: ($i > $o) > $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_506, type, sK92: $i > $o).
% 15.74/3.62 thf(func_def_519, type, sK105: $i > $i > $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_523, type, sK109: $i > $o).
% 15.74/3.62 thf(func_def_542, type, sK128: $i > $o).
% 15.74/3.62 thf(func_def_559, type, sK145: $i > $o).
% 15.74/3.62 thf(func_def_565, type, sK151: $i > $o).
% 15.74/3.62 thf(func_def_570, type, sK156: $i > $o).
% 15.74/3.62 thf(func_def_577, type, sK163: $i > $o).
% 15.74/3.62 thf(func_def_579, type, sK165: $i > $o).
% 15.74/3.62 thf(func_def_581, type, sK167: ($i > $o) > $i).
% 15.74/3.62 thf(func_def_582, type, sK168: ($i > $o) > $i).
% 15.74/3.62 thf(func_def_583, type, sK169: ($i > $o) > $i > $i > $i).
% 15.74/3.62 thf(func_def_584, type, sK170: ($i > $o) > $i > $i > $i).
% 15.74/3.62 thf(func_def_587, type, sK173: $i > $o).
% 15.74/3.62 thf(func_def_593, type, sK179: $i > $o).
% 15.74/3.62 thf(func_def_595, type, sK181: ($i > $o) > $i > $i).
% 15.74/3.62 thf(func_def_605, type, sK191: $i > ($i > $o) > $i).
% 15.74/3.62 thf(func_def_606, type, sK192: $i > $o).
% 15.74/3.62 thf(func_def_616, type, sK202: $i > $i).
% 15.74/3.62 thf(func_def_617, type, sK203: ($i > $i) > $i > $i > $i).
% 15.74/3.62 thf(func_def_627, type, sK213: $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_628, type, sK214: $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_644, type, sK230: $i > $i > $o).
% 15.74/3.62 thf(func_def_647, type, sK233: $i > $i > ($i > $i) > $i).
% 15.74/3.62 thf(func_def_648, type, sK234: $i > $i).
% 15.74/3.62 thf(func_def_713, type, sK299: $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_714, type, sK300: $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_715, type, sK301: $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_716, type, sK302: $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_720, type, sK306: $i > $i > $i).
% 15.74/3.62 thf(func_def_725, type, sK311: $i > $i > $i).
% 15.74/3.62 thf(func_def_731, type, sK317: $i > $o).
% 15.74/3.62 thf(func_def_732, type, sK318: $i > $o).
% 15.74/3.62 thf(func_def_733, type, sK319: ($i > $o) > ($i > $o) > $i).
% 15.74/3.62 thf(func_def_734, type, sK320: ($i > $o) > ($i > $o) > $i).
% 15.74/3.62 thf(func_def_736, type, sK322: $i > $o).
% 15.74/3.62 thf(func_def_739, type, sK325: $i > $i > $i).
% 15.74/3.62 thf(func_def_740, type, sK326: $i > $i > $i).
% 15.74/3.62 thf(func_def_741, type, sK327: $i > $i > $i).
% 15.74/3.62 thf(func_def_742, type, sK328: $i > $i > $i).
% 15.74/3.62 thf(func_def_743, type, sK329: $i > $i > $i).
% 15.74/3.62 thf(func_def_744, type, sK330: $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_745, type, sK331: $i > $i).
% 15.74/3.62 thf(func_def_746, type, sK332: $i > $i).
% 15.74/3.62 thf(func_def_747, type, sK333: $i > $i).
% 15.74/3.62 thf(func_def_748, type, sK334: $i > $i).
% 15.74/3.62 thf(func_def_749, type, sK335: $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_750, type, sK336: $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_751, type, sK337: $i > $i > $i).
% 15.74/3.62 thf(func_def_752, type, sK338: $i > $i > $i).
% 15.74/3.62 thf(func_def_753, type, sK339: $i > $i > $i).
% 15.74/3.62 thf(func_def_755, type, sK341: $i > $i).
% 15.74/3.62 thf(func_def_756, type, sK342: $i > $i).
% 15.74/3.62 thf(func_def_757, type, sK343: $i > $i).
% 15.74/3.62 thf(func_def_770, type, sK356: $i > $i).
% 15.74/3.62 thf(func_def_771, type, sK357: $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_772, type, sK358: $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_780, type, sK366: $i > $i > $i).
% 15.74/3.62 thf(func_def_781, type, sK367: $i > $i > $i).
% 15.74/3.62 thf(func_def_787, type, sK373: $i > $i > $o).
% 15.74/3.62 thf(func_def_799, type, sK385: ($i > $i) > $i > $i > $i).
% 15.74/3.62 thf(func_def_802, type, sK388: $i > $i).
% 15.74/3.62 thf(func_def_810, type, sK396: $i > $o).
% 15.74/3.62 thf(func_def_811, type, sK397: $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_818, type, sK404: $i > ($i > $o) > $i).
% 15.74/3.62 thf(func_def_819, type, sK405: $i > $o).
% 15.74/3.62 thf(func_def_829, type, sK415: $i > $o).
% 15.74/3.62 thf(func_def_848, type, sK434: $i > $o).
% 15.74/3.62 thf(func_def_851, type, sK437: $i > $i > ($i > $o) > $i).
% 15.74/3.62 thf(func_def_854, type, sK440: $i > $o).
% 15.74/3.62 thf(func_def_855, type, sK441: $i > $i).
% 15.74/3.62 thf(func_def_856, type, sK442: ($i > $o) > $i).
% 15.74/3.62 thf(func_def_859, type, sK445: $i > $o).
% 15.74/3.62 thf(func_def_861, type, sK447: ($i > $o) > $i > $i).
% 15.74/3.62 thf(func_def_862, type, sK448: ($i > $o) > $i > $i).
% 15.74/3.62 thf(func_def_881, type, sK467: $i > ($i > $i) > $i).
% 15.74/3.62 thf(func_def_882, type, sK468: $i > $i > ($i > $i) > $i).
% 15.74/3.62 thf(func_def_883, type, sK469: $i > $i).
% 15.74/3.62 thf(func_def_885, type, sK471: $i > $i).
% 15.74/3.62 thf(func_def_886, type, sK472: $i > $i).
% 15.74/3.62 thf(func_def_904, type, sK490: $i > $i).
% 15.74/3.62 thf(func_def_915, type, sK501: $i > $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_917, type, sK503: $i > $o).
% 15.74/3.62 thf(func_def_918, type, sK504: $i > $o).
% 15.74/3.62 thf(func_def_921, type, sK507: $i > ($i > $o) > $i).
% 15.74/3.62 thf(func_def_922, type, sK508: $i > ($i > $o) > $i).
% 15.74/3.62 thf(func_def_944, type, sK530: $i > $i).
% 15.74/3.62 thf(func_def_958, type, sK544: $i > $i > $o).
% 15.74/3.62 thf(func_def_977, type, sK563: $i > $i > $i).
% 15.74/3.62 thf(func_def_997, type, sK583: $i > $o).
% 15.74/3.62 thf(func_def_1018, type, sK604: $i > $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_1019, type, sK605: $i > $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_1020, type, sK606: $i > $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_1021, type, sK607: $i > $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_1022, type, sK608: $i > $i > $i).
% 15.74/3.62 thf(func_def_1028, type, sK614: $i > $i > $o).
% 15.74/3.62 thf(func_def_1031, type, sK617: $i > $i > $o).
% 15.74/3.62 thf(func_def_1056, type, sK642: $i > ($i > $i) > $i > $i).
% 15.74/3.62 thf(func_def_1058, type, sK644: $i > $i).
% 15.74/3.62 thf(func_def_1077, type, sK663: $i > $o).
% 15.74/3.62 thf(func_def_1079, type, sK665: $i > ($i > $o) > $i).
% 15.74/3.62 thf(func_def_1106, type, sK692: $i > $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_1107, type, sK693: $i > $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_1109, type, sK695: $i > $i).
% 15.74/3.62 thf(func_def_1111, type, sK697: $i > ($i > $i) > $i > $i).
% 15.74/3.62 thf(func_def_1113, type, sK699: $i > $i).
% 15.74/3.62 thf(func_def_1158, type, sK744: $i > $o).
% 15.74/3.62 thf(func_def_1159, type, sK745: ($i > $o) > $i).
% 15.74/3.62 thf(func_def_1169, type, sK755: $i > $o).
% 15.74/3.62 thf(func_def_1171, type, sK757: ($i > $o) > $i > $i > $i).
% 15.74/3.62 thf(func_def_1172, type, sK758: ($i > $o) > $i > $i > $i).
% 15.74/3.62 thf(func_def_1173, type, sK759: ($i > $i) > $i > $i > $i).
% 15.74/3.62 thf(func_def_1176, type, sK762: $i > $i).
