%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU805^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:37:21 AM UTC 2026
% Result : Theorem 229.80s 34.32s
% Output : Refutation 229.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 14
% Syntax : Number of formulae : 85 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 5659 (1554 equ; 0 cnn)
% Maximal formula atoms : 324 ( 66 avg)
% Number of connectives : 3044 ( 125 ~; 100 |;1027 &; 478 @)
% ( 7 <=>;1307 =>; 0 <=; 0 <~>)
% Maximal formula depth : 329 ( 31 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 613 ( 610 usr; 330 con; 0-6 aty)
% Number of variables : 174 ( 7 ^; 110 !; 57 ?; 174 :)
% 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_393,type,
sP4: $i > $i > $i > $i > $o ).
thf(func_def_395,type,
sP6: $o > $i > $i > $i > $o ).
thf(func_def_397,type,
sP8: $i > $i > $i > $o ).
thf(func_def_400,type,
sP11: $i > $i > $i > $o ).
thf(func_def_401,type,
sP12: $i > $i > $o ).
thf(func_def_402,type,
sP13: $i > $o ).
thf(func_def_403,type,
sP14: $i > $i > $o ).
thf(func_def_404,type,
sP15: $i > $i > $o ).
thf(func_def_411,type,
sK22: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_412,type,
sK23: $i > $i > $o ).
thf(func_def_415,type,
sK26: $i > $i ).
thf(func_def_431,type,
sK42: $i > $i > $i ).
thf(func_def_438,type,
sK49: $i > $i ).
thf(func_def_442,type,
sK53: $i > $o ).
thf(func_def_443,type,
sK54: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_444,type,
sK55: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_445,type,
sK56: $i > $o ).
thf(func_def_446,type,
sK57: $i > $o ).
thf(func_def_453,type,
sK64: $i > $i ).
thf(func_def_458,type,
sK69: $i > $i > ( $i > $i ) > $i ).
thf(func_def_459,type,
sK70: $i > $i ).
thf(func_def_465,type,
sK76: $i > $o ).
thf(func_def_466,type,
sK77: $i > $i ).
thf(func_def_467,type,
sK78: ( $i > $o ) > $i ).
thf(func_def_476,type,
sK87: $i > $i > $i > $i > $i > $i ).
thf(func_def_477,type,
sK88: $i > ( $i > $i ) > $i > $i ).
thf(func_def_479,type,
sK90: $i > $i ).
thf(func_def_482,type,
sK93: $i > $o ).
thf(func_def_484,type,
sK95: $i > ( $i > $o ) > $i > $i ).
thf(func_def_485,type,
sK96: $i > $o ).
thf(func_def_514,type,
sK125: $i > $o ).
thf(func_def_517,type,
sK128: $i > ( $i > $o ) > $i ).
thf(func_def_518,type,
sK129: $i > $o ).
thf(func_def_538,type,
sK149: $i > $i > $i ).
thf(func_def_542,type,
sK153: $i > $i ).
thf(func_def_545,type,
sK156: $i > $i > ( $i > $i ) > $i ).
thf(func_def_559,type,
sK170: $i > $i > $i ).
thf(func_def_575,type,
sK186: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_576,type,
sK187: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_579,type,
sK190: $i > $o ).
thf(func_def_580,type,
sK191: $i > $o ).
thf(func_def_590,type,
sK201: $o > $i > $i > $i > $i > $i > $i ).
thf(func_def_594,type,
sK205: $i > $i > $i > $i > $i ).
thf(func_def_612,type,
sK223: $i > $i > $o ).
thf(func_def_617,type,
sK228: $i > $i > $i ).
thf(func_def_625,type,
sK236: ( $i > $o ) > $i ).
thf(func_def_626,type,
sK237: $i > $o ).
thf(func_def_643,type,
sK254: $i > $i > $o ).
thf(func_def_672,type,
sK283: $i > $i > $i > $i ).
thf(func_def_679,type,
sK290: $i > $o ).
thf(func_def_682,type,
sK293: $i > ( $i > $o ) > $i ).
thf(func_def_695,type,
sK306: $i > $i ).
thf(func_def_697,type,
sK308: $i > $i ).
thf(func_def_706,type,
sK317: $i > $i > ( $i > $i ) > $i ).
thf(func_def_707,type,
sK318: $i > $i ).
thf(func_def_723,type,
sK334: $i > $o ).
thf(func_def_746,type,
sK357: $i > $i > $o ).
thf(func_def_750,type,
sK361: $i > $i ).
thf(func_def_762,type,
sK373: $i > $i ).
thf(func_def_776,type,
sK387: $i > $i > $i > $i ).
thf(func_def_780,type,
sK391: $i > $o ).
thf(func_def_783,type,
sK394: $i > ( $i > $o ) > $i ).
thf(func_def_790,type,
sK401: $i > $o ).
thf(func_def_793,type,
sK404: $i > ( $i > $o ) > $i ).
thf(func_def_794,type,
sK405: $i > ( $i > $o ) > $i ).
thf(func_def_804,type,
sK415: $i > $i > $i > $i > $i ).
thf(func_def_809,type,
sK420: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_810,type,
sK421: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_814,type,
sK425: $i > $o ).
thf(func_def_840,type,
sK451: $o > $i > $i > $i ).
thf(func_def_841,type,
sK452: $i > ( $i > $o ) > $i ).
thf(func_def_842,type,
sK453: $i > $o ).
thf(func_def_854,type,
sK465: $i > $i > $o ).
thf(func_def_857,type,
sK468: $i > $i ).
thf(func_def_862,type,
sK473: $i > $o ).
thf(func_def_869,type,
sK480: $i > $i > $i > $i > $i ).
thf(func_def_870,type,
sK481: $i > $i > $i > $i > $i ).
thf(func_def_871,type,
sK482: $i > $i > $i > $i > $i ).
thf(func_def_872,type,
sK483: $i > $i > $i > $i > $i ).
thf(func_def_901,type,
sK512: $i > $i > ( $i > $i ) > $i ).
thf(func_def_902,type,
sK513: $i > $i > $i > ( $i > $i ) > $i ).
thf(func_def_903,type,
sK514: $i > $i ).
thf(func_def_917,type,
sK528: $i > $o ).
thf(func_def_929,type,
sK540: $i > $i > $i ).
thf(func_def_932,type,
sK543: $i > $i ).
thf(func_def_934,type,
sK545: ( $i > $i ) > $i > $i > $i ).
thf(func_def_946,type,
sK557: $i > $i > $o ).
thf(func_def_960,type,
sK571: $i > $o ).
thf(func_def_969,type,
sK580: $i > $i ).
thf(func_def_972,type,
sK583: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1003,type,
sK614: $i > $i > $i > $i ).
thf(func_def_1004,type,
sK615: $i > $i > $i > $i ).
thf(func_def_1005,type,
sK616: $i > $i > $i > $i ).
thf(func_def_1006,type,
sK617: $i > $i > $i > $i ).
thf(func_def_1007,type,
sK618: $i > $o ).
thf(func_def_1008,type,
sK619: $i > $o ).
thf(func_def_1009,type,
sK620: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1010,type,
sK621: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1025,type,
sK636: $i > $o ).
thf(func_def_1027,type,
sK638: ( $i > $o ) > $i > $i > $i ).
thf(func_def_1028,type,
sK639: ( $i > $o ) > $i > $i > $i ).
thf(func_def_1031,type,
sK642: ( $i > $o ) > $i ).
thf(func_def_1032,type,
sK643: $i > $o ).
thf(func_def_1033,type,
sK644: $i > $i ).
thf(func_def_1034,type,
sK645: $i > $i > $o ).
thf(func_def_1036,type,
sK647: $i > $i ).
thf(func_def_1037,type,
sK648: $i > $i ).
thf(func_def_1038,type,
sK649: $i > ( $i > $i > $o ) > $i ).
thf(func_def_1039,type,
sK650: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_1040,type,
sK651: $i > ( $i > $i > $o ) > $i ).
thf(func_def_1064,type,
sK675: $i > $i > $i > $i ).
thf(func_def_1068,type,
sK679: $i > $i > $i > $i ).
thf(func_def_1095,type,
sK706: $i > $o ).
thf(func_def_1098,type,
sK709: $i > ( $i > $o ) > $i ).
thf(func_def_1130,type,
sK741: $i > $o ).
thf(func_def_1132,type,
sK743: ( $i > $o ) > $i > $i > $i ).
thf(func_def_1133,type,
sK744: ( $i > $o ) > $i > $i > $i ).
thf(func_def_1138,type,
sK749: $i > $i > $i ).
thf(func_def_1155,type,
sK766: $i > $i > $i ).
thf(func_def_1156,type,
sK767: $i > $i > $i ).
thf(func_def_1157,type,
sK768: $i > $i > $i ).
thf(func_def_1158,type,
sK769: $i > $i > $i ).
thf(func_def_1159,type,
sK770: $i > $i > $i > $i ).
thf(func_def_1160,type,
sK771: $i > $i ).
thf(func_def_1161,type,
sK772: $i > $i ).
thf(func_def_1162,type,
sK773: $i > $i ).
thf(func_def_1163,type,
sK774: $i > $i ).
thf(func_def_1164,type,
sK775: $i > $i > $i > $i ).
thf(func_def_1165,type,
sK776: $i > $i > $i > $i ).
thf(func_def_1166,type,
sK777: $i > $i > $i ).
thf(func_def_1167,type,
sK778: $i > $i > $i ).
thf(func_def_1168,type,
sK779: $i > $i > $i ).
thf(func_def_1169,type,
sK780: $i > $i ).
thf(func_def_1170,type,
sK781: $i > $i > $i ).
thf(func_def_1172,type,
sK783: $i > $i ).
thf(func_def_1173,type,
sK784: $i > $i ).
thf(func_def_1179,type,
sK790: $i > $i ).
thf(func_def_1188,type,
sK799: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1189,type,
sK800: $i > $i ).
thf(func_def_1205,type,
sK816: $i > $o ).
thf(func_def_1212,type,
sK823: $i > $i > $i ).
thf(func_def_1231,type,
sK842: $i > $i > $o ).
thf(func_def_1233,type,
sK844: $i > ( $i > $o ) > $i ).
thf(func_def_1234,type,
sK845: $i > $o ).
thf(func_def_1236,type,
sK847: $i > $o ).
thf(func_def_1239,type,
sK850: $i > ( $i > $o ) > $i ).
thf(func_def_1240,type,
sK851: $i > $o ).
thf(func_def_1242,type,
sK853: ( $i > $o ) > $i ).
thf(func_def_1243,type,
sK854: ( $i > $o ) > $i ).
thf(func_def_1255,type,
sK866: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1258,type,
sK869: $i > $i ).
thf(func_def_1263,type,
sK874: $i > $o ).
thf(func_def_1265,type,
sK876: ( $i > $o ) > $i > $i ).
thf(func_def_1266,type,
sK877: ( $i > $o ) > $i > $i ).
thf(func_def_1269,type,
sK880: $i > $o ).
thf(func_def_1277,type,
sK888: $i > $i > $i > $i > $i ).
thf(func_def_1278,type,
sK889: $i > $i > $i > $i > $i ).
thf(func_def_1288,type,
sK899: $i > ( $i > $o ) > $i ).
thf(func_def_1289,type,
sK900: $i > $o ).
thf(func_def_1301,type,
sK912: $i > $i > $i ).
thf(func_def_1302,type,
sK913: $i > $i > $i ).
thf(func_def_1306,type,
sK917: $i > $i > $i > $i ).
thf(func_def_1307,type,
sK918: $i > $i > $i > $i ).
thf(func_def_1310,type,
sK921: $i > $i > $o ).
thf(func_def_1315,type,
sK926: $i > $i > $i ).
thf(func_def_1330,type,
sK941: $i > $o ).
thf(func_def_1337,type,
sK948: $i > $i > $i > $i > $i ).
thf(func_def_1344,type,
sK955: $i > $o ).
thf(func_def_1346,type,
sK957: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_1347,type,
sK958: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_1365,type,
sK976: $i > $i > $i > $i ).
thf(func_def_1366,type,
sK977: $i > $i > $i > $i ).
thf(func_def_1367,type,
sK978: $i > $i ).
thf(func_def_1383,type,
sK994: $i > $i > $o ).
thf(func_def_1388,type,
sK999: $i > $i ).
thf(func_def_1389,type,
sK1000: $i > $i ).
thf(func_def_1390,type,
sK1001: $i > $i ).
thf(func_def_1391,type,
sK1002: ( $i > $i ) > $i > $i ).
thf(func_def_1392,type,
sK1003: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1428,type,
sK1039: $i > $o ).
thf(func_def_1430,type,
sK1041: $i > ( $i > $o ) > $i ).
thf(func_def_1437,type,
sK1048: $i > $o ).
thf(func_def_1454,type,
sK1065: $i > $o ).
thf(func_def_1469,type,
sK1080: $i > $o ).
thf(func_def_1475,type,
sK1086: ( $i > $o ) > $i ).
thf(func_def_1476,type,
sK1087: ( $i > $o ) > $i ).
thf(func_def_1477,type,
sK1088: $i > ( $i > $o ) > $i ).
thf(func_def_1478,type,
sK1089: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_1479,type,
sK1090: $i > $i ).
thf(func_def_1480,type,
sK1091: $i > ( $i > $o ) > $i ).
thf(func_def_1481,type,
sK1092: ( $i > $o ) > $i > $i ).
thf(func_def_1482,type,
sK1093: $i > ( $i > $o ) > $i ).
thf(func_def_1483,type,
sK1094: $i > ( $i > $o ) > $i ).
thf(func_def_1484,type,
sK1095: ( $i > $o ) > $i ).
thf(func_def_1485,type,
sK1096: ( $i > $o ) > $i > $i ).
thf(func_def_1486,type,
sK1097: $i > ( $i > $o ) > $i ).
thf(func_def_1487,type,
sK1098: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_1488,type,
sK1099: $i > ( $i > $o ) > $i ).
thf(func_def_1489,type,
sK1100: ( $i > $o ) > $i > $i ).
thf(func_def_1490,type,
sK1101: ( $i > $o ) > $i > $i ).
thf(func_def_1491,type,
sK1102: ( $i > $o ) > $i > $i ).
thf(func_def_1492,type,
sK1103: ( $i > $o ) > $i > $i ).
thf(func_def_1493,type,
sK1104: ( $i > $o ) > $i > $i ).
thf(func_def_1494,type,
sK1105: ( $i > $o ) > $i ).
thf(func_def_1495,type,
sK1106: $i > ( $i > $i ) > $i ).
thf(func_def_1496,type,
sK1107: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1497,type,
sK1108: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1498,type,
sK1109: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1499,type,
sK1110: ( $i > $o ) > $i ).
thf(func_def_1500,type,
sK1111: ( $i > $o ) > $i > $i ).
thf(func_def_1501,type,
sK1112: ( $i > $o ) > $i ).
thf(func_def_1502,type,
sK1113: ( $i > $o ) > $i > $i ).
thf(func_def_1503,type,
sK1114: ( $i > $o ) > $i > $i ).
thf(func_def_1504,type,
sK1115: ( $i > $o ) > $i ).
thf(func_def_1505,type,
sK1116: ( $i > $o ) > $i > $i ).
thf(func_def_1506,type,
sK1117: ( $i > $o ) > $i ).
thf(func_def_1507,type,
sK1118: ( $i > $o ) > $i ).
thf(func_def_1508,type,
sK1119: ( $i > $o ) > $i > $i ).
thf(func_def_1509,type,
sK1120: ( $i > $o ) > $i > $i ).
thf(func_def_1510,type,
sK1121: ( $i > $o ) > $i ).
thf(func_def_1511,type,
sK1122: ( $i > $o ) > $i > $i ).
thf(func_def_1512,type,
sK1123: ( $i > $o ) > $i ).
thf(func_def_1513,type,
sK1124: ( $i > $o ) > $i > $i ).
thf(func_def_1514,type,
sK1125: ( $i > $o ) > $i > $i ).
thf(func_def_1515,type,
sK1126: ( $i > $o ) > $i ).
thf(func_def_1516,type,
sK1127: $i > ( $i > $o ) > $i ).
thf(func_def_1517,type,
sK1128: ( $i > $o ) > $i ).
thf(func_def_1518,type,
sK1129: ( $i > $o ) > $i > $i ).
thf(func_def_1519,type,
sK1130: ( $i > $o ) > $i > $i ).
thf(func_def_1520,type,
sK1131: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_1521,type,
ph1132:
!>[X0: $tType] : X0 ).
thf(f44979,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f44978,f6603]) ).
thf(f6603,plain,
emptyset != sK137,
inference(equality_proxy_clausification,[status(thm)],[f6602]) ).
thf(f6602,plain,
( ( emptyset = sK137 )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f6601]) ).
thf(f6601,plain,
( ( emptyset != sK137 )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f5017]) ).
thf(f5017,plain,
( ( ^ [Y0: $i] : ( emptyset != Y0 )
@ sK137 )
= $true ),
inference(definition_unfolding,[status(thm)],[f3496,f4101]) ).
thf(f4101,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f805]) ).
thf(f805,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f804]) ).
thf(f804,plain,
( nonempty
= ( ^ [X0: $i] : ( emptyset != X0 ) ) ),
inference(rectify,[status(thm)],[f27]) ).
thf(f27,axiom,
( nonempty
= ( ^ [X1: $i] : ( emptyset != X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Th7rVCfvTI/DTF2THF_17306.p',nonempty) ).
thf(f3496,plain,
( ( nonempty @ sK137 )
= $true ),
inference(cnf_transformation,[status(thm)],[f1631]) ).
thf(f1631,plain,
( ( setadjoinAx = $true )
& ( kpairp = $true )
& ( secondinupair = $true )
& ( emptyI = $true )
& ( kfstpairEq = $true )
& ( app = $true )
& ( setukpairinjR12 = $true )
& ( subbreln = $true )
& ( setadjoinIR = $true )
& ( eqbreln1 = $true )
& ( funcinfuncset = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( notinemptyset = $true )
& ( surjCantorThm = $true )
& ( ubforcartprodlem3 = $true )
& ( breln1all1 = $true )
& ( iftrueProp2 = $true )
& ( binunionIL = $true )
& ( iftrue = $true )
& ( upairinpowunion = $true )
& ( ex1I2 = $true )
& ( powersetE1 = $true )
& ( nonemptyI = $true )
& ( dpsetconstrSub = $true )
& ( woz1_4 = $true )
& ( dpsetconstrEL2 = $true )
& ( upairsetE = $true )
& ( demorgan2a = $true )
& ( eqbreln = $true )
& ( binunionTEcontra = $true )
& ( exuE3u = $true )
& ( woz13rule4 = $true )
& ( subsetTrans = $true )
& ( binintersectSubset1 = $true )
& ( upairsubunion = $true )
& ( setukpairinjR1 = $true )
& ( setunionE = $true )
& ( image1Equiv = $true )
& ( iftrueorfalse = $true )
& ( lam2lamEq = $true )
& ( nonemptyImpWitness = $true )
& ( cartprodsndpairEq = $true )
& ( complementTnotintersectT = $true )
& ( funcext2 = $true )
& ( injFuncInInjFuncSet = $true )
& ( binunionTE = $true )
& ( setadjoinSub2 = $true )
& ( injFuncSetFuncInj = $true )
& ( doubleComplementSub1 = $true )
& ( notdallE = $true )
& ( quantDeMorgan4 = $true )
& ( contrasubsetT2 = $true )
& ( sepInPowerset = $true )
& ( setminusER = $true )
& ( theprop = $true )
& ( emptyinunitempty = $true )
& ( breln1unionCommutes = $true )
& ( iffalseProp2 = $true )
& ( symdiffE = $true )
& ( wellorderingAx = $true )
& ( ksndpairEq = $true )
& ( exuI3 = $true )
& ( woz1_2 = $true )
& ( doubleComplementI1 = $true )
& ( upairsetIL = $true )
& ( ex1E1 = $true )
& ( ( nonempty @ sK137 )
= $true )
& ! [X1: $i] :
( ( emptyset
!= ( binintersect @ X1 @ sK137 ) )
| ( ( in @ X1 @ sK137 )
!= $true ) )
& ( binintersectEL = $true )
& ( funcextLem = $true )
& ( singletonsuniq = $true )
& ( emptyinPowerset = $true )
& ( binunionRsub = $true )
& ( ap2apEq2 = $true )
& ( woz1_3 = $true )
& ( kpairiskpair = $true )
& ( woz2B = $true )
& ( ifSingleton = $true )
& ( notinsingleton = $true )
& ( emptysetimpfalse = $true )
& ( complementT_lem = $true )
& ( cartprodpairsurjEq = $true )
& ( notequalI1 = $true )
& ( powersetT_lem = $true )
& ( setminusEL = $true )
& ( powersetI = $true )
& ( setOfPairsIsBReln = $true )
& ( setunionsingleton1 = $true )
& ( powersetsubset = $true )
& ( binintersectSubset3 = $true )
& ( prop2set2propI = $true )
& ( setunionAx = $true )
& ( setminusERneg = $true )
& ( doubleComplementSub2 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( binintersectSubset2 = $true )
& ( subsetI2 = $true )
& ( ubforcartprodlem2 = $true )
& ( descrp = $true )
& ( upairsetIR = $true )
& ( contrasubsetT = $true )
& ( setextT = $true )
& ( dpsetconstrI = $true )
& ( setminusLsub = $true )
& ( singletoninpowerset = $true )
& ( demorgan2a2 = $true )
& ( notsubsetI = $true )
& ( descr__Cong = $true )
& ( omega__Cong = $true )
& ( setminusELneg = $true )
& ( upairset2IR = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( emptysetE = $true )
& ( image1Ex = $true )
& ( beta2 = $true )
& ( breln1invI = $true )
& ( setukpairinjR2 = $true )
& ( lamp = $true )
& ( setOfPairsIsBReln1 = $true )
& ( binunionTIRcontra = $true )
& ( quantDeMorgan1 = $true )
& ( omegaSAx = $true )
& ( setminusSubset1 = $true )
& ( binintersectI = $true )
& ( powersetAx = $true )
& ( complementTcontraSubset = $true )
& ( exuI1 = $true )
& ( binintersectT_lem = $true )
& ( iffalse = $true )
& ( eta1 = $true )
& ( eqinunit = $true )
& ( woz2A = $true )
& ( singletonprop = $true )
& ( exu__Cong = $true )
& ( cartprodfstpairEq = $true )
& ( binintersectSubset4 = $true )
& ( lam2p = $true )
& ( binunionT_lem = $true )
& ( subsetE2 = $true )
& ( iftrueProp1 = $true )
& ( eqimpsubset1 = $true )
& ( infuncsetfunc = $true )
& ( woz2Ex = $true )
& ( beta1 = $true )
& ( symdiffI1 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( setukpairinjL1 = $true )
& ( contraSubsetComplement = $true )
& ( cartprodmempair = $true )
& ( binintersectTELcontra = $true )
& ( surjFuncSetFuncSurj = $true )
& ( inPowerset = $true )
& ( apProp = $true )
& ( singletonsswitch = $true )
& ( demorgan2b = $true )
& ( eta2 = $true )
& ( setoftrueEq = $true )
& ( image1Ex1 = $true )
& ( ap2apEq1 = $true )
& ( dsetconstrEL = $true )
& ( setminusIRneg = $true )
& ( breln1invprop = $true )
& ( demorgan1a = $true )
& ( funcImageSingleton = $true )
& ( omegaIndAx = $true )
& ( bs114d = $true )
& ( cartprodpairmemEL = $true )
& ( upairset2E = $true )
& ( setbeta = $true )
& ( funcGraphProp1 = $true )
& ( injFuncSetFuncIn = $true )
& ( uniqinunit = $true )
& ( setextsub = $true )
& ( complementImpComplementIntersect = $true )
& ( disjointsetsI1 = $true )
& ( prop2setE = $true )
& ( brelnall1 = $true )
& ( theeq = $true )
& ( subsetemptysetimpeq = $true )
& ( setadjoinIL = $true )
& ( notdexE = $true )
& ( cartprodpairmemER = $true )
& ( symdiffI2 = $true )
& ( emptysetAx = $true )
& ( funcGraphProp2 = $true )
& ( setunion__Cong = $true )
& ( singletoninpowunion = $true )
& ( complementTI1 = $true )
& ( binunionTILcontra = $true )
& ( emptysetsubset = $true )
& ( setminusI = $true )
& ( cartprodmempaircEq = $true )
& ( binunionLsub = $true )
& ( powersetI1 = $true )
& ( binintersectLsub = $true )
& ( exuE3e = $true )
& ( woz13rule3 = $true )
& ( binunionIR = $true )
& ( exuEu = $true )
& ( breln1compE = $true )
& ( complementSubsetComplementIntersect = $true )
& ( choice2fnsingleton = $true )
& ( vacuousDall = $true )
& ( doubleComplementE1 = $true )
& ( upairequniteq = $true )
& ( binintersectSubset5 = $true )
& ( in__Cong = $true )
& ( demorgan2b2 = $true )
& ( woz13rule0 = $true )
& ( nonemptyE1 = $true )
& ( dpsetconstrEL1 = $true )
& ( breln1SetBreln1 = $true )
& ( setadjoinOr = $true )
& ( woz13rule1 = $true )
& ( breln1unionIR = $true )
& ( demorgan1b = $true )
& ( surjFuncSetFuncIn = $true )
& ( woz1_5 = $true )
& ( ap2p = $true )
& ( setadjoinSub = $true )
& ( cartprodpairin = $true )
& ( contrasubsetT3 = $true )
& ( binunionE = $true )
& ( singletonsubset = $true )
& ( setunionsingleton = $true )
& ( setukpairIR = $true )
& ( dpsetconstrERa = $true )
& ( subset2powerset = $true )
& ( dpsetconstrER = $true )
& ( ubforcartprodlem1 = $true )
& ( emptyE1 = $true )
& ( powersetTI1 = $true )
& ( setunionsingleton2 = $true )
& ( breln1unionIL = $true )
& ( breln1unionprop = $true )
& ( powerset__Cong = $true )
& ( woz1_1 = $true )
& ( setadjoin__Cong = $true )
& ( cartprodsndin = $true )
& ( subsetRefl = $true )
& ( funcGraphProp3 = $true )
& ( setextAx = $true )
& ( subsetE = $true )
& ( powersetTE1 = $true )
& ( binintersectRsub = $true )
& ( exuE2 = $true )
& ( lamProp = $true )
& ( setadjoinE = $true )
& ( emptyset__Cong = $true )
& ( setext = $true )
& ( subsetTI = $true )
& ( breln1unionEcases = $true )
& ( symdiffIneg2 = $true )
& ( foundationAx = $true )
& ( setminusSubset2 = $true )
& ( leftInvIsSurj = $true )
& ( ex1E2 = $true )
& ( binintersectTERcontra = $true )
& ( image1I = $true )
& ( powersetE = $true )
& ( symdiffIneg1 = $true )
& ( setunionE2 = $true )
& ( breln1compprop = $true )
& ( inCongP = $true )
& ( demorgan2a1 = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( notequalI2 = $true )
& ( setunionI = $true )
& ( subsetI1 = $true )
& ( breln1invE = $true )
& ( omega0Ax = $true )
& ( breln1all2 = $true )
& ( replAx = $true )
& ( setminusT_lem = $true )
& ( doubleComplementEq = $true )
& ( subbreln1 = $true )
& ( quantDeMorgan2 = $true )
& ( cartprodmempair1 = $true )
& ( dsetconstrI = $true )
& ( exuI2 = $true )
& ( breln1compEex = $true )
& ( brelnall2 = $true )
& ( setukpairIL = $true )
& ( dsetconstr__Cong = $true )
& ( setminusILneg = $true )
& ( eqimpsubset2 = $true )
& ( kfstsingleton = $true )
& ( funcGraphProp4 = $true )
& ( image1E = $true )
& ( setukpairinjL = $true )
& ( woz13rule2 = $true )
& ( binunionEcases = $true )
& ( quantDeMorgan3 = $true )
& ( kpairsurjEq = $true )
& ( breln1unionI = $true )
& ( emptyInPowerset = $true )
& ( nonemptyI1 = $true )
& ( dsetconstrER = $true )
& ( ksndsingleton = $true )
& ( breln1compI = $true )
& ( funcext = $true )
& ( subPowSU = $true )
& ( prop2setI = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( complementTE1 = $true )
& ( demorgan1 = $true )
& ( inIntersectImpInUnion = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( setukpairinjL2 = $true )
& ( setukpairinjR = $true )
& ( contrasubsetT1 = $true )
& ( breln1unionE = $true )
& ( setukpairinjR11 = $true )
& ( ex1I = $true )
& ( iffalseProp1 = $true )
& ( binintersectER = $true )
& ( cartprodfstin = $true )
& ( noeltsimpempty = $true )
& ( exuE1 = $true )
& ( ifp = $true )
& ( woz2W = $true )
& ( sepSubset = $true )
& ( demorgan2 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK137])],[f1247,f1630]) ).
thf(f1630,plain,
( ? [X0: $i] :
( ( ( nonempty @ X0 )
= $true )
& ! [X1: $i] :
( ( emptyset
!= ( binintersect @ X1 @ X0 ) )
| ( ( in @ X1 @ X0 )
!= $true ) ) )
=> ( ( ( nonempty @ sK137 )
= $true )
& ! [X1: $i] :
( ( emptyset
!= ( binintersect @ X1 @ sK137 ) )
| ( ( in @ X1 @ sK137 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1247,plain,
( ( setadjoinAx = $true )
& ( kpairp = $true )
& ( secondinupair = $true )
& ( emptyI = $true )
& ( kfstpairEq = $true )
& ( app = $true )
& ( setukpairinjR12 = $true )
& ( subbreln = $true )
& ( setadjoinIR = $true )
& ( eqbreln1 = $true )
& ( funcinfuncset = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( notinemptyset = $true )
& ( surjCantorThm = $true )
& ( ubforcartprodlem3 = $true )
& ( breln1all1 = $true )
& ( iftrueProp2 = $true )
& ( binunionIL = $true )
& ( iftrue = $true )
& ( upairinpowunion = $true )
& ( ex1I2 = $true )
& ( powersetE1 = $true )
& ( nonemptyI = $true )
& ( dpsetconstrSub = $true )
& ( woz1_4 = $true )
& ( dpsetconstrEL2 = $true )
& ( upairsetE = $true )
& ( demorgan2a = $true )
& ( eqbreln = $true )
& ( binunionTEcontra = $true )
& ( exuE3u = $true )
& ( woz13rule4 = $true )
& ( subsetTrans = $true )
& ( binintersectSubset1 = $true )
& ( upairsubunion = $true )
& ( setukpairinjR1 = $true )
& ( setunionE = $true )
& ( image1Equiv = $true )
& ( iftrueorfalse = $true )
& ( lam2lamEq = $true )
& ( nonemptyImpWitness = $true )
& ( cartprodsndpairEq = $true )
& ( complementTnotintersectT = $true )
& ( funcext2 = $true )
& ( injFuncInInjFuncSet = $true )
& ( binunionTE = $true )
& ( setadjoinSub2 = $true )
& ( injFuncSetFuncInj = $true )
& ( doubleComplementSub1 = $true )
& ( notdallE = $true )
& ( quantDeMorgan4 = $true )
& ( contrasubsetT2 = $true )
& ( sepInPowerset = $true )
& ( setminusER = $true )
& ( theprop = $true )
& ( emptyinunitempty = $true )
& ( breln1unionCommutes = $true )
& ( iffalseProp2 = $true )
& ( symdiffE = $true )
& ( wellorderingAx = $true )
& ( ksndpairEq = $true )
& ( exuI3 = $true )
& ( woz1_2 = $true )
& ( doubleComplementI1 = $true )
& ( upairsetIL = $true )
& ( ex1E1 = $true )
& ? [X0: $i] :
( ( ( nonempty @ X0 )
= $true )
& ! [X1: $i] :
( ( emptyset
!= ( binintersect @ X1 @ X0 ) )
| ( ( in @ X1 @ X0 )
!= $true ) ) )
& ( binintersectEL = $true )
& ( funcextLem = $true )
& ( singletonsuniq = $true )
& ( emptyinPowerset = $true )
& ( binunionRsub = $true )
& ( ap2apEq2 = $true )
& ( woz1_3 = $true )
& ( kpairiskpair = $true )
& ( woz2B = $true )
& ( ifSingleton = $true )
& ( notinsingleton = $true )
& ( emptysetimpfalse = $true )
& ( complementT_lem = $true )
& ( cartprodpairsurjEq = $true )
& ( notequalI1 = $true )
& ( powersetT_lem = $true )
& ( setminusEL = $true )
& ( powersetI = $true )
& ( setOfPairsIsBReln = $true )
& ( setunionsingleton1 = $true )
& ( powersetsubset = $true )
& ( binintersectSubset3 = $true )
& ( prop2set2propI = $true )
& ( setunionAx = $true )
& ( setminusERneg = $true )
& ( doubleComplementSub2 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( binintersectSubset2 = $true )
& ( subsetI2 = $true )
& ( ubforcartprodlem2 = $true )
& ( descrp = $true )
& ( upairsetIR = $true )
& ( contrasubsetT = $true )
& ( setextT = $true )
& ( dpsetconstrI = $true )
& ( setminusLsub = $true )
& ( singletoninpowerset = $true )
& ( demorgan2a2 = $true )
& ( notsubsetI = $true )
& ( descr__Cong = $true )
& ( omega__Cong = $true )
& ( setminusELneg = $true )
& ( upairset2IR = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( emptysetE = $true )
& ( image1Ex = $true )
& ( beta2 = $true )
& ( breln1invI = $true )
& ( setukpairinjR2 = $true )
& ( lamp = $true )
& ( setOfPairsIsBReln1 = $true )
& ( binunionTIRcontra = $true )
& ( quantDeMorgan1 = $true )
& ( omegaSAx = $true )
& ( setminusSubset1 = $true )
& ( binintersectI = $true )
& ( powersetAx = $true )
& ( complementTcontraSubset = $true )
& ( exuI1 = $true )
& ( binintersectT_lem = $true )
& ( iffalse = $true )
& ( eta1 = $true )
& ( eqinunit = $true )
& ( woz2A = $true )
& ( singletonprop = $true )
& ( exu__Cong = $true )
& ( cartprodfstpairEq = $true )
& ( binintersectSubset4 = $true )
& ( lam2p = $true )
& ( binunionT_lem = $true )
& ( subsetE2 = $true )
& ( iftrueProp1 = $true )
& ( eqimpsubset1 = $true )
& ( infuncsetfunc = $true )
& ( woz2Ex = $true )
& ( beta1 = $true )
& ( symdiffI1 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( setukpairinjL1 = $true )
& ( contraSubsetComplement = $true )
& ( cartprodmempair = $true )
& ( binintersectTELcontra = $true )
& ( surjFuncSetFuncSurj = $true )
& ( inPowerset = $true )
& ( apProp = $true )
& ( singletonsswitch = $true )
& ( demorgan2b = $true )
& ( eta2 = $true )
& ( setoftrueEq = $true )
& ( image1Ex1 = $true )
& ( ap2apEq1 = $true )
& ( dsetconstrEL = $true )
& ( setminusIRneg = $true )
& ( breln1invprop = $true )
& ( demorgan1a = $true )
& ( funcImageSingleton = $true )
& ( omegaIndAx = $true )
& ( bs114d = $true )
& ( cartprodpairmemEL = $true )
& ( upairset2E = $true )
& ( setbeta = $true )
& ( funcGraphProp1 = $true )
& ( injFuncSetFuncIn = $true )
& ( uniqinunit = $true )
& ( setextsub = $true )
& ( complementImpComplementIntersect = $true )
& ( disjointsetsI1 = $true )
& ( prop2setE = $true )
& ( brelnall1 = $true )
& ( theeq = $true )
& ( subsetemptysetimpeq = $true )
& ( setadjoinIL = $true )
& ( notdexE = $true )
& ( cartprodpairmemER = $true )
& ( symdiffI2 = $true )
& ( emptysetAx = $true )
& ( funcGraphProp2 = $true )
& ( setunion__Cong = $true )
& ( singletoninpowunion = $true )
& ( complementTI1 = $true )
& ( binunionTILcontra = $true )
& ( emptysetsubset = $true )
& ( setminusI = $true )
& ( cartprodmempaircEq = $true )
& ( binunionLsub = $true )
& ( powersetI1 = $true )
& ( binintersectLsub = $true )
& ( exuE3e = $true )
& ( woz13rule3 = $true )
& ( binunionIR = $true )
& ( exuEu = $true )
& ( breln1compE = $true )
& ( complementSubsetComplementIntersect = $true )
& ( choice2fnsingleton = $true )
& ( vacuousDall = $true )
& ( doubleComplementE1 = $true )
& ( upairequniteq = $true )
& ( binintersectSubset5 = $true )
& ( in__Cong = $true )
& ( demorgan2b2 = $true )
& ( woz13rule0 = $true )
& ( nonemptyE1 = $true )
& ( dpsetconstrEL1 = $true )
& ( breln1SetBreln1 = $true )
& ( setadjoinOr = $true )
& ( woz13rule1 = $true )
& ( breln1unionIR = $true )
& ( demorgan1b = $true )
& ( surjFuncSetFuncIn = $true )
& ( woz1_5 = $true )
& ( ap2p = $true )
& ( setadjoinSub = $true )
& ( cartprodpairin = $true )
& ( contrasubsetT3 = $true )
& ( binunionE = $true )
& ( singletonsubset = $true )
& ( setunionsingleton = $true )
& ( setukpairIR = $true )
& ( dpsetconstrERa = $true )
& ( subset2powerset = $true )
& ( dpsetconstrER = $true )
& ( ubforcartprodlem1 = $true )
& ( emptyE1 = $true )
& ( powersetTI1 = $true )
& ( setunionsingleton2 = $true )
& ( breln1unionIL = $true )
& ( breln1unionprop = $true )
& ( powerset__Cong = $true )
& ( woz1_1 = $true )
& ( setadjoin__Cong = $true )
& ( cartprodsndin = $true )
& ( subsetRefl = $true )
& ( funcGraphProp3 = $true )
& ( setextAx = $true )
& ( subsetE = $true )
& ( powersetTE1 = $true )
& ( binintersectRsub = $true )
& ( exuE2 = $true )
& ( lamProp = $true )
& ( setadjoinE = $true )
& ( emptyset__Cong = $true )
& ( setext = $true )
& ( subsetTI = $true )
& ( breln1unionEcases = $true )
& ( symdiffIneg2 = $true )
& ( foundationAx = $true )
& ( setminusSubset2 = $true )
& ( leftInvIsSurj = $true )
& ( ex1E2 = $true )
& ( binintersectTERcontra = $true )
& ( image1I = $true )
& ( powersetE = $true )
& ( symdiffIneg1 = $true )
& ( setunionE2 = $true )
& ( breln1compprop = $true )
& ( inCongP = $true )
& ( demorgan2a1 = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( notequalI2 = $true )
& ( setunionI = $true )
& ( subsetI1 = $true )
& ( breln1invE = $true )
& ( omega0Ax = $true )
& ( breln1all2 = $true )
& ( replAx = $true )
& ( setminusT_lem = $true )
& ( doubleComplementEq = $true )
& ( subbreln1 = $true )
& ( quantDeMorgan2 = $true )
& ( cartprodmempair1 = $true )
& ( dsetconstrI = $true )
& ( exuI2 = $true )
& ( breln1compEex = $true )
& ( brelnall2 = $true )
& ( setukpairIL = $true )
& ( dsetconstr__Cong = $true )
& ( setminusILneg = $true )
& ( eqimpsubset2 = $true )
& ( kfstsingleton = $true )
& ( funcGraphProp4 = $true )
& ( image1E = $true )
& ( setukpairinjL = $true )
& ( woz13rule2 = $true )
& ( binunionEcases = $true )
& ( quantDeMorgan3 = $true )
& ( kpairsurjEq = $true )
& ( breln1unionI = $true )
& ( emptyInPowerset = $true )
& ( nonemptyI1 = $true )
& ( dsetconstrER = $true )
& ( ksndsingleton = $true )
& ( breln1compI = $true )
& ( funcext = $true )
& ( subPowSU = $true )
& ( prop2setI = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( complementTE1 = $true )
& ( demorgan1 = $true )
& ( inIntersectImpInUnion = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( setukpairinjL2 = $true )
& ( setukpairinjR = $true )
& ( contrasubsetT1 = $true )
& ( breln1unionE = $true )
& ( setukpairinjR11 = $true )
& ( ex1I = $true )
& ( iffalseProp1 = $true )
& ( binintersectER = $true )
& ( cartprodfstin = $true )
& ( noeltsimpempty = $true )
& ( exuE1 = $true )
& ( ifp = $true )
& ( woz2W = $true )
& ( sepSubset = $true )
& ( demorgan2 = $true ) ),
inference(flattening,[status(thm)],[f1246]) ).
thf(f1246,plain,
( ? [X0: $i] :
( ( ( nonempty @ X0 )
= $true )
& ! [X1: $i] :
( ( emptyset
!= ( binintersect @ X1 @ X0 ) )
| ( ( in @ X1 @ X0 )
!= $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)],[f489]) ).
thf(f489,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 )
=> ! [X0: $i] :
( ( ( nonempty @ X0 )
= $true )
=> ? [X1: $i] :
( ( emptyset
= ( binintersect @ X1 @ X0 ) )
& ( ( in @ X1 @ X0 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f488]) ).
thf(f488,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
=> ! [X0: $i] :
( ( nonempty @ X0 )
=> ? [X1: $i] :
( ( in @ X1 @ X0 )
& ( emptyset
= ( binintersect @ X1 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f325]) ).
thf(f325,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
=> ! [X3: $i] :
( ( nonempty @ X3 )
=> ? [X11: $i] :
( ( in @ X11 @ X3 )
& ( emptyset
= ( binintersect @ X11 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f324]) ).
thf(f324,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
=> ! [X3: $i] :
( ( nonempty @ X3 )
=> ? [X11: $i] :
( ( in @ X11 @ X3 )
& ( emptyset
= ( binintersect @ X11 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Th7rVCfvTI/DTF2THF_17306.p',foundation2) ).
thf(f44978,plain,
emptyset = sK137,
inference(subsumption_resolution,[status(thm)],[f44973,f44479]) ).
thf(f44479,plain,
( ( in @ ( sK540 @ ( sK306 @ sK137 ) @ sK137 ) @ sK137 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f44465]) ).
thf(f44465,plain,
( ( $true != $true )
| ( ( in @ ( sK540 @ ( sK306 @ sK137 ) @ sK137 ) @ sK137 )
!= $true ) ),
inference(superposition,[status(thm)],[f6929,f44460]) ).
thf(f44460,plain,
( $true
= ( in @ ( sK540 @ ( sK306 @ sK137 ) @ sK137 ) @ ( sK306 @ sK137 ) ) ),
inference(subsumption_resolution,[status(thm)],[f44459,f6603]) ).
thf(f44459,plain,
( ( emptyset = sK137 )
| ( $true
= ( in @ ( sK540 @ ( sK306 @ sK137 ) @ sK137 ) @ ( sK306 @ sK137 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f44449]) ).
thf(f44449,plain,
( ( $true
= ( in @ ( sK540 @ ( sK306 @ sK137 ) @ sK137 ) @ ( sK306 @ sK137 ) ) )
| ( $true != $true )
| ( emptyset = sK137 ) ),
inference(superposition,[status(thm)],[f24022,f8023]) ).
thf(f8023,plain,
! [X0: $i] :
( ( ( in @ ( sK306 @ X0 ) @ X0 )
= $true )
| ( emptyset = X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f8004]) ).
thf(f8004,plain,
! [X0: $i] :
( ( emptyset = X0 )
| ( $true != $true )
| ( ( in @ ( sK306 @ X0 ) @ X0 )
= $true ) ),
inference(superposition,[status(thm)],[f6657,f7108]) ).
thf(f7108,plain,
! [X0: $i] :
( ( ( in @ ( sK361 @ X0 ) @ X0 )
= $true )
| ( emptyset = X0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f7107]) ).
thf(f7107,plain,
! [X0: $i] :
( ( ( emptyset = X0 )
= $true )
| ( ( in @ ( sK361 @ X0 ) @ X0 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f7106]) ).
thf(f7106,plain,
! [X0: $i] :
( ( ( in @ ( sK361 @ X0 ) @ X0 )
= $true )
| ( ( emptyset != X0 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f7105]) ).
thf(f7105,plain,
! [X0: $i] :
( ( ( ^ [Y0: $i] : ( emptyset != Y0 )
@ X0 )
!= $true )
| ( ( in @ ( sK361 @ X0 ) @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f5296]) ).
thf(f5296,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( in @ ( sK361 @ X0 ) @ X0 )
= $true )
| ( ( ^ [Y0: $i] : ( emptyset != Y0 )
@ X0 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f3865,f4101,f3522]) ).
thf(f3522,plain,
nonemptyImpWitness = $true,
inference(cnf_transformation,[status(thm)],[f1631]) ).
thf(f3865,plain,
! [X0: $i] :
( ( ( in @ ( sK361 @ X0 ) @ X0 )
= $true )
| ( ( nonempty @ X0 )
!= $true )
| ( nonemptyImpWitness != $true ) ),
inference(cnf_transformation,[status(thm)],[f1973]) ).
thf(f1973,plain,
( ( ! [X0: $i] :
( ( ( in @ ( sK361 @ X0 ) @ X0 )
= $true )
| ( ( nonempty @ X0 )
!= $true ) )
| ( nonemptyImpWitness != $true ) )
& ( ( nonemptyImpWitness = $true )
| ( ! [X3: $i] :
( ( in @ X3 @ sK362 )
!= $true )
& ( ( nonempty @ sK362 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK361,sK362])],[f1970,f1972,f1971]) ).
thf(f1971,plain,
! [X0: $i] :
( ? [X1: $i] :
( ( in @ X1 @ X0 )
= $true )
=> ( ( in @ ( sK361 @ X0 ) @ X0 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1972,plain,
( ? [X2: $i] :
( ! [X3: $i] :
( $true
!= ( in @ X3 @ X2 ) )
& ( ( nonempty @ X2 )
= $true ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ sK362 )
!= $true )
& ( ( nonempty @ sK362 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1970,plain,
( ( ! [X0: $i] :
( ? [X1: $i] :
( ( in @ X1 @ X0 )
= $true )
| ( ( nonempty @ X0 )
!= $true ) )
| ( nonemptyImpWitness != $true ) )
& ( ( nonemptyImpWitness = $true )
| ? [X2: $i] :
( ! [X3: $i] :
( $true
!= ( in @ X3 @ X2 ) )
& ( ( nonempty @ X2 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f1969]) ).
thf(f1969,plain,
( ( ! [X0: $i] :
( ? [X1: $i] :
( ( in @ X1 @ X0 )
= $true )
| ( ( nonempty @ X0 )
!= $true ) )
| ( nonemptyImpWitness != $true ) )
& ( ( nonemptyImpWitness = $true )
| ? [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
!= $true )
& ( ( nonempty @ X0 )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f1350]) ).
thf(f1350,plain,
( ! [X0: $i] :
( ? [X1: $i] :
( ( in @ X1 @ X0 )
= $true )
| ( ( nonempty @ X0 )
!= $true ) )
<=> ( nonemptyImpWitness = $true ) ),
inference(ennf_transformation,[status(thm)],[f1005]) ).
thf(f1005,plain,
( ! [X0: $i] :
( ( ( nonempty @ X0 )
= $true )
=> ? [X1: $i] :
( ( in @ X1 @ X0 )
= $true ) )
<=> ( nonemptyImpWitness = $true ) ),
inference(true_and_false_elimination,[status(thm)],[f749]) ).
thf(f749,plain,
( ( nonemptyImpWitness = $true )
<=> ! [X0: $i] :
( ( ( nonempty @ X0 )
= $true )
=> ? [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& $true ) ) ),
inference(fool_elimination,[status(thm)],[f748]) ).
thf(f748,plain,
( nonemptyImpWitness
= ( ! [X0: $i] :
( ( nonempty @ X0 )
=> ? [X1: $i] :
( ( in @ X1 @ X0 )
& $true ) ) ) ),
inference(rectify,[status(thm)],[f45]) ).
thf(f45,axiom,
( nonemptyImpWitness
= ( ! [X3: $i] :
( ( nonempty @ X3 )
=> ? [X1: $i] :
( ( in @ X1 @ X3 )
& $true ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Th7rVCfvTI/DTF2THF_17306.p',nonemptyImpWitness) ).
thf(f6657,plain,
! [X3: $i,X0: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ ( sK306 @ X0 ) @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f5225]) ).
thf(f5225,plain,
! [X3: $i,X0: $i] :
( ( ( in @ ( sK306 @ X0 ) @ X0 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f3796,f3309]) ).
thf(f3309,plain,
foundationAx = $true,
inference(cnf_transformation,[status(thm)],[f1631]) ).
thf(f3796,plain,
! [X3: $i,X0: $i] :
( ( ( in @ ( sK306 @ X0 ) @ X0 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( foundationAx != $true ) ),
inference(cnf_transformation,[status(thm)],[f1894]) ).
thf(f1894,plain,
( ( ! [X0: $i] :
( ( ( ( in @ ( sK306 @ X0 ) @ X0 )
= $true )
& ! [X2: $i] :
( ( $true
!= ( in @ X2 @ ( sK306 @ X0 ) ) )
| ( $true
!= ( in @ X2 @ X0 ) ) ) )
| ! [X3: $i] :
( ( in @ X3 @ X0 )
!= $true ) )
| ( foundationAx != $true ) )
& ( ( foundationAx = $true )
| ( ! [X5: $i] :
( ( ( in @ X5 @ sK307 )
!= $true )
| ( ( $true
= ( in @ ( sK308 @ X5 ) @ X5 ) )
& ( ( in @ ( sK308 @ X5 ) @ sK307 )
= $true ) ) )
& ( ( in @ sK309 @ sK307 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK306,sK307,sK308,sK309])],[f1889,f1893,f1892,f1891,f1890]) ).
thf(f1890,plain,
! [X0: $i] :
( ? [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( $true
!= ( in @ X2 @ X0 ) ) ) )
=> ( ( ( in @ ( sK306 @ X0 ) @ X0 )
= $true )
& ! [X2: $i] :
( ( $true
!= ( in @ X2 @ ( sK306 @ X0 ) ) )
| ( $true
!= ( in @ X2 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1891,plain,
( ? [X4: $i] :
( ! [X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
| ? [X6: $i] :
( ( ( in @ X6 @ X5 )
= $true )
& ( ( in @ X6 @ X4 )
= $true ) ) )
& ? [X7: $i] :
( ( in @ X7 @ X4 )
= $true ) )
=> ( ! [X5: $i] :
( ( ( in @ X5 @ sK307 )
!= $true )
| ? [X6: $i] :
( ( ( in @ X6 @ X5 )
= $true )
& ( ( in @ X6 @ sK307 )
= $true ) ) )
& ? [X7: $i] :
( ( in @ X7 @ sK307 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1892,plain,
! [X5: $i] :
( ? [X6: $i] :
( ( ( in @ X6 @ X5 )
= $true )
& ( ( in @ X6 @ sK307 )
= $true ) )
=> ( ( $true
= ( in @ ( sK308 @ X5 ) @ X5 ) )
& ( ( in @ ( sK308 @ X5 ) @ sK307 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1893,plain,
( ? [X7: $i] :
( ( in @ X7 @ sK307 )
= $true )
=> ( ( in @ sK309 @ sK307 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1889,plain,
( ( ! [X0: $i] :
( ? [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( $true
!= ( in @ X2 @ X0 ) ) ) )
| ! [X3: $i] :
( ( in @ X3 @ X0 )
!= $true ) )
| ( foundationAx != $true ) )
& ( ( foundationAx = $true )
| ? [X4: $i] :
( ! [X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
| ? [X6: $i] :
( ( ( in @ X6 @ X5 )
= $true )
& ( ( in @ X6 @ X4 )
= $true ) ) )
& ? [X7: $i] :
( ( in @ X7 @ X4 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f1888]) ).
thf(f1888,plain,
( ( ! [X0: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X2 ) )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
| ! [X1: $i] :
( ( in @ X1 @ X0 )
!= $true ) )
| ( foundationAx != $true ) )
& ( ( foundationAx = $true )
| ? [X0: $i] :
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ X0 ) )
| ? [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
& ( ( in @ X3 @ X0 )
= $true ) ) )
& ? [X1: $i] :
( ( in @ X1 @ X0 )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f1045]) ).
thf(f1045,plain,
( ! [X0: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X2 ) )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
| ! [X1: $i] :
( ( in @ X1 @ X0 )
!= $true ) )
<=> ( foundationAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f843]) ).
thf(f843,plain,
( ! [X0: $i] :
( ? [X1: $i] :
( ( in @ X1 @ X0 )
= $true )
=> ? [X2: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
& ~ ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( $true
= ( in @ X3 @ X2 ) ) ) ) )
<=> ( foundationAx = $true ) ),
inference(fool_elimination,[status(thm)],[f842]) ).
thf(f842,plain,
( foundationAx
= ( ! [X0: $i] :
( ? [X1: $i] : ( in @ X1 @ X0 )
=> ? [X2: $i] :
( ~ ? [X3: $i] :
( ( in @ X3 @ X2 )
& ( in @ X3 @ X0 ) )
& ( in @ X2 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,axiom,
( foundationAx
= ( ! [X3: $i] :
( ? [X1: $i] : ( in @ X1 @ X3 )
=> ? [X4: $i] :
( ~ ? [X1: $i] :
( ( in @ X1 @ X4 )
& ( in @ X1 @ X3 ) )
& ( in @ X4 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Th7rVCfvTI/DTF2THF_17306.p',foundationAx) ).
thf(f24022,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK137 )
!= $true )
| ( ( in @ ( sK540 @ X0 @ sK137 ) @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f23970]) ).
thf(f23970,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK137 )
!= $true )
| ( ( in @ ( sK540 @ X0 @ sK137 ) @ X0 )
= $true )
| ( emptyset != emptyset ) ),
inference(superposition,[status(thm)],[f3495,f6904]) ).
thf(f6904,plain,
! [X3: $i,X4: $i] :
( ( emptyset
= ( binintersect @ X4 @ X3 ) )
| ( ( in @ ( sK540 @ X4 @ X3 ) @ X4 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f5517]) ).
thf(f5517,plain,
! [X3: $i,X4: $i] :
( ( $true != $true )
| ( emptyset
= ( binintersect @ X4 @ X3 ) )
| ( ( in @ ( sK540 @ X4 @ X3 ) @ X4 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f4112,f3388]) ).
thf(f3388,plain,
disjointsetsI1 = $true,
inference(cnf_transformation,[status(thm)],[f1631]) ).
thf(f4112,plain,
! [X3: $i,X4: $i] :
( ( emptyset
= ( binintersect @ X4 @ X3 ) )
| ( ( in @ ( sK540 @ X4 @ X3 ) @ X4 )
= $true )
| ( disjointsetsI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f2250]) ).
thf(f2250,plain,
( ( ( disjointsetsI1 = $true )
| ( ( emptyset
!= ( binintersect @ sK539 @ sK538 ) )
& ! [X2: $i] :
( ( ( in @ X2 @ sK539 )
!= $true )
| ( ( in @ X2 @ sK538 )
!= $true ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( emptyset
= ( binintersect @ X4 @ X3 ) )
| ( ( ( in @ ( sK540 @ X4 @ X3 ) @ X4 )
= $true )
& ( ( in @ ( sK540 @ X4 @ X3 ) @ X3 )
= $true ) ) )
| ( disjointsetsI1 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK538,sK539,sK540])],[f2247,f2249,f2248]) ).
thf(f2248,plain,
( ? [X0: $i,X1: $i] :
( ( emptyset
!= ( binintersect @ X1 @ X0 ) )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( $true
!= ( in @ X2 @ X0 ) ) ) )
=> ( ( emptyset
!= ( binintersect @ sK539 @ sK538 ) )
& ! [X2: $i] :
( ( ( in @ X2 @ sK539 )
!= $true )
| ( ( in @ X2 @ sK538 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2249,plain,
! [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
& ( ( in @ X5 @ X3 )
= $true ) )
=> ( ( ( in @ ( sK540 @ X4 @ X3 ) @ X4 )
= $true )
& ( ( in @ ( sK540 @ X4 @ X3 ) @ X3 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2247,plain,
( ( ( disjointsetsI1 = $true )
| ? [X0: $i,X1: $i] :
( ( emptyset
!= ( binintersect @ X1 @ X0 ) )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( $true
!= ( in @ X2 @ X0 ) ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( emptyset
= ( binintersect @ X4 @ X3 ) )
| ? [X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
& ( ( in @ X5 @ X3 )
= $true ) ) )
| ( disjointsetsI1 != $true ) ) ),
inference(rectify,[status(thm)],[f2246]) ).
thf(f2246,plain,
( ( ( disjointsetsI1 = $true )
| ? [X0: $i,X1: $i] :
( ( emptyset
!= ( binintersect @ X1 @ X0 ) )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( $true
!= ( in @ X2 @ X0 ) ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ( emptyset
= ( binintersect @ X1 @ X0 ) )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( $true
= ( in @ X2 @ X0 ) ) ) )
| ( disjointsetsI1 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f1179]) ).
thf(f1179,plain,
( ( disjointsetsI1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( emptyset
= ( binintersect @ X1 @ X0 ) )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( $true
= ( in @ X2 @ X0 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f627]) ).
thf(f627,plain,
( ( disjointsetsI1 = $true )
<=> ! [X0: $i,X1: $i] :
( ~ ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( $true
= ( in @ X2 @ X0 ) ) )
=> ( emptyset
= ( binintersect @ X1 @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f626]) ).
thf(f626,plain,
! [X0: $i,X1: $i] :
( ( ~ ? [X2: $i] :
( ( in @ X2 @ X0 )
& ( in @ X2 @ X1 ) )
=> ( emptyset
= ( binintersect @ X1 @ X0 ) ) )
= disjointsetsI1 ),
inference(rectify,[status(thm)],[f115]) ).
thf(f115,axiom,
! [X4: $i,X3: $i] :
( ( ~ ? [X1: $i] :
( ( in @ X1 @ X4 )
& ( in @ X1 @ X3 ) )
=> ( emptyset
= ( binintersect @ X3 @ X4 ) ) )
= disjointsetsI1 ),
file('/export/starexec/sandbox2/tmp/tmp.Th7rVCfvTI/DTF2THF_17306.p',disjointsetsI1) ).
thf(f3495,plain,
! [X1: $i] :
( ( emptyset
!= ( binintersect @ X1 @ sK137 ) )
| ( ( in @ X1 @ sK137 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1631]) ).
thf(f6929,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( sK306 @ X1 ) )
!= $true )
| ( $true
!= ( in @ X0 @ X1 ) ) ),
inference(condensation,[status(thm)],[f6928]) ).
thf(f6928,plain,
! [X2: $i,X3: $i,X0: $i] :
( ( $true
!= ( in @ X2 @ X0 ) )
| ( ( in @ X3 @ X0 )
!= $true )
| ( $true
!= ( in @ X2 @ ( sK306 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f5226]) ).
thf(f5226,plain,
! [X2: $i,X3: $i,X0: $i] :
( ( $true
!= ( in @ X2 @ X0 ) )
| ( $true != $true )
| ( $true
!= ( in @ X2 @ ( sK306 @ X0 ) ) )
| ( ( in @ X3 @ X0 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f3795,f3309]) ).
thf(f3795,plain,
! [X2: $i,X3: $i,X0: $i] :
( ( $true
!= ( in @ X2 @ ( sK306 @ X0 ) ) )
| ( $true
!= ( in @ X2 @ X0 ) )
| ( ( in @ X3 @ X0 )
!= $true )
| ( foundationAx != $true ) ),
inference(cnf_transformation,[status(thm)],[f1894]) ).
thf(f44973,plain,
( ( ( in @ ( sK540 @ ( sK306 @ sK137 ) @ sK137 ) @ sK137 )
= $true )
| ( emptyset = sK137 ) ),
inference(trivial_inequality_removal,[status(thm)],[f44965]) ).
thf(f44965,plain,
( ( emptyset = sK137 )
| ( ( in @ ( sK540 @ ( sK306 @ sK137 ) @ sK137 ) @ sK137 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f24524,f8023]) ).
thf(f24524,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK137 )
!= $true )
| ( $true
= ( in @ ( sK540 @ X0 @ sK137 ) @ sK137 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f24472]) ).
thf(f24472,plain,
! [X0: $i] :
( ( $true
= ( in @ ( sK540 @ X0 @ sK137 ) @ sK137 ) )
| ( ( in @ X0 @ sK137 )
!= $true )
| ( emptyset != emptyset ) ),
inference(superposition,[status(thm)],[f3495,f7007]) ).
thf(f7007,plain,
! [X3: $i,X4: $i] :
( ( emptyset
= ( binintersect @ X4 @ X3 ) )
| ( ( in @ ( sK540 @ X4 @ X3 ) @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f5518]) ).
thf(f5518,plain,
! [X3: $i,X4: $i] :
( ( $true != $true )
| ( ( in @ ( sK540 @ X4 @ X3 ) @ X3 )
= $true )
| ( emptyset
= ( binintersect @ X4 @ X3 ) ) ),
inference(definition_unfolding,[status(thm)],[f4111,f3388]) ).
thf(f4111,plain,
! [X3: $i,X4: $i] :
( ( emptyset
= ( binintersect @ X4 @ X3 ) )
| ( ( in @ ( sK540 @ X4 @ X3 ) @ X3 )
= $true )
| ( disjointsetsI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f2250]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU805^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n001.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 12:35:20 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.45 ---- Original DTF file ---
% 0.20/0.45 thf(spec,logic,$$dhol).
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 % File : SEU805^1 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.45 % Domain : Set Theory
% 0.20/0.45 % Problem : The Foundation Axiom
% 0.20/0.45 % Version : Especial.
% 0.20/0.45 % English : (! A:i.nonempty A -> (? X:i.in X A & binintersect X A = emptyset))
% 0.20/0.45
% 0.20/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.20/0.45 % Source : [Bro08]
% 0.20/0.45 % Names : ZFC307g [Bro08]
% 0.20/0.45
% 0.20/0.45 % Status : Theorem
% 0.20/0.45 % Rating : 0.67 v9.1.0, 0.62 v9.0.0, 0.70 v8.2.0, 0.62 v8.1.0, 0.55 v7.5.0, 0.57 v7.4.0, 0.44 v7.3.0, 0.56 v7.2.0, 0.50 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.80 v6.2.0, 1.00 v6.0.0, 0.71 v5.5.0, 0.67 v5.4.0, 1.00 v3.7.0
% 0.20/0.45 % Syntax : Number of formulae : 698 ( 323 unt; 374 typ; 323 def)
% 0.20/0.45 % Number of atoms : 1994 ( 465 equ; 0 cnn)
% 0.20/0.45 % Maximal formula atoms : 324 ( 6 avg)
% 0.20/0.45 % Number of connectives : 4383 ( 74 ~; 14 |; 54 &;3192 @)
% 0.20/0.45 % ( 17 <=>;1032 =>; 0 <=; 0 <~>)
% 0.20/0.45 % Maximal formula depth : 328 ( 2 avg)
% 0.20/0.45 % Number of types : 2 ( 0 usr)
% 0.20/0.45 % Number of type conns : 176 ( 176 >; 0 *; 0 +; 0 <<)
% 0.20/0.45 % Number of symbols : 377 ( 374 usr; 325 con; 0-4 aty)
% 0.20/0.45 % Number of variables : 1143 ( 75 ^;1024 !; 44 ?;1143 :)
% 0.20/0.45 % SPC : TH0_THM_EQU_NAR
% 0.20/0.45
% 0.20/0.45 % Comments : http://mathgate.info/detsetitem.php?id=429
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 thf(in_type,type,
% 0.20/0.45 in: $i > $i > $o ).
% 0.20/0.45
% 0.20/0.45 thf(exu_type,type,
% 0.20/0.45 exu: ( $i > $o ) > $o ).
% 0.20/0.45
% 0.20/0.45 thf(exu,definition,
% 0.20/0.45 ( exu
% 0.20/0.45 = ( ^ [Xphi: $i > $o] :
% 0.20/0.45 ? [Xx: $i] :
% 0.20/0.45 ( ( Xphi @ Xx )
% 0.20/0.45 & ! [Xy: $i] :
% 0.20/0.45 ( ( Xphi @ Xy )
% 0.20/0.45 => ( Xx = Xy ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(setextAx_type,type,
% 0.20/0.45 setextAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(setextAx,definition,
% 0.20/0.45 ( setextAx
% 0.20/0.45 = ( ! [A: $i,B: $i] :
% 0.20/0.45 ( ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ A )
% 0.20/0.45 <=> ( in @ Xx @ B ) )
% 0.20/0.45 => ( A = B ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(emptyset_type,type,
% 0.20/0.45 emptyset: $i ).
% 0.20/0.45
% 0.20/0.45 thf(emptysetAx_type,type,
% 0.20/0.45 emptysetAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(emptysetAx,definition,
% 0.20/0.45 ( emptysetAx
% 0.20/0.45 = ( ! [Xx: $i] :
% 0.20/0.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(setadjoin_type,type,
% 0.20/0.45 setadjoin: $i > $i > $i ).
% 0.20/0.45
% 0.20/0.45 thf(setadjoinAx_type,type,
% 0.20/0.45 setadjoinAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(setadjoinAx,definition,
% 0.20/0.45 ( setadjoinAx
% 0.20/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.45 <=> ( ( Xy = Xx )
% 0.20/0.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(powerset_type,type,
% 0.20/0.45 powerset: $i > $i ).
% 0.20/0.45
% 0.20/0.45 thf(powersetAx_type,type,
% 0.20/0.45 powersetAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(powersetAx,definition,
% 0.20/0.45 ( powersetAx
% 0.20/0.45 = ( ! [A: $i,B: $i] :
% 0.20/0.45 ( ( in @ B @ ( powerset @ A ) )
% 0.20/0.45 <=> ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ B )
% 0.20/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(setunion_type,type,
% 0.20/0.45 setunion: $i > $i ).
% 0.20/0.45
% 0.20/0.45 thf(setunionAx_type,type,
% 0.20/0.45 setunionAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(setunionAx,definition,
% 0.20/0.45 ( setunionAx
% 0.20/0.45 = ( ! [A: $i,Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ ( setunion @ A ) )
% 0.20/0.45 <=> ? [B: $i] :
% 0.20/0.45 ( ( in @ Xx @ B )
% 0.20/0.45 & ( in @ B @ A ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(omega_type,type,
% 0.20/0.45 omega: $i ).
% 0.20/0.45
% 0.20/0.45 thf(omega0Ax_type,type,
% 0.20/0.45 omega0Ax: $o ).
% 0.20/0.45
% 0.20/0.45 thf(omega0Ax,definition,
% 0.20/0.45 ( omega0Ax
% 0.20/0.45 = ( in @ emptyset @ omega ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(omegaSAx_type,type,
% 0.20/0.45 omegaSAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(omegaSAx,definition,
% 0.20/0.45 ( omegaSAx
% 0.20/0.45 = ( ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ omega )
% 0.20/0.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(omegaIndAx_type,type,
% 0.20/0.45 omegaIndAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(omegaIndAx,definition,
% 0.20/0.45 ( omegaIndAx
% 0.20/0.45 = ( ! [A: $i] :
% 0.20/0.45 ( ( ( in @ emptyset @ A )
% 0.20/0.45 & ! [Xx: $i] :
% 0.20/0.45 ( ( ( in @ Xx @ omega )
% 0.20/0.45 & ( in @ Xx @ A ) )
% 0.20/0.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.20/0.45 => ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ omega )
% 0.20/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(replAx_type,type,
% 0.20/0.45 replAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(replAx,definition,
% 0.20/0.45 ( replAx
% 0.20/0.45 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.20/0.45 ( ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ A )
% 0.20/0.45 => ( exu
% 0.20/0.45 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.20/0.45 => ? [B: $i] :
% 0.20/0.45 ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ B )
% 0.20/0.45 <=> ? [Xy: $i] :
% 0.20/0.45 ( ( in @ Xy @ A )
% 0.20/0.45 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(foundationAx_type,type,
% 0.20/0.45 foundationAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(foundationAx,definition,
% 0.20/0.45 ( foundationAx
% 0.20/0.45 = ( ! [A: $i] :
% 0.20/0.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.20/0.45 => ? [B: $i] :
% 0.20/0.45 ( ( in @ B @ A )
% 0.20/0.45 & ~ ? [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ B )
% 0.20/0.45 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(wellorderingAx_type,type,
% 0.20/0.45 wellorderingAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(wellorderingAx,definition,
% 0.20/0.45 ( wellorderingAx
% 0.20/0.45 = ( ! [A: $i] :
% 0.20/0.45 ? [B: $i] :
% 0.20/0.45 ( ! [C: $i] :
% 0.20/0.45 ( ( in @ C @ B )
% 0.20/0.45 => ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ C )
% 0.20/0.45 => ( in @ Xx @ A ) ) )
% 0.20/0.45 & ! [Xx: $i,Xy: $i] :
% 0.20/0.45 ( ( ( in @ Xx @ A )
% 0.20/0.45 & ( in @ Xy @ A ) )
% 0.20/0.45 => ( ! [C: $i] :
% 0.20/0.45 ( ( in @ C @ B )
% 0.20/0.45 => ( ( in @ Xx @ C )
% 0.20/0.45 <=> ( in @ Xy @ C ) ) )
% 0.20/0.45 => ( Xx = Xy ) ) )
% 0.20/0.45 & ! [C: $i,D: $i] :
% 0.20/0.45 ( ( ( in @ C @ B )
% 0.20/0.45 & ( in @ D @ B ) )
% 0.20/0.45 => ( ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ C )
% 0.20/0.45 => ( in @ Xx @ D ) )
% 0.20/0.45 | ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ D )
% 0.20/0.45 => ( in @ Xx @ C ) ) ) )
% 0.20/0.45 & ! [C: $i] :
% 0.20/0.45 ( ( ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ C )
% 0.20/0.45 => ( in @ Xx @ A ) )
% 0.20/0.45 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.20/0.45 => ? [D: $i,Xx: $i] :
% 0.20/0.45 ( ( in @ D @ B )
% 0.20/0.45 & ( in @ Xx @ C )
% 0.20/0.45 & ~ ? [Xy: $i] :
% 0.20/0.45 ( ( in @ Xy @ D )
% 0.20/0.45 & ( in @ Xy @ C ) )
% 0.20/0.45 & ! [E: $i] :
% 0.20/0.45 ( ( in @ E @ B )
% 0.20/0.45 => ( ! [Xy: $i] :
% 0.20/0.45 ( ( in @ Xy @ E )
% 0.20/0.45 => ( in @ Xy @ D ) )
% 0.20/0.45 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(descr_type,type,
% 0.20/0.45 descr: ( $i > $o ) > $i ).
% 0.20/0.45
% 0.20/0.45 thf(descrp_type,type,
% 0.20/0.45 descrp: $o ).
% 0.20/0.45
% 0.20/0.45 thf(descrp,definition,
% 0.20/0.45 ( descrp
% 0.20/0.45 = ( ! [Xphi: $i > $o] :
% 0.20/0.45 ( ( exu
% 0.20/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.45 => ( Xphi
% 0.20/0.45 @ ( descr
% 0.20/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(dsetconstr_type,type,
% 0.20/0.45 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.20/0.45
% 0.20/0.45 thf(dsetconstrI_type,type,
% 0.20/0.45 dsetconstrI: $o ).
% 0.20/0.45
% 0.20/0.45 thf(dsetconstrI,definition,
% 0.20/0.45 ( dsetconstrI
% 0.20/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ A )
% 0.20/0.45 => ( ( Xphi @ Xx )
% 0.20/0.45 => ( in @ Xx
% 0.20/0.45 @ ( dsetconstr @ A
% 0.20/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(dsetconstrEL_type,type,
% 0.20/0.45 dsetconstrEL: $o ).
% 0.20/0.45
% 0.20/0.45 thf(dsetconstrEL,definition,
% 0.20/0.45 ( dsetconstrEL
% 0.20/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.45 ( ( in @ Xx
% 0.20/0.45 @ ( dsetconstr @ A
% 0.20/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.45 => ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(dsetconstrER_type,type,
% 0.20/0.45 dsetconstrER: $o ).
% 0.20/0.45
% 0.20/0.45 thf(dsetconstrER,definition,
% 0.20/0.45 ( dsetconstrER
% 0.20/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.45 ( ( in @ Xx
% 0.20/0.45 @ ( dsetconstr @ A
% 0.20/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.45 => ( Xphi @ Xx ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(exuE1_type,type,
% 0.20/0.45 exuE1: $o ).
% 0.20/0.45
% 0.20/0.45 thf(exuE1,definition,
% 0.20/0.45 ( exuE1
% 0.20/0.45 = ( ! [Xphi: $i > $o] :
% 0.20/0.45 ( ( exu
% 0.20/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.45 => ? [Xx: $i] :
% 0.20/0.45 ( ( Xphi @ Xx )
% 0.20/0.45 & ! [Xy: $i] :
% 0.20/0.45 ( ( Xphi @ Xy )
% 0.20/0.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(prop2set_type,type,
% 0.20/0.45 prop2set: $o > $i ).
% 0.20/0.45
% 0.20/0.45 thf(prop2setE_type,type,
% 0.20/0.45 prop2setE: $o ).
% 0.20/0.45
% 0.20/0.45 thf(prop2setE,definition,
% 0.20/0.45 ( prop2setE
% 0.20/0.45 = ( ! [Xphi: $o,Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.20/0.45 => Xphi ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(emptysetE_type,type,
% 0.20/0.45 emptysetE: $o ).
% 0.20/0.45
% 0.20/0.45 thf(emptysetE,definition,
% 0.20/0.45 ( emptysetE
% 0.20/0.45 = ( ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ emptyset )
% 0.20/0.45 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(emptysetimpfalse_type,type,
% 0.20/0.45 emptysetimpfalse: $o ).
% 0.20/0.45
% 0.20/0.45 thf(emptysetimpfalse,definition,
% 0.20/0.45 ( emptysetimpfalse
% 0.20/0.45 = ( ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ emptyset )
% 0.20/0.45 => $false ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(notinemptyset_type,type,
% 0.20/0.45 notinemptyset: $o ).
% 0.20/0.45
% 0.20/0.45 thf(notinemptyset,definition,
% 0.20/0.45 ( notinemptyset
% 0.20/0.45 = ( ! [Xx: $i] :
% 0.20/0.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(exuE3e_type,type,
% 0.20/0.45 exuE3e: $o ).
% 0.20/0.45
% 0.20/0.45 thf(exuE3e,definition,
% 0.20/0.45 ( exuE3e
% 0.20/0.45 = ( ! [Xphi: $i > $o] :
% 0.20/0.45 ( ( exu
% 0.20/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.45 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(setext_type,type,
% 0.20/0.45 setext: $o ).
% 0.20/0.45
% 0.20/0.45 thf(setext,definition,
% 0.20/0.45 ( setext
% 0.20/0.45 = ( ! [A: $i,B: $i] :
% 0.20/0.45 ( ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ A )
% 0.20/0.45 => ( in @ Xx @ B ) )
% 0.20/0.45 => ( ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ B )
% 0.20/0.45 => ( in @ Xx @ A ) )
% 0.20/0.45 => ( A = B ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(emptyI_type,type,
% 0.20/0.45 emptyI: $o ).
% 0.20/0.45
% 0.20/0.45 thf(emptyI,definition,
% 0.20/0.45 ( emptyI
% 0.20/0.45 = ( ! [A: $i] :
% 0.20/0.45 ( ! [Xx: $i] :
% 0.20/0.45 ~ ( in @ Xx @ A )
% 0.20/0.45 => ( A = emptyset ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(noeltsimpempty_type,type,
% 0.20/0.45 noeltsimpempty: $o ).
