%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU781^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n031.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 09:37:08 AM UTC 2026
% Result : Theorem 225.00s 33.32s
% Output : Refutation 225.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 21
% Syntax : Number of formulae : 124 ( 27 unt; 0 typ; 6 def)
% Number of atoms : 6808 (1731 equ; 0 cnn)
% Maximal formula atoms : 307 ( 54 avg)
% Number of connectives : 4950 ( 371 ~; 348 |;1016 &;1955 @)
% ( 11 <=>;1249 =>; 0 <=; 0 <~>)
% Maximal formula depth : 319 ( 23 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 834 ( 831 usr; 317 con; 0-5 aty)
% Number of variables : 323 ( 65 ^; 184 !; 74 ?; 323 :)
% 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,
sP1: $i > $i > $i > $i > $o ).
thf(func_def_364,type,
sP5: $i > $i > $i > $o ).
thf(func_def_365,type,
sP6: $i > $i > $i > $o > $o ).
thf(func_def_368,type,
sP9: $i > $i > $o ).
thf(func_def_369,type,
sP10: $i > $o ).
thf(func_def_370,type,
sP11: $i > $i > $o ).
thf(func_def_371,type,
sP12: $i > $i > $o ).
thf(func_def_373,type,
sP14: $i > $i > $i > $o ).
thf(func_def_380,type,
sK21: $i > $o ).
thf(func_def_383,type,
sK24: $i > $i ).
thf(func_def_386,type,
sK27: $i > $i > ( $i > $i ) > $i ).
thf(func_def_398,type,
sK39: $i > $o ).
thf(func_def_420,type,
sK61: $i > $i > $o ).
thf(func_def_438,type,
sK79: $i > $i > $o ).
thf(func_def_440,type,
sK81: $i > $i ).
thf(func_def_443,type,
sK84: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_444,type,
sK85: $i > ( $i > $o ) > $i ).
thf(func_def_445,type,
sK86: $i > $o ).
thf(func_def_451,type,
sK92: $i > $i > $o ).
thf(func_def_457,type,
sK98: $i > $o ).
thf(func_def_459,type,
sK100: ( $i > $o ) > $i > $i ).
thf(func_def_468,type,
sK109: $i > $o ).
thf(func_def_469,type,
sK110: $i > $o ).
thf(func_def_472,type,
sK113: $i > ( $i > $o ) > $i ).
thf(func_def_481,type,
sK122: $i > $i > $o ).
thf(func_def_482,type,
sK123: $i > $o ).
thf(func_def_485,type,
sK126: $i > ( $i > $o ) > $i ).
thf(func_def_486,type,
sK127: $i > ( $i > $o ) > $i ).
thf(func_def_491,type,
sK132: $i > $i > $o ).
thf(func_def_505,type,
sK146: ( $i > $o ) > $i > $i ).
thf(func_def_507,type,
sK148: $i > $o ).
thf(func_def_525,type,
sK166: $i > $i > $o ).
thf(func_def_533,type,
sK174: $i > $o ).
thf(func_def_540,type,
sK181: $i > $o ).
thf(func_def_542,type,
sK183: $i > $o ).
thf(func_def_544,type,
sK185: $i > ( $i > $o ) > $i > $i ).
thf(func_def_545,type,
sK186: $i > $o ).
thf(func_def_552,type,
sK193: $i > $i ).
thf(func_def_554,type,
sK195: $i > $i ).
thf(func_def_560,type,
sK201: $i > $i > $i ).
thf(func_def_577,type,
sK218: $i > $i ).
thf(func_def_580,type,
sK221: $i > $i > ( $i > $i ) > $i ).
thf(func_def_587,type,
sK228: $i > ( $i > $o ) > $i ).
thf(func_def_588,type,
sK229: $i > $o ).
thf(func_def_595,type,
sK236: $i > $o ).
thf(func_def_631,type,
sK272: $i > $i > $i ).
thf(func_def_639,type,
sK280: $i > $o ).
thf(func_def_644,type,
sK285: $i > $o ).
thf(func_def_646,type,
sK287: $i > ( $i > $o ) > $i ).
thf(func_def_649,type,
sK290: ( $i > $o ) > $i ).
thf(func_def_650,type,
sK291: ( $i > $o ) > $i ).
thf(func_def_651,type,
sK292: $i > $o ).
thf(func_def_663,type,
sK304: $i > $i > $i > $i > $i ).
thf(func_def_664,type,
sK305: $i > $i > $i > $i > $i ).
thf(func_def_665,type,
sK306: $i > $i > $i > $i > $i ).
thf(func_def_666,type,
sK307: $i > $i > $i > $i > $i ).
thf(func_def_676,type,
sK317: $i > $i > $i > $i > $i > $i ).
thf(func_def_702,type,
sK343: $i > $i > $i ).
thf(func_def_709,type,
sK350: $i > $i > $i ).
thf(func_def_713,type,
sK354: ( $i > $o ) > $i > $i > $i ).
thf(func_def_714,type,
sK355: ( $i > $o ) > $i > $i > $i ).
thf(func_def_717,type,
sK358: $i > $o ).
thf(func_def_719,type,
sK360: $i > $i > $i > $i ).
thf(func_def_755,type,
sK396: $i > $i > $i > $i ).
thf(func_def_759,type,
sK400: $i > $i > $i > $i ).
thf(func_def_765,type,
sK406: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_766,type,
sK407: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_770,type,
sK411: $i > $o ).
thf(func_def_777,type,
sK418: $i > $i ).
thf(func_def_780,type,
sK421: $i > $i > $i ).
thf(func_def_783,type,
sK424: $i > $i > $i > $i > $i ).
thf(func_def_795,type,
sK436: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_796,type,
sK437: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_800,type,
sK441: $i > $o ).
thf(func_def_802,type,
sK443: ( $i > $o ) > $i > $i > $i ).
thf(func_def_803,type,
sK444: ( $i > $o ) > $i > $i > $i ).
thf(func_def_806,type,
sK447: $i > $o ).
thf(func_def_810,type,
sK451: $i > $i > $i ).
thf(func_def_811,type,
sK452: $i > $i > $i ).
thf(func_def_816,type,
sK457: $i > ( $i > $o ) > $i ).
thf(func_def_817,type,
sK458: $i > $o ).
thf(func_def_844,type,
sK485: $i > $o ).
thf(func_def_860,type,
sK501: $i > ( $i > $i ) > $i > $i ).
thf(func_def_862,type,
sK503: $i > $i ).
thf(func_def_890,type,
sK531: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_891,type,
sK532: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_894,type,
sK535: $i > $o ).
thf(func_def_895,type,
sK536: $i > $o ).
thf(func_def_907,type,
sK548: $i > $o ).
thf(func_def_908,type,
sK549: $i > $i ).
thf(func_def_909,type,
sK550: ( $i > $o ) > $i ).
thf(func_def_914,type,
sK555: $i > $i > $i > $i > $i ).
thf(func_def_915,type,
sK556: $i > $i > $i > $i > $i ).
thf(func_def_927,type,
sK568: $i > $o ).