% 15.74/3.62 thf(func_def_1178, type, sK764: $i > $i > $o).
% 15.74/3.62 thf(func_def_1187, type, sK773: $i > ($i > $o) > $i).
% 15.74/3.62 thf(func_def_1188, type, sK774: $i > $o).
% 15.74/3.62 thf(func_def_1205, type, sK791: ($i > $o) > $i).
% 15.74/3.62 thf(func_def_1206, type, sK792: $i > $o).
% 15.74/3.62 thf(func_def_1207, type, sK793: $i > $i).
% 15.74/3.62 thf(func_def_1208, type, sK794: $i > ($i > $o) > $i).
% 15.74/3.62 thf(func_def_1209, type, sK795: $i > $o).
% 15.74/3.62 thf(func_def_1221, type, sK807: $i > $i > $i).
% 15.74/3.62 thf(func_def_1264, type, sK850: $i > $i > $i).
% 15.74/3.62 thf(func_def_1270, type, sK856: $i > $i > $i).
% 15.74/3.62 thf(func_def_1279, type, sK865: $i > $i).
% 15.74/3.62 thf(func_def_1292, type, sK878: $o > $i > $i > $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_1299, type, sK885: ($i > $o) > ($i > $o) > $i).
% 15.74/3.62 thf(func_def_1300, type, sK886: ($i > $o) > ($i > $o) > $i).
% 15.74/3.62 thf(func_def_1301, type, sK887: $i > $o).
% 15.74/3.62 thf(func_def_1302, type, sK888: $i > $o).
% 15.74/3.62 thf(func_def_1309, type, sK895: $i > $i > $o).
% 15.74/3.62 thf(func_def_1330, type, sK916: $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_1355, type, sK941: $i > ($i > $i > $o) > $i > $i).
% 15.74/3.62 thf(func_def_1357, type, sK943: $i > $i > $o).
% 15.74/3.62 thf(func_def_1361, type, sK947: $i > $i).
% 15.74/3.62 thf(func_def_1363, type, sK949: $i > $i).
% 15.74/3.62 thf(func_def_1366, type, sK952: $i > ($i > $i) > $i > $i).
% 15.74/3.62 thf(func_def_1381, type, sK967: $i > ($i > $i) > $i > $i).
% 15.74/3.62 thf(func_def_1383, type, sK969: $i > $i).
% 15.74/3.62 thf(func_def_1385, type, sK971: $i > $o).
% 15.74/3.62 thf(func_def_1400, type, sK986: $i > $o).
% 15.74/3.62 thf(func_def_1413, type, sK999: $o > $i > $i > $i).
% 15.74/3.62 thf(func_def_1428, type, sK1014: $i > $o).
% 15.74/3.62 thf(func_def_1430, type, sK1016: ($i > $o) > $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_1431, type, sK1017: ($i > $o) > $i > $i > $i > $i).
% 15.74/3.62 thf(func_def_1440, type, sK1026: $i > ($i > $o) > $i).
% 15.74/3.62 thf(func_def_1441, type, sK1027: $i > $o).
% 15.74/3.62 thf(func_def_1455, type, sK1041: $i > $i).
% 15.74/3.62 thf(func_def_1456, type, sK1042: $i > $i).
% 15.74/3.62 thf(func_def_1461, type, sK1047: $i > $i > $i).
% 15.74/3.62 thf(func_def_1466, type, sK1052: $i > ($i > $o) > $i).
% 15.74/3.62 thf(func_def_1467, type, sK1053: $i > $o).
% 15.74/3.62 thf(func_def_1470, type, sK1056: $i > $i).
% 15.74/3.62 thf(func_def_1474, type, sK1060: $i > $i > $o).
% 15.74/3.62 thf(func_def_1498, type, sK1084: ($i > $o) > ($i > $o) > $i > $i > $i).
% 15.74/3.62 thf(func_def_1499, type, sK1085: ($i > $o) > ($i > $o) > $i > $i > $i).
% 15.74/3.62 thf(func_def_1502, type, sK1088: $i > $o).
% 15.74/3.62 thf(func_def_1503, type, sK1089: $i > $o).
% 15.74/3.62 thf(func_def_1526, type, ph1112: !>[X0: $tType]:(X0)).
% 15.74/3.62 thf(f15607,plain,(
% 15.74/3.62 $false),
% 15.74/3.62 inference(avatar_sat_refutation,[status(thm)],[f7519,f10663,f11507,f12688,f13002,f13137,f13146,f13569,f13589,f15606])).
% 15.74/3.62 thf(f15606,plain,(
% 15.74/3.62 ~spl1111_498 | ~spl1111_539 | ~spl1111_1166 | ~spl1111_1645 | ~spl1111_1674),
% 15.74/3.62 inference(avatar_contradiction_clause,[status(thm)],[f15605])).
% 15.74/3.62 thf(f15605,plain,(
% 15.74/3.62 $false | (~spl1111_498 | ~spl1111_539 | ~spl1111_1166 | ~spl1111_1645 | ~spl1111_1674)),
% 15.74/3.62 inference(subsumption_resolution,[status(thm)],[f15601,f3476])).
% 15.74/3.62 thf(f3476,plain,(
% 15.74/3.62 ((transitiveset @ (setunion @ sK70)) != $true)),
% 15.74/3.62 inference(cnf_transformation,[status(thm)],[f1595])).
% 15.74/3.62 thf(f1595,plain,(
% 15.74/3.62 (setukpairinjR1 = $true) & (funcImageSingleton = $true) & (eta2 = $true) & (breln1unionEcases = $true) & (foundation2 = $true) & (doubleComplementSub1 = $true) & (setukpairinjR12 = $true) & (setadjoinIR = $true) & (breln1unionprop = $true) & (breln1all2 = $true) & (complementTE1 = $true) & (binintersectSubset1 = $true) & (eqimpsubset2 = $true) & (inCongP = $true) & (emptyI = $true) & (surjCantorThm = $true) & (disjointsetsI1 = $true) & (dsetconstrER = $true) & (symdiffIneg1 = $true) & (ifp = $true) & (singletoninpowunion = $true) & (doubleComplementSub2 = $true) & (woz1_5 = $true) & (quantDeMorgan3 = $true) & (setminusELneg = $true) & (ex1I = $true) & (cartprodsndin = $true) & (lamp = $true) & (setunion__Cong = $true) & (funcGraphProp4 = $true) & (eqbreln1 = $true) & (exuE2 = $true) & (image1I = $true) & (setunionsingleton2 = $true) & (demorgan2b = $true) & (breln1compprop = $true) & (app = $true) & (subbreln = $true) & (peano0notS = $true) & (iffalseProp2 = $true) & (eta1 = $true) & (ubforcartprodlem1 = $true) & (breln1unionIR = $true) & (doubleComplementI1 = $true) & (breln1SetBreln1 = $true) & (emptysetAx = $true) & (dpsetconstrEL1 = $true) & (omega0Ax = $true) & (emptyInPowerset = $true) & (ex1I2 = $true) & (complementTnotintersectT = $true) & (emptysetimpfalse = $true) & (binintersectRsub = $true) & (binunionEcases = $true) & (setOfPairsIsBReln1 = $true) & (ifSingleton = $true) & (setminusERneg = $true) & (singletonsubset = $true) & (subsetI1 = $true) & (woz2Ex = $true) & (powerset__Cong = $true) & (complementTcontraSubset = $true) & (demorgan2b2 = $true) & (lam2p = $true) & (woz1_1 = $true) & (symdiffE = $true) & (binintersectEL = $true) & (secondinupair = $true) & (subsetI2 = $true) & (emptysetsubset = $true) & (contrasubsetT = $true) & (injFuncSetFuncIn = $true) & (setunionTransitive = $true) & (symdiffI2 = $true) & (setukpairinjL2 = $true) & (binintersectI = $true) & (iftrueProp2 = $true) & (image1Equiv = $true) & (symdiffI1 = $true) & (notinsingleton = $true) & (subbreln1 = $true) & (exuI2 = $true) & (setoftrueEq = $true) & (funcGraphProp1 = $true) & (setminusT_lem = $true) & (binintersectTERcontra = $true) & (exuE1 = $true) & (beta2 = $true) & (iftrueProp1 = $true) & (iffalseProp1 = $true) & (subsetE = $true) & (setminusILneg = $true) & (emptyinunitempty = $true) & (kfstsingleton = $true) & (quantDeMorgan2 = $true) & (image1E = $true) & (setukpairinjL = $true) & (ordinalTransSet = $true) & (vacuousDall = $true) & (ksndpairEq = $true) & (ex1E2 = $true) & (demorgan2a2 = $true) & (powersetT_lem = $true) & (demorgan1 = $true) & (woz13rule2 = $true) & (cartprodfstpairEq = $true) & (omegaSclos = $true) & (iffalse = $true) & (setbeta = $true) & (breln1unionCommutes = $true) & (binintersectSubset3 = $true) & (singletonsuniq = $true) & (cartprodsndpairEq = $true) & (replAx = $true) & (cartprodpairmemEL = $true) & (ap2apEq1 = $true) & (surjFuncSetFuncSurj = $true) & (setminusIRneg = $true) & (doubleComplementE1 = $true) & (theeq = $true) & (exuEu = $true) & (breln1unionI = $true) & (setadjoinE = $true) & (woz13rule0 = $true) & (choice2fnsingleton = $true) & (complementImpComplementIntersect = $true) & (setminusSubset2 = $true) & (contrasubsetT2 = $true) & (nonemptyI = $true) & (breln1unionIL = $true) & (notinemptyset = $true) & (in__Cong = $true) & (breln1compE = $true) & (eqimpsubset1 = $true) & (inIntersectImpInUnion = $true) & (powersetAx = $true) & (powersetE = $true) & (powersetsubset = $true) & (binunionE = $true) & (notinself = $true) & (omega__Cong = $true) & (notequalI2 = $true) & (eqinunit = $true) & (setadjoinOr = $true) & (funcextLem = $true) & (funcext2 = $true) & (apProp = $true) & (setextsub = $true) & (notequalI1 = $true) & (setunionE2 = $true) & (complementInPowersetComplementIntersect = $true) & (inComplementUnionImpInComplement1 = $true) & (descr__Cong = $true) & (upairsetIR = $true) & (singletonsswitch = $true) & (woz13rule4 = $true) & (((transitiveset @ (setunion @ sK70)) != $true) & ! [X1 : $i] : (((ordinal @ X1) = $true) | ((in @ X1 @ sK70) != $true))) & (inComplementUnionImpNotIn1 = $true) & (dpsetconstrER = $true) & (upairsetIL = $true) & (ubforcartprodlem2 = $true) & (uniqinunit = $true) & (binunionLsub = $true) & (cartprodmempaircEq = $true) & (setextAx = $true) & (cartprodpairin = $true) & (cartprodmempair = $true) & (exuI1 = $true) & (setminusI = $true) & (theprop = $true) & (sepInPowerset = $true) & (nonemptyE1 = $true) & (injFuncSetFuncInj = $true) & (transitivesetOp1 = $true) & (dpsetconstrI = $true) & (foundationAx = $true) & (binintersectSubset2 = $true) & (breln1compEex = $true) & (upairset2IR = $true) & (image1Ex1 = $true) & (peanoSinj = $true) & (inPowerset = $true) & (powersetI = $true) & (singletoninpowerset = $true) & (breln1unionE = $true) & (quantDeMorgan1 = $true) & (binunionT_lem = $true) & (breln1invE = $true) & (setadjoin__Cong = $true) & (upairsubunion = $true) & (iftrueorfalse = $true) & (sepSubset = $true) & (nonemptyImpWitness = $true) & (exuE3e = $true) & (kpairp = $true) & (upairsetE = $true) & (dpsetconstrSub = $true) & (binunionTIRcontra = $true) & (binunionIL = $true) & (omegaSAx = $true) & (ex1E1 = $true) & (binunionRsub = $true) & (transitivesetOp2 = $true) & (iftrue = $true) & (ubforcartprodlem3 = $true) & (nonemptyI1 = $true) & (binunionTE = $true) & (cartprodpairsurjEq = $true) & (complementUnionInPowersetComplement = $true) & (setukpairinjL1 = $true) & (kfstpairEq = $true) & (notsubsetI = $true) & (woz2W = $true) & (omegaSp = $true) & (kpairiskpair = $true) & (kpairsurjEq = $true) & (setminusEL = $true) & (exu__Cong = $true) & (funcGraphProp3 = $true) & (setadjoinSub = $true) & (cartprodfstin = $true) & (binintersectLsub = $true) & (injFuncInInjFuncSet = $true) & (binintersectER = $true) & (emptyset__Cong = $true) & (exuE3u = $true) & (demorgan1a = $true) & (powersetTE1 = $true) & (dpsetconstrERa = $true) & (funcext = $true) & (dsetconstr__Cong = $true) & (notdexE = $true) & (setminusLsub = $true) & (singletonprop = $true) & (subPowSU = $true) & (infuncsetfunc = $true) & (brelnall1 = $true) & (wellorderingAx = $true) & (notdallE = $true) & (powersetTI1 = $true) & (complementTI1 = $true) & (demorgan2a1 = $true) & (setunionE = $true) & (ordinalTransSet1 = $true) & (subsetemptysetimpeq = $true) & (setukpairIR = $true) & (subsetTrans = $true) & (intersectInPowersetIntersectUnions = $true) & (binintersectSubset5 = $true) & (setukpairinjR = $true) & (exuI3 = $true) & (setunionI = $true) & (subsetTI = $true) & (ap2p = $true) & (ksndsingleton = $true) & (setukpairinjR11 = $true) & (eqbreln = $true) & (dsetconstrI = $true) & (image1Ex = $true) & (ap2apEq2 = $true) & (subsetRefl = $true) & (prop2setI = $true) & (subset2powerset = $true) & (contrasubsetT1 = $true) & (woz2B = $true) & (binintersectTELcontra = $true) & (upairinpowunion = $true) & (setextT = $true) & (leftInvIsSurj = $true) & (ordinalMinLem1 = $true) & (subsetE2 = $true) & (setminusER = $true) & (symdiffIneg2 = $true) & (setunionsingleton1 = $true) & (powersetI1 = $true) & (lamProp = $true) & (woz1_4 = $true) & (demorgan1b = $true) & (contraSubsetComplement = $true) & (brelnall2 = $true) & (funcGraphProp2 = $true) & (binunionIR = $true) & (setadjoinAx = $true) & (breln1compI = $true) & (upairequniteq = $true) & (notinself2 = $true) & (setminusSubset1 = $true) & (emptysetE = $true) & (noeltsimpempty = $true) & (prop2setE = $true) & (powersetE1 = $true) & (beta1 = $true) & (binintersectT_lem = $true) & (bs114d = $true) & (emptyE1 = $true) & (doubleComplementEq = $true) & (prop2set2propI = $true) & (setadjoinIL = $true) & (breln1all1 = $true) & (descrp = $true) & (binintTransitive = $true) & (dsetconstrEL = $true) & (inIntersectImpInUnion2 = $true) & (surjFuncSetFuncIn = $true) & (quantDeMorgan4 = $true) & (cartprodmempair1 = $true) & (inIntersectImpInIntersectUnions = $true) & (setOfPairsIsBReln = $true) & (setukpairinjR2 = $true) & (complementSubsetComplementIntersect = $true) & (setunionsingleton = $true) & (demorgan2 = $true) & (contrasubsetT3 = $true) & (breln1invI = $true) & (woz13rule3 = $true) & (woz2A = $true) & (demorgan2a = $true) & (binintersectSubset4 = $true) & (breln1invprop = $true) & (omegaIndAx = $true) & (woz1_2 = $true) & (setunionAx = $true) & (upairset2E = $true) & (cartprodpairmemER = $true) & (funcinfuncset = $true) & (lam2lamEq = $true) & (binunionTILcontra = $true) & (binunionTEcontra = $true) & (setukpairIL = $true) & (emptyinPowerset = $true) & (dpsetconstrEL2 = $true) & (woz13rule1 = $true) & (setadjoinSub2 = $true) & (setext = $true) & (woz1_3 = $true) & (complementT_lem = $true)),
% 15.74/3.62 inference(skolemisation,[status(esa),new_symbols(skolem,[sK70])],[f1270,f1594])).
% 15.74/3.62 thf(f1594,plain,(
% 15.74/3.62 ? [X0 : $i] : (((transitiveset @ (setunion @ X0)) != $true) & ! [X1 : $i] : (((ordinal @ X1) = $true) | ((in @ X1 @ X0) != $true))) => (((transitiveset @ (setunion @ sK70)) != $true) & ! [X1 : $i] : (((ordinal @ X1) = $true) | ((in @ X1 @ sK70) != $true)))),
% 15.74/3.62 introduced(definition,[],[choice_axiom])).