% 0.20/0.45
% 0.20/0.45 thf(noeltsimpempty,definition,
% 0.20/0.45 ( noeltsimpempty
% 0.20/0.45 = ( ! [A: $i] :
% 0.20/0.45 ( ! [Xx: $i] :
% 0.20/0.45 ~ ( in @ Xx @ A )
% 0.20/0.45 => ( A = emptyset ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(setbeta_type,type,
% 0.20/0.45 setbeta: $o ).
% 0.20/0.45
% 0.20/0.45 thf(setbeta,definition,
% 0.20/0.45 ( setbeta
% 0.20/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ A )
% 0.20/0.45 => ( ( in @ Xx
% 0.20/0.45 @ ( dsetconstr @ A
% 0.20/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.45 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(nonempty_type,type,
% 0.20/0.45 nonempty: $i > $o ).
% 0.20/0.45
% 0.20/0.45 thf(nonempty,definition,
% 0.20/0.45 ( nonempty
% 0.20/0.45 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(nonemptyE1_type,type,
% 0.20/0.45 nonemptyE1: $o ).
% 0.20/0.45
% 0.20/0.45 thf(nonemptyE1,definition,
% 0.20/0.45 ( nonemptyE1
% 0.20/0.45 = ( ! [A: $i] :
% 0.20/0.45 ( ( nonempty @ A )
% 0.20/0.45 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(nonemptyI_type,type,
% 0.20/0.45 nonemptyI: $o ).
% 0.20/0.45
% 0.20/0.45 thf(nonemptyI,definition,
% 0.20/0.45 ( nonemptyI
% 0.20/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ A )
% 0.20/0.45 => ( ( Xphi @ Xx )
% 0.20/0.45 => ( nonempty
% 0.20/0.45 @ ( dsetconstr @ A
% 0.20/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(nonemptyI1_type,type,
% 0.20/0.45 nonemptyI1: $o ).
% 0.20/0.45
% 0.20/0.45 thf(nonemptyI1,definition,
% 0.20/0.45 ( nonemptyI1
% 0.20/0.45 = ( ! [A: $i] :
% 0.20/0.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.20/0.45 => ( nonempty @ A ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(setadjoinIL_type,type,
% 0.20/0.45 setadjoinIL: $o ).
% 0.20/0.45
% 0.20/0.45 thf(setadjoinIL,definition,
% 0.20/0.45 ( setadjoinIL
% 0.20/0.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(emptyinunitempty_type,type,
% 0.20/0.45 emptyinunitempty: $o ).
% 0.20/0.45
% 0.20/0.45 thf(emptyinunitempty,definition,
% 0.20/0.45 ( emptyinunitempty
% 0.20/0.45 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(setadjoinIR_type,type,
% 0.20/0.45 setadjoinIR: $o ).
% 0.20/0.45
% 0.20/0.45 thf(setadjoinIR,definition,
% 0.20/0.45 ( setadjoinIR
% 0.20/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.45 ( ( in @ Xy @ A )
% 0.20/0.45 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(setadjoinE_type,type,
% 0.20/0.45 setadjoinE: $o ).
% 0.20/0.45
% 0.20/0.45 thf(setadjoinE,definition,
% 0.20/0.45 ( setadjoinE
% 0.20/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.45 => ! [Xphi: $o] :
% 0.20/0.45 ( ( ( Xy = Xx )
% 0.20/0.45 => Xphi )
% 0.20/0.45 => ( ( ( in @ Xy @ A )
% 0.20/0.45 => Xphi )
% 0.20/0.45 => Xphi ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(setadjoinOr_type,type,
% 0.20/0.45 setadjoinOr: $o ).
% 0.20/0.45
% 0.20/0.45 thf(setadjoinOr,definition,
% 0.20/0.45 ( setadjoinOr
% 0.20/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.45 => ( ( Xy = Xx )
% 0.20/0.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(setoftrueEq_type,type,
% 0.20/0.45 setoftrueEq: $o ).
% 0.20/0.45
% 0.20/0.45 thf(setoftrueEq,definition,
% 0.20/0.45 ( setoftrueEq
% 0.20/0.45 = ( ! [A: $i] :
% 0.20/0.45 ( ( dsetconstr @ A
% 0.20/0.45 @ ^ [Xx: $i] : $true )
% 0.20/0.45 = A ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(powersetI_type,type,
% 0.20/0.45 powersetI: $o ).
% 0.20/0.45
% 0.20/0.45 thf(powersetI,definition,
% 0.20/0.45 ( powersetI
% 0.20/0.45 = ( ! [A: $i,B: $i] :
% 0.20/0.45 ( ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ B )
% 0.20/0.45 => ( in @ Xx @ A ) )
% 0.20/0.45 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(emptyinPowerset_type,type,
% 0.20/0.45 emptyinPowerset: $o ).
% 0.20/0.45
% 0.20/0.45 thf(emptyinPowerset,definition,
% 0.20/0.45 ( emptyinPowerset
% 0.20/0.45 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(emptyInPowerset_type,type,
% 0.20/0.45 emptyInPowerset: $o ).
% 0.20/0.45
% 0.20/0.45 thf(emptyInPowerset,definition,
% 0.20/0.45 ( emptyInPowerset
% 0.20/0.45 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(powersetE_type,type,
% 0.20/0.45 powersetE: $o ).
% 0.20/0.45
% 0.20/0.45 thf(powersetE,definition,
% 0.20/0.45 ( powersetE
% 0.20/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.45 ( ( in @ B @ ( powerset @ A ) )
% 0.20/0.45 => ( ( in @ Xx @ B )
% 0.20/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(setunionI_type,type,
% 0.20/0.45 setunionI: $o ).
% 0.20/0.45
% 0.20/0.45 thf(setunionI,definition,
% 0.20/0.45 ( setunionI
% 0.20/0.45 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.20/0.45 ( ( in @ Xx @ B )
% 0.20/0.45 => ( ( in @ B @ A )
% 0.20/0.45 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(setunionE_type,type,
% 0.20/0.45 setunionE: $o ).
% 0.20/0.45
% 0.20/0.45 thf(setunionE,definition,
% 0.20/0.45 ( setunionE
% 0.20/0.45 = ( ! [A: $i,Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ ( setunion @ A ) )
% 0.20/0.45 => ! [Xphi: $o] :
% 0.20/0.45 ( ! [B: $i] :
% 0.20/0.45 ( ( in @ Xx @ B )
% 0.20/0.45 => ( ( in @ B @ A )
% 0.20/0.45 => Xphi ) )
% 0.20/0.45 => Xphi ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(subPowSU_type,type,
% 0.20/0.45 subPowSU: $o ).
% 0.20/0.45
% 0.20/0.45 thf(subPowSU,definition,
% 0.20/0.45 ( subPowSU
% 0.20/0.45 = ( ! [A: $i,Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ A )
% 0.20/0.45 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(exuE2_type,type,
% 0.20/0.45 exuE2: $o ).
% 0.20/0.45
% 0.20/0.45 thf(exuE2,definition,
% 0.20/0.45 ( exuE2
% 0.20/0.45 = ( ! [Xphi: $i > $o] :
% 0.20/0.45 ( ( exu
% 0.20/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.45 => ? [Xx: $i] :
% 0.20/0.45 ! [Xy: $i] :
% 0.20/0.45 ( ( Xphi @ Xy )
% 0.20/0.45 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(nonemptyImpWitness_type,type,
% 0.20/0.45 nonemptyImpWitness: $o ).
% 0.20/0.45
% 0.20/0.45 thf(nonemptyImpWitness,definition,
% 0.20/0.45 ( nonemptyImpWitness
% 0.20/0.45 = ( ! [A: $i] :
% 0.20/0.45 ( ( nonempty @ A )
% 0.20/0.45 => ? [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ A )
% 0.20/0.46 & $true ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(uniqinunit_type,type,
% 0.20/0.46 uniqinunit: $o ).
% 0.20/0.46
% 0.20/0.46 thf(uniqinunit,definition,
% 0.20/0.46 ( uniqinunit
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(notinsingleton_type,type,
% 0.20/0.46 notinsingleton: $o ).
% 0.20/0.46
% 0.20/0.46 thf(notinsingleton,definition,
% 0.20/0.46 ( notinsingleton
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx != Xy )
% 0.20/0.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(eqinunit_type,type,
% 0.20/0.46 eqinunit: $o ).
% 0.20/0.46
% 0.20/0.46 thf(eqinunit,definition,
% 0.20/0.46 ( eqinunit
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(singletonsswitch_type,type,
% 0.20/0.46 singletonsswitch: $o ).
% 0.20/0.46
% 0.20/0.46 thf(singletonsswitch,definition,
% 0.20/0.46 ( singletonsswitch
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.20/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(upairsetE_type,type,
% 0.20/0.46 upairsetE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairsetE,definition,
% 0.20/0.46 ( upairsetE
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.20/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.20/0.46 => ( ( Xz = Xx )
% 0.20/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(upairsetIL_type,type,
% 0.20/0.46 upairsetIL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairsetIL,definition,
% 0.20/0.46 ( upairsetIL
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(upairsetIR_type,type,
% 0.20/0.46 upairsetIR: $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairsetIR,definition,
% 0.20/0.46 ( upairsetIR
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptyE1_type,type,
% 0.20/0.46 emptyE1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptyE1,definition,
% 0.20/0.46 ( emptyE1
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( Xphi @ Xx ) )
% 0.20/0.46 => ( ( ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 = emptyset )
% 0.20/0.46 => $false ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(vacuousDall_type,type,
% 0.20/0.46 vacuousDall: $o ).
% 0.20/0.46
% 0.20/0.46 thf(vacuousDall,definition,
% 0.20/0.46 ( vacuousDall
% 0.20/0.46 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ emptyset )
% 0.20/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan1_type,type,
% 0.20/0.46 quantDeMorgan1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan1,definition,
% 0.20/0.46 ( quantDeMorgan1
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ~ ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( Xphi @ Xx ) )
% 0.20/0.46 => ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan2_type,type,
% 0.20/0.46 quantDeMorgan2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan2,definition,
% 0.20/0.46 ( quantDeMorgan2
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ~ ( Xphi @ Xx ) )
% 0.20/0.46 => ~ ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan3_type,type,
% 0.20/0.46 quantDeMorgan3: $o ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan3,definition,
% 0.20/0.46 ( quantDeMorgan3
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ~ ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( Xphi @ Xx ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan4_type,type,
% 0.20/0.46 quantDeMorgan4: $o ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan4,definition,
% 0.20/0.46 ( quantDeMorgan4
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ~ ( Xphi @ Xx ) )
% 0.20/0.46 => ~ ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(prop2setI_type,type,
% 0.20/0.46 prop2setI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(prop2setI,definition,
% 0.20/0.46 ( prop2setI
% 0.20/0.46 = ( ! [Xphi: $o] :
% 0.20/0.46 ( Xphi
% 0.20/0.46 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(set2prop_type,type,
% 0.20/0.46 set2prop: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(prop2set2propI_type,type,
% 0.20/0.46 prop2set2propI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(prop2set2propI,definition,
% 0.20/0.46 ( prop2set2propI
% 0.20/0.46 = ( ! [Xphi: $o] :
% 0.20/0.46 ( Xphi
% 0.20/0.46 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(notdexE_type,type,
% 0.20/0.46 notdexE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(notdexE,definition,
% 0.20/0.46 ( notdexE
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ~ ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( Xphi @ Xx ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(notdallE_type,type,
% 0.20/0.46 notdallE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(notdallE,definition,
% 0.20/0.46 ( notdallE
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ~ ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( Xphi @ Xx ) )
% 0.20/0.46 => ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuI1_type,type,
% 0.20/0.46 exuI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuI1,definition,
% 0.20/0.46 ( exuI1
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ? [Xx: $i] :
% 0.20/0.46 ( ( Xphi @ Xx )
% 0.20/0.46 & ! [Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) )
% 0.20/0.46 => ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuI3_type,type,
% 0.20/0.46 exuI3: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuI3,definition,
% 0.20/0.46 ( exuI3
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.20/0.46 => ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xx )
% 0.20/0.46 => ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) )
% 0.20/0.46 => ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuI2_type,type,
% 0.20/0.46 exuI2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuI2,definition,
% 0.20/0.46 ( exuI2
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ? [Xx: $i] :
% 0.20/0.46 ! [Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xy )
% 0.20/0.46 <=> ( Xy = Xx ) )
% 0.20/0.46 => ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(inCongP_type,type,
% 0.20/0.46 inCongP: $o ).
% 0.20/0.46
% 0.20/0.46 thf(inCongP,definition,
% 0.20/0.46 ( inCongP
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(in__Cong_type,type,
% 0.20/0.46 in__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(in__Cong,definition,
% 0.20/0.46 ( in__Cong
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ( ( in @ Xx @ A )
% 0.20/0.46 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuE3u_type,type,
% 0.20/0.46 exuE3u: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuE3u,definition,
% 0.20/0.46 ( exuE3u
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xx )
% 0.20/0.46 => ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exu__Cong_type,type,
% 0.20/0.46 exu__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exu__Cong,definition,
% 0.20/0.46 ( exu__Cong
% 0.20/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.20/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.20/0.46 => ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 <=> ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptyset__Cong_type,type,
% 0.20/0.46 emptyset__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptyset__Cong,definition,
% 0.20/0.46 ( emptyset__Cong
% 0.20/0.46 = ( emptyset = emptyset ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoin__Cong_type,type,
% 0.20/0.46 setadjoin__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoin__Cong,definition,
% 0.20/0.46 ( setadjoin__Cong
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ! [Xz: $i,Xu: $i] :
% 0.20/0.46 ( ( Xz = Xu )
% 0.20/0.46 => ( ( setadjoin @ Xx @ Xz )
% 0.20/0.46 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powerset__Cong_type,type,
% 0.20/0.46 powerset__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powerset__Cong,definition,
% 0.20/0.46 ( powerset__Cong
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ( ( powerset @ A )
% 0.20/0.46 = ( powerset @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setunion__Cong_type,type,
% 0.20/0.46 setunion__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setunion__Cong,definition,
% 0.20/0.46 ( setunion__Cong
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ( ( setunion @ A )
% 0.20/0.46 = ( setunion @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(omega__Cong_type,type,
% 0.20/0.46 omega__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(omega__Cong,definition,
% 0.20/0.46 ( omega__Cong
% 0.20/0.46 = ( omega = omega ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuEu_type,type,
% 0.20/0.46 exuEu: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuEu,definition,
% 0.20/0.46 ( exuEu
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xx )
% 0.20/0.46 => ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(descr__Cong_type,type,
% 0.20/0.46 descr__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(descr__Cong,definition,
% 0.20/0.46 ( descr__Cong
% 0.20/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.20/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.20/0.46 => ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.20/0.46 => ( ( descr
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 = ( descr
% 0.20/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstr__Cong_type,type,
% 0.20/0.46 dsetconstr__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstr__Cong,definition,
% 0.20/0.46 ( dsetconstr__Cong
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( Xx = Xy )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.20/0.46 => ( ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 = ( dsetconstr @ B
% 0.20/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subset_type,type,
% 0.20/0.46 subset: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(disjoint_type,type,
% 0.20/0.46 disjoint: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(setsmeet_type,type,
% 0.20/0.46 setsmeet: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetI1_type,type,
% 0.20/0.46 subsetI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetI1,definition,
% 0.20/0.46 ( subsetI1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ B ) )
% 0.20/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(eqimpsubset2_type,type,
% 0.20/0.46 eqimpsubset2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(eqimpsubset2,definition,
% 0.20/0.46 ( eqimpsubset2
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(eqimpsubset1_type,type,
% 0.20/0.46 eqimpsubset1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(eqimpsubset1,definition,
% 0.20/0.46 ( eqimpsubset1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subsetI2_type,type,
% 0.20/0.46 subsetI2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetI2,definition,
% 0.20/0.46 ( subsetI2
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ B ) )
% 0.20/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptysetsubset_type,type,
% 0.20/0.46 emptysetsubset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptysetsubset,definition,
% 0.20/0.46 ( emptysetsubset
% 0.20/0.46 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subsetE_type,type,
% 0.20/0.46 subsetE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetE,definition,
% 0.20/0.46 ( subsetE
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subsetE2_type,type,
% 0.20/0.46 subsetE2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetE2,definition,
% 0.20/0.46 ( subsetE2
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(notsubsetI_type,type,
% 0.20/0.46 notsubsetI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(notsubsetI,definition,
% 0.20/0.46 ( notsubsetI
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(notequalI1_type,type,
% 0.20/0.46 notequalI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(notequalI1,definition,
% 0.20/0.46 ( notequalI1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ~ ( subset @ A @ B )
% 0.20/0.46 => ( A != B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(notequalI2_type,type,
% 0.20/0.46 notequalI2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(notequalI2,definition,
% 0.20/0.46 ( notequalI2
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => ( A != B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subsetRefl_type,type,
% 0.20/0.46 subsetRefl: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetRefl,definition,
% 0.20/0.46 ( subsetRefl
% 0.20/0.46 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subsetTrans_type,type,
% 0.20/0.46 subsetTrans: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetTrans,definition,
% 0.20/0.46 ( subsetTrans
% 0.20/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( ( subset @ B @ C )
% 0.20/0.46 => ( subset @ A @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinSub_type,type,
% 0.20/0.46 setadjoinSub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinSub,definition,
% 0.20/0.46 ( setadjoinSub
% 0.20/0.46 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinSub2_type,type,
% 0.20/0.46 setadjoinSub2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinSub2,definition,
% 0.20/0.46 ( setadjoinSub2
% 0.20/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subset2powerset_type,type,
% 0.20/0.46 subset2powerset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subset2powerset,definition,
% 0.20/0.46 ( subset2powerset
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setextsub_type,type,
% 0.20/0.46 setextsub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setextsub,definition,
% 0.20/0.46 ( setextsub
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( ( subset @ B @ A )
% 0.20/0.46 => ( A = B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subsetemptysetimpeq_type,type,
% 0.20/0.46 subsetemptysetimpeq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetemptysetimpeq,definition,
% 0.20/0.46 ( subsetemptysetimpeq
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ( subset @ A @ emptyset )
% 0.20/0.46 => ( A = emptyset ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powersetI1_type,type,
% 0.20/0.46 powersetI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetI1,definition,
% 0.20/0.46 ( powersetI1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( subset @ B @ A )
% 0.20/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powersetE1_type,type,
% 0.20/0.46 powersetE1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetE1,definition,
% 0.20/0.46 ( powersetE1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.20/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(inPowerset_type,type,
% 0.20/0.46 inPowerset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(inPowerset,definition,
% 0.20/0.46 ( inPowerset
% 0.20/0.46 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powersetsubset_type,type,
% 0.20/0.46 powersetsubset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetsubset,definition,
% 0.20/0.46 ( powersetsubset
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sepInPowerset_type,type,
% 0.20/0.46 sepInPowerset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(sepInPowerset,definition,
% 0.20/0.46 ( sepInPowerset
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( in
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 @ ( powerset @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sepSubset_type,type,
% 0.20/0.46 sepSubset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(sepSubset,definition,
% 0.20/0.46 ( sepSubset
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( subset
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunion_type,type,
% 0.20/0.46 binunion: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(binunionIL_type,type,
% 0.20/0.46 binunionIL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionIL,definition,
% 0.20/0.46 ( binunionIL
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(upairset2IR_type,type,
% 0.20/0.46 upairset2IR: $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairset2IR,definition,
% 0.20/0.46 ( upairset2IR
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunionIR_type,type,
% 0.20/0.46 binunionIR: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionIR,definition,
% 0.20/0.46 ( binunionIR
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunionEcases_type,type,
% 0.20/0.46 binunionEcases: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionEcases,definition,
% 0.20/0.46 ( binunionEcases
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.20/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.20/0.46 => ( ( ( in @ Xx @ A )
% 0.20/0.46 => Xphi )
% 0.20/0.46 => ( ( ( in @ Xx @ B )
% 0.20/0.46 => Xphi )
% 0.20/0.46 => Xphi ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunionE_type,type,
% 0.20/0.46 binunionE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionE,definition,
% 0.20/0.46 ( binunionE
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.20/0.46 => ( ( in @ Xx @ A )
% 0.20/0.46 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunionLsub_type,type,
% 0.20/0.46 binunionLsub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionLsub,definition,
% 0.20/0.46 ( binunionLsub
% 0.20/0.46 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunionRsub_type,type,
% 0.20/0.46 binunionRsub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionRsub,definition,
% 0.20/0.46 ( binunionRsub
% 0.20/0.46 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersect_type,type,
% 0.20/0.46 binintersect: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectI_type,type,
% 0.20/0.46 binintersectI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectI,definition,
% 0.20/0.46 ( binintersectI
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset5_type,type,
% 0.20/0.46 binintersectSubset5: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset5,definition,
% 0.20/0.46 ( binintersectSubset5
% 0.20/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.20/0.46 ( ( subset @ C @ A )
% 0.20/0.46 => ( ( subset @ C @ B )
% 0.20/0.46 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectEL_type,type,
% 0.20/0.46 binintersectEL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectEL,definition,
% 0.20/0.46 ( binintersectEL
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.20/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectLsub_type,type,
% 0.20/0.46 binintersectLsub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectLsub,definition,
% 0.20/0.46 ( binintersectLsub
% 0.20/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset2_type,type,
% 0.20/0.46 binintersectSubset2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset2,definition,
% 0.20/0.46 ( binintersectSubset2
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( ( binintersect @ A @ B )
% 0.20/0.46 = A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset3_type,type,
% 0.20/0.46 binintersectSubset3: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset3,definition,
% 0.20/0.46 ( binintersectSubset3
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( ( binintersect @ A @ B )
% 0.20/0.46 = B )
% 0.20/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectER_type,type,
% 0.20/0.46 binintersectER: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectER,definition,
% 0.20/0.46 ( binintersectER
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.20/0.46 => ( in @ Xx @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(disjointsetsI1_type,type,
% 0.20/0.46 disjointsetsI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(disjointsetsI1,definition,
% 0.20/0.46 ( disjointsetsI1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ~ ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( in @ Xx @ B ) )
% 0.20/0.46 => ( ( binintersect @ A @ B )
% 0.20/0.46 = emptyset ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectRsub_type,type,
% 0.20/0.46 binintersectRsub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectRsub,definition,
% 0.20/0.46 ( binintersectRsub
% 0.20/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset4_type,type,
% 0.20/0.46 binintersectSubset4: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset4,definition,
% 0.20/0.46 ( binintersectSubset4
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( subset @ B @ A )
% 0.20/0.46 => ( ( binintersect @ A @ B )
% 0.20/0.46 = B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset1_type,type,
% 0.20/0.46 binintersectSubset1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset1,definition,
% 0.20/0.46 ( binintersectSubset1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( ( binintersect @ A @ B )
% 0.20/0.46 = A )
% 0.20/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(bs114d_type,type,
% 0.20/0.46 bs114d: $o ).
% 0.20/0.46
% 0.20/0.46 thf(bs114d,definition,
% 0.20/0.46 ( bs114d
% 0.20/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.20/0.46 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.20/0.46 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(regular_type,type,
% 0.20/0.46 regular: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminus_type,type,
% 0.20/0.46 setminus: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(setminusI_type,type,
% 0.20/0.46 setminusI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusI,definition,
% 0.20/0.46 ( setminusI
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusEL_type,type,
% 0.20/0.46 setminusEL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusEL,definition,
% 0.20/0.46 ( setminusEL
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.20/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusER_type,type,
% 0.20/0.46 setminusER: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusER,definition,
% 0.20/0.46 ( setminusER
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.20/0.46 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusSubset2_type,type,
% 0.20/0.46 setminusSubset2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusSubset2,definition,
% 0.20/0.46 ( setminusSubset2
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( ( setminus @ A @ B )
% 0.20/0.46 = emptyset ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusERneg_type,type,
% 0.20/0.46 setminusERneg: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusERneg,definition,
% 0.20/0.46 ( setminusERneg
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.20/0.46 => ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusELneg_type,type,
% 0.20/0.46 setminusELneg: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusELneg,definition,
% 0.20/0.46 ( setminusELneg
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusILneg_type,type,
% 0.20/0.46 setminusILneg: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusILneg,definition,
% 0.20/0.46 ( setminusILneg
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ~ ( in @ Xx @ A )
% 0.20/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusIRneg_type,type,
% 0.20/0.46 setminusIRneg: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusIRneg,definition,
% 0.20/0.46 ( setminusIRneg
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusLsub_type,type,
% 0.20/0.46 setminusLsub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusLsub,definition,
% 0.20/0.46 ( setminusLsub
% 0.20/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusSubset1_type,type,
% 0.20/0.46 setminusSubset1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusSubset1,definition,
% 0.20/0.46 ( setminusSubset1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( ( setminus @ A @ B )
% 0.20/0.46 = emptyset )
% 0.20/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(symdiff_type,type,
% 0.20/0.46 symdiff: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffE_type,type,
% 0.20/0.46 symdiffE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffE,definition,
% 0.20/0.46 ( symdiffE
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.20/0.46 => ! [Xphi: $o] :
% 0.20/0.46 ( ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => Xphi ) )
% 0.20/0.46 => ( ( ~ ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ B )
% 0.20/0.46 => Xphi ) )
% 0.20/0.46 => Xphi ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffI1_type,type,
% 0.20/0.46 symdiffI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffI1,definition,
% 0.20/0.46 ( symdiffI1
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffI2_type,type,
% 0.20/0.46 symdiffI2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffI2,definition,
% 0.20/0.46 ( symdiffI2
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ~ ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffIneg1_type,type,
% 0.20/0.46 symdiffIneg1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffIneg1,definition,
% 0.20/0.46 ( symdiffIneg1
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ B )
% 0.20/0.46 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffIneg2_type,type,
% 0.20/0.46 symdiffIneg2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffIneg2,definition,
% 0.20/0.46 ( symdiffIneg2
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ~ ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(iskpair_type,type,
% 0.20/0.46 iskpair: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(secondinupair_type,type,
% 0.20/0.46 secondinupair: $o ).
% 0.20/0.46
% 0.20/0.46 thf(secondinupair,definition,
% 0.20/0.46 ( secondinupair
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairIL_type,type,
% 0.20/0.46 setukpairIL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairIL,definition,
% 0.20/0.46 ( setukpairIL
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairIR_type,type,
% 0.20/0.46 setukpairIR: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairIR,definition,
% 0.20/0.46 ( setukpairIR
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(kpairiskpair_type,type,
% 0.20/0.46 kpairiskpair: $o ).
% 0.20/0.46
% 0.20/0.46 thf(kpairiskpair,definition,
% 0.20/0.46 ( kpairiskpair
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(kpair_type,type,
% 0.20/0.46 kpair: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(kpairp_type,type,
% 0.20/0.46 kpairp: $o ).
% 0.20/0.46
% 0.20/0.46 thf(kpairp,definition,
% 0.20/0.46 ( kpairp
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cartprod_type,type,
% 0.20/0.46 cartprod: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(singletonsubset_type,type,
% 0.20/0.46 singletonsubset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(singletonsubset,definition,
% 0.20/0.46 ( singletonsubset
% 0.20/0.46 = ( ! [A: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(singletoninpowerset_type,type,
% 0.20/0.46 singletoninpowerset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(singletoninpowerset,definition,
% 0.20/0.46 ( singletoninpowerset
% 0.20/0.46 = ( ! [A: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(singletoninpowunion_type,type,
% 0.20/0.46 singletoninpowunion: $o ).
% 0.20/0.46
% 0.20/0.46 thf(singletoninpowunion,definition,
% 0.20/0.46 ( singletoninpowunion
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(upairset2E_type,type,
% 0.20/0.46 upairset2E: $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairset2E,definition,
% 0.20/0.46 ( upairset2E
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.20/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.20/0.46 => ( ( Xz = Xx )
% 0.20/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(upairsubunion_type,type,
% 0.20/0.46 upairsubunion: $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairsubunion,definition,
% 0.20/0.46 ( upairsubunion
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(upairinpowunion_type,type,
% 0.20/0.46 upairinpowunion: $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairinpowunion,definition,
% 0.20/0.46 ( upairinpowunion
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ubforcartprodlem1_type,type,
% 0.20/0.46 ubforcartprodlem1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ubforcartprodlem1,definition,
% 0.20/0.46 ( ubforcartprodlem1
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ubforcartprodlem2_type,type,
% 0.20/0.46 ubforcartprodlem2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ubforcartprodlem2,definition,
% 0.20/0.46 ( ubforcartprodlem2
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ubforcartprodlem3_type,type,
% 0.20/0.46 ubforcartprodlem3: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ubforcartprodlem3,definition,
% 0.20/0.46 ( ubforcartprodlem3
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodpairin_type,type,
% 0.20/0.46 cartprodpairin: $o ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodpairin,definition,
% 0.20/0.46 ( cartprodpairin
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodmempair1_type,type,
% 0.20/0.46 cartprodmempair1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodmempair1,definition,
% 0.20/0.46 ( cartprodmempair1
% 0.20/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.20/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.20/0.46 => ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ? [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 & ( Xu
% 0.20/0.46 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodmempair_type,type,
% 0.20/0.46 cartprodmempair: $o ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodmempair,definition,
% 0.20/0.46 ( cartprodmempair
% 0.20/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.20/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.20/0.46 => ( iskpair @ Xu ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setunionE2_type,type,
% 0.20/0.46 setunionE2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setunionE2,definition,
% 0.20/0.46 ( setunionE2
% 0.20/0.46 = ( ! [A: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.20/0.46 => ? [X: $i] :
% 0.20/0.46 ( ( in @ X @ A )
% 0.20/0.46 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setunionsingleton1_type,type,
% 0.20/0.46 setunionsingleton1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setunionsingleton1,definition,
% 0.20/0.46 ( setunionsingleton1
% 0.20/0.46 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setunionsingleton2_type,type,
% 0.20/0.46 setunionsingleton2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setunionsingleton2,definition,
% 0.20/0.46 ( setunionsingleton2
% 0.20/0.46 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setunionsingleton_type,type,
% 0.20/0.46 setunionsingleton: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setunionsingleton,definition,
% 0.20/0.46 ( setunionsingleton
% 0.20/0.46 = ( ! [Xx: $i] :
% 0.20/0.46 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.20/0.46 = Xx ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(singleton_type,type,
% 0.20/0.46 singleton: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(singletonprop_type,type,
% 0.20/0.46 singletonprop: $o ).
% 0.20/0.46
% 0.20/0.46 thf(singletonprop,definition,
% 0.20/0.46 ( singletonprop
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 => ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) )
% 0.20/0.46 => ( ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( Xphi @ Xx ) )
% 0.20/0.46 => ( singleton
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ex1_type,type,
% 0.20/0.46 ex1: $i > ( $i > $o ) > $o ).
% 0.20/0.46
% 0.20/0.46 thf(ex1E1_type,type,
% 0.20/0.46 ex1E1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ex1E1,definition,
% 0.20/0.46 ( ex1E1
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ( ex1 @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ex1I_type,type,
% 0.20/0.46 ex1I: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ex1I,definition,
% 0.20/0.46 ( ex1I
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 => ( ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xy = Xx ) ) )
% 0.20/0.46 => ( ex1 @ A
% 0.20/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ex1I2_type,type,
% 0.20/0.46 ex1I2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ex1I2,definition,
% 0.20/0.46 ( ex1I2
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 => ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) )
% 0.20/0.46 => ( ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( Xphi @ Xx ) )
% 0.20/0.46 => ( ex1 @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(singletonsuniq_type,type,
% 0.20/0.46 singletonsuniq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(singletonsuniq,definition,
% 0.20/0.46 ( singletonsuniq
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( ( setadjoin @ Xx @ emptyset )
% 0.20/0.46 = ( setadjoin @ Xy @ emptyset ) )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(atmost1p_type,type,
% 0.20/0.46 atmost1p: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(atleast2p_type,type,
% 0.20/0.46 atleast2p: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(atmost2p_type,type,
% 0.20/0.46 atmost2p: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairsetp_type,type,
% 0.20/0.46 upairsetp: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjL1_type,type,
% 0.20/0.46 setukpairinjL1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjL1,definition,
% 0.20/0.46 ( setukpairinjL1
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.20/0.46 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.20/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(kfstsingleton_type,type,
% 0.20/0.46 kfstsingleton: $o ).
% 0.20/0.46
% 0.20/0.46 thf(kfstsingleton,definition,
% 0.20/0.46 ( kfstsingleton
% 0.20/0.46 = ( ! [Xu: $i] :
% 0.20/0.46 ( ( iskpair @ Xu )
% 0.20/0.46 => ( singleton
% 0.20/0.46 @ ( dsetconstr @ ( setunion @ Xu )
% 0.20/0.46 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(theprop_type,type,
% 0.20/0.46 theprop: $o ).
% 0.20/0.46
% 0.20/0.46 thf(theprop,definition,
% 0.20/0.46 ( theprop
% 0.20/0.46 = ( ! [X: $i] :
% 0.20/0.46 ( ( singleton @ X )
% 0.20/0.46 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(kfst_type,type,
% 0.20/0.46 kfst: $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(kfstpairEq_type,type,
% 0.20/0.46 kfstpairEq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(kfstpairEq,definition,
% 0.20/0.46 ( kfstpairEq
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.20/0.46 = Xx ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodfstin_type,type,
% 0.20/0.46 cartprodfstin: $o ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodfstin,definition,
% 0.20/0.46 ( cartprodfstin
% 0.20/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.20/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.20/0.46 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjL2_type,type,
% 0.20/0.46 setukpairinjL2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjL2,definition,
% 0.20/0.46 ( setukpairinjL2
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.20/0.46 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.20/0.46 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.20/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjL_type,type,
% 0.20/0.46 setukpairinjL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjL,definition,
% 0.20/0.46 ( setukpairinjL
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.20/0.46 ( ( ( kpair @ Xx @ Xy )
% 0.20/0.46 = ( kpair @ Xz @ Xu ) )
% 0.20/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR11_type,type,
% 0.20/0.46 setukpairinjR11: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR11,definition,
% 0.20/0.46 ( setukpairinjR11
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.20/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR12_type,type,
% 0.20/0.46 setukpairinjR12: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR12,definition,
% 0.20/0.46 ( setukpairinjR12
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.20/0.46 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR1_type,type,
% 0.20/0.46 setukpairinjR1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR1,definition,
% 0.20/0.46 ( setukpairinjR1
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.20/0.46 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.20/0.46 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.20/0.46 => ( ( Xz = Xu )
% 0.20/0.46 => ( Xy = Xu ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(upairequniteq_type,type,
% 0.20/0.46 upairequniteq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairequniteq,definition,
% 0.20/0.46 ( upairequniteq
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.20/0.46 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.20/0.46 = ( setadjoin @ Xz @ emptyset ) )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR2_type,type,
% 0.20/0.46 setukpairinjR2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR2,definition,
% 0.20/0.46 ( setukpairinjR2
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.20/0.46 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.20/0.46 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.20/0.46 => ( Xy = Xu ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR_type,type,
% 0.20/0.46 setukpairinjR: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR,definition,
% 0.20/0.46 ( setukpairinjR
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.20/0.46 ( ( ( kpair @ Xx @ Xy )
% 0.20/0.46 = ( kpair @ Xz @ Xu ) )
% 0.20/0.46 => ( Xy = Xu ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ksndsingleton_type,type,
% 0.20/0.46 ksndsingleton: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ksndsingleton,definition,
% 0.20/0.46 ( ksndsingleton
% 0.20/0.46 = ( ! [Xu: $i] :
% 0.20/0.46 ( ( iskpair @ Xu )
% 0.20/0.46 => ( singleton
% 0.20/0.46 @ ( dsetconstr @ ( setunion @ Xu )
% 0.20/0.46 @ ^ [Xx: $i] :
% 0.20/0.46 ( Xu
% 0.20/0.46 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ksnd_type,type,
% 0.20/0.46 ksnd: $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(ksndpairEq_type,type,
% 0.20/0.46 ksndpairEq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ksndpairEq,definition,
% 0.20/0.46 ( ksndpairEq
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.20/0.46 = Xy ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(kpairsurjEq_type,type,
% 0.20/0.46 kpairsurjEq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(kpairsurjEq,definition,
% 0.20/0.46 ( kpairsurjEq
% 0.20/0.46 = ( ! [Xu: $i] :
% 0.20/0.46 ( ( iskpair @ Xu )
% 0.20/0.46 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.20/0.46 = Xu ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodsndin_type,type,
% 0.20/0.46 cartprodsndin: $o ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodsndin,definition,
% 0.20/0.46 ( cartprodsndin
% 0.20/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.20/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.20/0.46 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodpairmemEL_type,type,
% 0.20/0.46 cartprodpairmemEL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodpairmemEL,definition,
% 0.20/0.46 ( cartprodpairmemEL
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.20/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodpairmemER_type,type,
% 0.20/0.46 cartprodpairmemER: $o ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodpairmemER,definition,
% 0.20/0.46 ( cartprodpairmemER
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.20/0.46 => ( in @ Xy @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodmempaircEq_type,type,
% 0.20/0.46 cartprodmempaircEq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodmempaircEq,definition,
% 0.20/0.46 ( cartprodmempaircEq
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( kpair @ Xx @ Xy )
% 0.20/0.46 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodfstpairEq_type,type,
% 0.20/0.46 cartprodfstpairEq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodfstpairEq,definition,
% 0.20/0.46 ( cartprodfstpairEq
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.20/0.46 = Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodsndpairEq_type,type,
% 0.20/0.46 cartprodsndpairEq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodsndpairEq,definition,
% 0.20/0.46 ( cartprodsndpairEq
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.20/0.46 = Xy ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodpairsurjEq_type,type,
% 0.20/0.46 cartprodpairsurjEq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodpairsurjEq,definition,
% 0.20/0.46 ( cartprodpairsurjEq
% 0.20/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.20/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.20/0.46 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.20/0.46 = Xu ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(breln_type,type,
% 0.20/0.46 breln: $i > $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(dpsetconstr_type,type,
% 0.20/0.46 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.20/0.46
% 0.20/0.46 thf(dpsetconstrI_type,type,
% 0.20/0.46 dpsetconstrI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(dpsetconstrI,definition,
% 0.20/0.46 ( dpsetconstrI
% 0.20/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( Xphi @ Xx @ Xy )
% 0.20/0.46 => ( in @ ( kpair @ Xx @ Xy )
% 0.20/0.46 @ ( dpsetconstr @ A @ B
% 0.20/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(dpsetconstrSub_type,type,
% 0.20/0.46 dpsetconstrSub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(dpsetconstrSub,definition,
% 0.20/0.46 ( dpsetconstrSub
% 0.20/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.20/0.46 ( subset
% 0.20/0.46 @ ( dpsetconstr @ A @ B
% 0.20/0.46 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.20/0.46 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setOfPairsIsBReln_type,type,
% 0.20/0.46 setOfPairsIsBReln: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setOfPairsIsBReln,definition,
% 0.20/0.46 ( setOfPairsIsBReln
% 0.20/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.20/0.46 ( breln @ A @ B
% 0.20/0.46 @ ( dpsetconstr @ A @ B
% 0.20/0.46 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(dpsetconstrERa_type,type,
% 0.20/0.46 dpsetconstrERa: $o ).
% 0.20/0.46
% 0.20/0.46 thf(dpsetconstrERa,definition,
% 0.20/0.46 ( dpsetconstrERa
% 0.20/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.20/0.46 @ ( dpsetconstr @ A @ B
% 0.20/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.20/0.46 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(dpsetconstrEL1_type,type,
% 0.20/0.46 dpsetconstrEL1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(dpsetconstrEL1,definition,
% 0.20/0.46 ( dpsetconstrEL1
% 0.20/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ ( kpair @ Xx @ Xy )
% 0.20/0.46 @ ( dpsetconstr @ A @ B
% 0.20/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.20/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(dpsetconstrEL2_type,type,
% 0.20/0.46 dpsetconstrEL2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(dpsetconstrEL2,definition,
% 0.20/0.46 ( dpsetconstrEL2
% 0.20/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ ( kpair @ Xx @ Xy )
% 0.20/0.46 @ ( dpsetconstr @ A @ B
% 0.20/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.20/0.46 => ( in @ Xy @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(dpsetconstrER_type,type,
% 0.20/0.46 dpsetconstrER: $o ).
% 0.20/0.46
% 0.20/0.46 thf(dpsetconstrER,definition,
% 0.20/0.46 ( dpsetconstrER
% 0.20/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ ( kpair @ Xx @ Xy )
% 0.20/0.46 @ ( dpsetconstr @ A @ B
% 0.20/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.20/0.46 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(func_type,type,
% 0.20/0.46 func: $i > $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(funcSet_type,type,
% 0.20/0.46 funcSet: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(funcImageSingleton_type,type,
% 0.20/0.46 funcImageSingleton: $o ).
% 0.20/0.46
% 0.20/0.46 thf(funcImageSingleton,definition,
% 0.20/0.46 ( funcImageSingleton
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( func @ A @ B @ Xf )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( singleton
% 0.20/0.46 @ ( dsetconstr @ B
% 0.20/0.46 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(apProp_type,type,
% 0.20/0.46 apProp: $o ).
% 0.20/0.46
% 0.20/0.46 thf(apProp,definition,
% 0.20/0.46 ( apProp
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( func @ A @ B @ Xf )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in
% 0.20/0.46 @ ( setunion
% 0.20/0.46 @ ( dsetconstr @ B
% 0.20/0.46 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.20/0.46 @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ap_type,type,
% 0.20/0.46 ap: $i > $i > $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(app_type,type,
% 0.20/0.46 app: $o ).
% 0.20/0.46
% 0.20/0.46 thf(app,definition,
% 0.20/0.46 ( app
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( func @ A @ B @ Xf )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(infuncsetfunc_type,type,
% 0.20/0.46 infuncsetfunc: $o ).
% 0.20/0.46
% 0.20/0.46 thf(infuncsetfunc,definition,
% 0.20/0.46 ( infuncsetfunc
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.20/0.46 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ap2p_type,type,
% 0.20/0.46 ap2p: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ap2p,definition,
% 0.20/0.46 ( ap2p
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(funcinfuncset_type,type,
% 0.20/0.46 funcinfuncset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(funcinfuncset,definition,
% 0.20/0.46 ( funcinfuncset
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( func @ A @ B @ Xf )
% 0.20/0.46 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(lamProp_type,type,
% 0.20/0.46 lamProp: $o ).
% 0.20/0.46
% 0.20/0.46 thf(lamProp,definition,
% 0.20/0.46 ( lamProp
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.20/0.46 => ( func @ A @ B
% 0.20/0.46 @ ( dpsetconstr @ A @ B
% 0.20/0.46 @ ^ [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xf @ Xx )
% 0.20/0.46 = Xy ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(lam_type,type,
% 0.20/0.46 lam: $i > $i > ( $i > $i ) > $i ).
% 0.20/0.46
% 0.20/0.46 thf(lamp_type,type,
% 0.20/0.46 lamp: $o ).
% 0.20/0.46
% 0.20/0.46 thf(lamp,definition,
% 0.20/0.46 ( lamp
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.20/0.46 => ( func @ A @ B
% 0.20/0.46 @ ( lam @ A @ B
% 0.20/0.46 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(lam2p_type,type,
% 0.20/0.46 lam2p: $o ).
% 0.20/0.46
% 0.20/0.46 thf(lam2p,definition,
% 0.20/0.46 ( lam2p
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.20/0.46 => ( in
% 0.20/0.46 @ ( lam @ A @ B
% 0.20/0.46 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.20/0.46 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(brelnall1_type,type,
% 0.20/0.46 brelnall1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(brelnall1,definition,
% 0.20/0.46 ( brelnall1
% 0.20/0.46 = ( ! [A: $i,B: $i,R: $i] :
% 0.20/0.46 ( ( breln @ A @ B @ R )
% 0.20/0.46 => ! [Xphi: $i > $o] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.20/0.46 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ R )
% 0.20/0.46 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(brelnall2_type,type,
% 0.20/0.46 brelnall2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(brelnall2,definition,
% 0.20/0.46 ( brelnall2
% 0.20/0.46 = ( ! [A: $i,B: $i,R: $i] :
% 0.20/0.46 ( ( breln @ A @ B @ R )
% 0.20/0.46 => ! [Xphi: $i > $o] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.20/0.46 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ R )
% 0.20/0.46 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ex1E2_type,type,
% 0.20/0.46 ex1E2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ex1E2,definition,
% 0.20/0.46 ( ex1E2
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ( ex1 @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 => ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(funcGraphProp1_type,type,
% 0.20/0.46 funcGraphProp1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(funcGraphProp1,definition,
% 0.20/0.46 ( funcGraphProp1
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( func @ A @ B @ Xf )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(funcGraphProp3_type,type,
% 0.20/0.46 funcGraphProp3: $o ).
% 0.20/0.46
% 0.20/0.46 thf(funcGraphProp3,definition,
% 0.20/0.46 ( funcGraphProp3
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(funcGraphProp2_type,type,
% 0.20/0.46 funcGraphProp2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(funcGraphProp2,definition,
% 0.20/0.46 ( funcGraphProp2
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( func @ A @ B @ Xf )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.20/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.20/0.46 = Xy ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(funcextLem_type,type,
% 0.20/0.46 funcextLem: $o ).
% 0.20/0.46
% 0.20/0.46 thf(funcextLem,definition,
% 0.20/0.46 ( funcextLem
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( func @ A @ B @ Xf )
% 0.20/0.46 => ! [Xg: $i] :
% 0.20/0.46 ( ( func @ A @ B @ Xg )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.20/0.46 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 0.20/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(funcGraphProp4_type,type,
% 0.20/0.46 funcGraphProp4: $o ).
% 0.20/0.46
% 0.20/0.46 thf(funcGraphProp4,definition,
% 0.20/0.46 ( funcGraphProp4
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.20/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.20/0.46 = Xy ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subbreln_type,type,
% 0.20/0.46 subbreln: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subbreln,definition,
% 0.20/0.46 ( subbreln
% 0.20/0.46 = ( ! [A: $i,B: $i,R: $i] :
% 0.20/0.46 ( ( breln @ A @ B @ R )
% 0.20/0.46 => ! [S: $i] :
% 0.20/0.46 ( ( breln @ A @ B @ S )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.20/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.20/0.46 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(eqbreln_type,type,
% 0.20/0.46 eqbreln: $o ).
% 0.20/0.46
% 0.20/0.46 thf(eqbreln,definition,
% 0.20/0.46 ( eqbreln
% 0.20/0.46 = ( ! [A: $i,B: $i,R: $i] :
% 0.20/0.46 ( ( breln @ A @ B @ R )
% 0.20/0.46 => ! [S: $i] :
% 0.20/0.46 ( ( breln @ A @ B @ S )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.20/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.20/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.20/0.46 => ( R = S ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(funcext_type,type,
% 0.20/0.46 funcext: $o ).
% 0.20/0.46
% 0.20/0.46 thf(funcext,definition,
% 0.20/0.46 ( funcext
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( func @ A @ B @ Xf )
% 0.20/0.46 => ! [Xg: $i] :
% 0.20/0.46 ( ( func @ A @ B @ Xg )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.20/0.46 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.20/0.46 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(funcext2_type,type,
% 0.20/0.46 funcext2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(funcext2,definition,
% 0.20/0.46 ( funcext2
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.20/0.46 => ! [Xg: $i] :
% 0.20/0.46 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.20/0.46 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.20/0.46 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ap2apEq1_type,type,
% 0.20/0.46 ap2apEq1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ap2apEq1,definition,
% 0.20/0.46 ( ap2apEq1
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.20/0.46 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ap2apEq2_type,type,
% 0.20/0.46 ap2apEq2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ap2apEq2,definition,
% 0.20/0.46 ( ap2apEq2
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( func @ A @ B @ Xf )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.20/0.46 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(beta1_type,type,
% 0.20/0.46 beta1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(beta1,definition,
% 0.20/0.46 ( beta1
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( ap @ A @ B
% 0.20/0.46 @ ( lam @ A @ B
% 0.20/0.46 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.20/0.46 @ Xx )
% 0.20/0.46 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(eta1_type,type,
% 0.20/0.46 eta1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(eta1,definition,
% 0.20/0.46 ( eta1
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( func @ A @ B @ Xf )
% 0.20/0.46 => ( ( lam @ A @ B
% 0.20/0.46 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.20/0.46 = Xf ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(lam2lamEq_type,type,
% 0.20/0.46 lam2lamEq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(lam2lamEq,definition,
% 0.20/0.46 ( lam2lamEq
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.20/0.46 => ( ( lam @ A @ B
% 0.20/0.46 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.20/0.46 = ( lam @ A @ B
% 0.20/0.46 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(beta2_type,type,
% 0.20/0.46 beta2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(beta2,definition,
% 0.20/0.46 ( beta2
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( ap @ A @ B
% 0.20/0.46 @ ( lam @ A @ B
% 0.20/0.46 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.20/0.46 @ Xx )
% 0.20/0.46 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(eta2_type,type,
% 0.20/0.46 eta2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(eta2,definition,
% 0.20/0.46 ( eta2
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.20/0.46 => ( ( lam @ A @ B
% 0.20/0.46 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.20/0.46 = Xf ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(iffalseProp1_type,type,
% 0.20/0.46 iffalseProp1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(iffalseProp1,definition,
% 0.20/0.46 ( iffalseProp1
% 0.20/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( ~ Xphi
% 0.20/0.46 => ( in @ Xy
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xz: $i] :
% 0.20/0.46 ( ( Xphi
% 0.20/0.46 & ( Xz = Xx ) )
% 0.20/0.46 | ( ~ Xphi
% 0.20/0.46 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(iffalseProp2_type,type,
% 0.20/0.46 iffalseProp2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(iffalseProp2,definition,
% 0.20/0.46 ( iffalseProp2
% 0.20/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( ~ Xphi
% 0.20/0.46 => ( ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xz: $i] :
% 0.20/0.46 ( ( Xphi
% 0.20/0.46 & ( Xz = Xx ) )
% 0.20/0.46 | ( ~ Xphi
% 0.20/0.46 & ( Xz = Xy ) ) ) )
% 0.20/0.46 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(iftrueProp1_type,type,
% 0.20/0.46 iftrueProp1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(iftrueProp1,definition,
% 0.20/0.46 ( iftrueProp1
% 0.20/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( Xphi
% 0.20/0.46 => ( in @ Xx
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xz: $i] :
% 0.20/0.46 ( ( Xphi
% 0.20/0.46 & ( Xz = Xx ) )
% 0.20/0.46 | ( ~ Xphi
% 0.20/0.46 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(iftrueProp2_type,type,
% 0.20/0.46 iftrueProp2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(iftrueProp2,definition,
% 0.20/0.46 ( iftrueProp2
% 0.20/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( Xphi
% 0.20/0.46 => ( ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xz: $i] :
% 0.20/0.46 ( ( Xphi
% 0.20/0.46 & ( Xz = Xx ) )
% 0.20/0.46 | ( ~ Xphi
% 0.20/0.46 & ( Xz = Xy ) ) ) )
% 0.20/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ifSingleton_type,type,
% 0.20/0.46 ifSingleton: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ifSingleton,definition,
% 0.20/0.46 ( ifSingleton
% 0.20/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( singleton
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xz: $i] :
% 0.20/0.46 ( ( Xphi
% 0.20/0.46 & ( Xz = Xx ) )
% 0.20/0.46 | ( ~ Xphi
% 0.20/0.46 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(if_type,type,
% 0.20/0.46 if: $i > $o > $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(ifp_type,type,
% 0.20/0.46 ifp: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ifp,definition,
% 0.20/0.46 ( ifp
% 0.20/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(theeq_type,type,
% 0.20/0.46 theeq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(theeq,definition,
% 0.20/0.46 ( theeq
% 0.20/0.46 = ( ! [X: $i] :
% 0.20/0.46 ( ( singleton @ X )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ X )
% 0.20/0.46 => ( ( setunion @ X )
% 0.20/0.46 = Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(iftrue_type,type,
% 0.20/0.46 iftrue: $o ).
% 0.20/0.46
% 0.20/0.46 thf(iftrue,definition,
% 0.20/0.46 ( iftrue
% 0.20/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( Xphi
% 0.20/0.46 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.20/0.46 = Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(iffalse_type,type,
% 0.20/0.46 iffalse: $o ).
% 0.20/0.46
% 0.20/0.46 thf(iffalse,definition,
% 0.20/0.46 ( iffalse
% 0.20/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( ~ Xphi
% 0.20/0.46 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.20/0.46 = Xy ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(iftrueorfalse_type,type,
% 0.20/0.46 iftrueorfalse: $o ).
% 0.20/0.46
% 0.20/0.46 thf(iftrueorfalse,definition,
% 0.20/0.46 ( iftrueorfalse
% 0.20/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectT_lem_type,type,
% 0.20/0.46 binintersectT_lem: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectT_lem,definition,
% 0.20/0.46 ( binintersectT_lem
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunionT_lem_type,type,
% 0.20/0.46 binunionT_lem: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionT_lem,definition,
% 0.20/0.46 ( binunionT_lem
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powersetT_lem_type,type,
% 0.20/0.46 powersetT_lem: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetT_lem,definition,
% 0.20/0.46 ( powersetT_lem
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusT_lem_type,type,
% 0.20/0.46 setminusT_lem: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusT_lem,definition,
% 0.20/0.46 ( setminusT_lem
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(complementT_lem_type,type,
% 0.20/0.46 complementT_lem: $o ).
% 0.20/0.46
% 0.20/0.46 thf(complementT_lem,definition,
% 0.20/0.46 ( complementT_lem
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setextT_type,type,
% 0.20/0.46 setextT: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setextT,definition,
% 0.20/0.46 ( setextT
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ X )
% 0.20/0.46 => ( in @ Xx @ Y ) ) )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ Y )
% 0.20/0.46 => ( in @ Xx @ X ) ) )
% 0.20/0.46 => ( X = Y ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subsetTI_type,type,
% 0.20/0.46 subsetTI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetTI,definition,
% 0.20/0.46 ( subsetTI
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ X )
% 0.20/0.46 => ( in @ Xx @ Y ) ) )
% 0.20/0.46 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powersetTI1_type,type,
% 0.20/0.46 powersetTI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetTI1,definition,
% 0.20/0.46 ( powersetTI1
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ X )
% 0.20/0.46 => ( in @ Xx @ Y ) ) )
% 0.20/0.46 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powersetTE1_type,type,
% 0.20/0.46 powersetTE1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetTE1,definition,
% 0.20/0.46 ( powersetTE1
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ X @ ( powerset @ Y ) )
% 0.20/0.46 => ( ( in @ Xx @ X )
% 0.20/0.46 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(complementTI1_type,type,
% 0.20/0.46 complementTI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(complementTI1,definition,
% 0.20/0.46 ( complementTI1
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ X )
% 0.20/0.46 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(complementTE1_type,type,
% 0.20/0.46 complementTE1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(complementTE1,definition,
% 0.20/0.46 ( complementTE1
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 0.20/0.46 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectTELcontra_type,type,
% 0.20/0.46 binintersectTELcontra: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectTELcontra,definition,
% 0.20/0.46 ( binintersectTELcontra
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ X )
% 0.20/0.46 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectTERcontra_type,type,
% 0.20/0.46 binintersectTERcontra: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectTERcontra,definition,
% 0.20/0.46 ( binintersectTERcontra
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ Y )
% 0.20/0.46 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(contrasubsetT_type,type,
% 0.20/0.46 contrasubsetT: $o ).
% 0.20/0.46
% 0.20/0.46 thf(contrasubsetT,definition,
% 0.20/0.46 ( contrasubsetT
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.20/0.46 => ( ( in @ Xx @ Y )
% 0.20/0.46 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(contrasubsetT1_type,type,
% 0.20/0.46 contrasubsetT1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(contrasubsetT1,definition,
% 0.20/0.46 ( contrasubsetT1
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( subset @ X @ Y )
% 0.20/0.46 => ( ~ ( in @ Xx @ Y )
% 0.20/0.46 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(contrasubsetT2_type,type,
% 0.20/0.46 contrasubsetT2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(contrasubsetT2,definition,
% 0.20/0.46 ( contrasubsetT2
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( ( subset @ X @ Y )
% 0.20/0.46 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(contrasubsetT3_type,type,
% 0.20/0.46 contrasubsetT3: $o ).
% 0.20/0.46
% 0.20/0.46 thf(contrasubsetT3,definition,
% 0.20/0.46 ( contrasubsetT3
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 0.20/0.46 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(doubleComplementI1_type,type,
% 0.20/0.46 doubleComplementI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(doubleComplementI1,definition,
% 0.20/0.46 ( doubleComplementI1
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ X )
% 0.20/0.46 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(doubleComplementE1_type,type,
% 0.20/0.46 doubleComplementE1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(doubleComplementE1,definition,
% 0.20/0.46 ( doubleComplementE1
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 0.20/0.46 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(doubleComplementSub1_type,type,
% 0.20/0.46 doubleComplementSub1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(doubleComplementSub1,definition,
% 0.20/0.46 ( doubleComplementSub1
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(doubleComplementSub2_type,type,
% 0.20/0.46 doubleComplementSub2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(doubleComplementSub2,definition,
% 0.20/0.46 ( doubleComplementSub2
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(doubleComplementEq_type,type,
% 0.20/0.46 doubleComplementEq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(doubleComplementEq,definition,
% 0.20/0.46 ( doubleComplementEq
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ( X
% 0.20/0.46 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(complementTnotintersectT_type,type,
% 0.20/0.46 complementTnotintersectT: $o ).
% 0.20/0.46
% 0.20/0.46 thf(complementTnotintersectT,definition,
% 0.20/0.46 ( complementTnotintersectT
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.20/0.46 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(complementImpComplementIntersect_type,type,
% 0.20/0.46 complementImpComplementIntersect: $o ).
% 0.20/0.46
% 0.20/0.46 thf(complementImpComplementIntersect,definition,
% 0.20/0.46 ( complementImpComplementIntersect
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.20/0.46 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(complementSubsetComplementIntersect_type,type,
% 0.20/0.46 complementSubsetComplementIntersect: $o ).
% 0.20/0.46
% 0.20/0.46 thf(complementSubsetComplementIntersect,definition,
% 0.20/0.46 ( complementSubsetComplementIntersect
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(complementInPowersetComplementIntersect_type,type,
% 0.20/0.46 complementInPowersetComplementIntersect: $o ).
% 0.20/0.46
% 0.20/0.46 thf(complementInPowersetComplementIntersect,definition,
% 0.20/0.46 ( complementInPowersetComplementIntersect
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(contraSubsetComplement_type,type,
% 0.20/0.46 contraSubsetComplement: $o ).
% 0.20/0.46
% 0.20/0.46 thf(contraSubsetComplement,definition,
% 0.20/0.46 ( contraSubsetComplement
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ Y )
% 0.20/0.46 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(complementTcontraSubset_type,type,
% 0.20/0.46 complementTcontraSubset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(complementTcontraSubset,definition,
% 0.20/0.46 ( complementTcontraSubset
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.20/0.46 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunionTILcontra_type,type,
% 0.20/0.46 binunionTILcontra: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionTILcontra,definition,
% 0.20/0.46 ( binunionTILcontra
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.20/0.46 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunionTIRcontra_type,type,
% 0.20/0.46 binunionTIRcontra: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionTIRcontra,definition,
% 0.20/0.46 ( binunionTIRcontra
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.20/0.46 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(inIntersectImpInUnion_type,type,
% 0.20/0.46 inIntersectImpInUnion: $o ).
% 0.20/0.46
% 0.20/0.46 thf(inIntersectImpInUnion,definition,
% 0.20/0.46 ( inIntersectImpInUnion
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Z: $i] :
% 0.20/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.20/0.46 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(inIntersectImpInUnion2_type,type,
% 0.20/0.46 inIntersectImpInUnion2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(inIntersectImpInUnion2,definition,
% 0.20/0.46 ( inIntersectImpInUnion2
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Z: $i] :
% 0.20/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.20/0.46 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(inIntersectImpInIntersectUnions_type,type,
% 0.20/0.46 inIntersectImpInIntersectUnions: $o ).
% 0.20/0.46
% 0.20/0.46 thf(inIntersectImpInIntersectUnions,definition,
% 0.20/0.46 ( inIntersectImpInIntersectUnions
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Z: $i] :
% 0.20/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.20/0.46 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(intersectInPowersetIntersectUnions_type,type,
% 0.20/0.46 intersectInPowersetIntersectUnions: $o ).
% 0.20/0.46
% 0.20/0.46 thf(intersectInPowersetIntersectUnions,definition,
% 0.20/0.46 ( intersectInPowersetIntersectUnions
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Z: $i] :
% 0.20/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.20/0.46 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(inComplementUnionImpNotIn1_type,type,
% 0.20/0.46 inComplementUnionImpNotIn1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(inComplementUnionImpNotIn1,definition,
% 0.20/0.46 ( inComplementUnionImpNotIn1
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.20/0.46 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(inComplementUnionImpInComplement1_type,type,
% 0.20/0.46 inComplementUnionImpInComplement1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(inComplementUnionImpInComplement1,definition,
% 0.20/0.46 ( inComplementUnionImpInComplement1
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.20/0.46 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunionTE_type,type,
% 0.20/0.46 binunionTE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionTE,definition,
% 0.20/0.46 ( binunionTE
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xphi: $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.20/0.46 => ( ( ( in @ Xx @ X )
% 0.20/0.46 => Xphi )
% 0.20/0.46 => ( ( ( in @ Xx @ Y )
% 0.20/0.46 => Xphi )
% 0.20/0.46 => Xphi ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunionTEcontra_type,type,
% 0.20/0.46 binunionTEcontra: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionTEcontra,definition,
% 0.20/0.46 ( binunionTEcontra
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ X )
% 0.20/0.46 => ( ~ ( in @ Xx @ Y )
% 0.20/0.46 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(demorgan2a1_type,type,
% 0.20/0.46 demorgan2a1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(demorgan2a1,definition,
% 0.20/0.46 ( demorgan2a1
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.20/0.46 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(complementUnionInPowersetComplement_type,type,
% 0.20/0.46 complementUnionInPowersetComplement: $o ).
% 0.20/0.46
% 0.20/0.46 thf(complementUnionInPowersetComplement,definition,
% 0.20/0.46 ( complementUnionInPowersetComplement
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(demorgan2a2_type,type,
% 0.20/0.46 demorgan2a2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(demorgan2a2,definition,
% 0.20/0.46 ( demorgan2a2
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.20/0.46 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(demorgan1a_type,type,
% 0.20/0.46 demorgan1a: $o ).
% 0.20/0.46
% 0.20/0.46 thf(demorgan1a,definition,
% 0.20/0.46 ( demorgan1a
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 0.20/0.46 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(demorgan1b_type,type,
% 0.20/0.46 demorgan1b: $o ).
% 0.20/0.46
% 0.20/0.46 thf(demorgan1b,definition,
% 0.20/0.46 ( demorgan1b
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.20/0.46 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(demorgan1_type,type,
% 0.20/0.46 demorgan1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(demorgan1,definition,
% 0.20/0.46 ( demorgan1
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 0.20/0.46 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(demorgan2a_type,type,
% 0.20/0.46 demorgan2a: $o ).
% 0.20/0.46
% 0.20/0.46 thf(demorgan2a,definition,
% 0.20/0.46 ( demorgan2a
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.20/0.46 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(demorgan2b2_type,type,
% 0.20/0.46 demorgan2b2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(demorgan2b2,definition,
% 0.20/0.46 ( demorgan2b2
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.20/0.46 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 0.20/0.46 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(demorgan2b_type,type,
% 0.20/0.46 demorgan2b: $o ).
% 0.20/0.46
% 0.20/0.46 thf(demorgan2b,definition,
% 0.20/0.46 ( demorgan2b
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.20/0.46 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(demorgan2_type,type,
% 0.20/0.46 demorgan2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(demorgan2,definition,
% 0.20/0.46 ( demorgan2
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 0.20/0.46 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(woz13rule0_type,type,
% 0.20/0.46 woz13rule0: $o ).
% 0.20/0.46
% 0.20/0.46 thf(woz13rule0,definition,
% 0.20/0.46 ( woz13rule0
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.20/0.46 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(woz13rule1_type,type,
% 0.20/0.46 woz13rule1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(woz13rule1,definition,
% 0.20/0.46 ( woz13rule1
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Z: $i] :
% 0.20/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.20/0.46 => ( ( subset @ X @ Z )
% 0.20/0.46 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(woz13rule2_type,type,
% 0.20/0.46 woz13rule2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(woz13rule2,definition,
% 0.20/0.46 ( woz13rule2
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Z: $i] :
% 0.20/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.20/0.46 => ( ( subset @ Y @ Z )
% 0.20/0.46 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(woz13rule3_type,type,
% 0.20/0.46 woz13rule3: $o ).
% 0.20/0.46
% 0.20/0.46 thf(woz13rule3,definition,
% 0.20/0.46 ( woz13rule3
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Z: $i] :
% 0.20/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.20/0.46 => ( ( subset @ X @ Y )
% 0.20/0.46 => ( ( subset @ X @ Z )
% 0.20/0.46 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(woz13rule4_type,type,
% 0.20/0.46 woz13rule4: $o ).
% 0.20/0.46
% 0.20/0.46 thf(woz13rule4,definition,
% 0.20/0.46 ( woz13rule4
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Z: $i] :
% 0.20/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.20/0.46 => ! [W: $i] :
% 0.20/0.46 ( ( in @ W @ ( powerset @ A ) )
% 0.20/0.46 => ( ( subset @ X @ Z )
% 0.20/0.46 => ( ( subset @ Y @ W )
% 0.20/0.46 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(woz1_1_type,type,
% 0.20/0.46 woz1_1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(woz1_1,definition,
% 0.20/0.46 ( woz1_1
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(woz1_2_type,type,
% 0.20/0.46 woz1_2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(woz1_2,definition,
% 0.20/0.46 ( woz1_2
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Z: $i] :
% 0.20/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.20/0.46 => ! [W: $i] :
% 0.20/0.46 ( ( in @ W @ ( powerset @ A ) )
% 0.20/0.46 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 0.20/0.46 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(woz1_3_type,type,
% 0.20/0.46 woz1_3: $o ).
% 0.20/0.46
% 0.20/0.46 thf(woz1_3,definition,
% 0.20/0.46 ( woz1_3
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Z: $i] :
% 0.20/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.20/0.46 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(woz1_4_type,type,
% 0.20/0.46 woz1_4: $o ).
% 0.20/0.46
% 0.20/0.46 thf(woz1_4,definition,
% 0.20/0.46 ( woz1_4
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.20/0.46 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(woz1_5_type,type,
% 0.20/0.46 woz1_5: $o ).
% 0.20/0.46
% 0.20/0.46 thf(woz1_5,definition,
% 0.20/0.46 ( woz1_5
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(breln1_type,type,
% 0.20/0.46 breln1: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(breln1all2_type,type,
% 0.20/0.46 breln1all2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(breln1all2,definition,
% 0.20/0.46 ( breln1all2
% 0.20/0.46 = ( ! [A: $i,R: $i] :
% 0.20/0.46 ( ( breln1 @ A @ R )
% 0.20/0.46 => ! [Xphi: $i > $o] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.20/0.46 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ R )
% 0.20/0.46 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(breln1Set_type,type,
% 0.20/0.46 breln1Set: $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(breln1SetBreln1_type,type,
% 0.20/0.46 breln1SetBreln1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(breln1SetBreln1,definition,
% 0.20/0.46 ( breln1SetBreln1
% 0.20/0.46 = ( ! [A: $i,R: $i] :
% 0.20/0.46 ( ( in @ R @ ( breln1Set @ A ) )
% 0.20/0.46 => ( breln1 @ A @ R ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(transitive_type,type,
% 0.20/0.46 transitive: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(antisymmetric_type,type,
% 0.20/0.46 antisymmetric: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(reflexive_type,type,
% 0.20/0.46 reflexive: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(refltransitive_type,type,
% 0.20/0.46 refltransitive: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(refllinearorder_type,type,
% 0.20/0.46 refllinearorder: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(reflwellordering_type,type,
% 0.20/0.46 reflwellordering: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(choice2fnsingleton_type,type,
% 0.20/0.46 choice2fnsingleton: $o ).
% 0.20/0.46
% 0.20/0.46 thf(choice2fnsingleton,definition,
% 0.20/0.46 ( choice2fnsingleton
% 0.20/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ? [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 & ( Xphi @ Xx @ Xy ) ) )
% 0.20/0.46 => ! [R: $i] :
% 0.20/0.46 ( ( in @ R @ ( breln1Set @ B ) )
% 0.20/0.46 => ( ( reflwellordering @ B @ R )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( singleton
% 0.20/0.46 @ ( dsetconstr @ B
% 0.20/0.46 @ ^ [Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xx @ Xy )
% 0.20/0.46 & ! [Xz: $i] :
% 0.20/0.46 ( ( in @ Xz @ B )
% 0.20/0.46 => ( ( Xphi @ Xx @ Xz )
% 0.20/0.46 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setOfPairsIsBReln1_type,type,
% 0.20/0.46 setOfPairsIsBReln1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setOfPairsIsBReln1,definition,
% 0.20/0.46 ( setOfPairsIsBReln1
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 0.20/0.46 ( breln1 @ A
% 0.20/0.46 @ ( dpsetconstr @ A @ A
% 0.20/0.46 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(breln1all1_type,type,
% 0.20/0.46 breln1all1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(breln1all1,definition,
% 0.20/0.46 ( breln1all1
% 0.20/0.46 = ( ! [A: $i,R: $i] :
% 0.20/0.46 ( ( breln1 @ A @ R )
% 0.20/0.46 => ! [Xphi: $i > $o] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.20/0.46 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ R )
% 0.20/0.46 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subbreln1_type,type,
% 0.20/0.46 subbreln1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subbreln1,definition,
% 0.20/0.46 ( subbreln1
% 0.20/0.46 = ( ! [A: $i,R: $i] :
% 0.20/0.46 ( ( breln1 @ A @ R )
% 0.20/0.46 => ! [S: $i] :
% 0.20/0.46 ( ( breln1 @ A @ S )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.20/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.20/0.46 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(eqbreln1_type,type,
% 0.20/0.46 eqbreln1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(eqbreln1,definition,
% 0.20/0.46 ( eqbreln1
% 0.20/0.46 = ( ! [A: $i,R: $i] :
% 0.20/0.46 ( ( breln1 @ A @ R )
% 0.20/0.46 => ! [S: $i] :
% 0.20/0.46 ( ( breln1 @ A @ S )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.20/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.20/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.20/0.46 => ( R = S ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(breln1invset_type,type,
% 0.20/0.46 breln1invset: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(breln1invprop_type,type,
% 0.20/0.46 breln1invprop: $o ).
% 0.20/0.46
% 0.20/0.46 thf(breln1invprop,definition,
% 0.20/0.46 ( breln1invprop
% 0.20/0.46 = ( ! [A: $i,R: $i] :
% 0.20/0.46 ( ( breln1 @ A @ R )
% 0.20/0.46 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(breln1invI_type,type,
% 0.20/0.46 breln1invI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(breln1invI,definition,
% 0.20/0.46 ( breln1invI
% 0.20/0.46 = ( ! [A: $i,R: $i] :
% 0.20/0.46 ( ( breln1 @ A @ R )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.20/0.46 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(breln1invE_type,type,
% 0.20/0.46 breln1invE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(breln1invE,definition,
% 0.20/0.46 ( breln1invE
% 0.20/0.46 = ( ! [A: $i,R: $i] :
% 0.20/0.46 ( ( breln1 @ A @ R )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 0.20/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(breln1compset_type,type,
% 0.20/0.46 breln1compset: $i > $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(breln1compprop_type,type,
% 0.20/0.46 breln1compprop: $o ).
% 0.20/0.46
% 0.20/0.46 thf(breln1compprop,definition,
% 0.20/0.46 ( breln1compprop
% 0.20/0.46 = ( ! [A: $i,R: $i] :
% 0.20/0.46 ( ( breln1 @ A @ R )
% 0.20/0.46 => ! [S: $i] :
% 0.20/0.46 ( ( breln1 @ A @ S )
% 0.20/0.46 => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(breln1compI_type,type,
% 0.20/0.46 breln1compI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(breln1compI,definition,
% 0.20/0.47 ( breln1compI
% 0.20/0.47 = ( ! [A: $i,R: $i] :
% 0.20/0.47 ( ( breln1 @ A @ R )
% 0.20/0.47 => ! [S: $i] :
% 0.20/0.47 ( ( breln1 @ A @ S )
% 0.20/0.47 => ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ! [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ A )
% 0.20/0.47 => ! [Xz: $i] :
% 0.20/0.47 ( ( in @ Xz @ A )
% 0.20/0.47 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.20/0.47 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 0.20/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(breln1compE_type,type,
% 0.20/0.47 breln1compE: $o ).
% 0.20/0.47
% 0.20/0.47 thf(breln1compE,definition,
% 0.20/0.47 ( breln1compE
% 0.20/0.47 = ( ! [A: $i,R: $i] :
% 0.20/0.47 ( ( breln1 @ A @ R )
% 0.20/0.47 => ! [S: $i] :
% 0.20/0.47 ( ( breln1 @ A @ S )
% 0.20/0.47 => ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ! [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ A )
% 0.20/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 0.20/0.47 => ? [Xz: $i] :
% 0.20/0.47 ( ( in @ Xz @ A )
% 0.20/0.47 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.20/0.47 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(breln1compEex_type,type,
% 0.20/0.47 breln1compEex: $o ).
% 0.20/0.47
% 0.20/0.47 thf(breln1compEex,definition,
% 0.20/0.47 ( breln1compEex
% 0.20/0.47 = ( ! [A: $i,R: $i] :
% 0.20/0.47 ( ( breln1 @ A @ R )
% 0.20/0.47 => ! [S: $i] :
% 0.20/0.47 ( ( breln1 @ A @ S )
% 0.20/0.47 => ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ! [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ A )
% 0.20/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 0.20/0.47 => ! [Xphi: $o] :
% 0.20/0.47 ( ! [Xz: $i] :
% 0.20/0.47 ( ( in @ Xz @ A )
% 0.20/0.47 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.20/0.47 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 0.20/0.47 => Xphi ) ) )
% 0.20/0.47 => Xphi ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(breln1unionprop_type,type,
% 0.20/0.47 breln1unionprop: $o ).
% 0.20/0.47
% 0.20/0.47 thf(breln1unionprop,definition,
% 0.20/0.47 ( breln1unionprop
% 0.20/0.47 = ( ! [A: $i,R: $i] :
% 0.20/0.47 ( ( breln1 @ A @ R )
% 0.20/0.47 => ! [S: $i] :
% 0.20/0.47 ( ( breln1 @ A @ S )
% 0.20/0.47 => ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(breln1unionIL_type,type,
% 0.20/0.47 breln1unionIL: $o ).
% 0.20/0.47
% 0.20/0.47 thf(breln1unionIL,definition,
% 0.20/0.47 ( breln1unionIL
% 0.20/0.47 = ( ! [A: $i,R: $i] :
% 0.20/0.47 ( ( breln1 @ A @ R )
% 0.20/0.47 => ! [S: $i] :
% 0.20/0.47 ( ( breln1 @ A @ S )
% 0.20/0.47 => ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ! [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ A )
% 0.20/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.20/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(breln1unionIR_type,type,
% 0.20/0.47 breln1unionIR: $o ).
% 0.20/0.47
% 0.20/0.47 thf(breln1unionIR,definition,
% 0.20/0.47 ( breln1unionIR
% 0.20/0.47 = ( ! [A: $i,R: $i] :
% 0.20/0.47 ( ( breln1 @ A @ R )
% 0.20/0.47 => ! [S: $i] :
% 0.20/0.47 ( ( breln1 @ A @ S )
% 0.20/0.47 => ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ! [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ A )
% 0.20/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.20/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(breln1unionI_type,type,
% 0.20/0.47 breln1unionI: $o ).