thf(func_def_938,type,
sK579: $i > $i > $i > $i ).
thf(func_def_939,type,
sK580: $i > $i > $i > $i ).
thf(func_def_945,type,
sK586: $i > $i ).
thf(func_def_952,type,
sK593: $i > $i > $i ).
thf(func_def_957,type,
sK598: $i > $o ).
thf(func_def_975,type,
sK616: $i > $i ).
thf(func_def_977,type,
sK618: ( $i > $i ) > $i > $i > $i ).
thf(func_def_992,type,
sK633: $i > $o ).
thf(func_def_993,type,
sK634: $i > $o ).
thf(func_def_994,type,
sK635: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_995,type,
sK636: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1005,type,
sK646: $i > $i > $i > $i ).
thf(func_def_1006,type,
sK647: $i > $i > $i ).
thf(func_def_1014,type,
sK655: $i > $i > $i > $i ).
thf(func_def_1015,type,
sK656: $i > $i > $i > $i ).
thf(func_def_1023,type,
sK664: $i > $i ).
thf(func_def_1029,type,
sK670: $i > $i > $i > $i > $i ).
thf(func_def_1036,type,
sK677: $i > $i > $o ).
thf(func_def_1045,type,
sK686: ( $i > $o ) > $i ).
thf(func_def_1046,type,
sK687: $i > $o ).
thf(func_def_1047,type,
sK688: $i > $i ).
thf(func_def_1053,type,
sK694: $i > $i ).
thf(func_def_1054,type,
sK695: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1055,type,
sK696: ( $i > $o ) > $i > $i ).
thf(func_def_1057,type,
sK698: $i > $o ).
thf(func_def_1059,type,
sK700: $i > $o ).
thf(func_def_1062,type,
sK703: $i > ( $i > $o ) > $i ).
thf(func_def_1063,type,
sK704: $i > ( $i > $o ) > $i ).
thf(func_def_1076,type,
sK717: $i > $i > $i > $i > $i ).
thf(func_def_1084,type,
sK725: $o > $i > $i > $i ).
thf(func_def_1088,type,
sK729: $i > $i > $i ).
thf(func_def_1089,type,
sK730: $i > $i > $i ).
thf(func_def_1090,type,
sK731: $i > $i > $i ).
thf(func_def_1091,type,
sK732: $i > $i > $i ).
thf(func_def_1092,type,
sK733: $i > $i > $i > $i ).
thf(func_def_1093,type,
sK734: $i > $i ).
thf(func_def_1094,type,
sK735: $i > $i ).
thf(func_def_1095,type,
sK736: $i > $i ).
thf(func_def_1096,type,
sK737: $i > $i ).
thf(func_def_1097,type,
sK738: $i > $i > $i ).
thf(func_def_1098,type,
sK739: $i > $i > $i > $i ).
thf(func_def_1099,type,
sK740: $i > $i > $i > $i ).
thf(func_def_1100,type,
sK741: $i > $i > $i ).
thf(func_def_1101,type,
sK742: $i > $i > $i ).
thf(func_def_1103,type,
sK744: $i > $i ).
thf(func_def_1104,type,
sK745: $i > $i ).
thf(func_def_1105,type,
sK746: $i > $i ).
thf(func_def_1106,type,
sK747: $i > $i > $i ).
thf(func_def_1121,type,
sK762: ( $i > $o ) > $i ).
thf(func_def_1122,type,
sK763: $i > $o ).
thf(func_def_1159,type,
sK800: $i > $i > $i ).
thf(func_def_1174,type,
sK815: $i > $i > $o ).
thf(func_def_1176,type,
sK817: $i > $i ).
thf(func_def_1177,type,
sK818: $i > $i ).
thf(func_def_1178,type,
sK819: $i > ( $i > $i > $o ) > $i ).
thf(func_def_1179,type,
sK820: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_1180,type,
sK821: $i > ( $i > $i > $o ) > $i ).
thf(func_def_1204,type,
sK845: $i > $i > $i > $i ).
thf(func_def_1205,type,
sK846: $i > $i > $i > $i ).
thf(func_def_1206,type,
sK847: $i > $i > $i > $i ).
thf(func_def_1207,type,
sK848: $i > $i > $i > $i ).
thf(func_def_1236,type,
sK877: $i > $o ).
thf(func_def_1237,type,
sK878: $i > $o ).
thf(func_def_1238,type,
sK879: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1239,type,
sK880: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1258,type,
sK899: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1259,type,
sK900: $i > $i ).
thf(func_def_1266,type,
sK907: ( $i > $o ) > $i > $i ).
thf(func_def_1268,type,
sK909: $i > $o ).
thf(func_def_1301,type,
sK942: $i > $i ).
thf(func_def_1305,type,
sK946: $i > $i > $o ).
thf(func_def_1311,type,
sK952: $i > $o ).
thf(func_def_1316,type,
sK957: $i > $i > $o ).
thf(func_def_1321,type,
sK962: $i > $o ).
thf(func_def_1335,type,
sK976: $i > $i ).
thf(func_def_1351,type,
sP992: $o > $o ).
thf(func_def_1352,type,
sP993: $o > $o ).
thf(func_def_1353,type,
sP994: $o > $o ).
thf(func_def_1354,type,
sP995: $o > $o ).
thf(func_def_1355,type,
sP996: $o > $o ).
thf(func_def_1356,type,
sP997: $o > $o ).
thf(func_def_1357,type,
sP998: $o > $o ).
thf(func_def_1358,type,
sP999: $o > $o ).
thf(func_def_1359,type,
sP1000: $o > $o ).
thf(func_def_1360,type,
sP1001: $i > $o ).
thf(func_def_1361,type,
sP1002: $o > $o ).
thf(func_def_1362,type,
sP1003: $o > $o ).
thf(func_def_1363,type,
sP1004: $o > $o ).
thf(func_def_1364,type,
sP1005: $i > $o ).
thf(func_def_1365,type,
sP1006: $o > $o ).
thf(func_def_1366,type,
sP1007: $o > $o ).
thf(func_def_1367,type,
sP1008: $o > $o ).
thf(func_def_1368,type,
sP1009: $o > $o ).
thf(func_def_1369,type,
sP1010: $o > $o ).
thf(func_def_1370,type,
sP1011: $o > $o ).
thf(func_def_1371,type,
sP1012: $o > $o ).
thf(func_def_1372,type,
sP1013: $o > $o ).
thf(func_def_1373,type,
sP1014: $o > $o ).
thf(func_def_1374,type,
sP1015: $o > $o ).
thf(func_def_1375,type,
sP1016: $o > $o ).
thf(func_def_1376,type,
sP1017: $o > $o ).
thf(func_def_1377,type,
sP1018: $o > $o ).
thf(func_def_1378,type,
sP1019: $o > $o ).
thf(func_def_1379,type,
sP1020: $o > $o ).
thf(func_def_1380,type,
sP1021: $o > $o ).
thf(func_def_1381,type,
sP1022: $o > $o ).
thf(func_def_1382,type,
sP1023: $i > $o ).
thf(func_def_1383,type,
sP1024: $o > $o ).