% 15.74/3.62 thf(f1270,plain,(
% 15.74/3.62 (setukpairinjR1 = $true) & (funcImageSingleton = $true) & (eta2 = $true) & (breln1unionEcases = $true) & (foundation2 = $true) & (doubleComplementSub1 = $true) & (setukpairinjR12 = $true) & (setadjoinIR = $true) & (breln1unionprop = $true) & (breln1all2 = $true) & (complementTE1 = $true) & (binintersectSubset1 = $true) & (eqimpsubset2 = $true) & (inCongP = $true) & (emptyI = $true) & (surjCantorThm = $true) & (disjointsetsI1 = $true) & (dsetconstrER = $true) & (symdiffIneg1 = $true) & (ifp = $true) & (singletoninpowunion = $true) & (doubleComplementSub2 = $true) & (woz1_5 = $true) & (quantDeMorgan3 = $true) & (setminusELneg = $true) & (ex1I = $true) & (cartprodsndin = $true) & (lamp = $true) & (setunion__Cong = $true) & (funcGraphProp4 = $true) & (eqbreln1 = $true) & (exuE2 = $true) & (image1I = $true) & (setunionsingleton2 = $true) & (demorgan2b = $true) & (breln1compprop = $true) & (app = $true) & (subbreln = $true) & (peano0notS = $true) & (iffalseProp2 = $true) & (eta1 = $true) & (ubforcartprodlem1 = $true) & (breln1unionIR = $true) & (doubleComplementI1 = $true) & (breln1SetBreln1 = $true) & (emptysetAx = $true) & (dpsetconstrEL1 = $true) & (omega0Ax = $true) & (emptyInPowerset = $true) & (ex1I2 = $true) & (complementTnotintersectT = $true) & (emptysetimpfalse = $true) & (binintersectRsub = $true) & (binunionEcases = $true) & (setOfPairsIsBReln1 = $true) & (ifSingleton = $true) & (setminusERneg = $true) & (singletonsubset = $true) & (subsetI1 = $true) & (woz2Ex = $true) & (powerset__Cong = $true) & (complementTcontraSubset = $true) & (demorgan2b2 = $true) & (lam2p = $true) & (woz1_1 = $true) & (symdiffE = $true) & (binintersectEL = $true) & (secondinupair = $true) & (subsetI2 = $true) & (emptysetsubset = $true) & (contrasubsetT = $true) & (injFuncSetFuncIn = $true) & (setunionTransitive = $true) & (symdiffI2 = $true) & (setukpairinjL2 = $true) & (binintersectI = $true) & (iftrueProp2 = $true) & (image1Equiv = $true) & (symdiffI1 = $true) & (notinsingleton = $true) & (subbreln1 = $true) & (exuI2 = $true) & (setoftrueEq = $true) & (funcGraphProp1 = $true) & (setminusT_lem = $true) & (binintersectTERcontra = $true) & (exuE1 = $true) & (beta2 = $true) & (iftrueProp1 = $true) & (iffalseProp1 = $true) & (subsetE = $true) & (setminusILneg = $true) & (emptyinunitempty = $true) & (kfstsingleton = $true) & (quantDeMorgan2 = $true) & (image1E = $true) & (setukpairinjL = $true) & (ordinalTransSet = $true) & (vacuousDall = $true) & (ksndpairEq = $true) & (ex1E2 = $true) & (demorgan2a2 = $true) & (powersetT_lem = $true) & (demorgan1 = $true) & (woz13rule2 = $true) & (cartprodfstpairEq = $true) & (omegaSclos = $true) & (iffalse = $true) & (setbeta = $true) & (breln1unionCommutes = $true) & (binintersectSubset3 = $true) & (singletonsuniq = $true) & (cartprodsndpairEq = $true) & (replAx = $true) & (cartprodpairmemEL = $true) & (ap2apEq1 = $true) & (surjFuncSetFuncSurj = $true) & (setminusIRneg = $true) & (doubleComplementE1 = $true) & (theeq = $true) & (exuEu = $true) & (breln1unionI = $true) & (setadjoinE = $true) & (woz13rule0 = $true) & (choice2fnsingleton = $true) & (complementImpComplementIntersect = $true) & (setminusSubset2 = $true) & (contrasubsetT2 = $true) & (nonemptyI = $true) & (breln1unionIL = $true) & (notinemptyset = $true) & (in__Cong = $true) & (breln1compE = $true) & (eqimpsubset1 = $true) & (inIntersectImpInUnion = $true) & (powersetAx = $true) & (powersetE = $true) & (powersetsubset = $true) & (binunionE = $true) & (notinself = $true) & (omega__Cong = $true) & (notequalI2 = $true) & (eqinunit = $true) & (setadjoinOr = $true) & (funcextLem = $true) & (funcext2 = $true) & (apProp = $true) & (setextsub = $true) & (notequalI1 = $true) & (setunionE2 = $true) & (complementInPowersetComplementIntersect = $true) & (inComplementUnionImpInComplement1 = $true) & (descr__Cong = $true) & (upairsetIR = $true) & (singletonsswitch = $true) & (woz13rule4 = $true) & ? [X0 : $i] : (((transitiveset @ (setunion @ X0)) != $true) & ! [X1 : $i] : (((ordinal @ X1) = $true) | ((in @ X1 @ X0) != $true))) & (inComplementUnionImpNotIn1 = $true) & (dpsetconstrER = $true) & (upairsetIL = $true) & (ubforcartprodlem2 = $true) & (uniqinunit = $true) & (binunionLsub = $true) & (cartprodmempaircEq = $true) & (setextAx = $true) & (cartprodpairin = $true) & (cartprodmempair = $true) & (exuI1 = $true) & (setminusI = $true) & (theprop = $true) & (sepInPowerset = $true) & (nonemptyE1 = $true) & (injFuncSetFuncInj = $true) & (transitivesetOp1 = $true) & (dpsetconstrI = $true) & (foundationAx = $true) & (binintersectSubset2 = $true) & (breln1compEex = $true) & (upairset2IR = $true) & (image1Ex1 = $true) & (peanoSinj = $true) & (inPowerset = $true) & (powersetI = $true) & (singletoninpowerset = $true) & (breln1unionE = $true) & (quantDeMorgan1 = $true) & (binunionT_lem = $true) & (breln1invE = $true) & (setadjoin__Cong = $true) & (upairsubunion = $true) & (iftrueorfalse = $true) & (sepSubset = $true) & (nonemptyImpWitness = $true) & (exuE3e = $true) & (kpairp = $true) & (upairsetE = $true) & (dpsetconstrSub = $true) & (binunionTIRcontra = $true) & (binunionIL = $true) & (omegaSAx = $true) & (ex1E1 = $true) & (binunionRsub = $true) & (transitivesetOp2 = $true) & (iftrue = $true) & (ubforcartprodlem3 = $true) & (nonemptyI1 = $true) & (binunionTE = $true) & (cartprodpairsurjEq = $true) & (complementUnionInPowersetComplement = $true) & (setukpairinjL1 = $true) & (kfstpairEq = $true) & (notsubsetI = $true) & (woz2W = $true) & (omegaSp = $true) & (kpairiskpair = $true) & (kpairsurjEq = $true) & (setminusEL = $true) & (exu__Cong = $true) & (funcGraphProp3 = $true) & (setadjoinSub = $true) & (cartprodfstin = $true) & (binintersectLsub = $true) & (injFuncInInjFuncSet = $true) & (binintersectER = $true) & (emptyset__Cong = $true) & (exuE3u = $true) & (demorgan1a = $true) & (powersetTE1 = $true) & (dpsetconstrERa = $true) & (funcext = $true) & (dsetconstr__Cong = $true) & (notdexE = $true) & (setminusLsub = $true) & (singletonprop = $true) & (subPowSU = $true) & (infuncsetfunc = $true) & (brelnall1 = $true) & (wellorderingAx = $true) & (notdallE = $true) & (powersetTI1 = $true) & (complementTI1 = $true) & (demorgan2a1 = $true) & (setunionE = $true) & (ordinalTransSet1 = $true) & (subsetemptysetimpeq = $true) & (setukpairIR = $true) & (subsetTrans = $true) & (intersectInPowersetIntersectUnions = $true) & (binintersectSubset5 = $true) & (setukpairinjR = $true) & (exuI3 = $true) & (setunionI = $true) & (subsetTI = $true) & (ap2p = $true) & (ksndsingleton = $true) & (setukpairinjR11 = $true) & (eqbreln = $true) & (dsetconstrI = $true) & (image1Ex = $true) & (ap2apEq2 = $true) & (subsetRefl = $true) & (prop2setI = $true) & (subset2powerset = $true) & (contrasubsetT1 = $true) & (woz2B = $true) & (binintersectTELcontra = $true) & (upairinpowunion = $true) & (setextT = $true) & (leftInvIsSurj = $true) & (ordinalMinLem1 = $true) & (subsetE2 = $true) & (setminusER = $true) & (symdiffIneg2 = $true) & (setunionsingleton1 = $true) & (powersetI1 = $true) & (lamProp = $true) & (woz1_4 = $true) & (demorgan1b = $true) & (contraSubsetComplement = $true) & (brelnall2 = $true) & (funcGraphProp2 = $true) & (binunionIR = $true) & (setadjoinAx = $true) & (breln1compI = $true) & (upairequniteq = $true) & (notinself2 = $true) & (setminusSubset1 = $true) & (emptysetE = $true) & (noeltsimpempty = $true) & (prop2setE = $true) & (powersetE1 = $true) & (beta1 = $true) & (binintersectT_lem = $true) & (bs114d = $true) & (emptyE1 = $true) & (doubleComplementEq = $true) & (prop2set2propI = $true) & (setadjoinIL = $true) & (breln1all1 = $true) & (descrp = $true) & (binintTransitive = $true) & (dsetconstrEL = $true) & (inIntersectImpInUnion2 = $true) & (surjFuncSetFuncIn = $true) & (quantDeMorgan4 = $true) & (cartprodmempair1 = $true) & (inIntersectImpInIntersectUnions = $true) & (setOfPairsIsBReln = $true) & (setukpairinjR2 = $true) & (complementSubsetComplementIntersect = $true) & (setunionsingleton = $true) & (demorgan2 = $true) & (contrasubsetT3 = $true) & (breln1invI = $true) & (woz13rule3 = $true) & (woz2A = $true) & (demorgan2a = $true) & (binintersectSubset4 = $true) & (breln1invprop = $true) & (omegaIndAx = $true) & (woz1_2 = $true) & (setunionAx = $true) & (upairset2E = $true) & (cartprodpairmemER = $true) & (funcinfuncset = $true) & (lam2lamEq = $true) & (binunionTILcontra = $true) & (binunionTEcontra = $true) & (setukpairIL = $true) & (emptyinPowerset = $true) & (dpsetconstrEL2 = $true) & (woz13rule1 = $true) & (setadjoinSub2 = $true) & (setext = $true) & (woz1_3 = $true) & (complementT_lem = $true)),
% 15.74/3.62 inference(flattening,[status(thm)],[f1269])).