% 0.20/0.47
% 0.20/0.47 thf(breln1unionI,definition,
% 0.20/0.47 ( breln1unionI
% 0.20/0.47 = ( ! [A: $i,R: $i] :
% 0.20/0.47 ( ( breln1 @ A @ R )
% 0.20/0.47 => ! [S: $i] :
% 0.20/0.47 ( ( breln1 @ A @ S )
% 0.20/0.47 => ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ! [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ A )
% 0.20/0.47 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.20/0.47 | ( in @ ( kpair @ Xx @ Xy ) @ S ) )
% 0.20/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(breln1unionE_type,type,
% 0.20/0.47 breln1unionE: $o ).
% 0.20/0.47
% 0.20/0.47 thf(breln1unionE,definition,
% 0.20/0.47 ( breln1unionE
% 0.20/0.47 = ( ! [A: $i,R: $i] :
% 0.20/0.47 ( ( breln1 @ A @ R )
% 0.20/0.47 => ! [S: $i] :
% 0.20/0.47 ( ( breln1 @ A @ S )
% 0.20/0.47 => ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ! [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ A )
% 0.20/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 0.20/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.20/0.47 | ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(breln1unionEcases_type,type,
% 0.20/0.47 breln1unionEcases: $o ).
% 0.20/0.47
% 0.20/0.47 thf(breln1unionEcases,definition,
% 0.20/0.47 ( breln1unionEcases
% 0.20/0.47 = ( ! [A: $i,R: $i] :
% 0.20/0.47 ( ( breln1 @ A @ R )
% 0.20/0.47 => ! [S: $i] :
% 0.20/0.47 ( ( breln1 @ A @ S )
% 0.20/0.47 => ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ! [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ A )
% 0.20/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 0.20/0.47 => ! [Xphi: $o] :
% 0.20/0.47 ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.20/0.47 => Xphi )
% 0.20/0.47 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.20/0.47 => Xphi )
% 0.20/0.47 => Xphi ) ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(breln1unionCommutes_type,type,
% 0.20/0.47 breln1unionCommutes: $o ).
% 0.20/0.47
% 0.20/0.47 thf(breln1unionCommutes,definition,
% 0.20/0.47 ( breln1unionCommutes
% 0.20/0.47 = ( ! [A: $i,R: $i] :
% 0.20/0.47 ( ( breln1 @ A @ R )
% 0.20/0.47 => ! [S: $i] :
% 0.20/0.47 ( ( breln1 @ A @ S )
% 0.20/0.47 => ( ( binunion @ R @ S )
% 0.20/0.47 = ( binunion @ S @ R ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(woz2Ex_type,type,
% 0.20/0.47 woz2Ex: $o ).
% 0.20/0.47
% 0.20/0.47 thf(woz2Ex,definition,
% 0.20/0.47 ( woz2Ex
% 0.20/0.47 = ( ! [A: $i,R: $i] :
% 0.20/0.47 ( ( breln1 @ A @ R )
% 0.20/0.47 => ( R
% 0.20/0.47 = ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(woz2W_type,type,
% 0.20/0.47 woz2W: $o ).
% 0.20/0.47
% 0.20/0.47 thf(woz2W,definition,
% 0.20/0.47 ( woz2W
% 0.20/0.47 = ( ! [A: $i,R: $i] :
% 0.20/0.47 ( ( breln1 @ A @ R )
% 0.20/0.47 => ! [S: $i] :
% 0.20/0.47 ( ( breln1 @ A @ S )
% 0.20/0.47 => ( ( breln1invset @ A @ ( breln1compset @ A @ R @ S ) )
% 0.20/0.47 = ( breln1compset @ A @ ( breln1invset @ A @ S ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(woz2A_type,type,
% 0.20/0.47 woz2A: $o ).
% 0.20/0.47
% 0.20/0.47 thf(woz2A,definition,
% 0.20/0.47 ( woz2A
% 0.20/0.47 = ( ! [A: $i,R: $i] :
% 0.20/0.47 ( ( breln1 @ A @ R )
% 0.20/0.47 => ! [S: $i] :
% 0.20/0.47 ( ( breln1 @ A @ S )
% 0.20/0.47 => ! [T: $i] :
% 0.20/0.47 ( ( breln1 @ A @ T )
% 0.20/0.47 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 0.20/0.47 = ( binunion @ ( breln1compset @ A @ R @ T ) @ ( breln1compset @ A @ S @ T ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(woz2B_type,type,
% 0.20/0.47 woz2B: $o ).
% 0.20/0.47
% 0.20/0.47 thf(woz2B,definition,
% 0.20/0.47 ( woz2B
% 0.20/0.47 = ( ! [A: $i,R: $i] :
% 0.20/0.47 ( ( breln1 @ A @ R )
% 0.20/0.47 => ! [S: $i] :
% 0.20/0.47 ( ( breln1 @ A @ S )
% 0.20/0.47 => ! [T: $i] :
% 0.20/0.47 ( ( breln1 @ A @ T )
% 0.20/0.47 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 0.20/0.47 = ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ S ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(image1Ex_type,type,
% 0.20/0.47 image1Ex: $o ).
% 0.20/0.47
% 0.20/0.47 thf(image1Ex,definition,
% 0.20/0.47 ( image1Ex
% 0.20/0.47 = ( ! [A: $i,Xf: $i > $i] :
% 0.20/0.47 ? [B: $i] :
% 0.20/0.47 ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ B )
% 0.20/0.47 <=> ? [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ A )
% 0.20/0.47 & ( Xx
% 0.20/0.47 = ( Xf @ Xy ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(image1Ex1_type,type,
% 0.20/0.47 image1Ex1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(image1Ex1,definition,
% 0.20/0.47 ( image1Ex1
% 0.20/0.47 = ( ! [A: $i,Xf: $i > $i] :
% 0.20/0.47 ( exu
% 0.20/0.47 @ ^ [B: $i] :
% 0.20/0.47 ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ B )
% 0.20/0.47 <=> ? [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ A )
% 0.20/0.47 & ( Xx
% 0.20/0.47 = ( Xf @ Xy ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(image1_type,type,
% 0.20/0.47 image1: $i > ( $i > $i ) > $i ).
% 0.20/0.47
% 0.20/0.47 thf(image1Equiv_type,type,
% 0.20/0.47 image1Equiv: $o ).
% 0.20/0.47
% 0.20/0.47 thf(image1Equiv,definition,
% 0.20/0.47 ( image1Equiv
% 0.20/0.47 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx
% 0.20/0.47 @ ( image1 @ A
% 0.20/0.47 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 0.20/0.47 <=> ? [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ A )
% 0.20/0.47 & ( Xx
% 0.20/0.47 = ( Xf @ Xy ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(image1E_type,type,
% 0.20/0.47 image1E: $o ).
% 0.20/0.47
% 0.20/0.47 thf(image1E,definition,
% 0.20/0.47 ( image1E
% 0.20/0.47 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx
% 0.20/0.47 @ ( image1 @ A
% 0.20/0.47 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 0.20/0.47 => ? [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ A )
% 0.20/0.47 & ( Xx
% 0.20/0.47 = ( Xf @ Xy ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(image1I_type,type,
% 0.20/0.47 image1I: $o ).
% 0.20/0.47
% 0.20/0.47 thf(image1I,definition,
% 0.20/0.47 ( image1I
% 0.20/0.47 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 0.20/0.47 ( ? [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ A )
% 0.20/0.47 & ( Xx
% 0.20/0.47 = ( Xf @ Xy ) ) )
% 0.20/0.47 => ( in @ Xx
% 0.20/0.47 @ ( image1 @ A
% 0.20/0.47 @ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(injective_type,type,
% 0.20/0.47 injective: $i > $i > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(injFuncSet_type,type,
% 0.20/0.47 injFuncSet: $i > $i > $i ).
% 0.20/0.47
% 0.20/0.47 thf(injFuncInInjFuncSet_type,type,
% 0.20/0.47 injFuncInInjFuncSet: $o ).
% 0.20/0.47
% 0.20/0.47 thf(injFuncInInjFuncSet,definition,
% 0.20/0.47 ( injFuncInInjFuncSet
% 0.20/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.20/0.47 => ( ( injective @ A @ B @ Xf )
% 0.20/0.47 => ( in @ Xf @ ( injFuncSet @ A @ B ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(injFuncSetFuncIn_type,type,
% 0.20/0.47 injFuncSetFuncIn: $o ).
% 0.20/0.47
% 0.20/0.47 thf(injFuncSetFuncIn,definition,
% 0.20/0.47 ( injFuncSetFuncIn
% 0.20/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.47 ( ( in @ Xf @ ( injFuncSet @ A @ B ) )
% 0.20/0.47 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(injFuncSetFuncInj_type,type,
% 0.20/0.47 injFuncSetFuncInj: $o ).
% 0.20/0.47
% 0.20/0.47 thf(injFuncSetFuncInj,definition,
% 0.20/0.47 ( injFuncSetFuncInj
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i,Xf: $i] :
% 0.20/0.47 ( ( in @ Xf @ ( injFuncSet @ Xx @ Xy ) )
% 0.20/0.47 => ( injective @ Xx @ Xy @ Xf ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(surjective_type,type,
% 0.20/0.47 surjective: $i > $i > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(surjFuncSet_type,type,
% 0.20/0.47 surjFuncSet: $i > $i > $i ).
% 0.20/0.47
% 0.20/0.47 thf(surjFuncSetFuncIn_type,type,
% 0.20/0.47 surjFuncSetFuncIn: $o ).
% 0.20/0.47
% 0.20/0.47 thf(surjFuncSetFuncIn,definition,
% 0.20/0.47 ( surjFuncSetFuncIn
% 0.20/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.47 ( ( in @ Xf @ ( surjFuncSet @ A @ B ) )
% 0.20/0.47 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(surjFuncSetFuncSurj_type,type,
% 0.20/0.47 surjFuncSetFuncSurj: $o ).
% 0.20/0.47
% 0.20/0.47 thf(surjFuncSetFuncSurj,definition,
% 0.20/0.47 ( surjFuncSetFuncSurj
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i,Xf: $i] :
% 0.20/0.47 ( ( in @ Xf @ ( surjFuncSet @ Xx @ Xy ) )
% 0.20/0.47 => ( surjective @ Xx @ Xy @ Xf ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(leftInvIsSurj_type,type,
% 0.20/0.47 leftInvIsSurj: $o ).
% 0.20/0.47
% 0.20/0.47 thf(leftInvIsSurj,definition,
% 0.20/0.47 ( leftInvIsSurj
% 0.20/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.20/0.47 ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.20/0.47 => ! [Xg: $i] :
% 0.20/0.47 ( ( in @ Xg @ ( funcSet @ B @ A ) )
% 0.20/0.47 => ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( ( ap @ B @ A @ Xg @ ( Xf @ Xx ) )
% 0.20/0.47 = Xx ) )
% 0.20/0.47 => ( surjective @ B @ A @ Xg ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(surjCantorThm_type,type,
% 0.20/0.47 surjCantorThm: $o ).
% 0.20/0.47
% 0.20/0.47 thf(surjCantorThm,definition,
% 0.20/0.47 ( surjCantorThm
% 0.20/0.47 = ( ! [A: $i,Xf: $i] :
% 0.20/0.47 ( ( in @ Xf @ ( funcSet @ A @ ( powerset @ A ) ) )
% 0.20/0.47 => ~ ( surjective @ A @ ( powerset @ A ) @ Xf ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(foundation2,conjecture,
% 0.20/0.47 ( setextAx
% 0.20/0.47 => ( emptysetAx
% 0.20/0.47 => ( setadjoinAx
% 0.20/0.47 => ( powersetAx
% 0.20/0.47 => ( setunionAx
% 0.20/0.47 => ( omega0Ax
% 0.20/0.47 => ( omegaSAx
% 0.20/0.47 => ( omegaIndAx
% 0.20/0.47 => ( replAx
% 0.20/0.47 => ( foundationAx
% 0.20/0.47 => ( wellorderingAx
% 0.20/0.47 => ( descrp
% 0.20/0.47 => ( dsetconstrI
% 0.20/0.47 => ( dsetconstrEL
% 0.20/0.47 => ( dsetconstrER
% 0.20/0.47 => ( exuE1
% 0.20/0.47 => ( prop2setE
% 0.20/0.47 => ( emptysetE
% 0.20/0.47 => ( emptysetimpfalse
% 0.20/0.47 => ( notinemptyset
% 0.20/0.47 => ( exuE3e
% 0.20/0.47 => ( setext
% 0.20/0.47 => ( emptyI
% 0.20/0.47 => ( noeltsimpempty
% 0.20/0.47 => ( setbeta
% 0.20/0.47 => ( nonemptyE1
% 0.20/0.47 => ( nonemptyI
% 0.20/0.47 => ( nonemptyI1
% 0.20/0.47 => ( setadjoinIL
% 0.20/0.47 => ( emptyinunitempty
% 0.20/0.47 => ( setadjoinIR
% 0.20/0.47 => ( setadjoinE
% 0.20/0.47 => ( setadjoinOr
% 0.20/0.47 => ( setoftrueEq
% 0.20/0.47 => ( powersetI
% 0.20/0.47 => ( emptyinPowerset
% 0.20/0.47 => ( emptyInPowerset
% 0.20/0.47 => ( powersetE
% 0.20/0.47 => ( setunionI
% 0.20/0.47 => ( setunionE
% 0.20/0.47 => ( subPowSU
% 0.20/0.47 => ( exuE2
% 0.20/0.47 => ( nonemptyImpWitness
% 0.20/0.47 => ( uniqinunit
% 0.20/0.47 => ( notinsingleton
% 0.20/0.47 => ( eqinunit
% 0.20/0.47 => ( singletonsswitch
% 0.20/0.47 => ( upairsetE
% 0.20/0.47 => ( upairsetIL
% 0.20/0.47 => ( upairsetIR
% 0.20/0.47 => ( emptyE1
% 0.20/0.47 => ( vacuousDall
% 0.20/0.47 => ( quantDeMorgan1
% 0.20/0.47 => ( quantDeMorgan2
% 0.20/0.47 => ( quantDeMorgan3
% 0.20/0.47 => ( quantDeMorgan4
% 0.20/0.47 => ( prop2setI
% 0.20/0.47 => ( prop2set2propI
% 0.20/0.47 => ( notdexE
% 0.20/0.47 => ( notdallE
% 0.20/0.47 => ( exuI1
% 0.20/0.47 => ( exuI3
% 0.20/0.47 => ( exuI2
% 0.20/0.47 => ( inCongP
% 0.20/0.47 => ( in__Cong
% 0.20/0.47 => ( exuE3u
% 0.20/0.47 => ( exu__Cong
% 0.20/0.47 => ( emptyset__Cong
% 0.20/0.47 => ( setadjoin__Cong
% 0.20/0.47 => ( powerset__Cong
% 0.20/0.47 => ( setunion__Cong
% 0.20/0.47 => ( omega__Cong
% 0.20/0.47 => ( exuEu
% 0.20/0.47 => ( descr__Cong
% 0.20/0.47 => ( dsetconstr__Cong
% 0.20/0.47 => ( subsetI1
% 0.20/0.47 => ( eqimpsubset2
% 0.20/0.47 => ( eqimpsubset1
% 0.20/0.47 => ( subsetI2
% 0.20/0.47 => ( emptysetsubset
% 0.20/0.47 => ( subsetE
% 0.20/0.47 => ( subsetE2
% 0.20/0.47 => ( notsubsetI
% 0.20/0.47 => ( notequalI1
% 0.20/0.47 => ( notequalI2
% 0.20/0.47 => ( subsetRefl
% 0.20/0.47 => ( subsetTrans
% 0.20/0.47 => ( setadjoinSub
% 0.20/0.47 => ( setadjoinSub2
% 0.20/0.47 => ( subset2powerset
% 0.20/0.47 => ( setextsub
% 0.20/0.47 => ( subsetemptysetimpeq
% 0.20/0.47 => ( powersetI1
% 0.20/0.47 => ( powersetE1
% 0.20/0.47 => ( inPowerset
% 0.20/0.47 => ( powersetsubset
% 0.20/0.47 => ( sepInPowerset
% 0.20/0.47 => ( sepSubset
% 0.20/0.47 => ( binunionIL
% 0.20/0.47 => ( upairset2IR
% 0.20/0.47 => ( binunionIR
% 0.20/0.47 => ( binunionEcases
% 0.20/0.47 => ( binunionE
% 0.20/0.47 => ( binunionLsub
% 0.20/0.47 => ( binunionRsub
% 0.20/0.47 => ( binintersectI
% 0.20/0.47 => ( binintersectSubset5
% 0.20/0.47 => ( binintersectEL
% 0.20/0.47 => ( binintersectLsub
% 0.20/0.47 => ( binintersectSubset2
% 0.20/0.47 => ( binintersectSubset3
% 0.20/0.47 => ( binintersectER
% 0.20/0.47 => ( disjointsetsI1
% 0.20/0.47 => ( binintersectRsub
% 0.20/0.47 => ( binintersectSubset4
% 0.20/0.47 => ( binintersectSubset1
% 0.20/0.47 => ( bs114d
% 0.20/0.47 => ( setminusI
% 0.20/0.47 => ( setminusEL
% 0.20/0.47 => ( setminusER
% 0.20/0.47 => ( setminusSubset2
% 0.20/0.47 => ( setminusERneg
% 0.20/0.47 => ( setminusELneg
% 0.20/0.47 => ( setminusILneg
% 0.20/0.47 => ( setminusIRneg
% 0.20/0.47 => ( setminusLsub
% 0.20/0.47 => ( setminusSubset1
% 0.20/0.47 => ( symdiffE
% 0.20/0.47 => ( symdiffI1
% 0.20/0.47 => ( symdiffI2
% 0.20/0.47 => ( symdiffIneg1
% 0.20/0.47 => ( symdiffIneg2
% 0.20/0.47 => ( secondinupair
% 0.20/0.47 => ( setukpairIL
% 0.20/0.47 => ( setukpairIR
% 0.20/0.47 => ( kpairiskpair
% 0.20/0.47 => ( kpairp
% 0.20/0.47 => ( singletonsubset
% 0.20/0.47 => ( singletoninpowerset
% 0.20/0.47 => ( singletoninpowunion
% 0.20/0.47 => ( upairset2E
% 0.20/0.47 => ( upairsubunion
% 0.20/0.47 => ( upairinpowunion
% 0.20/0.47 => ( ubforcartprodlem1
% 0.20/0.47 => ( ubforcartprodlem2
% 0.20/0.47 => ( ubforcartprodlem3
% 0.20/0.47 => ( cartprodpairin
% 0.20/0.47 => ( cartprodmempair1
% 0.20/0.47 => ( cartprodmempair
% 0.20/0.47 => ( setunionE2
% 0.20/0.47 => ( setunionsingleton1
% 0.20/0.47 => ( setunionsingleton2
% 0.20/0.47 => ( setunionsingleton
% 0.20/0.47 => ( singletonprop
% 0.20/0.47 => ( ex1E1
% 0.20/0.47 => ( ex1I
% 0.20/0.47 => ( ex1I2
% 0.20/0.47 => ( singletonsuniq
% 0.20/0.47 => ( setukpairinjL1
% 0.20/0.47 => ( kfstsingleton
% 0.20/0.47 => ( theprop
% 0.20/0.47 => ( kfstpairEq
% 0.20/0.47 => ( cartprodfstin
% 0.20/0.47 => ( setukpairinjL2
% 0.20/0.47 => ( setukpairinjL
% 0.20/0.47 => ( setukpairinjR11
% 0.20/0.47 => ( setukpairinjR12
% 0.20/0.47 => ( setukpairinjR1
% 0.20/0.47 => ( upairequniteq
% 0.20/0.47 => ( setukpairinjR2
% 0.20/0.47 => ( setukpairinjR
% 0.20/0.47 => ( ksndsingleton
% 0.20/0.47 => ( ksndpairEq
% 0.20/0.47 => ( kpairsurjEq
% 0.20/0.47 => ( cartprodsndin
% 0.20/0.47 => ( cartprodpairmemEL
% 0.20/0.47 => ( cartprodpairmemER
% 0.20/0.47 => ( cartprodmempaircEq
% 0.20/0.47 => ( cartprodfstpairEq
% 0.20/0.47 => ( cartprodsndpairEq
% 0.20/0.47 => ( cartprodpairsurjEq
% 0.20/0.47 => ( dpsetconstrI
% 0.20/0.47 => ( dpsetconstrSub
% 0.20/0.47 => ( setOfPairsIsBReln
% 0.20/0.47 => ( dpsetconstrERa
% 0.20/0.47 => ( dpsetconstrEL1
% 0.20/0.47 => ( dpsetconstrEL2
% 0.20/0.47 => ( dpsetconstrER
% 0.20/0.47 => ( funcImageSingleton
% 0.20/0.47 => ( apProp
% 0.20/0.47 => ( app
% 0.20/0.47 => ( infuncsetfunc
% 0.20/0.47 => ( ap2p
% 0.20/0.47 => ( funcinfuncset
% 0.20/0.47 => ( lamProp
% 0.20/0.47 => ( lamp
% 0.20/0.47 => ( lam2p
% 0.20/0.47 => ( brelnall1
% 0.20/0.47 => ( brelnall2
% 0.20/0.47 => ( ex1E2
% 0.20/0.47 => ( funcGraphProp1
% 0.20/0.47 => ( funcGraphProp3
% 0.20/0.47 => ( funcGraphProp2
% 0.20/0.47 => ( funcextLem
% 0.20/0.47 => ( funcGraphProp4
% 0.20/0.47 => ( subbreln
% 0.20/0.47 => ( eqbreln
% 0.20/0.47 => ( funcext
% 0.20/0.47 => ( funcext2
% 0.20/0.47 => ( ap2apEq1
% 0.20/0.47 => ( ap2apEq2
% 0.20/0.47 => ( beta1
% 0.20/0.47 => ( eta1
% 0.20/0.47 => ( lam2lamEq
% 0.20/0.47 => ( beta2
% 0.20/0.47 => ( eta2
% 0.20/0.47 => ( iffalseProp1
% 0.20/0.47 => ( iffalseProp2
% 0.20/0.47 => ( iftrueProp1
% 0.20/0.47 => ( iftrueProp2
% 0.20/0.47 => ( ifSingleton
% 0.20/0.47 => ( ifp
% 0.20/0.47 => ( theeq
% 0.20/0.47 => ( iftrue
% 0.20/0.47 => ( iffalse
% 0.20/0.47 => ( iftrueorfalse
% 0.20/0.47 => ( binintersectT_lem
% 0.20/0.47 => ( binunionT_lem
% 0.20/0.47 => ( powersetT_lem
% 0.20/0.47 => ( setminusT_lem
% 0.20/0.47 => ( complementT_lem
% 0.20/0.47 => ( setextT
% 0.20/0.47 => ( subsetTI
% 0.20/0.47 => ( powersetTI1
% 0.20/0.47 => ( powersetTE1
% 0.20/0.47 => ( complementTI1
% 0.20/0.47 => ( complementTE1
% 0.20/0.47 => ( binintersectTELcontra
% 0.20/0.47 => ( binintersectTERcontra
% 0.20/0.47 => ( contrasubsetT
% 0.20/0.47 => ( contrasubsetT1
% 0.20/0.47 => ( contrasubsetT2
% 0.20/0.47 => ( contrasubsetT3
% 0.20/0.47 => ( doubleComplementI1
% 0.20/0.47 => ( doubleComplementE1
% 0.20/0.47 => ( doubleComplementSub1
% 0.20/0.47 => ( doubleComplementSub2
% 0.20/0.47 => ( doubleComplementEq
% 0.20/0.47 => ( complementTnotintersectT
% 0.20/0.47 => ( complementImpComplementIntersect
% 0.20/0.47 => ( complementSubsetComplementIntersect
% 0.20/0.47 => ( complementInPowersetComplementIntersect
% 0.20/0.47 => ( contraSubsetComplement
% 0.20/0.47 => ( complementTcontraSubset
% 0.20/0.47 => ( binunionTILcontra
% 0.20/0.47 => ( binunionTIRcontra
% 0.20/0.47 => ( inIntersectImpInUnion
% 0.20/0.47 => ( inIntersectImpInUnion2
% 0.20/0.47 => ( inIntersectImpInIntersectUnions
% 0.20/0.47 => ( intersectInPowersetIntersectUnions
% 0.20/0.47 => ( inComplementUnionImpNotIn1
% 0.20/0.47 => ( inComplementUnionImpInComplement1
% 0.20/0.47 => ( binunionTE
% 0.20/0.47 => ( binunionTEcontra
% 0.20/0.47 => ( demorgan2a1
% 0.20/0.47 => ( complementUnionInPowersetComplement
% 0.20/0.47 => ( demorgan2a2
% 0.20/0.47 => ( demorgan1a
% 0.20/0.47 => ( demorgan1b
% 0.20/0.47 => ( demorgan1
% 0.20/0.47 => ( demorgan2a
% 0.20/0.47 => ( demorgan2b2
% 0.20/0.47 => ( demorgan2b
% 0.20/0.47 => ( demorgan2
% 0.20/0.47 => ( woz13rule0
% 0.20/0.47 => ( woz13rule1
% 0.20/0.47 => ( woz13rule2
% 0.20/0.47 => ( woz13rule3
% 0.20/0.47 => ( woz13rule4
% 0.20/0.47 => ( woz1_1
% 0.20/0.47 => ( woz1_2
% 0.20/0.47 => ( woz1_3
% 0.20/0.47 => ( woz1_4
% 0.20/0.47 => ( woz1_5
% 0.20/0.47 => ( breln1all2
% 0.20/0.47 => ( breln1SetBreln1
% 0.20/0.47 => ( choice2fnsingleton
% 0.20/0.47 => ( setOfPairsIsBReln1
% 0.20/0.47 => ( breln1all1
% 0.20/0.47 => ( subbreln1
% 0.20/0.47 => ( eqbreln1
% 0.20/0.47 => ( breln1invprop
% 0.20/0.47 => ( breln1invI
% 0.20/0.47 => ( breln1invE
% 0.20/0.47 => ( breln1compprop
% 0.20/0.47 => ( breln1compI
% 0.20/0.47 => ( breln1compE
% 0.20/0.47 => ( breln1compEex
% 0.20/0.47 => ( breln1unionprop
% 0.20/0.47 => ( breln1unionIL
% 0.20/0.47 => ( breln1unionIR
% 0.20/0.47 => ( breln1unionI
% 0.20/0.47 => ( breln1unionE
% 0.20/0.47 => ( breln1unionEcases
% 0.20/0.47 => ( breln1unionCommutes
% 0.20/0.47 => ( woz2Ex
% 0.20/0.47 => ( woz2W
% 0.20/0.47 => ( woz2A
% 0.20/0.47 => ( woz2B
% 0.20/0.47 => ( image1Ex
% 0.20/0.47 => ( image1Ex1
% 0.20/0.47 => ( image1Equiv
% 0.20/0.47 => ( image1E
% 0.20/0.47 => ( image1I
% 0.20/0.47 => ( injFuncInInjFuncSet
% 0.20/0.47 => ( injFuncSetFuncIn
% 0.20/0.47 => ( injFuncSetFuncInj
% 0.20/0.47 => ( surjFuncSetFuncIn
% 0.20/0.47 => ( surjFuncSetFuncSurj
% 0.20/0.47 => ( leftInvIsSurj
% 0.20/0.47 => ( surjCantorThm
% 0.20/0.47 => ! [A: $i] :
% 0.20/0.47 ( ( nonempty @ A )
% 0.20/0.47 => ? [X: $i] :
% 0.20/0.47 ( ( in @ X @ A )
% 0.20/0.47 & ( ( binintersect @ X @ A )
% 0.20/0.47 = emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 ------------------------
% 3.02/1.55 ---- Embedded in THF ---
% 3.02/1.55 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.02/1.55 %%% Generated on Tue Feb 24 12:35:21 EST 2026
% 3.02/1.55 %%% using '$$dhol' embedding, version 1.3.0.
% 3.02/1.55 %%% Logic specification used:
% 3.02/1.55 %%% thf(spec, logic, $$dhol).
% 3.02/1.55
% 3.02/1.55 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.Th7rVCfvTI/DTF2DTF17306.p
% See solution above
% 3.02/1.55 ------------------------
% 3.02/1.59 ---- Cleaned THF ---
% 3.02/1.59 thf(in_type,type,
% 3.02/1.59 in: $i > $i > $o ).
% 3.02/1.59
% 3.02/1.59 thf(exu_type,type,
% 3.02/1.59 exu: ( $i > $o ) > $o ).
% 3.02/1.59
% 3.02/1.59 thf(exu,definition,
% 3.02/1.59 ( exu
% 3.02/1.59 = ( ^ [Xphi: $i > $o] :
% 3.02/1.59 ? [Xx: $i] :
% 3.02/1.59 ( ( Xphi @ Xx )
% 3.02/1.59 & ! [Xy: $i] :
% 3.02/1.59 ( ( Xphi @ Xy )
% 3.02/1.59 => ( Xx = Xy ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(setextAx_type,type,
% 3.02/1.59 setextAx: $o ).
% 3.02/1.59
% 3.02/1.59 thf(setextAx,definition,
% 3.02/1.59 ( setextAx
% 3.02/1.59 = ( ! [A: $i,B: $i] :
% 3.02/1.59 ( ! [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ A )
% 3.02/1.59 <=> ( in @ Xx @ B ) )
% 3.02/1.59 => ( A = B ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(emptyset_type,type,
% 3.02/1.59 emptyset: $i ).
% 3.02/1.59
% 3.02/1.59 thf(emptysetAx_type,type,
% 3.02/1.59 emptysetAx: $o ).
% 3.02/1.59
% 3.02/1.59 thf(emptysetAx,definition,
% 3.02/1.59 ( emptysetAx
% 3.02/1.59 = ( ! [Xx: $i] :
% 3.02/1.59 ~ ( in @ Xx @ emptyset ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(setadjoin_type,type,
% 3.02/1.59 setadjoin: $i > $i > $i ).
% 3.02/1.59
% 3.02/1.59 thf(setadjoinAx_type,type,
% 3.02/1.59 setadjoinAx: $o ).
% 3.02/1.59
% 3.02/1.59 thf(setadjoinAx,definition,
% 3.02/1.59 ( setadjoinAx
% 3.02/1.59 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.02/1.59 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.02/1.59 <=> ( ( Xy = Xx )
% 3.02/1.59 | ( in @ Xy @ A ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(powerset_type,type,
% 3.02/1.59 powerset: $i > $i ).
% 3.02/1.59
% 3.02/1.59 thf(powersetAx_type,type,
% 3.02/1.59 powersetAx: $o ).
% 3.02/1.59
% 3.02/1.59 thf(powersetAx,definition,
% 3.02/1.59 ( powersetAx
% 3.02/1.59 = ( ! [A: $i,B: $i] :
% 3.02/1.59 ( ( in @ B @ ( powerset @ A ) )
% 3.02/1.59 <=> ! [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ B )
% 3.02/1.59 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(setunion_type,type,
% 3.02/1.59 setunion: $i > $i ).
% 3.02/1.59
% 3.02/1.59 thf(setunionAx_type,type,
% 3.02/1.59 setunionAx: $o ).
% 3.02/1.59
% 3.02/1.59 thf(setunionAx,definition,
% 3.02/1.59 ( setunionAx
% 3.02/1.59 = ( ! [A: $i,Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ ( setunion @ A ) )
% 3.02/1.59 <=> ? [B: $i] :
% 3.02/1.59 ( ( in @ Xx @ B )
% 3.02/1.59 & ( in @ B @ A ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(omega_type,type,
% 3.02/1.59 omega: $i ).
% 3.02/1.59
% 3.02/1.59 thf(omega0Ax_type,type,
% 3.02/1.59 omega0Ax: $o ).
% 3.02/1.59
% 3.02/1.59 thf(omega0Ax,definition,
% 3.02/1.59 ( omega0Ax
% 3.02/1.59 = ( in @ emptyset @ omega ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(omegaSAx_type,type,
% 3.02/1.59 omegaSAx: $o ).
% 3.02/1.59
% 3.02/1.59 thf(omegaSAx,definition,
% 3.02/1.59 ( omegaSAx
% 3.02/1.59 = ( ! [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ omega )
% 3.02/1.59 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(omegaIndAx_type,type,
% 3.02/1.59 omegaIndAx: $o ).
% 3.02/1.59
% 3.02/1.59 thf(omegaIndAx,definition,
% 3.02/1.59 ( omegaIndAx
% 3.02/1.59 = ( ! [A: $i] :
% 3.02/1.59 ( ( ( in @ emptyset @ A )
% 3.02/1.59 & ! [Xx: $i] :
% 3.02/1.59 ( ( ( in @ Xx @ omega )
% 3.02/1.59 & ( in @ Xx @ A ) )
% 3.02/1.59 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 3.02/1.59 => ! [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ omega )
% 3.02/1.59 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(replAx_type,type,
% 3.02/1.59 replAx: $o ).
% 3.02/1.59
% 3.02/1.59 thf(replAx,definition,
% 3.02/1.59 ( replAx
% 3.02/1.59 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 3.02/1.59 ( ! [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ A )
% 3.02/1.59 => ( exu
% 3.02/1.59 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 3.02/1.59 => ? [B: $i] :
% 3.02/1.59 ! [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ B )
% 3.02/1.59 <=> ? [Xy: $i] :
% 3.02/1.59 ( ( in @ Xy @ A )
% 3.02/1.59 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(foundationAx_type,type,
% 3.02/1.59 foundationAx: $o ).
% 3.02/1.59
% 3.02/1.59 thf(foundationAx,definition,
% 3.02/1.59 ( foundationAx
% 3.02/1.59 = ( ! [A: $i] :
% 3.02/1.59 ( ? [Xx: $i] : ( in @ Xx @ A )
% 3.02/1.59 => ? [B: $i] :
% 3.02/1.59 ( ( in @ B @ A )
% 3.02/1.59 & ~ ? [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ B )
% 3.02/1.59 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(wellorderingAx_type,type,
% 3.02/1.59 wellorderingAx: $o ).
% 3.02/1.59
% 3.02/1.59 thf(wellorderingAx,definition,
% 3.02/1.59 ( wellorderingAx
% 3.02/1.59 = ( ! [A: $i] :
% 3.02/1.59 ? [B: $i] :
% 3.02/1.59 ( ! [C: $i] :
% 3.02/1.59 ( ( in @ C @ B )
% 3.02/1.59 => ! [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ C )
% 3.02/1.59 => ( in @ Xx @ A ) ) )
% 3.02/1.59 & ! [Xx: $i,Xy: $i] :
% 3.02/1.59 ( ( ( in @ Xx @ A )
% 3.02/1.59 & ( in @ Xy @ A ) )
% 3.02/1.59 => ( ! [C: $i] :
% 3.02/1.59 ( ( in @ C @ B )
% 3.02/1.59 => ( ( in @ Xx @ C )
% 3.02/1.59 <=> ( in @ Xy @ C ) ) )
% 3.02/1.59 => ( Xx = Xy ) ) )
% 3.02/1.59 & ! [C: $i,D: $i] :
% 3.02/1.59 ( ( ( in @ C @ B )
% 3.02/1.59 & ( in @ D @ B ) )
% 3.02/1.59 => ( ! [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ C )
% 3.02/1.59 => ( in @ Xx @ D ) )
% 3.02/1.59 | ! [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ D )
% 3.02/1.59 => ( in @ Xx @ C ) ) ) )
% 3.02/1.59 & ! [C: $i] :
% 3.02/1.59 ( ( ! [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ C )
% 3.02/1.59 => ( in @ Xx @ A ) )
% 3.02/1.59 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 3.02/1.59 => ? [D: $i,Xx: $i] :
% 3.02/1.59 ( ( in @ D @ B )
% 3.02/1.59 & ( in @ Xx @ C )
% 3.02/1.59 & ~ ? [Xy: $i] :
% 3.02/1.59 ( ( in @ Xy @ D )
% 3.02/1.59 & ( in @ Xy @ C ) )
% 3.02/1.59 & ! [E: $i] :
% 3.02/1.59 ( ( in @ E @ B )
% 3.02/1.59 => ( ! [Xy: $i] :
% 3.02/1.59 ( ( in @ Xy @ E )
% 3.02/1.59 => ( in @ Xy @ D ) )
% 3.02/1.59 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(descr_type,type,
% 3.02/1.59 descr: ( $i > $o ) > $i ).
% 3.02/1.59
% 3.02/1.59 thf(descrp_type,type,
% 3.02/1.59 descrp: $o ).
% 3.02/1.59
% 3.02/1.59 thf(descrp,definition,
% 3.02/1.59 ( descrp
% 3.02/1.59 = ( ! [Xphi: $i > $o] :
% 3.02/1.59 ( ( exu
% 3.02/1.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.02/1.59 => ( Xphi
% 3.02/1.59 @ ( descr
% 3.02/1.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(dsetconstr_type,type,
% 3.02/1.59 dsetconstr: $i > ( $i > $o ) > $i ).
% 3.02/1.59
% 3.02/1.59 thf(dsetconstrI_type,type,
% 3.02/1.59 dsetconstrI: $o ).
% 3.02/1.59
% 3.02/1.59 thf(dsetconstrI,definition,
% 3.02/1.59 ( dsetconstrI
% 3.02/1.59 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ A )
% 3.02/1.59 => ( ( Xphi @ Xx )
% 3.02/1.59 => ( in @ Xx
% 3.02/1.59 @ ( dsetconstr @ A
% 3.02/1.59 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(dsetconstrEL_type,type,
% 3.02/1.59 dsetconstrEL: $o ).
% 3.02/1.59
% 3.02/1.59 thf(dsetconstrEL,definition,
% 3.02/1.59 ( dsetconstrEL
% 3.02/1.59 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.02/1.59 ( ( in @ Xx
% 3.02/1.59 @ ( dsetconstr @ A
% 3.02/1.59 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.02/1.59 => ( in @ Xx @ A ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(dsetconstrER_type,type,
% 3.02/1.59 dsetconstrER: $o ).
% 3.02/1.59
% 3.02/1.59 thf(dsetconstrER,definition,
% 3.02/1.59 ( dsetconstrER
% 3.02/1.59 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.02/1.59 ( ( in @ Xx
% 3.02/1.59 @ ( dsetconstr @ A
% 3.02/1.59 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.02/1.59 => ( Xphi @ Xx ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(exuE1_type,type,
% 3.02/1.59 exuE1: $o ).
% 3.02/1.59
% 3.02/1.59 thf(exuE1,definition,
% 3.02/1.59 ( exuE1
% 3.02/1.59 = ( ! [Xphi: $i > $o] :
% 3.02/1.59 ( ( exu
% 3.02/1.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.02/1.59 => ? [Xx: $i] :
% 3.02/1.59 ( ( Xphi @ Xx )
% 3.02/1.59 & ! [Xy: $i] :
% 3.02/1.59 ( ( Xphi @ Xy )
% 3.02/1.59 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(prop2set_type,type,
% 3.02/1.59 prop2set: $o > $i ).
% 3.02/1.59
% 3.02/1.59 thf(prop2setE_type,type,
% 3.02/1.59 prop2setE: $o ).
% 3.02/1.59
% 3.02/1.59 thf(prop2setE,definition,
% 3.02/1.59 ( prop2setE
% 3.02/1.59 = ( ! [Xphi: $o,Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 3.02/1.59 => Xphi ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(emptysetE_type,type,
% 3.02/1.59 emptysetE: $o ).
% 3.02/1.59
% 3.02/1.59 thf(emptysetE,definition,
% 3.02/1.59 ( emptysetE
% 3.02/1.59 = ( ! [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ emptyset )
% 3.02/1.59 => ! [Xphi: $o] : Xphi ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(emptysetimpfalse_type,type,
% 3.02/1.59 emptysetimpfalse: $o ).
% 3.02/1.59
% 3.02/1.59 thf(emptysetimpfalse,definition,
% 3.02/1.59 ( emptysetimpfalse
% 3.02/1.59 = ( ! [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ emptyset )
% 3.02/1.59 => $false ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(notinemptyset_type,type,
% 3.02/1.59 notinemptyset: $o ).
% 3.02/1.59
% 3.02/1.59 thf(notinemptyset,definition,
% 3.02/1.59 ( notinemptyset
% 3.02/1.59 = ( ! [Xx: $i] :
% 3.02/1.59 ~ ( in @ Xx @ emptyset ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(exuE3e_type,type,
% 3.02/1.59 exuE3e: $o ).
% 3.02/1.59
% 3.02/1.59 thf(exuE3e,definition,
% 3.02/1.59 ( exuE3e
% 3.02/1.59 = ( ! [Xphi: $i > $o] :
% 3.02/1.59 ( ( exu
% 3.02/1.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.02/1.59 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(setext_type,type,
% 3.02/1.59 setext: $o ).
% 3.02/1.59
% 3.02/1.59 thf(setext,definition,
% 3.02/1.59 ( setext
% 3.02/1.59 = ( ! [A: $i,B: $i] :
% 3.02/1.59 ( ! [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ A )
% 3.02/1.59 => ( in @ Xx @ B ) )
% 3.02/1.59 => ( ! [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ B )
% 3.02/1.59 => ( in @ Xx @ A ) )
% 3.02/1.59 => ( A = B ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(emptyI_type,type,
% 3.02/1.59 emptyI: $o ).
% 3.02/1.59
% 3.02/1.59 thf(emptyI,definition,
% 3.02/1.59 ( emptyI
% 3.02/1.59 = ( ! [A: $i] :
% 3.02/1.59 ( ! [Xx: $i] :
% 3.02/1.59 ~ ( in @ Xx @ A )
% 3.02/1.59 => ( A = emptyset ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(noeltsimpempty_type,type,
% 3.02/1.59 noeltsimpempty: $o ).
% 3.02/1.59
% 3.02/1.59 thf(noeltsimpempty,definition,
% 3.02/1.59 ( noeltsimpempty
% 3.02/1.59 = ( ! [A: $i] :
% 3.02/1.59 ( ! [Xx: $i] :
% 3.02/1.59 ~ ( in @ Xx @ A )
% 3.02/1.59 => ( A = emptyset ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(setbeta_type,type,
% 3.02/1.59 setbeta: $o ).
% 3.02/1.59
% 3.02/1.59 thf(setbeta,definition,
% 3.02/1.59 ( setbeta
% 3.02/1.59 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ A )
% 3.02/1.59 => ( ( in @ Xx
% 3.02/1.59 @ ( dsetconstr @ A
% 3.02/1.59 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.02/1.59 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(nonempty_type,type,
% 3.02/1.59 nonempty: $i > $o ).
% 3.02/1.59
% 3.02/1.59 thf(nonempty,definition,
% 3.02/1.59 ( nonempty
% 3.02/1.59 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(nonemptyE1_type,type,
% 3.02/1.59 nonemptyE1: $o ).
% 3.02/1.59
% 3.02/1.59 thf(nonemptyE1,definition,
% 3.02/1.59 ( nonemptyE1
% 3.02/1.59 = ( ! [A: $i] :
% 3.02/1.59 ( ( nonempty @ A )
% 3.02/1.59 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(nonemptyI_type,type,
% 3.02/1.59 nonemptyI: $o ).
% 3.02/1.59
% 3.02/1.59 thf(nonemptyI,definition,
% 3.02/1.59 ( nonemptyI
% 3.02/1.59 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ A )
% 3.02/1.59 => ( ( Xphi @ Xx )
% 3.02/1.59 => ( nonempty
% 3.02/1.59 @ ( dsetconstr @ A
% 3.02/1.59 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(nonemptyI1_type,type,
% 3.02/1.59 nonemptyI1: $o ).
% 3.02/1.59
% 3.02/1.59 thf(nonemptyI1,definition,
% 3.02/1.59 ( nonemptyI1
% 3.02/1.59 = ( ! [A: $i] :
% 3.02/1.59 ( ? [Xx: $i] : ( in @ Xx @ A )
% 3.02/1.59 => ( nonempty @ A ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(setadjoinIL_type,type,
% 3.02/1.59 setadjoinIL: $o ).
% 3.02/1.59
% 3.02/1.59 thf(setadjoinIL,definition,
% 3.02/1.59 ( setadjoinIL
% 3.02/1.59 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(emptyinunitempty_type,type,
% 3.02/1.59 emptyinunitempty: $o ).
% 3.02/1.59
% 3.02/1.59 thf(emptyinunitempty,definition,
% 3.02/1.59 ( emptyinunitempty
% 3.02/1.59 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(setadjoinIR_type,type,
% 3.02/1.59 setadjoinIR: $o ).
% 3.02/1.59
% 3.02/1.59 thf(setadjoinIR,definition,
% 3.02/1.59 ( setadjoinIR
% 3.02/1.59 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.02/1.59 ( ( in @ Xy @ A )
% 3.02/1.59 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(setadjoinE_type,type,
% 3.02/1.59 setadjoinE: $o ).
% 3.02/1.59
% 3.02/1.59 thf(setadjoinE,definition,
% 3.02/1.59 ( setadjoinE
% 3.02/1.59 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.02/1.59 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.02/1.59 => ! [Xphi: $o] :
% 3.02/1.59 ( ( ( Xy = Xx )
% 3.02/1.59 => Xphi )
% 3.02/1.59 => ( ( ( in @ Xy @ A )
% 3.02/1.59 => Xphi )
% 3.02/1.59 => Xphi ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(setadjoinOr_type,type,
% 3.02/1.59 setadjoinOr: $o ).
% 3.02/1.59
% 3.02/1.59 thf(setadjoinOr,definition,
% 3.02/1.59 ( setadjoinOr
% 3.02/1.59 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.02/1.59 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.02/1.59 => ( ( Xy = Xx )
% 3.02/1.59 | ( in @ Xy @ A ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(setoftrueEq_type,type,
% 3.02/1.59 setoftrueEq: $o ).
% 3.02/1.59
% 3.02/1.59 thf(setoftrueEq,definition,
% 3.02/1.59 ( setoftrueEq
% 3.02/1.59 = ( ! [A: $i] :
% 3.02/1.59 ( ( dsetconstr @ A
% 3.02/1.59 @ ^ [Xx: $i] : $true )
% 3.02/1.59 = A ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(powersetI_type,type,
% 3.02/1.59 powersetI: $o ).
% 3.02/1.59
% 3.02/1.59 thf(powersetI,definition,
% 3.02/1.59 ( powersetI
% 3.02/1.59 = ( ! [A: $i,B: $i] :
% 3.02/1.59 ( ! [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ B )
% 3.02/1.59 => ( in @ Xx @ A ) )
% 3.02/1.59 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(emptyinPowerset_type,type,
% 3.02/1.59 emptyinPowerset: $o ).
% 3.02/1.59
% 3.02/1.59 thf(emptyinPowerset,definition,
% 3.02/1.59 ( emptyinPowerset
% 3.02/1.59 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(emptyInPowerset_type,type,
% 3.02/1.59 emptyInPowerset: $o ).
% 3.02/1.59
% 3.02/1.59 thf(emptyInPowerset,definition,
% 3.02/1.59 ( emptyInPowerset
% 3.02/1.59 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(powersetE_type,type,
% 3.02/1.59 powersetE: $o ).
% 3.02/1.59
% 3.02/1.59 thf(powersetE,definition,
% 3.02/1.59 ( powersetE
% 3.02/1.59 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.59 ( ( in @ B @ ( powerset @ A ) )
% 3.02/1.59 => ( ( in @ Xx @ B )
% 3.02/1.59 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(setunionI_type,type,
% 3.02/1.59 setunionI: $o ).
% 3.02/1.59
% 3.02/1.59 thf(setunionI,definition,
% 3.02/1.59 ( setunionI
% 3.02/1.59 = ( ! [A: $i,Xx: $i,B: $i] :
% 3.02/1.59 ( ( in @ Xx @ B )
% 3.02/1.59 => ( ( in @ B @ A )
% 3.02/1.59 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(setunionE_type,type,
% 3.02/1.59 setunionE: $o ).
% 3.02/1.59
% 3.02/1.59 thf(setunionE,definition,
% 3.02/1.59 ( setunionE
% 3.02/1.59 = ( ! [A: $i,Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ ( setunion @ A ) )
% 3.02/1.59 => ! [Xphi: $o] :
% 3.02/1.59 ( ! [B: $i] :
% 3.02/1.59 ( ( in @ Xx @ B )
% 3.02/1.59 => ( ( in @ B @ A )
% 3.02/1.59 => Xphi ) )
% 3.02/1.59 => Xphi ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(subPowSU_type,type,
% 3.02/1.59 subPowSU: $o ).
% 3.02/1.59
% 3.02/1.59 thf(subPowSU,definition,
% 3.02/1.59 ( subPowSU
% 3.02/1.59 = ( ! [A: $i,Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ A )
% 3.02/1.59 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(exuE2_type,type,
% 3.02/1.59 exuE2: $o ).
% 3.02/1.59
% 3.02/1.59 thf(exuE2,definition,
% 3.02/1.59 ( exuE2
% 3.02/1.59 = ( ! [Xphi: $i > $o] :
% 3.02/1.59 ( ( exu
% 3.02/1.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.02/1.59 => ? [Xx: $i] :
% 3.02/1.59 ! [Xy: $i] :
% 3.02/1.59 ( ( Xphi @ Xy )
% 3.02/1.59 <=> ( Xy = Xx ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(nonemptyImpWitness_type,type,
% 3.02/1.59 nonemptyImpWitness: $o ).
% 3.02/1.59
% 3.02/1.59 thf(nonemptyImpWitness,definition,
% 3.02/1.59 ( nonemptyImpWitness
% 3.02/1.59 = ( ! [A: $i] :
% 3.02/1.59 ( ( nonempty @ A )
% 3.02/1.59 => ? [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ A )
% 3.02/1.59 & $true ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(uniqinunit_type,type,
% 3.02/1.59 uniqinunit: $o ).
% 3.02/1.59
% 3.02/1.59 thf(uniqinunit,definition,
% 3.02/1.59 ( uniqinunit
% 3.02/1.59 = ( ! [Xx: $i,Xy: $i] :
% 3.02/1.59 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.02/1.59 => ( Xx = Xy ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(notinsingleton_type,type,
% 3.02/1.59 notinsingleton: $o ).
% 3.02/1.59
% 3.02/1.59 thf(notinsingleton,definition,
% 3.02/1.59 ( notinsingleton
% 3.02/1.59 = ( ! [Xx: $i,Xy: $i] :
% 3.02/1.59 ( ( Xx != Xy )
% 3.02/1.59 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(eqinunit_type,type,
% 3.02/1.59 eqinunit: $o ).
% 3.02/1.59
% 3.02/1.59 thf(eqinunit,definition,
% 3.02/1.59 ( eqinunit
% 3.02/1.59 = ( ! [Xx: $i,Xy: $i] :
% 3.02/1.59 ( ( Xx = Xy )
% 3.02/1.59 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(singletonsswitch_type,type,
% 3.02/1.59 singletonsswitch: $o ).
% 3.02/1.59
% 3.02/1.59 thf(singletonsswitch,definition,
% 3.02/1.59 ( singletonsswitch
% 3.02/1.59 = ( ! [Xx: $i,Xy: $i] :
% 3.02/1.59 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.02/1.59 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(upairsetE_type,type,
% 3.02/1.59 upairsetE: $o ).
% 3.02/1.59
% 3.02/1.59 thf(upairsetE,definition,
% 3.02/1.59 ( upairsetE
% 3.02/1.59 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.02/1.59 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 3.02/1.59 => ( ( Xz = Xx )
% 3.02/1.59 | ( Xz = Xy ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(upairsetIL_type,type,
% 3.02/1.59 upairsetIL: $o ).
% 3.02/1.59
% 3.02/1.59 thf(upairsetIL,definition,
% 3.02/1.59 ( upairsetIL
% 3.02/1.59 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(upairsetIR_type,type,
% 3.02/1.59 upairsetIR: $o ).
% 3.02/1.59
% 3.02/1.59 thf(upairsetIR,definition,
% 3.02/1.59 ( upairsetIR
% 3.02/1.59 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(emptyE1_type,type,
% 3.02/1.59 emptyE1: $o ).
% 3.02/1.59
% 3.02/1.59 thf(emptyE1,definition,
% 3.02/1.59 ( emptyE1
% 3.02/1.59 = ( ! [A: $i,Xphi: $i > $o] :
% 3.02/1.59 ( ? [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ A )
% 3.02/1.59 & ( Xphi @ Xx ) )
% 3.02/1.59 => ( ( ( dsetconstr @ A
% 3.02/1.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.02/1.59 = emptyset )
% 3.02/1.59 => $false ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(vacuousDall_type,type,
% 3.02/1.59 vacuousDall: $o ).
% 3.02/1.59
% 3.02/1.59 thf(vacuousDall,definition,
% 3.02/1.59 ( vacuousDall
% 3.02/1.59 = ( ! [Xphi: $i > $o,Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ emptyset )
% 3.02/1.59 => ( Xphi @ Xx ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(quantDeMorgan1_type,type,
% 3.02/1.59 quantDeMorgan1: $o ).
% 3.02/1.59
% 3.02/1.59 thf(quantDeMorgan1,definition,
% 3.02/1.59 ( quantDeMorgan1
% 3.02/1.59 = ( ! [A: $i,Xphi: $i > $o] :
% 3.02/1.59 ( ~ ! [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ A )
% 3.02/1.59 => ( Xphi @ Xx ) )
% 3.02/1.59 => ? [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ A )
% 3.02/1.59 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(quantDeMorgan2_type,type,
% 3.02/1.59 quantDeMorgan2: $o ).
% 3.02/1.59
% 3.02/1.59 thf(quantDeMorgan2,definition,
% 3.02/1.59 ( quantDeMorgan2
% 3.02/1.59 = ( ! [A: $i,Xphi: $i > $o] :
% 3.02/1.59 ( ! [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ A )
% 3.02/1.59 => ~ ( Xphi @ Xx ) )
% 3.02/1.59 => ~ ? [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ A )
% 3.02/1.59 & ( Xphi @ Xx ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(quantDeMorgan3_type,type,
% 3.02/1.59 quantDeMorgan3: $o ).
% 3.02/1.59
% 3.02/1.59 thf(quantDeMorgan3,definition,
% 3.02/1.59 ( quantDeMorgan3
% 3.02/1.59 = ( ! [A: $i,Xphi: $i > $o] :
% 3.02/1.59 ( ~ ? [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ A )
% 3.02/1.59 & ( Xphi @ Xx ) )
% 3.02/1.59 => ! [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ A )
% 3.02/1.59 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(quantDeMorgan4_type,type,
% 3.02/1.59 quantDeMorgan4: $o ).
% 3.02/1.59
% 3.02/1.59 thf(quantDeMorgan4,definition,
% 3.02/1.59 ( quantDeMorgan4
% 3.02/1.59 = ( ! [A: $i,Xphi: $i > $o] :
% 3.02/1.59 ( ? [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ A )
% 3.02/1.59 & ~ ( Xphi @ Xx ) )
% 3.02/1.59 => ~ ! [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ A )
% 3.02/1.59 => ( Xphi @ Xx ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(prop2setI_type,type,
% 3.02/1.59 prop2setI: $o ).
% 3.02/1.59
% 3.02/1.59 thf(prop2setI,definition,
% 3.02/1.59 ( prop2setI
% 3.02/1.59 = ( ! [Xphi: $o] :
% 3.02/1.59 ( Xphi
% 3.02/1.59 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(set2prop_type,type,
% 3.02/1.59 set2prop: $i > $o ).
% 3.02/1.59
% 3.02/1.59 thf(prop2set2propI_type,type,
% 3.02/1.59 prop2set2propI: $o ).
% 3.02/1.59
% 3.02/1.59 thf(prop2set2propI,definition,
% 3.02/1.59 ( prop2set2propI
% 3.02/1.59 = ( ! [Xphi: $o] :
% 3.02/1.59 ( Xphi
% 3.02/1.59 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(notdexE_type,type,
% 3.02/1.59 notdexE: $o ).
% 3.02/1.59
% 3.02/1.59 thf(notdexE,definition,
% 3.02/1.59 ( notdexE
% 3.02/1.59 = ( ! [A: $i,Xphi: $i > $o] :
% 3.02/1.59 ( ~ ? [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ A )
% 3.02/1.59 & ( Xphi @ Xx ) )
% 3.02/1.59 => ! [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ A )
% 3.02/1.59 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(notdallE_type,type,
% 3.02/1.59 notdallE: $o ).
% 3.02/1.59
% 3.02/1.59 thf(notdallE,definition,
% 3.02/1.59 ( notdallE
% 3.02/1.59 = ( ! [A: $i,Xphi: $i > $o] :
% 3.02/1.59 ( ~ ! [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ A )
% 3.02/1.59 => ( Xphi @ Xx ) )
% 3.02/1.59 => ? [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ A )
% 3.02/1.59 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(exuI1_type,type,
% 3.02/1.59 exuI1: $o ).
% 3.02/1.59
% 3.02/1.59 thf(exuI1,definition,
% 3.02/1.59 ( exuI1
% 3.02/1.59 = ( ! [Xphi: $i > $o] :
% 3.02/1.59 ( ? [Xx: $i] :
% 3.02/1.59 ( ( Xphi @ Xx )
% 3.02/1.59 & ! [Xy: $i] :
% 3.02/1.59 ( ( Xphi @ Xy )
% 3.02/1.59 => ( Xx = Xy ) ) )
% 3.02/1.59 => ( exu
% 3.02/1.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(exuI3_type,type,
% 3.02/1.59 exuI3: $o ).
% 3.02/1.59
% 3.02/1.59 thf(exuI3,definition,
% 3.02/1.59 ( exuI3
% 3.02/1.59 = ( ! [Xphi: $i > $o] :
% 3.02/1.59 ( ? [Xx: $i] : ( Xphi @ Xx )
% 3.02/1.59 => ( ! [Xx: $i,Xy: $i] :
% 3.02/1.59 ( ( Xphi @ Xx )
% 3.02/1.59 => ( ( Xphi @ Xy )
% 3.02/1.59 => ( Xx = Xy ) ) )
% 3.02/1.59 => ( exu
% 3.02/1.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(exuI2_type,type,
% 3.02/1.59 exuI2: $o ).
% 3.02/1.59
% 3.02/1.59 thf(exuI2,definition,
% 3.02/1.59 ( exuI2
% 3.02/1.59 = ( ! [Xphi: $i > $o] :
% 3.02/1.59 ( ? [Xx: $i] :
% 3.02/1.59 ! [Xy: $i] :
% 3.02/1.59 ( ( Xphi @ Xy )
% 3.02/1.59 <=> ( Xy = Xx ) )
% 3.02/1.59 => ( exu
% 3.02/1.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(inCongP_type,type,
% 3.02/1.59 inCongP: $o ).
% 3.02/1.59
% 3.02/1.59 thf(inCongP,definition,
% 3.02/1.59 ( inCongP
% 3.02/1.59 = ( ! [A: $i,B: $i] :
% 3.02/1.59 ( ( A = B )
% 3.02/1.59 => ! [Xx: $i,Xy: $i] :
% 3.02/1.59 ( ( Xx = Xy )
% 3.02/1.59 => ( ( in @ Xx @ A )
% 3.02/1.59 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(in__Cong_type,type,
% 3.02/1.59 in__Cong: $o ).
% 3.02/1.59
% 3.02/1.59 thf(in__Cong,definition,
% 3.02/1.59 ( in__Cong
% 3.02/1.59 = ( ! [A: $i,B: $i] :
% 3.02/1.59 ( ( A = B )
% 3.02/1.59 => ! [Xx: $i,Xy: $i] :
% 3.02/1.59 ( ( Xx = Xy )
% 3.02/1.59 => ( ( in @ Xx @ A )
% 3.02/1.59 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(exuE3u_type,type,
% 3.02/1.59 exuE3u: $o ).
% 3.02/1.59
% 3.02/1.59 thf(exuE3u,definition,
% 3.02/1.59 ( exuE3u
% 3.02/1.59 = ( ! [Xphi: $i > $o] :
% 3.02/1.59 ( ( exu
% 3.02/1.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.02/1.59 => ! [Xx: $i,Xy: $i] :
% 3.02/1.59 ( ( Xphi @ Xx )
% 3.02/1.59 => ( ( Xphi @ Xy )
% 3.02/1.59 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(exu__Cong_type,type,
% 3.02/1.59 exu__Cong: $o ).
% 3.02/1.59
% 3.02/1.59 thf(exu__Cong,definition,
% 3.02/1.59 ( exu__Cong
% 3.02/1.59 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.02/1.59 ( ! [Xx: $i,Xy: $i] :
% 3.02/1.59 ( ( Xx = Xy )
% 3.02/1.59 => ( ( Xphi @ Xx )
% 3.02/1.59 <=> ( Xpsi @ Xy ) ) )
% 3.02/1.59 => ( ( exu
% 3.02/1.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.02/1.59 <=> ( exu
% 3.02/1.59 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(emptyset__Cong_type,type,
% 3.02/1.59 emptyset__Cong: $o ).
% 3.02/1.59
% 3.02/1.59 thf(emptyset__Cong,definition,
% 3.02/1.59 ( emptyset__Cong
% 3.02/1.59 = ( emptyset = emptyset ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(setadjoin__Cong_type,type,
% 3.02/1.59 setadjoin__Cong: $o ).
% 3.02/1.59
% 3.02/1.59 thf(setadjoin__Cong,definition,
% 3.02/1.59 ( setadjoin__Cong
% 3.02/1.59 = ( ! [Xx: $i,Xy: $i] :
% 3.02/1.59 ( ( Xx = Xy )
% 3.02/1.59 => ! [Xz: $i,Xu: $i] :
% 3.02/1.59 ( ( Xz = Xu )
% 3.02/1.59 => ( ( setadjoin @ Xx @ Xz )
% 3.02/1.59 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(powerset__Cong_type,type,
% 3.02/1.59 powerset__Cong: $o ).
% 3.02/1.59
% 3.02/1.59 thf(powerset__Cong,definition,
% 3.02/1.59 ( powerset__Cong
% 3.02/1.59 = ( ! [A: $i,B: $i] :
% 3.02/1.59 ( ( A = B )
% 3.02/1.59 => ( ( powerset @ A )
% 3.02/1.59 = ( powerset @ B ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(setunion__Cong_type,type,
% 3.02/1.59 setunion__Cong: $o ).
% 3.02/1.59
% 3.02/1.59 thf(setunion__Cong,definition,
% 3.02/1.59 ( setunion__Cong
% 3.02/1.59 = ( ! [A: $i,B: $i] :
% 3.02/1.59 ( ( A = B )
% 3.02/1.59 => ( ( setunion @ A )
% 3.02/1.59 = ( setunion @ B ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(omega__Cong_type,type,
% 3.02/1.59 omega__Cong: $o ).
% 3.02/1.59
% 3.02/1.59 thf(omega__Cong,definition,
% 3.02/1.59 ( omega__Cong
% 3.02/1.59 = ( omega = omega ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(exuEu_type,type,
% 3.02/1.59 exuEu: $o ).
% 3.02/1.59
% 3.02/1.59 thf(exuEu,definition,
% 3.02/1.59 ( exuEu
% 3.02/1.59 = ( ! [Xphi: $i > $o] :
% 3.02/1.59 ( ( exu
% 3.02/1.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.02/1.59 => ! [Xx: $i,Xy: $i] :
% 3.02/1.59 ( ( Xphi @ Xx )
% 3.02/1.59 => ( ( Xphi @ Xy )
% 3.02/1.59 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(descr__Cong_type,type,
% 3.02/1.59 descr__Cong: $o ).
% 3.02/1.59
% 3.02/1.59 thf(descr__Cong,definition,
% 3.02/1.59 ( descr__Cong
% 3.02/1.59 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.02/1.59 ( ! [Xx: $i,Xy: $i] :
% 3.02/1.59 ( ( Xx = Xy )
% 3.02/1.59 => ( ( Xphi @ Xx )
% 3.02/1.59 <=> ( Xpsi @ Xy ) ) )
% 3.02/1.59 => ( ( exu
% 3.02/1.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.02/1.59 => ( ( exu
% 3.02/1.59 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 3.02/1.59 => ( ( descr
% 3.02/1.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.02/1.59 = ( descr
% 3.02/1.59 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(dsetconstr__Cong_type,type,
% 3.02/1.59 dsetconstr__Cong: $o ).
% 3.02/1.59
% 3.02/1.59 thf(dsetconstr__Cong,definition,
% 3.02/1.59 ( dsetconstr__Cong
% 3.02/1.59 = ( ! [A: $i,B: $i] :
% 3.02/1.59 ( ( A = B )
% 3.02/1.59 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.02/1.59 ( ! [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ A )
% 3.02/1.59 => ! [Xy: $i] :
% 3.02/1.59 ( ( in @ Xy @ B )
% 3.02/1.59 => ( ( Xx = Xy )
% 3.02/1.59 => ( ( Xphi @ Xx )
% 3.02/1.59 <=> ( Xpsi @ Xy ) ) ) ) )
% 3.02/1.59 => ( ( dsetconstr @ A
% 3.02/1.59 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.02/1.59 = ( dsetconstr @ B
% 3.02/1.59 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(subset_type,type,
% 3.02/1.59 subset: $i > $i > $o ).
% 3.02/1.59
% 3.02/1.59 thf(disjoint_type,type,
% 3.02/1.59 disjoint: $i > $i > $o ).
% 3.02/1.59
% 3.02/1.59 thf(setsmeet_type,type,
% 3.02/1.59 setsmeet: $i > $i > $o ).
% 3.02/1.59
% 3.02/1.59 thf(subsetI1_type,type,
% 3.02/1.59 subsetI1: $o ).
% 3.02/1.59
% 3.02/1.59 thf(subsetI1,definition,
% 3.02/1.59 ( subsetI1
% 3.02/1.59 = ( ! [A: $i,B: $i] :
% 3.02/1.59 ( ! [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ A )
% 3.02/1.59 => ( in @ Xx @ B ) )
% 3.02/1.59 => ( subset @ A @ B ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(eqimpsubset2_type,type,
% 3.02/1.59 eqimpsubset2: $o ).
% 3.02/1.59
% 3.02/1.59 thf(eqimpsubset2,definition,
% 3.02/1.59 ( eqimpsubset2
% 3.02/1.59 = ( ! [A: $i,B: $i] :
% 3.02/1.59 ( ( A = B )
% 3.02/1.59 => ( subset @ B @ A ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(eqimpsubset1_type,type,
% 3.02/1.59 eqimpsubset1: $o ).
% 3.02/1.59
% 3.02/1.59 thf(eqimpsubset1,definition,
% 3.02/1.59 ( eqimpsubset1
% 3.02/1.59 = ( ! [A: $i,B: $i] :
% 3.02/1.59 ( ( A = B )
% 3.02/1.59 => ( subset @ A @ B ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(subsetI2_type,type,
% 3.02/1.59 subsetI2: $o ).
% 3.02/1.59
% 3.02/1.59 thf(subsetI2,definition,
% 3.02/1.59 ( subsetI2
% 3.02/1.59 = ( ! [A: $i,B: $i] :
% 3.02/1.59 ( ! [Xx: $i] :
% 3.02/1.59 ( ( in @ Xx @ A )
% 3.02/1.59 => ( in @ Xx @ B ) )
% 3.02/1.59 => ( subset @ A @ B ) ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(emptysetsubset_type,type,
% 3.02/1.59 emptysetsubset: $o ).
% 3.02/1.59
% 3.02/1.59 thf(emptysetsubset,definition,
% 3.02/1.59 ( emptysetsubset
% 3.02/1.59 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 3.02/1.59
% 3.02/1.59 thf(subsetE_type,type,
% 3.02/1.59 subsetE: $o ).
% 3.02/1.59
% 3.02/1.59 thf(subsetE,definition,
% 3.02/1.59 ( subsetE
% 3.02/1.59 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.59 ( ( subset @ A @ B )
% 3.02/1.59 => ( ( in @ Xx @ A )
% 3.02/1.60 => ( in @ Xx @ B ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(subsetE2_type,type,
% 3.02/1.60 subsetE2: $o ).
% 3.02/1.60
% 3.02/1.60 thf(subsetE2,definition,
% 3.02/1.60 ( subsetE2
% 3.02/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.60 ( ( subset @ A @ B )
% 3.02/1.60 => ( ~ ( in @ Xx @ B )
% 3.02/1.60 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(notsubsetI_type,type,
% 3.02/1.60 notsubsetI: $o ).
% 3.02/1.60
% 3.02/1.60 thf(notsubsetI,definition,
% 3.02/1.60 ( notsubsetI
% 3.02/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ A )
% 3.02/1.60 => ( ~ ( in @ Xx @ B )
% 3.02/1.60 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(notequalI1_type,type,
% 3.02/1.60 notequalI1: $o ).
% 3.02/1.60
% 3.02/1.60 thf(notequalI1,definition,
% 3.02/1.60 ( notequalI1
% 3.02/1.60 = ( ! [A: $i,B: $i] :
% 3.02/1.60 ( ~ ( subset @ A @ B )
% 3.02/1.60 => ( A != B ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(notequalI2_type,type,
% 3.02/1.60 notequalI2: $o ).
% 3.02/1.60
% 3.02/1.60 thf(notequalI2,definition,
% 3.02/1.60 ( notequalI2
% 3.02/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ A )
% 3.02/1.60 => ( ~ ( in @ Xx @ B )
% 3.02/1.60 => ( A != B ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(subsetRefl_type,type,
% 3.02/1.60 subsetRefl: $o ).
% 3.02/1.60
% 3.02/1.60 thf(subsetRefl,definition,
% 3.02/1.60 ( subsetRefl
% 3.02/1.60 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(subsetTrans_type,type,
% 3.02/1.60 subsetTrans: $o ).
% 3.02/1.60
% 3.02/1.60 thf(subsetTrans,definition,
% 3.02/1.60 ( subsetTrans
% 3.02/1.60 = ( ! [A: $i,B: $i,C: $i] :
% 3.02/1.60 ( ( subset @ A @ B )
% 3.02/1.60 => ( ( subset @ B @ C )
% 3.02/1.60 => ( subset @ A @ C ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(setadjoinSub_type,type,
% 3.02/1.60 setadjoinSub: $o ).
% 3.02/1.60
% 3.02/1.60 thf(setadjoinSub,definition,
% 3.02/1.60 ( setadjoinSub
% 3.02/1.60 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(setadjoinSub2_type,type,
% 3.02/1.60 setadjoinSub2: $o ).
% 3.02/1.60
% 3.02/1.60 thf(setadjoinSub2,definition,
% 3.02/1.60 ( setadjoinSub2
% 3.02/1.60 = ( ! [A: $i,Xx: $i,B: $i] :
% 3.02/1.60 ( ( subset @ A @ B )
% 3.02/1.60 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(subset2powerset_type,type,
% 3.02/1.60 subset2powerset: $o ).
% 3.02/1.60
% 3.02/1.60 thf(subset2powerset,definition,
% 3.02/1.60 ( subset2powerset
% 3.02/1.60 = ( ! [A: $i,B: $i] :
% 3.02/1.60 ( ( subset @ A @ B )
% 3.02/1.60 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(setextsub_type,type,
% 3.02/1.60 setextsub: $o ).
% 3.02/1.60
% 3.02/1.60 thf(setextsub,definition,
% 3.02/1.60 ( setextsub
% 3.02/1.60 = ( ! [A: $i,B: $i] :
% 3.02/1.60 ( ( subset @ A @ B )
% 3.02/1.60 => ( ( subset @ B @ A )
% 3.02/1.60 => ( A = B ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(subsetemptysetimpeq_type,type,
% 3.02/1.60 subsetemptysetimpeq: $o ).
% 3.02/1.60
% 3.02/1.60 thf(subsetemptysetimpeq,definition,
% 3.02/1.60 ( subsetemptysetimpeq
% 3.02/1.60 = ( ! [A: $i] :
% 3.02/1.60 ( ( subset @ A @ emptyset )
% 3.02/1.60 => ( A = emptyset ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(powersetI1_type,type,
% 3.02/1.60 powersetI1: $o ).
% 3.02/1.60
% 3.02/1.60 thf(powersetI1,definition,
% 3.02/1.60 ( powersetI1
% 3.02/1.60 = ( ! [A: $i,B: $i] :
% 3.02/1.60 ( ( subset @ B @ A )
% 3.02/1.60 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(powersetE1_type,type,
% 3.02/1.60 powersetE1: $o ).
% 3.02/1.60
% 3.02/1.60 thf(powersetE1,definition,
% 3.02/1.60 ( powersetE1
% 3.02/1.60 = ( ! [A: $i,B: $i] :
% 3.02/1.60 ( ( in @ B @ ( powerset @ A ) )
% 3.02/1.60 => ( subset @ B @ A ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(inPowerset_type,type,
% 3.02/1.60 inPowerset: $o ).
% 3.02/1.60
% 3.02/1.60 thf(inPowerset,definition,
% 3.02/1.60 ( inPowerset
% 3.02/1.60 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(powersetsubset_type,type,
% 3.02/1.60 powersetsubset: $o ).
% 3.02/1.60
% 3.02/1.60 thf(powersetsubset,definition,
% 3.02/1.60 ( powersetsubset
% 3.02/1.60 = ( ! [A: $i,B: $i] :
% 3.02/1.60 ( ( subset @ A @ B )
% 3.02/1.60 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(sepInPowerset_type,type,
% 3.02/1.60 sepInPowerset: $o ).
% 3.02/1.60
% 3.02/1.60 thf(sepInPowerset,definition,
% 3.02/1.60 ( sepInPowerset
% 3.02/1.60 = ( ! [A: $i,Xphi: $i > $o] :
% 3.02/1.60 ( in
% 3.02/1.60 @ ( dsetconstr @ A
% 3.02/1.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.02/1.60 @ ( powerset @ A ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(sepSubset_type,type,
% 3.02/1.60 sepSubset: $o ).
% 3.02/1.60
% 3.02/1.60 thf(sepSubset,definition,
% 3.02/1.60 ( sepSubset
% 3.02/1.60 = ( ! [A: $i,Xphi: $i > $o] :
% 3.02/1.60 ( subset
% 3.02/1.60 @ ( dsetconstr @ A
% 3.02/1.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.02/1.60 @ A ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(binunion_type,type,
% 3.02/1.60 binunion: $i > $i > $i ).
% 3.02/1.60
% 3.02/1.60 thf(binunionIL_type,type,
% 3.02/1.60 binunionIL: $o ).
% 3.02/1.60
% 3.02/1.60 thf(binunionIL,definition,
% 3.02/1.60 ( binunionIL
% 3.02/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ A )
% 3.02/1.60 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(upairset2IR_type,type,
% 3.02/1.60 upairset2IR: $o ).
% 3.02/1.60
% 3.02/1.60 thf(upairset2IR,definition,
% 3.02/1.60 ( upairset2IR
% 3.02/1.60 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(binunionIR_type,type,
% 3.02/1.60 binunionIR: $o ).
% 3.02/1.60
% 3.02/1.60 thf(binunionIR,definition,
% 3.02/1.60 ( binunionIR
% 3.02/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ B )
% 3.02/1.60 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(binunionEcases_type,type,
% 3.02/1.60 binunionEcases: $o ).
% 3.02/1.60
% 3.02/1.60 thf(binunionEcases,definition,
% 3.02/1.60 ( binunionEcases
% 3.02/1.60 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 3.02/1.60 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 3.02/1.60 => ( ( ( in @ Xx @ A )
% 3.02/1.60 => Xphi )
% 3.02/1.60 => ( ( ( in @ Xx @ B )
% 3.02/1.60 => Xphi )
% 3.02/1.60 => Xphi ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(binunionE_type,type,
% 3.02/1.60 binunionE: $o ).
% 3.02/1.60
% 3.02/1.60 thf(binunionE,definition,
% 3.02/1.60 ( binunionE
% 3.02/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 3.02/1.60 => ( ( in @ Xx @ A )
% 3.02/1.60 | ( in @ Xx @ B ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(binunionLsub_type,type,
% 3.02/1.60 binunionLsub: $o ).