thf(func_def_1384,type,
sP1025: $o > $o ).
thf(func_def_1385,type,
sP1026: $o > $o ).
thf(func_def_1386,type,
sP1027: $o > $o ).
thf(func_def_1387,type,
sP1028: $o > $o ).
thf(func_def_1388,type,
sP1029: $o > $o ).
thf(func_def_1389,type,
sP1030: $o > $o ).
thf(func_def_1390,type,
sP1031: $o > $o ).
thf(func_def_1391,type,
sP1032: $o > $o ).
thf(func_def_1392,type,
sP1033: $o > $o ).
thf(func_def_1393,type,
sP1034: $o > $o ).
thf(func_def_1394,type,
sP1035: $o > $o ).
thf(func_def_1395,type,
sP1036: $o > $o ).
thf(func_def_1396,type,
sP1037: $o > $o ).
thf(func_def_1397,type,
sP1038: $o > $o ).
thf(func_def_1398,type,
sP1039: $o > $o ).
thf(func_def_1399,type,
sP1040: $o > $o ).
thf(func_def_1400,type,
sP1041: $o > $o ).
thf(func_def_1401,type,
sP1042: $o > $o ).
thf(func_def_1402,type,
sP1043: $i > $o ).
thf(func_def_1403,type,
sP1044: $o > $o ).
thf(func_def_1404,type,
sP1045: $o > $o ).
thf(func_def_1405,type,
sP1046: $o > $o ).
thf(func_def_1406,type,
sP1047: $o > $o ).
thf(func_def_1407,type,
sP1048: $o > $o ).
thf(func_def_1408,type,
sP1049: $o > $o ).
thf(func_def_1409,type,
sP1050: $o > $o ).
thf(func_def_1410,type,
sP1051: $o > $o ).
thf(func_def_1411,type,
sP1052: $i > $o ).
thf(func_def_1412,type,
sP1053: $o > $o ).
thf(func_def_1413,type,
sP1054: $o > $o ).
thf(func_def_1414,type,
sP1055: $o > $o ).
thf(func_def_1415,type,
sP1056: $o > $o ).
thf(func_def_1416,type,
sP1057: $o > $o ).
thf(func_def_1417,type,
sP1058: $o > $o ).
thf(func_def_1418,type,
sP1059: $o > $o ).
thf(func_def_1419,type,
sP1060: $o > $o ).
thf(func_def_1420,type,
sP1061: $o > $o ).
thf(func_def_1421,type,
sP1062: $o > $o ).
thf(func_def_1422,type,
sP1063: $o > $o ).
thf(func_def_1423,type,
sP1064: $o > $o ).
thf(func_def_1424,type,
sP1065: $o > $o ).
thf(func_def_1425,type,
sP1066: $o > $o ).
thf(func_def_1426,type,
sP1067: $o > $o ).
thf(func_def_1427,type,
sP1068: $o > $o ).
thf(func_def_1428,type,
sP1069: $o > $o ).
thf(func_def_1429,type,
sP1070: $o > $o ).
thf(func_def_1430,type,
sP1071: $o > $o ).
thf(func_def_1431,type,
sP1072: $o > $o ).
thf(func_def_1432,type,
sP1073: $o > $o ).
thf(func_def_1433,type,
sP1074: $o > $o ).
thf(func_def_1434,type,
sP1075: $o > $o ).
thf(func_def_1435,type,
sP1076: $o > $o ).
thf(func_def_1436,type,
sP1077: $o > $o ).
thf(func_def_1437,type,
sP1078: $i > $o ).
thf(func_def_1438,type,
sP1079: $o > $o ).
thf(func_def_1439,type,
sP1080: $o > $o ).
thf(func_def_1440,type,
sP1081: $o > $o ).
thf(func_def_1441,type,
sP1082: $i > $o ).
thf(func_def_1442,type,
sP1083: $o > $o ).
thf(func_def_1443,type,
sP1084: $o > $o ).
thf(func_def_1444,type,
sP1085: $o > $o ).
thf(func_def_1445,type,
sP1086: $o > $o ).
thf(func_def_1446,type,
sP1087: $o > $o ).
thf(func_def_1447,type,
sP1088: $o > $o ).
thf(func_def_1448,type,
sP1089: $o > $o ).
thf(func_def_1449,type,
sP1090: $i > $o ).
thf(func_def_1450,type,
sP1091: $o > $o ).
thf(func_def_1451,type,
sP1092: $i > $o ).
thf(func_def_1452,type,
sP1093: $i > $o ).
thf(func_def_1453,type,
sP1094: $o > $o ).
thf(func_def_1454,type,
sP1095: $o > $o ).
thf(func_def_1455,type,
sP1096: $o > $o ).
thf(func_def_1456,type,
sP1097: $o > $o ).
thf(func_def_1457,type,
sP1098: $o > $o ).
thf(func_def_1458,type,
sP1099: $o > $o ).
thf(func_def_1459,type,
sP1100: $o > $o ).
thf(func_def_1460,type,
sP1101: $o > $o ).
thf(func_def_1461,type,
sP1102: $o > $o ).
thf(func_def_1462,type,
sP1103: $o > $o ).
thf(func_def_1463,type,
sP1104: $o > $o ).
thf(func_def_1464,type,
sP1105: $o > $o ).
thf(func_def_1465,type,
sP1106: $o > $o ).
thf(func_def_1466,type,
sP1107: $o > $o ).
thf(func_def_1467,type,
sP1108: $o > $o ).
thf(func_def_1468,type,
sP1109: $o > $o ).
thf(func_def_1469,type,
sP1110: $o > $o ).
thf(func_def_1470,type,
sP1111: $o > $o ).
thf(func_def_1471,type,
sP1112: $o > $o ).
thf(func_def_1472,type,
sP1113: $o > $o ).
thf(func_def_1473,type,
sP1114: $o > $o ).
thf(func_def_1474,type,
sP1115: $i > $o ).
thf(func_def_1475,type,
sP1116: $o > $o ).
thf(func_def_1476,type,
sP1117: $o > $o ).
thf(func_def_1477,type,
sP1118: $o > $o ).
thf(func_def_1478,type,
sP1119: $i > $o ).
thf(func_def_1479,type,
sP1120: $o > $o ).
thf(func_def_1480,type,
sP1121: $o > $o ).
thf(func_def_1481,type,
sP1122: $o > $o ).
thf(func_def_1482,type,
sP1123: $o > $o ).
thf(func_def_1483,type,
sP1124: $o > $o ).
thf(func_def_1484,type,
sP1125: $o > $o ).
thf(func_def_1485,type,
sP1126: $o > $o ).
thf(func_def_1486,type,
sP1127: $o > $o ).
thf(func_def_1487,type,
sP1128: $o > $o ).
thf(func_def_1488,type,
sP1129: $o > $o ).
thf(func_def_1489,type,
sP1130: $i > $o ).
thf(func_def_1490,type,
sP1131: $o > $o ).
thf(func_def_1491,type,
sP1132: $o > $o ).
thf(func_def_1492,type,
sP1133: $i > $o ).
thf(func_def_1493,type,
sP1134: $o > $o ).