% 15.74/3.62 thf(f1269,plain,(
% 15.74/3.62 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i] : (((transitiveset @ (setunion @ X0)) != $true) & ! [X1 : $i] : (((ordinal @ X1) = $true) | ((in @ X1 @ X0) != $true))) & (ordinalTransSet1 = $true)) & (ordinalTransSet = $true)) & (ordinalMinLem1 = $true)) & (setunionTransitive = $true)) & (transitivesetOp2 = $true)) & (binintTransitive = $true)) & (transitivesetOp1 = $true)) & (peanoSinj = $true)) & (peano0notS = $true)) & (omegaSclos = $true)) & (omegaSp = $true)) & (notinself2 = $true)) & (notinself = $true)) & (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)),
% 15.74/3.62 inference(ennf_transformation,[status(thm)],[f665])).
% 15.74/3.62 thf(f665,plain,(
% 15.74/3.62 ~((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) => ((notinself = $true) => ((notinself2 = $true) => ((omegaSp = $true) => ((omegaSclos = $true) => ((peano0notS = $true) => ((peanoSinj = $true) => ((transitivesetOp1 = $true) => ((binintTransitive = $true) => ((transitivesetOp2 = $true) => ((setunionTransitive = $true) => ((ordinalMinLem1 = $true) => ((ordinalTransSet = $true) => ((ordinalTransSet1 = $true) => ! [X0 : $i] : (! [X1 : $i] : (((in @ X1 @ X0) = $true) => ((ordinal @ X1) = $true)) => ((transitiveset @ (setunion @ X0)) = $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 15.74/3.62 inference(fool_elimination,[status(thm)],[f664])).
% 15.74/3.62 thf(f664,plain,(
% 15.74/3.62 ~(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 => (notinself => (notinself2 => (omegaSp => (omegaSclos => (peano0notS => (peanoSinj => (transitivesetOp1 => (binintTransitive => (transitivesetOp2 => (setunionTransitive => (ordinalMinLem1 => (ordinalTransSet => (ordinalTransSet1 => ! [X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (ordinal @ X1)) => (transitiveset @ (setunion @ X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 15.74/3.62 inference(rectify,[status(thm)],[f343])).
% 15.74/3.62 thf(f343,negated_conjecture,(
% 15.74/3.62 ~(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 => (notinself => (notinself2 => (omegaSp => (omegaSclos => (peano0notS => (peanoSinj => (transitivesetOp1 => (binintTransitive => (transitivesetOp2 => (setunionTransitive => (ordinalMinLem1 => (ordinalTransSet => (ordinalTransSet1 => ! [X11 : $i] : (! [X1 : $i] : ((in @ X1 @ X11) => (ordinal @ X1)) => (transitiveset @ (setunion @ X11))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 15.74/3.62 inference(negated_conjecture,[status(cth)],[f342])).
% 15.74/3.62 thf(f342,conjecture,(
% 15.74/3.62 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 => (notinself => (notinself2 => (omegaSp => (omegaSclos => (peano0notS => (peanoSinj => (transitivesetOp1 => (binintTransitive => (transitivesetOp2 => (setunionTransitive => (ordinalMinLem1 => (ordinalTransSet => (ordinalTransSet1 => ! [X11 : $i] : (! [X1 : $i] : ((in @ X1 @ X11) => (ordinal @ X1)) => (transitiveset @ (setunion @ X11)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 15.74/3.62 file('/export/starexec/sandbox/tmp/tmp.d0DxC7kphv/DTF2THF_20722.p',setunionOrdinalLem1)).
% 15.74/3.62 thf(f15601,plain,(
% 15.74/3.62 ((transitiveset @ (setunion @ sK70)) = $true) | (~spl1111_498 | ~spl1111_539 | ~spl1111_1166 | ~spl1111_1645 | ~spl1111_1674)),
% 15.74/3.62 inference(trivial_inequality_removal,[status(thm)],[f15597])).
% 15.74/3.62 thf(f15597,plain,(
% 15.74/3.62 ($true != $true) | ((transitiveset @ (setunion @ sK70)) = $true) | (~spl1111_498 | ~spl1111_539 | ~spl1111_1166 | ~spl1111_1645 | ~spl1111_1674)),
% 15.74/3.62 inference(superposition,[status(thm)],[f10662,f15546])).
% 15.74/3.62 thf(f15546,plain,(
% 15.74/3.62 ((transitiveset @ (sK81 @ sK70)) = $true) | (~spl1111_498 | ~spl1111_539 | ~spl1111_1645 | ~spl1111_1674)),
% 15.74/3.62 inference(forward_demodulation,[status(thm)],[f15545,f14001])).
% 15.74/3.62 thf(f14001,plain,(
% 15.74/3.62 ( ! [X0 : $i] : (((binintersect @ X0 @ X0) = X0)) ) | (~spl1111_498 | ~spl1111_539)),
% 15.74/3.62 inference(trivial_inequality_removal,[status(thm)],[f13984])).
% 15.74/3.62 thf(f13984,plain,(
% 15.74/3.62 ( ! [X0 : $i] : (($true != $true) | ((binintersect @ X0 @ X0) = X0)) ) | (~spl1111_498 | ~spl1111_539)),
% 15.74/3.62 inference(superposition,[status(thm)],[f7514,f7701])).
% 15.74/3.62 thf(f7701,plain,(
% 15.74/3.62 ( ! [X0 : $i] : (((subset @ X0 @ X0) = $true)) ) | ~spl1111_539),
% 15.74/3.62 inference(avatar_component_clause,[status(thm)],[f7700])).
% 15.74/3.62 thf(f7700,definition,(
% 15.74/3.62 spl1111_539 <=> ! [X0 : $i] : ((subset @ X0 @ X0) = $true)),
% 15.74/3.62 introduced(definition,[new_symbols(naming,[spl1111_539])],[avatar_definition])).
% 15.74/3.62 thf(f7514,plain,(
% 15.74/3.62 ( ! [X2 : $i,X3 : $i] : (((subset @ X2 @ X3) != $true) | ((binintersect @ X3 @ X2) = X2)) ) | ~spl1111_498),
% 15.74/3.62 inference(avatar_component_clause,[status(thm)],[f7513])).
% 15.74/3.62 thf(f7513,definition,(
% 15.74/3.62 spl1111_498 <=> ! [X2 : $i,X3 : $i] : (((subset @ X2 @ X3) != $true) | ((binintersect @ X3 @ X2) = X2))),
% 15.74/3.62 introduced(definition,[new_symbols(naming,[spl1111_498])],[avatar_definition])).
% 15.74/3.62 thf(f15545,plain,(
% 15.74/3.62 ((transitiveset @ (binintersect @ (sK81 @ sK70) @ (sK81 @ sK70))) = $true) | (~spl1111_1645 | ~spl1111_1674)),
% 15.74/3.62 inference(trivial_inequality_removal,[status(thm)],[f15536])).
% 15.74/3.62 thf(f15536,plain,(
% 15.74/3.62 ((transitiveset @ (binintersect @ (sK81 @ sK70) @ (sK81 @ sK70))) = $true) | ($true != $true) | (~spl1111_1645 | ~spl1111_1674)),
% 15.74/3.62 inference(superposition,[status(thm)],[f15214,f14351])).