% 3.02/1.60
% 3.02/1.60 thf(binunionLsub,definition,
% 3.02/1.60 ( binunionLsub
% 3.02/1.60 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(binunionRsub_type,type,
% 3.02/1.60 binunionRsub: $o ).
% 3.02/1.60
% 3.02/1.60 thf(binunionRsub,definition,
% 3.02/1.60 ( binunionRsub
% 3.02/1.60 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(binintersect_type,type,
% 3.02/1.60 binintersect: $i > $i > $i ).
% 3.02/1.60
% 3.02/1.60 thf(binintersectI_type,type,
% 3.02/1.60 binintersectI: $o ).
% 3.02/1.60
% 3.02/1.60 thf(binintersectI,definition,
% 3.02/1.60 ( binintersectI
% 3.02/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ A )
% 3.02/1.60 => ( ( in @ Xx @ B )
% 3.02/1.60 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(binintersectSubset5_type,type,
% 3.02/1.60 binintersectSubset5: $o ).
% 3.02/1.60
% 3.02/1.60 thf(binintersectSubset5,definition,
% 3.02/1.60 ( binintersectSubset5
% 3.02/1.60 = ( ! [A: $i,B: $i,C: $i] :
% 3.02/1.60 ( ( subset @ C @ A )
% 3.02/1.60 => ( ( subset @ C @ B )
% 3.02/1.60 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(binintersectEL_type,type,
% 3.02/1.60 binintersectEL: $o ).
% 3.02/1.60
% 3.02/1.60 thf(binintersectEL,definition,
% 3.02/1.60 ( binintersectEL
% 3.02/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 3.02/1.60 => ( in @ Xx @ A ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(binintersectLsub_type,type,
% 3.02/1.60 binintersectLsub: $o ).
% 3.02/1.60
% 3.02/1.60 thf(binintersectLsub,definition,
% 3.02/1.60 ( binintersectLsub
% 3.02/1.60 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(binintersectSubset2_type,type,
% 3.02/1.60 binintersectSubset2: $o ).
% 3.02/1.60
% 3.02/1.60 thf(binintersectSubset2,definition,
% 3.02/1.60 ( binintersectSubset2
% 3.02/1.60 = ( ! [A: $i,B: $i] :
% 3.02/1.60 ( ( subset @ A @ B )
% 3.02/1.60 => ( ( binintersect @ A @ B )
% 3.02/1.60 = A ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(binintersectSubset3_type,type,
% 3.02/1.60 binintersectSubset3: $o ).
% 3.02/1.60
% 3.02/1.60 thf(binintersectSubset3,definition,
% 3.02/1.60 ( binintersectSubset3
% 3.02/1.60 = ( ! [A: $i,B: $i] :
% 3.02/1.60 ( ( ( binintersect @ A @ B )
% 3.02/1.60 = B )
% 3.02/1.60 => ( subset @ B @ A ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(binintersectER_type,type,
% 3.02/1.60 binintersectER: $o ).
% 3.02/1.60
% 3.02/1.60 thf(binintersectER,definition,
% 3.02/1.60 ( binintersectER
% 3.02/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 3.02/1.60 => ( in @ Xx @ B ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(disjointsetsI1_type,type,
% 3.02/1.60 disjointsetsI1: $o ).
% 3.02/1.60
% 3.02/1.60 thf(disjointsetsI1,definition,
% 3.02/1.60 ( disjointsetsI1
% 3.02/1.60 = ( ! [A: $i,B: $i] :
% 3.02/1.60 ( ~ ? [Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ A )
% 3.02/1.60 & ( in @ Xx @ B ) )
% 3.02/1.60 => ( ( binintersect @ A @ B )
% 3.02/1.60 = emptyset ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(binintersectRsub_type,type,
% 3.02/1.60 binintersectRsub: $o ).
% 3.02/1.60
% 3.02/1.60 thf(binintersectRsub,definition,
% 3.02/1.60 ( binintersectRsub
% 3.02/1.60 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(binintersectSubset4_type,type,
% 3.02/1.60 binintersectSubset4: $o ).
% 3.02/1.60
% 3.02/1.60 thf(binintersectSubset4,definition,
% 3.02/1.60 ( binintersectSubset4
% 3.02/1.60 = ( ! [A: $i,B: $i] :
% 3.02/1.60 ( ( subset @ B @ A )
% 3.02/1.60 => ( ( binintersect @ A @ B )
% 3.02/1.60 = B ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(binintersectSubset1_type,type,
% 3.02/1.60 binintersectSubset1: $o ).
% 3.02/1.60
% 3.02/1.60 thf(binintersectSubset1,definition,
% 3.02/1.60 ( binintersectSubset1
% 3.02/1.60 = ( ! [A: $i,B: $i] :
% 3.02/1.60 ( ( ( binintersect @ A @ B )
% 3.02/1.60 = A )
% 3.02/1.60 => ( subset @ A @ B ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(bs114d_type,type,
% 3.02/1.60 bs114d: $o ).
% 3.02/1.60
% 3.02/1.60 thf(bs114d,definition,
% 3.02/1.60 ( bs114d
% 3.02/1.60 = ( ! [A: $i,B: $i,C: $i] :
% 3.02/1.60 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 3.02/1.60 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(regular_type,type,
% 3.02/1.60 regular: $i > $o ).
% 3.02/1.60
% 3.02/1.60 thf(setminus_type,type,
% 3.02/1.60 setminus: $i > $i > $i ).
% 3.02/1.60
% 3.02/1.60 thf(setminusI_type,type,
% 3.02/1.60 setminusI: $o ).
% 3.02/1.60
% 3.02/1.60 thf(setminusI,definition,
% 3.02/1.60 ( setminusI
% 3.02/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ A )
% 3.02/1.60 => ( ~ ( in @ Xx @ B )
% 3.02/1.60 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(setminusEL_type,type,
% 3.02/1.60 setminusEL: $o ).
% 3.02/1.60
% 3.02/1.60 thf(setminusEL,definition,
% 3.02/1.60 ( setminusEL
% 3.02/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 3.02/1.60 => ( in @ Xx @ A ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(setminusER_type,type,
% 3.02/1.60 setminusER: $o ).
% 3.02/1.60
% 3.02/1.60 thf(setminusER,definition,
% 3.02/1.60 ( setminusER
% 3.02/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 3.02/1.60 => ~ ( in @ Xx @ B ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(setminusSubset2_type,type,
% 3.02/1.60 setminusSubset2: $o ).
% 3.02/1.60
% 3.02/1.60 thf(setminusSubset2,definition,
% 3.02/1.60 ( setminusSubset2
% 3.02/1.60 = ( ! [A: $i,B: $i] :
% 3.02/1.60 ( ( subset @ A @ B )
% 3.02/1.60 => ( ( setminus @ A @ B )
% 3.02/1.60 = emptyset ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(setminusERneg_type,type,
% 3.02/1.60 setminusERneg: $o ).
% 3.02/1.60
% 3.02/1.60 thf(setminusERneg,definition,
% 3.02/1.60 ( setminusERneg
% 3.02/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.60 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 3.02/1.60 => ( ( in @ Xx @ A )
% 3.02/1.60 => ( in @ Xx @ B ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(setminusELneg_type,type,
% 3.02/1.60 setminusELneg: $o ).
% 3.02/1.60
% 3.02/1.60 thf(setminusELneg,definition,
% 3.02/1.60 ( setminusELneg
% 3.02/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.60 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 3.02/1.60 => ( ~ ( in @ Xx @ B )
% 3.02/1.60 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(setminusILneg_type,type,
% 3.02/1.60 setminusILneg: $o ).
% 3.02/1.60
% 3.02/1.60 thf(setminusILneg,definition,
% 3.02/1.60 ( setminusILneg
% 3.02/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.60 ( ~ ( in @ Xx @ A )
% 3.02/1.60 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(setminusIRneg_type,type,
% 3.02/1.60 setminusIRneg: $o ).
% 3.02/1.60
% 3.02/1.60 thf(setminusIRneg,definition,
% 3.02/1.60 ( setminusIRneg
% 3.02/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ B )
% 3.02/1.60 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(setminusLsub_type,type,
% 3.02/1.60 setminusLsub: $o ).
% 3.02/1.60
% 3.02/1.60 thf(setminusLsub,definition,
% 3.02/1.60 ( setminusLsub
% 3.02/1.60 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(setminusSubset1_type,type,
% 3.02/1.60 setminusSubset1: $o ).
% 3.02/1.60
% 3.02/1.60 thf(setminusSubset1,definition,
% 3.02/1.60 ( setminusSubset1
% 3.02/1.60 = ( ! [A: $i,B: $i] :
% 3.02/1.60 ( ( ( setminus @ A @ B )
% 3.02/1.60 = emptyset )
% 3.02/1.60 => ( subset @ A @ B ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(symdiff_type,type,
% 3.02/1.60 symdiff: $i > $i > $i ).
% 3.02/1.60
% 3.02/1.60 thf(symdiffE_type,type,
% 3.02/1.60 symdiffE: $o ).
% 3.02/1.60
% 3.02/1.60 thf(symdiffE,definition,
% 3.02/1.60 ( symdiffE
% 3.02/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 3.02/1.60 => ! [Xphi: $o] :
% 3.02/1.60 ( ( ( in @ Xx @ A )
% 3.02/1.60 => ( ~ ( in @ Xx @ B )
% 3.02/1.60 => Xphi ) )
% 3.02/1.60 => ( ( ~ ( in @ Xx @ A )
% 3.02/1.60 => ( ( in @ Xx @ B )
% 3.02/1.60 => Xphi ) )
% 3.02/1.60 => Xphi ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(symdiffI1_type,type,
% 3.02/1.60 symdiffI1: $o ).
% 3.02/1.60
% 3.02/1.60 thf(symdiffI1,definition,
% 3.02/1.60 ( symdiffI1
% 3.02/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ A )
% 3.02/1.60 => ( ~ ( in @ Xx @ B )
% 3.02/1.60 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(symdiffI2_type,type,
% 3.02/1.60 symdiffI2: $o ).
% 3.02/1.60
% 3.02/1.60 thf(symdiffI2,definition,
% 3.02/1.60 ( symdiffI2
% 3.02/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.60 ( ~ ( in @ Xx @ A )
% 3.02/1.60 => ( ( in @ Xx @ B )
% 3.02/1.60 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(symdiffIneg1_type,type,
% 3.02/1.60 symdiffIneg1: $o ).
% 3.02/1.60
% 3.02/1.60 thf(symdiffIneg1,definition,
% 3.02/1.60 ( symdiffIneg1
% 3.02/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ A )
% 3.02/1.60 => ( ( in @ Xx @ B )
% 3.02/1.60 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(symdiffIneg2_type,type,
% 3.02/1.60 symdiffIneg2: $o ).
% 3.02/1.60
% 3.02/1.60 thf(symdiffIneg2,definition,
% 3.02/1.60 ( symdiffIneg2
% 3.02/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.60 ( ~ ( in @ Xx @ A )
% 3.02/1.60 => ( ~ ( in @ Xx @ B )
% 3.02/1.60 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(iskpair_type,type,
% 3.02/1.60 iskpair: $i > $o ).
% 3.02/1.60
% 3.02/1.60 thf(secondinupair_type,type,
% 3.02/1.60 secondinupair: $o ).
% 3.02/1.60
% 3.02/1.60 thf(secondinupair,definition,
% 3.02/1.60 ( secondinupair
% 3.02/1.60 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(setukpairIL_type,type,
% 3.02/1.60 setukpairIL: $o ).
% 3.02/1.60
% 3.02/1.60 thf(setukpairIL,definition,
% 3.02/1.60 ( setukpairIL
% 3.02/1.60 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(setukpairIR_type,type,
% 3.02/1.60 setukpairIR: $o ).
% 3.02/1.60
% 3.02/1.60 thf(setukpairIR,definition,
% 3.02/1.60 ( setukpairIR
% 3.02/1.60 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(kpairiskpair_type,type,
% 3.02/1.60 kpairiskpair: $o ).
% 3.02/1.60
% 3.02/1.60 thf(kpairiskpair,definition,
% 3.02/1.60 ( kpairiskpair
% 3.02/1.60 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(kpair_type,type,
% 3.02/1.60 kpair: $i > $i > $i ).
% 3.02/1.60
% 3.02/1.60 thf(kpairp_type,type,
% 3.02/1.60 kpairp: $o ).
% 3.02/1.60
% 3.02/1.60 thf(kpairp,definition,
% 3.02/1.60 ( kpairp
% 3.02/1.60 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(cartprod_type,type,
% 3.02/1.60 cartprod: $i > $i > $i ).
% 3.02/1.60
% 3.02/1.60 thf(singletonsubset_type,type,
% 3.02/1.60 singletonsubset: $o ).
% 3.02/1.60
% 3.02/1.60 thf(singletonsubset,definition,
% 3.02/1.60 ( singletonsubset
% 3.02/1.60 = ( ! [A: $i,Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ A )
% 3.02/1.60 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(singletoninpowerset_type,type,
% 3.02/1.60 singletoninpowerset: $o ).
% 3.02/1.60
% 3.02/1.60 thf(singletoninpowerset,definition,
% 3.02/1.60 ( singletoninpowerset
% 3.02/1.60 = ( ! [A: $i,Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ A )
% 3.02/1.60 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(singletoninpowunion_type,type,
% 3.02/1.60 singletoninpowunion: $o ).
% 3.02/1.60
% 3.02/1.60 thf(singletoninpowunion,definition,
% 3.02/1.60 ( singletoninpowunion
% 3.02/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ A )
% 3.02/1.60 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(upairset2E_type,type,
% 3.02/1.60 upairset2E: $o ).
% 3.02/1.60
% 3.02/1.60 thf(upairset2E,definition,
% 3.02/1.60 ( upairset2E
% 3.02/1.60 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.02/1.60 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 3.02/1.60 => ( ( Xz = Xx )
% 3.02/1.60 | ( Xz = Xy ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(upairsubunion_type,type,
% 3.02/1.60 upairsubunion: $o ).
% 3.02/1.60
% 3.02/1.60 thf(upairsubunion,definition,
% 3.02/1.60 ( upairsubunion
% 3.02/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ A )
% 3.02/1.60 => ! [Xy: $i] :
% 3.02/1.60 ( ( in @ Xy @ B )
% 3.02/1.60 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(upairinpowunion_type,type,
% 3.02/1.60 upairinpowunion: $o ).
% 3.02/1.60
% 3.02/1.60 thf(upairinpowunion,definition,
% 3.02/1.60 ( upairinpowunion
% 3.02/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ A )
% 3.02/1.60 => ! [Xy: $i] :
% 3.02/1.60 ( ( in @ Xy @ B )
% 3.02/1.60 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(ubforcartprodlem1_type,type,
% 3.02/1.60 ubforcartprodlem1: $o ).
% 3.02/1.60
% 3.02/1.60 thf(ubforcartprodlem1,definition,
% 3.02/1.60 ( ubforcartprodlem1
% 3.02/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ A )
% 3.02/1.60 => ! [Xy: $i] :
% 3.02/1.60 ( ( in @ Xy @ B )
% 3.02/1.60 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(ubforcartprodlem2_type,type,
% 3.02/1.60 ubforcartprodlem2: $o ).
% 3.02/1.60
% 3.02/1.60 thf(ubforcartprodlem2,definition,
% 3.02/1.60 ( ubforcartprodlem2
% 3.02/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ A )
% 3.02/1.60 => ! [Xy: $i] :
% 3.02/1.60 ( ( in @ Xy @ B )
% 3.02/1.60 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(ubforcartprodlem3_type,type,
% 3.02/1.60 ubforcartprodlem3: $o ).
% 3.02/1.60
% 3.02/1.60 thf(ubforcartprodlem3,definition,
% 3.02/1.60 ( ubforcartprodlem3
% 3.02/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ A )
% 3.02/1.60 => ! [Xy: $i] :
% 3.02/1.60 ( ( in @ Xy @ B )
% 3.02/1.60 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(cartprodpairin_type,type,
% 3.02/1.60 cartprodpairin: $o ).
% 3.02/1.60
% 3.02/1.60 thf(cartprodpairin,definition,
% 3.02/1.60 ( cartprodpairin
% 3.02/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ A )
% 3.02/1.60 => ! [Xy: $i] :
% 3.02/1.60 ( ( in @ Xy @ B )
% 3.02/1.60 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(cartprodmempair1_type,type,
% 3.02/1.60 cartprodmempair1: $o ).
% 3.02/1.60
% 3.02/1.60 thf(cartprodmempair1,definition,
% 3.02/1.60 ( cartprodmempair1
% 3.02/1.60 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.02/1.60 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.02/1.60 => ? [Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ A )
% 3.02/1.60 & ? [Xy: $i] :
% 3.02/1.60 ( ( in @ Xy @ B )
% 3.02/1.60 & ( Xu
% 3.02/1.60 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(cartprodmempair_type,type,
% 3.02/1.60 cartprodmempair: $o ).
% 3.02/1.60
% 3.02/1.60 thf(cartprodmempair,definition,
% 3.02/1.60 ( cartprodmempair
% 3.02/1.60 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.02/1.60 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.02/1.60 => ( iskpair @ Xu ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(setunionE2_type,type,
% 3.02/1.60 setunionE2: $o ).
% 3.02/1.60
% 3.02/1.60 thf(setunionE2,definition,
% 3.02/1.60 ( setunionE2
% 3.02/1.60 = ( ! [A: $i,Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ ( setunion @ A ) )
% 3.02/1.60 => ? [X: $i] :
% 3.02/1.60 ( ( in @ X @ A )
% 3.02/1.60 & ( in @ Xx @ X ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(setunionsingleton1_type,type,
% 3.02/1.60 setunionsingleton1: $o ).
% 3.02/1.60
% 3.02/1.60 thf(setunionsingleton1,definition,
% 3.02/1.60 ( setunionsingleton1
% 3.02/1.60 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(setunionsingleton2_type,type,
% 3.02/1.60 setunionsingleton2: $o ).
% 3.02/1.60
% 3.02/1.60 thf(setunionsingleton2,definition,
% 3.02/1.60 ( setunionsingleton2
% 3.02/1.60 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(setunionsingleton_type,type,
% 3.02/1.60 setunionsingleton: $o ).
% 3.02/1.60
% 3.02/1.60 thf(setunionsingleton,definition,
% 3.02/1.60 ( setunionsingleton
% 3.02/1.60 = ( ! [Xx: $i] :
% 3.02/1.60 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 3.02/1.60 = Xx ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(singleton_type,type,
% 3.02/1.60 singleton: $i > $o ).
% 3.02/1.60
% 3.02/1.60 thf(singletonprop_type,type,
% 3.02/1.60 singletonprop: $o ).
% 3.02/1.60
% 3.02/1.60 thf(singletonprop,definition,
% 3.02/1.60 ( singletonprop
% 3.02/1.60 = ( ! [A: $i,Xphi: $i > $o] :
% 3.02/1.60 ( ! [Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ A )
% 3.02/1.60 => ! [Xy: $i] :
% 3.02/1.60 ( ( in @ Xy @ A )
% 3.02/1.60 => ( ( Xphi @ Xx )
% 3.02/1.60 => ( ( Xphi @ Xy )
% 3.02/1.60 => ( Xx = Xy ) ) ) ) )
% 3.02/1.60 => ( ? [Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ A )
% 3.02/1.60 & ( Xphi @ Xx ) )
% 3.02/1.60 => ( singleton
% 3.02/1.60 @ ( dsetconstr @ A
% 3.02/1.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(ex1_type,type,
% 3.02/1.60 ex1: $i > ( $i > $o ) > $o ).
% 3.02/1.60
% 3.02/1.60 thf(ex1E1_type,type,
% 3.02/1.60 ex1E1: $o ).
% 3.02/1.60
% 3.02/1.60 thf(ex1E1,definition,
% 3.02/1.60 ( ex1E1
% 3.02/1.60 = ( ! [A: $i,Xphi: $i > $o] :
% 3.02/1.60 ( ( ex1 @ A
% 3.02/1.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.02/1.60 => ? [Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ A )
% 3.02/1.60 & ( Xphi @ Xx ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(ex1I_type,type,
% 3.02/1.60 ex1I: $o ).
% 3.02/1.60
% 3.02/1.60 thf(ex1I,definition,
% 3.02/1.60 ( ex1I
% 3.02/1.60 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ A )
% 3.02/1.60 => ( ( Xphi @ Xx )
% 3.02/1.60 => ( ! [Xy: $i] :
% 3.02/1.60 ( ( in @ Xy @ A )
% 3.02/1.60 => ( ( Xphi @ Xy )
% 3.02/1.60 => ( Xy = Xx ) ) )
% 3.02/1.60 => ( ex1 @ A
% 3.02/1.60 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(ex1I2_type,type,
% 3.02/1.60 ex1I2: $o ).
% 3.02/1.60
% 3.02/1.60 thf(ex1I2,definition,
% 3.02/1.60 ( ex1I2
% 3.02/1.60 = ( ! [A: $i,Xphi: $i > $o] :
% 3.02/1.60 ( ! [Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ A )
% 3.02/1.60 => ! [Xy: $i] :
% 3.02/1.60 ( ( in @ Xy @ A )
% 3.02/1.60 => ( ( Xphi @ Xx )
% 3.02/1.60 => ( ( Xphi @ Xy )
% 3.02/1.60 => ( Xx = Xy ) ) ) ) )
% 3.02/1.60 => ( ? [Xx: $i] :
% 3.02/1.60 ( ( in @ Xx @ A )
% 3.02/1.60 & ( Xphi @ Xx ) )
% 3.02/1.60 => ( ex1 @ A
% 3.02/1.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(singletonsuniq_type,type,
% 3.02/1.60 singletonsuniq: $o ).
% 3.02/1.60
% 3.02/1.60 thf(singletonsuniq,definition,
% 3.02/1.60 ( singletonsuniq
% 3.02/1.60 = ( ! [Xx: $i,Xy: $i] :
% 3.02/1.60 ( ( ( setadjoin @ Xx @ emptyset )
% 3.02/1.60 = ( setadjoin @ Xy @ emptyset ) )
% 3.02/1.60 => ( Xx = Xy ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(atmost1p_type,type,
% 3.02/1.60 atmost1p: $i > $o ).
% 3.02/1.60
% 3.02/1.60 thf(atleast2p_type,type,
% 3.02/1.60 atleast2p: $i > $o ).
% 3.02/1.60
% 3.02/1.60 thf(atmost2p_type,type,
% 3.02/1.60 atmost2p: $i > $o ).
% 3.02/1.60
% 3.02/1.60 thf(upairsetp_type,type,
% 3.02/1.60 upairsetp: $i > $o ).
% 3.02/1.60
% 3.02/1.60 thf(setukpairinjL1_type,type,
% 3.02/1.60 setukpairinjL1: $o ).
% 3.02/1.60
% 3.02/1.60 thf(setukpairinjL1,definition,
% 3.02/1.60 ( setukpairinjL1
% 3.02/1.60 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.02/1.60 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 3.02/1.60 => ( Xx = Xz ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(kfstsingleton_type,type,
% 3.02/1.60 kfstsingleton: $o ).
% 3.02/1.60
% 3.02/1.60 thf(kfstsingleton,definition,
% 3.02/1.60 ( kfstsingleton
% 3.02/1.60 = ( ! [Xu: $i] :
% 3.02/1.60 ( ( iskpair @ Xu )
% 3.02/1.60 => ( singleton
% 3.02/1.60 @ ( dsetconstr @ ( setunion @ Xu )
% 3.02/1.60 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(theprop_type,type,
% 3.02/1.60 theprop: $o ).
% 3.02/1.60
% 3.02/1.60 thf(theprop,definition,
% 3.02/1.60 ( theprop
% 3.02/1.60 = ( ! [X: $i] :
% 3.02/1.60 ( ( singleton @ X )
% 3.02/1.60 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(kfst_type,type,
% 3.02/1.60 kfst: $i > $i ).
% 3.02/1.60
% 3.02/1.60 thf(kfstpairEq_type,type,
% 3.02/1.60 kfstpairEq: $o ).
% 3.02/1.60
% 3.02/1.60 thf(kfstpairEq,definition,
% 3.02/1.60 ( kfstpairEq
% 3.02/1.60 = ( ! [Xx: $i,Xy: $i] :
% 3.02/1.60 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 3.02/1.60 = Xx ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(cartprodfstin_type,type,
% 3.02/1.60 cartprodfstin: $o ).
% 3.02/1.60
% 3.02/1.60 thf(cartprodfstin,definition,
% 3.02/1.60 ( cartprodfstin
% 3.02/1.60 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.02/1.60 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.02/1.60 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(setukpairinjL2_type,type,
% 3.02/1.60 setukpairinjL2: $o ).
% 3.02/1.60
% 3.02/1.60 thf(setukpairinjL2,definition,
% 3.02/1.60 ( setukpairinjL2
% 3.02/1.60 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.02/1.60 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.02/1.60 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.02/1.60 => ( Xx = Xz ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(setukpairinjL_type,type,
% 3.02/1.60 setukpairinjL: $o ).
% 3.02/1.60
% 3.02/1.60 thf(setukpairinjL,definition,
% 3.02/1.60 ( setukpairinjL
% 3.02/1.60 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.02/1.60 ( ( ( kpair @ Xx @ Xy )
% 3.02/1.60 = ( kpair @ Xz @ Xu ) )
% 3.02/1.60 => ( Xx = Xz ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(setukpairinjR11_type,type,
% 3.02/1.60 setukpairinjR11: $o ).
% 3.02/1.60
% 3.02/1.60 thf(setukpairinjR11,definition,
% 3.02/1.60 ( setukpairinjR11
% 3.02/1.60 = ( ! [Xx: $i,Xy: $i] :
% 3.02/1.60 ( ( Xx = Xy )
% 3.02/1.60 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.02/1.60 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(setukpairinjR12_type,type,
% 3.02/1.60 setukpairinjR12: $o ).
% 3.02/1.60
% 3.02/1.60 thf(setukpairinjR12,definition,
% 3.02/1.60 ( setukpairinjR12
% 3.02/1.60 = ( ! [Xx: $i,Xy: $i] :
% 3.02/1.60 ( ( Xx = Xy )
% 3.02/1.60 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.02/1.60 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(setukpairinjR1_type,type,
% 3.02/1.60 setukpairinjR1: $o ).
% 3.02/1.60
% 3.02/1.60 thf(setukpairinjR1,definition,
% 3.02/1.60 ( setukpairinjR1
% 3.02/1.60 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.02/1.60 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.02/1.60 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.02/1.60 => ( ( Xz = Xu )
% 3.02/1.60 => ( Xy = Xu ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(upairequniteq_type,type,
% 3.02/1.60 upairequniteq: $o ).
% 3.02/1.60
% 3.02/1.60 thf(upairequniteq,definition,
% 3.02/1.60 ( upairequniteq
% 3.02/1.60 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.02/1.60 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.02/1.60 = ( setadjoin @ Xz @ emptyset ) )
% 3.02/1.60 => ( Xx = Xy ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(setukpairinjR2_type,type,
% 3.02/1.60 setukpairinjR2: $o ).
% 3.02/1.60
% 3.02/1.60 thf(setukpairinjR2,definition,
% 3.02/1.60 ( setukpairinjR2
% 3.02/1.60 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.02/1.60 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.02/1.60 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.02/1.60 => ( Xy = Xu ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(setukpairinjR_type,type,
% 3.02/1.60 setukpairinjR: $o ).
% 3.02/1.60
% 3.02/1.60 thf(setukpairinjR,definition,
% 3.02/1.60 ( setukpairinjR
% 3.02/1.60 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.02/1.60 ( ( ( kpair @ Xx @ Xy )
% 3.02/1.60 = ( kpair @ Xz @ Xu ) )
% 3.02/1.60 => ( Xy = Xu ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(ksndsingleton_type,type,
% 3.02/1.60 ksndsingleton: $o ).
% 3.02/1.60
% 3.02/1.60 thf(ksndsingleton,definition,
% 3.02/1.60 ( ksndsingleton
% 3.02/1.60 = ( ! [Xu: $i] :
% 3.02/1.60 ( ( iskpair @ Xu )
% 3.02/1.60 => ( singleton
% 3.02/1.60 @ ( dsetconstr @ ( setunion @ Xu )
% 3.02/1.60 @ ^ [Xx: $i] :
% 3.02/1.60 ( Xu
% 3.02/1.60 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(ksnd_type,type,
% 3.02/1.60 ksnd: $i > $i ).
% 3.02/1.60
% 3.02/1.60 thf(ksndpairEq_type,type,
% 3.02/1.60 ksndpairEq: $o ).
% 3.02/1.60
% 3.02/1.60 thf(ksndpairEq,definition,
% 3.02/1.60 ( ksndpairEq
% 3.02/1.60 = ( ! [Xx: $i,Xy: $i] :
% 3.02/1.60 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 3.02/1.60 = Xy ) ) ) ).
% 3.02/1.60
% 3.02/1.60 thf(kpairsurjEq_type,type,
% 3.02/1.60 kpairsurjEq: $o ).
% 3.02/1.60
% 3.02/1.60 thf(kpairsurjEq,definition,
% 3.20/1.60 ( kpairsurjEq
% 3.20/1.60 = ( ! [Xu: $i] :
% 3.20/1.60 ( ( iskpair @ Xu )
% 3.20/1.60 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 3.20/1.60 = Xu ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(cartprodsndin_type,type,
% 3.20/1.60 cartprodsndin: $o ).
% 3.20/1.60
% 3.20/1.60 thf(cartprodsndin,definition,
% 3.20/1.60 ( cartprodsndin
% 3.20/1.60 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.20/1.60 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.20/1.60 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(cartprodpairmemEL_type,type,
% 3.20/1.60 cartprodpairmemEL: $o ).
% 3.20/1.60
% 3.20/1.60 thf(cartprodpairmemEL,definition,
% 3.20/1.60 ( cartprodpairmemEL
% 3.20/1.60 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 3.20/1.60 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 3.20/1.60 => ( in @ Xx @ A ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(cartprodpairmemER_type,type,
% 3.20/1.60 cartprodpairmemER: $o ).
% 3.20/1.60
% 3.20/1.60 thf(cartprodpairmemER,definition,
% 3.20/1.60 ( cartprodpairmemER
% 3.20/1.60 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 3.20/1.60 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 3.20/1.60 => ( in @ Xy @ B ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(cartprodmempaircEq_type,type,
% 3.20/1.60 cartprodmempaircEq: $o ).
% 3.20/1.60
% 3.20/1.60 thf(cartprodmempaircEq,definition,
% 3.20/1.60 ( cartprodmempaircEq
% 3.20/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ B )
% 3.20/1.60 => ( ( kpair @ Xx @ Xy )
% 3.20/1.60 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(cartprodfstpairEq_type,type,
% 3.20/1.60 cartprodfstpairEq: $o ).
% 3.20/1.60
% 3.20/1.60 thf(cartprodfstpairEq,definition,
% 3.20/1.60 ( cartprodfstpairEq
% 3.20/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ B )
% 3.20/1.60 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 3.20/1.60 = Xx ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(cartprodsndpairEq_type,type,
% 3.20/1.60 cartprodsndpairEq: $o ).
% 3.20/1.60
% 3.20/1.60 thf(cartprodsndpairEq,definition,
% 3.20/1.60 ( cartprodsndpairEq
% 3.20/1.60 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ B )
% 3.20/1.60 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 3.20/1.60 = Xy ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(cartprodpairsurjEq_type,type,
% 3.20/1.60 cartprodpairsurjEq: $o ).
% 3.20/1.60
% 3.20/1.60 thf(cartprodpairsurjEq,definition,
% 3.20/1.60 ( cartprodpairsurjEq
% 3.20/1.60 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.20/1.60 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.20/1.60 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 3.20/1.60 = Xu ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(breln_type,type,
% 3.20/1.60 breln: $i > $i > $i > $o ).
% 3.20/1.60
% 3.20/1.60 thf(dpsetconstr_type,type,
% 3.20/1.60 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 3.20/1.60
% 3.20/1.60 thf(dpsetconstrI_type,type,
% 3.20/1.60 dpsetconstrI: $o ).
% 3.20/1.60
% 3.20/1.60 thf(dpsetconstrI,definition,
% 3.20/1.60 ( dpsetconstrI
% 3.20/1.60 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ B )
% 3.20/1.60 => ( ( Xphi @ Xx @ Xy )
% 3.20/1.60 => ( in @ ( kpair @ Xx @ Xy )
% 3.20/1.60 @ ( dpsetconstr @ A @ B
% 3.20/1.60 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(dpsetconstrSub_type,type,
% 3.20/1.60 dpsetconstrSub: $o ).
% 3.20/1.60
% 3.20/1.60 thf(dpsetconstrSub,definition,
% 3.20/1.60 ( dpsetconstrSub
% 3.20/1.60 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.20/1.60 ( subset
% 3.20/1.60 @ ( dpsetconstr @ A @ B
% 3.20/1.60 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 3.20/1.60 @ ( cartprod @ A @ B ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(setOfPairsIsBReln_type,type,
% 3.20/1.60 setOfPairsIsBReln: $o ).
% 3.20/1.60
% 3.20/1.60 thf(setOfPairsIsBReln,definition,
% 3.20/1.60 ( setOfPairsIsBReln
% 3.20/1.60 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.20/1.60 ( breln @ A @ B
% 3.20/1.60 @ ( dpsetconstr @ A @ B
% 3.20/1.60 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(dpsetconstrERa_type,type,
% 3.20/1.60 dpsetconstrERa: $o ).
% 3.20/1.60
% 3.20/1.60 thf(dpsetconstrERa,definition,
% 3.20/1.60 ( dpsetconstrERa
% 3.20/1.60 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ B )
% 3.20/1.60 => ( ( in @ ( kpair @ Xx @ Xy )
% 3.20/1.60 @ ( dpsetconstr @ A @ B
% 3.20/1.60 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.20/1.60 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(dpsetconstrEL1_type,type,
% 3.20/1.60 dpsetconstrEL1: $o ).
% 3.20/1.60
% 3.20/1.60 thf(dpsetconstrEL1,definition,
% 3.20/1.60 ( dpsetconstrEL1
% 3.20/1.60 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.20/1.60 ( ( in @ ( kpair @ Xx @ Xy )
% 3.20/1.60 @ ( dpsetconstr @ A @ B
% 3.20/1.60 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.20/1.60 => ( in @ Xx @ A ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(dpsetconstrEL2_type,type,
% 3.20/1.60 dpsetconstrEL2: $o ).
% 3.20/1.60
% 3.20/1.60 thf(dpsetconstrEL2,definition,
% 3.20/1.60 ( dpsetconstrEL2
% 3.20/1.60 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.20/1.60 ( ( in @ ( kpair @ Xx @ Xy )
% 3.20/1.60 @ ( dpsetconstr @ A @ B
% 3.20/1.60 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.20/1.60 => ( in @ Xy @ B ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(dpsetconstrER_type,type,
% 3.20/1.60 dpsetconstrER: $o ).
% 3.20/1.60
% 3.20/1.60 thf(dpsetconstrER,definition,
% 3.20/1.60 ( dpsetconstrER
% 3.20/1.60 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.20/1.60 ( ( in @ ( kpair @ Xx @ Xy )
% 3.20/1.60 @ ( dpsetconstr @ A @ B
% 3.20/1.60 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.20/1.60 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(func_type,type,
% 3.20/1.60 func: $i > $i > $i > $o ).
% 3.20/1.60
% 3.20/1.60 thf(funcSet_type,type,
% 3.20/1.60 funcSet: $i > $i > $i ).
% 3.20/1.60
% 3.20/1.60 thf(funcImageSingleton_type,type,
% 3.20/1.60 funcImageSingleton: $o ).
% 3.20/1.60
% 3.20/1.60 thf(funcImageSingleton,definition,
% 3.20/1.60 ( funcImageSingleton
% 3.20/1.60 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.20/1.60 ( ( func @ A @ B @ Xf )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( singleton
% 3.20/1.60 @ ( dsetconstr @ B
% 3.20/1.60 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(apProp_type,type,
% 3.20/1.60 apProp: $o ).
% 3.20/1.60
% 3.20/1.60 thf(apProp,definition,
% 3.20/1.60 ( apProp
% 3.20/1.60 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.20/1.60 ( ( func @ A @ B @ Xf )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( in
% 3.20/1.60 @ ( setunion
% 3.20/1.60 @ ( dsetconstr @ B
% 3.20/1.60 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 3.20/1.60 @ B ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(ap_type,type,
% 3.20/1.60 ap: $i > $i > $i > $i > $i ).
% 3.20/1.60
% 3.20/1.60 thf(app_type,type,
% 3.20/1.60 app: $o ).
% 3.20/1.60
% 3.20/1.60 thf(app,definition,
% 3.20/1.60 ( app
% 3.20/1.60 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.20/1.60 ( ( func @ A @ B @ Xf )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(infuncsetfunc_type,type,
% 3.20/1.60 infuncsetfunc: $o ).
% 3.20/1.60
% 3.20/1.60 thf(infuncsetfunc,definition,
% 3.20/1.60 ( infuncsetfunc
% 3.20/1.60 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.20/1.60 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.20/1.60 => ( func @ A @ B @ Xf ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(ap2p_type,type,
% 3.20/1.60 ap2p: $o ).
% 3.20/1.60
% 3.20/1.60 thf(ap2p,definition,
% 3.20/1.60 ( ap2p
% 3.20/1.60 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.20/1.60 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(funcinfuncset_type,type,
% 3.20/1.60 funcinfuncset: $o ).
% 3.20/1.60
% 3.20/1.60 thf(funcinfuncset,definition,
% 3.20/1.60 ( funcinfuncset
% 3.20/1.60 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.20/1.60 ( ( func @ A @ B @ Xf )
% 3.20/1.60 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(lamProp_type,type,
% 3.20/1.60 lamProp: $o ).
% 3.20/1.60
% 3.20/1.60 thf(lamProp,definition,
% 3.20/1.60 ( lamProp
% 3.20/1.60 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.20/1.60 ( ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.20/1.60 => ( func @ A @ B
% 3.20/1.60 @ ( dpsetconstr @ A @ B
% 3.20/1.60 @ ^ [Xx: $i,Xy: $i] :
% 3.20/1.60 ( ( Xf @ Xx )
% 3.20/1.60 = Xy ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(lam_type,type,
% 3.20/1.60 lam: $i > $i > ( $i > $i ) > $i ).
% 3.20/1.60
% 3.20/1.60 thf(lamp_type,type,
% 3.20/1.60 lamp: $o ).
% 3.20/1.60
% 3.20/1.60 thf(lamp,definition,
% 3.20/1.60 ( lamp
% 3.20/1.60 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.20/1.60 ( ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.20/1.60 => ( func @ A @ B
% 3.20/1.60 @ ( lam @ A @ B
% 3.20/1.60 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(lam2p_type,type,
% 3.20/1.60 lam2p: $o ).
% 3.20/1.60
% 3.20/1.60 thf(lam2p,definition,
% 3.20/1.60 ( lam2p
% 3.20/1.60 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.20/1.60 ( ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.20/1.60 => ( in
% 3.20/1.60 @ ( lam @ A @ B
% 3.20/1.60 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 3.20/1.60 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(brelnall1_type,type,
% 3.20/1.60 brelnall1: $o ).
% 3.20/1.60
% 3.20/1.60 thf(brelnall1,definition,
% 3.20/1.60 ( brelnall1
% 3.20/1.60 = ( ! [A: $i,B: $i,R: $i] :
% 3.20/1.60 ( ( breln @ A @ B @ R )
% 3.20/1.60 => ! [Xphi: $i > $o] :
% 3.20/1.60 ( ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ B )
% 3.20/1.60 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.20/1.60 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ R )
% 3.20/1.60 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(brelnall2_type,type,
% 3.20/1.60 brelnall2: $o ).
% 3.20/1.60
% 3.20/1.60 thf(brelnall2,definition,
% 3.20/1.60 ( brelnall2
% 3.20/1.60 = ( ! [A: $i,B: $i,R: $i] :
% 3.20/1.60 ( ( breln @ A @ B @ R )
% 3.20/1.60 => ! [Xphi: $i > $o] :
% 3.20/1.60 ( ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ B )
% 3.20/1.60 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.20/1.60 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ R )
% 3.20/1.60 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(ex1E2_type,type,
% 3.20/1.60 ex1E2: $o ).
% 3.20/1.60
% 3.20/1.60 thf(ex1E2,definition,
% 3.20/1.60 ( ex1E2
% 3.20/1.60 = ( ! [A: $i,Xphi: $i > $o] :
% 3.20/1.60 ( ( ex1 @ A
% 3.20/1.60 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 => ( ( Xphi @ Xx )
% 3.20/1.60 => ( ( Xphi @ Xy )
% 3.20/1.60 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(funcGraphProp1_type,type,
% 3.20/1.60 funcGraphProp1: $o ).
% 3.20/1.60
% 3.20/1.60 thf(funcGraphProp1,definition,
% 3.20/1.60 ( funcGraphProp1
% 3.20/1.60 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.20/1.60 ( ( func @ A @ B @ Xf )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(funcGraphProp3_type,type,
% 3.20/1.60 funcGraphProp3: $o ).
% 3.20/1.60
% 3.20/1.60 thf(funcGraphProp3,definition,
% 3.20/1.60 ( funcGraphProp3
% 3.20/1.60 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.20/1.60 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(funcGraphProp2_type,type,
% 3.20/1.60 funcGraphProp2: $o ).
% 3.20/1.60
% 3.20/1.60 thf(funcGraphProp2,definition,
% 3.20/1.60 ( funcGraphProp2
% 3.20/1.60 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.20/1.60 ( ( func @ A @ B @ Xf )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ B )
% 3.20/1.60 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 3.20/1.60 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.20/1.60 = Xy ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(funcextLem_type,type,
% 3.20/1.60 funcextLem: $o ).
% 3.20/1.60
% 3.20/1.60 thf(funcextLem,definition,
% 3.20/1.60 ( funcextLem
% 3.20/1.60 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.20/1.60 ( ( func @ A @ B @ Xf )
% 3.20/1.60 => ! [Xg: $i] :
% 3.20/1.60 ( ( func @ A @ B @ Xg )
% 3.20/1.60 => ( ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.20/1.60 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ B )
% 3.20/1.60 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 3.20/1.60 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(funcGraphProp4_type,type,
% 3.20/1.60 funcGraphProp4: $o ).
% 3.20/1.60
% 3.20/1.60 thf(funcGraphProp4,definition,
% 3.20/1.60 ( funcGraphProp4
% 3.20/1.60 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.20/1.60 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ B )
% 3.20/1.60 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 3.20/1.60 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.20/1.60 = Xy ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(subbreln_type,type,
% 3.20/1.60 subbreln: $o ).
% 3.20/1.60
% 3.20/1.60 thf(subbreln,definition,
% 3.20/1.60 ( subbreln
% 3.20/1.60 = ( ! [A: $i,B: $i,R: $i] :
% 3.20/1.60 ( ( breln @ A @ B @ R )
% 3.20/1.60 => ! [S: $i] :
% 3.20/1.60 ( ( breln @ A @ B @ S )
% 3.20/1.60 => ( ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ B )
% 3.20/1.60 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.20/1.60 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.20/1.60 => ( subset @ R @ S ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(eqbreln_type,type,
% 3.20/1.60 eqbreln: $o ).
% 3.20/1.60
% 3.20/1.60 thf(eqbreln,definition,
% 3.20/1.60 ( eqbreln
% 3.20/1.60 = ( ! [A: $i,B: $i,R: $i] :
% 3.20/1.60 ( ( breln @ A @ B @ R )
% 3.20/1.60 => ! [S: $i] :
% 3.20/1.60 ( ( breln @ A @ B @ S )
% 3.20/1.60 => ( ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ B )
% 3.20/1.60 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.20/1.60 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.20/1.60 => ( ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ B )
% 3.20/1.60 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.20/1.60 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 3.20/1.60 => ( R = S ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(funcext_type,type,
% 3.20/1.60 funcext: $o ).
% 3.20/1.60
% 3.20/1.60 thf(funcext,definition,
% 3.20/1.60 ( funcext
% 3.20/1.60 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.20/1.60 ( ( func @ A @ B @ Xf )
% 3.20/1.60 => ! [Xg: $i] :
% 3.20/1.60 ( ( func @ A @ B @ Xg )
% 3.20/1.60 => ( ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.20/1.60 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.20/1.60 => ( Xf = Xg ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(funcext2_type,type,
% 3.20/1.60 funcext2: $o ).
% 3.20/1.60
% 3.20/1.60 thf(funcext2,definition,
% 3.20/1.60 ( funcext2
% 3.20/1.60 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.20/1.60 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.20/1.60 => ! [Xg: $i] :
% 3.20/1.60 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 3.20/1.60 => ( ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.20/1.60 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.20/1.60 => ( Xf = Xg ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(ap2apEq1_type,type,
% 3.20/1.60 ap2apEq1: $o ).
% 3.20/1.60
% 3.20/1.60 thf(ap2apEq1,definition,
% 3.20/1.60 ( ap2apEq1
% 3.20/1.60 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.20/1.60 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.20/1.60 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(ap2apEq2_type,type,
% 3.20/1.60 ap2apEq2: $o ).
% 3.20/1.60
% 3.20/1.60 thf(ap2apEq2,definition,
% 3.20/1.60 ( ap2apEq2
% 3.20/1.60 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.20/1.60 ( ( func @ A @ B @ Xf )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.20/1.60 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(beta1_type,type,
% 3.20/1.60 beta1: $o ).
% 3.20/1.60
% 3.20/1.60 thf(beta1,definition,
% 3.20/1.60 ( beta1
% 3.20/1.60 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.20/1.60 ( ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( ap @ A @ B
% 3.20/1.60 @ ( lam @ A @ B
% 3.20/1.60 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 3.20/1.60 @ Xx )
% 3.20/1.60 = ( Xf @ Xx ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(eta1_type,type,
% 3.20/1.60 eta1: $o ).
% 3.20/1.60
% 3.20/1.60 thf(eta1,definition,
% 3.20/1.60 ( eta1
% 3.20/1.60 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.20/1.60 ( ( func @ A @ B @ Xf )
% 3.20/1.60 => ( ( lam @ A @ B
% 3.20/1.60 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 3.20/1.60 = Xf ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(lam2lamEq_type,type,
% 3.20/1.60 lam2lamEq: $o ).
% 3.20/1.60
% 3.20/1.60 thf(lam2lamEq,definition,
% 3.20/1.60 ( lam2lamEq
% 3.20/1.60 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.20/1.60 ( ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.20/1.60 => ( ( lam @ A @ B
% 3.20/1.60 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 3.20/1.60 = ( lam @ A @ B
% 3.20/1.60 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(beta2_type,type,
% 3.20/1.60 beta2: $o ).
% 3.20/1.60
% 3.20/1.60 thf(beta2,definition,
% 3.20/1.60 ( beta2
% 3.20/1.60 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.20/1.60 ( ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( ap @ A @ B
% 3.20/1.60 @ ( lam @ A @ B
% 3.20/1.60 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 3.20/1.60 @ Xx )
% 3.20/1.60 = ( Xf @ Xx ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(eta2_type,type,
% 3.20/1.60 eta2: $o ).
% 3.20/1.60
% 3.20/1.60 thf(eta2,definition,
% 3.20/1.60 ( eta2
% 3.20/1.60 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.20/1.60 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.20/1.60 => ( ( lam @ A @ B
% 3.20/1.60 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 3.20/1.60 = Xf ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(iffalseProp1_type,type,
% 3.20/1.60 iffalseProp1: $o ).
% 3.20/1.60
% 3.20/1.60 thf(iffalseProp1,definition,
% 3.20/1.60 ( iffalseProp1
% 3.20/1.60 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 => ( ~ Xphi
% 3.20/1.60 => ( in @ Xy
% 3.20/1.60 @ ( dsetconstr @ A
% 3.20/1.60 @ ^ [Xz: $i] :
% 3.20/1.60 ( ( Xphi
% 3.20/1.60 & ( Xz = Xx ) )
% 3.20/1.60 | ( ~ Xphi
% 3.20/1.60 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(iffalseProp2_type,type,
% 3.20/1.60 iffalseProp2: $o ).
% 3.20/1.60
% 3.20/1.60 thf(iffalseProp2,definition,
% 3.20/1.60 ( iffalseProp2
% 3.20/1.60 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 => ( ~ Xphi
% 3.20/1.60 => ( ( dsetconstr @ A
% 3.20/1.60 @ ^ [Xz: $i] :
% 3.20/1.60 ( ( Xphi
% 3.20/1.60 & ( Xz = Xx ) )
% 3.20/1.60 | ( ~ Xphi
% 3.20/1.60 & ( Xz = Xy ) ) ) )
% 3.20/1.60 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(iftrueProp1_type,type,
% 3.20/1.60 iftrueProp1: $o ).
% 3.20/1.60
% 3.20/1.60 thf(iftrueProp1,definition,
% 3.20/1.60 ( iftrueProp1
% 3.20/1.60 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 => ( Xphi
% 3.20/1.60 => ( in @ Xx
% 3.20/1.60 @ ( dsetconstr @ A
% 3.20/1.60 @ ^ [Xz: $i] :
% 3.20/1.60 ( ( Xphi
% 3.20/1.60 & ( Xz = Xx ) )
% 3.20/1.60 | ( ~ Xphi
% 3.20/1.60 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(iftrueProp2_type,type,
% 3.20/1.60 iftrueProp2: $o ).
% 3.20/1.60
% 3.20/1.60 thf(iftrueProp2,definition,
% 3.20/1.60 ( iftrueProp2
% 3.20/1.60 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 => ( Xphi
% 3.20/1.60 => ( ( dsetconstr @ A
% 3.20/1.60 @ ^ [Xz: $i] :
% 3.20/1.60 ( ( Xphi
% 3.20/1.60 & ( Xz = Xx ) )
% 3.20/1.60 | ( ~ Xphi
% 3.20/1.60 & ( Xz = Xy ) ) ) )
% 3.20/1.60 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(ifSingleton_type,type,
% 3.20/1.60 ifSingleton: $o ).
% 3.20/1.60
% 3.20/1.60 thf(ifSingleton,definition,
% 3.20/1.60 ( ifSingleton
% 3.20/1.60 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 => ( singleton
% 3.20/1.60 @ ( dsetconstr @ A
% 3.20/1.60 @ ^ [Xz: $i] :
% 3.20/1.60 ( ( Xphi
% 3.20/1.60 & ( Xz = Xx ) )
% 3.20/1.60 | ( ~ Xphi
% 3.20/1.60 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(if_type,type,
% 3.20/1.60 if: $i > $o > $i > $i > $i ).
% 3.20/1.60
% 3.20/1.60 thf(ifp_type,type,
% 3.20/1.60 ifp: $o ).
% 3.20/1.60
% 3.20/1.60 thf(ifp,definition,
% 3.20/1.60 ( ifp
% 3.20/1.60 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(theeq_type,type,
% 3.20/1.60 theeq: $o ).
% 3.20/1.60
% 3.20/1.60 thf(theeq,definition,
% 3.20/1.60 ( theeq
% 3.20/1.60 = ( ! [X: $i] :
% 3.20/1.60 ( ( singleton @ X )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ X )
% 3.20/1.60 => ( ( setunion @ X )
% 3.20/1.60 = Xx ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(iftrue_type,type,
% 3.20/1.60 iftrue: $o ).
% 3.20/1.60
% 3.20/1.60 thf(iftrue,definition,
% 3.20/1.60 ( iftrue
% 3.20/1.60 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 => ( Xphi
% 3.20/1.60 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 3.20/1.60 = Xx ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(iffalse_type,type,
% 3.20/1.60 iffalse: $o ).
% 3.20/1.60
% 3.20/1.60 thf(iffalse,definition,
% 3.20/1.60 ( iffalse
% 3.20/1.60 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 => ( ~ Xphi
% 3.20/1.60 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 3.20/1.60 = Xy ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(iftrueorfalse_type,type,
% 3.20/1.60 iftrueorfalse: $o ).
% 3.20/1.60
% 3.20/1.60 thf(iftrueorfalse,definition,
% 3.20/1.60 ( iftrueorfalse
% 3.20/1.60 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(binintersectT_lem_type,type,
% 3.20/1.60 binintersectT_lem: $o ).
% 3.20/1.60
% 3.20/1.60 thf(binintersectT_lem,definition,
% 3.20/1.60 ( binintersectT_lem
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(binunionT_lem_type,type,
% 3.20/1.60 binunionT_lem: $o ).
% 3.20/1.60
% 3.20/1.60 thf(binunionT_lem,definition,
% 3.20/1.60 ( binunionT_lem
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(powersetT_lem_type,type,
% 3.20/1.60 powersetT_lem: $o ).
% 3.20/1.60
% 3.20/1.60 thf(powersetT_lem,definition,
% 3.20/1.60 ( powersetT_lem
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(setminusT_lem_type,type,
% 3.20/1.60 setminusT_lem: $o ).
% 3.20/1.60
% 3.20/1.60 thf(setminusT_lem,definition,
% 3.20/1.60 ( setminusT_lem
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(complementT_lem_type,type,
% 3.20/1.60 complementT_lem: $o ).
% 3.20/1.60
% 3.20/1.60 thf(complementT_lem,definition,
% 3.20/1.60 ( complementT_lem
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(setextT_type,type,
% 3.20/1.60 setextT: $o ).
% 3.20/1.60
% 3.20/1.60 thf(setextT,definition,
% 3.20/1.60 ( setextT
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ( ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( in @ Xx @ X )
% 3.20/1.60 => ( in @ Xx @ Y ) ) )
% 3.20/1.60 => ( ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( in @ Xx @ Y )
% 3.20/1.60 => ( in @ Xx @ X ) ) )
% 3.20/1.60 => ( X = Y ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(subsetTI_type,type,
% 3.20/1.60 subsetTI: $o ).
% 3.20/1.60
% 3.20/1.60 thf(subsetTI,definition,
% 3.20/1.60 ( subsetTI
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ( ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( in @ Xx @ X )
% 3.20/1.60 => ( in @ Xx @ Y ) ) )
% 3.20/1.60 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(powersetTI1_type,type,
% 3.20/1.60 powersetTI1: $o ).
% 3.20/1.60
% 3.20/1.60 thf(powersetTI1,definition,
% 3.20/1.60 ( powersetTI1
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ( ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( in @ Xx @ X )
% 3.20/1.60 => ( in @ Xx @ Y ) ) )
% 3.20/1.60 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(powersetTE1_type,type,
% 3.20/1.60 powersetTE1: $o ).
% 3.20/1.60
% 3.20/1.60 thf(powersetTE1,definition,
% 3.20/1.60 ( powersetTE1
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( in @ X @ ( powerset @ Y ) )
% 3.20/1.60 => ( ( in @ Xx @ X )
% 3.20/1.60 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(complementTI1_type,type,
% 3.20/1.60 complementTI1: $o ).
% 3.20/1.60
% 3.20/1.60 thf(complementTI1,definition,
% 3.20/1.60 ( complementTI1
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( in @ Xx @ X )
% 3.20/1.60 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(complementTE1_type,type,
% 3.20/1.60 complementTE1: $o ).
% 3.20/1.60
% 3.20/1.60 thf(complementTE1,definition,
% 3.20/1.60 ( complementTE1
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 3.20/1.60 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(binintersectTELcontra_type,type,
% 3.20/1.60 binintersectTELcontra: $o ).
% 3.20/1.60
% 3.20/1.60 thf(binintersectTELcontra,definition,
% 3.20/1.60 ( binintersectTELcontra
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ~ ( in @ Xx @ X )
% 3.20/1.60 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(binintersectTERcontra_type,type,
% 3.20/1.60 binintersectTERcontra: $o ).
% 3.20/1.60
% 3.20/1.60 thf(binintersectTERcontra,definition,
% 3.20/1.60 ( binintersectTERcontra
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ~ ( in @ Xx @ Y )
% 3.20/1.60 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(contrasubsetT_type,type,
% 3.20/1.60 contrasubsetT: $o ).
% 3.20/1.60
% 3.20/1.60 thf(contrasubsetT,definition,
% 3.20/1.60 ( contrasubsetT
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.20/1.60 => ( ( in @ Xx @ Y )
% 3.20/1.60 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(contrasubsetT1_type,type,
% 3.20/1.60 contrasubsetT1: $o ).
% 3.20/1.60
% 3.20/1.60 thf(contrasubsetT1,definition,
% 3.20/1.60 ( contrasubsetT1
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( subset @ X @ Y )
% 3.20/1.60 => ( ~ ( in @ Xx @ Y )
% 3.20/1.60 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(contrasubsetT2_type,type,
% 3.20/1.60 contrasubsetT2: $o ).
% 3.20/1.60
% 3.20/1.60 thf(contrasubsetT2,definition,
% 3.20/1.60 ( contrasubsetT2
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ( ( subset @ X @ Y )
% 3.20/1.60 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(contrasubsetT3_type,type,
% 3.20/1.60 contrasubsetT3: $o ).
% 3.20/1.60
% 3.20/1.60 thf(contrasubsetT3,definition,
% 3.20/1.60 ( contrasubsetT3
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 3.20/1.60 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(doubleComplementI1_type,type,
% 3.20/1.60 doubleComplementI1: $o ).
% 3.20/1.60
% 3.20/1.60 thf(doubleComplementI1,definition,
% 3.20/1.60 ( doubleComplementI1
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( in @ Xx @ X )
% 3.20/1.60 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(doubleComplementE1_type,type,
% 3.20/1.60 doubleComplementE1: $o ).
% 3.20/1.60
% 3.20/1.60 thf(doubleComplementE1,definition,
% 3.20/1.60 ( doubleComplementE1
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 3.20/1.60 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(doubleComplementSub1_type,type,
% 3.20/1.60 doubleComplementSub1: $o ).
% 3.20/1.60
% 3.20/1.60 thf(doubleComplementSub1,definition,
% 3.20/1.60 ( doubleComplementSub1
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(doubleComplementSub2_type,type,
% 3.20/1.60 doubleComplementSub2: $o ).
% 3.20/1.60
% 3.20/1.60 thf(doubleComplementSub2,definition,
% 3.20/1.60 ( doubleComplementSub2
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(doubleComplementEq_type,type,
% 3.20/1.60 doubleComplementEq: $o ).
% 3.20/1.60
% 3.20/1.60 thf(doubleComplementEq,definition,
% 3.20/1.60 ( doubleComplementEq
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ( X
% 3.20/1.60 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(complementTnotintersectT_type,type,
% 3.20/1.60 complementTnotintersectT: $o ).
% 3.20/1.60
% 3.20/1.60 thf(complementTnotintersectT,definition,
% 3.20/1.60 ( complementTnotintersectT
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.20/1.60 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(complementImpComplementIntersect_type,type,
% 3.20/1.60 complementImpComplementIntersect: $o ).
% 3.20/1.60
% 3.20/1.60 thf(complementImpComplementIntersect,definition,
% 3.20/1.60 ( complementImpComplementIntersect
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.20/1.60 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(complementSubsetComplementIntersect_type,type,
% 3.20/1.60 complementSubsetComplementIntersect: $o ).
% 3.20/1.60
% 3.20/1.60 thf(complementSubsetComplementIntersect,definition,
% 3.20/1.60 ( complementSubsetComplementIntersect
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(complementInPowersetComplementIntersect_type,type,
% 3.20/1.60 complementInPowersetComplementIntersect: $o ).
% 3.20/1.60
% 3.20/1.60 thf(complementInPowersetComplementIntersect,definition,
% 3.20/1.60 ( complementInPowersetComplementIntersect
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(contraSubsetComplement_type,type,
% 3.20/1.60 contraSubsetComplement: $o ).
% 3.20/1.60
% 3.20/1.60 thf(contraSubsetComplement,definition,
% 3.20/1.60 ( contraSubsetComplement
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( in @ Xx @ Y )
% 3.20/1.60 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(complementTcontraSubset_type,type,
% 3.20/1.60 complementTcontraSubset: $o ).
% 3.20/1.60
% 3.20/1.60 thf(complementTcontraSubset,definition,
% 3.20/1.60 ( complementTcontraSubset
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.20/1.60 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(binunionTILcontra_type,type,
% 3.20/1.60 binunionTILcontra: $o ).
% 3.20/1.60
% 3.20/1.60 thf(binunionTILcontra,definition,
% 3.20/1.60 ( binunionTILcontra
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.20/1.60 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(binunionTIRcontra_type,type,
% 3.20/1.60 binunionTIRcontra: $o ).
% 3.20/1.60
% 3.20/1.60 thf(binunionTIRcontra,definition,
% 3.20/1.60 ( binunionTIRcontra
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.20/1.60 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(inIntersectImpInUnion_type,type,
% 3.20/1.60 inIntersectImpInUnion: $o ).
% 3.20/1.60
% 3.20/1.60 thf(inIntersectImpInUnion,definition,
% 3.20/1.60 ( inIntersectImpInUnion
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Z: $i] :
% 3.20/1.60 ( ( in @ Z @ ( powerset @ A ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.20/1.60 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(inIntersectImpInUnion2_type,type,
% 3.20/1.60 inIntersectImpInUnion2: $o ).
% 3.20/1.60
% 3.20/1.60 thf(inIntersectImpInUnion2,definition,
% 3.20/1.60 ( inIntersectImpInUnion2
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Z: $i] :
% 3.20/1.60 ( ( in @ Z @ ( powerset @ A ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.20/1.60 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(inIntersectImpInIntersectUnions_type,type,
% 3.20/1.60 inIntersectImpInIntersectUnions: $o ).
% 3.20/1.60
% 3.20/1.60 thf(inIntersectImpInIntersectUnions,definition,
% 3.20/1.60 ( inIntersectImpInIntersectUnions
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Z: $i] :
% 3.20/1.60 ( ( in @ Z @ ( powerset @ A ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.20/1.60 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(intersectInPowersetIntersectUnions_type,type,
% 3.20/1.60 intersectInPowersetIntersectUnions: $o ).
% 3.20/1.60
% 3.20/1.60 thf(intersectInPowersetIntersectUnions,definition,
% 3.20/1.60 ( intersectInPowersetIntersectUnions
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Z: $i] :
% 3.20/1.60 ( ( in @ Z @ ( powerset @ A ) )
% 3.20/1.60 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(inComplementUnionImpNotIn1_type,type,
% 3.20/1.60 inComplementUnionImpNotIn1: $o ).
% 3.20/1.60
% 3.20/1.60 thf(inComplementUnionImpNotIn1,definition,
% 3.20/1.60 ( inComplementUnionImpNotIn1
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.20/1.60 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(inComplementUnionImpInComplement1_type,type,
% 3.20/1.60 inComplementUnionImpInComplement1: $o ).
% 3.20/1.60
% 3.20/1.60 thf(inComplementUnionImpInComplement1,definition,
% 3.20/1.60 ( inComplementUnionImpInComplement1
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.20/1.60 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(binunionTE_type,type,
% 3.20/1.60 binunionTE: $o ).
% 3.20/1.60
% 3.20/1.60 thf(binunionTE,definition,
% 3.20/1.60 ( binunionTE
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Xphi: $o,Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.20/1.60 => ( ( ( in @ Xx @ X )
% 3.20/1.60 => Xphi )
% 3.20/1.60 => ( ( ( in @ Xx @ Y )
% 3.20/1.60 => Xphi )
% 3.20/1.60 => Xphi ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(binunionTEcontra_type,type,
% 3.20/1.60 binunionTEcontra: $o ).
% 3.20/1.60
% 3.20/1.60 thf(binunionTEcontra,definition,
% 3.20/1.60 ( binunionTEcontra
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ~ ( in @ Xx @ X )
% 3.20/1.60 => ( ~ ( in @ Xx @ Y )
% 3.20/1.60 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(demorgan2a1_type,type,
% 3.20/1.60 demorgan2a1: $o ).
% 3.20/1.60
% 3.20/1.60 thf(demorgan2a1,definition,
% 3.20/1.60 ( demorgan2a1
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.20/1.60 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(complementUnionInPowersetComplement_type,type,
% 3.20/1.60 complementUnionInPowersetComplement: $o ).
% 3.20/1.60
% 3.20/1.60 thf(complementUnionInPowersetComplement,definition,
% 3.20/1.60 ( complementUnionInPowersetComplement
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(demorgan2a2_type,type,
% 3.20/1.60 demorgan2a2: $o ).
% 3.20/1.60
% 3.20/1.60 thf(demorgan2a2,definition,
% 3.20/1.60 ( demorgan2a2
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.20/1.60 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(demorgan1a_type,type,
% 3.20/1.60 demorgan1a: $o ).
% 3.20/1.60
% 3.20/1.60 thf(demorgan1a,definition,
% 3.20/1.60 ( demorgan1a
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 3.20/1.60 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(demorgan1b_type,type,
% 3.20/1.60 demorgan1b: $o ).
% 3.20/1.60
% 3.20/1.60 thf(demorgan1b,definition,
% 3.20/1.60 ( demorgan1b
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 3.20/1.60 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(demorgan1_type,type,
% 3.20/1.60 demorgan1: $o ).
% 3.20/1.60
% 3.20/1.60 thf(demorgan1,definition,
% 3.20/1.60 ( demorgan1
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 3.20/1.60 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(demorgan2a_type,type,
% 3.20/1.60 demorgan2a: $o ).
% 3.20/1.60
% 3.20/1.60 thf(demorgan2a,definition,
% 3.20/1.60 ( demorgan2a
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.20/1.60 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(demorgan2b2_type,type,
% 3.20/1.60 demorgan2b2: $o ).
% 3.20/1.60
% 3.20/1.60 thf(demorgan2b2,definition,
% 3.20/1.60 ( demorgan2b2
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.20/1.60 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 3.20/1.60 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(demorgan2b_type,type,
% 3.20/1.60 demorgan2b: $o ).
% 3.20/1.60
% 3.20/1.60 thf(demorgan2b,definition,
% 3.20/1.60 ( demorgan2b
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 3.20/1.60 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(demorgan2_type,type,
% 3.20/1.60 demorgan2: $o ).
% 3.20/1.60
% 3.20/1.60 thf(demorgan2,definition,
% 3.20/1.60 ( demorgan2
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 3.20/1.60 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(woz13rule0_type,type,
% 3.20/1.60 woz13rule0: $o ).
% 3.20/1.60
% 3.20/1.60 thf(woz13rule0,definition,
% 3.20/1.60 ( woz13rule0
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.20/1.60 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(woz13rule1_type,type,
% 3.20/1.60 woz13rule1: $o ).
% 3.20/1.60
% 3.20/1.60 thf(woz13rule1,definition,
% 3.20/1.60 ( woz13rule1
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Z: $i] :
% 3.20/1.60 ( ( in @ Z @ ( powerset @ A ) )
% 3.20/1.60 => ( ( subset @ X @ Z )
% 3.20/1.60 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(woz13rule2_type,type,
% 3.20/1.60 woz13rule2: $o ).
% 3.20/1.60
% 3.20/1.60 thf(woz13rule2,definition,
% 3.20/1.60 ( woz13rule2
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Z: $i] :
% 3.20/1.60 ( ( in @ Z @ ( powerset @ A ) )
% 3.20/1.60 => ( ( subset @ Y @ Z )
% 3.20/1.60 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(woz13rule3_type,type,
% 3.20/1.60 woz13rule3: $o ).
% 3.20/1.60
% 3.20/1.60 thf(woz13rule3,definition,
% 3.20/1.60 ( woz13rule3
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Z: $i] :
% 3.20/1.60 ( ( in @ Z @ ( powerset @ A ) )
% 3.20/1.60 => ( ( subset @ X @ Y )
% 3.20/1.60 => ( ( subset @ X @ Z )
% 3.20/1.60 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(woz13rule4_type,type,
% 3.20/1.60 woz13rule4: $o ).
% 3.20/1.60
% 3.20/1.60 thf(woz13rule4,definition,
% 3.20/1.60 ( woz13rule4
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Z: $i] :
% 3.20/1.60 ( ( in @ Z @ ( powerset @ A ) )
% 3.20/1.60 => ! [W: $i] :
% 3.20/1.60 ( ( in @ W @ ( powerset @ A ) )
% 3.20/1.60 => ( ( subset @ X @ Z )
% 3.20/1.60 => ( ( subset @ Y @ W )
% 3.20/1.60 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(woz1_1_type,type,
% 3.20/1.60 woz1_1: $o ).
% 3.20/1.60
% 3.20/1.60 thf(woz1_1,definition,
% 3.20/1.60 ( woz1_1
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(woz1_2_type,type,
% 3.20/1.60 woz1_2: $o ).
% 3.20/1.60
% 3.20/1.60 thf(woz1_2,definition,
% 3.20/1.60 ( woz1_2
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Z: $i] :
% 3.20/1.60 ( ( in @ Z @ ( powerset @ A ) )
% 3.20/1.60 => ! [W: $i] :
% 3.20/1.60 ( ( in @ W @ ( powerset @ A ) )
% 3.20/1.60 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 3.20/1.60 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(woz1_3_type,type,
% 3.20/1.60 woz1_3: $o ).
% 3.20/1.60
% 3.20/1.60 thf(woz1_3,definition,
% 3.20/1.60 ( woz1_3
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ! [Z: $i] :
% 3.20/1.60 ( ( in @ Z @ ( powerset @ A ) )
% 3.20/1.60 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(woz1_4_type,type,
% 3.20/1.60 woz1_4: $o ).
% 3.20/1.60
% 3.20/1.60 thf(woz1_4,definition,
% 3.20/1.60 ( woz1_4
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.20/1.60 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(woz1_5_type,type,
% 3.20/1.60 woz1_5: $o ).
% 3.20/1.60
% 3.20/1.60 thf(woz1_5,definition,
% 3.20/1.60 ( woz1_5
% 3.20/1.60 = ( ! [A: $i,X: $i] :
% 3.20/1.60 ( ( in @ X @ ( powerset @ A ) )
% 3.20/1.60 => ! [Y: $i] :
% 3.20/1.60 ( ( in @ Y @ ( powerset @ A ) )
% 3.20/1.60 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(breln1_type,type,
% 3.20/1.60 breln1: $i > $i > $o ).
% 3.20/1.60
% 3.20/1.60 thf(breln1all2_type,type,
% 3.20/1.60 breln1all2: $o ).
% 3.20/1.60
% 3.20/1.60 thf(breln1all2,definition,
% 3.20/1.60 ( breln1all2
% 3.20/1.60 = ( ! [A: $i,R: $i] :
% 3.20/1.60 ( ( breln1 @ A @ R )
% 3.20/1.60 => ! [Xphi: $i > $o] :
% 3.20/1.60 ( ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.20/1.60 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ R )
% 3.20/1.60 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(breln1Set_type,type,
% 3.20/1.60 breln1Set: $i > $i ).
% 3.20/1.60
% 3.20/1.60 thf(breln1SetBreln1_type,type,
% 3.20/1.60 breln1SetBreln1: $o ).
% 3.20/1.60
% 3.20/1.60 thf(breln1SetBreln1,definition,
% 3.20/1.60 ( breln1SetBreln1
% 3.20/1.60 = ( ! [A: $i,R: $i] :
% 3.20/1.60 ( ( in @ R @ ( breln1Set @ A ) )
% 3.20/1.60 => ( breln1 @ A @ R ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(transitive_type,type,
% 3.20/1.60 transitive: $i > $i > $o ).
% 3.20/1.60
% 3.20/1.60 thf(antisymmetric_type,type,
% 3.20/1.60 antisymmetric: $i > $i > $o ).
% 3.20/1.60
% 3.20/1.60 thf(reflexive_type,type,
% 3.20/1.60 reflexive: $i > $i > $o ).
% 3.20/1.60
% 3.20/1.60 thf(refltransitive_type,type,
% 3.20/1.60 refltransitive: $i > $i > $o ).
% 3.20/1.60
% 3.20/1.60 thf(refllinearorder_type,type,
% 3.20/1.60 refllinearorder: $i > $i > $o ).
% 3.20/1.60
% 3.20/1.60 thf(reflwellordering_type,type,
% 3.20/1.60 reflwellordering: $i > $i > $o ).
% 3.20/1.60
% 3.20/1.60 thf(choice2fnsingleton_type,type,
% 3.20/1.60 choice2fnsingleton: $o ).
% 3.20/1.60
% 3.20/1.60 thf(choice2fnsingleton,definition,
% 3.20/1.60 ( choice2fnsingleton
% 3.20/1.60 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.20/1.60 ( ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ? [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ B )
% 3.20/1.60 & ( Xphi @ Xx @ Xy ) ) )
% 3.20/1.60 => ! [R: $i] :
% 3.20/1.60 ( ( in @ R @ ( breln1Set @ B ) )
% 3.20/1.60 => ( ( reflwellordering @ B @ R )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( singleton
% 3.20/1.60 @ ( dsetconstr @ B
% 3.20/1.60 @ ^ [Xy: $i] :
% 3.20/1.60 ( ( Xphi @ Xx @ Xy )
% 3.20/1.60 & ! [Xz: $i] :
% 3.20/1.60 ( ( in @ Xz @ B )
% 3.20/1.60 => ( ( Xphi @ Xx @ Xz )
% 3.20/1.60 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(setOfPairsIsBReln1_type,type,
% 3.20/1.60 setOfPairsIsBReln1: $o ).
% 3.20/1.60
% 3.20/1.60 thf(setOfPairsIsBReln1,definition,
% 3.20/1.60 ( setOfPairsIsBReln1
% 3.20/1.60 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 3.20/1.60 ( breln1 @ A
% 3.20/1.60 @ ( dpsetconstr @ A @ A
% 3.20/1.60 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(breln1all1_type,type,
% 3.20/1.60 breln1all1: $o ).
% 3.20/1.60
% 3.20/1.60 thf(breln1all1,definition,
% 3.20/1.60 ( breln1all1
% 3.20/1.60 = ( ! [A: $i,R: $i] :
% 3.20/1.60 ( ( breln1 @ A @ R )
% 3.20/1.60 => ! [Xphi: $i > $o] :
% 3.20/1.60 ( ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.20/1.60 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ R )
% 3.20/1.60 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(subbreln1_type,type,
% 3.20/1.60 subbreln1: $o ).
% 3.20/1.60
% 3.20/1.60 thf(subbreln1,definition,
% 3.20/1.60 ( subbreln1
% 3.20/1.60 = ( ! [A: $i,R: $i] :
% 3.20/1.60 ( ( breln1 @ A @ R )
% 3.20/1.60 => ! [S: $i] :
% 3.20/1.60 ( ( breln1 @ A @ S )
% 3.20/1.60 => ( ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.20/1.60 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.20/1.60 => ( subset @ R @ S ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(eqbreln1_type,type,
% 3.20/1.60 eqbreln1: $o ).
% 3.20/1.60
% 3.20/1.60 thf(eqbreln1,definition,
% 3.20/1.60 ( eqbreln1
% 3.20/1.60 = ( ! [A: $i,R: $i] :
% 3.20/1.60 ( ( breln1 @ A @ R )
% 3.20/1.60 => ! [S: $i] :
% 3.20/1.60 ( ( breln1 @ A @ S )
% 3.20/1.60 => ( ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.20/1.60 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.20/1.60 => ( ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.20/1.60 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 3.20/1.60 => ( R = S ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(breln1invset_type,type,
% 3.20/1.60 breln1invset: $i > $i > $i ).
% 3.20/1.60
% 3.20/1.60 thf(breln1invprop_type,type,
% 3.20/1.60 breln1invprop: $o ).
% 3.20/1.60
% 3.20/1.60 thf(breln1invprop,definition,
% 3.20/1.60 ( breln1invprop
% 3.20/1.60 = ( ! [A: $i,R: $i] :
% 3.20/1.60 ( ( breln1 @ A @ R )
% 3.20/1.60 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(breln1invI_type,type,
% 3.20/1.60 breln1invI: $o ).
% 3.20/1.60
% 3.20/1.60 thf(breln1invI,definition,
% 3.20/1.60 ( breln1invI
% 3.20/1.60 = ( ! [A: $i,R: $i] :
% 3.20/1.60 ( ( breln1 @ A @ R )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.20/1.60 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(breln1invE_type,type,
% 3.20/1.60 breln1invE: $o ).