thf(func_def_1494,type,
sP1135: $o > $o ).
thf(func_def_1495,type,
sP1136: $i > $o ).
thf(func_def_1496,type,
sP1137: $o > $o ).
thf(func_def_1497,type,
sP1138: $o > $o ).
thf(func_def_1498,type,
sP1139: $o > $o ).
thf(func_def_1499,type,
sP1140: $o > $o ).
thf(func_def_1500,type,
sP1141: $o > $o ).
thf(func_def_1501,type,
sP1142: $o > $o ).
thf(func_def_1502,type,
sP1143: $i > $o ).
thf(func_def_1503,type,
sP1144: $o > $o ).
thf(func_def_1504,type,
sP1145: $i > $o ).
thf(func_def_1505,type,
sP1146: $i > $o ).
thf(func_def_1506,type,
sP1147: $o > $o ).
thf(func_def_1507,type,
sP1148: $o > $o ).
thf(func_def_1508,type,
sP1149: $o > $o ).
thf(func_def_1509,type,
sP1150: $o > $o ).
thf(func_def_1510,type,
sP1151: $i > $o ).
thf(func_def_1511,type,
sP1152: $o > $o ).
thf(func_def_1512,type,
sP1153: $i > $o ).
thf(func_def_1513,type,
sP1154: $o > $o ).
thf(func_def_1514,type,
sP1155: $i > $o ).
thf(func_def_1515,type,
sP1156: $i > $o ).
thf(func_def_1516,type,
sP1157: $o > $o ).
thf(func_def_1517,type,
sP1158: $o > $o ).
thf(func_def_1518,type,
sP1159: $o > $o ).
thf(func_def_1519,type,
sP1160: $o > $o ).
thf(func_def_1520,type,
sP1161: $o > $o ).
thf(func_def_1521,type,
sP1162: $o > $o ).
thf(func_def_1522,type,
sP1163: $o > $o ).
thf(func_def_1523,type,
sP1164: $o > $o ).
thf(func_def_1524,type,
sP1165: $i > $o ).
thf(func_def_1525,type,
sP1166: $o > $o ).
thf(func_def_1526,type,
sP1167: $o > $o ).
thf(func_def_1527,type,
sP1168: $o > $o ).
thf(func_def_1528,type,
sP1169: $o > $o ).
thf(func_def_1529,type,
sP1170: $o > $o ).
thf(func_def_1530,type,
sP1171: $o > $o ).
thf(func_def_1531,type,
sP1172: $o > $o ).
thf(func_def_1532,type,
sP1173: $i > $o ).
thf(func_def_1533,type,
sP1174: $i > $o ).
thf(func_def_1534,type,
sP1175: $o > $o ).
thf(func_def_1535,type,
sP1176: $o > $o ).
thf(func_def_1536,type,
sP1177: $o > $o ).
thf(func_def_1537,type,
sP1178: $o > $o ).
thf(func_def_1538,type,
sP1179: $o > $o ).
thf(func_def_1539,type,
sP1180: $o > $o ).
thf(func_def_1540,type,
sP1181: $o > $o ).
thf(func_def_1541,type,
sP1182: $o > $o ).
thf(func_def_1542,type,
sP1183: $i > $o ).
thf(func_def_1543,type,
sP1184: $o > $o ).
thf(func_def_1544,type,
sP1185: $i > $o ).
thf(func_def_1545,type,
sP1186: $o > $o ).
thf(func_def_1546,type,
sP1187: $o > $o ).
thf(func_def_1547,type,
sP1188: $o > $o ).
thf(func_def_1548,type,
sP1189: $i > $o ).
thf(func_def_1549,type,
sP1190: $o > $o ).
thf(func_def_1550,type,
sP1191: $o > $o ).
thf(func_def_1551,type,
sP1192: $i > $o ).
thf(func_def_1552,type,
sP1193: $o > $o ).
thf(func_def_1553,type,
sP1194: $i > $o ).
thf(func_def_1554,type,
sP1195: $o > $o ).
thf(func_def_1555,type,
sP1196: $o > $o ).
thf(func_def_1556,type,
sP1197: $i > $o ).
thf(func_def_1557,type,
sP1198: $o > $o ).
thf(func_def_1558,type,
sP1199: $o > $o ).
thf(func_def_1559,type,
sP1200: $o > $o ).
thf(func_def_1560,type,
sP1201: $o > $o ).
thf(func_def_1561,type,
sP1202: $o > $o ).
thf(func_def_1562,type,
sP1203: $o > $o ).
thf(func_def_1563,type,
sP1204: $o > $o ).
thf(func_def_1564,type,
sP1205: $o > $o ).
thf(func_def_1565,type,
sP1206: $o > $o ).
thf(func_def_1566,type,
sP1207: $i > $o ).
thf(func_def_1567,type,
sP1208: $i > $o ).
thf(func_def_1568,type,
sP1209: $o > $o ).
thf(func_def_1569,type,
sP1210: $o > $o ).
thf(func_def_1570,type,
sP1211: $o > $o ).
thf(func_def_1571,type,
sP1212: $i > $o ).
thf(func_def_1572,type,
sP1213: $o > $o ).
thf(func_def_1573,type,
sP1214: $o > $o ).
thf(func_def_1574,type,
sP1215: $i > $o ).
thf(func_def_1575,type,
sP1216: $o > $o ).
thf(func_def_1576,type,
sP1217: $i > $o ).
thf(func_def_1577,type,
sP1218: $o > $o ).
thf(func_def_1578,type,
sP1219: $o > $o ).
thf(func_def_1579,type,
sP1220: $i > $o ).
thf(func_def_1580,type,
sP1221: $o > $o ).
thf(func_def_1581,type,
sP1222: $o > $o ).
thf(func_def_1582,type,
sP1223: $o > $o ).
thf(func_def_1583,type,
sP1224: $o > $o ).
thf(func_def_1584,type,
sP1225: $o > $o ).
thf(func_def_1585,type,
sP1226: $i > $o ).
thf(func_def_1586,type,
sP1227: $o > $o ).
thf(func_def_1587,type,
sP1228: $o > $o ).
thf(func_def_1588,type,
sP1229: $o > $o ).
thf(func_def_1589,type,
sP1230: $o > $o ).
thf(func_def_1590,type,
sP1231: $o > $o ).
thf(func_def_1591,type,
sP1232: $o > $o ).
thf(func_def_1592,type,
sP1233: $o > $o ).
thf(func_def_1593,type,
sP1234: $o > $o ).
thf(func_def_1594,type,
sP1235: $i > $o ).
thf(func_def_1595,type,
sP1236: $o > $o ).
thf(func_def_1596,type,
sP1237: $o > $o ).
thf(func_def_1597,type,
sP1238: $o > $o ).
thf(func_def_1598,type,
sP1239: $o > $o ).
thf(func_def_1599,type,
sP1240: $o > $o ).
thf(func_def_1600,type,
sP1241: $o > $o ).
thf(func_def_1601,type,
sP1242: $o > $o ).
thf(func_def_1602,type,
sP1243: $o > $o ).
thf(func_def_1603,type,
sP1244: $o > $o ).