% 15.74/3.62 thf(f14351,plain,(
% 15.74/3.62 ((ordinal @ (sK81 @ sK70)) = $true) | ~spl1111_1645),
% 15.74/3.62 inference(subsumption_resolution,[status(thm)],[f14347,f3476])).
% 15.74/3.62 thf(f14347,plain,(
% 15.74/3.62 ((ordinal @ (sK81 @ sK70)) = $true) | ((transitiveset @ (setunion @ sK70)) = $true) | ~spl1111_1645),
% 15.74/3.62 inference(trivial_inequality_removal,[status(thm)],[f14345])).
% 15.74/3.62 thf(f14345,plain,(
% 15.74/3.62 ($true != $true) | ((ordinal @ (sK81 @ sK70)) = $true) | ((transitiveset @ (setunion @ sK70)) = $true) | ~spl1111_1645),
% 15.74/3.62 inference(superposition,[status(thm)],[f3475,f13001])).
% 15.74/3.62 thf(f13001,plain,(
% 15.74/3.62 ( ! [X2 : $i] : (((in @ (sK81 @ X2) @ X2) = $true) | ((transitiveset @ (setunion @ X2)) = $true)) ) | ~spl1111_1645),
% 15.74/3.62 inference(avatar_component_clause,[status(thm)],[f13000])).
% 15.74/3.62 thf(f13000,definition,(
% 15.74/3.62 spl1111_1645 <=> ! [X2 : $i] : (((transitiveset @ (setunion @ X2)) = $true) | ((in @ (sK81 @ X2) @ X2) = $true))),
% 15.74/3.62 introduced(definition,[new_symbols(naming,[spl1111_1645])],[avatar_definition])).
% 15.74/3.62 thf(f3475,plain,(
% 15.74/3.62 ( ! [X1 : $i] : (((in @ X1 @ sK70) != $true) | ((ordinal @ X1) = $true)) )),
% 15.74/3.62 inference(cnf_transformation,[status(thm)],[f1595])).
% 15.74/3.62 thf(f15214,plain,(
% 15.74/3.62 ( ! [X0 : $i] : (((ordinal @ X0) != $true) | ((transitiveset @ (binintersect @ X0 @ (sK81 @ sK70))) = $true)) ) | (~spl1111_1645 | ~spl1111_1674)),
% 15.74/3.62 inference(trivial_inequality_removal,[status(thm)],[f15209])).
% 15.74/3.62 thf(f15209,plain,(
% 15.74/3.62 ( ! [X0 : $i] : (((ordinal @ X0) != $true) | ((transitiveset @ (binintersect @ X0 @ (sK81 @ sK70))) = $true) | ($true != $true)) ) | (~spl1111_1645 | ~spl1111_1674)),
% 15.74/3.62 inference(superposition,[status(thm)],[f13145,f14351])).
% 15.74/3.62 thf(f13145,plain,(
% 15.74/3.62 ( ! [X0 : $i,X1 : $i] : (((ordinal @ X1) != $true) | ((transitiveset @ (binintersect @ X0 @ X1)) = $true) | ((ordinal @ X0) != $true)) ) | ~spl1111_1674),
% 15.74/3.62 inference(avatar_component_clause,[status(thm)],[f13144])).
% 15.74/3.62 thf(f13144,definition,(
% 15.74/3.62 spl1111_1674 <=> ! [X0 : $i,X1 : $i] : (((transitiveset @ (binintersect @ X0 @ X1)) = $true) | ((ordinal @ X1) != $true) | ((ordinal @ X0) != $true))),
% 15.74/3.62 introduced(definition,[new_symbols(naming,[spl1111_1674])],[avatar_definition])).
% 15.74/3.62 thf(f10662,plain,(
% 15.74/3.62 ( ! [X2 : $i] : (((transitiveset @ (sK81 @ X2)) != $true) | ((transitiveset @ (setunion @ X2)) = $true)) ) | ~spl1111_1166),
% 15.74/3.62 inference(avatar_component_clause,[status(thm)],[f10661])).
% 15.74/3.62 thf(f10661,definition,(
% 15.74/3.62 spl1111_1166 <=> ! [X2 : $i] : (((transitiveset @ (sK81 @ X2)) != $true) | ((transitiveset @ (setunion @ X2)) = $true))),
% 15.74/3.62 introduced(definition,[new_symbols(naming,[spl1111_1166])],[avatar_definition])).
% 15.74/3.62 thf(f13589,plain,(
% 15.74/3.62 spl1111_731),
% 15.74/3.62 inference(avatar_split_clause,[status(thm)],[f3560,f8574])).
% 15.74/3.62 thf(f8574,definition,(
% 15.74/3.62 spl1111_731 <=> (setunionTransitive = $true)),
% 15.74/3.62 introduced(definition,[new_symbols(naming,[spl1111_731])],[avatar_definition])).
% 15.74/3.62 thf(f3560,plain,(
% 15.74/3.62 (setunionTransitive = $true)),
% 15.74/3.62 inference(cnf_transformation,[status(thm)],[f1595])).
% 15.74/3.62 thf(f13569,plain,(
% 15.74/3.62 spl1111_857),
% 15.74/3.62 inference(avatar_split_clause,[status(thm)],[f3499,f9170])).
% 15.74/3.62 thf(f9170,definition,(
% 15.74/3.62 spl1111_857 <=> (eqimpsubset1 = $true)),
% 15.74/3.62 introduced(definition,[new_symbols(naming,[spl1111_857])],[avatar_definition])).
% 15.74/3.62 thf(f3499,plain,(
% 15.74/3.62 (eqimpsubset1 = $true)),
% 15.74/3.62 inference(cnf_transformation,[status(thm)],[f1595])).
% 15.74/3.62 thf(f13146,plain,(
% 15.74/3.62 ~spl1111_495 | spl1111_1674),
% 15.74/3.62 inference(avatar_split_clause,[status(thm)],[f3270,f13144,f7497])).
% 15.74/3.62 thf(f7497,definition,(
% 15.74/3.62 spl1111_495 <=> (ordinalMinLem1 = $true)),
% 15.74/3.62 introduced(definition,[new_symbols(naming,[spl1111_495])],[avatar_definition])).
% 15.74/3.62 thf(f3270,plain,(
% 15.74/3.62 ( ! [X0 : $i,X1 : $i] : (((transitiveset @ (binintersect @ X0 @ X1)) = $true) | (ordinalMinLem1 != $true) | ((ordinal @ X0) != $true) | ((ordinal @ X1) != $true)) )),
% 15.74/3.62 inference(cnf_transformation,[status(thm)],[f1575])).
% 15.74/3.62 thf(f1575,plain,(
% 15.74/3.62 (! [X0 : $i] : (((ordinal @ X0) != $true) | ! [X1 : $i] : (((transitiveset @ (binintersect @ X0 @ X1)) = $true) | ((ordinal @ X1) != $true))) | (ordinalMinLem1 != $true)) & ((ordinalMinLem1 = $true) | (((ordinal @ sK56) = $true) & (((transitiveset @ (binintersect @ sK56 @ sK57)) != $true) & ((ordinal @ sK57) = $true))))),
% 15.74/3.62 inference(skolemisation,[status(esa),new_symbols(skolem,[sK56,sK57])],[f1572,f1574,f1573])).
% 15.74/3.62 thf(f1573,plain,(
% 15.74/3.62 ? [X2 : $i] : (((ordinal @ X2) = $true) & ? [X3 : $i] : (((transitiveset @ (binintersect @ X2 @ X3)) != $true) & ((ordinal @ X3) = $true))) => (((ordinal @ sK56) = $true) & ? [X3 : $i] : (((transitiveset @ (binintersect @ sK56 @ X3)) != $true) & ((ordinal @ X3) = $true)))),
% 15.74/3.62 introduced(definition,[],[choice_axiom])).
% 15.74/3.62 thf(f1574,plain,(
% 15.74/3.62 ? [X3 : $i] : (((transitiveset @ (binintersect @ sK56 @ X3)) != $true) & ((ordinal @ X3) = $true)) => (((transitiveset @ (binintersect @ sK56 @ sK57)) != $true) & ((ordinal @ sK57) = $true))),
% 15.74/3.62 introduced(definition,[],[choice_axiom])).
% 15.74/3.62 thf(f1572,plain,(
% 15.74/3.62 (! [X0 : $i] : (((ordinal @ X0) != $true) | ! [X1 : $i] : (((transitiveset @ (binintersect @ X0 @ X1)) = $true) | ((ordinal @ X1) != $true))) | (ordinalMinLem1 != $true)) & ((ordinalMinLem1 = $true) | ? [X2 : $i] : (((ordinal @ X2) = $true) & ? [X3 : $i] : (((transitiveset @ (binintersect @ X2 @ X3)) != $true) & ((ordinal @ X3) = $true))))),
% 15.74/3.62 inference(rectify,[status(thm)],[f1571])).