% 3.20/1.60
% 3.20/1.60 thf(breln1invE,definition,
% 3.20/1.60 ( breln1invE
% 3.20/1.60 = ( ! [A: $i,R: $i] :
% 3.20/1.60 ( ( breln1 @ A @ R )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 3.20/1.60 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(breln1compset_type,type,
% 3.20/1.60 breln1compset: $i > $i > $i > $i ).
% 3.20/1.60
% 3.20/1.60 thf(breln1compprop_type,type,
% 3.20/1.60 breln1compprop: $o ).
% 3.20/1.60
% 3.20/1.60 thf(breln1compprop,definition,
% 3.20/1.60 ( breln1compprop
% 3.20/1.60 = ( ! [A: $i,R: $i] :
% 3.20/1.60 ( ( breln1 @ A @ R )
% 3.20/1.60 => ! [S: $i] :
% 3.20/1.60 ( ( breln1 @ A @ S )
% 3.20/1.60 => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(breln1compI_type,type,
% 3.20/1.60 breln1compI: $o ).
% 3.20/1.60
% 3.20/1.60 thf(breln1compI,definition,
% 3.20/1.60 ( breln1compI
% 3.20/1.60 = ( ! [A: $i,R: $i] :
% 3.20/1.60 ( ( breln1 @ A @ R )
% 3.20/1.60 => ! [S: $i] :
% 3.20/1.60 ( ( breln1 @ A @ S )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 => ! [Xz: $i] :
% 3.20/1.60 ( ( in @ Xz @ A )
% 3.20/1.60 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 3.20/1.60 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 3.20/1.60 => ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(breln1compE_type,type,
% 3.20/1.60 breln1compE: $o ).
% 3.20/1.60
% 3.20/1.60 thf(breln1compE,definition,
% 3.20/1.60 ( breln1compE
% 3.20/1.60 = ( ! [A: $i,R: $i] :
% 3.20/1.60 ( ( breln1 @ A @ R )
% 3.20/1.60 => ! [S: $i] :
% 3.20/1.60 ( ( breln1 @ A @ S )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 3.20/1.60 => ? [Xz: $i] :
% 3.20/1.60 ( ( in @ Xz @ A )
% 3.20/1.60 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 3.20/1.60 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(breln1compEex_type,type,
% 3.20/1.60 breln1compEex: $o ).
% 3.20/1.60
% 3.20/1.60 thf(breln1compEex,definition,
% 3.20/1.60 ( breln1compEex
% 3.20/1.60 = ( ! [A: $i,R: $i] :
% 3.20/1.60 ( ( breln1 @ A @ R )
% 3.20/1.60 => ! [S: $i] :
% 3.20/1.60 ( ( breln1 @ A @ S )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 3.20/1.60 => ! [Xphi: $o] :
% 3.20/1.60 ( ! [Xz: $i] :
% 3.20/1.60 ( ( in @ Xz @ A )
% 3.20/1.60 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 3.20/1.60 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 3.20/1.60 => Xphi ) ) )
% 3.20/1.60 => Xphi ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(breln1unionprop_type,type,
% 3.20/1.60 breln1unionprop: $o ).
% 3.20/1.60
% 3.20/1.60 thf(breln1unionprop,definition,
% 3.20/1.60 ( breln1unionprop
% 3.20/1.60 = ( ! [A: $i,R: $i] :
% 3.20/1.60 ( ( breln1 @ A @ R )
% 3.20/1.60 => ! [S: $i] :
% 3.20/1.60 ( ( breln1 @ A @ S )
% 3.20/1.60 => ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(breln1unionIL_type,type,
% 3.20/1.60 breln1unionIL: $o ).
% 3.20/1.60
% 3.20/1.60 thf(breln1unionIL,definition,
% 3.20/1.60 ( breln1unionIL
% 3.20/1.60 = ( ! [A: $i,R: $i] :
% 3.20/1.60 ( ( breln1 @ A @ R )
% 3.20/1.60 => ! [S: $i] :
% 3.20/1.60 ( ( breln1 @ A @ S )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.20/1.60 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(breln1unionIR_type,type,
% 3.20/1.60 breln1unionIR: $o ).
% 3.20/1.60
% 3.20/1.60 thf(breln1unionIR,definition,
% 3.20/1.60 ( breln1unionIR
% 3.20/1.60 = ( ! [A: $i,R: $i] :
% 3.20/1.60 ( ( breln1 @ A @ R )
% 3.20/1.60 => ! [S: $i] :
% 3.20/1.60 ( ( breln1 @ A @ S )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.20/1.60 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(breln1unionI_type,type,
% 3.20/1.60 breln1unionI: $o ).
% 3.20/1.60
% 3.20/1.60 thf(breln1unionI,definition,
% 3.20/1.60 ( breln1unionI
% 3.20/1.60 = ( ! [A: $i,R: $i] :
% 3.20/1.60 ( ( breln1 @ A @ R )
% 3.20/1.60 => ! [S: $i] :
% 3.20/1.60 ( ( breln1 @ A @ S )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.20/1.60 | ( in @ ( kpair @ Xx @ Xy ) @ S ) )
% 3.20/1.60 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(breln1unionE_type,type,
% 3.20/1.60 breln1unionE: $o ).
% 3.20/1.60
% 3.20/1.60 thf(breln1unionE,definition,
% 3.20/1.60 ( breln1unionE
% 3.20/1.60 = ( ! [A: $i,R: $i] :
% 3.20/1.60 ( ( breln1 @ A @ R )
% 3.20/1.60 => ! [S: $i] :
% 3.20/1.60 ( ( breln1 @ A @ S )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 3.20/1.60 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.20/1.60 | ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(breln1unionEcases_type,type,
% 3.20/1.60 breln1unionEcases: $o ).
% 3.20/1.60
% 3.20/1.60 thf(breln1unionEcases,definition,
% 3.20/1.60 ( breln1unionEcases
% 3.20/1.60 = ( ! [A: $i,R: $i] :
% 3.20/1.60 ( ( breln1 @ A @ R )
% 3.20/1.60 => ! [S: $i] :
% 3.20/1.60 ( ( breln1 @ A @ S )
% 3.20/1.60 => ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ! [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 3.20/1.60 => ! [Xphi: $o] :
% 3.20/1.60 ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.20/1.60 => Xphi )
% 3.20/1.60 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.20/1.60 => Xphi )
% 3.20/1.60 => Xphi ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(breln1unionCommutes_type,type,
% 3.20/1.60 breln1unionCommutes: $o ).
% 3.20/1.60
% 3.20/1.60 thf(breln1unionCommutes,definition,
% 3.20/1.60 ( breln1unionCommutes
% 3.20/1.60 = ( ! [A: $i,R: $i] :
% 3.20/1.60 ( ( breln1 @ A @ R )
% 3.20/1.60 => ! [S: $i] :
% 3.20/1.60 ( ( breln1 @ A @ S )
% 3.20/1.60 => ( ( binunion @ R @ S )
% 3.20/1.60 = ( binunion @ S @ R ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(woz2Ex_type,type,
% 3.20/1.60 woz2Ex: $o ).
% 3.20/1.60
% 3.20/1.60 thf(woz2Ex,definition,
% 3.20/1.60 ( woz2Ex
% 3.20/1.60 = ( ! [A: $i,R: $i] :
% 3.20/1.60 ( ( breln1 @ A @ R )
% 3.20/1.60 => ( R
% 3.20/1.60 = ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(woz2W_type,type,
% 3.20/1.60 woz2W: $o ).
% 3.20/1.60
% 3.20/1.60 thf(woz2W,definition,
% 3.20/1.60 ( woz2W
% 3.20/1.60 = ( ! [A: $i,R: $i] :
% 3.20/1.60 ( ( breln1 @ A @ R )
% 3.20/1.60 => ! [S: $i] :
% 3.20/1.60 ( ( breln1 @ A @ S )
% 3.20/1.60 => ( ( breln1invset @ A @ ( breln1compset @ A @ R @ S ) )
% 3.20/1.60 = ( breln1compset @ A @ ( breln1invset @ A @ S ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(woz2A_type,type,
% 3.20/1.60 woz2A: $o ).
% 3.20/1.60
% 3.20/1.60 thf(woz2A,definition,
% 3.20/1.60 ( woz2A
% 3.20/1.60 = ( ! [A: $i,R: $i] :
% 3.20/1.60 ( ( breln1 @ A @ R )
% 3.20/1.60 => ! [S: $i] :
% 3.20/1.60 ( ( breln1 @ A @ S )
% 3.20/1.60 => ! [T: $i] :
% 3.20/1.60 ( ( breln1 @ A @ T )
% 3.20/1.60 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 3.20/1.60 = ( binunion @ ( breln1compset @ A @ R @ T ) @ ( breln1compset @ A @ S @ T ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(woz2B_type,type,
% 3.20/1.60 woz2B: $o ).
% 3.20/1.60
% 3.20/1.60 thf(woz2B,definition,
% 3.20/1.60 ( woz2B
% 3.20/1.60 = ( ! [A: $i,R: $i] :
% 3.20/1.60 ( ( breln1 @ A @ R )
% 3.20/1.60 => ! [S: $i] :
% 3.20/1.60 ( ( breln1 @ A @ S )
% 3.20/1.60 => ! [T: $i] :
% 3.20/1.60 ( ( breln1 @ A @ T )
% 3.20/1.60 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 3.20/1.60 = ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ S ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(image1Ex_type,type,
% 3.20/1.60 image1Ex: $o ).
% 3.20/1.60
% 3.20/1.60 thf(image1Ex,definition,
% 3.20/1.60 ( image1Ex
% 3.20/1.60 = ( ! [A: $i,Xf: $i > $i] :
% 3.20/1.60 ? [B: $i] :
% 3.20/1.60 ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ B )
% 3.20/1.60 <=> ? [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 & ( Xx
% 3.20/1.60 = ( Xf @ Xy ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(image1Ex1_type,type,
% 3.20/1.60 image1Ex1: $o ).
% 3.20/1.60
% 3.20/1.60 thf(image1Ex1,definition,
% 3.20/1.60 ( image1Ex1
% 3.20/1.60 = ( ! [A: $i,Xf: $i > $i] :
% 3.20/1.60 ( exu
% 3.20/1.60 @ ^ [B: $i] :
% 3.20/1.60 ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ B )
% 3.20/1.60 <=> ? [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 & ( Xx
% 3.20/1.60 = ( Xf @ Xy ) ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(image1_type,type,
% 3.20/1.60 image1: $i > ( $i > $i ) > $i ).
% 3.20/1.60
% 3.20/1.60 thf(image1Equiv_type,type,
% 3.20/1.60 image1Equiv: $o ).
% 3.20/1.60
% 3.20/1.60 thf(image1Equiv,definition,
% 3.20/1.60 ( image1Equiv
% 3.20/1.60 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 3.20/1.60 ( ( in @ Xx
% 3.20/1.60 @ ( image1 @ A
% 3.20/1.60 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 3.20/1.60 <=> ? [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 & ( Xx
% 3.20/1.60 = ( Xf @ Xy ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(image1E_type,type,
% 3.20/1.60 image1E: $o ).
% 3.20/1.60
% 3.20/1.60 thf(image1E,definition,
% 3.20/1.60 ( image1E
% 3.20/1.60 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 3.20/1.60 ( ( in @ Xx
% 3.20/1.60 @ ( image1 @ A
% 3.20/1.60 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 3.20/1.60 => ? [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 & ( Xx
% 3.20/1.60 = ( Xf @ Xy ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(image1I_type,type,
% 3.20/1.60 image1I: $o ).
% 3.20/1.60
% 3.20/1.60 thf(image1I,definition,
% 3.20/1.60 ( image1I
% 3.20/1.60 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 3.20/1.60 ( ? [Xy: $i] :
% 3.20/1.60 ( ( in @ Xy @ A )
% 3.20/1.60 & ( Xx
% 3.20/1.60 = ( Xf @ Xy ) ) )
% 3.20/1.60 => ( in @ Xx
% 3.20/1.60 @ ( image1 @ A
% 3.20/1.60 @ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(injective_type,type,
% 3.20/1.60 injective: $i > $i > $i > $o ).
% 3.20/1.60
% 3.20/1.60 thf(injFuncSet_type,type,
% 3.20/1.60 injFuncSet: $i > $i > $i ).
% 3.20/1.60
% 3.20/1.60 thf(injFuncInInjFuncSet_type,type,
% 3.20/1.60 injFuncInInjFuncSet: $o ).
% 3.20/1.60
% 3.20/1.60 thf(injFuncInInjFuncSet,definition,
% 3.20/1.60 ( injFuncInInjFuncSet
% 3.20/1.60 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.20/1.60 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.20/1.60 => ( ( injective @ A @ B @ Xf )
% 3.20/1.60 => ( in @ Xf @ ( injFuncSet @ A @ B ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(injFuncSetFuncIn_type,type,
% 3.20/1.60 injFuncSetFuncIn: $o ).
% 3.20/1.60
% 3.20/1.60 thf(injFuncSetFuncIn,definition,
% 3.20/1.60 ( injFuncSetFuncIn
% 3.20/1.60 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.20/1.60 ( ( in @ Xf @ ( injFuncSet @ A @ B ) )
% 3.20/1.60 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(injFuncSetFuncInj_type,type,
% 3.20/1.60 injFuncSetFuncInj: $o ).
% 3.20/1.60
% 3.20/1.60 thf(injFuncSetFuncInj,definition,
% 3.20/1.60 ( injFuncSetFuncInj
% 3.20/1.60 = ( ! [Xx: $i,Xy: $i,Xf: $i] :
% 3.20/1.60 ( ( in @ Xf @ ( injFuncSet @ Xx @ Xy ) )
% 3.20/1.60 => ( injective @ Xx @ Xy @ Xf ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(surjective_type,type,
% 3.20/1.60 surjective: $i > $i > $i > $o ).
% 3.20/1.60
% 3.20/1.60 thf(surjFuncSet_type,type,
% 3.20/1.60 surjFuncSet: $i > $i > $i ).
% 3.20/1.60
% 3.20/1.60 thf(surjFuncSetFuncIn_type,type,
% 3.20/1.60 surjFuncSetFuncIn: $o ).
% 3.20/1.60
% 3.20/1.60 thf(surjFuncSetFuncIn,definition,
% 3.20/1.60 ( surjFuncSetFuncIn
% 3.20/1.60 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.20/1.60 ( ( in @ Xf @ ( surjFuncSet @ A @ B ) )
% 3.20/1.60 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(surjFuncSetFuncSurj_type,type,
% 3.20/1.60 surjFuncSetFuncSurj: $o ).
% 3.20/1.60
% 3.20/1.60 thf(surjFuncSetFuncSurj,definition,
% 3.20/1.60 ( surjFuncSetFuncSurj
% 3.20/1.60 = ( ! [Xx: $i,Xy: $i,Xf: $i] :
% 3.20/1.60 ( ( in @ Xf @ ( surjFuncSet @ Xx @ Xy ) )
% 3.20/1.60 => ( surjective @ Xx @ Xy @ Xf ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(leftInvIsSurj_type,type,
% 3.20/1.60 leftInvIsSurj: $o ).
% 3.20/1.60
% 3.20/1.60 thf(leftInvIsSurj,definition,
% 3.20/1.60 ( leftInvIsSurj
% 3.20/1.60 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.20/1.60 ( ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.20/1.60 => ! [Xg: $i] :
% 3.20/1.60 ( ( in @ Xg @ ( funcSet @ B @ A ) )
% 3.20/1.60 => ( ! [Xx: $i] :
% 3.20/1.60 ( ( in @ Xx @ A )
% 3.20/1.60 => ( ( ap @ B @ A @ Xg @ ( Xf @ Xx ) )
% 3.20/1.60 = Xx ) )
% 3.20/1.60 => ( surjective @ B @ A @ Xg ) ) ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(surjCantorThm_type,type,
% 3.20/1.60 surjCantorThm: $o ).
% 3.20/1.60
% 3.20/1.60 thf(surjCantorThm,definition,
% 3.20/1.60 ( surjCantorThm
% 3.20/1.60 = ( ! [A: $i,Xf: $i] :
% 3.20/1.60 ( ( in @ Xf @ ( funcSet @ A @ ( powerset @ A ) ) )
% 3.20/1.60 => ~ ( surjective @ A @ ( powerset @ A ) @ Xf ) ) ) ) ).
% 3.20/1.60
% 3.20/1.60 thf(foundation2,conjecture,
% 3.20/1.60 ( setextAx
% 3.20/1.60 => ( emptysetAx
% 3.20/1.60 => ( setadjoinAx
% 3.20/1.60 => ( powersetAx
% 3.20/1.60 => ( setunionAx
% 3.20/1.60 => ( omega0Ax
% 3.20/1.60 => ( omegaSAx
% 3.20/1.60 => ( omegaIndAx
% 3.20/1.60 => ( replAx
% 3.20/1.60 => ( foundationAx
% 3.20/1.60 => ( wellorderingAx
% 3.20/1.60 => ( descrp
% 3.20/1.60 => ( dsetconstrI
% 3.20/1.60 => ( dsetconstrEL
% 3.20/1.60 => ( dsetconstrER
% 3.20/1.60 => ( exuE1
% 3.20/1.60 => ( prop2setE
% 3.20/1.60 => ( emptysetE
% 3.20/1.60 => ( emptysetimpfalse
% 3.20/1.60 => ( notinemptyset
% 3.20/1.60 => ( exuE3e
% 3.20/1.60 => ( setext
% 3.20/1.60 => ( emptyI
% 3.20/1.60 => ( noeltsimpempty
% 3.20/1.60 => ( setbeta
% 3.20/1.60 => ( nonemptyE1
% 3.20/1.60 => ( nonemptyI
% 3.20/1.60 => ( nonemptyI1
% 3.20/1.60 => ( setadjoinIL
% 3.20/1.60 => ( emptyinunitempty
% 3.20/1.60 => ( setadjoinIR
% 3.20/1.60 => ( setadjoinE
% 3.20/1.60 => ( setadjoinOr
% 3.20/1.60 => ( setoftrueEq
% 3.20/1.60 => ( powersetI
% 3.20/1.60 => ( emptyinPowerset
% 3.20/1.60 => ( emptyInPowerset
% 3.20/1.60 => ( powersetE
% 3.20/1.60 => ( setunionI
% 3.20/1.60 => ( setunionE
% 3.20/1.60 => ( subPowSU
% 3.20/1.60 => ( exuE2
% 3.20/1.60 => ( nonemptyImpWitness
% 3.20/1.60 => ( uniqinunit
% 3.20/1.60 => ( notinsingleton
% 3.20/1.60 => ( eqinunit
% 3.20/1.60 => ( singletonsswitch
% 3.20/1.60 => ( upairsetE
% 3.20/1.60 => ( upairsetIL
% 3.20/1.60 => ( upairsetIR
% 3.20/1.60 => ( emptyE1
% 3.20/1.60 => ( vacuousDall
% 3.20/1.60 => ( quantDeMorgan1
% 3.20/1.60 => ( quantDeMorgan2
% 3.20/1.60 => ( quantDeMorgan3
% 3.20/1.60 => ( quantDeMorgan4
% 3.20/1.60 => ( prop2setI
% 3.20/1.60 => ( prop2set2propI
% 3.20/1.60 => ( notdexE
% 3.20/1.60 => ( notdallE
% 3.20/1.60 => ( exuI1
% 3.20/1.60 => ( exuI3
% 3.20/1.60 => ( exuI2
% 3.20/1.60 => ( inCongP
% 3.20/1.60 => ( in__Cong
% 3.20/1.60 => ( exuE3u
% 3.20/1.60 => ( exu__Cong
% 3.20/1.60 => ( emptyset__Cong
% 3.20/1.60 => ( setadjoin__Cong
% 3.20/1.60 => ( powerset__Cong
% 3.20/1.60 => ( setunion__Cong
% 3.20/1.60 => ( omega__Cong
% 3.20/1.60 => ( exuEu
% 3.20/1.60 => ( descr__Cong
% 3.20/1.60 => ( dsetconstr__Cong
% 3.20/1.60 => ( subsetI1
% 3.20/1.60 => ( eqimpsubset2
% 3.20/1.60 => ( eqimpsubset1
% 3.20/1.60 => ( subsetI2
% 3.20/1.60 => ( emptysetsubset
% 3.20/1.60 => ( subsetE
% 3.20/1.60 => ( subsetE2
% 3.20/1.60 => ( notsubsetI
% 3.20/1.60 => ( notequalI1
% 3.20/1.60 => ( notequalI2
% 3.20/1.60 => ( subsetRefl
% 3.20/1.60 => ( subsetTrans
% 3.20/1.60 => ( setadjoinSub
% 3.20/1.60 => ( setadjoinSub2
% 3.20/1.60 => ( subset2powerset
% 3.20/1.60 => ( setextsub
% 3.20/1.60 => ( subsetemptysetimpeq
% 3.20/1.60 => ( powersetI1
% 3.20/1.60 => ( powersetE1
% 3.20/1.60 => ( inPowerset
% 3.20/1.60 => ( powersetsubset
% 3.20/1.60 => ( sepInPowerset
% 3.20/1.60 => ( sepSubset
% 3.20/1.60 => ( binunionIL
% 3.20/1.60 => ( upairset2IR
% 3.20/1.60 => ( binunionIR
% 3.20/1.60 => ( binunionEcases
% 3.20/1.60 => ( binunionE
% 3.20/1.60 => ( binunionLsub
% 3.20/1.60 => ( binunionRsub
% 3.20/1.60 => ( binintersectI
% 3.20/1.60 => ( binintersectSubset5
% 3.20/1.60 => ( binintersectEL
% 3.20/1.60 => ( binintersectLsub
% 3.20/1.60 => ( binintersectSubset2
% 3.20/1.60 => ( binintersectSubset3
% 3.20/1.60 => ( binintersectER
% 3.20/1.60 => ( disjointsetsI1
% 3.20/1.60 => ( binintersectRsub
% 3.20/1.60 => ( binintersectSubset4
% 3.20/1.60 => ( binintersectSubset1
% 3.20/1.60 => ( bs114d
% 3.20/1.60 => ( setminusI
% 3.20/1.60 => ( setminusEL
% 3.20/1.60 => ( setminusER
% 3.20/1.60 => ( setminusSubset2
% 3.20/1.60 => ( setminusERneg
% 3.20/1.60 => ( setminusELneg
% 3.20/1.60 => ( setminusILneg
% 3.20/1.60 => ( setminusIRneg
% 3.20/1.60 => ( setminusLsub
% 3.20/1.60 => ( setminusSubset1
% 3.20/1.60 => ( symdiffE
% 3.20/1.60 => ( symdiffI1
% 3.20/1.60 => ( symdiffI2
% 3.20/1.60 => ( symdiffIneg1
% 3.20/1.60 => ( symdiffIneg2
% 3.20/1.60 => ( secondinupair
% 3.20/1.60 => ( setukpairIL
% 3.20/1.60 => ( setukpairIR
% 3.20/1.60 => ( kpairiskpair
% 3.20/1.60 => ( kpairp
% 3.20/1.60 => ( singletonsubset
% 3.20/1.60 => ( singletoninpowerset
% 3.20/1.60 => ( singletoninpowunion
% 3.20/1.60 => ( upairset2E
% 3.20/1.60 => ( upairsubunion
% 3.20/1.60 => ( upairinpowunion
% 3.20/1.60 => ( ubforcartprodlem1
% 3.20/1.60 => ( ubforcartprodlem2
% 3.20/1.60 => ( ubforcartprodlem3
% 3.20/1.60 => ( cartprodpairin
% 3.20/1.60 => ( cartprodmempair1
% 3.20/1.60 => ( cartprodmempair
% 3.20/1.60 => ( setunionE2
% 3.20/1.60 => ( setunionsingleton1
% 3.20/1.60 => ( setunionsingleton2
% 3.20/1.60 => ( setunionsingleton
% 3.20/1.60 => ( singletonprop
% 3.20/1.60 => ( ex1E1
% 3.20/1.60 => ( ex1I
% 3.20/1.60 => ( ex1I2
% 3.20/1.60 => ( singletonsuniq
% 3.20/1.60 => ( setukpairinjL1
% 3.20/1.60 => ( kfstsingleton
% 3.20/1.60 => ( theprop
% 3.20/1.60 => ( kfstpairEq
% 3.20/1.60 => ( cartprodfstin
% 3.20/1.60 => ( setukpairinjL2
% 3.20/1.60 => ( setukpairinjL
% 3.20/1.60 => ( setukpairinjR11
% 3.20/1.60 => ( setukpairinjR12
% 3.20/1.60 => ( setukpairinjR1
% 3.20/1.60 => ( upairequniteq
% 3.20/1.60 => ( setukpairinjR2
% 3.20/1.60 => ( setukpairinjR
% 3.20/1.60 => ( ksndsingleton
% 3.20/1.60 => ( ksndpairEq
% 3.20/1.60 => ( kpairsurjEq
% 3.20/1.60 => ( cartprodsndin
% 3.20/1.60 => ( cartprodpairmemEL
% 3.20/1.60 => ( cartprodpairmemER
% 3.20/1.60 => ( cartprodmempaircEq
% 3.20/1.60 => ( cartprodfstpairEq
% 3.20/1.60 => ( cartprodsndpairEq
% 3.20/1.60 => ( cartprodpairsurjEq
% 3.20/1.60 => ( dpsetconstrI
% 3.20/1.60 => ( dpsetconstrSub
% 3.20/1.60 => ( setOfPairsIsBReln
% 3.20/1.60 => ( dpsetconstrERa
% 3.20/1.60 => ( dpsetconstrEL1
% 3.20/1.60 => ( dpsetconstrEL2
% 3.20/1.60 => ( dpsetconstrER
% 3.20/1.60 => ( funcImageSingleton
% 3.20/1.60 => ( apProp
% 3.20/1.60 => ( app
% 3.20/1.60 => ( infuncsetfunc
% 3.20/1.60 => ( ap2p
% 3.20/1.60 => ( funcinfuncset
% 3.20/1.60 => ( lamProp
% 3.20/1.60 => ( lamp
% 3.20/1.60 => ( lam2p
% 3.20/1.60 => ( brelnall1
% 3.20/1.60 => ( brelnall2
% 3.20/1.60 => ( ex1E2
% 3.20/1.60 => ( funcGraphProp1
% 3.20/1.60 => ( funcGraphProp3
% 3.20/1.60 => ( funcGraphProp2
% 3.20/1.60 => ( funcextLem
% 3.20/1.60 => ( funcGraphProp4
% 3.20/1.60 => ( subbreln
% 3.20/1.60 => ( eqbreln
% 3.20/1.60 => ( funcext
% 3.20/1.60 => ( funcext2
% 3.20/1.60 => ( ap2apEq1
% 3.20/1.60 => ( ap2apEq2
% 3.20/1.60 => ( beta1
% 3.20/1.60 => ( eta1
% 3.20/1.60 => ( lam2lamEq
% 3.20/1.60 => ( beta2
% 3.20/1.60 => ( eta2
% 3.20/1.60 => ( iffalseProp1
% 3.20/1.60 => ( iffalseProp2
% 3.20/1.60 => ( iftrueProp1
% 3.20/1.60 => ( iftrueProp2
% 3.20/1.60 => ( ifSingleton
% 3.20/1.60 => ( ifp
% 3.20/1.60 => ( theeq
% 3.20/1.60 => ( iftrue
% 3.20/1.60 => ( iffalse
% 3.20/1.60 => ( iftrueorfalse
% 3.20/1.60 => ( binintersectT_lem
% 3.20/1.60 => ( binunionT_lem
% 3.20/1.60 => ( powersetT_lem
% 3.20/1.60 => ( setminusT_lem
% 3.20/1.60 => ( complementT_lem
% 3.20/1.60 => ( setextT
% 3.20/1.60 => ( subsetTI
% 3.20/1.60 => ( powersetTI1
% 3.20/1.60 => ( powersetTE1
% 3.20/1.60 => ( complementTI1
% 3.20/1.60 => ( complementTE1
% 3.20/1.60 => ( binintersectTELcontra
% 3.20/1.60 => ( binintersectTERcontra
% 3.20/1.60 => ( contrasubsetT
% 3.20/1.60 => ( contrasubsetT1
% 3.20/1.60 => ( contrasubsetT2
% 3.20/1.60 => ( contrasubsetT3
% 3.20/1.60 => ( doubleComplementI1
% 3.20/1.60 => ( doubleComplementE1
% 3.20/1.60 => ( doubleComplementSub1
% 3.20/1.60 => ( doubleComplementSub2
% 3.20/1.60 => ( doubleComplementEq
% 3.20/1.60 => ( complementTnotintersectT
% 3.20/1.60 => ( complementImpComplementIntersect
% 3.20/1.60 => ( complementSubsetComplementIntersect
% 3.20/1.60 => ( complementInPowersetComplementIntersect
% 3.20/1.60 => ( contraSubsetComplement
% 3.20/1.60 => ( complementTcontraSubset
% 3.20/1.60 => ( binunionTILcontra
% 3.20/1.60 => ( binunionTIRcontra
% 3.20/1.60 => ( inIntersectImpInUnion
% 3.20/1.60 => ( inIntersectImpInUnion2
% 3.20/1.60 => ( inIntersectImpInIntersectUnions
% 3.20/1.60 => ( intersectInPowersetIntersectUnions
% 3.20/1.60 => ( inComplementUnionImpNotIn1
% 3.20/1.60 => ( inComplementUnionImpInComplement1
% 3.20/1.60 => ( binunionTE
% 3.20/1.60 => ( binunionTEcontra
% 3.20/1.60 => ( demorgan2a1
% 3.20/1.60 => ( complementUnionInPowersetComplement
% 3.20/1.60 => ( demorgan2a2
% 3.20/1.60 => ( demorgan1a
% 3.20/1.60 => ( demorgan1b
% 3.20/1.60 => ( demorgan1
% 3.20/1.60 => ( demorgan2a
% 3.20/1.60 => ( demorgan2b2
% 3.20/1.60 => ( demorgan2b
% 3.20/1.60 => ( demorgan2
% 3.20/1.60 => ( woz13rule0
% 3.20/1.60 => ( woz13rule1
% 3.20/1.60 => ( woz13rule2
% 3.20/1.60 => ( woz13rule3
% 3.20/1.60 => ( woz13rule4
% 3.20/1.60 => ( woz1_1
% 3.20/1.60 => ( woz1_2
% 3.20/1.60 => ( woz1_3
% 3.20/1.60 => ( woz1_4
% 3.20/1.60 => ( woz1_5
% 3.20/1.60 => ( breln1all2
% 3.20/1.60 => ( breln1SetBreln1
% 3.20/1.60 => ( choice2fnsingleton
% 3.20/1.60 => ( setOfPairsIsBReln1
% 3.20/1.60 => ( breln1all1
% 3.20/1.60 => ( subbreln1
% 3.20/1.60 => ( eqbreln1
% 3.20/1.60 => ( breln1invprop
% 3.20/1.60 => ( breln1invI
% 3.20/1.60 => ( breln1invE
% 3.20/1.60 => ( breln1compprop
% 3.20/1.60 => ( breln1compI
% 3.20/1.60 => ( breln1compE
% 3.20/1.60 => ( breln1compEex
% 3.20/1.60 => ( breln1unionprop
% 3.20/1.60 => ( breln1unionIL
% 3.20/1.60 => ( breln1unionIR
% 3.20/1.60 => ( breln1unionI
% 3.20/1.60 => ( breln1unionE
% 3.20/1.60 => ( breln1unionEcases
% 3.20/1.60 => ( breln1unionCommutes
% 3.20/1.60 => ( woz2Ex
% 3.20/1.60 => ( woz2W
% 3.20/1.60 => ( woz2A
% 3.20/1.60 => ( woz2B
% 3.20/1.60 => ( image1Ex
% 3.20/1.60 => ( image1Ex1
% 3.20/1.60 => ( image1Equiv
% 3.20/1.60 => ( image1E
% 3.20/1.60 => ( image1I
% 3.20/1.60 => ( injFuncInInjFuncSet
% 3.20/1.60 => ( injFuncSetFuncIn
% 3.20/1.60 => ( injFuncSetFuncInj
% 3.20/1.60 => ( surjFuncSetFuncIn
% 3.20/1.60 => ( surjFuncSetFuncSurj
% 3.20/1.60 => ( leftInvIsSurj
% 3.20/1.60 => ( surjCantorThm
% 3.20/1.60 => ! [A: $i] :
% 3.20/1.60 ( ( nonempty @ A )
% 3.20/1.60 => ? [X: $i] :
% 3.20/1.60 ( ( in @ X @ A )
% 3.20/1.60 & ( ( binintersect @ X @ A )
% 3.20/1.60 = emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.20/1.60 ------------------------
% 3.20/1.63 % (17479)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17306 for (2999ds/183Mi)
% 3.20/1.64 % (17483)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_17306 for (2999ds/2Mi)
% 3.20/1.64 % (17482)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17306 for (2999ds/2Mi)
% 3.20/1.64 % (17481)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_17306 for (2999ds/27Mi)
% 3.20/1.64 % (17484)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_17306 for (2999ds/275Mi)
% 3.20/1.64 % (17482)Instruction limit reached!
% 3.20/1.64 % (17482)------------------------------
% 3.20/1.64 % (17482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.64 % (17482)Termination reason: Unknown
% 3.20/1.64 % (17482)Termination phase: shuffling
% 3.20/1.64 % (17483)Instruction limit reached!
% 3.20/1.64 % (17483)------------------------------
% 3.20/1.64 % (17483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.64 % (17483)Termination reason: Unknown
% 3.20/1.64 % (17483)Termination phase: shuffling
% 3.20/1.64
% 3.20/1.64 % (17483)Memory used [KB]: 1663
% 3.20/1.64 % (17483)Time elapsed: 0.003 s
% 3.20/1.64 % (17483)Instructions burned: 3 (million)
% 3.20/1.64 % (17483)------------------------------
% 3.20/1.64 % (17483)------------------------------
% 3.20/1.64
% 3.20/1.64 % (17482)Memory used [KB]: 1663
% 3.20/1.64 % (17482)Time elapsed: 0.003 s
% 3.20/1.64 % (17482)Instructions burned: 3 (million)
% 3.20/1.64 % (17482)------------------------------
% 3.20/1.64 % (17482)------------------------------
% 3.20/1.64 % (17485)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17306 for (2999ds/18Mi)
% 3.20/1.64 % (17480)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_17306 for (2999ds/4Mi)
% 3.20/1.65 % (17480)Instruction limit reached!
% 3.20/1.65 % (17480)------------------------------
% 3.20/1.65 % (17480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.65 % (17480)Termination reason: Unknown
% 3.20/1.65 % (17480)Termination phase: shuffling
% 3.20/1.65
% 3.20/1.65 % (17480)Memory used [KB]: 1663
% 3.20/1.65 % (17480)Time elapsed: 0.003 s
% 3.20/1.65 % (17480)Instructions burned: 7 (million)
% 3.20/1.65 % (17480)------------------------------
% 3.20/1.65 % (17480)------------------------------
% 3.20/1.65 % (17485)Instruction limit reached!
% 3.20/1.65 % (17485)------------------------------
% 3.20/1.65 % (17485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.65 % (17485)Termination reason: Unknown
% 3.20/1.65 % (17485)Termination phase: shuffling
% 3.20/1.65
% 3.20/1.65 % (17485)Memory used [KB]: 1918
% 3.20/1.65 % (17485)Time elapsed: 0.012 s
% 3.20/1.65 % (17485)Instructions burned: 19 (million)
% 3.20/1.65 % (17485)------------------------------
% 3.20/1.65 % (17485)------------------------------
% 3.20/1.65 % (17481)Instruction limit reached!
% 3.20/1.65 % (17481)------------------------------
% 3.20/1.65 % (17481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.65 % (17481)Termination reason: Unknown
% 3.20/1.65 % (17481)Termination phase: shuffling
% 3.20/1.65
% 3.20/1.65 % (17481)Memory used [KB]: 2174
% 3.20/1.65 % (17481)Time elapsed: 0.014 s
% 3.20/1.65 % (17481)Instructions burned: 27 (million)
% 3.20/1.65 % (17481)------------------------------
% 3.20/1.65 % (17481)------------------------------
% 3.20/1.66 % (17488)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_17306 for (2999ds/3Mi)
% 3.20/1.66 % (17488)Instruction limit reached!
% 3.20/1.66 % (17488)------------------------------
% 3.20/1.66 % (17488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.66 % (17488)Termination reason: Unknown
% 3.20/1.66 % (17488)Termination phase: shuffling
% 3.20/1.66
% 3.20/1.66 % (17488)Memory used [KB]: 1663
% 3.20/1.66 % (17488)Time elapsed: 0.003 s
% 3.20/1.66 % (17488)Instructions burned: 3 (million)
% 3.20/1.66 % (17488)------------------------------
% 3.20/1.66 % (17488)------------------------------
% 3.20/1.66 % (17489)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_17306 for (2999ds/37Mi)
% 3.20/1.66 % (17492)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_17306 for (2999ds/15Mi)
% 3.20/1.67 % (17495)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_17306 for (2999ds/1041Mi)
% 3.20/1.67 % (17494)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_17306 for (2999ds/3Mi)
% 3.20/1.67 % (17494)Instruction limit reached!
% 3.20/1.67 % (17494)------------------------------
% 3.20/1.67 % (17494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.67 % (17494)Termination reason: Unknown
% 3.20/1.67 % (17494)Termination phase: shuffling
% 3.20/1.67
% 3.20/1.67 % (17494)Memory used [KB]: 1663
% 3.20/1.67 % (17494)Time elapsed: 0.003 s
% 3.20/1.67 % (17494)Instructions burned: 3 (million)
% 3.20/1.67 % (17494)------------------------------
% 3.20/1.67 % (17494)------------------------------
% 3.20/1.67 % (17492)Instruction limit reached!
% 3.20/1.67 % (17492)------------------------------
% 3.20/1.67 % (17492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.67 % (17492)Termination reason: Unknown
% 3.20/1.67 % (17492)Termination phase: shuffling
% 3.20/1.67
% 3.20/1.67 % (17492)Memory used [KB]: 1918
% 3.20/1.67 % (17492)Time elapsed: 0.010 s
% 3.20/1.67 % (17492)Instructions burned: 16 (million)
% 3.20/1.67 % (17492)------------------------------
% 3.20/1.67 % (17492)------------------------------
% 3.20/1.68 % (17498)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_17306 for (2999ds/7Mi)
% 3.20/1.68 % (17489)Instruction limit reached!
% 3.20/1.68 % (17489)------------------------------
% 3.20/1.68 % (17489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.68 % (17489)Termination reason: Unknown
% 3.20/1.68 % (17489)Termination phase: shuffling
% 3.20/1.68
% 3.20/1.68 % (17489)Memory used [KB]: 2430
% 3.20/1.68 % (17489)Time elapsed: 0.018 s
% 3.20/1.68 % (17489)Instructions burned: 37 (million)
% 3.20/1.68 % (17489)------------------------------
% 3.20/1.68 % (17489)------------------------------
% 3.20/1.68 % (17498)Instruction limit reached!
% 3.20/1.68 % (17498)------------------------------
% 3.20/1.68 % (17498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.68 % (17498)Termination reason: Unknown
% 3.20/1.68 % (17498)Termination phase: shuffling
% 3.20/1.68
% 3.20/1.68 % (17498)Memory used [KB]: 1663
% 3.20/1.68 % (17498)Time elapsed: 0.005 s
% 3.20/1.68 % (17498)Instructions burned: 7 (million)
% 3.20/1.68 % (17498)------------------------------
% 3.20/1.68 % (17498)------------------------------
% 3.20/1.68 % (17479)Instruction limit reached!
% 3.20/1.68 % (17479)------------------------------
% 3.20/1.68 % (17479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.68 % (17479)Termination reason: Unknown
% 3.20/1.68 % (17479)Termination phase: Property scanning
% 3.20/1.68
% 3.20/1.68 % (17479)Memory used [KB]: 3070
% 3.20/1.68 % (17479)Time elapsed: 0.050 s
% 3.20/1.68 % (17479)Instructions burned: 185 (million)
% 3.20/1.68 % (17479)------------------------------
% 3.20/1.68 % (17479)------------------------------
% 3.20/1.69 % (17503)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_17306 for (2999ds/3Mi)
% 3.20/1.69 % (17502)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_17306 for (2999ds/16Mi)
% 3.20/1.69 % (17503)Instruction limit reached!
% 3.20/1.69 % (17503)------------------------------
% 3.20/1.69 % (17503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.69 % (17503)Termination reason: Unknown
% 3.20/1.69 % (17503)Termination phase: shuffling
% 3.20/1.69
% 3.20/1.69 % (17503)Memory used [KB]: 1663
% 3.20/1.69 % (17503)Time elapsed: 0.003 s
% 3.20/1.69 % (17503)Instructions burned: 3 (million)
% 3.20/1.69 % (17503)------------------------------
% 3.20/1.69 % (17503)------------------------------
% 3.20/1.69 % (17506)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_17306 for (2999ds/3Mi)
% 3.20/1.69 % (17506)Instruction limit reached!
% 3.20/1.69 % (17506)------------------------------
% 3.20/1.69 % (17506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.69 % (17506)Termination reason: Unknown
% 3.20/1.69 % (17506)Termination phase: shuffling
% 3.20/1.69
% 3.20/1.69 % (17506)Memory used [KB]: 1663
% 3.20/1.69 % (17506)Time elapsed: 0.003 s
% 3.20/1.69 % (17506)Instructions burned: 5 (million)
% 3.20/1.69 % (17506)------------------------------
% 3.20/1.69 % (17506)------------------------------
% 3.20/1.69 % (17504)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_17306 for (2999ds/3Mi)
% 3.20/1.70 % (17504)Instruction limit reached!
% 3.20/1.70 % (17504)------------------------------
% 3.20/1.70 % (17504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.70 % (17504)Termination reason: Unknown
% 3.20/1.70 % (17504)Termination phase: shuffling
% 3.20/1.70
% 3.20/1.70 % (17504)Memory used [KB]: 1663
% 3.20/1.70 % (17504)Time elapsed: 0.003 s
% 3.20/1.70 % (17504)Instructions burned: 3 (million)
% 3.20/1.70 % (17504)------------------------------
% 3.20/1.70 % (17504)------------------------------
% 3.20/1.70 % (17502)Instruction limit reached!
% 3.20/1.70 % (17502)------------------------------
% 3.20/1.70 % (17502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.70 % (17502)Termination reason: Unknown
% 3.20/1.70 % (17502)Termination phase: shuffling
% 3.20/1.70
% 3.20/1.70 % (17502)Memory used [KB]: 1918
% 3.20/1.70 % (17502)Time elapsed: 0.010 s
% 3.20/1.70 % (17502)Instructions burned: 16 (million)
% 3.20/1.70 % (17502)------------------------------
% 3.20/1.70 % (17502)------------------------------
% 3.20/1.70 % (17505)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_17306 for (2999ds/7Mi)
% 3.20/1.70 % (17505)Instruction limit reached!
% 3.20/1.70 % (17505)------------------------------
% 3.20/1.70 % (17505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.70 % (17505)Termination reason: Unknown
% 3.20/1.70 % (17505)Termination phase: shuffling
% 3.20/1.70
% 3.20/1.70 % (17505)Memory used [KB]: 1663
% 3.20/1.70 % (17505)Time elapsed: 0.005 s
% 3.20/1.70 % (17505)Instructions burned: 7 (million)
% 3.20/1.70 % (17505)------------------------------
% 3.20/1.70 % (17505)------------------------------
% 3.20/1.70 % (17511)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_17306 for (2999ds/18Mi)
% 3.20/1.71 % (17510)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_17306 for (2999ds/4Mi)
% 3.20/1.71 % (17511)Instruction limit reached!
% 3.20/1.71 % (17511)------------------------------
% 3.20/1.71 % (17511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.71 % (17511)Termination reason: Unknown
% 3.20/1.71 % (17511)Termination phase: shuffling
% 3.20/1.71
% 3.20/1.71 % (17511)Memory used [KB]: 1918
% 3.20/1.71 % (17511)Time elapsed: 0.007 s
% 3.20/1.71 % (17511)Instructions burned: 21 (million)
% 3.20/1.71 % (17511)------------------------------
% 3.20/1.71 % (17511)------------------------------
% 3.20/1.71 % (17510)Instruction limit reached!
% 3.20/1.71 % (17510)------------------------------
% 3.20/1.71 % (17510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.71 % (17510)Termination reason: Unknown
% 3.20/1.71 % (17510)Termination phase: shuffling
% 3.20/1.71
% 3.20/1.71 % (17510)Memory used [KB]: 1663
% 3.20/1.71 % (17510)Time elapsed: 0.004 s
% 3.20/1.71 % (17510)Instructions burned: 5 (million)
% 3.20/1.71 % (17510)------------------------------
% 3.20/1.71 % (17510)------------------------------
% 3.20/1.71 % (17512)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_17306 for (2999ds/710Mi)
% 3.20/1.71 % (17513)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_17306 for (2999ds/6Mi)
% 3.20/1.72 % (17513)Instruction limit reached!
% 3.20/1.72 % (17513)------------------------------
% 3.20/1.72 % (17513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.72 % (17513)Termination reason: Unknown
% 3.20/1.72 % (17513)Termination phase: shuffling
% 3.20/1.72
% 3.20/1.72 % (17513)Memory used [KB]: 1663
% 3.20/1.72 % (17513)Time elapsed: 0.005 s
% 3.20/1.72 % (17513)Instructions burned: 8 (million)
% 3.20/1.72 % (17513)------------------------------
% 3.20/1.72 % (17513)------------------------------
% 3.20/1.72 % (17517)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_17306 for (2998ds/21Mi)
% 3.20/1.72 % (17514)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_17306 for (2999ds/902Mi)
% 3.20/1.73 % (17517)Instruction limit reached!
% 3.20/1.73 % (17517)------------------------------
% 3.20/1.73 % (17517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.73 % (17517)Termination reason: Unknown
% 3.20/1.73 % (17517)Termination phase: shuffling
% 3.20/1.73
% 3.20/1.73 % (17517)Memory used [KB]: 2046
% 3.20/1.73 % (17517)Time elapsed: 0.008 s
% 3.20/1.73 % (17517)Instructions burned: 24 (million)
% 3.20/1.73 % (17517)------------------------------
% 3.20/1.73 % (17517)------------------------------
% 3.20/1.73 % (17518)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_17306 for (2998ds/5Mi)
% 3.20/1.73 % (17518)Instruction limit reached!
% 3.20/1.73 % (17518)------------------------------
% 3.20/1.73 % (17518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.73 % (17518)Termination reason: Unknown
% 3.20/1.73 % (17518)Termination phase: shuffling
% 3.20/1.73
% 3.20/1.73 % (17518)Memory used [KB]: 1663
% 3.20/1.73 % (17518)Time elapsed: 0.004 s
% 3.20/1.73 % (17518)Instructions burned: 6 (million)
% 3.20/1.73 % (17518)------------------------------
% 3.20/1.73 % (17518)------------------------------
% 3.20/1.74 % (17522)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_17306 for (2998ds/377Mi)
% 3.20/1.74 % (17521)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_17306 for (2998ds/6Mi)
% 3.20/1.74 % (17521)Instruction limit reached!
% 3.20/1.74 % (17521)------------------------------
% 3.20/1.74 % (17521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.74 % (17521)Termination reason: Unknown
% 3.20/1.74 % (17521)Termination phase: shuffling
% 3.20/1.74
% 3.20/1.74 % (17521)Memory used [KB]: 1663
% 3.20/1.74 % (17521)Time elapsed: 0.005 s
% 3.20/1.74 % (17521)Instructions burned: 7 (million)
% 3.20/1.74 % (17521)------------------------------
% 3.20/1.74 % (17521)------------------------------
% 3.20/1.75 % (17523)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_17306 for (2998ds/779Mi)
% 3.20/1.76 % (17525)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_17306 for (2998ds/19Mi)
% 3.20/1.76 % (17525)Instruction limit reached!
% 3.20/1.76 % (17525)------------------------------
% 3.20/1.76 % (17525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.76 % (17525)Termination reason: Unknown
% 3.20/1.76 % (17525)Termination phase: shuffling
% 3.20/1.76
% 3.20/1.76 % (17525)Memory used [KB]: 1918
% 3.20/1.76 % (17525)Time elapsed: 0.011 s
% 3.20/1.76 % (17525)Instructions burned: 21 (million)
% 3.20/1.76 % (17525)------------------------------
% 3.20/1.76 % (17525)------------------------------
% 3.20/1.77 % (17484)Instruction limit reached!
% 3.20/1.77 % (17484)------------------------------
% 3.20/1.77 % (17484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.77 % (17484)Termination reason: Unknown
% 3.20/1.77 % (17484)Termination phase: Property scanning
% 3.20/1.77
% 3.20/1.77 % (17484)Memory used [KB]: 5884
% 3.20/1.77 % (17484)Time elapsed: 0.128 s
% 3.20/1.77 % (17484)Instructions burned: 275 (million)
% 3.20/1.77 % (17484)------------------------------
% 3.20/1.77 % (17484)------------------------------
% 3.20/1.78 % (17528)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_17306 for (2998ds/879Mi)
% 3.20/1.78 % (17529)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_17306 for (2998ds/17Mi)
% 3.20/1.79 % (17529)Instruction limit reached!
% 3.20/1.79 % (17529)------------------------------
% 3.20/1.79 % (17529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.79 % (17529)Termination reason: Unknown
% 3.20/1.79 % (17529)Termination phase: shuffling
% 3.20/1.79
% 3.20/1.79 % (17529)Memory used [KB]: 1918
% 3.20/1.79 % (17529)Time elapsed: 0.010 s
% 3.20/1.79 % (17529)Instructions burned: 18 (million)
% 3.20/1.79 % (17529)------------------------------
% 3.20/1.79 % (17529)------------------------------
% 3.20/1.81 % (17531)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_17306 for (2998ds/3Mi)
% 3.20/1.81 % (17531)Instruction limit reached!
% 3.20/1.81 % (17531)------------------------------
% 3.20/1.81 % (17531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.81 % (17531)Termination reason: Unknown
% 3.20/1.81 % (17531)Termination phase: shuffling
% 3.20/1.81
% 3.20/1.81 % (17531)Memory used [KB]: 1663
% 3.20/1.81 % (17531)Time elapsed: 0.004 s
% 3.20/1.81 % (17531)Instructions burned: 4 (million)
% 3.20/1.81 % (17531)------------------------------
% 3.20/1.81 % (17531)------------------------------
% 3.20/1.83 % (17532)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_17306 for (2997ds/30Mi)
% 3.20/1.84 % (17522)Instruction limit reached!
% 3.20/1.84 % (17522)------------------------------
% 3.20/1.84 % (17522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.84 % (17522)Termination reason: Unknown
% 3.20/1.84 % (17522)Termination phase: Saturation
% 3.20/1.84
% 3.20/1.84 % (17522)Memory used [KB]: 9466
% 3.20/1.84 % (17522)Time elapsed: 0.102 s
% 3.20/1.84 % (17522)Instructions burned: 378 (million)
% 3.20/1.84 % (17522)------------------------------
% 3.20/1.84 % (17522)------------------------------
% 3.20/1.84 % (17532)Instruction limit reached!
% 3.20/1.84 % (17532)------------------------------
% 3.20/1.84 % (17532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.84 % (17532)Termination reason: Unknown
% 3.20/1.84 % (17532)Termination phase: shuffling
% 3.20/1.84
% 3.20/1.84 % (17532)Memory used [KB]: 2174
% 3.20/1.84 % (17532)Time elapsed: 0.016 s
% 3.20/1.84 % (17532)Instructions burned: 30 (million)
% 3.20/1.84 % (17532)------------------------------
% 3.20/1.84 % (17532)------------------------------
% 3.20/1.85 % (17533)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_17306 for (2997ds/127Mi)
% 3.20/1.86 % (17534)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_17306 for (2997ds/100Mi)
% 3.20/1.88 % (17533)Instruction limit reached!
% 3.20/1.88 % (17533)------------------------------
% 3.20/1.88 % (17533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.88 % (17533)Termination reason: Unknown
% 3.20/1.88 % (17533)Termination phase: Property scanning
% 3.20/1.88
% 3.20/1.88 % (17533)Memory used [KB]: 2942
% 3.20/1.88 % (17533)Time elapsed: 0.035 s
% 3.20/1.88 % (17533)Instructions burned: 130 (million)
% 3.20/1.88 % (17533)------------------------------
% 3.20/1.88 % (17533)------------------------------
% 3.20/1.89 % (17536)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_17306 for (2997ds/3Mi)
% 3.20/1.89 % (17536)Instruction limit reached!
% 3.20/1.89 % (17536)------------------------------
% 3.20/1.89 % (17536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.89 % (17536)Termination reason: Unknown
% 3.20/1.89 % (17536)Termination phase: shuffling
% 3.20/1.89
% 3.20/1.89 % (17536)Memory used [KB]: 1663
% 3.20/1.89 % (17536)Time elapsed: 0.003 s
% 3.20/1.89 % (17536)Instructions burned: 3 (million)
% 3.20/1.89 % (17536)------------------------------
% 3.20/1.89 % (17536)------------------------------
% 3.20/1.90 % (17534)Instruction limit reached!
% 3.20/1.90 % (17534)------------------------------
% 3.20/1.90 % (17534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.90 % (17534)Termination reason: Unknown
% 3.20/1.90 % (17534)Termination phase: Preprocessing 3
% 3.20/1.90
% 3.20/1.90 % (17534)Memory used [KB]: 2814
% 3.20/1.90 % (17534)Time elapsed: 0.047 s
% 3.20/1.90 % (17534)Instructions burned: 101 (million)
% 3.20/1.90 % (17534)------------------------------
% 3.20/1.90 % (17534)------------------------------
% 3.20/1.91 % (17538)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_17306 for (2997ds/20Mi)
% 3.20/1.92 % (17538)Instruction limit reached!
% 3.20/1.92 % (17538)------------------------------
% 3.20/1.92 % (17538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.92 % (17538)Termination reason: Unknown
% 3.20/1.92 % (17538)Termination phase: shuffling
% 3.20/1.92
% 3.20/1.92 % (17538)Memory used [KB]: 1918
% 3.20/1.92 % (17538)Time elapsed: 0.012 s
% 3.20/1.92 % (17538)Instructions burned: 20 (million)
% 3.20/1.92 % (17538)------------------------------
% 3.20/1.92 % (17538)------------------------------
% 3.20/1.92 % (17540)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_17306 for (2997ds/86Mi)
% 3.20/1.94 % (17543)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_17306 for (2996ds/107Mi)
% 3.20/1.96 % (17540)Instruction limit reached!
% 3.20/1.96 % (17540)------------------------------
% 3.20/1.96 % (17540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.96 % (17540)Termination reason: Unknown
% 3.20/1.96 % (17540)Termination phase: Property scanning
% 3.20/1.96
% 3.20/1.96 % (17540)Memory used [KB]: 2814
% 3.20/1.96 % (17540)Time elapsed: 0.041 s
% 3.20/1.96 % (17540)Instructions burned: 87 (million)
% 3.20/1.96 % (17540)------------------------------
% 3.20/1.96 % (17540)------------------------------
% 3.20/1.98 % (17547)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_17306 for (2996ds/39Mi)
% 3.20/1.99 % (17543)Instruction limit reached!
% 3.20/1.99 % (17543)------------------------------
% 3.20/1.99 % (17543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.99 % (17543)Termination reason: Unknown
% 3.20/1.99 % (17543)Termination phase: SInE selection
% 3.20/1.99
% 3.20/1.99 % (17543)Memory used [KB]: 2814
% 3.20/1.99 % (17543)Time elapsed: 0.051 s
% 3.20/1.99 % (17543)Instructions burned: 108 (million)
% 3.20/1.99 % (17543)------------------------------
% 3.20/1.99 % (17543)------------------------------
% 3.20/1.99 % (17547)Instruction limit reached!
% 3.20/1.99 % (17547)------------------------------
% 3.20/1.99 % (17547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.99 % (17547)Termination reason: Unknown
% 3.20/1.99 % (17547)Termination phase: shuffling
% 3.20/1.99
% 3.20/1.99 % (17547)Memory used [KB]: 2430
% 3.20/1.99 % (17547)Time elapsed: 0.019 s
% 3.20/1.99 % (17547)Instructions burned: 39 (million)
% 3.20/1.99 % (17547)------------------------------
% 3.20/1.99 % (17547)------------------------------
% 3.20/2.01 % (17552)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_17306 for (2996ds/46Mi)
% 3.20/2.01 % (17550)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_17306 for (2996ds/448Mi)
% 5.85/2.03 % (17552)Instruction limit reached!
% 5.85/2.03 % (17552)------------------------------
% 5.85/2.03 % (17552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.85/2.03 % (17552)Termination reason: Unknown
% 5.85/2.03 % (17552)Termination phase: shuffling
% 5.85/2.03
% 5.85/2.03 % (17552)Memory used [KB]: 2558
% 5.85/2.03 % (17552)Time elapsed: 0.023 s
% 5.85/2.03 % (17552)Instructions burned: 47 (million)
% 5.85/2.03 % (17552)------------------------------
% 5.85/2.03 % (17552)------------------------------
% 5.85/2.04 % (17495)Instruction limit reached!
% 5.85/2.04 % (17495)------------------------------
% 5.85/2.04 % (17495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.85/2.04 % (17495)Termination reason: Unknown
% 5.85/2.04 % (17495)Termination phase: Saturation
% 5.85/2.04
% 5.85/2.04 % (17495)Memory used [KB]: 18166
% 5.85/2.04 % (17495)Time elapsed: 0.393 s
% 5.85/2.04 % (17495)Instructions burned: 1041 (million)
% 5.85/2.04 % (17495)------------------------------
% 5.85/2.04 % (17495)------------------------------
% 5.85/2.05 % (17523)Instruction limit reached!
% 5.85/2.05 % (17523)------------------------------
% 5.85/2.05 % (17523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.85/2.05 % (17523)Termination reason: Unknown
% 5.85/2.05 % (17523)Termination phase: Saturation
% 5.85/2.05
% 5.85/2.05 % (17523)Memory used [KB]: 7931
% 5.85/2.05 % (17523)Time elapsed: 0.302 s
% 5.85/2.05 % (17523)Instructions burned: 780 (million)
% 5.85/2.05 % (17523)------------------------------
% 5.85/2.05 % (17523)------------------------------
% 5.85/2.05 % (17556)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_17306 for (2995ds/98Mi)
% 5.85/2.05 % (17557)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_17306 for (2995ds/507Mi)
% 5.85/2.07 % (17558)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_17306 for (2995ds/149Mi)
% 5.85/2.07 % (17512)Instruction limit reached!
% 5.85/2.07 % (17512)------------------------------
% 5.85/2.07 % (17512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.85/2.07 % (17512)Termination reason: Unknown
% 5.85/2.07 % (17512)Termination phase: Saturation
% 5.85/2.07
% 5.85/2.07 % (17512)Memory used [KB]: 11769
% 5.85/2.07 % (17512)Time elapsed: 0.385 s
% 5.85/2.07 % (17512)Instructions burned: 710 (million)
% 5.85/2.07 % (17512)------------------------------
% 5.85/2.07 % (17512)------------------------------
% 5.85/2.09 % (17562)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_17306 for (2995ds/39Mi)
% 5.85/2.09 % (17556)Instruction limit reached!
% 5.85/2.09 % (17556)------------------------------
% 5.85/2.09 % (17556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.85/2.09 % (17556)Termination reason: Unknown
% 5.85/2.09 % (17556)Termination phase: Property scanning
% 5.85/2.09
% 5.85/2.09 % (17556)Memory used [KB]: 2814
% 5.85/2.09 % (17556)Time elapsed: 0.046 s
% 5.85/2.09 % (17556)Instructions burned: 99 (million)
% 5.85/2.09 % (17556)------------------------------
% 5.85/2.09 % (17556)------------------------------
% 5.85/2.10 % (17562)Instruction limit reached!
% 5.85/2.10 % (17562)------------------------------
% 5.85/2.10 % (17562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.85/2.10 % (17562)Termination reason: Unknown
% 5.85/2.10 % (17562)Termination phase: shuffling
% 5.85/2.10
% 5.85/2.10 % (17562)Memory used [KB]: 2430
% 5.85/2.10 % (17562)Time elapsed: 0.013 s
% 5.85/2.10 % (17562)Instructions burned: 41 (million)
% 5.85/2.10 % (17562)------------------------------
% 5.85/2.10 % (17562)------------------------------
% 5.85/2.11 % (17566)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_17306 for (2995ds/6Mi)
% 5.85/2.11 % (17567)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_17306 for (2995ds/1087Mi)
% 5.85/2.11 % (17566)Instruction limit reached!
% 5.85/2.11 % (17566)------------------------------
% 5.85/2.11 % (17566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.85/2.11 % (17566)Termination reason: Unknown
% 5.85/2.11 % (17566)Termination phase: shuffling
% 5.85/2.11
% 5.85/2.11 % (17566)Memory used [KB]: 1663
% 5.85/2.11 % (17566)Time elapsed: 0.005 s
% 5.85/2.11 % (17566)Instructions burned: 7 (million)
% 5.85/2.11 % (17566)------------------------------
% 5.85/2.11 % (17566)------------------------------
% 5.85/2.13 % (17568)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_17306 for (2995ds/47Mi)
% 6.44/2.14 % (17558)Instruction limit reached!
% 6.44/2.14 % (17558)------------------------------
% 6.44/2.14 % (17558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.14 % (17558)Termination reason: Unknown
% 6.44/2.14 % (17558)Termination phase: Function definition elimination
% 6.44/2.14
% 6.44/2.14 % (17558)Memory used [KB]: 2942
% 6.44/2.14 % (17558)Time elapsed: 0.068 s
% 6.44/2.14 % (17558)Instructions burned: 149 (million)
% 6.44/2.14 % (17558)------------------------------
% 6.44/2.14 % (17558)------------------------------
% 6.44/2.14 % (17568)Instruction limit reached!
% 6.44/2.14 % (17568)------------------------------
% 6.44/2.14 % (17568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.14 % (17568)Termination reason: Unknown
% 6.44/2.14 % (17568)Termination phase: shuffling
% 6.44/2.14
% 6.44/2.14 % (17568)Memory used [KB]: 2558
% 6.44/2.14 % (17568)Time elapsed: 0.015 s
% 6.44/2.14 % (17568)Instructions burned: 47 (million)
% 6.44/2.14 % (17568)------------------------------
% 6.44/2.14 % (17568)------------------------------
% 6.44/2.15 % (17514)Instruction limit reached!
% 6.44/2.15 % (17514)------------------------------
% 6.44/2.15 % (17514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.15 % (17514)Termination reason: Unknown
% 6.44/2.15 % (17514)Termination phase: Saturation
% 6.44/2.15
% 6.44/2.15 % (17514)Memory used [KB]: 13560
% 6.44/2.15 % (17514)Time elapsed: 0.429 s
% 6.44/2.15 % (17514)Instructions burned: 902 (million)
% 6.44/2.15 % (17514)------------------------------
% 6.44/2.15 % (17514)------------------------------
% 6.44/2.15 % (17572)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_17306 for (2994ds/44Mi)
% 6.44/2.15 % (17573)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_17306 for (2994ds/432Mi)
% 6.44/2.16 % (17574)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_17306 for (2994ds/62Mi)
% 6.44/2.17 % (17572)Instruction limit reached!
% 6.44/2.17 % (17572)------------------------------
% 6.44/2.17 % (17572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.17 % (17572)Termination reason: Unknown
% 6.44/2.17 % (17572)Termination phase: shuffling
% 6.44/2.17
% 6.44/2.17 % (17572)Memory used [KB]: 2430
% 6.44/2.17 % (17572)Time elapsed: 0.021 s
% 6.44/2.17 % (17572)Instructions burned: 44 (million)
% 6.44/2.17 % (17572)------------------------------
% 6.44/2.17 % (17572)------------------------------
% 6.44/2.18 % (17550)Instruction limit reached!
% 6.44/2.18 % (17550)------------------------------
% 6.44/2.18 % (17550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.18 % (17550)Termination reason: Unknown
% 6.44/2.18 % (17550)Termination phase: Saturation
% 6.44/2.18
% 6.44/2.18 % (17550)Memory used [KB]: 7803
% 6.44/2.18 % (17550)Time elapsed: 0.169 s
% 6.44/2.18 % (17550)Instructions burned: 449 (million)
% 6.44/2.18 % (17550)------------------------------
% 6.44/2.18 % (17550)------------------------------
% 6.44/2.18 % (17574)Instruction limit reached!
% 6.44/2.18 % (17574)------------------------------
% 6.44/2.18 % (17574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.18 % (17574)Termination reason: Unknown
% 6.44/2.18 % (17574)Termination phase: shuffling
% 6.44/2.18
% 6.44/2.18 % (17574)Memory used [KB]: 2686
% 6.44/2.18 % (17574)Time elapsed: 0.025 s
% 6.44/2.18 % (17574)Instructions burned: 62 (million)
% 6.44/2.18 % (17574)------------------------------
% 6.44/2.18 % (17574)------------------------------
% 6.44/2.19 % (17528)Instruction limit reached!
% 6.44/2.19 % (17528)------------------------------
% 6.44/2.19 % (17528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.19 % (17528)Termination reason: Unknown
% 6.44/2.19 % (17528)Termination phase: Saturation
% 6.44/2.19
% 6.44/2.19 % (17528)Memory used [KB]: 10746
% 6.44/2.19 % (17528)Time elapsed: 0.407 s
% 6.44/2.19 % (17528)Instructions burned: 880 (million)
% 6.44/2.19 % (17528)------------------------------
% 6.44/2.19 % (17528)------------------------------
% 6.44/2.19 % (17581)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_17306 for (2994ds/453Mi)
% 6.44/2.20 % (17577)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_17306 for (2994ds/31Mi)
% 6.44/2.20 % (17579)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_17306 for (2994ds/96Mi)
% 6.76/2.20 % (17582)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_17306 for (2994ds/71Mi)
% 6.76/2.21 % (17577)Instruction limit reached!
% 6.76/2.21 % (17577)------------------------------
% 6.76/2.21 % (17577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.21 % (17577)Termination reason: Unknown
% 6.76/2.21 % (17577)Termination phase: shuffling
% 6.76/2.21
% 6.76/2.21 % (17577)Memory used [KB]: 2302
% 6.76/2.21 % (17577)Time elapsed: 0.016 s
% 6.76/2.21 % (17577)Instructions burned: 31 (million)
% 6.76/2.21 % (17577)------------------------------
% 6.76/2.21 % (17577)------------------------------
% 6.76/2.23 % (17585)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_17306 for (2994ds/83Mi)
% 6.76/2.23 % (17579)Instruction limit reached!
% 6.76/2.23 % (17579)------------------------------
% 6.76/2.23 % (17579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.23 % (17579)Termination reason: Unknown
% 6.76/2.23 % (17579)Termination phase: Property scanning
% 6.76/2.23
% 6.76/2.23 % (17579)Memory used [KB]: 2814
% 6.76/2.23 % (17579)Time elapsed: 0.035 s
% 6.76/2.23 % (17579)Instructions burned: 97 (million)
% 6.76/2.23 % (17579)------------------------------
% 6.76/2.23 % (17579)------------------------------
% 6.76/2.24 % (17582)Instruction limit reached!
% 6.76/2.24 % (17582)------------------------------
% 6.76/2.24 % (17582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.24 % (17582)Termination reason: Unknown
% 6.76/2.24 % (17582)Termination phase: Property scanning
% 6.76/2.24
% 6.76/2.24 % (17582)Memory used [KB]: 2814
% 6.76/2.24 % (17582)Time elapsed: 0.034 s
% 6.76/2.24 % (17582)Instructions burned: 71 (million)
% 6.76/2.24 % (17582)------------------------------
% 6.76/2.24 % (17582)------------------------------
% 6.76/2.24 % (17557)Instruction limit reached!
% 6.76/2.24 % (17557)------------------------------
% 6.76/2.24 % (17557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.24 % (17557)Termination reason: Unknown
% 6.76/2.24 % (17557)Termination phase: Saturation
% 6.76/2.24
% 6.76/2.24 % (17557)Memory used [KB]: 8315
% 6.76/2.24 % (17557)Time elapsed: 0.191 s
% 6.76/2.24 % (17557)Instructions burned: 508 (million)
% 6.76/2.24 % (17557)------------------------------
% 6.76/2.24 % (17557)------------------------------
% 6.76/2.25 % (17588)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_17306 for (2993ds/11Mi)
% 6.76/2.25 % (17588)Instruction limit reached!
% 6.76/2.25 % (17588)------------------------------
% 6.76/2.25 % (17588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.25 % (17588)Termination reason: Unknown
% 6.76/2.25 % (17588)Termination phase: shuffling
% 6.76/2.25
% 6.76/2.25 % (17588)Memory used [KB]: 1791
% 6.76/2.25 % (17588)Time elapsed: 0.007 s
% 6.76/2.25 % (17588)Instructions burned: 11 (million)
% 6.76/2.25 % (17588)------------------------------
% 6.76/2.25 % (17588)------------------------------
% 6.76/2.25 % (17589)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_17306 for (2993ds/41Mi)
% 6.76/2.25 % (17590)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_17306 for (2993ds/6Mi)
% 6.76/2.26 % (17590)Instruction limit reached!
% 6.76/2.26 % (17590)------------------------------
% 6.76/2.26 % (17590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.26 % (17590)Termination reason: Unknown
% 6.76/2.26 % (17590)Termination phase: shuffling
% 6.76/2.26
% 6.76/2.26 % (17590)Memory used [KB]: 1663
% 6.76/2.26 % (17590)Time elapsed: 0.003 s
% 6.76/2.26 % (17590)Instructions burned: 6 (million)
% 6.76/2.26 % (17590)------------------------------
% 6.76/2.26 % (17590)------------------------------
% 6.76/2.27 % (17592)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_17306 for (2993ds/343Mi)
% 6.76/2.27 % (17585)Instruction limit reached!
% 6.76/2.27 % (17585)------------------------------
% 6.76/2.27 % (17585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.27 % (17585)Termination reason: Unknown
% 6.76/2.27 % (17585)Termination phase: Property scanning
% 6.76/2.27
% 6.76/2.27 % (17585)Memory used [KB]: 2814
% 6.76/2.27 % (17585)Time elapsed: 0.040 s
% 6.76/2.27 % (17585)Instructions burned: 84 (million)
% 6.76/2.27 % (17585)------------------------------
% 6.76/2.27 % (17585)------------------------------
% 6.76/2.27 % (17591)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_17306 for (2993ds/150Mi)
% 6.76/2.27 % (17589)Instruction limit reached!
% 6.76/2.27 % (17589)------------------------------
% 6.76/2.27 % (17589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.27 % (17589)Termination reason: Unknown
% 6.76/2.27 % (17589)Termination phase: shuffling
% 6.76/2.27
% 6.76/2.27 % (17589)Memory used [KB]: 2430
% 6.76/2.27 % (17589)Time elapsed: 0.020 s
% 6.76/2.27 % (17589)Instructions burned: 41 (million)
% 6.76/2.27 % (17589)------------------------------
% 6.76/2.27 % (17589)------------------------------
% 6.76/2.28 % (17595)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_17306 for (2993ds/109Mi)
% 6.76/2.29 % (17596)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_17306 for (2993ds/253Mi)
% 7.22/2.32 % (17591)Instruction limit reached!
% 7.22/2.32 % (17591)------------------------------
% 7.22/2.32 % (17591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.22/2.32 % (17591)Termination reason: Unknown
% 7.22/2.32 % (17591)Termination phase: Preprocessing 3
% 7.22/2.32
% 7.22/2.32 % (17591)Memory used [KB]: 5245
% 7.22/2.32 % (17591)Time elapsed: 0.050 s
% 7.22/2.32 % (17591)Instructions burned: 150 (million)
% 7.22/2.32 % (17591)------------------------------
% 7.22/2.32 % (17591)------------------------------
% 7.22/2.33 % (17573)Instruction limit reached!
% 7.22/2.33 % (17573)------------------------------
% 7.22/2.33 % (17573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.22/2.33 % (17573)Termination reason: Unknown
% 7.22/2.33 % (17573)Termination phase: Saturation
% 7.22/2.33
% 7.22/2.33 % (17573)Memory used [KB]: 3326
% 7.22/2.33 % (17573)Time elapsed: 0.174 s
% 7.22/2.33 % (17573)Instructions burned: 432 (million)
% 7.22/2.33 % (17573)------------------------------
% 7.22/2.33 % (17573)------------------------------
% 7.22/2.33 % (17595)Instruction limit reached!
% 7.22/2.33 % (17595)------------------------------
% 7.22/2.33 % (17595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.22/2.33 % (17595)Termination reason: Unknown
% 7.22/2.33 % (17595)Termination phase: SInE selection
% 7.22/2.33
% 7.22/2.33 % (17595)Memory used [KB]: 2814
% 7.22/2.33 % (17595)Time elapsed: 0.051 s
% 7.22/2.33 % (17595)Instructions burned: 109 (million)
% 7.22/2.33 % (17595)------------------------------
% 7.22/2.33 % (17595)------------------------------
% 7.22/2.33 % (17599)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_17306 for (2992ds/140Mi)
% 7.22/2.34 % (17601)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_17306 for (2992ds/202Mi)
% 7.22/2.35 % (17600)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_17306 for (2992ds/614Mi)
% 7.22/2.37 % (17581)Instruction limit reached!
% 7.22/2.37 % (17581)------------------------------
% 7.22/2.37 % (17581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.22/2.37 % (17581)Termination reason: Unknown
% 7.22/2.37 % (17581)Termination phase: Saturation
% 7.22/2.37
% 7.22/2.37 % (17581)Memory used [KB]: 7803
% 7.22/2.37 % (17581)Time elapsed: 0.176 s
% 7.22/2.37 % (17581)Instructions burned: 454 (million)
% 7.22/2.37 % (17581)------------------------------
% 7.22/2.37 % (17581)------------------------------
% 7.22/2.39 % (17604)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_17306 for (2992ds/339Mi)
% 7.22/2.39 % (17599)Instruction limit reached!
% 7.22/2.39 % (17599)------------------------------
% 7.22/2.39 % (17599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.22/2.39 % (17599)Termination reason: Unknown
% 7.22/2.39 % (17599)Termination phase: Property scanning
% 7.22/2.39
% 7.22/2.39 % (17599)Memory used [KB]: 2942
% 7.22/2.39 % (17599)Time elapsed: 0.061 s
% 7.22/2.39 % (17599)Instructions burned: 141 (million)
% 7.22/2.39 % (17599)------------------------------
% 7.22/2.39 % (17599)------------------------------
% 7.81/2.40 % (17601)Instruction limit reached!
% 7.81/2.40 % (17601)------------------------------
% 7.81/2.40 % (17601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.40 % (17601)Termination reason: Unknown
% 7.81/2.40 % (17601)Termination phase: Property scanning
% 7.81/2.40
% 7.81/2.40 % (17601)Memory used [KB]: 5628
% 7.81/2.40 % (17601)Time elapsed: 0.060 s
% 7.81/2.40 % (17601)Instructions burned: 205 (million)
% 7.81/2.40 % (17601)------------------------------
% 7.81/2.40 % (17601)------------------------------
% 7.81/2.41 % (17596)Instruction limit reached!
% 7.81/2.41 % (17596)------------------------------
% 7.81/2.41 % (17596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.41 % (17596)Termination reason: Unknown
% 7.81/2.41 % (17596)Termination phase: Property scanning
% 7.81/2.41
% 7.81/2.41 % (17596)Memory used [KB]: 5884
% 7.81/2.41 % (17596)Time elapsed: 0.120 s
% 7.81/2.41 % (17596)Instructions burned: 253 (million)
% 7.81/2.41 % (17596)------------------------------
% 7.81/2.41 % (17596)------------------------------
% 7.81/2.41 % (17592)Instruction limit reached!