thf(func_def_1604,type,
sP1245: $o > $o ).
thf(func_def_1605,type,
sP1246: $o > $o ).
thf(func_def_1606,type,
sP1247: $o > $o ).
thf(func_def_1607,type,
sP1248: $o > $o ).
thf(func_def_1609,type,
sK1250: ( $i > $o ) > $i ).
thf(func_def_1610,type,
sK1251: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_1611,type,
sK1252: ( $i > $o ) > $i ).
thf(func_def_1612,type,
sK1253: $i > ( $i > $o ) > $i ).
thf(func_def_1613,type,
sK1254: $i > ( $i > $o ) > $i ).
thf(func_def_1614,type,
sK1255: ( $i > $o ) > $i ).
thf(func_def_1615,type,
sK1256: ( $i > $o ) > $i ).
thf(func_def_1616,type,
sK1257: ( $i > $o ) > $i > $i ).
thf(func_def_1617,type,
sK1258: ( $i > $o ) > $i > $i ).
thf(func_def_1618,type,
sK1259: ( $i > $o ) > $i ).
thf(func_def_1619,type,
sK1260: ( $i > $o ) > $i > $i ).
thf(func_def_1620,type,
sK1261: ( $i > $o ) > $i > $i ).
thf(func_def_1621,type,
sK1262: ( $i > $o ) > $i ).
thf(func_def_1622,type,
sK1263: ( $i > $o ) > $i > $i ).
thf(func_def_1623,type,
sK1264: $i > ( $i > $o ) > $i ).
thf(func_def_1624,type,
sK1265: ( $i > $o ) > $i > $i ).
thf(func_def_1625,type,
sK1266: ( $i > $o ) > $i ).
thf(func_def_1626,type,
sK1267: ( $i > $o ) > $i ).
thf(func_def_1627,type,
sK1268: ( $i > $o ) > $i ).
thf(func_def_1628,type,
sK1269: ( $i > $o ) > $i > $i ).
thf(func_def_1629,type,
sK1270: ( $i > $o ) > $i ).
thf(func_def_1630,type,
sK1271: ( $i > $o ) > $i ).
thf(func_def_1631,type,
sK1272: ( $i > $o ) > $i > $i ).
thf(func_def_1632,type,
sK1273: ( $i > $o ) > $i > $i ).
thf(func_def_1633,type,
sK1274: $i > $i ).
thf(func_def_1634,type,
sK1275: ( $i > $o ) > $i ).
thf(func_def_1635,type,
sK1276: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_1636,type,
sK1277: $i > ( $i > $o ) > $i ).
thf(func_def_1637,type,
sK1278: $i > ( $i > $o ) > $i ).
thf(func_def_1638,type,
sK1279: ( $i > $o ) > $i > $i ).
thf(func_def_1639,type,
sK1280: ( $i > $o ) > $i > $i ).
thf(func_def_1640,type,
sK1281: $i > ( $i > $o ) > $i ).
thf(func_def_1641,type,
sK1282: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_1642,type,
sK1283: ( $i > $o ) > $i > $i ).
thf(func_def_1643,type,
sK1284: ( $i > $o ) > $i > $i ).
thf(func_def_1644,type,
sK1285: ( $i > $o ) > $i > $i ).
thf(func_def_1645,type,
sK1286: $i > ( $i > $o ) > $i ).
thf(func_def_1646,type,
sK1287: $i > ( $i > $o ) > $i ).
thf(func_def_1647,type,
sK1288: ( $i > $o ) > $i > $i ).
thf(func_def_1648,type,
sK1289: ( $i > $o ) > $i > $i ).
thf(func_def_1649,type,
sK1290: $i > ( $i > $o ) > $i ).
thf(func_def_1650,type,
sK1291: ( $i > $o ) > $i ).
thf(func_def_1651,type,
sK1292: ( $i > $o ) > $i ).
thf(func_def_1652,type,
ph1293:
!>[X0: $tType] : X0 ).
thf(f22114,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f7219,f7285,f7388,f7443,f7517,f8392,f22113]) ).
thf(f22113,plain,
( ~ spl1249_11
| ~ spl1249_26
| ~ spl1249_47
| ~ spl1249_56 ),
inference(avatar_contradiction_clause,[status(thm)],[f22112]) ).
thf(f22112,plain,
( $false
| ~ spl1249_11
| ~ spl1249_26
| ~ spl1249_47
| ~ spl1249_56 ),
inference(trivial_inequality_removal,[status(thm)],[f22111]) ).
thf(f22111,plain,
( ( $true = $false )
| ~ spl1249_11
| ~ spl1249_26
| ~ spl1249_47
| ~ spl1249_56 ),
inference(backward_demodulation,[status(thm)],[f16335,f22110]) ).
thf(f22110,plain,
( ( ( in @ ( kpair @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) @ sK641 ) @ sK639 )
= $false )
| ~ spl1249_26
| ~ spl1249_47
| ~ spl1249_56 ),
inference(trivial_inequality_removal,[status(thm)],[f22109]) ).
thf(f22109,plain,
( ( ( in @ ( kpair @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) @ sK641 ) @ sK639 )
= $false )
| ( $true = $false )
| ~ spl1249_26
| ~ spl1249_47
| ~ spl1249_56 ),
inference(forward_demodulation,[status(thm)],[f22092,f16318]) ).
thf(f16318,plain,
( ( $true
= ( in @ ( kpair @ sK640 @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) ) @ sK637 ) )
| ~ spl1249_47 ),
inference(trivial_inequality_removal,[status(thm)],[f16317]) ).
thf(f16317,plain,
( ( $true
= ( in @ ( kpair @ sK640 @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) ) @ sK637 ) )
| ( $true != $true )
| ~ spl1249_47 ),
inference(forward_demodulation,[status(thm)],[f16316,f3896]) ).
thf(f3896,plain,
( $true
= ( in @ sK641 @ sK638 ) ),
inference(cnf_transformation,[status(thm)],[f2293]) ).