% 15.74/3.62 thf(f1571,plain,(
% 15.74/3.62 (! [X0 : $i] : (((ordinal @ X0) != $true) | ! [X1 : $i] : (((transitiveset @ (binintersect @ X0 @ X1)) = $true) | ((ordinal @ X1) != $true))) | (ordinalMinLem1 != $true)) & ((ordinalMinLem1 = $true) | ? [X0 : $i] : (((ordinal @ X0) = $true) & ? [X1 : $i] : (((transitiveset @ (binintersect @ X0 @ X1)) != $true) & ((ordinal @ X1) = $true))))),
% 15.74/3.62 inference(nnf_transformation,[status(thm)],[f1427])).
% 15.74/3.62 thf(f1427,plain,(
% 15.74/3.62 ! [X0 : $i] : (((ordinal @ X0) != $true) | ! [X1 : $i] : (((transitiveset @ (binintersect @ X0 @ X1)) = $true) | ((ordinal @ X1) != $true))) <=> (ordinalMinLem1 = $true)),
% 15.74/3.62 inference(ennf_transformation,[status(thm)],[f976])).
% 15.74/3.62 thf(f976,plain,(
% 15.74/3.62 (ordinalMinLem1 = $true) <=> ! [X0 : $i] : (((ordinal @ X0) = $true) => ! [X1 : $i] : (((ordinal @ X1) = $true) => ((transitiveset @ (binintersect @ X0 @ X1)) = $true)))),
% 15.74/3.62 inference(fool_elimination,[status(thm)],[f975])).
% 15.74/3.62 thf(f975,plain,(
% 15.74/3.62 (ordinalMinLem1 = ! [X0 : $i] : ((ordinal @ X0) => ! [X1 : $i] : ((ordinal @ X1) => (transitiveset @ (binintersect @ X0 @ X1)))))),
% 15.74/3.62 inference(rectify,[status(thm)],[f339])).
% 15.74/3.62 thf(f339,axiom,(
% 15.74/3.62 (ordinalMinLem1 = ! [X11 : $i] : ((ordinal @ X11) => ! [X16 : $i] : ((ordinal @ X16) => (transitiveset @ (binintersect @ X11 @ X16)))))),
% 15.74/3.62 file('/export/starexec/sandbox/tmp/tmp.d0DxC7kphv/DTF2THF_20722.p',ordinalMinLem1)).
% 15.74/3.62 thf(f13137,plain,(
% 15.74/3.62 spl1111_539 | ~spl1111_857),
% 15.74/3.62 inference(avatar_split_clause,[status(thm)],[f5102,f9170,f7700])).
% 15.74/3.62 thf(f5102,plain,(
% 15.74/3.62 ( ! [X1 : $i] : ((eqimpsubset1 != $true) | ((subset @ X1 @ X1) = $true)) )),
% 15.74/3.62 inference(equality_resolution,[status(thm)],[f4480])).
% 15.74/3.62 thf(f4480,plain,(
% 15.74/3.62 ( ! [X0 : $i,X1 : $i] : ((X0 != X1) | ((subset @ X1 @ X0) = $true) | (eqimpsubset1 != $true)) )),
% 15.74/3.62 inference(cnf_transformation,[status(thm)],[f2548])).
% 15.74/3.62 thf(f2548,plain,(
% 15.74/3.62 (! [X0 : $i,X1 : $i] : ((X0 != X1) | ((subset @ X1 @ X0) = $true)) | (eqimpsubset1 != $true)) & ((eqimpsubset1 = $true) | ((sK667 = sK666) & ((subset @ sK667 @ sK666) != $true)))),
% 15.74/3.62 inference(skolemisation,[status(esa),new_symbols(skolem,[sK666,sK667])],[f2546,f2547])).
% 15.74/3.62 thf(f2547,plain,(
% 15.74/3.62 ? [X2 : $i,X3 : $i] : ((X2 = X3) & ((subset @ X3 @ X2) != $true)) => ((sK667 = sK666) & ((subset @ sK667 @ sK666) != $true))),
% 15.74/3.62 introduced(definition,[],[choice_axiom])).
% 15.74/3.62 thf(f2546,plain,(
% 15.74/3.62 (! [X0 : $i,X1 : $i] : ((X0 != X1) | ((subset @ X1 @ X0) = $true)) | (eqimpsubset1 != $true)) & ((eqimpsubset1 = $true) | ? [X2 : $i,X3 : $i] : ((X2 = X3) & ((subset @ X3 @ X2) != $true)))),
% 15.74/3.62 inference(rectify,[status(thm)],[f2545])).
% 15.74/3.62 thf(f2545,plain,(
% 15.74/3.62 (! [X0 : $i,X1 : $i] : ((X0 != X1) | ((subset @ X1 @ X0) = $true)) | (eqimpsubset1 != $true)) & ((eqimpsubset1 = $true) | ? [X0 : $i,X1 : $i] : ((X0 = X1) & ((subset @ X1 @ X0) != $true)))),
% 15.74/3.62 inference(nnf_transformation,[status(thm)],[f1358])).
% 15.74/3.62 thf(f1358,plain,(
% 15.74/3.62 ! [X0 : $i,X1 : $i] : ((X0 != X1) | ((subset @ X1 @ X0) = $true)) <=> (eqimpsubset1 = $true)),
% 15.74/3.62 inference(ennf_transformation,[status(thm)],[f370])).
% 15.74/3.62 thf(f370,plain,(
% 15.74/3.62 ! [X0 : $i,X1 : $i] : ((X0 = X1) => ((subset @ X1 @ X0) = $true)) <=> (eqimpsubset1 = $true)),
% 15.74/3.62 inference(fool_elimination,[status(thm)],[f369])).
% 15.74/3.62 thf(f369,plain,(
% 15.74/3.62 (eqimpsubset1 = ! [X0 : $i,X1 : $i] : ((X0 = X1) => (subset @ X1 @ X0)))),
% 15.74/3.62 inference(rectify,[status(thm)],[f80])).
% 15.74/3.62 thf(f80,axiom,(
% 15.74/3.62 (eqimpsubset1 = ! [X4 : $i,X3 : $i] : ((X3 = X4) => (subset @ X3 @ X4)))),
% 15.74/3.62 file('/export/starexec/sandbox/tmp/tmp.d0DxC7kphv/DTF2THF_20722.p',eqimpsubset1)).
% 15.74/3.62 thf(f13002,plain,(
% 15.74/3.62 ~spl1111_731 | spl1111_1645),
% 15.74/3.62 inference(avatar_split_clause,[status(thm)],[f3648,f13000,f8574])).
% 15.74/3.62 thf(f3648,plain,(
% 15.74/3.62 ( ! [X2 : $i] : ((setunionTransitive != $true) | ((transitiveset @ (setunion @ X2)) = $true) | ((in @ (sK81 @ X2) @ X2) = $true)) )),
% 15.74/3.62 inference(cnf_transformation,[status(thm)],[f1619])).
% 15.74/3.62 thf(f1619,plain,(
% 15.74/3.62 ((setunionTransitive = $true) | (! [X1 : $i] : (((transitiveset @ X1) = $true) | ((in @ X1 @ sK80) != $true)) & ((transitiveset @ (setunion @ sK80)) != $true))) & (! [X2 : $i] : ((((transitiveset @ (sK81 @ X2)) != $true) & ((in @ (sK81 @ X2) @ X2) = $true)) | ((transitiveset @ (setunion @ X2)) = $true)) | (setunionTransitive != $true))),
% 15.74/3.62 inference(skolemisation,[status(esa),new_symbols(skolem,[sK80,sK81])],[f1616,f1618,f1617])).
% 15.74/3.62 thf(f1617,plain,(
% 15.74/3.62 ? [X0 : $i] : (! [X1 : $i] : (((transitiveset @ X1) = $true) | ((in @ X1 @ X0) != $true)) & ((transitiveset @ (setunion @ X0)) != $true)) => (! [X1 : $i] : (((transitiveset @ X1) = $true) | ((in @ X1 @ sK80) != $true)) & ((transitiveset @ (setunion @ sK80)) != $true))),
% 15.74/3.62 introduced(definition,[],[choice_axiom])).
% 15.74/3.62 thf(f1618,plain,(
% 15.74/3.62 ! [X2 : $i] : (? [X3 : $i] : (((transitiveset @ X3) != $true) & ((in @ X3 @ X2) = $true)) => (((transitiveset @ (sK81 @ X2)) != $true) & ((in @ (sK81 @ X2) @ X2) = $true)))),
% 15.74/3.62 introduced(definition,[],[choice_axiom])).