% 7.81/2.41 % (17592)------------------------------
% 7.81/2.41 % (17592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.41 % (17592)Termination reason: Unknown
% 7.81/2.41 % (17592)Termination phase: Saturation
% 7.81/2.41
% 7.81/2.41 % (17592)Memory used [KB]: 8443
% 7.81/2.41 % (17592)Time elapsed: 0.144 s
% 7.81/2.41 % (17592)Instructions burned: 343 (million)
% 7.81/2.41 % (17592)------------------------------
% 7.81/2.41 % (17592)------------------------------
% 7.81/2.41 % (17606)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_17306 for (2992ds/283Mi)
% 7.81/2.41 % (17607)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_17306 for (2992ds/134Mi)
% 7.81/2.42 % (17608)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_17306 for (2992ds/298Mi)
% 7.81/2.43 % (17609)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_17306 for (2992ds/192Mi)
% 7.81/2.47 % (17607)Instruction limit reached!
% 7.81/2.47 % (17607)------------------------------
% 7.81/2.47 % (17607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.47 % (17607)Termination reason: Unknown
% 7.81/2.47 % (17607)Termination phase: Property scanning
% 7.81/2.47
% 7.81/2.47 % (17607)Memory used [KB]: 2942
% 7.81/2.47 % (17607)Time elapsed: 0.054 s
% 7.81/2.47 % (17607)Instructions burned: 135 (million)
% 7.81/2.47 % (17607)------------------------------
% 7.81/2.47 % (17607)------------------------------
% 7.81/2.48 % (17614)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_17306 for (2991ds/258Mi)
% 8.23/2.50 % (17606)Instruction limit reached!
% 8.23/2.50 % (17606)------------------------------
% 8.23/2.50 % (17606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.23/2.50 % (17606)Termination reason: Unknown
% 8.23/2.50 % (17606)Termination phase: Saturation
% 8.23/2.50
% 8.23/2.50 % (17606)Memory used [KB]: 7675
% 8.23/2.50 % (17606)Time elapsed: 0.098 s
% 8.23/2.50 % (17606)Instructions burned: 286 (million)
% 8.23/2.50 % (17606)------------------------------
% 8.23/2.50 % (17606)------------------------------
% 8.23/2.51 % (17604)Instruction limit reached!
% 8.23/2.51 % (17604)------------------------------
% 8.23/2.51 % (17604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.23/2.51 % (17604)Termination reason: Unknown
% 8.23/2.51 % (17604)Termination phase: Saturation
% 8.23/2.51
% 8.23/2.51 % (17604)Memory used [KB]: 8315
% 8.23/2.51 % (17604)Time elapsed: 0.125 s
% 8.23/2.51 % (17604)Instructions burned: 340 (million)
% 8.23/2.51 % (17604)------------------------------
% 8.23/2.51 % (17604)------------------------------
% 8.23/2.51 % (17609)Instruction limit reached!
% 8.23/2.51 % (17609)------------------------------
% 8.23/2.51 % (17609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.23/2.51 % (17609)Termination reason: Unknown
% 8.23/2.51 % (17609)Termination phase: Property scanning
% 8.23/2.51
% 8.23/2.51 % (17609)Memory used [KB]: 3070
% 8.23/2.51 % (17609)Time elapsed: 0.088 s
% 8.23/2.51 % (17609)Instructions burned: 194 (million)
% 8.23/2.51 % (17609)------------------------------
% 8.23/2.51 % (17609)------------------------------
% 8.23/2.52 % (17618)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_17306 for (2991ds/90Mi)
% 8.23/2.52 % (17619)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_17306 for (2991ds/231Mi)
% 8.23/2.53 % (17621)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_17306 for (2990ds/458Mi)
% 8.23/2.54 % (17608)Instruction limit reached!
% 8.23/2.54 % (17608)------------------------------
% 8.23/2.54 % (17608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.23/2.54 % (17608)Termination reason: Unknown
% 8.23/2.54 % (17608)Termination phase: Saturation
% 8.23/2.54
% 8.23/2.54 % (17608)Memory used [KB]: 7675
% 8.23/2.54 % (17608)Time elapsed: 0.123 s
% 8.23/2.54 % (17608)Instructions burned: 300 (million)
% 8.23/2.54 % (17608)------------------------------
% 8.23/2.54 % (17608)------------------------------
% 8.23/2.56 % (17618)Instruction limit reached!
% 8.23/2.56 % (17618)------------------------------
% 8.23/2.56 % (17618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.23/2.56 % (17618)Termination reason: Unknown
% 8.23/2.56 % (17618)Termination phase: Property scanning
% 8.23/2.56
% 8.23/2.56 % (17618)Memory used [KB]: 2814
% 8.23/2.56 % (17618)Time elapsed: 0.040 s
% 8.23/2.56 % (17618)Instructions burned: 90 (million)
% 8.23/2.56 % (17618)------------------------------
% 8.23/2.56 % (17618)------------------------------
% 8.23/2.56 % (17622)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_17306 for (2990ds/31Mi)
% 8.23/2.58 % (17622)Instruction limit reached!
% 8.23/2.58 % (17622)------------------------------
% 8.23/2.58 % (17622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.23/2.58 % (17622)Termination reason: Unknown
% 8.23/2.58 % (17622)Termination phase: shuffling
% 8.23/2.58
% 8.23/2.58 % (17622)Memory used [KB]: 2302
% 8.23/2.58 % (17622)Time elapsed: 0.017 s
% 8.23/2.58 % (17622)Instructions burned: 32 (million)
% 8.23/2.58 % (17622)------------------------------
% 8.23/2.58 % (17622)------------------------------
% 8.23/2.58 % (17625)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_17306 for (2990ds/297Mi)
% 8.23/2.59 % (17627)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_17306 for (2990ds/987Mi)
% 8.23/2.60 % (17614)Instruction limit reached!
% 8.23/2.60 % (17614)------------------------------
% 8.23/2.60 % (17614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.23/2.60 % (17614)Termination reason: Unknown
% 8.23/2.60 % (17614)Termination phase: Saturation
% 8.23/2.60
% 8.23/2.60 % (17614)Memory used [KB]: 7931
% 8.23/2.60 % (17614)Time elapsed: 0.114 s
% 8.23/2.60 % (17614)Instructions burned: 258 (million)
% 8.23/2.60 % (17614)------------------------------
% 8.23/2.60 % (17614)------------------------------
% 8.80/2.61 % (17600)Instruction limit reached!
% 8.80/2.61 % (17600)------------------------------
% 8.80/2.61 % (17600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.80/2.61 % (17600)Termination reason: Unknown
% 8.80/2.61 % (17600)Termination phase: Saturation
% 8.80/2.61
% 8.80/2.61 % (17600)Memory used [KB]: 10362
% 8.80/2.61 % (17600)Time elapsed: 0.262 s
% 8.80/2.61 % (17600)Instructions burned: 615 (million)
% 8.80/2.61 % (17600)------------------------------
% 8.80/2.61 % (17600)------------------------------
% 8.80/2.61 % (17629)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_17306 for (2990ds/182Mi)
% 8.80/2.62 % (17567)Instruction limit reached!
% 8.80/2.62 % (17567)------------------------------
% 8.80/2.62 % (17567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.80/2.62 % (17567)Termination reason: Unknown
% 8.80/2.62 % (17567)Termination phase: Saturation
% 8.80/2.62
% 8.80/2.62 % (17567)Memory used [KB]: 13304
% 8.80/2.62 % (17567)Time elapsed: 0.508 s
% 8.80/2.62 % (17567)Instructions burned: 1088 (million)
% 8.80/2.62 % (17567)------------------------------
% 8.80/2.62 % (17567)------------------------------
% 8.80/2.62 % (17631)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_17306 for (2990ds/182Mi)
% 8.80/2.62 % (17619)Instruction limit reached!
% 8.80/2.62 % (17619)------------------------------
% 8.80/2.62 % (17619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.80/2.62 % (17619)Termination reason: Unknown
% 8.80/2.62 % (17619)Termination phase: Property scanning
% 8.80/2.62
% 8.80/2.62 % (17619)Memory used [KB]: 4349
% 8.80/2.62 % (17619)Time elapsed: 0.102 s
% 8.80/2.62 % (17619)Instructions burned: 232 (million)
% 8.80/2.62 % (17619)------------------------------
% 8.80/2.62 % (17619)------------------------------
% 8.80/2.64 % (17633)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_17306 for (2989ds/154Mi)
% 8.80/2.64 % (17634)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_17306 for (2989ds/79Mi)
% 8.80/2.67 % (17634)Instruction limit reached!
% 8.80/2.67 % (17634)------------------------------
% 8.80/2.67 % (17634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.80/2.67 % (17634)Termination reason: Unknown
% 8.80/2.67 % (17634)Termination phase: Property scanning
% 8.80/2.67
% 8.80/2.67 % (17634)Memory used [KB]: 2814
% 8.80/2.67 % (17634)Time elapsed: 0.036 s
% 8.80/2.67 % (17634)Instructions burned: 80 (million)
% 8.80/2.67 % (17634)------------------------------
% 8.80/2.67 % (17634)------------------------------
% 8.80/2.68 % (17631)Instruction limit reached!
% 8.80/2.68 % (17631)------------------------------
% 8.80/2.68 % (17631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.80/2.68 % (17631)Termination reason: Unknown
% 8.80/2.68 % (17631)Termination phase: Property scanning
% 8.80/2.68
% 8.80/2.68 % (17631)Memory used [KB]: 5628
% 8.80/2.68 % (17631)Time elapsed: 0.064 s
% 8.80/2.68 % (17631)Instructions burned: 183 (million)
% 8.80/2.68 % (17631)------------------------------
% 8.80/2.68 % (17631)------------------------------
% 8.80/2.69 % (17633)Instruction limit reached!
% 8.80/2.69 % (17633)------------------------------
% 8.80/2.69 % (17633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.80/2.69 % (17633)Termination reason: Unknown
% 8.80/2.69 % (17633)Termination phase: Function definition elimination
% 8.80/2.69
% 8.80/2.69 % (17633)Memory used [KB]: 2942
% 8.80/2.69 % (17633)Time elapsed: 0.053 s
% 8.80/2.69 % (17633)Instructions burned: 155 (million)
% 8.80/2.69 % (17633)------------------------------
% 8.80/2.69 % (17633)------------------------------
% 8.80/2.69 % (17641)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_17306 for (2989ds/216Mi)
% 8.80/2.69 % (17629)Instruction limit reached!
% 8.80/2.69 % (17629)------------------------------
% 8.80/2.69 % (17629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.80/2.69 % (17629)Termination reason: Unknown
% 8.80/2.69 % (17629)Termination phase: Property scanning
% 8.80/2.69
% 8.80/2.69 % (17629)Memory used [KB]: 3070
% 8.80/2.69 % (17629)Time elapsed: 0.082 s
% 8.80/2.69 % (17629)Instructions burned: 183 (million)
% 8.80/2.69 % (17629)------------------------------
% 8.80/2.69 % (17629)------------------------------
% 10.12/2.70 % (17644)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_17306 for (2989ds/922Mi)
% 10.12/2.70 % (17625)Instruction limit reached!
% 10.12/2.70 % (17625)------------------------------
% 10.12/2.70 % (17625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.12/2.70 % (17625)Termination reason: Unknown
% 10.12/2.70 % (17625)Termination phase: Saturation
% 10.12/2.70
% 10.12/2.70 % (17625)Memory used [KB]: 7675
% 10.12/2.70 % (17625)Time elapsed: 0.125 s
% 10.12/2.70 % (17625)Instructions burned: 297 (million)
% 10.12/2.70 % (17625)------------------------------
% 10.12/2.70 % (17625)------------------------------
% 10.12/2.70 % (17642)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_17306 for (2989ds/114Mi)
% 10.12/2.71 % (17645)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_17306 for (2989ds/182Mi)
% 10.12/2.72 % (17646)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_17306 for (2989ds/164Mi)
% 10.12/2.73 % (17621)Instruction limit reached!
% 10.12/2.73 % (17621)------------------------------
% 10.12/2.73 % (17621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.12/2.73 % (17621)Termination reason: Unknown
% 10.12/2.73 % (17621)Termination phase: Saturation
% 10.12/2.73
% 10.12/2.73 % (17621)Memory used [KB]: 9722
% 10.12/2.73 % (17621)Time elapsed: 0.203 s
% 10.12/2.73 % (17621)Instructions burned: 458 (million)
% 10.12/2.73 % (17621)------------------------------
% 10.12/2.73 % (17621)------------------------------
% 10.12/2.75 % (17649)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_17306 for (2988ds/50Mi)
% 10.12/2.75 % (17642)Instruction limit reached!
% 10.12/2.75 % (17642)------------------------------
% 10.12/2.75 % (17642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.12/2.75 % (17642)Termination reason: Unknown
% 10.12/2.75 % (17642)Termination phase: Property scanning
% 10.12/2.75
% 10.12/2.75 % (17642)Memory used [KB]: 2942
% 10.12/2.75 % (17642)Time elapsed: 0.053 s
% 10.12/2.75 % (17642)Instructions burned: 115 (million)
% 10.12/2.75 % (17642)------------------------------
% 10.12/2.75 % (17642)------------------------------
% 10.12/2.77 % (17649)Instruction limit reached!
% 10.12/2.77 % (17649)------------------------------
% 10.12/2.77 % (17649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.12/2.77 % (17649)Termination reason: Unknown
% 10.12/2.77 % (17649)Termination phase: shuffling
% 10.12/2.77
% 10.12/2.77 % (17649)Memory used [KB]: 2558
% 10.12/2.77 % (17649)Time elapsed: 0.024 s
% 10.12/2.77 % (17649)Instructions burned: 50 (million)
% 10.12/2.77 % (17649)------------------------------
% 10.12/2.77 % (17649)------------------------------
% 10.12/2.77 % (17651)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_17306 for (2988ds/368Mi)
% 10.12/2.77 % (17645)Instruction limit reached!
% 10.12/2.77 % (17645)------------------------------
% 10.12/2.77 % (17645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.12/2.77 % (17645)Termination reason: Unknown
% 10.12/2.77 % (17645)Termination phase: Property scanning
% 10.12/2.77
% 10.12/2.77 % (17645)Memory used [KB]: 3198
% 10.12/2.77 % (17645)Time elapsed: 0.064 s
% 10.12/2.77 % (17645)Instructions burned: 186 (million)
% 10.12/2.77 % (17645)------------------------------
% 10.12/2.77 % (17645)------------------------------
% 10.12/2.78 % (17641)Instruction limit reached!
% 10.12/2.78 % (17641)------------------------------
% 10.12/2.78 % (17641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.12/2.78 % (17641)Termination reason: Unknown
% 10.12/2.78 % (17641)Termination phase: Property scanning
% 10.12/2.78
% 10.12/2.78 % (17641)Memory used [KB]: 3198
% 10.12/2.78 % (17641)Time elapsed: 0.091 s
% 10.12/2.78 % (17641)Instructions burned: 216 (million)
% 10.12/2.78 % (17641)------------------------------
% 10.12/2.78 % (17641)------------------------------
% 10.12/2.78 % (17653)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_17306 for (2988ds/267Mi)
% 10.12/2.79 % (17652)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_17306 for (2988ds/1021Mi)
% 10.12/2.79 % (17646)Instruction limit reached!
% 10.12/2.79 % (17646)------------------------------
% 10.12/2.79 % (17646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.12/2.79 % (17646)Termination reason: Unknown
% 10.12/2.79 % (17646)Termination phase: Property scanning
% 10.12/2.79
% 10.12/2.79 % (17646)Memory used [KB]: 2942
% 10.12/2.79 % (17646)Time elapsed: 0.071 s
% 10.12/2.79 % (17646)Instructions burned: 165 (million)
% 10.12/2.79 % (17646)------------------------------
% 10.12/2.79 % (17646)------------------------------
% 10.86/2.80 % (17654)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_17306 for (2988ds/204Mi)
% 10.86/2.81 % (17655)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_17306 for (2988ds/26Mi)
% 10.86/2.82 % (17655)Instruction limit reached!
% 10.86/2.82 % (17655)------------------------------
% 10.86/2.82 % (17655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.86/2.82 % (17655)Termination reason: Unknown
% 10.86/2.82 % (17655)Termination phase: shuffling
% 10.86/2.82
% 10.86/2.82 % (17655)Memory used [KB]: 2174
% 10.86/2.82 % (17655)Time elapsed: 0.014 s
% 10.86/2.82 % (17655)Instructions burned: 26 (million)
% 10.86/2.82 % (17655)------------------------------
% 10.86/2.82 % (17655)------------------------------
% 10.86/2.84 % (17658)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_17306 for (2987ds/53Mi)
% 10.86/2.86 % (17658)Instruction limit reached!
% 10.86/2.86 % (17658)------------------------------
% 10.86/2.86 % (17658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.86/2.86 % (17658)Termination reason: Unknown
% 10.86/2.86 % (17658)Termination phase: shuffling
% 10.86/2.86
% 10.86/2.86 % (17658)Memory used [KB]: 2558
% 10.86/2.86 % (17658)Time elapsed: 0.027 s
% 10.86/2.86 % (17658)Instructions burned: 54 (million)
% 10.86/2.86 % (17658)------------------------------
% 10.86/2.86 % (17658)------------------------------
% 10.86/2.87 % (17653)Instruction limit reached!
% 10.86/2.87 % (17653)------------------------------
% 10.86/2.87 % (17653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.86/2.87 % (17653)Termination reason: Unknown
% 10.86/2.87 % (17653)Termination phase: Saturation
% 10.86/2.87
% 10.86/2.87 % (17653)Memory used [KB]: 7675
% 10.86/2.87 % (17653)Time elapsed: 0.084 s
% 10.86/2.87 % (17653)Instructions burned: 267 (million)
% 10.86/2.87 % (17653)------------------------------
% 10.86/2.87 % (17653)------------------------------
% 10.86/2.87 % (17654)Instruction limit reached!
% 10.86/2.87 % (17654)------------------------------
% 10.86/2.87 % (17654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.86/2.87 % (17654)Termination reason: Unknown
% 10.86/2.87 % (17654)Termination phase: Property scanning
% 10.86/2.87
% 10.86/2.87 % (17654)Memory used [KB]: 3070
% 10.86/2.87 % (17654)Time elapsed: 0.074 s
% 10.86/2.87 % (17654)Instructions burned: 206 (million)
% 10.86/2.87 % (17654)------------------------------
% 10.86/2.87 % (17654)------------------------------
% 10.86/2.88 % (17661)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_17306 for (2987ds/4436Mi)
% 10.86/2.89 % (17662)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_17306 for (2987ds/1539Mi)
% 10.86/2.89 % (17663)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_17306 for (2987ds/408Mi)
% 11.12/2.91 % (17627)Instruction limit reached!
% 11.12/2.91 % (17627)------------------------------
% 11.12/2.91 % (17627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/2.91 % (17627)Termination reason: Unknown
% 11.12/2.91 % (17627)Termination phase: Saturation
% 11.12/2.91
% 11.12/2.91 % (17627)Memory used [KB]: 14072
% 11.12/2.91 % (17627)Time elapsed: 0.321 s
% 11.12/2.91 % (17627)Instructions burned: 987 (million)
% 11.12/2.91 % (17627)------------------------------
% 11.12/2.91 % (17627)------------------------------
% 11.12/2.93 % (17665)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_17306 for (2986ds/5205Mi)
% 11.12/2.93 % (17651)Instruction limit reached!
% 11.12/2.93 % (17651)------------------------------
% 11.12/2.93 % (17651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.12/2.93 % (17651)Termination reason: Unknown
% 11.12/2.93 % (17651)Termination phase: Saturation
% 11.12/2.93
% 11.12/2.93 % (17651)Memory used [KB]: 9466
% 11.12/2.93 % (17651)Time elapsed: 0.165 s
% 11.12/2.93 % (17651)Instructions burned: 368 (million)
% 11.12/2.93 % (17651)------------------------------
% 11.12/2.93 % (17651)------------------------------
% 11.12/2.95 % (17666)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_17306 for (2986ds/1913Mi)
% 12.82/3.08 % (17663)Instruction limit reached!
% 12.82/3.08 % (17663)------------------------------
% 12.82/3.08 % (17663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.82/3.08 % (17663)Termination reason: Unknown
% 12.82/3.08 % (17663)Termination phase: Saturation
% 12.82/3.08
% 12.82/3.08 % (17663)Memory used [KB]: 11897
% 12.82/3.08 % (17663)Time elapsed: 0.197 s
% 12.82/3.08 % (17663)Instructions burned: 409 (million)
% 12.82/3.08 % (17663)------------------------------
% 12.82/3.08 % (17663)------------------------------
% 12.82/3.10 % (17669)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_17306 for (2985ds/4350Mi)
% 13.52/3.14 % (17644)Instruction limit reached!
% 13.52/3.14 % (17644)------------------------------
% 13.52/3.14 % (17644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.52/3.14 % (17644)Termination reason: Unknown
% 13.52/3.14 % (17644)Termination phase: Saturation
% 13.52/3.14
% 13.52/3.14 % (17644)Memory used [KB]: 13048
% 13.52/3.14 % (17644)Time elapsed: 0.441 s
% 13.52/3.14 % (17644)Instructions burned: 923 (million)
% 13.52/3.14 % (17644)------------------------------
% 13.52/3.14 % (17644)------------------------------
% 13.52/3.16 % (17671)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_17306 for (2984ds/68Mi)
% 13.52/3.19 % (17671)Instruction limit reached!
% 13.52/3.19 % (17671)------------------------------
% 13.52/3.19 % (17671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.52/3.19 % (17671)Termination reason: Unknown
% 13.52/3.19 % (17671)Termination phase: Property scanning
% 13.52/3.19
% 13.52/3.19 % (17671)Memory used [KB]: 2814
% 13.52/3.19 % (17671)Time elapsed: 0.033 s
% 13.52/3.19 % (17671)Instructions burned: 69 (million)
% 13.52/3.19 % (17671)------------------------------
% 13.52/3.19 % (17671)------------------------------
% 13.94/3.21 % (17673)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_17306 for (2984ds/358Mi)
% 13.94/3.28 % (17652)Instruction limit reached!
% 13.94/3.28 % (17652)------------------------------
% 13.94/3.28 % (17652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.94/3.28 % (17652)Termination reason: Unknown
% 13.94/3.28 % (17652)Termination phase: Saturation
% 13.94/3.28
% 13.94/3.28 % (17652)Memory used [KB]: 13176
% 13.94/3.28 % (17652)Time elapsed: 0.493 s
% 13.94/3.28 % (17652)Instructions burned: 1021 (million)
% 13.94/3.28 % (17652)------------------------------
% 13.94/3.28 % (17652)------------------------------
% 14.42/3.30 % (17676)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_17306 for (2983ds/31Mi)
% 14.42/3.31 % (17676)Instruction limit reached!
% 14.42/3.31 % (17676)------------------------------
% 14.42/3.31 % (17676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.42/3.31 % (17676)Termination reason: Unknown
% 14.42/3.31 % (17676)Termination phase: shuffling
% 14.42/3.31
% 14.42/3.31 % (17676)Memory used [KB]: 2302
% 14.42/3.31 % (17676)Time elapsed: 0.016 s
% 14.42/3.31 % (17676)Instructions burned: 32 (million)
% 14.42/3.31 % (17676)------------------------------
% 14.42/3.31 % (17676)------------------------------
% 14.42/3.33 % (17677)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_17306 for (2982ds/279Mi)
% 14.42/3.36 % (17673)Instruction limit reached!
% 14.42/3.36 % (17673)------------------------------
% 14.42/3.36 % (17673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.42/3.36 % (17673)Termination reason: Unknown
% 14.42/3.36 % (17673)Termination phase: Saturation
% 14.42/3.36
% 14.42/3.36 % (17673)Memory used [KB]: 8443
% 14.42/3.36 % (17673)Time elapsed: 0.156 s
% 14.42/3.36 % (17673)Instructions burned: 358 (million)
% 14.42/3.36 % (17673)------------------------------
% 14.42/3.36 % (17673)------------------------------
% 14.42/3.38 % (17680)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_17306 for (2982ds/258Mi)
% 15.02/3.44 % (17662)Instruction limit reached!
% 15.02/3.44 % (17662)------------------------------
% 15.02/3.44 % (17662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.02/3.44 % (17662)Termination reason: Unknown
% 15.02/3.44 % (17662)Termination phase: Saturation
% 15.02/3.44
% 15.02/3.44 % (17662)Memory used [KB]: 11129
% 15.02/3.44 % (17662)Time elapsed: 0.557 s
% 15.02/3.44 % (17662)Instructions burned: 1539 (million)
% 15.02/3.44 % (17662)------------------------------
% 15.02/3.44 % (17662)------------------------------
% 15.02/3.44 % (17677)Instruction limit reached!
% 15.02/3.44 % (17677)------------------------------
% 15.02/3.44 % (17677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.02/3.44 % (17677)Termination reason: Unknown
% 15.02/3.44 % (17677)Termination phase: Saturation
% 15.02/3.44
% 15.02/3.44 % (17677)Memory used [KB]: 7675
% 15.02/3.44 % (17677)Time elapsed: 0.114 s
% 15.02/3.44 % (17677)Instructions burned: 279 (million)
% 15.02/3.44 % (17677)------------------------------
% 15.02/3.44 % (17677)------------------------------
% 15.02/3.45 % (17684)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_17306 for (2981ds/995Mi)
% 15.02/3.46 % (17683)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_17306 for (2981ds/26Mi)
% 15.02/3.47 % (17683)Instruction limit reached!
% 15.02/3.47 % (17683)------------------------------
% 15.02/3.47 % (17683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.02/3.47 % (17683)Termination reason: Unknown
% 15.02/3.47 % (17683)Termination phase: shuffling
% 15.02/3.47
% 15.02/3.47 % (17683)Memory used [KB]: 2174
% 15.02/3.47 % (17683)Time elapsed: 0.014 s
% 15.02/3.47 % (17683)Instructions burned: 27 (million)
% 15.02/3.47 % (17683)------------------------------
% 15.02/3.47 % (17683)------------------------------
% 15.02/3.48 % (17680)Instruction limit reached!
% 15.02/3.48 % (17680)------------------------------
% 15.02/3.48 % (17680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.02/3.48 % (17680)Termination reason: Unknown
% 15.02/3.48 % (17680)Termination phase: Saturation
% 15.02/3.48
% 15.02/3.48 % (17680)Memory used [KB]: 8315
% 15.02/3.48 % (17680)Time elapsed: 0.105 s
% 15.02/3.48 % (17680)Instructions burned: 258 (million)
% 15.02/3.48 % (17680)------------------------------
% 15.02/3.48 % (17680)------------------------------
% 15.02/3.49 % (17685)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_17306 for (2981ds/373Mi)
% 15.65/3.50 % (17686)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_17306 for (2981ds/253Mi)
% 15.65/3.58 % (17686)Instruction limit reached!
% 15.65/3.58 % (17686)------------------------------
% 15.65/3.58 % (17686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.65/3.58 % (17686)Termination reason: Unknown
% 15.65/3.58 % (17686)Termination phase: Saturation
% 15.65/3.58
% 15.65/3.58 % (17686)Memory used [KB]: 7675
% 15.65/3.58 % (17686)Time elapsed: 0.086 s
% 15.65/3.58 % (17686)Instructions burned: 255 (million)
% 15.65/3.58 % (17686)------------------------------
% 15.65/3.58 % (17686)------------------------------
% 15.65/3.59 % (17690)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_17306 for (2980ds/832Mi)
% 16.05/3.64 % (17685)Instruction limit reached!
% 16.05/3.64 % (17685)------------------------------
% 16.05/3.64 % (17685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.05/3.64 % (17685)Termination reason: Unknown
% 16.05/3.64 % (17685)Termination phase: Saturation
% 16.05/3.64
% 16.05/3.64 % (17685)Memory used [KB]: 9466
% 16.05/3.64 % (17685)Time elapsed: 0.154 s
% 16.05/3.64 % (17685)Instructions burned: 373 (million)
% 16.05/3.64 % (17685)------------------------------
% 16.05/3.64 % (17685)------------------------------
% 16.05/3.66 % (17691)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_17306 for (2979ds/668Mi)
% 16.51/3.80 % (17684)Instruction limit reached!
% 16.51/3.80 % (17684)------------------------------
% 16.51/3.80 % (17684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.82/3.80 % (17684)Termination reason: Unknown
% 16.82/3.80 % (17684)Termination phase: Saturation
% 16.82/3.80
% 16.82/3.80 % (17684)Memory used [KB]: 18293
% 16.82/3.80 % (17684)Time elapsed: 0.346 s
% 16.82/3.80 % (17684)Instructions burned: 997 (million)
% 16.82/3.80 % (17684)------------------------------
% 16.82/3.80 % (17684)------------------------------
% 16.82/3.82 % (17696)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_17306 for (2978ds/40Mi)
% 16.82/3.83 % (17666)Instruction limit reached!
% 16.82/3.83 % (17666)------------------------------
% 16.82/3.83 % (17666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.82/3.83 % (17666)Termination reason: Unknown
% 16.82/3.83 % (17666)Termination phase: Saturation
% 16.82/3.83
% 16.82/3.83 % (17666)Memory used [KB]: 6524
% 16.82/3.83 % (17666)Time elapsed: 0.880 s
% 16.82/3.83 % (17666)Instructions burned: 1914 (million)
% 16.82/3.83 % (17666)------------------------------
% 16.82/3.83 % (17666)------------------------------
% 16.82/3.83 % (17696)Instruction limit reached!
% 16.82/3.83 % (17696)------------------------------
% 16.82/3.83 % (17696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.82/3.83 % (17696)Termination reason: Unknown
% 16.82/3.83 % (17696)Termination phase: shuffling
% 16.82/3.83
% 16.82/3.83 % (17696)Memory used [KB]: 2430
% 16.82/3.83 % (17696)Time elapsed: 0.019 s
% 16.82/3.83 % (17696)Instructions burned: 40 (million)
% 16.82/3.83 % (17696)------------------------------
% 16.82/3.83 % (17696)------------------------------
% 16.82/3.84 % (17700)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_17306 for (2977ds/187Mi)
% 16.82/3.85 % (17699)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_17306 for (2977ds/294Mi)
% 16.82/3.89 % (17700)Instruction limit reached!
% 16.82/3.89 % (17700)------------------------------
% 16.82/3.89 % (17700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.82/3.89 % (17700)Termination reason: Unknown
% 16.82/3.89 % (17700)Termination phase: Property scanning
% 16.82/3.89
% 16.82/3.89 % (17700)Memory used [KB]: 3070
% 16.82/3.89 % (17700)Time elapsed: 0.049 s
% 16.82/3.89 % (17700)Instructions burned: 187 (million)
% 16.82/3.89 % (17700)------------------------------
% 16.82/3.89 % (17700)------------------------------
% 16.82/3.90 % (17691)Instruction limit reached!
% 16.82/3.90 % (17691)------------------------------
% 16.82/3.90 % (17691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.82/3.90 % (17691)Termination reason: Unknown
% 16.82/3.90 % (17691)Termination phase: Saturation
% 16.82/3.90
% 16.82/3.90 % (17691)Memory used [KB]: 12281
% 16.82/3.90 % (17691)Time elapsed: 0.241 s
% 16.82/3.90 % (17691)Instructions burned: 668 (million)
% 16.82/3.90 % (17691)------------------------------
% 16.82/3.90 % (17691)------------------------------
% 17.52/3.90 % (17704)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_17306 for (2977ds/371Mi)
% 17.52/3.92 % (17705)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_17306 for (2977ds/1827Mi)
% 17.52/3.94 % (17690)Instruction limit reached!
% 17.52/3.94 % (17690)------------------------------
% 17.52/3.94 % (17690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.52/3.94 % (17690)Termination reason: Unknown
% 17.52/3.94 % (17690)Termination phase: Saturation
% 17.52/3.94
% 17.52/3.94 % (17690)Memory used [KB]: 13048
% 17.52/3.94 % (17690)Time elapsed: 0.350 s
% 17.52/3.94 % (17690)Instructions burned: 833 (million)
% 17.52/3.94 % (17690)------------------------------
% 17.52/3.94 % (17690)------------------------------
% 17.52/3.96 % (17707)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_17306 for (2976ds/70Mi)
% 17.52/3.97 % (17699)Instruction limit reached!
% 17.52/3.97 % (17699)------------------------------
% 17.52/3.97 % (17699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.52/3.97 % (17699)Termination reason: Unknown
% 17.52/3.97 % (17699)Termination phase: Saturation
% 17.52/3.97
% 17.52/3.97 % (17699)Memory used [KB]: 7675
% 17.52/3.97 % (17699)Time elapsed: 0.125 s
% 17.52/3.97 % (17699)Instructions burned: 294 (million)
% 17.52/3.97 % (17699)------------------------------
% 17.52/3.97 % (17699)------------------------------
% 17.52/3.99 % (17707)Instruction limit reached!
% 17.52/3.99 % (17707)------------------------------
% 17.52/3.99 % (17707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.52/3.99 % (17707)Termination reason: Unknown
% 17.52/3.99 % (17707)Termination phase: Property scanning
% 17.52/3.99
% 17.52/3.99 % (17707)Memory used [KB]: 2814
% 17.52/3.99 % (17707)Time elapsed: 0.033 s
% 17.52/3.99 % (17707)Instructions burned: 70 (million)
% 17.52/3.99 % (17707)------------------------------
% 17.52/3.99 % (17707)------------------------------
% 17.52/3.99 % (17708)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_17306 for (2976ds/316Mi)
% 17.52/4.01 % (17710)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_17306 for (2976ds/932Mi)
% 19.79/4.05 % (17704)Instruction limit reached!
% 19.79/4.05 % (17704)------------------------------
% 19.79/4.05 % (17704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.79/4.05 % (17704)Termination reason: Unknown
% 19.79/4.05 % (17704)Termination phase: Saturation
% 19.79/4.05
% 19.79/4.05 % (17704)Memory used [KB]: 8827
% 19.79/4.05 % (17704)Time elapsed: 0.153 s
% 19.79/4.05 % (17704)Instructions burned: 372 (million)
% 19.79/4.05 % (17704)------------------------------
% 19.79/4.05 % (17704)------------------------------
% 19.79/4.07 % (17711)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_17306 for (2975ds/4714Mi)
% 19.79/4.12 % (17708)Instruction limit reached!
% 19.79/4.12 % (17708)------------------------------
% 19.79/4.12 % (17708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.79/4.12 % (17708)Termination reason: Unknown
% 19.79/4.12 % (17708)Termination phase: Saturation
% 19.79/4.12
% 19.79/4.12 % (17708)Memory used [KB]: 7675
% 19.79/4.12 % (17708)Time elapsed: 0.085 s
% 19.79/4.12 % (17708)Instructions burned: 319 (million)
% 19.79/4.12 % (17708)------------------------------
% 19.79/4.12 % (17708)------------------------------
% 20.37/4.13 % (17712)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_17306 for (2974ds/8250Mi)
% 21.22/4.37 % (17710)Instruction limit reached!
% 21.22/4.37 % (17710)------------------------------
% 21.22/4.37 % (17710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.22/4.37 % (17710)Termination reason: Unknown
% 21.22/4.37 % (17710)Termination phase: Saturation
% 21.22/4.37
% 21.22/4.37 % (17710)Memory used [KB]: 15351
% 21.22/4.37 % (17710)Time elapsed: 0.316 s
% 21.22/4.37 % (17710)Instructions burned: 932 (million)
% 21.22/4.37 % (17710)------------------------------
% 21.22/4.37 % (17710)------------------------------
% 21.22/4.39 % (17714)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_17306 for (2972ds/770Mi)
% 22.51/4.69 % (17714)Instruction limit reached!
% 22.51/4.69 % (17714)------------------------------
% 22.51/4.69 % (17714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.51/4.69 % (17714)Termination reason: Unknown
% 22.51/4.69 % (17714)Termination phase: Saturation
% 22.51/4.69
% 22.51/4.69 % (17714)Memory used [KB]: 7931
% 22.51/4.69 % (17714)Time elapsed: 0.323 s
% 22.51/4.69 % (17714)Instructions burned: 770 (million)
% 22.51/4.69 % (17714)------------------------------
% 22.51/4.69 % (17714)------------------------------
% 23.22/4.71 % (17705)Instruction limit reached!
% 23.22/4.71 % (17705)------------------------------
% 23.22/4.71 % (17705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.22/4.71 % (17705)Termination reason: Unknown
% 23.22/4.71 % (17705)Termination phase: Saturation
% 23.22/4.71
% 23.22/4.71 % (17705)Memory used [KB]: 22003
% 23.22/4.71 % (17705)Time elapsed: 0.817 s
% 23.22/4.71 % (17705)Instructions burned: 1828 (million)
% 23.22/4.71 % (17705)------------------------------
% 23.22/4.71 % (17705)------------------------------
% 23.22/4.72 % (17717)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_17306 for (2969ds/794Mi)
% 23.22/4.73 % (17718)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_17306 for (2969ds/464Mi)
% 23.55/4.81 % (17665)Instruction limit reached!
% 23.55/4.81 % (17665)------------------------------
% 23.55/4.81 % (17665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.55/4.81 % (17665)Termination reason: Unknown
% 23.55/4.81 % (17665)Termination phase: Saturation
% 23.55/4.81
% 23.55/4.81 % (17665)Memory used [KB]: 19701
% 23.55/4.81 % (17665)Time elapsed: 1.888 s
% 23.55/4.81 % (17665)Instructions burned: 5206 (million)
% 23.55/4.81 % (17665)------------------------------
% 23.55/4.81 % (17665)------------------------------
% 23.55/4.83 % (17720)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_17306 for (2968ds/1376Mi)
% 23.77/4.93 % (17718)Instruction limit reached!
% 23.77/4.93 % (17718)------------------------------
% 23.77/4.93 % (17718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.77/4.93 % (17718)Termination reason: Unknown
% 23.77/4.93 % (17718)Termination phase: Saturation
% 23.77/4.93
% 23.77/4.93 % (17718)Memory used [KB]: 9722
% 23.77/4.93 % (17718)Time elapsed: 0.200 s
% 23.77/4.93 % (17718)Instructions burned: 464 (million)
% 23.77/4.93 % (17718)------------------------------
% 23.77/4.93 % (17718)------------------------------
% 23.77/4.95 % (17723)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_17306 for (2966ds/906Mi)
% 26.61/5.01 % (17661)Instruction limit reached!
% 26.61/5.01 % (17661)------------------------------
% 26.61/5.01 % (17661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.61/5.01 % (17661)Termination reason: Unknown
% 26.61/5.01 % (17661)Termination phase: Saturation
% 26.61/5.01
% 26.61/5.01 % (17661)Memory used [KB]: 17782
% 26.61/5.01 % (17661)Time elapsed: 2.135 s
% 26.61/5.01 % (17661)Instructions burned: 4436 (million)
% 26.61/5.01 % (17661)------------------------------
% 26.61/5.01 % (17661)------------------------------
% 26.61/5.03 % (17725)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_17306 for (2965ds/434Mi)
% 26.61/5.09 % (17717)Instruction limit reached!
% 26.61/5.09 % (17717)------------------------------
% 26.61/5.09 % (17717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.61/5.09 % (17717)Termination reason: Unknown
% 26.61/5.09 % (17717)Termination phase: Saturation
% 26.61/5.09
% 26.61/5.09 % (17717)Memory used [KB]: 6396
% 26.61/5.09 % (17717)Time elapsed: 0.399 s
% 26.61/5.09 % (17717)Instructions burned: 795 (million)
% 26.61/5.09 % (17717)------------------------------
% 26.61/5.09 % (17717)------------------------------
% 26.61/5.11 % (17728)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_17306 for (2965ds/865Mi)
% 27.22/5.16 % (17725)Instruction limit reached!
% 27.22/5.16 % (17725)------------------------------
% 27.22/5.16 % (17725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.22/5.16 % (17725)Termination reason: Unknown
% 27.22/5.16 % (17725)Termination phase: Saturation
% 27.22/5.16
% 27.22/5.16 % (17725)Memory used [KB]: 11769
% 27.22/5.16 % (17725)Time elapsed: 0.140 s
% 27.22/5.16 % (17725)Instructions burned: 435 (million)
% 27.22/5.16 % (17725)------------------------------
% 27.22/5.16 % (17725)------------------------------
% 27.22/5.17 % (17669)Instruction limit reached!
% 27.22/5.17 % (17669)------------------------------
% 27.22/5.17 % (17669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.22/5.17 % (17669)Termination reason: Unknown
% 27.22/5.17 % (17669)Termination phase: Saturation
% 27.22/5.17
% 27.22/5.17 % (17669)Memory used [KB]: 14200
% 27.22/5.17 % (17669)Time elapsed: 2.069 s
% 27.22/5.17 % (17669)Instructions burned: 4350 (million)
% 27.22/5.17 % (17669)------------------------------
% 27.22/5.17 % (17669)------------------------------
% 27.22/5.18 % (17730)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_17306 for (2964ds/593Mi)
% 27.76/5.20 % (17731)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_17306 for (2964ds/443Mi)
% 28.16/5.34 % (17720)Instruction limit reached!
% 28.16/5.34 % (17720)------------------------------
% 28.16/5.34 % (17720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.16/5.34 % (17720)Termination reason: Unknown
% 28.16/5.34 % (17720)Termination phase: Saturation
% 28.16/5.34
% 28.16/5.34 % (17720)Memory used [KB]: 10106
% 28.16/5.34 % (17720)Time elapsed: 0.510 s
% 28.16/5.34 % (17720)Instructions burned: 1378 (million)
% 28.16/5.34 % (17720)------------------------------
% 28.16/5.34 % (17720)------------------------------
% 28.16/5.35 % (17723)Instruction limit reached!
% 28.16/5.35 % (17723)------------------------------
% 28.16/5.35 % (17723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.16/5.35 % (17723)Termination reason: Unknown
% 28.16/5.35 % (17723)Termination phase: Saturation
% 28.16/5.35
% 28.16/5.35 % (17723)Memory used [KB]: 11641
% 28.16/5.35 % (17723)Time elapsed: 0.425 s
% 28.16/5.35 % (17723)Instructions burned: 908 (million)
% 28.16/5.35 % (17723)------------------------------
% 28.16/5.35 % (17723)------------------------------
% 28.16/5.36 % (17731)Instruction limit reached!
% 28.16/5.36 % (17731)------------------------------
% 28.16/5.36 % (17731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.16/5.36 % (17731)Termination reason: Unknown
% 28.16/5.36 % (17731)Termination phase: Saturation
% 28.16/5.36
% 28.16/5.36 % (17731)Memory used [KB]: 9594
% 28.16/5.36 % (17731)Time elapsed: 0.158 s
% 28.16/5.36 % (17731)Instructions burned: 443 (million)
% 28.16/5.36 % (17731)------------------------------
% 28.16/5.36 % (17731)------------------------------
% 28.16/5.36 % (17736)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_17306 for (2962ds/594Mi)
% 28.16/5.37 % (17738)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_17306 for (2962ds/327Mi)
% 28.16/5.38 % (17739)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_17306 for (2962ds/5411Mi)
% 28.65/5.42 % (17730)Instruction limit reached!
% 28.65/5.42 % (17730)------------------------------
% 28.65/5.42 % (17730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.65/5.42 % (17730)Termination reason: Unknown
% 28.65/5.42 % (17730)Termination phase: Saturation
% 28.65/5.42
% 28.65/5.42 % (17730)Memory used [KB]: 7803
% 28.65/5.42 % (17730)Time elapsed: 0.237 s
% 28.65/5.42 % (17730)Instructions burned: 594 (million)
% 28.65/5.42 % (17730)------------------------------
% 28.65/5.42 % (17730)------------------------------
% 28.65/5.44 % (17742)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_17306 for (2961ds/1762Mi)
% 29.09/5.52 % (17728)Instruction limit reached!
% 29.09/5.52 % (17728)------------------------------
% 29.09/5.52 % (17728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.09/5.52 % (17728)Termination reason: Unknown
% 29.09/5.52 % (17728)Termination phase: Saturation
% 29.09/5.52
% 29.09/5.52 % (17728)Memory used [KB]: 10874
% 29.09/5.52 % (17728)Time elapsed: 0.407 s
% 29.09/5.52 % (17728)Instructions burned: 867 (million)
% 29.09/5.52 % (17728)------------------------------
% 29.09/5.52 % (17728)------------------------------
% 29.09/5.52 % (17738)Instruction limit reached!
% 29.09/5.52 % (17738)------------------------------
% 29.09/5.52 % (17738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.09/5.52 % (17738)Termination reason: Unknown
% 29.09/5.52 % (17738)Termination phase: Saturation
% 29.09/5.52
% 29.09/5.52 % (17738)Memory used [KB]: 11257
% 29.09/5.52 % (17738)Time elapsed: 0.152 s
% 29.09/5.52 % (17738)Instructions burned: 328 (million)
% 29.09/5.52 % (17738)------------------------------
% 29.09/5.52 % (17738)------------------------------
% 29.09/5.53 % (17747)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_17306 for (2960ds/503Mi)
% 29.09/5.53 % (17746)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_17306 for (2960ds/96Mi)
% 29.09/5.55 % (17736)Instruction limit reached!
% 29.09/5.55 % (17736)------------------------------
% 29.09/5.55 % (17736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.09/5.55 % (17736)Termination reason: Unknown
% 29.09/5.55 % (17736)Termination phase: Saturation
% 29.09/5.55
% 29.09/5.55 % (17736)Memory used [KB]: 10106
% 29.09/5.55 % (17736)Time elapsed: 0.186 s
% 29.09/5.55 % (17736)Instructions burned: 595 (million)
% 29.09/5.55 % (17736)------------------------------
% 29.09/5.55 % (17736)------------------------------
% 29.09/5.56 % (17748)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_17306 for (2960ds/90Mi)
% 29.09/5.57 % (17746)Instruction limit reached!
% 29.09/5.57 % (17746)------------------------------
% 29.09/5.57 % (17746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.09/5.57 % (17746)Termination reason: Unknown
% 29.09/5.57 % (17746)Termination phase: Property scanning
% 29.09/5.57
% 29.09/5.57 % (17746)Memory used [KB]: 2814
% 29.09/5.57 % (17746)Time elapsed: 0.036 s
% 29.09/5.57 % (17746)Instructions burned: 96 (million)
% 29.09/5.57 % (17746)------------------------------
% 29.09/5.57 % (17746)------------------------------
% 29.09/5.58 % (17748)Instruction limit reached!
% 29.09/5.58 % (17748)------------------------------
% 29.09/5.58 % (17748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.09/5.58 % (17748)Termination reason: Unknown
% 29.09/5.58 % (17748)Termination phase: Property scanning
% 29.09/5.58
% 29.09/5.58 % (17748)Memory used [KB]: 2814
% 29.09/5.58 % (17748)Time elapsed: 0.026 s
% 29.09/5.58 % (17748)Instructions burned: 92 (million)
% 29.09/5.58 % (17748)------------------------------
% 29.09/5.58 % (17748)------------------------------
% 29.09/5.58 % (17749)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_17306 for (2960ds/593Mi)
% 29.09/5.59 % (17750)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_17306 for (2960ds/1512Mi)
% 30.17/5.66 % (17711)Instruction limit reached!
% 30.17/5.66 % (17711)------------------------------
% 30.17/5.66 % (17711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.17/5.66 % (17711)Termination reason: Unknown
% 30.17/5.66 % (17711)Termination phase: Saturation
% 30.17/5.66
% 30.17/5.66 % (17711)Memory used [KB]: 7931
% 30.17/5.66 % (17711)Time elapsed: 1.587 s
% 30.17/5.66 % (17711)Instructions burned: 4716 (million)
% 30.17/5.66 % (17711)------------------------------
% 30.17/5.66 % (17711)------------------------------
% 30.17/5.67 % (17753)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_17306 for (2959ds/569Mi)
% 30.33/5.76 % (17747)Instruction limit reached!
% 30.33/5.76 % (17747)------------------------------
% 30.33/5.76 % (17747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.33/5.76 % (17747)Termination reason: Unknown
% 30.33/5.76 % (17747)Termination phase: Saturation
% 30.33/5.76
% 30.33/5.76 % (17747)Memory used [KB]: 10106
% 30.33/5.76 % (17747)Time elapsed: 0.228 s
% 30.33/5.76 % (17747)Instructions burned: 503 (million)
% 30.33/5.76 % (17747)------------------------------
% 30.33/5.76 % (17747)------------------------------
% 30.33/5.77 % (17754)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_17306 for (2958ds/501Mi)
% 30.66/5.85 % (17749)Instruction limit reached!
% 30.66/5.85 % (17749)------------------------------
% 30.66/5.85 % (17749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.66/5.85 % (17749)Termination reason: Unknown
% 30.66/5.85 % (17749)Termination phase: Saturation
% 30.66/5.85
% 30.66/5.85 % (17749)Memory used [KB]: 10362
% 30.66/5.85 % (17749)Time elapsed: 0.263 s
% 30.66/5.85 % (17749)Instructions burned: 593 (million)
% 30.66/5.85 % (17749)------------------------------
% 30.66/5.85 % (17749)------------------------------
% 30.66/5.86 % (17757)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_17306 for (2957ds/562Mi)
% 30.66/5.88 % (17753)Instruction limit reached!
% 30.66/5.88 % (17753)------------------------------
% 30.66/5.88 % (17753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.66/5.88 % (17753)Termination reason: Unknown
% 30.66/5.88 % (17753)Termination phase: Saturation
% 30.66/5.88
% 30.66/5.88 % (17753)Memory used [KB]: 7803
% 30.66/5.88 % (17753)Time elapsed: 0.206 s
% 30.66/5.88 % (17753)Instructions burned: 570 (million)
% 30.66/5.88 % (17753)------------------------------
% 30.66/5.88 % (17753)------------------------------
% 30.66/5.89 % (17759)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_17306 for (2957ds/406Mi)
% 31.26/5.98 % (17754)Instruction limit reached!
% 31.26/5.98 % (17754)------------------------------
% 31.26/5.98 % (17754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.26/5.98 % (17754)Termination reason: Unknown
% 31.26/5.98 % (17754)Termination phase: Saturation
% 31.26/5.98
% 31.26/5.98 % (17754)Memory used [KB]: 11129
% 31.26/5.98 % (17754)Time elapsed: 0.210 s
% 31.26/5.98 % (17754)Instructions burned: 503 (million)
% 31.26/5.98 % (17754)------------------------------
% 31.26/5.98 % (17754)------------------------------
% 31.26/5.99 % (17761)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_17306 for (2956ds/582Mi)
% 33.61/6.08 % (17759)Instruction limit reached!
% 33.61/6.08 % (17759)------------------------------
% 33.61/6.08 % (17759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.61/6.08 % (17759)Termination reason: Unknown
% 33.61/6.08 % (17759)Termination phase: Saturation
% 33.61/6.08
% 33.61/6.08 % (17759)Memory used [KB]: 8059
% 33.61/6.08 % (17759)Time elapsed: 0.189 s
% 33.61/6.08 % (17759)Instructions burned: 406 (million)
% 33.61/6.08 % (17759)------------------------------
% 33.61/6.08 % (17759)------------------------------
% 33.61/6.09 % (17742)Instruction limit reached!
% 33.61/6.09 % (17742)------------------------------
% 33.61/6.09 % (17742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.61/6.09 % (17742)Termination reason: Unknown
% 33.61/6.09 % (17742)Termination phase: Saturation
% 33.61/6.09
% 33.61/6.09 % (17742)Memory used [KB]: 21620
% 33.61/6.09 % (17742)Time elapsed: 0.649 s
% 33.61/6.09 % (17742)Instructions burned: 1763 (million)
% 33.61/6.09 % (17742)------------------------------
% 33.61/6.09 % (17742)------------------------------
% 33.61/6.10 % (17764)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_17306 for (2955ds/456Mi)
% 33.61/6.11 % (17765)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_17306 for (2955ds/393Mi)
% 33.61/6.13 % (17757)Instruction limit reached!
% 33.61/6.13 % (17757)------------------------------
% 33.61/6.13 % (17757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.61/6.13 % (17757)Termination reason: Unknown
% 33.61/6.13 % (17757)Termination phase: Saturation
% 33.61/6.13
% 33.61/6.13 % (17757)Memory used [KB]: 9466
% 33.61/6.13 % (17757)Time elapsed: 0.263 s
% 33.61/6.13 % (17757)Instructions burned: 562 (million)
% 33.61/6.13 % (17757)------------------------------
% 33.61/6.13 % (17757)------------------------------
% 34.03/6.14 % (17766)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_17306 for (2954ds/1335Mi)
% 34.03/6.18 % (17761)Instruction limit reached!
% 34.03/6.18 % (17761)------------------------------
% 34.03/6.18 % (17761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.03/6.18 % (17761)Termination reason: Unknown
% 34.03/6.18 % (17761)Termination phase: Saturation
% 34.03/6.18
% 34.03/6.18 % (17761)Memory used [KB]: 11385
% 34.03/6.18 % (17761)Time elapsed: 0.194 s
% 34.03/6.18 % (17761)Instructions burned: 582 (million)
% 34.03/6.18 % (17761)------------------------------
% 34.03/6.18 % (17761)------------------------------
% 34.03/6.19 % (17769)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_17306 for (2954ds/3373Mi)
% 34.57/6.23 % (17750)Instruction limit reached!
% 34.57/6.23 % (17750)------------------------------
% 34.57/6.23 % (17750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.57/6.23 % (17750)Termination reason: Unknown
% 34.57/6.23 % (17750)Termination phase: Saturation
% 34.57/6.23
% 34.57/6.23 % (17750)Memory used [KB]: 16758
% 34.57/6.23 % (17750)Time elapsed: 0.641 s
% 34.57/6.23 % (17750)Instructions burned: 1513 (million)
% 34.57/6.23 % (17750)------------------------------
% 34.57/6.23 % (17750)------------------------------
% 34.57/6.26 % (17770)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_17306 for (2953ds/474Mi)
% 34.57/6.28 % (17765)Instruction limit reached!
% 34.57/6.28 % (17765)------------------------------
% 34.57/6.28 % (17765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.57/6.28 % (17765)Termination reason: Unknown
% 34.57/6.28 % (17765)Termination phase: Saturation
% 34.57/6.28
% 34.57/6.28 % (17765)Memory used [KB]: 9978
% 34.57/6.28 % (17765)Time elapsed: 0.174 s
% 34.57/6.28 % (17765)Instructions burned: 393 (million)
% 34.57/6.28 % (17765)------------------------------
% 34.57/6.28 % (17765)------------------------------
% 35.00/6.30 % (17764)Instruction limit reached!
% 35.00/6.30 % (17764)------------------------------
% 35.00/6.30 % (17764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.00/6.30 % (17764)Termination reason: Unknown
% 35.00/6.30 % (17764)Termination phase: Saturation
% 35.00/6.30
% 35.00/6.30 % (17764)Memory used [KB]: 9850
% 35.00/6.30 % (17764)Time elapsed: 0.203 s
% 35.00/6.30 % (17764)Instructions burned: 456 (million)
% 35.00/6.30 % (17764)------------------------------
% 35.00/6.30 % (17764)------------------------------
% 35.00/6.31 % (17773)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_17306 for (2953ds/157Mi)
% 35.00/6.32 % (17775)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_17306 for (2953ds/590Mi)
% 35.00/6.35 % (17773)Instruction limit reached!
% 35.00/6.35 % (17773)------------------------------
% 35.00/6.35 % (17773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.00/6.35 % (17773)Termination reason: Unknown
% 35.00/6.35 % (17773)Termination phase: Property scanning
% 35.00/6.35
% 35.00/6.35 % (17773)Memory used [KB]: 2814
% 35.00/6.35 % (17773)Time elapsed: 0.042 s
% 35.00/6.35 % (17773)Instructions burned: 158 (million)
% 35.00/6.35 % (17773)------------------------------
% 35.00/6.35 % (17773)------------------------------
% 35.00/6.36 % (17777)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_17306 for (2952ds/104Mi)
% 35.47/6.41 % (17777)Instruction limit reached!
% 35.47/6.41 % (17777)------------------------------
% 35.47/6.41 % (17777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.47/6.41 % (17777)Termination reason: Unknown
% 35.47/6.41 % (17777)Termination phase: shuffling
% 35.47/6.41
% 35.47/6.41 % (17777)Memory used [KB]: 2942
% 35.47/6.41 % (17777)Time elapsed: 0.048 s
% 35.47/6.41 % (17777)Instructions burned: 104 (million)
% 35.47/6.41 % (17777)------------------------------
% 35.47/6.41 % (17777)------------------------------
% 35.47/6.43 % (17778)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_17306 for (2951ds/414Mi)
% 35.47/6.45 % (17770)Instruction limit reached!
% 35.47/6.45 % (17770)------------------------------
% 35.47/6.45 % (17770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.47/6.45 % (17770)Termination reason: Unknown
% 35.47/6.45 % (17770)Termination phase: Saturation
% 35.47/6.45
% 35.47/6.45 % (17770)Memory used [KB]: 7803
% 35.47/6.45 % (17770)Time elapsed: 0.198 s
% 35.47/6.45 % (17770)Instructions burned: 475 (million)
% 35.47/6.45 % (17770)------------------------------
% 35.47/6.45 % (17770)------------------------------
% 35.47/6.47 % (17780)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_17306 for (2951ds/715Mi)
% 35.96/6.55 % (17775)Instruction limit reached!
% 35.96/6.55 % (17775)------------------------------
% 35.96/6.55 % (17775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.96/6.55 % (17775)Termination reason: Unknown
% 35.96/6.55 % (17775)Termination phase: Saturation
% 35.96/6.55
% 35.96/6.55 % (17775)Memory used [KB]: 8827
% 35.96/6.55 % (17775)Time elapsed: 0.203 s
% 35.96/6.55 % (17775)Instructions burned: 591 (million)
% 35.96/6.55 % (17775)------------------------------
% 35.96/6.55 % (17775)------------------------------
% 35.96/6.57 % (17783)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_17306 for (2950ds/961Mi)
% 36.38/6.61 % (17778)Instruction limit reached!
% 36.38/6.61 % (17778)------------------------------
% 36.38/6.61 % (17778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.38/6.61 % (17778)Termination reason: Unknown
% 36.38/6.61 % (17778)Termination phase: Saturation
% 36.38/6.61
% 36.38/6.61 % (17778)Memory used [KB]: 7803
% 36.38/6.61 % (17778)Time elapsed: 0.155 s
% 36.38/6.61 % (17778)Instructions burned: 415 (million)
% 36.38/6.61 % (17778)------------------------------
% 36.38/6.61 % (17778)------------------------------
% 36.38/6.64 % (17784)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_17306 for (2949ds/1213Mi)
% 36.38/6.65 % (17766)Instruction limit reached!
% 36.38/6.65 % (17766)------------------------------
% 36.38/6.65 % (17766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.38/6.65 % (17766)Termination reason: Unknown
% 36.38/6.65 % (17766)Termination phase: Saturation
% 36.38/6.65
% 36.38/6.65 % (17766)Memory used [KB]: 10874
% 36.38/6.65 % (17766)Time elapsed: 0.495 s
% 36.38/6.65 % (17766)Instructions burned: 1335 (million)
% 36.38/6.65 % (17766)------------------------------
% 36.38/6.65 % (17766)------------------------------
% 36.38/6.67 % (17786)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_17306 for (2949ds/1979Mi)
% 37.25/6.77 % (17780)Instruction limit reached!
% 37.25/6.77 % (17780)------------------------------
% 37.25/6.77 % (17780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.25/6.77 % (17780)Termination reason: Unknown
% 37.25/6.77 % (17780)Termination phase: Saturation
% 37.25/6.77
% 37.25/6.77 % (17780)Memory used [KB]: 5884
% 37.25/6.77 % (17780)Time elapsed: 0.307 s
% 37.25/6.77 % (17780)Instructions burned: 715 (million)
% 37.25/6.77 % (17780)------------------------------
% 37.25/6.77 % (17780)------------------------------
% 37.25/6.79 % (17788)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_17306 for (2948ds/481Mi)
% 37.96/6.98 % (17788)Instruction limit reached!
% 37.96/6.98 % (17788)------------------------------
% 37.96/6.98 % (17788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.96/6.98 % (17788)Termination reason: Unknown
% 37.96/6.98 % (17788)Termination phase: Saturation
% 37.96/6.98
% 37.96/6.98 % (17788)Memory used [KB]: 7803
% 37.96/6.98 % (17788)Time elapsed: 0.188 s
% 37.96/6.98 % (17788)Instructions burned: 482 (million)
% 37.96/6.98 % (17788)------------------------------
% 37.96/6.98 % (17788)------------------------------
% 37.96/7.00 % (17792)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_17306 for (2946ds/783Mi)
% 40.44/7.03 % (17783)Instruction limit reached!
% 40.44/7.03 % (17783)------------------------------
% 40.44/7.03 % (17783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.44/7.03 % (17783)Termination reason: Unknown
% 40.44/7.03 % (17783)Termination phase: Saturation
% 40.44/7.03
% 40.44/7.03 % (17783)Memory used [KB]: 10618
% 40.44/7.03 % (17783)Time elapsed: 0.457 s
% 40.44/7.03 % (17783)Instructions burned: 962 (million)
% 40.44/7.03 % (17783)------------------------------
% 40.44/7.03 % (17783)------------------------------
% 40.44/7.05 % (17793)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_17306 for (2945ds/432Mi)
% 41.54/7.21 % (17793)Instruction limit reached!
% 41.54/7.21 % (17793)------------------------------
% 41.54/7.21 % (17793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.54/7.21 % (17793)Termination reason: Unknown
% 41.54/7.21 % (17793)Termination phase: Saturation
% 41.54/7.21
% 41.54/7.21 % (17793)Memory used [KB]: 9850
% 41.54/7.21 % (17793)Time elapsed: 0.171 s
% 41.54/7.21 % (17793)Instructions burned: 435 (million)
% 41.54/7.21 % (17793)------------------------------
% 41.54/7.21 % (17793)------------------------------
% 41.54/7.23 % (17796)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_17306 for (2943ds/1670Mi)
% 41.54/7.23 % (17784)Instruction limit reached!
% 41.54/7.23 % (17784)------------------------------
% 41.54/7.23 % (17784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.54/7.23 % (17784)Termination reason: Unknown
% 41.54/7.23 % (17784)Termination phase: Saturation
% 41.54/7.23
% 41.54/7.23 % (17784)Memory used [KB]: 16119
% 41.54/7.23 % (17784)Time elapsed: 0.613 s
% 41.54/7.23 % (17784)Instructions burned: 1214 (million)
% 41.54/7.23 % (17784)------------------------------
% 41.54/7.23 % (17784)------------------------------
% 41.54/7.24 % (17797)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_17306 for (2943ds/90Mi)
% 41.54/7.28 % (17797)Instruction limit reached!
% 41.54/7.28 % (17797)------------------------------
% 41.54/7.28 % (17797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.54/7.28 % (17797)Termination reason: Unknown
% 41.54/7.28 % (17797)Termination phase: Property scanning
% 41.54/7.28
% 41.54/7.28 % (17797)Memory used [KB]: 2814
% 41.54/7.28 % (17797)Time elapsed: 0.041 s
% 41.54/7.28 % (17797)Instructions burned: 90 (million)
% 41.54/7.28 % (17797)------------------------------
% 41.54/7.28 % (17797)------------------------------
% 42.31/7.31 % (17799)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_17306 for (2943ds/346Mi)
% 42.31/7.39 % (17792)Instruction limit reached!
% 42.31/7.39 % (17792)------------------------------
% 42.31/7.39 % (17792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.31/7.39 % (17792)Termination reason: Unknown
% 42.31/7.39 % (17792)Termination phase: Saturation
% 42.31/7.39
% 42.31/7.39 % (17792)Memory used [KB]: 12537
% 42.31/7.39 % (17792)Time elapsed: 0.391 s
% 42.31/7.39 % (17792)Instructions burned: 783 (million)
% 42.31/7.39 % (17792)------------------------------
% 42.31/7.39 % (17792)------------------------------
% 42.78/7.41 % (17802)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_17306 for (2942ds/401Mi)
% 42.78/7.46 % (17799)Instruction limit reached!
% 42.78/7.46 % (17799)------------------------------
% 42.78/7.46 % (17799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.78/7.46 % (17799)Termination reason: Unknown
% 42.78/7.46 % (17799)Termination phase: Saturation
% 42.78/7.46
% 42.78/7.46 % (17799)Memory used [KB]: 7675
% 42.78/7.46 % (17799)Time elapsed: 0.127 s
% 42.78/7.46 % (17799)Instructions burned: 347 (million)
% 42.78/7.46 % (17799)------------------------------
% 42.78/7.46 % (17799)------------------------------
% 42.78/7.48 % (17803)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_17306 for (2941ds/6454Mi)
% 43.33/7.54 % (17802)Instruction limit reached!
% 43.33/7.54 % (17802)------------------------------
% 43.33/7.54 % (17802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.33/7.54 % (17802)Termination reason: Unknown
% 43.33/7.54 % (17802)Termination phase: Saturation
% 43.33/7.54
% 43.33/7.54 % (17802)Memory used [KB]: 7803
% 43.33/7.54 % (17802)Time elapsed: 0.125 s
% 43.33/7.54 % (17802)Instructions burned: 403 (million)
% 43.33/7.54 % (17802)------------------------------
% 43.33/7.54 % (17802)------------------------------
% 43.33/7.56 % (17806)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_17306 for (2940ds/283Mi)
% 43.33/7.57 % (17786)Instruction limit reached!
% 43.33/7.57 % (17786)------------------------------
% 43.33/7.57 % (17786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.33/7.57 % (17786)Termination reason: Unknown
% 43.33/7.57 % (17786)Termination phase: Saturation
% 43.33/7.57
% 43.33/7.57 % (17786)Memory used [KB]: 11001
% 43.33/7.57 % (17786)Time elapsed: 0.906 s
% 43.33/7.57 % (17786)Instructions burned: 1979 (million)
% 43.33/7.57 % (17786)------------------------------
% 43.33/7.57 % (17786)------------------------------
% 43.33/7.58 % (17808)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_17306 for (2940ds/865Mi)
% 43.85/7.68 % (17806)Instruction limit reached!
% 43.85/7.68 % (17806)------------------------------
% 43.85/7.68 % (17806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.85/7.68 % (17806)Termination reason: Unknown
% 43.85/7.68 % (17806)Termination phase: Saturation
% 43.85/7.68
% 43.85/7.68 % (17806)Memory used [KB]: 8315
% 43.85/7.68 % (17806)Time elapsed: 0.127 s
% 43.85/7.68 % (17806)Instructions burned: 283 (million)
% 43.85/7.68 % (17806)------------------------------
% 43.85/7.68 % (17806)------------------------------
% 44.29/7.70 % (17812)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_17306 for (2939ds/4528Mi)
% 44.29/7.74 % (17769)Instruction limit reached!
% 44.29/7.74 % (17769)------------------------------
% 44.29/7.74 % (17769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.29/7.74 % (17769)Termination reason: Unknown
% 44.29/7.74 % (17769)Termination phase: Saturation
% 44.29/7.74
% 44.29/7.74 % (17769)Memory used [KB]: 13944
% 44.29/7.74 % (17769)Time elapsed: 1.573 s
% 44.29/7.74 % (17769)Instructions burned: 3374 (million)
% 44.29/7.74 % (17769)------------------------------
% 44.29/7.74 % (17769)------------------------------
% 44.29/7.75 % (17814)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_17306 for (2938ds/1001Mi)
% 44.52/7.85 % (17796)Instruction limit reached!
% 44.52/7.85 % (17796)------------------------------
% 44.52/7.85 % (17796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.52/7.85 % (17796)Termination reason: Unknown
% 44.52/7.85 % (17796)Termination phase: Saturation
% 44.52/7.85
% 44.52/7.85 % (17796)Memory used [KB]: 20084
% 44.52/7.85 % (17796)Time elapsed: 0.623 s
% 44.52/7.85 % (17796)Instructions burned: 1672 (million)
% 44.52/7.85 % (17796)------------------------------
% 44.52/7.85 % (17796)------------------------------
% 44.52/7.87 % (17815)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_17306 for (2937ds/102Mi)
% 45.35/7.91 % (17739)Instruction limit reached!
% 45.35/7.91 % (17739)------------------------------
% 45.35/7.91 % (17739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.35/7.91 % (17739)Termination reason: Unknown
% 45.35/7.91 % (17739)Termination phase: Saturation
% 45.35/7.91
% 45.35/7.91 % (17739)Memory used [KB]: 17526
% 45.35/7.91 % (17739)Time elapsed: 2.548 s
% 45.35/7.91 % (17739)Instructions burned: 5412 (million)
% 45.35/7.91 % (17739)------------------------------
% 45.35/7.91 % (17739)------------------------------
% 45.35/7.91 % (17815)Instruction limit reached!
% 45.35/7.91 % (17815)------------------------------
% 45.35/7.91 % (17815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.35/7.91 % (17815)Termination reason: Unknown
% 45.35/7.91 % (17815)Termination phase: Property scanning
% 45.35/7.91
% 45.35/7.91 % (17815)Memory used [KB]: 2942
% 45.35/7.91 % (17815)Time elapsed: 0.049 s
% 45.35/7.91 % (17815)Instructions burned: 103 (million)
% 45.35/7.91 % (17815)------------------------------
% 45.35/7.91 % (17815)------------------------------
% 45.35/7.92 % (17808)Instruction limit reached!
% 45.35/7.92 % (17808)------------------------------
% 45.35/7.92 % (17808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.35/7.92 % (17808)Termination reason: Unknown
% 45.35/7.92 % (17808)Termination phase: Saturation
% 45.35/7.92
% 45.35/7.92 % (17808)Memory used [KB]: 8571
% 45.35/7.92 % (17808)Time elapsed: 0.341 s
% 45.35/7.92 % (17808)Instructions burned: 865 (million)
% 45.35/7.92 % (17808)------------------------------
% 45.35/7.92 % (17808)------------------------------
% 45.35/7.93 % (17819)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_17306 for (2937ds/952Mi)
% 45.35/7.93 % (17820)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_17306 for (2937ds/578Mi)
% 45.35/7.94 % (17821)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_17306 for (2936ds/643Mi)
% 47.29/8.07 % (17812)Refutation not found, incomplete strategy
% 47.29/8.07 % (17812)------------------------------
% 47.29/8.07 % (17812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.29/8.07 % (17812)Termination reason: Refutation not found, incomplete strategy
% 47.29/8.07
% 47.29/8.07
% 47.29/8.07 % (17812)Memory used [KB]: 3326
% 47.29/8.07 % (17812)Time elapsed: 0.369 s
% 47.29/8.07 % (17812)Instructions burned: 911 (million)
% 47.29/8.07 % (17812)------------------------------
% 47.29/8.07 % (17812)------------------------------
% 47.29/8.09 % (17824)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_17306 for (2935ds/865Mi)
% 47.95/8.12 % (17712)Instruction limit reached!
% 47.95/8.12 % (17712)------------------------------
% 47.95/8.12 % (17712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.95/8.12 % (17712)Termination reason: Unknown
% 47.95/8.12 % (17712)Termination phase: Saturation
% 47.95/8.12
% 47.95/8.12 % (17712)Memory used [KB]: 30703
% 47.95/8.12 % (17712)Time elapsed: 4.006 s
% 47.95/8.12 % (17712)Instructions burned: 8251 (million)
% 47.95/8.12 % (17712)------------------------------
% 47.95/8.12 % (17712)------------------------------
% 47.95/8.13 % (17827)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_17306 for (2934ds/1174Mi)
% 47.95/8.14 % (17821)Instruction limit reached!
% 47.95/8.14 % (17821)------------------------------
% 47.95/8.14 % (17821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.95/8.14 % (17821)Termination reason: Unknown
% 47.95/8.14 % (17821)Termination phase: Saturation
% 47.95/8.14
% 47.95/8.14 % (17821)Memory used [KB]: 7803
% 47.95/8.14 % (17821)Time elapsed: 0.206 s
% 47.95/8.14 % (17821)Instructions burned: 643 (million)
% 47.95/8.14 % (17821)------------------------------
% 47.95/8.14 % (17821)------------------------------
% 47.95/8.16 % (17828)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_17306 for (2934ds/644Mi)
% 47.95/8.16 % (17820)Instruction limit reached!
% 47.95/8.16 % (17820)------------------------------
% 47.95/8.16 % (17820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.95/8.16 % (17820)Termination reason: Unknown
% 47.95/8.16 % (17820)Termination phase: Saturation
% 47.95/8.16
% 47.95/8.16 % (17820)Memory used [KB]: 11769
% 47.95/8.16 % (17820)Time elapsed: 0.235 s
% 47.95/8.16 % (17820)Instructions burned: 580 (million)
% 47.95/8.16 % (17820)------------------------------
% 47.95/8.16 % (17820)------------------------------
% 47.95/8.18 % (17829)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_17306 for (2934ds/1201Mi)
% 47.95/8.19 % (17814)Instruction limit reached!
% 47.95/8.19 % (17814)------------------------------
% 47.95/8.19 % (17814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.95/8.19 % (17814)Termination reason: Unknown
% 47.95/8.19 % (17814)Termination phase: Saturation
% 47.95/8.19
% 47.95/8.19 % (17814)Memory used [KB]: 11129
% 47.95/8.19 % (17814)Time elapsed: 0.442 s
% 47.95/8.19 % (17814)Instructions burned: 1001 (million)
% 47.95/8.19 % (17814)------------------------------
% 47.95/8.19 % (17814)------------------------------
% 48.33/8.21 % (17831)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_17306 for (2934ds/1046Mi)
% 48.53/8.35 % (17819)Instruction limit reached!
% 48.53/8.35 % (17819)------------------------------
% 48.53/8.35 % (17819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.53/8.35 % (17819)Termination reason: Unknown
% 48.53/8.35 % (17819)Termination phase: Saturation
% 48.53/8.35
% 48.53/8.35 % (17819)Memory used [KB]: 11001
% 48.53/8.35 % (17819)Time elapsed: 0.441 s
% 48.53/8.35 % (17819)Instructions burned: 952 (million)
% 48.53/8.35 % (17819)------------------------------
% 48.53/8.35 % (17819)------------------------------
% 48.53/8.37 % (17835)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_17306 for (2932ds/222Mi)
% 48.70/8.42 % (17824)Instruction limit reached!
% 48.70/8.42 % (17824)------------------------------
% 48.70/8.42 % (17824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.70/8.42 % (17824)Termination reason: Unknown
% 48.70/8.42 % (17824)Termination phase: Saturation
% 48.70/8.42
% 48.70/8.42 % (17824)Memory used [KB]: 8059
% 48.70/8.42 % (17824)Time elapsed: 0.334 s
% 48.70/8.42 % (17824)Instructions burned: 866 (million)
% 48.70/8.42 % (17824)------------------------------
% 48.70/8.42 % (17824)------------------------------
% 48.70/8.44 % (17838)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_17306 for (2931ds/68Mi)
% 48.70/8.44 % (17828)Instruction limit reached!
% 48.70/8.44 % (17828)------------------------------
% 48.70/8.44 % (17828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.70/8.44 % (17828)Termination reason: Unknown
% 48.70/8.44 % (17828)Termination phase: Saturation
% 48.70/8.44
% 48.70/8.44 % (17828)Memory used [KB]: 8699
% 48.70/8.44 % (17828)Time elapsed: 0.282 s
% 48.70/8.44 % (17828)Instructions burned: 644 (million)
% 48.70/8.44 % (17828)------------------------------
% 48.70/8.44 % (17828)------------------------------
% 48.70/8.46 % (17835)Instruction limit reached!