thf(f2293,plain,
( ( binintersectT_lem = $true )
& ( foundationAx = $true )
& ( powersetTE1 = $true )
& ( notinsingleton = $true )
& ( setminusLsub = $true )
& ( setunionE = $true )
& ( complementTnotintersectT = $true )
& ( exuEu = $true )
& ( powersetTI1 = $true )
& ( setextT = $true )
& ( ap2apEq1 = $true )
& ( setoftrueEq = $true )
& ( apProp = $true )
& ( cartprodpairin = $true )
& ( subsetE2 = $true )
& ( exuE1 = $true )
& ( replAx = $true )
& ( singletonprop = $true )
& ( emptysetsubset = $true )
& ( binintersectLsub = $true )
& ( funcinfuncset = $true )
& ( demorgan2a2 = $true )
& ( ap2apEq2 = $true )
& ( app = $true )
& ( binunionEcases = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( binunionE = $true )
& ( singletoninpowerset = $true )
& ( contrasubsetT3 = $true )
& ( ex1E2 = $true )
& ( lamp = $true )
& ( cartprodfstpairEq = $true )
& ( binunionRsub = $true )
& ( ubforcartprodlem3 = $true )
& ( upairset2IR = $true )
& ( binintersectER = $true )
& ( uniqinunit = $true )
& ( setadjoinE = $true )
& ( ubforcartprodlem1 = $true )
& ( upairsubunion = $true )
& ( breln1invI = $true )
& ( ksndsingleton = $true )
& ( sepSubset = $true )
& ( binintersectTELcontra = $true )
& ( beta2 = $true )
& ( setunionsingleton = $true )
& ( dpsetconstrERa = $true )
& ( woz1_2 = $true )
& ( nonemptyI = $true )
& ( doubleComplementEq = $true )
& ( demorgan2 = $true )
& ( singletonsubset = $true )
& ( binintersectSubset2 = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( omegaSAx = $true )
& ( setminusI = $true )
& ( nonemptyE1 = $true )
& ( binintersectSubset1 = $true )
& ( subPowSU = $true )
& ( wellorderingAx = $true )
& ( kpairp = $true )
& ( beta1 = $true )
& ( emptyinunitempty = $true )
& ( woz13rule3 = $true )
& ( setukpairinjR = $true )
& ( symdiffE = $true )
& ( funcImageSingleton = $true )
& ( symdiffI2 = $true )
& ( doubleComplementE1 = $true )
& ( funcext = $true )
& ( emptysetE = $true )
& ( notequalI2 = $true )
& ( exuE3e = $true )
& ( upairsetE = $true )
& ( binintersectSubset5 = $true )
& ( lam2lamEq = $true )
& ( eta2 = $true )
& ( cartprodmempair = $true )
& ( iftrueProp1 = $true )
& ( symdiffIneg1 = $true )
& ( ifSingleton = $true )
& ( cartprodsndpairEq = $true )
& ( inIntersectImpInUnion = $true )
& ( woz1_5 = $true )
& ( setOfPairsIsBReln1 = $true )
& ( ap2p = $true )
& ( dpsetconstrI = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( $true
= ( breln1 @ sK638 @ sK639 ) )
& ( sK642 != $true )
& ! [X6: $i] :
( ( sK642 = $true )
| ( $true
!= ( in @ ( kpair @ sK640 @ X6 ) @ sK637 ) )
| ( $true
!= ( in @ X6 @ sK638 ) )
| ( $true
!= ( in @ ( kpair @ X6 @ sK641 ) @ sK639 ) ) )
& ( $true
= ( in @ sK641 @ sK638 ) )
& ( $true
= ( in @ ( kpair @ sK640 @ sK641 ) @ ( breln1compset @ sK638 @ sK637 @ sK639 ) ) )
& ( $true
= ( in @ sK640 @ sK638 ) )
& ( $true
= ( breln1 @ sK638 @ sK637 ) )
& ( binintersectSubset3 = $true )
& ( subbreln = $true )
& ( iftrueProp2 = $true )
& ( funcGraphProp2 = $true )
& ( subsetI1 = $true )
& ( funcextLem = $true )
& ( emptyE1 = $true )
& ( setukpairinjL2 = $true )
& ( quantDeMorgan4 = $true )
& ( binunionTE = $true )
& ( complementT_lem = $true )
& ( notinemptyset = $true )
& ( singletoninpowunion = $true )
& ( setext = $true )
& ( setadjoinOr = $true )
& ( omega0Ax = $true )
& ( setunionI = $true )
& ( ex1I2 = $true )
& ( cartprodmempaircEq = $true )
& ( demorgan2b = $true )
& ( inCongP = $true )
& ( woz13rule4 = $true )
& ( contrasubsetT1 = $true )
& ( subsetTI = $true )
& ( setadjoin__Cong = $true )
& ( breln1invprop = $true )
& ( dpsetconstrER = $true )
& ( setukpairinjR1 = $true )
& ( binintersectEL = $true )
& ( in__Cong = $true )
& ( theprop = $true )
& ( exu__Cong = $true )
& ( exuE2 = $true )
& ( cartprodfstin = $true )
& ( brelnall1 = $true )
& ( subsetemptysetimpeq = $true )
& ( complementSubsetComplementIntersect = $true )
& ( inPowerset = $true )
& ( dsetconstrEL = $true )
& ( lam2p = $true )
& ( vacuousDall = $true )
& ( funcext2 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( demorgan2a = $true )
& ( binunionT_lem = $true )
& ( funcGraphProp1 = $true )
& ( emptyInPowerset = $true )
& ( iffalseProp2 = $true )
& ( complementImpComplementIntersect = $true )
& ( setminusSubset1 = $true )
& ( nonemptyI1 = $true )
& ( complementTE1 = $true )
& ( powersetsubset = $true )
& ( iftrueorfalse = $true )
& ( setOfPairsIsBReln = $true )
& ( woz1_1 = $true )
& ( prop2setI = $true )
& ( upairequniteq = $true )
& ( descrp = $true )
& ( setadjoinSub2 = $true )
& ( setextAx = $true )
& ( sepInPowerset = $true )
& ( exuI2 = $true )
& ( doubleComplementSub1 = $true )
& ( breln1SetBreln1 = $true )
& ( complementTcontraSubset = $true )
& ( woz13rule1 = $true )
& ( emptysetimpfalse = $true )
& ( subbreln1 = $true )
& ( dpsetconstrEL2 = $true )
& ( notsubsetI = $true )
& ( setunionE2 = $true )
& ( contraSubsetComplement = $true )
& ( disjointsetsI1 = $true )
& ( bs114d = $true )
& ( binunionLsub = $true )
& ( setminusIRneg = $true )
& ( symdiffI1 = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( dsetconstrER = $true )
& ( upairinpowunion = $true )
& ( eqimpsubset1 = $true )
& ( setminusERneg = $true )
& ( setukpairinjR2 = $true )
& ( cartprodpairmemEL = $true )
& ( demorgan1 = $true )
& ( setunion__Cong = $true )
& ( setminusELneg = $true )
& ( setadjoinAx = $true )
& ( powersetE1 = $true )
& ( cartprodpairsurjEq = $true )