% 15.74/3.62 thf(f1616,plain,(
% 15.74/3.62 ((setunionTransitive = $true) | ? [X0 : $i] : (! [X1 : $i] : (((transitiveset @ X1) = $true) | ((in @ X1 @ X0) != $true)) & ((transitiveset @ (setunion @ X0)) != $true))) & (! [X2 : $i] : (? [X3 : $i] : (((transitiveset @ X3) != $true) & ((in @ X3 @ X2) = $true)) | ((transitiveset @ (setunion @ X2)) = $true)) | (setunionTransitive != $true))),
% 15.74/3.62 inference(rectify,[status(thm)],[f1615])).
% 15.74/3.62 thf(f1615,plain,(
% 15.74/3.62 ((setunionTransitive = $true) | ? [X0 : $i] : (! [X1 : $i] : (((transitiveset @ X1) = $true) | ((in @ X1 @ X0) != $true)) & ((transitiveset @ (setunion @ X0)) != $true))) & (! [X0 : $i] : (? [X1 : $i] : (((transitiveset @ X1) != $true) & ((in @ X1 @ X0) = $true)) | ((transitiveset @ (setunion @ X0)) = $true)) | (setunionTransitive != $true))),
% 15.74/3.62 inference(nnf_transformation,[status(thm)],[f1262])).
% 15.74/3.62 thf(f1262,plain,(
% 15.74/3.62 (setunionTransitive = $true) <=> ! [X0 : $i] : (? [X1 : $i] : (((transitiveset @ X1) != $true) & ((in @ X1 @ X0) = $true)) | ((transitiveset @ (setunion @ X0)) = $true))),
% 15.74/3.62 inference(ennf_transformation,[status(thm)],[f627])).
% 15.74/3.62 thf(f627,plain,(
% 15.74/3.62 ! [X0 : $i] : (! [X1 : $i] : (((in @ X1 @ X0) = $true) => ((transitiveset @ X1) = $true)) => ((transitiveset @ (setunion @ X0)) = $true)) <=> (setunionTransitive = $true)),
% 15.74/3.62 inference(fool_elimination,[status(thm)],[f626])).
% 15.74/3.62 thf(f626,plain,(
% 15.74/3.62 (! [X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (transitiveset @ X1)) => (transitiveset @ (setunion @ X0))) = setunionTransitive)),
% 15.74/3.62 inference(rectify,[status(thm)],[f335])).
% 15.74/3.62 thf(f335,axiom,(
% 15.74/3.62 (! [X11 : $i] : (! [X1 : $i] : ((in @ X1 @ X11) => (transitiveset @ X1)) => (transitiveset @ (setunion @ X11))) = setunionTransitive)),
% 15.74/3.62 file('/export/starexec/sandbox/tmp/tmp.d0DxC7kphv/DTF2THF_20722.p',setunionTransitive)).
% 15.74/3.62 thf(f12688,plain,(
% 15.74/3.62 spl1111_495),
% 15.74/3.62 inference(avatar_split_clause,[status(thm)],[f3362,f7497])).
% 15.74/3.62 thf(f3362,plain,(
% 15.74/3.62 (ordinalMinLem1 = $true)),
% 15.74/3.62 inference(cnf_transformation,[status(thm)],[f1595])).
% 15.74/3.62 thf(f11507,plain,(
% 15.74/3.62 spl1111_499),
% 15.74/3.62 inference(avatar_split_clause,[status(thm)],[f3314,f7516])).
% 15.74/3.62 thf(f7516,definition,(
% 15.74/3.62 spl1111_499 <=> (binintersectSubset4 = $true)),
% 15.74/3.62 introduced(definition,[new_symbols(naming,[spl1111_499])],[avatar_definition])).
% 15.74/3.62 thf(f3314,plain,(
% 15.74/3.62 (binintersectSubset4 = $true)),
% 15.74/3.62 inference(cnf_transformation,[status(thm)],[f1595])).
% 15.74/3.62 thf(f10663,plain,(
% 15.74/3.62 spl1111_1166 | ~spl1111_731),
% 15.74/3.62 inference(avatar_split_clause,[status(thm)],[f3649,f8574,f10661])).
% 15.74/3.62 thf(f3649,plain,(
% 15.74/3.62 ( ! [X2 : $i] : ((setunionTransitive != $true) | ((transitiveset @ (sK81 @ X2)) != $true) | ((transitiveset @ (setunion @ X2)) = $true)) )),
% 15.74/3.62 inference(cnf_transformation,[status(thm)],[f1619])).
% 15.74/3.62 thf(f7519,plain,(
% 15.74/3.62 spl1111_498 | ~spl1111_499),
% 15.74/3.62 inference(avatar_split_clause,[status(thm)],[f4735,f7516,f7513])).
% 15.74/3.62 thf(f4735,plain,(
% 15.74/3.62 ( ! [X2 : $i,X3 : $i] : ((binintersectSubset4 != $true) | ((subset @ X2 @ X3) != $true) | ((binintersect @ X3 @ X2) = X2)) )),
% 15.74/3.62 inference(cnf_transformation,[status(thm)],[f2844])).
% 15.74/3.62 thf(f2844,plain,(
% 15.74/3.62 ((binintersectSubset4 = $true) | (((binintersect @ sK864 @ sK863) != sK863) & ((subset @ sK863 @ sK864) = $true))) & (! [X2 : $i,X3 : $i] : (((binintersect @ X3 @ X2) = X2) | ((subset @ X2 @ X3) != $true)) | (binintersectSubset4 != $true))),
% 15.74/3.62 inference(skolemisation,[status(esa),new_symbols(skolem,[sK863,sK864])],[f2842,f2843])).
% 15.74/3.62 thf(f2843,plain,(
% 15.74/3.62 ? [X0 : $i,X1 : $i] : (((binintersect @ X1 @ X0) != X0) & ((subset @ X0 @ X1) = $true)) => (((binintersect @ sK864 @ sK863) != sK863) & ((subset @ sK863 @ sK864) = $true))),
% 15.74/3.62 introduced(definition,[],[choice_axiom])).
% 15.74/3.62 thf(f2842,plain,(
% 15.74/3.62 ((binintersectSubset4 = $true) | ? [X0 : $i,X1 : $i] : (((binintersect @ X1 @ X0) != X0) & ((subset @ X0 @ X1) = $true))) & (! [X2 : $i,X3 : $i] : (((binintersect @ X3 @ X2) = X2) | ((subset @ X2 @ X3) != $true)) | (binintersectSubset4 != $true))),
% 15.74/3.62 inference(rectify,[status(thm)],[f2841])).
% 15.74/3.62 thf(f2841,plain,(
% 15.74/3.62 ((binintersectSubset4 = $true) | ? [X0 : $i,X1 : $i] : (((binintersect @ X1 @ X0) != X0) & ((subset @ X0 @ X1) = $true))) & (! [X0 : $i,X1 : $i] : (((binintersect @ X1 @ X0) = X0) | ((subset @ X0 @ X1) != $true)) | (binintersectSubset4 != $true))),
% 15.74/3.62 inference(nnf_transformation,[status(thm)],[f1279])).
% 15.74/3.62 thf(f1279,plain,(
% 15.74/3.62 (binintersectSubset4 = $true) <=> ! [X0 : $i,X1 : $i] : (((binintersect @ X1 @ X0) = X0) | ((subset @ X0 @ X1) != $true))),
% 15.74/3.62 inference(ennf_transformation,[status(thm)],[f557])).
% 15.74/3.62 thf(f557,plain,(
% 15.74/3.62 (binintersectSubset4 = $true) <=> ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) => ((binintersect @ X1 @ X0) = X0))),
% 15.74/3.62 inference(fool_elimination,[status(thm)],[f556])).
% 15.74/3.62 thf(f556,plain,(
% 15.74/3.62 (! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((binintersect @ X1 @ X0) = X0)) = binintersectSubset4)),
% 15.74/3.62 inference(rectify,[status(thm)],[f117])).
% 15.74/3.62 thf(f117,axiom,(
% 15.74/3.62 (! [X4 : $i,X3 : $i] : ((subset @ X4 @ X3) => ((binintersect @ X3 @ X4) = X4)) = binintersectSubset4)),
% 15.74/3.62 file('/export/starexec/sandbox/tmp/tmp.d0DxC7kphv/DTF2THF_20722.p',binintersectSubset4)).
% 15.74/3.62 % SZS output end Proof for DTF2THF_20722
% 15.74/3.62 % (21286)------------------------------
% 15.74/3.62 % (21286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.74/3.62 % (21286)Termination reason: Refutation
% 15.74/3.62
% 15.74/3.62 % (21286)Memory used [KB]: 17270
% 15.74/3.62 % (21286)Time elapsed: 0.287 s
% 15.74/3.62 % (21286)Instructions burned: 863 (million)
% 15.74/3.62 % (21286)------------------------------
% 15.74/3.62 % (21286)------------------------------
% 15.74/3.62 % (20976)Success in time 1.971 s
%------------------------------------------------------------------------------