% 48.70/8.46 % (17835)------------------------------
% 48.70/8.46 % (17835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.70/8.46 % (17835)Termination reason: Unknown
% 48.70/8.46 % (17835)Termination phase: Saturation
% 48.70/8.46
% 48.70/8.46 % (17835)Memory used [KB]: 7675
% 48.70/8.46 % (17835)Time elapsed: 0.089 s
% 48.70/8.46 % (17835)Instructions burned: 225 (million)
% 48.70/8.46 % (17835)------------------------------
% 48.70/8.46 % (17835)------------------------------
% 48.70/8.46 % (17841)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=454:si=on:rtra=on_0 on DTF2THF_17306 for (2931ds/454Mi)
% 48.70/8.47 % (17838)Instruction limit reached!
% 48.70/8.47 % (17838)------------------------------
% 48.70/8.47 % (17838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.70/8.47 % (17838)Termination reason: Unknown
% 48.70/8.47 % (17838)Termination phase: Property scanning
% 48.70/8.47
% 48.70/8.47 % (17838)Memory used [KB]: 2814
% 48.70/8.47 % (17838)Time elapsed: 0.033 s
% 48.70/8.47 % (17838)Instructions burned: 68 (million)
% 48.70/8.47 % (17838)------------------------------
% 48.70/8.47 % (17838)------------------------------
% 48.70/8.47 % (17842)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_17306 for (2931ds/360Mi)
% 48.70/8.49 % (17843)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_17306 for (2931ds/157Mi)
% 49.59/8.56 % (17843)Instruction limit reached!
% 49.59/8.56 % (17843)------------------------------
% 49.59/8.56 % (17843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.59/8.56 % (17843)Termination reason: Unknown
% 49.59/8.56 % (17843)Termination phase: Function definition elimination
% 49.59/8.56
% 49.59/8.56 % (17843)Memory used [KB]: 2942
% 49.59/8.56 % (17843)Time elapsed: 0.071 s
% 49.59/8.56 % (17843)Instructions burned: 160 (million)
% 49.59/8.56 % (17843)------------------------------
% 49.59/8.56 % (17843)------------------------------
% 49.59/8.57 % (17846)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_17306 for (2930ds/5061Mi)
% 49.59/8.60 % (17827)Instruction limit reached!
% 49.59/8.60 % (17827)------------------------------
% 49.59/8.60 % (17827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.59/8.60 % (17827)Termination reason: Unknown
% 49.59/8.60 % (17827)Termination phase: Saturation
% 49.59/8.60
% 49.59/8.60 % (17827)Memory used [KB]: 11001
% 49.59/8.60 % (17827)Time elapsed: 0.468 s
% 49.59/8.60 % (17827)Instructions burned: 1175 (million)
% 49.59/8.60 % (17827)------------------------------
% 49.59/8.60 % (17827)------------------------------
% 49.77/8.60 % (17831)Instruction limit reached!
% 49.77/8.60 % (17831)------------------------------
% 49.77/8.60 % (17831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.77/8.60 % (17831)Termination reason: Unknown
% 49.77/8.60 % (17831)Termination phase: Saturation
% 49.77/8.60
% 49.77/8.60 % (17831)Memory used [KB]: 7931
% 49.77/8.60 % (17831)Time elapsed: 0.393 s
% 49.77/8.60 % (17831)Instructions burned: 1046 (million)
% 49.77/8.60 % (17831)------------------------------
% 49.77/8.60 % (17831)------------------------------
% 49.77/8.62 % (17848)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_17306 for (2930ds/2401Mi)
% 49.77/8.62 % (17849)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_17306 for (2930ds/5798Mi)
% 49.77/8.62 % (17842)Instruction limit reached!
% 49.77/8.62 % (17842)------------------------------
% 49.77/8.62 % (17842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.77/8.62 % (17842)Termination reason: Unknown
% 49.77/8.62 % (17842)Termination phase: Saturation
% 49.77/8.62
% 49.77/8.62 % (17842)Memory used [KB]: 7803
% 49.77/8.62 % (17842)Time elapsed: 0.150 s
% 49.77/8.62 % (17842)Instructions burned: 361 (million)
% 49.77/8.62 % (17842)------------------------------
% 49.77/8.62 % (17842)------------------------------
% 49.77/8.63 % (17829)Instruction limit reached!
% 49.77/8.63 % (17829)------------------------------
% 49.77/8.63 % (17829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.77/8.63 % (17829)Termination reason: Unknown
% 49.77/8.63 % (17829)Termination phase: Saturation
% 49.77/8.63
% 49.77/8.63 % (17829)Memory used [KB]: 11129
% 49.77/8.63 % (17829)Time elapsed: 0.457 s
% 49.77/8.63 % (17829)Instructions burned: 1201 (million)
% 49.77/8.64 % (17829)------------------------------
% 49.77/8.64 % (17829)------------------------------
% 49.77/8.64 % (17850)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_17306 for (2929ds/346Mi)
% 49.77/8.64 % (17841)Instruction limit reached!
% 49.77/8.64 % (17841)------------------------------
% 49.77/8.64 % (17841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.77/8.64 % (17841)Termination reason: Unknown
% 49.77/8.64 % (17841)Termination phase: Saturation
% 49.77/8.64
% 49.77/8.64 % (17841)Memory used [KB]: 12281
% 49.77/8.64 % (17841)Time elapsed: 0.182 s
% 49.77/8.64 % (17841)Instructions burned: 454 (million)
% 49.77/8.64 % (17841)------------------------------
% 49.77/8.64 % (17841)------------------------------
% 49.77/8.65 % (17851)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_17306 for (2929ds/1321Mi)
% 49.77/8.65 % (17852)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_17306 for (2929ds/1312Mi)
% 51.59/8.77 % (17850)Instruction limit reached!
% 51.59/8.77 % (17850)------------------------------
% 51.59/8.77 % (17850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.59/8.77 % (17850)Termination reason: Unknown
% 51.59/8.77 % (17850)Termination phase: Saturation
% 51.59/8.77
% 51.59/8.77 % (17850)Memory used [KB]: 7675
% 51.59/8.77 % (17850)Time elapsed: 0.133 s
% 51.59/8.77 % (17850)Instructions burned: 346 (million)
% 51.59/8.77 % (17850)------------------------------
% 51.59/8.77 % (17850)------------------------------
% 51.59/8.79 % (17853)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_17306 for (2928ds/672Mi)
% 54.34/9.07 % (17853)Instruction limit reached!
% 54.34/9.07 % (17853)------------------------------
% 54.34/9.07 % (17853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.34/9.07 % (17853)Termination reason: Unknown
% 54.34/9.07 % (17853)Termination phase: Saturation
% 54.34/9.07
% 54.34/9.07 % (17853)Memory used [KB]: 11769
% 54.34/9.07 % (17853)Time elapsed: 0.291 s
% 54.34/9.07 % (17853)Instructions burned: 672 (million)
% 54.34/9.07 % (17853)------------------------------
% 54.34/9.07 % (17853)------------------------------
% 54.34/9.09 % (17857)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_17306 for (2925ds/1897Mi)
% 55.04/9.14 % (17852)Instruction limit reached!
% 55.04/9.14 % (17852)------------------------------
% 55.04/9.14 % (17852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.04/9.14 % (17852)Termination reason: Unknown
% 55.04/9.14 % (17852)Termination phase: Saturation
% 55.04/9.14
% 55.04/9.14 % (17852)Memory used [KB]: 18166
% 55.04/9.14 % (17852)Time elapsed: 0.491 s
% 55.04/9.14 % (17852)Instructions burned: 1312 (million)
% 55.04/9.14 % (17852)------------------------------
% 55.04/9.14 % (17852)------------------------------
% 55.04/9.15 % (17859)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_17306 for (2924ds/1202Mi)
% 55.41/9.25 % (17851)Instruction limit reached!
% 55.41/9.25 % (17851)------------------------------
% 55.41/9.25 % (17851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.41/9.25 % (17851)Termination reason: Unknown
% 55.41/9.25 % (17851)Termination phase: Saturation
% 55.41/9.25
% 55.41/9.25 % (17851)Memory used [KB]: 8955
% 55.41/9.25 % (17851)Time elapsed: 0.603 s
% 55.41/9.25 % (17851)Instructions burned: 1322 (million)
% 55.41/9.25 % (17851)------------------------------
% 55.41/9.25 % (17851)------------------------------
% 55.41/9.27 % (17860)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_17306 for (2923ds/1493Mi)
% 57.09/9.68 % (17859)Instruction limit reached!
% 57.09/9.68 % (17859)------------------------------
% 57.09/9.68 % (17859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.09/9.68 % (17859)Termination reason: Unknown
% 57.09/9.68 % (17859)Termination phase: Saturation
% 57.09/9.68
% 57.09/9.68 % (17859)Memory used [KB]: 10106
% 57.09/9.68 % (17859)Time elapsed: 0.527 s
% 57.09/9.68 % (17859)Instructions burned: 1202 (million)
% 57.09/9.68 % (17859)------------------------------
% 57.09/9.68 % (17859)------------------------------
% 58.03/9.70 % (17865)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_17306 for (2919ds/7679Mi)
% 58.03/9.71 % (17848)Instruction limit reached!
% 58.03/9.71 % (17848)------------------------------
% 58.03/9.71 % (17848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.03/9.71 % (17848)Termination reason: Unknown
% 58.03/9.71 % (17848)Termination phase: Saturation
% 58.03/9.71
% 58.03/9.71 % (17848)Memory used [KB]: 9466
% 58.03/9.71 % (17848)Time elapsed: 1.092 s
% 58.03/9.71 % (17848)Instructions burned: 2402 (million)
% 58.03/9.71 % (17848)------------------------------
% 58.03/9.71 % (17848)------------------------------
% 58.03/9.73 % (17866)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_17306 for (2919ds/340Mi)
% 58.35/9.82 % (17860)Instruction limit reached!
% 58.35/9.82 % (17860)------------------------------
% 58.35/9.82 % (17860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.35/9.82 % (17860)Termination reason: Unknown
% 58.35/9.82 % (17860)Termination phase: Saturation
% 58.35/9.82
% 58.35/9.82 % (17860)Memory used [KB]: 8315
% 58.35/9.82 % (17860)Time elapsed: 0.549 s
% 58.35/9.82 % (17860)Instructions burned: 1493 (million)
% 58.35/9.82 % (17860)------------------------------
% 58.35/9.82 % (17860)------------------------------
% 58.35/9.84 % (17868)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_17306 for (2917ds/3672Mi)
% 58.35/9.85 % (17866)Instruction limit reached!
% 58.35/9.85 % (17866)------------------------------
% 58.35/9.85 % (17866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.35/9.85 % (17866)Termination reason: Unknown
% 58.35/9.85 % (17866)Termination phase: Saturation
% 58.35/9.85
% 58.35/9.85 % (17866)Memory used [KB]: 11129
% 58.35/9.85 % (17866)Time elapsed: 0.121 s
% 58.35/9.85 % (17866)Instructions burned: 342 (million)
% 58.35/9.85 % (17866)------------------------------
% 58.35/9.85 % (17866)------------------------------
% 58.35/9.86 % (17869)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_17306 for (2917ds/1535Mi)
% 59.34/9.95 % (17857)Instruction limit reached!
% 59.34/9.95 % (17857)------------------------------
% 59.34/9.95 % (17857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.34/9.95 % (17857)Termination reason: Unknown
% 59.34/9.95 % (17857)Termination phase: Saturation
% 59.34/9.95
% 59.34/9.95 % (17857)Memory used [KB]: 14328
% 59.34/9.95 % (17857)Time elapsed: 0.859 s
% 59.34/9.95 % (17857)Instructions burned: 1898 (million)
% 59.34/9.95 % (17857)------------------------------
% 59.34/9.95 % (17857)------------------------------
% 59.34/9.97 % (17870)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_17306 for (2916ds/4637Mi)
% 62.56/10.29 % (17846)Instruction limit reached!
% 62.56/10.29 % (17846)------------------------------
% 62.56/10.29 % (17846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.56/10.29 % (17846)Termination reason: Unknown
% 62.56/10.29 % (17846)Termination phase: Saturation
% 62.56/10.29
% 62.56/10.29 % (17846)Memory used [KB]: 8059
% 62.56/10.29 % (17846)Time elapsed: 1.716 s
% 62.56/10.29 % (17846)Instructions burned: 5062 (million)
% 62.56/10.29 % (17846)------------------------------
% 62.56/10.29 % (17846)------------------------------
% 63.25/10.30 % (17874)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_17306 for (2913ds/3174Mi)
% 63.25/10.39 % (17803)Instruction limit reached!
% 63.25/10.39 % (17803)------------------------------
% 63.25/10.39 % (17803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.25/10.39 % (17803)Termination reason: Unknown
% 63.25/10.39 % (17803)Termination phase: Saturation
% 63.25/10.39
% 63.25/10.39 % (17803)Memory used [KB]: 14711
% 63.25/10.39 % (17803)Time elapsed: 2.915 s
% 63.25/10.39 % (17803)Instructions burned: 6454 (million)
% 63.25/10.39 % (17803)------------------------------
% 63.25/10.39 % (17803)------------------------------
% 63.87/10.41 % (17877)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_17306 for (2912ds/307Mi)
% 63.87/10.43 % (17869)Instruction limit reached!
% 63.87/10.43 % (17869)------------------------------
% 63.87/10.43 % (17869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.87/10.43 % (17869)Termination reason: Unknown
% 63.87/10.43 % (17869)Termination phase: Saturation
% 63.87/10.43
% 63.87/10.43 % (17869)Memory used [KB]: 15479
% 63.87/10.43 % (17869)Time elapsed: 0.577 s
% 63.87/10.43 % (17869)Instructions burned: 1535 (million)
% 63.87/10.43 % (17869)------------------------------
% 63.87/10.43 % (17869)------------------------------
% 63.87/10.46 % (17878)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_17306 for (2911ds/3619Mi)
% 64.31/10.54 % (17877)Instruction limit reached!
% 64.31/10.54 % (17877)------------------------------
% 64.31/10.54 % (17877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.31/10.54 % (17877)Termination reason: Unknown
% 64.31/10.54 % (17877)Termination phase: Saturation
% 64.31/10.54
% 64.31/10.54 % (17877)Memory used [KB]: 7675
% 64.31/10.54 % (17877)Time elapsed: 0.131 s
% 64.31/10.54 % (17877)Instructions burned: 308 (million)
% 64.31/10.54 % (17877)------------------------------
% 64.31/10.54 % (17877)------------------------------
% 64.31/10.56 % (17879)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_17306 for (2910ds/2325Mi)
% 69.09/11.15 % (17849)Instruction limit reached!
% 69.09/11.15 % (17849)------------------------------
% 69.09/11.15 % (17849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.09/11.15 % (17849)Termination reason: Unknown
% 69.09/11.15 % (17849)Termination phase: Saturation
% 69.09/11.15
% 69.09/11.15 % (17849)Memory used [KB]: 13688
% 69.09/11.15 % (17849)Time elapsed: 2.535 s
% 69.09/11.15 % (17849)Instructions burned: 5799 (million)
% 69.09/11.15 % (17849)------------------------------
% 69.09/11.15 % (17849)------------------------------
% 69.09/11.16 % (17881)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_17306 for (2904ds/2341Mi)
% 71.30/11.59 % (17879)Refutation not found, non-redundant clauses discarded% (17879)------------------------------
% 71.30/11.59 % (17879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.30/11.59 % (17879)Termination reason: Refutation not found, non-redundant clauses discarded
% 71.30/11.59
% 71.30/11.59 % (17879)Memory used [KB]: 17910
% 71.30/11.59 % (17879)Time elapsed: 1.032 s
% 71.30/11.59 % (17879)Instructions burned: 2121 (million)
% 71.30/11.59 % (17879)------------------------------
% 71.30/11.59 % (17879)------------------------------
% 71.90/11.60 % (17889)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_17306 for (2900ds/7257Mi)
% 71.90/11.62 % (17868)Instruction limit reached!
% 71.90/11.62 % (17868)------------------------------
% 71.90/11.62 % (17868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.90/11.62 % (17868)Termination reason: Unknown
% 71.90/11.62 % (17868)Termination phase: Saturation
% 71.90/11.62
% 71.90/11.62 % (17868)Memory used [KB]: 14072
% 71.90/11.62 % (17868)Time elapsed: 1.799 s
% 71.90/11.62 % (17868)Instructions burned: 3672 (million)
% 71.90/11.62 % (17868)------------------------------
% 71.90/11.62 % (17868)------------------------------
% 71.90/11.63 % (17890)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_17306 for (2899ds/3710Mi)
% 72.73/11.83 % (17874)Instruction limit reached!
% 72.73/11.83 % (17874)------------------------------
% 72.73/11.83 % (17874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.73/11.83 % (17874)Termination reason: Unknown
% 72.73/11.83 % (17874)Termination phase: Saturation
% 72.73/11.83
% 72.73/11.83 % (17874)Memory used [KB]: 19445
% 72.73/11.83 % (17874)Time elapsed: 1.543 s
% 72.73/11.83 % (17874)Instructions burned: 3174 (million)
% 72.73/11.83 % (17874)------------------------------
% 72.73/11.83 % (17874)------------------------------
% 72.73/11.85 % (17893)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_17306 for (2897ds/326Mi)
% 73.08/11.95 % (17878)Instruction limit reached!
% 73.08/11.95 % (17878)------------------------------
% 73.08/11.95 % (17878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.08/11.95 % (17878)Termination reason: Unknown
% 73.08/11.95 % (17878)Termination phase: Saturation
% 73.08/11.95
% 73.08/11.95 % (17878)Memory used [KB]: 24050
% 73.08/11.95 % (17878)Time elapsed: 1.514 s
% 73.08/11.95 % (17878)Instructions burned: 3620 (million)
% 73.08/11.95 % (17878)------------------------------
% 73.08/11.95 % (17878)------------------------------
% 73.08/11.97 % (17895)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_17306 for (2896ds/1100Mi)
% 73.08/11.97 % (17893)Instruction limit reached!
% 73.08/11.97 % (17893)------------------------------
% 73.08/11.97 % (17893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.08/11.97 % (17893)Termination reason: Unknown
% 73.08/11.97 % (17893)Termination phase: Saturation
% 73.08/11.97
% 73.08/11.97 % (17893)Memory used [KB]: 8571
% 73.08/11.97 % (17893)Time elapsed: 0.127 s
% 73.08/11.97 % (17893)Instructions burned: 328 (million)
% 73.08/11.97 % (17893)------------------------------
% 73.08/11.97 % (17893)------------------------------
% 73.08/11.98 % (17896)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_17306 for (2896ds/406Mi)
% 75.35/12.12 % (17870)Instruction limit reached!
% 75.35/12.12 % (17870)------------------------------
% 75.35/12.12 % (17870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.35/12.12 % (17870)Termination reason: Unknown
% 75.35/12.12 % (17870)Termination phase: Saturation
% 75.35/12.12
% 75.35/12.12 % (17870)Memory used [KB]: 12281
% 75.35/12.12 % (17870)Time elapsed: 2.169 s
% 75.35/12.12 % (17870)Instructions burned: 4637 (million)
% 75.35/12.12 % (17870)------------------------------
% 75.35/12.12 % (17870)------------------------------
% 75.35/12.13 % (17881)Instruction limit reached!
% 75.35/12.13 % (17881)------------------------------
% 75.35/12.13 % (17881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.35/12.13 % (17881)Termination reason: Unknown
% 75.35/12.13 % (17881)Termination phase: Saturation
% 75.35/12.13
% 75.35/12.13 % (17881)Memory used [KB]: 11897
% 75.35/12.13 % (17881)Time elapsed: 0.969 s
% 75.35/12.13 % (17881)Instructions burned: 2341 (million)
% 75.35/12.13 % (17881)------------------------------
% 75.35/12.13 % (17881)------------------------------
% 75.35/12.14 % (17899)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_17306 for (2894ds/1871Mi)
% 76.07/12.15 % (17900)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_17306 for (2894ds/1194Mi)
% 76.07/12.18 % (17896)Instruction limit reached!
% 76.07/12.18 % (17896)------------------------------
% 76.07/12.18 % (17896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.07/12.18 % (17896)Termination reason: Unknown
% 76.07/12.18 % (17896)Termination phase: Saturation
% 76.07/12.18
% 76.07/12.18 % (17896)Memory used [KB]: 7931
% 76.07/12.18 % (17896)Time elapsed: 0.188 s
% 76.07/12.18 % (17896)Instructions burned: 407 (million)
% 76.07/12.18 % (17896)------------------------------
% 76.07/12.18 % (17896)------------------------------
% 76.37/12.20 % (17901)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_17306 for (2894ds/474Mi)
% 76.77/12.39 % (17901)Instruction limit reached!
% 76.77/12.39 % (17901)------------------------------
% 76.77/12.39 % (17901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.77/12.39 % (17901)Termination reason: Unknown
% 76.77/12.39 % (17901)Termination phase: Saturation
% 76.77/12.39
% 76.77/12.39 % (17901)Memory used [KB]: 7803
% 76.77/12.39 % (17901)Time elapsed: 0.190 s
% 76.77/12.39 % (17901)Instructions burned: 475 (million)
% 76.77/12.39 % (17901)------------------------------
% 76.77/12.39 % (17901)------------------------------
% 77.37/12.41 % (17903)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_17306 for (2892ds/3115Mi)
% 77.77/12.52 % (17895)Instruction limit reached!
% 77.77/12.52 % (17895)------------------------------
% 77.77/12.52 % (17895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.77/12.52 % (17895)Termination reason: Unknown
% 77.77/12.52 % (17895)Termination phase: Saturation
% 77.77/12.52
% 77.77/12.52 % (17895)Memory used [KB]: 17270
% 77.77/12.52 % (17895)Time elapsed: 0.552 s
% 77.77/12.52 % (17895)Instructions burned: 1100 (million)
% 77.77/12.52 % (17895)------------------------------
% 77.77/12.52 % (17895)------------------------------
% 77.77/12.54 % (17906)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_17306 for (2890ds/831Mi)
% 78.41/12.71 % (17900)Instruction limit reached!
% 78.41/12.71 % (17900)------------------------------
% 78.41/12.71 % (17900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.41/12.71 % (17900)Termination reason: Unknown
% 78.41/12.71 % (17900)Termination phase: Saturation
% 78.41/12.71
% 78.41/12.71 % (17900)Memory used [KB]: 13304
% 78.41/12.71 % (17900)Time elapsed: 0.559 s
% 78.41/12.71 % (17900)Instructions burned: 1195 (million)
% 78.41/12.71 % (17900)------------------------------
% 78.41/12.71 % (17900)------------------------------
% 78.41/12.73 % (17910)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_17306 for (2888ds/1188Mi)
% 79.55/12.92 % (17890)Instruction limit reached!
% 79.55/12.92 % (17890)------------------------------
% 79.55/12.92 % (17890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.55/12.92 % (17890)Termination reason: Unknown
% 79.55/12.92 % (17890)Termination phase: Saturation
% 79.55/12.92
% 79.55/12.92 % (17890)Memory used [KB]: 21364
% 79.55/12.92 % (17890)Time elapsed: 1.251 s
% 79.55/12.92 % (17890)Instructions burned: 3711 (million)
% 79.55/12.92 % (17890)------------------------------
% 79.55/12.92 % (17890)------------------------------
% 79.55/12.92 % (17906)Instruction limit reached!
% 79.55/12.92 % (17906)------------------------------
% 79.55/12.92 % (17906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.55/12.92 % (17906)Termination reason: Unknown
% 79.55/12.92 % (17906)Termination phase: Saturation
% 79.55/12.92
% 79.55/12.92 % (17906)Memory used [KB]: 10618
% 79.55/12.92 % (17906)Time elapsed: 0.380 s
% 79.55/12.92 % (17906)Instructions burned: 832 (million)
% 79.55/12.92 % (17906)------------------------------
% 79.55/12.92 % (17906)------------------------------
% 79.55/12.93 % (17913)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_17306 for (2886ds/1516Mi)
% 79.55/12.94 % (17912)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_17306 for (2886ds/2868Mi)
% 79.55/12.99 % (17899)Instruction limit reached!
% 79.55/12.99 % (17899)------------------------------
% 79.55/12.99 % (17899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.55/12.99 % (17899)Termination reason: Unknown
% 79.55/12.99 % (17899)Termination phase: Saturation
% 79.55/12.99
% 79.55/12.99 % (17899)Memory used [KB]: 21108
% 79.55/12.99 % (17899)Time elapsed: 0.859 s
% 79.55/12.99 % (17899)Instructions burned: 1871 (million)
% 79.55/12.99 % (17899)------------------------------
% 79.55/12.99 % (17899)------------------------------
% 79.55/13.01 % (17915)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_17306 for (2886ds/2321Mi)
% 83.37/13.21 % (17910)Instruction limit reached!
% 83.37/13.21 % (17910)------------------------------
% 83.37/13.21 % (17910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.37/13.21 % (17910)Termination reason: Unknown
% 83.37/13.21 % (17910)Termination phase: Saturation
% 83.37/13.21
% 83.37/13.21 % (17910)Memory used [KB]: 18549
% 83.37/13.21 % (17910)Time elapsed: 0.485 s
% 83.37/13.21 % (17910)Instructions burned: 1189 (million)
% 83.37/13.21 % (17910)------------------------------
% 83.37/13.21 % (17910)------------------------------
% 83.37/13.23 % (17917)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_17306 for (2883ds/2812Mi)
% 83.37/13.24 % (17865)Instruction limit reached!
% 83.37/13.24 % (17865)------------------------------
% 83.37/13.24 % (17865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.37/13.24 % (17865)Termination reason: Unknown
% 83.37/13.24 % (17865)Termination phase: Saturation
% 83.37/13.24
% 83.37/13.24 % (17865)Memory used [KB]: 18805
% 83.37/13.24 % (17865)Time elapsed: 3.560 s
% 83.37/13.24 % (17865)Instructions burned: 7679 (million)
% 83.37/13.24 % (17865)------------------------------
% 83.37/13.24 % (17865)------------------------------
% 83.37/13.26 % (17918)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_17306 for (2883ds/4604Mi)
% 84.96/13.51 % (17903)Instruction limit reached!
% 84.96/13.51 % (17903)------------------------------
% 84.96/13.51 % (17903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 84.96/13.51 % (17903)Termination reason: Unknown
% 84.96/13.51 % (17903)Termination phase: Saturation
% 84.96/13.51
% 84.96/13.51 % (17903)Memory used [KB]: 19573
% 84.96/13.51 % (17903)Time elapsed: 1.103 s
% 84.96/13.51 % (17903)Instructions burned: 3115 (million)
% 84.96/13.51 % (17903)------------------------------
% 84.96/13.51 % (17903)------------------------------
% 84.96/13.53 % (17920)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_17306 for (2880ds/2678Mi)
% 85.38/13.61 % (17913)Instruction limit reached!
% 85.38/13.61 % (17913)------------------------------
% 85.38/13.61 % (17913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.38/13.61 % (17913)Termination reason: Unknown
% 85.38/13.61 % (17913)Termination phase: Saturation
% 85.38/13.61
% 85.38/13.61 % (17913)Memory used [KB]: 12920
% 85.38/13.61 % (17913)Time elapsed: 0.678 s
% 85.38/13.61 % (17913)Instructions burned: 1516 (million)
% 85.38/13.61 % (17913)------------------------------
% 85.38/13.61 % (17913)------------------------------
% 85.38/13.63 % (17923)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_17306 for (2879ds/643Mi)
% 86.00/13.82 % (17915)Instruction limit reached!
% 86.00/13.82 % (17915)------------------------------
% 86.00/13.82 % (17915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 86.00/13.82 % (17915)Termination reason: Unknown
% 86.00/13.82 % (17915)Termination phase: Saturation
% 86.00/13.82
% 86.00/13.82 % (17915)Memory used [KB]: 18677
% 86.00/13.82 % (17915)Time elapsed: 0.803 s
% 86.00/13.82 % (17915)Instructions burned: 2322 (million)
% 86.00/13.82 % (17915)------------------------------
% 86.00/13.82 % (17915)------------------------------
% 86.00/13.84 % (17926)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_17306 for (2877ds/458Mi)
% 86.00/13.85 % (17923)Instruction limit reached!
% 86.00/13.85 % (17923)------------------------------
% 86.00/13.85 % (17923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 86.00/13.85 % (17923)Termination reason: Unknown
% 86.00/13.85 % (17923)Termination phase: Saturation
% 86.00/13.85
% 86.00/13.85 % (17923)Memory used [KB]: 7931
% 86.00/13.85 % (17923)Time elapsed: 0.228 s
% 86.00/13.85 % (17923)Instructions burned: 643 (million)
% 86.00/13.85 % (17923)------------------------------
% 86.00/13.85 % (17923)------------------------------
% 86.00/13.86 % (17928)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_17306 for (2877ds/2546Mi)
% 86.49/13.94 % (17912)Instruction limit reached!
% 86.49/13.94 % (17912)------------------------------
% 86.49/13.94 % (17912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 86.49/13.94 % (17912)Termination reason: Unknown
% 86.49/13.94 % (17912)Termination phase: Saturation
% 86.49/13.94
% 86.49/13.94 % (17912)Memory used [KB]: 7931
% 86.49/13.94 % (17912)Time elapsed: 1.008 s
% 86.49/13.94 % (17912)Instructions burned: 2869 (million)
% 86.49/13.94 % (17912)------------------------------
% 86.49/13.94 % (17912)------------------------------
% 86.49/13.96 % (17931)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_17306 for (2876ds/1432Mi)
% 86.49/14.02 % (17926)Instruction limit reached!
% 86.49/14.02 % (17926)------------------------------
% 86.49/14.02 % (17926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 86.49/14.02 % (17926)Termination reason: Unknown
% 86.49/14.02 % (17926)Termination phase: Saturation
% 86.49/14.02
% 86.49/14.02 % (17926)Memory used [KB]: 7803
% 86.49/14.02 % (17926)Time elapsed: 0.180 s
% 86.49/14.02 % (17926)Instructions burned: 459 (million)
% 86.49/14.02 % (17926)------------------------------
% 86.49/14.02 % (17926)------------------------------
% 89.17/14.04 % (17932)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_17306 for (2875ds/386Mi)
% 89.78/14.15 % (17932)Instruction limit reached!
% 89.78/14.15 % (17932)------------------------------
% 89.78/14.15 % (17932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 89.78/14.15 % (17932)Termination reason: Unknown
% 89.78/14.15 % (17932)Termination phase: Saturation
% 89.78/14.15
% 89.78/14.15 % (17932)Memory used [KB]: 7803
% 89.78/14.15 % (17932)Time elapsed: 0.118 s
% 89.78/14.15 % (17932)Instructions burned: 388 (million)
% 89.78/14.15 % (17932)------------------------------
% 89.78/14.15 % (17932)------------------------------
% 89.78/14.16 % (17935)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_17306 for (2874ds/360Mi)
% 90.33/14.26 % (17935)Instruction limit reached!
% 90.33/14.26 % (17935)------------------------------
% 90.33/14.26 % (17935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.33/14.26 % (17935)Termination reason: Unknown
% 90.33/14.26 % (17935)Termination phase: Saturation
% 90.33/14.26
% 90.33/14.26 % (17935)Memory used [KB]: 7803
% 90.33/14.26 % (17935)Time elapsed: 0.100 s
% 90.33/14.26 % (17935)Instructions burned: 361 (million)
% 90.33/14.26 % (17935)------------------------------
% 90.33/14.26 % (17935)------------------------------
% 90.33/14.27 % (17936)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_17306 for (2873ds/5446Mi)
% 91.63/14.46 % (17920)Instruction limit reached!
% 91.63/14.46 % (17920)------------------------------
% 91.63/14.46 % (17920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.63/14.46 % (17920)Termination reason: Unknown
% 91.63/14.46 % (17920)Termination phase: Saturation
% 91.63/14.46
% 91.63/14.46 % (17920)Memory used [KB]: 33389
% 91.63/14.46 % (17920)Time elapsed: 0.928 s
% 91.63/14.46 % (17920)Instructions burned: 2678 (million)
% 91.63/14.46 % (17920)------------------------------
% 91.63/14.46 % (17920)------------------------------
% 91.63/14.48 % (17931)Instruction limit reached!
% 91.63/14.48 % (17931)------------------------------
% 91.63/14.48 % (17931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.63/14.48 % (17931)Termination reason: Unknown
% 91.63/14.48 % (17931)Termination phase: Saturation
% 91.63/14.48
% 91.63/14.48 % (17931)Memory used [KB]: 14583
% 91.63/14.48 % (17931)Time elapsed: 0.527 s
% 91.63/14.48 % (17931)Instructions burned: 1433 (million)
% 91.63/14.48 % (17931)------------------------------
% 91.63/14.48 % (17931)------------------------------
% 91.63/14.48 % (17937)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_17306 for (2871ds/2573Mi)
% 92.20/14.50 % (17938)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=2655:si=on:rtra=on_0 on DTF2THF_17306 for (2871ds/2655Mi)
% 92.20/14.55 % (17917)Instruction limit reached!
% 92.20/14.55 % (17917)------------------------------
% 92.20/14.55 % (17917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 92.20/14.55 % (17917)Termination reason: Unknown
% 92.20/14.55 % (17917)Termination phase: Saturation
% 92.20/14.55
% 92.20/14.55 % (17917)Memory used [KB]: 13816
% 92.20/14.55 % (17917)Time elapsed: 1.325 s
% 92.20/14.55 % (17917)Instructions burned: 2813 (million)
% 92.20/14.55 % (17917)------------------------------
% 92.20/14.55 % (17917)------------------------------
% 92.20/14.57 % (17939)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_17306 for (2870ds/2781Mi)
% 93.19/14.86 % (17889)Instruction limit reached!
% 93.19/14.86 % (17889)------------------------------
% 93.19/14.86 % (17889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 93.19/14.86 % (17889)Termination reason: Unknown
% 93.19/14.86 % (17889)Termination phase: Saturation
% 93.19/14.86
% 93.19/14.86 % (17889)Memory used [KB]: 11513
% 93.19/14.86 % (17889)Time elapsed: 3.260 s
% 93.19/14.86 % (17889)Instructions burned: 7258 (million)
% 93.19/14.86 % (17889)------------------------------
% 93.19/14.86 % (17889)------------------------------
% 93.19/14.88 % (17944)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_17306 for (2867ds/307Mi)
% 93.45/14.97 % (17928)Instruction limit reached!
% 93.45/14.97 % (17928)------------------------------
% 93.45/14.97 % (17928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 93.45/14.97 % (17928)Termination reason: Unknown
% 93.45/14.97 % (17928)Termination phase: Saturation
% 93.45/14.97
% 93.45/14.97 % (17928)Memory used [KB]: 10874
% 93.45/14.97 % (17928)Time elapsed: 1.106 s
% 93.45/14.97 % (17928)Instructions burned: 2546 (million)
% 93.45/14.97 % (17928)------------------------------
% 93.45/14.97 % (17928)------------------------------
% 93.45/14.98 % (17946)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_17306 for (2866ds/1548Mi)
% 93.45/15.01 % (17944)Instruction limit reached!
% 93.45/15.01 % (17944)------------------------------
% 93.45/15.01 % (17944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 93.45/15.01 % (17944)Termination reason: Unknown
% 93.45/15.01 % (17944)Termination phase: Saturation
% 93.45/15.01
% 93.45/15.01 % (17944)Memory used [KB]: 7675
% 93.45/15.01 % (17944)Time elapsed: 0.130 s
% 93.45/15.01 % (17944)Instructions burned: 307 (million)
% 93.45/15.01 % (17944)------------------------------
% 93.45/15.01 % (17944)------------------------------
% 95.72/15.02 % (17947)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on DTF2THF_17306 for (2866ds/5214Mi)
% 98.02/15.43 % (17918)Instruction limit reached!
% 98.02/15.43 % (17918)------------------------------
% 98.02/15.43 % (17918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.02/15.43 % (17918)Termination reason: Unknown
% 98.02/15.43 % (17918)Termination phase: Saturation
% 98.02/15.43
% 98.02/15.43 % (17918)Memory used [KB]: 14711
% 98.02/15.43 % (17918)Time elapsed: 2.174 s
% 98.02/15.43 % (17918)Instructions burned: 4604 (million)
% 98.02/15.43 % (17918)------------------------------
% 98.02/15.43 % (17918)------------------------------
% 98.02/15.45 % (17952)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_17306 for (2861ds/3201Mi)
% 98.02/15.48 % (17937)Instruction limit reached!
% 98.02/15.48 % (17937)------------------------------
% 98.02/15.48 % (17937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.02/15.48 % (17937)Termination reason: Unknown
% 98.02/15.48 % (17937)Termination phase: Saturation
% 98.02/15.48
% 98.02/15.48 % (17937)Memory used [KB]: 21492
% 98.02/15.48 % (17937)Time elapsed: 1.020 s
% 98.02/15.48 % (17937)Instructions burned: 2573 (million)
% 98.02/15.48 % (17937)------------------------------
% 98.02/15.48 % (17937)------------------------------
% 98.55/15.50 % (17954)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=454:si=on:rtra=on_0 on DTF2THF_17306 for (2861ds/454Mi)
% 98.55/15.54 % (17938)Instruction limit reached!
% 98.55/15.54 % (17938)------------------------------
% 98.55/15.54 % (17938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.55/15.54 % (17938)Termination reason: Unknown
% 98.55/15.54 % (17938)Termination phase: Saturation
% 98.55/15.54
% 98.55/15.54 % (17938)Memory used [KB]: 6268
% 98.55/15.54 % (17938)Time elapsed: 1.040 s
% 98.55/15.54 % (17938)Instructions burned: 2655 (million)
% 98.55/15.54 % (17938)------------------------------
% 98.55/15.54 % (17938)------------------------------
% 98.55/15.55 % (17955)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on DTF2THF_17306 for (2860ds/3049Mi)
% 98.91/15.65 % (17954)Instruction limit reached!
% 98.91/15.65 % (17954)------------------------------
% 98.91/15.65 % (17954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.91/15.65 % (17954)Termination reason: Unknown
% 98.91/15.65 % (17954)Termination phase: Saturation
% 98.91/15.65
% 98.91/15.65 % (17954)Memory used [KB]: 12281
% 98.91/15.65 % (17954)Time elapsed: 0.151 s
% 98.91/15.65 % (17954)Instructions burned: 455 (million)
% 98.91/15.65 % (17954)------------------------------
% 98.91/15.65 % (17954)------------------------------
% 98.91/15.66 % (17957)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on DTF2THF_17306 for (2859ds/7311Mi)
% 99.39/15.70 % (17946)Instruction limit reached!
% 99.39/15.70 % (17946)------------------------------
% 99.39/15.70 % (17946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 99.39/15.70 % (17946)Termination reason: Unknown
% 99.39/15.70 % (17946)Termination phase: Saturation
% 99.39/15.70
% 99.39/15.70 % (17946)Memory used [KB]: 10874
% 99.39/15.70 % (17946)Time elapsed: 0.728 s
% 99.39/15.70 % (17946)Instructions burned: 1550 (million)
% 99.39/15.70 % (17946)------------------------------
% 99.39/15.70 % (17946)------------------------------
% 99.39/15.72 % (17958)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=6804:si=on:rtra=on_0 on DTF2THF_17306 for (2859ds/6804Mi)
% 99.60/15.83 % (17939)Instruction limit reached!
% 99.60/15.83 % (17939)------------------------------
% 99.60/15.83 % (17939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 99.60/15.83 % (17939)Termination reason: Unknown
% 99.60/15.83 % (17939)Termination phase: Saturation
% 99.60/15.83
% 99.60/15.83 % (17939)Memory used [KB]: 11257
% 99.60/15.83 % (17939)Time elapsed: 1.269 s
% 99.60/15.83 % (17939)Instructions burned: 2781 (million)
% 99.60/15.83 % (17939)------------------------------
% 99.60/15.83 % (17939)------------------------------
% 99.60/15.85 % (17959)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_17306 for (2857ds/1683Mi)
% 106.80/16.61 % (17959)Instruction limit reached!
% 106.80/16.61 % (17959)------------------------------
% 106.80/16.61 % (17959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 106.80/16.61 % (17959)Termination reason: Unknown
% 106.80/16.61 % (17959)Termination phase: Saturation
% 106.80/16.61
% 106.80/16.61 % (17959)Memory used [KB]: 21875
% 106.80/16.61 % (17959)Time elapsed: 0.780 s
% 106.80/16.61 % (17959)Instructions burned: 1684 (million)
% 106.80/16.61 % (17959)------------------------------
% 106.80/16.61 % (17959)------------------------------
% 106.80/16.63 % (17966)lrs+10_8:1_au=on:av=off:bd=off:cs=on:e2e=on:hfsq=on:hfsqc=50:hfsql=off:nm=0:i=4688:si=on:rtra=on_0 on DTF2THF_17306 for (2850ds/4688Mi)
% 107.43/16.72 % (17936)Instruction limit reached!
% 107.43/16.72 % (17936)------------------------------
% 107.43/16.72 % (17936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 107.43/16.72 % (17936)Termination reason: Unknown
% 107.43/16.72 % (17936)Termination phase: Saturation
% 107.43/16.72
% 107.43/16.72 % (17936)Memory used [KB]: 16247
% 107.43/16.72 % (17936)Time elapsed: 2.455 s
% 107.43/16.72 % (17936)Instructions burned: 5447 (million)
% 107.43/16.72 % (17936)------------------------------
% 107.43/16.72 % (17936)------------------------------
% 107.43/16.74 % (17967)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_17306 for (2848ds/2207Mi)
% 107.96/16.85 % (17952)Instruction limit reached!
% 107.96/16.85 % (17952)------------------------------
% 107.96/16.85 % (17952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 107.96/16.86 % (17952)Termination reason: Unknown
% 107.96/16.86 % (17952)Termination phase: Saturation
% 107.96/16.86
% 107.96/16.86 % (17952)Memory used [KB]: 13944
% 107.96/16.86 % (17952)Time elapsed: 1.410 s
% 107.96/16.86 % (17952)Instructions burned: 3202 (million)
% 107.96/16.86 % (17952)------------------------------
% 107.96/16.86 % (17952)------------------------------
% 107.96/16.88 % (17970)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=8216:si=on:rtra=on_0 on DTF2THF_17306 for (2847ds/8216Mi)
% 108.43/16.97 % (17955)Instruction limit reached!
% 108.43/16.97 % (17955)------------------------------
% 108.43/16.97 % (17955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 108.43/16.97 % (17955)Termination reason: Unknown
% 108.43/16.97 % (17955)Termination phase: Saturation
% 108.43/16.97
% 108.43/16.97 % (17955)Memory used [KB]: 11897
% 108.43/16.97 % (17955)Time elapsed: 1.417 s
% 108.43/16.97 % (17955)Instructions burned: 3049 (million)
% 108.43/16.97 % (17955)------------------------------
% 108.43/16.97 % (17955)------------------------------
% 108.43/16.99 % (17972)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=430:si=on:rtra=on_0 on DTF2THF_17306 for (2846ds/430Mi)
% 110.52/17.16 % (17972)Instruction limit reached!
% 110.52/17.16 % (17972)------------------------------
% 110.52/17.16 % (17972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 110.52/17.16 % (17972)Termination reason: Unknown
% 110.52/17.16 % (17972)Termination phase: Saturation
% 110.52/17.16
% 110.52/17.16 % (17972)Memory used [KB]: 7803
% 110.52/17.16 % (17972)Time elapsed: 0.178 s
% 110.52/17.16 % (17972)Instructions burned: 430 (million)
% 110.52/17.16 % (17972)------------------------------
% 110.52/17.16 % (17972)------------------------------
% 110.52/17.18 % (17974)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=2012:si=on:rtra=on_0 on DTF2THF_17306 for (2844ds/2012Mi)
% 111.57/17.34 % (17947)Instruction limit reached!
% 111.57/17.34 % (17947)------------------------------
% 111.57/17.34 % (17947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 111.57/17.34 % (17947)Termination reason: Unknown
% 111.57/17.34 % (17947)Termination phase: Saturation
% 111.57/17.34
% 111.57/17.34 % (17947)Memory used [KB]: 11897
% 111.57/17.34 % (17947)Time elapsed: 2.319 s
% 111.57/17.34 % (17947)Instructions burned: 5215 (million)
% 111.57/17.34 % (17947)------------------------------
% 111.57/17.34 % (17947)------------------------------
% 111.57/17.36 % (17976)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=631:si=on:rtra=on_0 on DTF2THF_17306 for (2842ds/631Mi)
% 113.14/17.64 % (17976)Instruction limit reached!
% 113.14/17.64 % (17976)------------------------------
% 113.14/17.64 % (17976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 113.14/17.64 % (17976)Termination reason: Unknown
% 113.14/17.64 % (17976)Termination phase: Saturation
% 113.14/17.64
% 113.14/17.64 % (17976)Memory used [KB]: 8571
% 113.14/17.64 % (17976)Time elapsed: 0.283 s
% 113.14/17.64 % (17976)Instructions burned: 631 (million)
% 113.14/17.64 % (17976)------------------------------
% 113.14/17.64 % (17976)------------------------------
% 113.14/17.66 % (17977)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=8785:si=on:rtra=on_0 on DTF2THF_17306 for (2839ds/8785Mi)
% 113.14/17.67 % (17967)Instruction limit reached!
% 113.14/17.67 % (17967)------------------------------
% 113.14/17.67 % (17967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 113.14/17.67 % (17967)Termination reason: Unknown
% 113.14/17.67 % (17967)Termination phase: Saturation
% 113.14/17.67
% 113.14/17.67 % (17967)Memory used [KB]: 11897
% 113.14/17.67 % (17967)Time elapsed: 0.952 s
% 113.14/17.67 % (17967)Instructions burned: 2207 (million)
% 113.14/17.67 % (17967)------------------------------
% 113.14/17.67 % (17967)------------------------------
% 113.14/17.69 % (17979)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=739:si=on:rtra=on_0 on DTF2THF_17306 for (2839ds/739Mi)
% 114.31/17.87 % (17974)Instruction limit reached!
% 114.31/17.87 % (17974)------------------------------
% 114.31/17.87 % (17974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 114.31/17.87 % (17974)Termination reason: Unknown
% 114.31/17.87 % (17974)Termination phase: Saturation
% 114.31/17.87
% 114.31/17.87 % (17974)Memory used [KB]: 12409
% 114.31/17.87 % (17974)Time elapsed: 0.686 s
% 114.31/17.87 % (17974)Instructions burned: 2013 (million)
% 114.31/17.87 % (17974)------------------------------
% 114.31/17.87 % (17974)------------------------------
% 114.31/17.89 % (17980)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_17306 for (2837ds/5473Mi)
% 116.69/18.02 % (17979)Instruction limit reached!
% 116.69/18.02 % (17979)------------------------------
% 116.69/18.02 % (17979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 116.69/18.02 % (17979)Termination reason: Unknown
% 116.69/18.02 % (17979)Termination phase: Saturation
% 116.69/18.02
% 116.69/18.02 % (17979)Memory used [KB]: 14967
% 116.69/18.02 % (17979)Time elapsed: 0.329 s
% 116.69/18.02 % (17979)Instructions burned: 739 (million)
% 116.69/18.02 % (17979)------------------------------
% 116.69/18.02 % (17979)------------------------------
% 116.69/18.04 % (17982)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=43570:si=on:rtra=on_0 on DTF2THF_17306 for (2835ds/43570Mi)
% 121.37/18.80 % (17966)Instruction limit reached!
% 121.37/18.80 % (17966)------------------------------
% 121.37/18.80 % (17966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 121.37/18.80 % (17966)Termination reason: Unknown
% 121.37/18.80 % (17966)Termination phase: Saturation
% 121.37/18.80
% 121.37/18.80 % (17966)Memory used [KB]: 15479
% 121.37/18.80 % (17966)Time elapsed: 2.199 s
% 121.37/18.80 % (17966)Instructions burned: 4689 (million)
% 121.37/18.80 % (17966)------------------------------
% 121.37/18.80 % (17966)------------------------------
% 121.37/18.82 % (17985)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=8382:si=on:rtra=on_0 on DTF2THF_17306 for (2828ds/8382Mi)
% 121.37/18.88 % (17958)Instruction limit reached!
% 121.37/18.88 % (17958)------------------------------
% 121.37/18.88 % (17958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 121.37/18.88 % (17958)Termination reason: Unknown
% 121.37/18.88 % (17958)Termination phase: Saturation
% 121.37/18.88
% 121.37/18.88 % (17958)Memory used [KB]: 20084
% 121.37/18.88 % (17958)Time elapsed: 3.181 s
% 121.37/18.88 % (17958)Instructions burned: 6804 (million)
% 121.37/18.88 % (17958)------------------------------
% 121.37/18.88 % (17958)------------------------------
% 121.37/18.90 % (17986)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_17306 for (2827ds/407Mi)
% 121.89/19.00 % (17986)Instruction limit reached!
% 121.89/19.00 % (17986)------------------------------
% 121.89/19.00 % (17986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 121.89/19.00 % (17986)Termination reason: Unknown
% 121.89/19.00 % (17986)Termination phase: Saturation
% 121.89/19.00
% 121.89/19.00 % (17986)Memory used [KB]: 9722
% 121.89/19.00 % (17986)Time elapsed: 0.108 s
% 121.89/19.00 % (17986)Instructions burned: 410 (million)
% 121.89/19.00 % (17986)------------------------------
% 121.89/19.00 % (17986)------------------------------
% 121.89/19.01 % (17988)lrs+10_1:50_cbe=off:cnfonf=lazy_pi_sigma_gen:fe=off:hud=5:plsq=on:plsqr=1,32:sos=all:i=2971:si=on:rtra=on_0 on DTF2THF_17306 for (2826ds/2971Mi)
% 123.72/19.09 % (17957)Refutation not found, non-redundant clauses discarded% (17957)------------------------------
% 123.72/19.09 % (17957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 123.72/19.09 % (17957)Termination reason: Refutation not found, non-redundant clauses discarded
% 123.72/19.09
% 123.72/19.09 % (17957)Memory used [KB]: 19573
% 123.72/19.09 % (17957)Time elapsed: 3.428 s
% 123.72/19.09 % (17957)Instructions burned: 7282 (million)
% 123.72/19.09 % (17957)------------------------------
% 123.72/19.09 % (17957)------------------------------
% 123.72/19.11 % (17989)lrs+1002_1:1_aac=none:bd=off:e2e=on:fde=none:fe=off:piset=or:prag=on:rawr=on:sos=on:updr=off:i=9822:si=on:rtra=on_0 on DTF2THF_17306 for (2825ds/9822Mi)
% 126.66/19.64 % (17970)Instruction limit reached!
% 126.66/19.64 % (17970)------------------------------
% 126.66/19.64 % (17970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 126.66/19.64 % (17970)Termination reason: Unknown
% 126.66/19.64 % (17970)Termination phase: Saturation
% 126.66/19.64
% 126.66/19.64 % (17970)Memory used [KB]: 8187
% 126.66/19.64 % (17970)Time elapsed: 2.766 s
% 126.66/19.64 % (17970)Instructions burned: 8217 (million)
% 126.66/19.64 % (17970)------------------------------
% 126.66/19.64 % (17970)------------------------------
% 126.66/19.66 % (17993)dis+10_5:1_av=off:ntd=on:s2a=on:s2at=3.0:sgt=16:sp=unary_frequency:ss=axioms:i=8425:si=on:rtra=on_0 on DTF2THF_17306 for (2819ds/8425Mi)
% 127.91/20.00 % (17988)Instruction limit reached!
% 127.91/20.00 % (17988)------------------------------
% 127.91/20.00 % (17988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 127.91/20.00 % (17988)Termination reason: Unknown
% 127.91/20.00 % (17988)Termination phase: Saturation
% 127.91/20.00
% 127.91/20.00 % (17988)Memory used [KB]: 7931
% 127.91/20.00 % (17988)Time elapsed: 0.986 s
% 127.91/20.00 % (17988)Instructions burned: 2974 (million)
% 127.91/20.00 % (17988)------------------------------
% 127.91/20.00 % (17988)------------------------------
% 127.91/20.01 % (17994)lrs+30_1:1_aac=none:au=on:cbe=off:cs=on:nm=2:rawr=on:sos=on:i=3107:si=on:rtra=on_0 on DTF2THF_17306 for (2816ds/3107Mi)
% 132.35/20.39 % (17980)Instruction limit reached!
% 132.35/20.39 % (17980)------------------------------
% 132.35/20.39 % (17980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 132.35/20.39 % (17980)Termination reason: Unknown
% 132.35/20.39 % (17980)Termination phase: Saturation
% 132.35/20.39
% 132.35/20.39 % (17980)Memory used [KB]: 13944
% 132.35/20.39 % (17980)Time elapsed: 2.515 s
% 132.35/20.39 % (17980)Instructions burned: 5473 (million)
% 132.35/20.39 % (17980)------------------------------
% 132.35/20.39 % (17980)------------------------------
% 132.95/20.41 % (17996)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=7967:si=on:rtra=on_0 on DTF2THF_17306 for (2812ds/7967Mi)
% 139.59/21.40 % (17994)Instruction limit reached!
% 139.59/21.40 % (17994)------------------------------
% 139.59/21.40 % (17994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 139.59/21.40 % (17994)Termination reason: Unknown
% 139.59/21.40 % (17994)Termination phase: Saturation
% 139.59/21.40
% 139.59/21.40 % (17994)Memory used [KB]: 21875
% 139.59/21.40 % (17994)Time elapsed: 1.389 s
% 139.59/21.40 % (17994)Instructions burned: 3108 (million)
% 139.59/21.40 % (17994)------------------------------
% 139.59/21.40 % (17994)------------------------------
% 138.90/21.42 % (18001)lrs+1010_10:959_abs=on:acc=on:bd=off:ccuc=small_ones:cha=on:cnfonf=lazy_simp:fd=preordered:fe=off:hud=3:ile=on:kws=inv_frequency:nm=2:piset=and:sd=5:sp=frequency:spb=goal_then_units:ss=axioms:st=4.5:i=3629:si=on:rtra=on_0 on DTF2THF_17306 for (2802ds/3629Mi)
% 142.09/21.73 % (17977)Instruction limit reached!
% 142.09/21.73 % (17977)------------------------------
% 142.09/21.73 % (17977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 142.09/21.73 % (17977)Termination reason: Unknown
% 142.09/21.73 % (17977)Termination phase: Saturation
% 142.09/21.73
% 142.09/21.73 % (17977)Memory used [KB]: 21620
% 142.09/21.73 % (17977)Time elapsed: 4.074 s
% 142.09/21.73 % (17977)Instructions burned: 8786 (million)
% 142.09/21.73 % (17977)------------------------------
% 142.09/21.73 % (17977)------------------------------
% 142.09/21.75 % (18004)lrs+1010_1:1024_au=on:fe=axiom:lwlo=on:nm=0:ntd=on:nwc=10.0:spb=non_intro:uhcvi=on:i=939:si=on:rtra=on_0 on DTF2THF_17306 for (2798ds/939Mi)
% 145.39/22.19 % (18004)Instruction limit reached!
% 145.39/22.19 % (18004)------------------------------
% 145.39/22.19 % (18004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 145.39/22.19 % (18004)Termination reason: Unknown
% 145.39/22.19 % (18004)Termination phase: Saturation
% 145.39/22.19
% 145.39/22.19 % (18004)Memory used [KB]: 10874
% 145.39/22.19 % (18004)Time elapsed: 0.447 s
% 145.39/22.19 % (18004)Instructions burned: 939 (million)
% 145.39/22.19 % (18004)------------------------------
% 145.39/22.19 % (18004)------------------------------
% 145.87/22.21 % (18007)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_17306 for (2794ds/1188Mi)
% 147.06/22.48 % (17985)Instruction limit reached!
% 147.06/22.48 % (17985)------------------------------
% 147.06/22.48 % (17985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 147.06/22.48 % (17985)Termination reason: Unknown
% 147.06/22.48 % (17985)Termination phase: Saturation
% 147.06/22.48
% 147.06/22.48 % (17985)Memory used [KB]: 14839
% 147.06/22.48 % (17985)Time elapsed: 3.666 s
% 147.06/22.48 % (17985)Instructions burned: 8383 (million)
% 147.06/22.48 % (17985)------------------------------
% 147.06/22.48 % (17985)------------------------------
% 147.66/22.51 % (18009)dis+21_3:2_avsq=on:cbe=off:e2e=on:flr=on:ile=on:nwc=5.0:piset=or:rawr=on:sp=occurrence:i=3205:si=on:rtra=on_0 on DTF2THF_17306 for (2791ds/3205Mi)
% 147.66/22.55 % (18001)Instruction limit reached!
% 147.66/22.55 % (18001)------------------------------
% 147.66/22.55 % (18001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 147.66/22.55 % (18001)Termination reason: Unknown
% 147.66/22.55 % (18001)Termination phase: Saturation
% 147.66/22.55
% 147.66/22.55 % (18001)Memory used [KB]: 8059
% 147.66/22.55 % (18001)Time elapsed: 1.139 s
% 147.66/22.55 % (18001)Instructions burned: 3630 (million)
% 147.66/22.55 % (18001)------------------------------
% 147.66/22.55 % (18001)------------------------------
% 147.66/22.57 % (18010)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_17306 for (2790ds/865Mi)
% 148.11/22.66 % (18007)Instruction limit reached!
% 148.11/22.66 % (18007)------------------------------
% 148.11/22.66 % (18007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 148.11/22.66 % (18007)Termination reason: Unknown
% 148.11/22.66 % (18007)Termination phase: Saturation
% 148.11/22.66
% 148.11/22.66 % (18007)Memory used [KB]: 18549
% 148.11/22.66 % (18007)Time elapsed: 0.456 s
% 148.11/22.66 % (18007)Instructions burned: 1188 (million)
% 148.11/22.66 % (18007)------------------------------
% 148.11/22.66 % (18007)------------------------------
% 148.11/22.68 % (18012)ott+1002_1:1_au=on:bd=off:cbe=off:cha=on:cnfonf=lazy_pi_sigma_gen:fd=off:fe=off:ntd=on:sp=const_frequency:i=7469:si=on:rtra=on_0 on DTF2THF_17306 for (2789ds/7469Mi)
% 149.39/22.87 % (18010)Instruction limit reached!
% 149.39/22.87 % (18010)------------------------------
% 149.39/22.87 % (18010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 149.39/22.87 % (18010)Termination reason: Unknown
% 149.39/22.87 % (18010)Termination phase: Saturation
% 149.39/22.87
% 149.39/22.87 % (18010)Memory used [KB]: 8059
% 149.39/22.87 % (18010)Time elapsed: 0.305 s
% 149.39/22.87 % (18010)Instructions burned: 866 (million)
% 149.39/22.87 % (18010)------------------------------
% 149.39/22.87 % (18010)------------------------------
% 149.39/22.89 % (18014)dis+10_1:10_bd=preordered:e2e=on:fde=none:fe=axiom:hud=3:kws=precedence:nwc=3.0:prag=on:sp=const_max:tgt=full:i=4165:si=on:rtra=on_0 on DTF2THF_17306 for (2787ds/4165Mi)
% 152.32/23.16 % (17996)Instruction limit reached!
% 152.32/23.16 % (17996)------------------------------
% 152.32/23.16 % (17996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 152.32/23.16 % (17996)Termination reason: Unknown
% 152.32/23.16 % (17996)Termination phase: Saturation
% 152.32/23.16
% 152.32/23.16 % (17996)Memory used [KB]: 18677
% 152.32/23.16 % (17996)Time elapsed: 2.753 s
% 152.32/23.16 % (17996)Instructions burned: 7969 (million)
% 152.32/23.16 % (17996)------------------------------
% 152.32/23.16 % (17996)------------------------------
% 152.32/23.17 % (18018)dis+1010_1:1_au=on:avsq=on:cnfonf=lazy_simp:fsr=off:ntd=on:nwc=10.0:sp=reverse_frequency:ss=axioms:st=1.5:i=13468:si=on:rtra=on_0 on DTF2THF_17306 for (2784ds/13468Mi)
% 153.42/23.34 % (17993)Instruction limit reached!
% 153.42/23.34 % (17993)------------------------------
% 153.42/23.34 % (17993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 153.42/23.34 % (17993)Termination reason: Unknown
% 153.42/23.34 % (17993)Termination phase: Saturation
% 153.42/23.34
% 153.42/23.34 % (17993)Memory used [KB]: 12792
% 153.42/23.34 % (17993)Time elapsed: 3.673 s
% 153.42/23.34 % (17993)Instructions burned: 8426 (million)
% 153.42/23.34 % (17993)------------------------------
% 153.42/23.34 % (17993)------------------------------
% 153.42/23.36 % (17989)Instruction limit reached!
% 153.42/23.36 % (17989)------------------------------
% 153.42/23.36 % (17989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 153.42/23.36 % (18019)dis+1002_1:1_au=on:bsr=unit_only:cbe=off:fe=off:fsr=off:nm=10:nwc=6.0:plsq=on:plsqc=1:plsqr=32,1:sos=all:i=2635:si=on:rtra=on_0 on DTF2THF_17306 for (2782ds/2635Mi)
% 153.42/23.36 % (17989)Termination reason: Unknown
% 153.42/23.36 % (17989)Termination phase: Saturation
% 153.42/23.36
% 153.42/23.36 % (17989)Memory used [KB]: 33773
% 153.42/23.36 % (17989)Time elapsed: 4.264 s
% 153.42/23.36 % (17989)Instructions burned: 9822 (million)
% 153.42/23.36 % (17989)------------------------------
% 153.42/23.36 % (17989)------------------------------
% 153.42/23.38 % (18020)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=631:si=on:rtra=on_0 on DTF2THF_17306 for (2782ds/631Mi)
% 154.76/23.60 % (18020)Instruction limit reached!
% 154.76/23.60 % (18020)------------------------------
% 154.76/23.60 % (18020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 154.76/23.60 % (18020)Termination reason: Unknown
% 154.76/23.60 % (18020)Termination phase: Saturation
% 154.76/23.60
% 154.76/23.60 % (18020)Memory used [KB]: 7803
% 154.76/23.60 % (18020)Time elapsed: 0.225 s
% 154.76/23.60 % (18020)Instructions burned: 633 (million)
% 154.76/23.60 % (18020)------------------------------
% 154.76/23.60 % (18020)------------------------------
% 154.76/23.61 % (18021)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=15557:si=on:rtra=on_0 on DTF2THF_17306 for (2780ds/15557Mi)
% 156.19/23.98 % (18009)Instruction limit reached!
% 156.19/23.98 % (18009)------------------------------
% 156.19/23.98 % (18009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 156.19/23.98 % (18009)Termination reason: Unknown
% 156.19/23.98 % (18009)Termination phase: Saturation
% 156.19/23.98
% 156.19/23.98 % (18009)Memory used [KB]: 16630
% 156.19/23.98 % (18009)Time elapsed: 1.487 s
% 156.19/23.98 % (18009)Instructions burned: 3206 (million)
% 156.19/23.98 % (18009)------------------------------
% 156.19/23.98 % (18009)------------------------------
% 156.19/24.00 % (18025)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2142:si=on:rtra=on_0 on DTF2THF_17306 for (2776ds/2142Mi)
% 162.61/24.64 % (18019)Instruction limit reached!
% 162.61/24.64 % (18019)------------------------------
% 162.61/24.64 % (18019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 162.61/24.64 % (18019)Termination reason: Unknown
% 162.61/24.64 % (18019)Termination phase: Saturation
% 162.61/24.64
% 162.61/24.64 % (18019)Memory used [KB]: 12665
% 162.61/24.64 % (18019)Time elapsed: 1.307 s
% 162.61/24.64 % (18019)Instructions burned: 2636 (million)
% 162.61/24.64 % (18019)------------------------------
% 162.61/24.64 % (18019)------------------------------
% 162.61/24.66 % (18028)dis+1002_1:1_aac=none:au=on:bd=off:cnfonf=conj_eager:nwc=5.0:sgt=5:sp=reverse_arity:ss=axioms:i=5624:si=on:rtra=on_0 on DTF2THF_17306 for (2769ds/5624Mi)
% 163.28/24.78 % (18025)Instruction limit reached!
% 163.28/24.78 % (18025)------------------------------
% 163.28/24.78 % (18025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 163.28/24.78 % (18025)Termination reason: Unknown
% 163.28/24.78 % (18025)Termination phase: Saturation
% 163.28/24.78
% 163.28/24.78 % (18025)Memory used [KB]: 11641
% 163.28/24.78 % (18025)Time elapsed: 0.809 s
% 163.28/24.78 % (18025)Instructions burned: 2143 (million)
% 163.28/24.78 % (18025)------------------------------
% 163.28/24.78 % (18025)------------------------------
% 163.86/24.80 % (18029)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=1665:si=on:rtra=on_0 on DTF2THF_17306 for (2768ds/1665Mi)
% 164.37/24.91 % (18014)Instruction limit reached!
% 164.37/24.91 % (18014)------------------------------
% 164.37/24.91 % (18014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 164.37/24.91 % (18014)Termination reason: Unknown
% 164.37/24.91 % (18014)Termination phase: Saturation
% 164.37/24.91
% 164.37/24.91 % (18014)Memory used [KB]: 26609
% 164.37/24.91 % (18014)Time elapsed: 2.025 s
% 164.37/24.91 % (18014)Instructions burned: 4166 (million)
% 164.37/24.91 % (18014)------------------------------
% 164.37/24.91 % (18014)------------------------------
% 164.37/24.93 % (18031)dis+1002_1:1_av=off:prag=on:sd=1:sos=on:sp=occurrence:ss=axioms:i=64912:si=on:rtra=on_0 on DTF2THF_17306 for (2767ds/64912Mi)
% 167.51/25.39 % (18029)Instruction limit reached!
% 167.51/25.39 % (18029)------------------------------
% 167.51/25.39 % (18029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 167.51/25.39 % (18029)Termination reason: Unknown
% 167.51/25.39 % (18029)Termination phase: Saturation
% 167.51/25.39
% 167.51/25.39 % (18029)Memory used [KB]: 18549
% 167.51/25.39 % (18029)Time elapsed: 0.612 s
% 167.51/25.39 % (18029)Instructions burned: 1667 (million)
% 167.51/25.39 % (18029)------------------------------
% 167.51/25.39 % (18029)------------------------------
% 168.21/25.41 % (18033)lrs+10_1:32_atotf=0.1:avsq=on:bsr=on:cnfonf=lazy_gen:fde=unused:i=7801:si=on:rtra=on_0 on DTF2THF_17306 for (2762ds/7801Mi)
% 170.01/25.78 % (18012)Instruction limit reached!
% 170.01/25.78 % (18012)------------------------------
% 170.01/25.78 % (18012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 170.01/25.78 % (18012)Termination reason: Unknown
% 170.01/25.78 % (18012)Termination phase: Saturation
% 170.01/25.78
% 170.01/25.78 % (18012)Memory used [KB]: 10874
% 170.01/25.78 % (18012)Time elapsed: 3.103 s
% 170.01/25.78 % (18012)Instructions burned: 7470 (million)
% 170.01/25.78 % (18012)------------------------------
% 170.01/25.78 % (18012)------------------------------
% 170.59/25.80 % (18034)ott+2_1:1_au=on:hfsq=on:hfsqc=5:hfsql=off:nwc=5.0:sd=3:ss=axioms:st=5.0:i=15194:si=on:rtra=on_0 on DTF2THF_17306 for (2758ds/15194Mi)
% 181.47/27.39 % (18028)Instruction limit reached!
% 181.47/27.39 % (18028)------------------------------
% 181.47/27.39 % (18028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 181.47/27.39 % (18028)Termination reason: Unknown
% 181.47/27.39 % (18028)Termination phase: Saturation
% 181.47/27.39
% 181.47/27.39 % (18028)Memory used [KB]: 15351
% 181.47/27.39 % (18028)Time elapsed: 2.750 s
% 181.47/27.39 % (18028)Instructions burned: 5625 (million)
% 181.47/27.39 % (18028)------------------------------
% 181.47/27.39 % (18028)------------------------------
% 182.18/27.41 % (18039)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=6753:si=on:rtra=on_0 on DTF2THF_17306 for (2742ds/6753Mi)
% 182.79/27.56 % (18018)Instruction limit reached!
% 182.79/27.56 % (18018)------------------------------
% 182.79/27.56 % (18018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 182.79/27.56 % (18018)Termination reason: Unknown
% 182.79/27.56 % (18018)Termination phase: Saturation
% 182.79/27.56
% 182.79/27.56 % (18018)Memory used [KB]: 8187
% 182.79/27.56 % (18018)Time elapsed: 4.373 s
% 182.79/27.56 % (18018)Instructions burned: 13470 (million)
% 182.79/27.56 % (18018)------------------------------
% 182.79/27.56 % (18018)------------------------------
% 182.79/27.58 % (18041)lrs+1002_1:28_bd=off:cnfonf=lazy_simp:plsq=on:plsqr=1,1:prag=on:i=1003:si=on:rtra=on_0 on DTF2THF_17306 for (2740ds/1003Mi)
% 184.84/27.94 % (18041)Instruction limit reached!
% 184.84/27.94 % (18041)------------------------------
% 184.84/27.94 % (18041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 184.84/27.94 % (18041)Termination reason: Unknown
% 184.84/27.94 % (18041)Termination phase: Saturation
% 184.84/27.94
% 184.84/27.94 % (18041)Memory used [KB]: 7931
% 184.84/27.94 % (18041)Time elapsed: 0.365 s
% 184.84/27.94 % (18041)Instructions burned: 1005 (million)
% 184.84/27.94 % (18041)------------------------------
% 184.84/27.94 % (18041)------------------------------
% 184.84/27.97 % (18044)ott-21_5:4_atotf=0.3:e2e=on:hud=15:ins=1:plsq=on:plsqc=1:plsqr=32,1:sp=unary_frequency:tnu=2:i=13018:si=on:rtra=on_0 on DTF2THF_17306 for (2736ds/13018Mi)
% 191.92/28.84 % (18033)Instruction limit reached!
% 191.92/28.84 % (18033)------------------------------
% 191.92/28.84 % (18033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 191.92/28.84 % (18033)Termination reason: Unknown
% 191.92/28.84 % (18033)Termination phase: Saturation
% 191.92/28.84
% 191.92/28.84 % (18033)Memory used [KB]: 15223
% 191.92/28.84 % (18033)Time elapsed: 3.443 s
% 191.92/28.84 % (18033)Instructions burned: 7801 (million)
% 191.92/28.84 % (18033)------------------------------
% 191.92/28.84 % (18033)------------------------------
% 191.92/28.85 % (18047)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1267:si=on:rtra=on_0 on DTF2THF_17306 for (2727ds/1267Mi)
% 192.57/28.97 % (18021)Instruction limit reached!
% 192.57/28.97 % (18021)------------------------------
% 192.57/28.97 % (18021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 192.57/28.97 % (18021)Termination reason: Unknown
% 192.57/28.97 % (18021)Termination phase: Saturation
% 192.57/28.97
% 192.57/28.97 % (18021)Memory used [KB]: 20084
% 192.57/28.97 % (18021)Time elapsed: 5.367 s
% 192.57/28.97 % (18021)Instructions burned: 15557 (million)
% 192.57/28.97 % (18021)------------------------------
% 192.57/28.97 % (18021)------------------------------
% 192.57/28.99 % (18049)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=2570:si=on:rtra=on_0 on DTF2THF_17306 for (2726ds/2570Mi)
% 196.08/29.45 % (18047)Instruction limit reached!
% 196.08/29.45 % (18047)------------------------------
% 196.08/29.45 % (18047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 196.08/29.45 % (18047)Termination reason: Unknown
% 196.08/29.45 % (18047)Termination phase: Saturation
% 196.08/29.45
% 196.08/29.45 % (18047)Memory used [KB]: 12665
% 196.08/29.45 % (18047)Time elapsed: 0.621 s
% 196.08/29.45 % (18047)Instructions burned: 1267 (million)
% 196.08/29.45 % (18047)------------------------------
% 196.08/29.45 % (18047)------------------------------
% 196.08/29.47 % (18050)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=13163:si=on:rtra=on_0 on DTF2THF_17306 for (2721ds/13163Mi)
% 199.15/29.90 % (18049)Instruction limit reached!
% 199.15/29.90 % (18049)------------------------------
% 199.15/29.90 % (18049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 199.15/29.90 % (18049)Termination reason: Unknown
% 199.15/29.90 % (18049)Termination phase: Saturation
% 199.15/29.90
% 199.15/29.90 % (18049)Memory used [KB]: 28400
% 199.15/29.90 % (18049)Time elapsed: 0.912 s
% 199.15/29.90 % (18049)Instructions burned: 2573 (million)
% 199.15/29.90 % (18049)------------------------------
% 199.15/29.90 % (18049)------------------------------
% 199.15/29.91 % (18052)lrs+1666_1:1_au=on:s2a=on:sd=2:ss=axioms:st=5.0:i=5087:si=on:rtra=on_0 on DTF2THF_17306 for (2717ds/5087Mi)
% 203.78/30.51 % (18039)Instruction limit reached!
% 203.78/30.51 % (18039)------------------------------
% 203.78/30.51 % (18039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 203.78/30.51 % (18039)Termination reason: Unknown
% 203.78/30.51 % (18039)Termination phase: Saturation
% 203.78/30.51
% 203.78/30.51 % (18039)Memory used [KB]: 27888
% 203.78/30.51 % (18039)Time elapsed: 3.123 s
% 203.78/30.51 % (18039)Instructions burned: 6754 (million)
% 203.78/30.51 % (18039)------------------------------
% 203.78/30.51 % (18039)------------------------------
% 203.78/30.53 % (18054)lrs+1002_1:1_aac=none:au=on:bd=off:cnfonf=lazy_pi_sigma_gen:s2a=on:sac=on:sd=1:sgt=20:ss=axioms:i=10380:si=on:rtra=on_0 on DTF2THF_17306 for (2710ds/10380Mi)
% 216.33/32.34 % (18052)Instruction limit reached!
% 216.33/32.34 % (18052)------------------------------
% 216.33/32.34 % (18052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 216.33/32.34 % (18052)Termination reason: Unknown
% 216.33/32.34 % (18052)Termination phase: Saturation
% 216.33/32.34
% 216.33/32.34 % (18052)Memory used [KB]: 14711
% 216.33/32.34 % (18052)Time elapsed: 2.432 s
% 216.33/32.34 % (18052)Instructions burned: 5088 (million)
% 216.33/32.34 % (18052)------------------------------
% 216.33/32.34 % (18052)------------------------------
% 216.33/32.36 % (18058)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4218:si=on:rtra=on_0 on DTF2THF_17306 for (2692ds/4218Mi)
% 217.58/32.52 % (18034)Instruction limit reached!
% 217.58/32.52 % (18034)------------------------------
% 217.58/32.52 % (18034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 217.58/32.52 % (18034)Termination reason: Unknown
% 217.58/32.52 % (18034)Termination phase: Saturation
% 217.58/32.52
% 217.58/32.52 % (18034)Memory used [KB]: 21620
% 217.58/32.52 % (18034)Time elapsed: 6.737 s
% 217.58/32.52 % (18034)Instructions burned: 15195 (million)
% 217.58/32.52 % (18034)------------------------------
% 217.58/32.52 % (18034)------------------------------
% 217.58/32.54 % (18059)ott+1666_1:1_hfaw=0:hfsq=on:hfsql=off:hfsqr=1,16:hud=15:slsq=on:slsqr=1,2:tnu=2:i=3971:si=on:rtra=on_0 on DTF2THF_17306 for (2690ds/3971Mi)
% 227.51/34.02 % (18054)Instruction limit reached!