& ( eqinunit = $true )
& ( doubleComplementSub2 = $true )
& ( dsetconstr__Cong = $true )
& ( breln1compprop = $true )
& ( woz1_3 = $true )
& ( iffalseProp1 = $true )
& ( ifp = $true )
& ( setminusER = $true )
& ( upairsetIL = $true )
& ( setunionsingleton2 = $true )
& ( setadjoinSub = $true )
& ( ksndpairEq = $true )
& ( kpairsurjEq = $true )
& ( cartprodmempair1 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( kpairiskpair = $true )
& ( demorgan2b2 = $true )
& ( upairsetIR = $true )
& ( omega__Cong = $true )
& ( subsetI2 = $true )
& ( kfstsingleton = $true )
& ( kfstpairEq = $true )
& ( notequalI1 = $true )
& ( contrasubsetT = $true )
& ( breln1all1 = $true )
& ( choice2fnsingleton = $true )
& ( symdiffIneg2 = $true )
& ( theeq = $true )
& ( demorgan1a = $true )
& ( funcGraphProp3 = $true )
& ( secondinupair = $true )
& ( setminusILneg = $true )
& ( lamProp = $true )
& ( contrasubsetT2 = $true )
& ( powersetI = $true )
& ( breln1compE = $true )
& ( powerset__Cong = $true )
& ( setukpairIL = $true )
& ( setextsub = $true )
& ( binunionIL = $true )
& ( descr__Cong = $true )
& ( setminusEL = $true )
& ( eqbreln = $true )
& ( subsetTrans = $true )
& ( setbeta = $true )
& ( complementUnionInPowersetComplement = $true )
& ( powersetAx = $true )
& ( powersetT_lem = $true )
& ( cartprodsndin = $true )
& ( notdexE = $true )
& ( setukpairinjL1 = $true )
& ( woz13rule0 = $true )
& ( setadjoinIL = $true )
& ( emptyinPowerset = $true )
& ( demorgan2a1 = $true )
& ( iffalse = $true )
& ( ex1I = $true )
& ( quantDeMorgan2 = $true )
& ( powersetI1 = $true )
& ( omegaIndAx = $true )
& ( upairset2E = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjR12 = $true )
& ( ex1E1 = $true )
& ( emptyset__Cong = $true )
& ( doubleComplementI1 = $true )
& ( breln1compI = $true )
& ( prop2setE = $true )
& ( setunionsingleton1 = $true )
& ( woz1_4 = $true )
& ( infuncsetfunc = $true )
& ( setminusT_lem = $true )
& ( setukpairIR = $true )
& ( brelnall2 = $true )
& ( dpsetconstrSub = $true )
& ( woz13rule2 = $true )
& ( ubforcartprodlem2 = $true )
& ( setukpairinjL = $true )
& ( binintersectSubset4 = $true )
& ( singletonsswitch = $true )
& ( setminusSubset2 = $true )
& ( setunionAx = $true )
& ( binintersectI = $true )
& ( powersetE = $true )
& ( breln1invE = $true )
& ( quantDeMorgan1 = $true )
& ( dsetconstrI = $true )
& ( breln1all2 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( subset2powerset = $true )
& ( nonemptyImpWitness = $true )
& ( eqbreln1 = $true )
& ( complementTI1 = $true )
& ( cartprodpairmemER = $true )
& ( emptyI = $true )
& ( setadjoinIR = $true )
& ( eta1 = $true )
& ( quantDeMorgan3 = $true )
& ( binintersectRsub = $true )
& ( emptysetAx = $true )
& ( eqimpsubset2 = $true )
& ( binintersectTERcontra = $true )
& ( binunionTILcontra = $true )
& ( iftrue = $true )
& ( noeltsimpempty = $true )
& ( demorgan1b = $true )
& ( subsetE = $true )
& ( prop2set2propI = $true )
& ( binunionIR = $true )
& ( singletonsuniq = $true )
& ( dpsetconstrEL1 = $true )
& ( subsetRefl = $true )
& ( funcGraphProp4 = $true )
& ( binunionTEcontra = $true )
& ( binunionTIRcontra = $true )
& ( exuE3u = $true )
& ( notdallE = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK637,sK638,sK639,sK640,sK641,sK642])],[f1015,f2292,f2291,f2290,f2289,f2288]) ).
thf(f2288,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( breln1 @ X1 @ X2 ) )
& ? [X3: $i] :
( ? [X4: $i] :
( ? [X5: $o] :
( ( $true != X5 )
& ! [X6: $i] :
( ( $true = X5 )
| ( $true
!= ( in @ ( kpair @ X3 @ X6 ) @ X0 ) )
| ( $true
!= ( in @ X6 @ X1 ) )
| ( $true
!= ( in @ ( kpair @ X6 @ X4 ) @ X2 ) ) ) )
& ( $true
= ( in @ X4 @ X1 ) )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ X1 ) ) ) )
& ( $true
= ( breln1 @ X1 @ X0 ) ) )
=> ( ? [X2: $i] :
( ( $true
= ( breln1 @ sK638 @ X2 ) )
& ? [X3: $i] :
( ? [X4: $i] :
( ? [X5: $o] :
( ( $true != X5 )
& ! [X6: $i] :
( ( $true = X5 )
| ( ( in @ ( kpair @ X3 @ X6 ) @ sK637 )
!= $true )
| ( $true
!= ( in @ X6 @ sK638 ) )
| ( $true
!= ( in @ ( kpair @ X6 @ X4 ) @ X2 ) ) ) )
& ( $true
= ( in @ X4 @ sK638 ) )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK638 @ sK637 @ X2 ) ) ) )
& ( ( in @ X3 @ sK638 )
= $true ) ) )
& ( $true
= ( breln1 @ sK638 @ sK637 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2289,plain,
( ? [X2: $i] :
( ( $true
= ( breln1 @ sK638 @ X2 ) )
& ? [X3: $i] :
( ? [X4: $i] :
( ? [X5: $o] :
( ( $true != X5 )
& ! [X6: $i] :
( ( $true = X5 )
| ( ( in @ ( kpair @ X3 @ X6 ) @ sK637 )
!= $true )
| ( $true
!= ( in @ X6 @ sK638 ) )
| ( $true
!= ( in @ ( kpair @ X6 @ X4 ) @ X2 ) ) ) )
& ( $true
= ( in @ X4 @ sK638 ) )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK638 @ sK637 @ X2 ) ) ) )
& ( ( in @ X3 @ sK638 )
= $true ) ) )
=> ( ( $true
= ( breln1 @ sK638 @ sK639 ) )
& ? [X3: $i] :
( ? [X4: $i] :
( ? [X5: $o] :
( ( $true != X5 )
& ! [X6: $i] :
( ( $true = X5 )
| ( ( in @ ( kpair @ X3 @ X6 ) @ sK637 )
!= $true )
| ( $true
!= ( in @ X6 @ sK638 ) )
| ( $true
!= ( in @ ( kpair @ X6 @ X4 ) @ sK639 ) ) ) )
& ( $true
= ( in @ X4 @ sK638 ) )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK638 @ sK637 @ sK639 ) ) ) )
& ( ( in @ X3 @ sK638 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2290,plain,
( ? [X3: $i] :
( ? [X4: $i] :
( ? [X5: $o] :
( ( $true != X5 )
& ! [X6: $i] :
( ( $true = X5 )
| ( ( in @ ( kpair @ X3 @ X6 ) @ sK637 )
!= $true )
| ( $true