% 227.51/34.02 % (18054)------------------------------
% 227.51/34.02 % (18054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 227.51/34.02 % (18054)Termination reason: Unknown
% 227.51/34.02 % (18054)Termination phase: Saturation
% 227.51/34.02
% 227.51/34.02 % (18054)Memory used [KB]: 7931
% 227.51/34.02 % (18054)Time elapsed: 3.480 s
% 227.51/34.02 % (18054)Instructions burned: 10382 (million)
% 227.51/34.02 % (18054)------------------------------
% 227.51/34.02 % (18054)------------------------------
% 228.37/34.03 % (18066)dis+1010_1:1_anc=all_dependent:au=on:bs=on:sd=5:sp=occurrence:ss=axioms:st=2.0:i=14014:si=on:rtra=on_0 on DTF2THF_17306 for (2675ds/14014Mi)
% 228.37/34.06 % (18044)Instruction limit reached!
% 228.37/34.06 % (18044)------------------------------
% 228.37/34.06 % (18044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 228.37/34.06 % (18044)Termination reason: Unknown
% 228.37/34.06 % (18044)Termination phase: Saturation
% 228.37/34.06
% 228.37/34.06 % (18044)Memory used [KB]: 39274
% 228.37/34.06 % (18044)Time elapsed: 6.111 s
% 228.37/34.06 % (18044)Instructions burned: 13018 (million)
% 228.37/34.06 % (18044)------------------------------
% 228.37/34.06 % (18044)------------------------------
% 228.37/34.08 % (18067)lrs+10_1:1_ins=1:sgt=8:ss=axioms:i=8517:si=on:rtra=on_0 on DTF2THF_17306 for (2675ds/8517Mi)
% 229.31/34.28 % (18059)Instruction limit reached!
% 229.31/34.28 % (18059)------------------------------
% 229.31/34.28 % (18059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 229.31/34.28 % (18059)Termination reason: Unknown
% 229.31/34.28 % (18059)Termination phase: Saturation
% 229.31/34.28
% 229.31/34.28 % (18059)Memory used [KB]: 16119
% 229.31/34.28 % (18059)Time elapsed: 1.746 s
% 229.31/34.28 % (18059)Instructions burned: 3971 (million)
% 229.31/34.28 % (18059)------------------------------
% 229.31/34.28 % (18059)------------------------------
% 229.31/34.29 % (18058)Refutation not found, non-redundant clauses discarded% (18058)------------------------------
% 229.31/34.29 % (18058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 229.31/34.29 % (18058)Termination reason: Refutation not found, non-redundant clauses discarded
% 229.31/34.29
% 229.31/34.29 % (18058)Memory used [KB]: 14200
% 229.31/34.29 % (18058)Time elapsed: 1.919 s
% 229.31/34.29 % (18058)Instructions burned: 4168 (million)
% 229.31/34.29 % (18058)------------------------------
% 229.31/34.29 % (18058)------------------------------
% 229.80/34.30 % (18070)lrs+10_1:2_ntd=on:nwc=10.0:plsq=on:plsqc=1:plsqr=2,1:ss=axioms:i=9078:si=on:rtra=on_0 on DTF2THF_17306 for (2673ds/9078Mi)
% 229.80/34.30 % (18069)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=10148:si=on:rtra=on_0 on DTF2THF_17306 for (2673ds/10148Mi)
% 229.80/34.30 % (18050)First to succeed.
% 229.80/34.32 % (18050)Refutation found. Thanks to Tanya!
% 229.80/34.32 % SZS status Theorem for DTF2THF_17306
% 229.80/34.32 % SZS output start Proof for DTF2THF_17306
% 229.80/34.32 thf(func_def_0, type, in: $i > $i > $o).
% 229.80/34.32 thf(func_def_1, type, exu: ($i > $o) > $o).
% 229.80/34.32 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 229.80/34.32 thf(func_def_8, type, powerset: $i > $i).
% 229.80/34.32 thf(func_def_10, type, setunion: $i > $i).
% 229.80/34.32 thf(func_def_19, type, descr: ($i > $o) > $i).
% 229.80/34.32 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 229.80/34.32 thf(func_def_26, type, prop2set: $o > $i).
% 229.80/34.32 thf(func_def_36, type, nonempty: $i > $o).
% 229.80/34.32 thf(func_def_69, type, set2prop: $i > $o).
% 229.80/34.32 thf(func_def_88, type, subset: $i > $i > $o).
% 229.80/34.32 thf(func_def_89, type, disjoint: $i > $i > $o).
% 229.80/34.32 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 229.80/34.32 thf(func_def_114, type, binunion: $i > $i > $i).
% 229.80/34.32 thf(func_def_122, type, binintersect: $i > $i > $i).
% 229.80/34.32 thf(func_def_135, type, regular: $i > $o).
% 229.80/34.32 thf(func_def_136, type, setminus: $i > $i > $i).
% 229.80/34.32 thf(func_def_147, type, symdiff: $i > $i > $i).
% 229.80/34.32 thf(func_def_153, type, iskpair: $i > $o).
% 229.80/34.32 thf(func_def_158, type, kpair: $i > $i > $i).
% 229.80/34.32 thf(func_def_160, type, cartprod: $i > $i > $i).
% 229.80/34.32 thf(func_def_177, type, singleton: $i > $o).
% 229.80/34.32 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 229.80/34.32 thf(func_def_184, type, atmost1p: $i > $o).
% 229.80/34.32 thf(func_def_185, type, atleast2p: $i > $o).
% 229.80/34.32 thf(func_def_186, type, atmost2p: $i > $o).
% 229.80/34.32 thf(func_def_187, type, upairsetp: $i > $o).
% 229.80/34.32 thf(func_def_191, type, kfst: $i > $i).
% 229.80/34.32 thf(func_def_203, type, ksnd: $i > $i).
% 229.80/34.32 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 229.80/34.32 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 229.80/34.32 thf(func_def_222, type, func: $i > $i > $i > $o).
% 229.80/34.32 thf(func_def_223, type, funcSet: $i > $i > $i).
% 229.80/34.32 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 229.80/34.32 thf(func_def_259, type, if: $i > $o > $i > $i > $i).
% 229.80/34.32 thf(func_def_323, type, breln1: $i > $i > $o).
% 229.80/34.32 thf(func_def_325, type, breln1Set: $i > $i).
% 229.80/34.32 thf(func_def_327, type, transitive: $i > $i > $o).
% 229.80/34.32 thf(func_def_328, type, antisymmetric: $i > $i > $o).
% 229.80/34.32 thf(func_def_329, type, reflexive: $i > $i > $o).
% 229.80/34.32 thf(func_def_330, type, refltransitive: $i > $i > $o).
% 229.80/34.32 thf(func_def_331, type, refllinearorder: $i > $i > $o).
% 229.80/34.32 thf(func_def_332, type, reflwellordering: $i > $i > $o).
% 229.80/34.32 thf(func_def_338, type, breln1invset: $i > $i > $i).
% 229.80/34.32 thf(func_def_342, type, breln1compset: $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_360, type, image1: $i > ($i > $i) > $i).
% 229.80/34.32 thf(func_def_364, type, injective: $i > $i > $i > $o).
% 229.80/34.32 thf(func_def_365, type, injFuncSet: $i > $i > $i).
% 229.80/34.32 thf(func_def_369, type, surjective: $i > $i > $i > $o).
% 229.80/34.32 thf(func_def_370, type, surjFuncSet: $i > $i > $i).
% 229.80/34.32 thf(func_def_393, type, sP4: $i > $i > $i > $i > $o).
% 229.80/34.32 thf(func_def_395, type, sP6: $o > $i > $i > $i > $o).
% 229.80/34.32 thf(func_def_397, type, sP8: $i > $i > $i > $o).
% 229.80/34.32 thf(func_def_400, type, sP11: $i > $i > $i > $o).
% 229.80/34.32 thf(func_def_401, type, sP12: $i > $i > $o).
% 229.80/34.32 thf(func_def_402, type, sP13: $i > $o).
% 229.80/34.32 thf(func_def_403, type, sP14: $i > $i > $o).
% 229.80/34.32 thf(func_def_404, type, sP15: $i > $i > $o).
% 229.80/34.32 thf(func_def_411, type, sK22: $i > $i > ($i > $i > $o) > $i).
% 229.80/34.32 thf(func_def_412, type, sK23: $i > $i > $o).
% 229.80/34.32 thf(func_def_415, type, sK26: $i > $i).
% 229.80/34.32 thf(func_def_431, type, sK42: $i > $i > $i).
% 229.80/34.32 thf(func_def_438, type, sK49: $i > $i).
% 229.80/34.32 thf(func_def_442, type, sK53: $i > $o).
% 229.80/34.32 thf(func_def_443, type, sK54: ($i > $o) > ($i > $o) > $i).
% 229.80/34.32 thf(func_def_444, type, sK55: ($i > $o) > ($i > $o) > $i).
% 229.80/34.32 thf(func_def_445, type, sK56: $i > $o).
% 229.80/34.32 thf(func_def_446, type, sK57: $i > $o).
% 229.80/34.32 thf(func_def_453, type, sK64: $i > $i).
% 229.80/34.32 thf(func_def_458, type, sK69: $i > $i > ($i > $i) > $i).
% 229.80/34.32 thf(func_def_459, type, sK70: $i > $i).
% 229.80/34.32 thf(func_def_465, type, sK76: $i > $o).
% 229.80/34.32 thf(func_def_466, type, sK77: $i > $i).
% 229.80/34.32 thf(func_def_467, type, sK78: ($i > $o) > $i).
% 229.80/34.32 thf(func_def_476, type, sK87: $i > $i > $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_477, type, sK88: $i > ($i > $i) > $i > $i).
% 229.80/34.32 thf(func_def_479, type, sK90: $i > $i).
% 229.80/34.32 thf(func_def_482, type, sK93: $i > $o).
% 229.80/34.32 thf(func_def_484, type, sK95: $i > ($i > $o) > $i > $i).
% 229.80/34.32 thf(func_def_485, type, sK96: $i > $o).
% 229.80/34.32 thf(func_def_514, type, sK125: $i > $o).
% 229.80/34.32 thf(func_def_517, type, sK128: $i > ($i > $o) > $i).
% 229.80/34.32 thf(func_def_518, type, sK129: $i > $o).
% 229.80/34.32 thf(func_def_538, type, sK149: $i > $i > $i).
% 229.80/34.32 thf(func_def_542, type, sK153: $i > $i).
% 229.80/34.32 thf(func_def_545, type, sK156: $i > $i > ($i > $i) > $i).
% 229.80/34.32 thf(func_def_559, type, sK170: $i > $i > $i).
% 229.80/34.32 thf(func_def_575, type, sK186: ($i > $o) > ($i > $o) > $i > $i > $i).
% 229.80/34.32 thf(func_def_576, type, sK187: ($i > $o) > ($i > $o) > $i > $i > $i).
% 229.80/34.32 thf(func_def_579, type, sK190: $i > $o).
% 229.80/34.32 thf(func_def_580, type, sK191: $i > $o).
% 229.80/34.32 thf(func_def_590, type, sK201: $o > $i > $i > $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_594, type, sK205: $i > $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_612, type, sK223: $i > $i > $o).
% 229.80/34.32 thf(func_def_617, type, sK228: $i > $i > $i).
% 229.80/34.32 thf(func_def_625, type, sK236: ($i > $o) > $i).
% 229.80/34.32 thf(func_def_626, type, sK237: $i > $o).
% 229.80/34.32 thf(func_def_643, type, sK254: $i > $i > $o).
% 229.80/34.32 thf(func_def_672, type, sK283: $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_679, type, sK290: $i > $o).
% 229.80/34.32 thf(func_def_682, type, sK293: $i > ($i > $o) > $i).
% 229.80/34.32 thf(func_def_695, type, sK306: $i > $i).
% 229.80/34.32 thf(func_def_697, type, sK308: $i > $i).
% 229.80/34.32 thf(func_def_706, type, sK317: $i > $i > ($i > $i) > $i).
% 229.80/34.32 thf(func_def_707, type, sK318: $i > $i).
% 229.80/34.32 thf(func_def_723, type, sK334: $i > $o).
% 229.80/34.32 thf(func_def_746, type, sK357: $i > $i > $o).
% 229.80/34.32 thf(func_def_750, type, sK361: $i > $i).
% 229.80/34.32 thf(func_def_762, type, sK373: $i > $i).
% 229.80/34.32 thf(func_def_776, type, sK387: $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_780, type, sK391: $i > $o).
% 229.80/34.32 thf(func_def_783, type, sK394: $i > ($i > $o) > $i).
% 229.80/34.32 thf(func_def_790, type, sK401: $i > $o).
% 229.80/34.32 thf(func_def_793, type, sK404: $i > ($i > $o) > $i).
% 229.80/34.32 thf(func_def_794, type, sK405: $i > ($i > $o) > $i).
% 229.80/34.32 thf(func_def_804, type, sK415: $i > $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_809, type, sK420: ($i > $o) > $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_810, type, sK421: ($i > $o) > $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_814, type, sK425: $i > $o).
% 229.80/34.32 thf(func_def_840, type, sK451: $o > $i > $i > $i).
% 229.80/34.32 thf(func_def_841, type, sK452: $i > ($i > $o) > $i).
% 229.80/34.32 thf(func_def_842, type, sK453: $i > $o).
% 229.80/34.32 thf(func_def_854, type, sK465: $i > $i > $o).
% 229.80/34.32 thf(func_def_857, type, sK468: $i > $i).
% 229.80/34.32 thf(func_def_862, type, sK473: $i > $o).
% 229.80/34.32 thf(func_def_869, type, sK480: $i > $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_870, type, sK481: $i > $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_871, type, sK482: $i > $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_872, type, sK483: $i > $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_901, type, sK512: $i > $i > ($i > $i) > $i).
% 229.80/34.32 thf(func_def_902, type, sK513: $i > $i > $i > ($i > $i) > $i).
% 229.80/34.32 thf(func_def_903, type, sK514: $i > $i).
% 229.80/34.32 thf(func_def_917, type, sK528: $i > $o).
% 229.80/34.32 thf(func_def_929, type, sK540: $i > $i > $i).
% 229.80/34.32 thf(func_def_932, type, sK543: $i > $i).
% 229.80/34.32 thf(func_def_934, type, sK545: ($i > $i) > $i > $i > $i).
% 229.80/34.32 thf(func_def_946, type, sK557: $i > $i > $o).
% 229.80/34.32 thf(func_def_960, type, sK571: $i > $o).
% 229.80/34.32 thf(func_def_969, type, sK580: $i > $i).
% 229.80/34.32 thf(func_def_972, type, sK583: $i > $i > ($i > $i) > $i).
% 229.80/34.32 thf(func_def_1003, type, sK614: $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_1004, type, sK615: $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_1005, type, sK616: $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_1006, type, sK617: $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_1007, type, sK618: $i > $o).
% 229.80/34.32 thf(func_def_1008, type, sK619: $i > $o).
% 229.80/34.32 thf(func_def_1009, type, sK620: ($i > $o) > ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1010, type, sK621: ($i > $o) > ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1025, type, sK636: $i > $o).
% 229.80/34.32 thf(func_def_1027, type, sK638: ($i > $o) > $i > $i > $i).
% 229.80/34.32 thf(func_def_1028, type, sK639: ($i > $o) > $i > $i > $i).
% 229.80/34.32 thf(func_def_1031, type, sK642: ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1032, type, sK643: $i > $o).
% 229.80/34.32 thf(func_def_1033, type, sK644: $i > $i).
% 229.80/34.32 thf(func_def_1034, type, sK645: $i > $i > $o).
% 229.80/34.32 thf(func_def_1036, type, sK647: $i > $i).
% 229.80/34.32 thf(func_def_1037, type, sK648: $i > $i).
% 229.80/34.32 thf(func_def_1038, type, sK649: $i > ($i > $i > $o) > $i).
% 229.80/34.32 thf(func_def_1039, type, sK650: $i > $i > ($i > $i > $o) > $i).
% 229.80/34.32 thf(func_def_1040, type, sK651: $i > ($i > $i > $o) > $i).
% 229.80/34.32 thf(func_def_1064, type, sK675: $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_1068, type, sK679: $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_1095, type, sK706: $i > $o).
% 229.80/34.32 thf(func_def_1098, type, sK709: $i > ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1130, type, sK741: $i > $o).
% 229.80/34.32 thf(func_def_1132, type, sK743: ($i > $o) > $i > $i > $i).
% 229.80/34.32 thf(func_def_1133, type, sK744: ($i > $o) > $i > $i > $i).
% 229.80/34.32 thf(func_def_1138, type, sK749: $i > $i > $i).
% 229.80/34.32 thf(func_def_1155, type, sK766: $i > $i > $i).
% 229.80/34.32 thf(func_def_1156, type, sK767: $i > $i > $i).
% 229.80/34.32 thf(func_def_1157, type, sK768: $i > $i > $i).
% 229.80/34.32 thf(func_def_1158, type, sK769: $i > $i > $i).
% 229.80/34.32 thf(func_def_1159, type, sK770: $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_1160, type, sK771: $i > $i).
% 229.80/34.32 thf(func_def_1161, type, sK772: $i > $i).
% 229.80/34.32 thf(func_def_1162, type, sK773: $i > $i).
% 229.80/34.32 thf(func_def_1163, type, sK774: $i > $i).
% 229.80/34.32 thf(func_def_1164, type, sK775: $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_1165, type, sK776: $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_1166, type, sK777: $i > $i > $i).
% 229.80/34.32 thf(func_def_1167, type, sK778: $i > $i > $i).
% 229.80/34.32 thf(func_def_1168, type, sK779: $i > $i > $i).
% 229.80/34.32 thf(func_def_1169, type, sK780: $i > $i).
% 229.80/34.32 thf(func_def_1170, type, sK781: $i > $i > $i).
% 229.80/34.32 thf(func_def_1172, type, sK783: $i > $i).
% 229.80/34.32 thf(func_def_1173, type, sK784: $i > $i).
% 229.80/34.32 thf(func_def_1179, type, sK790: $i > $i).
% 229.80/34.32 thf(func_def_1188, type, sK799: $i > $i > ($i > $i) > $i).
% 229.80/34.32 thf(func_def_1189, type, sK800: $i > $i).
% 229.80/34.32 thf(func_def_1205, type, sK816: $i > $o).
% 229.80/34.32 thf(func_def_1212, type, sK823: $i > $i > $i).
% 229.80/34.32 thf(func_def_1231, type, sK842: $i > $i > $o).
% 229.80/34.32 thf(func_def_1233, type, sK844: $i > ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1234, type, sK845: $i > $o).
% 229.80/34.32 thf(func_def_1236, type, sK847: $i > $o).
% 229.80/34.32 thf(func_def_1239, type, sK850: $i > ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1240, type, sK851: $i > $o).
% 229.80/34.32 thf(func_def_1242, type, sK853: ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1243, type, sK854: ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1255, type, sK866: ($i > $i) > $i > $i > $i).
% 229.80/34.32 thf(func_def_1258, type, sK869: $i > $i).
% 229.80/34.32 thf(func_def_1263, type, sK874: $i > $o).
% 229.80/34.32 thf(func_def_1265, type, sK876: ($i > $o) > $i > $i).
% 229.80/34.32 thf(func_def_1266, type, sK877: ($i > $o) > $i > $i).
% 229.80/34.32 thf(func_def_1269, type, sK880: $i > $o).
% 229.80/34.32 thf(func_def_1277, type, sK888: $i > $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_1278, type, sK889: $i > $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_1288, type, sK899: $i > ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1289, type, sK900: $i > $o).
% 229.80/34.32 thf(func_def_1301, type, sK912: $i > $i > $i).
% 229.80/34.32 thf(func_def_1302, type, sK913: $i > $i > $i).
% 229.80/34.32 thf(func_def_1306, type, sK917: $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_1307, type, sK918: $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_1310, type, sK921: $i > $i > $o).
% 229.80/34.32 thf(func_def_1315, type, sK926: $i > $i > $i).
% 229.80/34.32 thf(func_def_1330, type, sK941: $i > $o).
% 229.80/34.32 thf(func_def_1337, type, sK948: $i > $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_1344, type, sK955: $i > $o).
% 229.80/34.32 thf(func_def_1346, type, sK957: ($i > $o) > $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_1347, type, sK958: ($i > $o) > $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_1365, type, sK976: $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_1366, type, sK977: $i > $i > $i > $i).
% 229.80/34.32 thf(func_def_1367, type, sK978: $i > $i).
% 229.80/34.32 thf(func_def_1383, type, sK994: $i > $i > $o).
% 229.80/34.32 thf(func_def_1388, type, sK999: $i > $i).
% 229.80/34.32 thf(func_def_1389, type, sK1000: $i > $i).
% 229.80/34.32 thf(func_def_1390, type, sK1001: $i > $i).
% 229.80/34.32 thf(func_def_1391, type, sK1002: ($i > $i) > $i > $i).
% 229.80/34.32 thf(func_def_1392, type, sK1003: $i > ($i > $i) > $i > $i).
% 229.80/34.32 thf(func_def_1428, type, sK1039: $i > $o).
% 229.80/34.32 thf(func_def_1430, type, sK1041: $i > ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1437, type, sK1048: $i > $o).
% 229.80/34.32 thf(func_def_1454, type, sK1065: $i > $o).
% 229.80/34.32 thf(func_def_1469, type, sK1080: $i > $o).
% 229.80/34.32 thf(func_def_1475, type, sK1086: ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1476, type, sK1087: ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1477, type, sK1088: $i > ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1478, type, sK1089: $i > ($i > $i > $o) > $i > $i).
% 229.80/34.32 thf(func_def_1479, type, sK1090: $i > $i).
% 229.80/34.32 thf(func_def_1480, type, sK1091: $i > ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1481, type, sK1092: ($i > $o) > $i > $i).
% 229.80/34.32 thf(func_def_1482, type, sK1093: $i > ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1483, type, sK1094: $i > ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1484, type, sK1095: ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1485, type, sK1096: ($i > $o) > $i > $i).
% 229.80/34.32 thf(func_def_1486, type, sK1097: $i > ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1487, type, sK1098: $i > ($i > $i > $o) > $i > $i).
% 229.80/34.32 thf(func_def_1488, type, sK1099: $i > ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1489, type, sK1100: ($i > $o) > $i > $i).
% 229.80/34.32 thf(func_def_1490, type, sK1101: ($i > $o) > $i > $i).
% 229.80/34.32 thf(func_def_1491, type, sK1102: ($i > $o) > $i > $i).
% 229.80/34.32 thf(func_def_1492, type, sK1103: ($i > $o) > $i > $i).
% 229.80/34.32 thf(func_def_1493, type, sK1104: ($i > $o) > $i > $i).
% 229.80/34.32 thf(func_def_1494, type, sK1105: ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1495, type, sK1106: $i > ($i > $i) > $i).
% 229.80/34.32 thf(func_def_1496, type, sK1107: $i > $i > ($i > $i) > $i).
% 229.80/34.32 thf(func_def_1497, type, sK1108: $i > $i > ($i > $i) > $i).
% 229.80/34.32 thf(func_def_1498, type, sK1109: $i > $i > ($i > $i) > $i).
% 229.80/34.32 thf(func_def_1499, type, sK1110: ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1500, type, sK1111: ($i > $o) > $i > $i).
% 229.80/34.32 thf(func_def_1501, type, sK1112: ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1502, type, sK1113: ($i > $o) > $i > $i).
% 229.80/34.32 thf(func_def_1503, type, sK1114: ($i > $o) > $i > $i).
% 229.80/34.32 thf(func_def_1504, type, sK1115: ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1505, type, sK1116: ($i > $o) > $i > $i).
% 229.80/34.32 thf(func_def_1506, type, sK1117: ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1507, type, sK1118: ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1508, type, sK1119: ($i > $o) > $i > $i).
% 229.80/34.32 thf(func_def_1509, type, sK1120: ($i > $o) > $i > $i).
% 229.80/34.32 thf(func_def_1510, type, sK1121: ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1511, type, sK1122: ($i > $o) > $i > $i).
% 229.80/34.32 thf(func_def_1512, type, sK1123: ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1513, type, sK1124: ($i > $o) > $i > $i).
% 229.80/34.32 thf(func_def_1514, type, sK1125: ($i > $o) > $i > $i).
% 229.80/34.32 thf(func_def_1515, type, sK1126: ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1516, type, sK1127: $i > ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1517, type, sK1128: ($i > $o) > $i).
% 229.80/34.32 thf(func_def_1518, type, sK1129: ($i > $o) > $i > $i).
% 229.80/34.32 thf(func_def_1519, type, sK1130: ($i > $o) > $i > $i).
% 229.80/34.32 thf(func_def_1520, type, sK1131: $i > ($i > $i > $o) > $i > $i).
% 229.80/34.32 thf(func_def_1521, type, ph1132: !>[X0: $tType]:(X0)).
% 229.80/34.32 thf(f44979,plain,(
% 229.80/34.32 $false),
% 229.80/34.32 inference(subsumption_resolution,[status(thm)],[f44978,f6603])).
% 229.80/34.32 thf(f6603,plain,(
% 229.80/34.32 (emptyset != sK137)),
% 229.80/34.32 inference(equality_proxy_clausification,[status(thm)],[f6602])).
% 229.80/34.32 thf(f6602,plain,(
% 229.80/34.32 ((emptyset = sK137) = $false)),
% 229.80/34.32 inference(not_proxy_clausification,[status(thm)],[f6601])).
% 229.80/34.32 thf(f6601,plain,(
% 229.80/34.32 ((~ (emptyset = sK137)) = $true)),
% 229.80/34.32 inference(beta_eta_normalization,[status(thm)],[f5017])).
% 229.80/34.32 thf(f5017,plain,(
% 229.80/34.32 (((^[Y0 : $i]: (~ (emptyset = Y0))) @ sK137) = $true)),
% 229.80/34.32 inference(definition_unfolding,[status(thm)],[f3496,f4101])).
% 229.80/34.32 thf(f4101,plain,(
% 229.80/34.32 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 229.80/34.32 inference(cnf_transformation,[status(thm)],[f805])).
% 229.80/34.32 thf(f805,plain,(
% 229.80/34.32 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 229.80/34.32 inference(fool_elimination,[status(thm)],[f804])).
% 229.80/34.32 thf(f804,plain,(
% 229.80/34.32 (nonempty = (^[X0 : $i] : ((emptyset != X0))))),
% 229.80/34.32 inference(rectify,[status(thm)],[f27])).
% 229.80/34.32 thf(f27,axiom,(
% 229.80/34.32 (nonempty = (^[X1 : $i] : ((emptyset != X1))))),
% 229.80/34.32 file('/export/starexec/sandbox2/tmp/tmp.Th7rVCfvTI/DTF2THF_17306.p',nonempty)).
% 229.80/34.32 thf(f3496,plain,(
% 229.80/34.32 ((nonempty @ sK137) = $true)),
% 229.80/34.32 inference(cnf_transformation,[status(thm)],[f1631])).
% 229.80/34.32 thf(f1631,plain,(
% 229.80/34.32 (setadjoinAx = $true) & (kpairp = $true) & (secondinupair = $true) & (emptyI = $true) & (kfstpairEq = $true) & (app = $true) & (setukpairinjR12 = $true) & (subbreln = $true) & (setadjoinIR = $true) & (eqbreln1 = $true) & (funcinfuncset = $true) & (inComplementUnionImpNotIn1 = $true) & (notinemptyset = $true) & (surjCantorThm = $true) & (ubforcartprodlem3 = $true) & (breln1all1 = $true) & (iftrueProp2 = $true) & (binunionIL = $true) & (iftrue = $true) & (upairinpowunion = $true) & (ex1I2 = $true) & (powersetE1 = $true) & (nonemptyI = $true) & (dpsetconstrSub = $true) & (woz1_4 = $true) & (dpsetconstrEL2 = $true) & (upairsetE = $true) & (demorgan2a = $true) & (eqbreln = $true) & (binunionTEcontra = $true) & (exuE3u = $true) & (woz13rule4 = $true) & (subsetTrans = $true) & (binintersectSubset1 = $true) & (upairsubunion = $true) & (setukpairinjR1 = $true) & (setunionE = $true) & (image1Equiv = $true) & (iftrueorfalse = $true) & (lam2lamEq = $true) & (nonemptyImpWitness = $true) & (cartprodsndpairEq = $true) & (complementTnotintersectT = $true) & (funcext2 = $true) & (injFuncInInjFuncSet = $true) & (binunionTE = $true) & (setadjoinSub2 = $true) & (injFuncSetFuncInj = $true) & (doubleComplementSub1 = $true) & (notdallE = $true) & (quantDeMorgan4 = $true) & (contrasubsetT2 = $true) & (sepInPowerset = $true) & (setminusER = $true) & (theprop = $true) & (emptyinunitempty = $true) & (breln1unionCommutes = $true) & (iffalseProp2 = $true) & (symdiffE = $true) & (wellorderingAx = $true) & (ksndpairEq = $true) & (exuI3 = $true) & (woz1_2 = $true) & (doubleComplementI1 = $true) & (upairsetIL = $true) & (ex1E1 = $true) & (((nonempty @ sK137) = $true) & ! [X1 : $i] : ((emptyset != (binintersect @ X1 @ sK137)) | ((in @ X1 @ sK137) != $true))) & (binintersectEL = $true) & (funcextLem = $true) & (singletonsuniq = $true) & (emptyinPowerset = $true) & (binunionRsub = $true) & (ap2apEq2 = $true) & (woz1_3 = $true) & (kpairiskpair = $true) & (woz2B = $true) & (ifSingleton = $true) & (notinsingleton = $true) & (emptysetimpfalse = $true) & (complementT_lem = $true) & (cartprodpairsurjEq = $true) & (notequalI1 = $true) & (powersetT_lem = $true) & (setminusEL = $true) & (powersetI = $true) & (setOfPairsIsBReln = $true) & (setunionsingleton1 = $true) & (powersetsubset = $true) & (binintersectSubset3 = $true) & (prop2set2propI = $true) & (setunionAx = $true) & (setminusERneg = $true) & (doubleComplementSub2 = $true) & (inIntersectImpInUnion2 = $true) & (binintersectSubset2 = $true) & (subsetI2 = $true) & (ubforcartprodlem2 = $true) & (descrp = $true) & (upairsetIR = $true) & (contrasubsetT = $true) & (setextT = $true) & (dpsetconstrI = $true) & (setminusLsub = $true) & (singletoninpowerset = $true) & (demorgan2a2 = $true) & (notsubsetI = $true) & (descr__Cong = $true) & (omega__Cong = $true) & (setminusELneg = $true) & (upairset2IR = $true) & (inComplementUnionImpInComplement1 = $true) & (emptysetE = $true) & (image1Ex = $true) & (beta2 = $true) & (breln1invI = $true) & (setukpairinjR2 = $true) & (lamp = $true) & (setOfPairsIsBReln1 = $true) & (binunionTIRcontra = $true) & (quantDeMorgan1 = $true) & (omegaSAx = $true) & (setminusSubset1 = $true) & (binintersectI = $true) & (powersetAx = $true) & (complementTcontraSubset = $true) & (exuI1 = $true) & (binintersectT_lem = $true) & (iffalse = $true) & (eta1 = $true) & (eqinunit = $true) & (woz2A = $true) & (singletonprop = $true) & (exu__Cong = $true) & (cartprodfstpairEq = $true) & (binintersectSubset4 = $true) & (lam2p = $true) & (binunionT_lem = $true) & (subsetE2 = $true) & (iftrueProp1 = $true) & (eqimpsubset1 = $true) & (infuncsetfunc = $true) & (woz2Ex = $true) & (beta1 = $true) & (symdiffI1 = $true) & (complementUnionInPowersetComplement = $true) & (setukpairinjL1 = $true) & (contraSubsetComplement = $true) & (cartprodmempair = $true) & (binintersectTELcontra = $true) & (surjFuncSetFuncSurj = $true) & (inPowerset = $true) & (apProp = $true) & (singletonsswitch = $true) & (demorgan2b = $true) & (eta2 = $true) & (setoftrueEq = $true) & (image1Ex1 = $true) & (ap2apEq1 = $true) & (dsetconstrEL = $true) & (setminusIRneg = $true) & (breln1invprop = $true) & (demorgan1a = $true) & (funcImageSingleton = $true) & (omegaIndAx = $true) & (bs114d = $true) & (cartprodpairmemEL = $true) & (upairset2E = $true) & (setbeta = $true) & (funcGraphProp1 = $true) & (injFuncSetFuncIn = $true) & (uniqinunit = $true) & (setextsub = $true) & (complementImpComplementIntersect = $true) & (disjointsetsI1 = $true) & (prop2setE = $true) & (brelnall1 = $true) & (theeq = $true) & (subsetemptysetimpeq = $true) & (setadjoinIL = $true) & (notdexE = $true) & (cartprodpairmemER = $true) & (symdiffI2 = $true) & (emptysetAx = $true) & (funcGraphProp2 = $true) & (setunion__Cong = $true) & (singletoninpowunion = $true) & (complementTI1 = $true) & (binunionTILcontra = $true) & (emptysetsubset = $true) & (setminusI = $true) & (cartprodmempaircEq = $true) & (binunionLsub = $true) & (powersetI1 = $true) & (binintersectLsub = $true) & (exuE3e = $true) & (woz13rule3 = $true) & (binunionIR = $true) & (exuEu = $true) & (breln1compE = $true) & (complementSubsetComplementIntersect = $true) & (choice2fnsingleton = $true) & (vacuousDall = $true) & (doubleComplementE1 = $true) & (upairequniteq = $true) & (binintersectSubset5 = $true) & (in__Cong = $true) & (demorgan2b2 = $true) & (woz13rule0 = $true) & (nonemptyE1 = $true) & (dpsetconstrEL1 = $true) & (breln1SetBreln1 = $true) & (setadjoinOr = $true) & (woz13rule1 = $true) & (breln1unionIR = $true) & (demorgan1b = $true) & (surjFuncSetFuncIn = $true) & (woz1_5 = $true) & (ap2p = $true) & (setadjoinSub = $true) & (cartprodpairin = $true) & (contrasubsetT3 = $true) & (binunionE = $true) & (singletonsubset = $true) & (setunionsingleton = $true) & (setukpairIR = $true) & (dpsetconstrERa = $true) & (subset2powerset = $true) & (dpsetconstrER = $true) & (ubforcartprodlem1 = $true) & (emptyE1 = $true) & (powersetTI1 = $true) & (setunionsingleton2 = $true) & (breln1unionIL = $true) & (breln1unionprop = $true) & (powerset__Cong = $true) & (woz1_1 = $true) & (setadjoin__Cong = $true) & (cartprodsndin = $true) & (subsetRefl = $true) & (funcGraphProp3 = $true) & (setextAx = $true) & (subsetE = $true) & (powersetTE1 = $true) & (binintersectRsub = $true) & (exuE2 = $true) & (lamProp = $true) & (setadjoinE = $true) & (emptyset__Cong = $true) & (setext = $true) & (subsetTI = $true) & (breln1unionEcases = $true) & (symdiffIneg2 = $true) & (foundationAx = $true) & (setminusSubset2 = $true) & (leftInvIsSurj = $true) & (ex1E2 = $true) & (binintersectTERcontra = $true) & (image1I = $true) & (powersetE = $true) & (symdiffIneg1 = $true) & (setunionE2 = $true) & (breln1compprop = $true) & (inCongP = $true) & (demorgan2a1 = $true) & (complementInPowersetComplementIntersect = $true) & (notequalI2 = $true) & (setunionI = $true) & (subsetI1 = $true) & (breln1invE = $true) & (omega0Ax = $true) & (breln1all2 = $true) & (replAx = $true) & (setminusT_lem = $true) & (doubleComplementEq = $true) & (subbreln1 = $true) & (quantDeMorgan2 = $true) & (cartprodmempair1 = $true) & (dsetconstrI = $true) & (exuI2 = $true) & (breln1compEex = $true) & (brelnall2 = $true) & (setukpairIL = $true) & (dsetconstr__Cong = $true) & (setminusILneg = $true) & (eqimpsubset2 = $true) & (kfstsingleton = $true) & (funcGraphProp4 = $true) & (image1E = $true) & (setukpairinjL = $true) & (woz13rule2 = $true) & (binunionEcases = $true) & (quantDeMorgan3 = $true) & (kpairsurjEq = $true) & (breln1unionI = $true) & (emptyInPowerset = $true) & (nonemptyI1 = $true) & (dsetconstrER = $true) & (ksndsingleton = $true) & (breln1compI = $true) & (funcext = $true) & (subPowSU = $true) & (prop2setI = $true) & (inIntersectImpInIntersectUnions = $true) & (complementTE1 = $true) & (demorgan1 = $true) & (inIntersectImpInUnion = $true) & (intersectInPowersetIntersectUnions = $true) & (setukpairinjL2 = $true) & (setukpairinjR = $true) & (contrasubsetT1 = $true) & (breln1unionE = $true) & (setukpairinjR11 = $true) & (ex1I = $true) & (iffalseProp1 = $true) & (binintersectER = $true) & (cartprodfstin = $true) & (noeltsimpempty = $true) & (exuE1 = $true) & (ifp = $true) & (woz2W = $true) & (sepSubset = $true) & (demorgan2 = $true)),
% 229.80/34.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK137])],[f1247,f1630])).
% 229.80/34.32 thf(f1630,plain,(
% 229.80/34.32 ? [X0 : $i] : (((nonempty @ X0) = $true) & ! [X1 : $i] : ((emptyset != (binintersect @ X1 @ X0)) | ((in @ X1 @ X0) != $true))) => (((nonempty @ sK137) = $true) & ! [X1 : $i] : ((emptyset != (binintersect @ X1 @ sK137)) | ((in @ X1 @ sK137) != $true)))),
% 229.80/34.32 introduced(definition,[],[choice_axiom])).
% 229.80/34.32 thf(f1247,plain,(
% 229.80/34.32 (setadjoinAx = $true) & (kpairp = $true) & (secondinupair = $true) & (emptyI = $true) & (kfstpairEq = $true) & (app = $true) & (setukpairinjR12 = $true) & (subbreln = $true) & (setadjoinIR = $true) & (eqbreln1 = $true) & (funcinfuncset = $true) & (inComplementUnionImpNotIn1 = $true) & (notinemptyset = $true) & (surjCantorThm = $true) & (ubforcartprodlem3 = $true) & (breln1all1 = $true) & (iftrueProp2 = $true) & (binunionIL = $true) & (iftrue = $true) & (upairinpowunion = $true) & (ex1I2 = $true) & (powersetE1 = $true) & (nonemptyI = $true) & (dpsetconstrSub = $true) & (woz1_4 = $true) & (dpsetconstrEL2 = $true) & (upairsetE = $true) & (demorgan2a = $true) & (eqbreln = $true) & (binunionTEcontra = $true) & (exuE3u = $true) & (woz13rule4 = $true) & (subsetTrans = $true) & (binintersectSubset1 = $true) & (upairsubunion = $true) & (setukpairinjR1 = $true) & (setunionE = $true) & (image1Equiv = $true) & (iftrueorfalse = $true) & (lam2lamEq = $true) & (nonemptyImpWitness = $true) & (cartprodsndpairEq = $true) & (complementTnotintersectT = $true) & (funcext2 = $true) & (injFuncInInjFuncSet = $true) & (binunionTE = $true) & (setadjoinSub2 = $true) & (injFuncSetFuncInj = $true) & (doubleComplementSub1 = $true) & (notdallE = $true) & (quantDeMorgan4 = $true) & (contrasubsetT2 = $true) & (sepInPowerset = $true) & (setminusER = $true) & (theprop = $true) & (emptyinunitempty = $true) & (breln1unionCommutes = $true) & (iffalseProp2 = $true) & (symdiffE = $true) & (wellorderingAx = $true) & (ksndpairEq = $true) & (exuI3 = $true) & (woz1_2 = $true) & (doubleComplementI1 = $true) & (upairsetIL = $true) & (ex1E1 = $true) & ? [X0 : $i] : (((nonempty @ X0) = $true) & ! [X1 : $i] : ((emptyset != (binintersect @ X1 @ X0)) | ((in @ X1 @ X0) != $true))) & (binintersectEL = $true) & (funcextLem = $true) & (singletonsuniq = $true) & (emptyinPowerset = $true) & (binunionRsub = $true) & (ap2apEq2 = $true) & (woz1_3 = $true) & (kpairiskpair = $true) & (woz2B = $true) & (ifSingleton = $true) & (notinsingleton = $true) & (emptysetimpfalse = $true) & (complementT_lem = $true) & (cartprodpairsurjEq = $true) & (notequalI1 = $true) & (powersetT_lem = $true) & (setminusEL = $true) & (powersetI = $true) & (setOfPairsIsBReln = $true) & (setunionsingleton1 = $true) & (powersetsubset = $true) & (binintersectSubset3 = $true) & (prop2set2propI = $true) & (setunionAx = $true) & (setminusERneg = $true) & (doubleComplementSub2 = $true) & (inIntersectImpInUnion2 = $true) & (binintersectSubset2 = $true) & (subsetI2 = $true) & (ubforcartprodlem2 = $true) & (descrp = $true) & (upairsetIR = $true) & (contrasubsetT = $true) & (setextT = $true) & (dpsetconstrI = $true) & (setminusLsub = $true) & (singletoninpowerset = $true) & (demorgan2a2 = $true) & (notsubsetI = $true) & (descr__Cong = $true) & (omega__Cong = $true) & (setminusELneg = $true) & (upairset2IR = $true) & (inComplementUnionImpInComplement1 = $true) & (emptysetE = $true) & (image1Ex = $true) & (beta2 = $true) & (breln1invI = $true) & (setukpairinjR2 = $true) & (lamp = $true) & (setOfPairsIsBReln1 = $true) & (binunionTIRcontra = $true) & (quantDeMorgan1 = $true) & (omegaSAx = $true) & (setminusSubset1 = $true) & (binintersectI = $true) & (powersetAx = $true) & (complementTcontraSubset = $true) & (exuI1 = $true) & (binintersectT_lem = $true) & (iffalse = $true) & (eta1 = $true) & (eqinunit = $true) & (woz2A = $true) & (singletonprop = $true) & (exu__Cong = $true) & (cartprodfstpairEq = $true) & (binintersectSubset4 = $true) & (lam2p = $true) & (binunionT_lem = $true) & (subsetE2 = $true) & (iftrueProp1 = $true) & (eqimpsubset1 = $true) & (infuncsetfunc = $true) & (woz2Ex = $true) & (beta1 = $true) & (symdiffI1 = $true) & (complementUnionInPowersetComplement = $true) & (setukpairinjL1 = $true) & (contraSubsetComplement = $true) & (cartprodmempair = $true) & (binintersectTELcontra = $true) & (surjFuncSetFuncSurj = $true) & (inPowerset = $true) & (apProp = $true) & (singletonsswitch = $true) & (demorgan2b = $true) & (eta2 = $true) & (setoftrueEq = $true) & (image1Ex1 = $true) & (ap2apEq1 = $true) & (dsetconstrEL = $true) & (setminusIRneg = $true) & (breln1invprop = $true) & (demorgan1a = $true) & (funcImageSingleton = $true) & (omegaIndAx = $true) & (bs114d = $true) & (cartprodpairmemEL = $true) & (upairset2E = $true) & (setbeta = $true) & (funcGraphProp1 = $true) & (injFuncSetFuncIn = $true) & (uniqinunit = $true) & (setextsub = $true) & (complementImpComplementIntersect = $true) & (disjointsetsI1 = $true) & (prop2setE = $true) & (brelnall1 = $true) & (theeq = $true) & (subsetemptysetimpeq = $true) & (setadjoinIL = $true) & (notdexE = $true) & (cartprodpairmemER = $true) & (symdiffI2 = $true) & (emptysetAx = $true) & (funcGraphProp2 = $true) & (setunion__Cong = $true) & (singletoninpowunion = $true) & (complementTI1 = $true) & (binunionTILcontra = $true) & (emptysetsubset = $true) & (setminusI = $true) & (cartprodmempaircEq = $true) & (binunionLsub = $true) & (powersetI1 = $true) & (binintersectLsub = $true) & (exuE3e = $true) & (woz13rule3 = $true) & (binunionIR = $true) & (exuEu = $true) & (breln1compE = $true) & (complementSubsetComplementIntersect = $true) & (choice2fnsingleton = $true) & (vacuousDall = $true) & (doubleComplementE1 = $true) & (upairequniteq = $true) & (binintersectSubset5 = $true) & (in__Cong = $true) & (demorgan2b2 = $true) & (woz13rule0 = $true) & (nonemptyE1 = $true) & (dpsetconstrEL1 = $true) & (breln1SetBreln1 = $true) & (setadjoinOr = $true) & (woz13rule1 = $true) & (breln1unionIR = $true) & (demorgan1b = $true) & (surjFuncSetFuncIn = $true) & (woz1_5 = $true) & (ap2p = $true) & (setadjoinSub = $true) & (cartprodpairin = $true) & (contrasubsetT3 = $true) & (binunionE = $true) & (singletonsubset = $true) & (setunionsingleton = $true) & (setukpairIR = $true) & (dpsetconstrERa = $true) & (subset2powerset = $true) & (dpsetconstrER = $true) & (ubforcartprodlem1 = $true) & (emptyE1 = $true) & (powersetTI1 = $true) & (setunionsingleton2 = $true) & (breln1unionIL = $true) & (breln1unionprop = $true) & (powerset__Cong = $true) & (woz1_1 = $true) & (setadjoin__Cong = $true) & (cartprodsndin = $true) & (subsetRefl = $true) & (funcGraphProp3 = $true) & (setextAx = $true) & (subsetE = $true) & (powersetTE1 = $true) & (binintersectRsub = $true) & (exuE2 = $true) & (lamProp = $true) & (setadjoinE = $true) & (emptyset__Cong = $true) & (setext = $true) & (subsetTI = $true) & (breln1unionEcases = $true) & (symdiffIneg2 = $true) & (foundationAx = $true) & (setminusSubset2 = $true) & (leftInvIsSurj = $true) & (ex1E2 = $true) & (binintersectTERcontra = $true) & (image1I = $true) & (powersetE = $true) & (symdiffIneg1 = $true) & (setunionE2 = $true) & (breln1compprop = $true) & (inCongP = $true) & (demorgan2a1 = $true) & (complementInPowersetComplementIntersect = $true) & (notequalI2 = $true) & (setunionI = $true) & (subsetI1 = $true) & (breln1invE = $true) & (omega0Ax = $true) & (breln1all2 = $true) & (replAx = $true) & (setminusT_lem = $true) & (doubleComplementEq = $true) & (subbreln1 = $true) & (quantDeMorgan2 = $true) & (cartprodmempair1 = $true) & (dsetconstrI = $true) & (exuI2 = $true) & (breln1compEex = $true) & (brelnall2 = $true) & (setukpairIL = $true) & (dsetconstr__Cong = $true) & (setminusILneg = $true) & (eqimpsubset2 = $true) & (kfstsingleton = $true) & (funcGraphProp4 = $true) & (image1E = $true) & (setukpairinjL = $true) & (woz13rule2 = $true) & (binunionEcases = $true) & (quantDeMorgan3 = $true) & (kpairsurjEq = $true) & (breln1unionI = $true) & (emptyInPowerset = $true) & (nonemptyI1 = $true) & (dsetconstrER = $true) & (ksndsingleton = $true) & (breln1compI = $true) & (funcext = $true) & (subPowSU = $true) & (prop2setI = $true) & (inIntersectImpInIntersectUnions = $true) & (complementTE1 = $true) & (demorgan1 = $true) & (inIntersectImpInUnion = $true) & (intersectInPowersetIntersectUnions = $true) & (setukpairinjL2 = $true) & (setukpairinjR = $true) & (contrasubsetT1 = $true) & (breln1unionE = $true) & (setukpairinjR11 = $true) & (ex1I = $true) & (iffalseProp1 = $true) & (binintersectER = $true) & (cartprodfstin = $true) & (noeltsimpempty = $true) & (exuE1 = $true) & (ifp = $true) & (woz2W = $true) & (sepSubset = $true) & (demorgan2 = $true)),
% 229.80/34.32 inference(flattening,[status(thm)],[f1246])).
% 229.80/34.32 thf(f1246,plain,(
% 229.80/34.32 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i] : (((nonempty @ X0) = $true) & ! [X1 : $i] : ((emptyset != (binintersect @ X1 @ X0)) | ((in @ X1 @ X0) != $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)),
% 229.80/34.32 inference(ennf_transformation,[status(thm)],[f489])).
% 229.80/34.32 thf(f489,plain,(
% 229.80/34.32 ~((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) => ! [X0 : $i] : (((nonempty @ X0) = $true) => ? [X1 : $i] : ((emptyset = (binintersect @ X1 @ X0)) & ((in @ X1 @ X0) = $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 229.80/34.32 inference(fool_elimination,[status(thm)],[f488])).
% 229.80/34.32 thf(f488,plain,(
% 229.80/34.32 ~(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 => ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : ((in @ X1 @ X0) & (emptyset = (binintersect @ X1 @ X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 229.80/34.32 inference(rectify,[status(thm)],[f325])).
% 229.80/34.32 thf(f325,negated_conjecture,(
% 229.80/34.32 ~(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 => ! [X3 : $i] : ((nonempty @ X3) => ? [X11 : $i] : ((in @ X11 @ X3) & (emptyset = (binintersect @ X11 @ X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 229.80/34.32 inference(negated_conjecture,[status(cth)],[f324])).
% 229.80/34.32 thf(f324,conjecture,(
% 229.80/34.32 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 => ! [X3 : $i] : ((nonempty @ X3) => ? [X11 : $i] : ((in @ X11 @ X3) & (emptyset = (binintersect @ X11 @ X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 229.80/34.32 file('/export/starexec/sandbox2/tmp/tmp.Th7rVCfvTI/DTF2THF_17306.p',foundation2)).
% 229.80/34.32 thf(f44978,plain,(
% 229.80/34.32 (emptyset = sK137)),
% 229.80/34.32 inference(subsumption_resolution,[status(thm)],[f44973,f44479])).
% 229.80/34.32 thf(f44479,plain,(
% 229.80/34.32 ((in @ (sK540 @ (sK306 @ sK137) @ sK137) @ sK137) != $true)),
% 229.80/34.32 inference(trivial_inequality_removal,[status(thm)],[f44465])).
% 229.80/34.32 thf(f44465,plain,(
% 229.80/34.32 ($true != $true) | ((in @ (sK540 @ (sK306 @ sK137) @ sK137) @ sK137) != $true)),
% 229.80/34.32 inference(superposition,[status(thm)],[f6929,f44460])).
% 229.80/34.32 thf(f44460,plain,(
% 229.80/34.32 ($true = (in @ (sK540 @ (sK306 @ sK137) @ sK137) @ (sK306 @ sK137)))),
% 229.80/34.32 inference(subsumption_resolution,[status(thm)],[f44459,f6603])).
% 229.80/34.32 thf(f44459,plain,(
% 229.80/34.32 (emptyset = sK137) | ($true = (in @ (sK540 @ (sK306 @ sK137) @ sK137) @ (sK306 @ sK137)))),
% 229.80/34.32 inference(trivial_inequality_removal,[status(thm)],[f44449])).
% 229.80/34.32 thf(f44449,plain,(
% 229.80/34.32 ($true = (in @ (sK540 @ (sK306 @ sK137) @ sK137) @ (sK306 @ sK137))) | ($true != $true) | (emptyset = sK137)),
% 229.80/34.32 inference(superposition,[status(thm)],[f24022,f8023])).
% 229.80/34.32 thf(f8023,plain,(
% 229.80/34.32 ( ! [X0 : $i] : (((in @ (sK306 @ X0) @ X0) = $true) | (emptyset = X0)) )),
% 229.80/34.32 inference(trivial_inequality_removal,[status(thm)],[f8004])).
% 229.80/34.32 thf(f8004,plain,(
% 229.80/34.32 ( ! [X0 : $i] : ((emptyset = X0) | ($true != $true) | ((in @ (sK306 @ X0) @ X0) = $true)) )),
% 229.80/34.32 inference(superposition,[status(thm)],[f6657,f7108])).
% 229.80/34.32 thf(f7108,plain,(
% 229.80/34.32 ( ! [X0 : $i] : (((in @ (sK361 @ X0) @ X0) = $true) | (emptyset = X0)) )),
% 229.80/34.32 inference(equality_proxy_clausification,[status(thm)],[f7107])).
% 229.80/34.32 thf(f7107,plain,(
% 229.80/34.32 ( ! [X0 : $i] : (((emptyset = X0) = $true) | ((in @ (sK361 @ X0) @ X0) = $true)) )),
% 229.80/34.32 inference(not_proxy_clausification,[status(thm)],[f7106])).
% 229.80/34.32 thf(f7106,plain,(
% 229.80/34.32 ( ! [X0 : $i] : (((in @ (sK361 @ X0) @ X0) = $true) | ((~ (emptyset = X0)) != $true)) )),
% 229.80/34.32 inference(beta_eta_normalization,[status(thm)],[f7105])).
% 229.80/34.32 thf(f7105,plain,(
% 229.80/34.32 ( ! [X0 : $i] : ((((^[Y0 : $i]: (~ (emptyset = Y0))) @ X0) != $true) | ((in @ (sK361 @ X0) @ X0) = $true)) )),
% 229.80/34.32 inference(trivial_inequality_removal,[status(thm)],[f5296])).
% 229.80/34.32 thf(f5296,plain,(
% 229.80/34.32 ( ! [X0 : $i] : (($true != $true) | ((in @ (sK361 @ X0) @ X0) = $true) | (((^[Y0 : $i]: (~ (emptyset = Y0))) @ X0) != $true)) )),
% 229.80/34.32 inference(definition_unfolding,[status(thm)],[f3865,f4101,f3522])).
% 229.80/34.32 thf(f3522,plain,(
% 229.80/34.32 (nonemptyImpWitness = $true)),
% 229.80/34.32 inference(cnf_transformation,[status(thm)],[f1631])).
% 229.80/34.32 thf(f3865,plain,(
% 229.80/34.32 ( ! [X0 : $i] : (((in @ (sK361 @ X0) @ X0) = $true) | ((nonempty @ X0) != $true) | (nonemptyImpWitness != $true)) )),
% 229.80/34.32 inference(cnf_transformation,[status(thm)],[f1973])).
% 229.80/34.32 thf(f1973,plain,(
% 229.80/34.32 (! [X0 : $i] : (((in @ (sK361 @ X0) @ X0) = $true) | ((nonempty @ X0) != $true)) | (nonemptyImpWitness != $true)) & ((nonemptyImpWitness = $true) | (! [X3 : $i] : ((in @ X3 @ sK362) != $true) & ((nonempty @ sK362) = $true)))),
% 229.80/34.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK361,sK362])],[f1970,f1972,f1971])).
% 229.80/34.32 thf(f1971,plain,(
% 229.80/34.32 ! [X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) = $true) => ((in @ (sK361 @ X0) @ X0) = $true))),
% 229.80/34.32 introduced(definition,[],[choice_axiom])).
% 229.80/34.32 thf(f1972,plain,(
% 229.80/34.32 ? [X2 : $i] : (! [X3 : $i] : ($true != (in @ X3 @ X2)) & ((nonempty @ X2) = $true)) => (! [X3 : $i] : ((in @ X3 @ sK362) != $true) & ((nonempty @ sK362) = $true))),
% 229.80/34.32 introduced(definition,[],[choice_axiom])).
% 229.80/34.32 thf(f1970,plain,(
% 229.80/34.32 (! [X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) = $true) | ((nonempty @ X0) != $true)) | (nonemptyImpWitness != $true)) & ((nonemptyImpWitness = $true) | ? [X2 : $i] : (! [X3 : $i] : ($true != (in @ X3 @ X2)) & ((nonempty @ X2) = $true)))),
% 229.80/34.32 inference(rectify,[status(thm)],[f1969])).
% 229.80/34.32 thf(f1969,plain,(
% 229.80/34.32 (! [X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) = $true) | ((nonempty @ X0) != $true)) | (nonemptyImpWitness != $true)) & ((nonemptyImpWitness = $true) | ? [X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) != $true) & ((nonempty @ X0) = $true)))),
% 229.80/34.32 inference(nnf_transformation,[status(thm)],[f1350])).
% 229.80/34.32 thf(f1350,plain,(
% 229.80/34.32 ! [X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) = $true) | ((nonempty @ X0) != $true)) <=> (nonemptyImpWitness = $true)),
% 229.80/34.32 inference(ennf_transformation,[status(thm)],[f1005])).
% 229.80/34.32 thf(f1005,plain,(
% 229.80/34.32 ! [X0 : $i] : (((nonempty @ X0) = $true) => ? [X1 : $i] : ((in @ X1 @ X0) = $true)) <=> (nonemptyImpWitness = $true)),
% 229.80/34.32 inference(true_and_false_elimination,[status(thm)],[f749])).
% 229.80/34.32 thf(f749,plain,(
% 229.80/34.32 (nonemptyImpWitness = $true) <=> ! [X0 : $i] : (((nonempty @ X0) = $true) => ? [X1 : $i] : (((in @ X1 @ X0) = $true) & $true))),
% 229.80/34.32 inference(fool_elimination,[status(thm)],[f748])).
% 229.80/34.32 thf(f748,plain,(
% 229.80/34.32 (nonemptyImpWitness = ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : ((in @ X1 @ X0) & $true)))),
% 229.80/34.32 inference(rectify,[status(thm)],[f45])).
% 229.80/34.32 thf(f45,axiom,(
% 229.80/34.32 (nonemptyImpWitness = ! [X3 : $i] : ((nonempty @ X3) => ? [X1 : $i] : ((in @ X1 @ X3) & $true)))),
% 229.80/34.32 file('/export/starexec/sandbox2/tmp/tmp.Th7rVCfvTI/DTF2THF_17306.p',nonemptyImpWitness)).
% 229.80/34.32 thf(f6657,plain,(
% 229.80/34.32 ( ! [X3 : $i,X0 : $i] : (((in @ X3 @ X0) != $true) | ((in @ (sK306 @ X0) @ X0) = $true)) )),
% 229.80/34.32 inference(trivial_inequality_removal,[status(thm)],[f5225])).
% 229.80/34.32 thf(f5225,plain,(
% 229.80/34.32 ( ! [X3 : $i,X0 : $i] : (((in @ (sK306 @ X0) @ X0) = $true) | ((in @ X3 @ X0) != $true) | ($true != $true)) )),
% 229.80/34.32 inference(definition_unfolding,[status(thm)],[f3796,f3309])).
% 229.80/34.32 thf(f3309,plain,(
% 229.80/34.32 (foundationAx = $true)),
% 229.80/34.32 inference(cnf_transformation,[status(thm)],[f1631])).
% 229.80/34.32 thf(f3796,plain,(
% 229.80/34.32 ( ! [X3 : $i,X0 : $i] : (((in @ (sK306 @ X0) @ X0) = $true) | ((in @ X3 @ X0) != $true) | (foundationAx != $true)) )),
% 229.80/34.32 inference(cnf_transformation,[status(thm)],[f1894])).
% 229.80/34.32 thf(f1894,plain,(
% 229.80/34.32 (! [X0 : $i] : ((((in @ (sK306 @ X0) @ X0) = $true) & ! [X2 : $i] : (($true != (in @ X2 @ (sK306 @ X0))) | ($true != (in @ X2 @ X0)))) | ! [X3 : $i] : ((in @ X3 @ X0) != $true)) | (foundationAx != $true)) & ((foundationAx = $true) | (! [X5 : $i] : (((in @ X5 @ sK307) != $true) | (($true = (in @ (sK308 @ X5) @ X5)) & ((in @ (sK308 @ X5) @ sK307) = $true))) & ((in @ sK309 @ sK307) = $true)))),
% 229.80/34.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK306,sK307,sK308,sK309])],[f1889,f1893,f1892,f1891,f1890])).
% 229.80/34.32 thf(f1890,plain,(
% 229.80/34.32 ! [X0 : $i] : (? [X1 : $i] : (((in @ X1 @ X0) = $true) & ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ($true != (in @ X2 @ X0)))) => (((in @ (sK306 @ X0) @ X0) = $true) & ! [X2 : $i] : (($true != (in @ X2 @ (sK306 @ X0))) | ($true != (in @ X2 @ X0)))))),
% 229.80/34.32 introduced(definition,[],[choice_axiom])).
% 229.80/34.32 thf(f1891,plain,(
% 229.80/34.32 ? [X4 : $i] : (! [X5 : $i] : (((in @ X5 @ X4) != $true) | ? [X6 : $i] : (((in @ X6 @ X5) = $true) & ((in @ X6 @ X4) = $true))) & ? [X7 : $i] : ((in @ X7 @ X4) = $true)) => (! [X5 : $i] : (((in @ X5 @ sK307) != $true) | ? [X6 : $i] : (((in @ X6 @ X5) = $true) & ((in @ X6 @ sK307) = $true))) & ? [X7 : $i] : ((in @ X7 @ sK307) = $true))),
% 229.80/34.32 introduced(definition,[],[choice_axiom])).
% 229.80/34.32 thf(f1892,plain,(
% 229.80/34.32 ! [X5 : $i] : (? [X6 : $i] : (((in @ X6 @ X5) = $true) & ((in @ X6 @ sK307) = $true)) => (($true = (in @ (sK308 @ X5) @ X5)) & ((in @ (sK308 @ X5) @ sK307) = $true)))),
% 229.80/34.32 introduced(definition,[],[choice_axiom])).
% 229.80/34.32 thf(f1893,plain,(
% 229.80/34.32 ? [X7 : $i] : ((in @ X7 @ sK307) = $true) => ((in @ sK309 @ sK307) = $true)),
% 229.80/34.32 introduced(definition,[],[choice_axiom])).
% 229.80/34.32 thf(f1889,plain,(
% 229.80/34.32 (! [X0 : $i] : (? [X1 : $i] : (((in @ X1 @ X0) = $true) & ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ($true != (in @ X2 @ X0)))) | ! [X3 : $i] : ((in @ X3 @ X0) != $true)) | (foundationAx != $true)) & ((foundationAx = $true) | ? [X4 : $i] : (! [X5 : $i] : (((in @ X5 @ X4) != $true) | ? [X6 : $i] : (((in @ X6 @ X5) = $true) & ((in @ X6 @ X4) = $true))) & ? [X7 : $i] : ((in @ X7 @ X4) = $true)))),
% 229.80/34.32 inference(rectify,[status(thm)],[f1888])).
% 229.80/34.32 thf(f1888,plain,(
% 229.80/34.32 (! [X0 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ X0)) & ! [X3 : $i] : (($true != (in @ X3 @ X2)) | ((in @ X3 @ X0) != $true))) | ! [X1 : $i] : ((in @ X1 @ X0) != $true)) | (foundationAx != $true)) & ((foundationAx = $true) | ? [X0 : $i] : (! [X2 : $i] : (($true != (in @ X2 @ X0)) | ? [X3 : $i] : (($true = (in @ X3 @ X2)) & ((in @ X3 @ X0) = $true))) & ? [X1 : $i] : ((in @ X1 @ X0) = $true)))),
% 229.80/34.32 inference(nnf_transformation,[status(thm)],[f1045])).
% 229.80/34.32 thf(f1045,plain,(
% 229.80/34.32 ! [X0 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ X0)) & ! [X3 : $i] : (($true != (in @ X3 @ X2)) | ((in @ X3 @ X0) != $true))) | ! [X1 : $i] : ((in @ X1 @ X0) != $true)) <=> (foundationAx = $true)),
% 229.80/34.32 inference(ennf_transformation,[status(thm)],[f843])).
% 229.80/34.32 thf(f843,plain,(
% 229.80/34.32 ! [X0 : $i] : (? [X1 : $i] : ((in @ X1 @ X0) = $true) => ? [X2 : $i] : (($true = (in @ X2 @ X0)) & ~? [X3 : $i] : (((in @ X3 @ X0) = $true) & ($true = (in @ X3 @ X2))))) <=> (foundationAx = $true)),
% 229.80/34.32 inference(fool_elimination,[status(thm)],[f842])).
% 229.80/34.32 thf(f842,plain,(
% 229.80/34.32 (foundationAx = ! [X0 : $i] : (? [X1 : $i] : (in @ X1 @ X0) => ? [X2 : $i] : (~? [X3 : $i] : ((in @ X3 @ X2) & (in @ X3 @ X0)) & (in @ X2 @ X0))))),
% 229.80/34.32 inference(rectify,[status(thm)],[f11])).
% 229.80/34.32 thf(f11,axiom,(
% 229.80/34.32 (foundationAx = ! [X3 : $i] : (? [X1 : $i] : (in @ X1 @ X3) => ? [X4 : $i] : (~? [X1 : $i] : ((in @ X1 @ X4) & (in @ X1 @ X3)) & (in @ X4 @ X3))))),
% 229.80/34.32 file('/export/starexec/sandbox2/tmp/tmp.Th7rVCfvTI/DTF2THF_17306.p',foundationAx)).
% 229.80/34.32 thf(f24022,plain,(
% 229.80/34.32 ( ! [X0 : $i] : (((in @ X0 @ sK137) != $true) | ((in @ (sK540 @ X0 @ sK137) @ X0) = $true)) )),
% 229.80/34.32 inference(trivial_inequality_removal,[status(thm)],[f23970])).
% 229.80/34.32 thf(f23970,plain,(
% 229.80/34.32 ( ! [X0 : $i] : (((in @ X0 @ sK137) != $true) | ((in @ (sK540 @ X0 @ sK137) @ X0) = $true) | (emptyset != emptyset)) )),
% 229.80/34.32 inference(superposition,[status(thm)],[f3495,f6904])).
% 229.80/34.32 thf(f6904,plain,(
% 229.80/34.32 ( ! [X3 : $i,X4 : $i] : ((emptyset = (binintersect @ X4 @ X3)) | ((in @ (sK540 @ X4 @ X3) @ X4) = $true)) )),
% 229.80/34.32 inference(trivial_inequality_removal,[status(thm)],[f5517])).
% 229.80/34.32 thf(f5517,plain,(
% 229.80/34.32 ( ! [X3 : $i,X4 : $i] : (($true != $true) | (emptyset = (binintersect @ X4 @ X3)) | ((in @ (sK540 @ X4 @ X3) @ X4) = $true)) )),
% 229.80/34.32 inference(definition_unfolding,[status(thm)],[f4112,f3388])).
% 229.80/34.32 thf(f3388,plain,(
% 229.80/34.32 (disjointsetsI1 = $true)),
% 229.80/34.32 inference(cnf_transformation,[status(thm)],[f1631])).
% 229.80/34.32 thf(f4112,plain,(
% 229.80/34.32 ( ! [X3 : $i,X4 : $i] : ((emptyset = (binintersect @ X4 @ X3)) | ((in @ (sK540 @ X4 @ X3) @ X4) = $true) | (disjointsetsI1 != $true)) )),
% 229.80/34.32 inference(cnf_transformation,[status(thm)],[f2250])).
% 229.80/34.32 thf(f2250,plain,(
% 229.80/34.32 ((disjointsetsI1 = $true) | ((emptyset != (binintersect @ sK539 @ sK538)) & ! [X2 : $i] : (((in @ X2 @ sK539) != $true) | ((in @ X2 @ sK538) != $true)))) & (! [X3 : $i,X4 : $i] : ((emptyset = (binintersect @ X4 @ X3)) | (((in @ (sK540 @ X4 @ X3) @ X4) = $true) & ((in @ (sK540 @ X4 @ X3) @ X3) = $true))) | (disjointsetsI1 != $true))),
% 229.80/34.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK538,sK539,sK540])],[f2247,f2249,f2248])).
% 229.80/34.32 thf(f2248,plain,(
% 229.80/34.32 ? [X0 : $i,X1 : $i] : ((emptyset != (binintersect @ X1 @ X0)) & ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ($true != (in @ X2 @ X0)))) => ((emptyset != (binintersect @ sK539 @ sK538)) & ! [X2 : $i] : (((in @ X2 @ sK539) != $true) | ((in @ X2 @ sK538) != $true)))),
% 229.80/34.32 introduced(definition,[],[choice_axiom])).
% 229.80/34.32 thf(f2249,plain,(
% 229.80/34.32 ! [X3 : $i,X4 : $i] : (? [X5 : $i] : (((in @ X5 @ X4) = $true) & ((in @ X5 @ X3) = $true)) => (((in @ (sK540 @ X4 @ X3) @ X4) = $true) & ((in @ (sK540 @ X4 @ X3) @ X3) = $true)))),
% 229.80/34.32 introduced(definition,[],[choice_axiom])).
% 229.80/34.32 thf(f2247,plain,(
% 229.80/34.32 ((disjointsetsI1 = $true) | ? [X0 : $i,X1 : $i] : ((emptyset != (binintersect @ X1 @ X0)) & ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ($true != (in @ X2 @ X0))))) & (! [X3 : $i,X4 : $i] : ((emptyset = (binintersect @ X4 @ X3)) | ? [X5 : $i] : (((in @ X5 @ X4) = $true) & ((in @ X5 @ X3) = $true))) | (disjointsetsI1 != $true))),
% 229.80/34.32 inference(rectify,[status(thm)],[f2246])).
% 229.80/34.32 thf(f2246,plain,(
% 229.80/34.32 ((disjointsetsI1 = $true) | ? [X0 : $i,X1 : $i] : ((emptyset != (binintersect @ X1 @ X0)) & ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ($true != (in @ X2 @ X0))))) & (! [X0 : $i,X1 : $i] : ((emptyset = (binintersect @ X1 @ X0)) | ? [X2 : $i] : (((in @ X2 @ X1) = $true) & ($true = (in @ X2 @ X0)))) | (disjointsetsI1 != $true))),
% 229.80/34.32 inference(nnf_transformation,[status(thm)],[f1179])).
% 229.80/34.32 thf(f1179,plain,(
% 229.80/34.32 (disjointsetsI1 = $true) <=> ! [X0 : $i,X1 : $i] : ((emptyset = (binintersect @ X1 @ X0)) | ? [X2 : $i] : (((in @ X2 @ X1) = $true) & ($true = (in @ X2 @ X0))))),
% 229.80/34.32 inference(ennf_transformation,[status(thm)],[f627])).
% 229.80/34.32 thf(f627,plain,(
% 229.80/34.32 (disjointsetsI1 = $true) <=> ! [X0 : $i,X1 : $i] : (~? [X2 : $i] : (((in @ X2 @ X1) = $true) & ($true = (in @ X2 @ X0))) => (emptyset = (binintersect @ X1 @ X0)))),
% 229.80/34.32 inference(fool_elimination,[status(thm)],[f626])).
% 229.80/34.32 thf(f626,plain,(
% 229.80/34.32 (! [X0 : $i,X1 : $i] : (~? [X2 : $i] : ((in @ X2 @ X0) & (in @ X2 @ X1)) => (emptyset = (binintersect @ X1 @ X0))) = disjointsetsI1)),
% 229.80/34.32 inference(rectify,[status(thm)],[f115])).
% 229.80/34.32 thf(f115,axiom,(
% 229.80/34.32 (! [X4 : $i,X3 : $i] : (~? [X1 : $i] : ((in @ X1 @ X4) & (in @ X1 @ X3)) => (emptyset = (binintersect @ X3 @ X4))) = disjointsetsI1)),
% 229.80/34.32 file('/export/starexec/sandbox2/tmp/tmp.Th7rVCfvTI/DTF2THF_17306.p',disjointsetsI1)).
% 229.80/34.32 thf(f3495,plain,(
% 229.80/34.32 ( ! [X1 : $i] : ((emptyset != (binintersect @ X1 @ sK137)) | ((in @ X1 @ sK137) != $true)) )),
% 229.80/34.32 inference(cnf_transformation,[status(thm)],[f1631])).
% 229.80/34.32 thf(f6929,plain,(
% 229.80/34.32 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ (sK306 @ X1)) != $true) | ($true != (in @ X0 @ X1))) )),
% 229.80/34.32 inference(condensation,[status(thm)],[f6928])).
% 229.80/34.32 thf(f6928,plain,(
% 229.80/34.32 ( ! [X2 : $i,X3 : $i,X0 : $i] : (($true != (in @ X2 @ X0)) | ((in @ X3 @ X0) != $true) | ($true != (in @ X2 @ (sK306 @ X0)))) )),
% 229.80/34.32 inference(trivial_inequality_removal,[status(thm)],[f5226])).
% 229.80/34.32 thf(f5226,plain,(
% 229.80/34.32 ( ! [X2 : $i,X3 : $i,X0 : $i] : (($true != (in @ X2 @ X0)) | ($true != $true) | ($true != (in @ X2 @ (sK306 @ X0))) | ((in @ X3 @ X0) != $true)) )),
% 229.80/34.32 inference(definition_unfolding,[status(thm)],[f3795,f3309])).
% 229.80/34.32 thf(f3795,plain,(
% 229.80/34.32 ( ! [X2 : $i,X3 : $i,X0 : $i] : (($true != (in @ X2 @ (sK306 @ X0))) | ($true != (in @ X2 @ X0)) | ((in @ X3 @ X0) != $true) | (foundationAx != $true)) )),
% 229.80/34.32 inference(cnf_transformation,[status(thm)],[f1894])).
% 229.80/34.32 thf(f44973,plain,(
% 229.80/34.32 ((in @ (sK540 @ (sK306 @ sK137) @ sK137) @ sK137) = $true) | (emptyset = sK137)),
% 229.80/34.32 inference(trivial_inequality_removal,[status(thm)],[f44965])).
% 229.80/34.32 thf(f44965,plain,(
% 229.80/34.32 (emptyset = sK137) | ((in @ (sK540 @ (sK306 @ sK137) @ sK137) @ sK137) = $true) | ($true != $true)),
% 229.80/34.32 inference(superposition,[status(thm)],[f24524,f8023])).
% 229.80/34.32 thf(f24524,plain,(
% 229.80/34.32 ( ! [X0 : $i] : (((in @ X0 @ sK137) != $true) | ($true = (in @ (sK540 @ X0 @ sK137) @ sK137))) )),
% 229.80/34.32 inference(trivial_inequality_removal,[status(thm)],[f24472])).
% 229.80/34.32 thf(f24472,plain,(
% 229.80/34.32 ( ! [X0 : $i] : (($true = (in @ (sK540 @ X0 @ sK137) @ sK137)) | ((in @ X0 @ sK137) != $true) | (emptyset != emptyset)) )),
% 229.80/34.32 inference(superposition,[status(thm)],[f3495,f7007])).
% 229.80/34.32 thf(f7007,plain,(
% 229.80/34.32 ( ! [X3 : $i,X4 : $i] : ((emptyset = (binintersect @ X4 @ X3)) | ((in @ (sK540 @ X4 @ X3) @ X3) = $true)) )),
% 229.80/34.32 inference(trivial_inequality_removal,[status(thm)],[f5518])).
% 229.80/34.32 thf(f5518,plain,(
% 229.80/34.32 ( ! [X3 : $i,X4 : $i] : (($true != $true) | ((in @ (sK540 @ X4 @ X3) @ X3) = $true) | (emptyset = (binintersect @ X4 @ X3))) )),
% 229.80/34.32 inference(definition_unfolding,[status(thm)],[f4111,f3388])).
% 229.80/34.32 thf(f4111,plain,(
% 229.80/34.32 ( ! [X3 : $i,X4 : $i] : ((emptyset = (binintersect @ X4 @ X3)) | ((in @ (sK540 @ X4 @ X3) @ X3) = $true) | (disjointsetsI1 != $true)) )),
% 229.80/34.32 inference(cnf_transformation,[status(thm)],[f2250])).
% 229.80/34.32 % SZS output end Proof for DTF2THF_17306
% 229.80/34.32 % (18050)------------------------------
% 229.80/34.32 % (18050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 229.80/34.32 % (18050)Termination reason: Refutation
% 229.80/34.32
% 229.80/34.32 % (18050)Memory used [KB]: 25458
% 229.80/34.32 % (18050)Time elapsed: 4.845 s
% 229.80/34.32 % (18050)Instructions burned: 11249 (million)
% 229.80/34.32 % (18050)------------------------------
% 229.80/34.32 % (18050)------------------------------
% 229.80/34.32 % (17465)Success in time 32.705 s
%------------------------------------------------------------------------------