!= ( in @ X6 @ sK638 ) )
| ( $true
!= ( in @ ( kpair @ X6 @ X4 ) @ sK639 ) ) ) )
& ( $true
= ( in @ X4 @ sK638 ) )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK638 @ sK637 @ sK639 ) ) ) )
& ( ( in @ X3 @ sK638 )
= $true ) )
=> ( ? [X4: $i] :
( ? [X5: $o] :
( ( $true != X5 )
& ! [X6: $i] :
( ( $true = X5 )
| ( $true
!= ( in @ ( kpair @ sK640 @ X6 ) @ sK637 ) )
| ( $true
!= ( in @ X6 @ sK638 ) )
| ( $true
!= ( in @ ( kpair @ X6 @ X4 ) @ sK639 ) ) ) )
& ( $true
= ( in @ X4 @ sK638 ) )
& ( $true
= ( in @ ( kpair @ sK640 @ X4 ) @ ( breln1compset @ sK638 @ sK637 @ sK639 ) ) ) )
& ( $true
= ( in @ sK640 @ sK638 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2291,plain,
( ? [X4: $i] :
( ? [X5: $o] :
( ( $true != X5 )
& ! [X6: $i] :
( ( $true = X5 )
| ( $true
!= ( in @ ( kpair @ sK640 @ X6 ) @ sK637 ) )
| ( $true
!= ( in @ X6 @ sK638 ) )
| ( $true
!= ( in @ ( kpair @ X6 @ X4 ) @ sK639 ) ) ) )
& ( $true
= ( in @ X4 @ sK638 ) )
& ( $true
= ( in @ ( kpair @ sK640 @ X4 ) @ ( breln1compset @ sK638 @ sK637 @ sK639 ) ) ) )
=> ( ? [X5: $o] :
( ( $true != X5 )
& ! [X6: $i] :
( ( $true = X5 )
| ( $true
!= ( in @ ( kpair @ sK640 @ X6 ) @ sK637 ) )
| ( $true
!= ( in @ X6 @ sK638 ) )
| ( $true
!= ( in @ ( kpair @ X6 @ sK641 ) @ sK639 ) ) ) )
& ( $true
= ( in @ sK641 @ sK638 ) )
& ( $true
= ( in @ ( kpair @ sK640 @ sK641 ) @ ( breln1compset @ sK638 @ sK637 @ sK639 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2292,plain,
( ? [X5: $o] :
( ( $true != X5 )
& ! [X6: $i] :
( ( $true = X5 )
| ( $true
!= ( in @ ( kpair @ sK640 @ X6 ) @ sK637 ) )
| ( $true
!= ( in @ X6 @ sK638 ) )
| ( $true
!= ( in @ ( kpair @ X6 @ sK641 ) @ sK639 ) ) ) )
=> ( ( sK642 != $true )
& ! [X6: $i] :
( ( sK642 = $true )
| ( $true
!= ( in @ ( kpair @ sK640 @ X6 ) @ sK637 ) )
| ( $true
!= ( in @ X6 @ sK638 ) )
| ( $true
!= ( in @ ( kpair @ X6 @ sK641 ) @ sK639 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1015,plain,
( ( binintersectT_lem = $true )
& ( foundationAx = $true )
& ( powersetTE1 = $true )
& ( notinsingleton = $true )
& ( setminusLsub = $true )
& ( setunionE = $true )
& ( complementTnotintersectT = $true )
& ( exuEu = $true )
& ( powersetTI1 = $true )
& ( setextT = $true )
& ( ap2apEq1 = $true )
& ( setoftrueEq = $true )
& ( apProp = $true )
& ( cartprodpairin = $true )
& ( subsetE2 = $true )
& ( exuE1 = $true )
& ( replAx = $true )
& ( singletonprop = $true )
& ( emptysetsubset = $true )
& ( binintersectLsub = $true )
& ( funcinfuncset = $true )
& ( demorgan2a2 = $true )
& ( ap2apEq2 = $true )
& ( app = $true )
& ( binunionEcases = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( binunionE = $true )
& ( singletoninpowerset = $true )
& ( contrasubsetT3 = $true )
& ( ex1E2 = $true )
& ( lamp = $true )
& ( cartprodfstpairEq = $true )
& ( binunionRsub = $true )
& ( ubforcartprodlem3 = $true )
& ( upairset2IR = $true )
& ( binintersectER = $true )
& ( uniqinunit = $true )
& ( setadjoinE = $true )
& ( ubforcartprodlem1 = $true )
& ( upairsubunion = $true )
& ( breln1invI = $true )
& ( ksndsingleton = $true )
& ( sepSubset = $true )
& ( binintersectTELcontra = $true )
& ( beta2 = $true )
& ( setunionsingleton = $true )
& ( dpsetconstrERa = $true )
& ( woz1_2 = $true )
& ( nonemptyI = $true )
& ( doubleComplementEq = $true )
& ( demorgan2 = $true )
& ( singletonsubset = $true )
& ( binintersectSubset2 = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( omegaSAx = $true )
& ( setminusI = $true )
& ( nonemptyE1 = $true )
& ( binintersectSubset1 = $true )
& ( subPowSU = $true )
& ( wellorderingAx = $true )
& ( kpairp = $true )
& ( beta1 = $true )
& ( emptyinunitempty = $true )
& ( woz13rule3 = $true )
& ( setukpairinjR = $true )
& ( symdiffE = $true )
& ( funcImageSingleton = $true )
& ( symdiffI2 = $true )
& ( doubleComplementE1 = $true )
& ( funcext = $true )
& ( emptysetE = $true )
& ( notequalI2 = $true )
& ( exuE3e = $true )
& ( upairsetE = $true )
& ( binintersectSubset5 = $true )
& ( lam2lamEq = $true )
& ( eta2 = $true )
& ( cartprodmempair = $true )
& ( iftrueProp1 = $true )
& ( symdiffIneg1 = $true )
& ( ifSingleton = $true )
& ( cartprodsndpairEq = $true )
& ( inIntersectImpInUnion = $true )
& ( woz1_5 = $true )
& ( setOfPairsIsBReln1 = $true )
& ( ap2p = $true )
& ( dpsetconstrI = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( breln1 @ X1 @ X2 ) )
& ? [X3: $i] :
( ? [X4: $i] :
( ? [X5: $o] :
( ( $true != X5 )
& ! [X6: $i] :
( ( $true = X5 )
| ( $true
!= ( in @ ( kpair @ X3 @ X6 ) @ X0 ) )
| ( $true
!= ( in @ X6 @ X1 ) )
| ( $true
!= ( in @ ( kpair @ X6 @ X4 ) @ X2 ) ) ) )
& ( $true
= ( in @ X4 @ X1 ) )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ X1 ) ) ) )
& ( $true
= ( breln1 @ X1 @ X0 ) ) )
& ( binintersectSubset3 = $true )
& ( subbreln = $true )
& ( iftrueProp2 = $true )
& ( funcGraphProp2 = $true )
& ( subsetI1 = $true )
& ( funcextLem = $true )
& ( emptyE1 = $true )
& ( setukpairinjL2 = $true )
& ( quantDeMorgan4 = $true )
& ( binunionTE = $true )
& ( complementT_lem = $true )
& ( notinemptyset = $true )
& ( singletoninpowunion = $true )
& ( setext = $true )
& ( setadjoinOr = $true )
& ( omega0Ax = $true )
& ( setunionI = $true )
& ( ex1I2 = $true )
& ( cartprodmempaircEq = $true )
& ( demorgan2b = $true )
& ( inCongP = $true )
& ( woz13rule4 = $true )
& ( contrasubsetT1 = $true )
& ( subsetTI = $true )
& ( setadjoin__Cong = $true )
& ( breln1invprop = $true )
& ( dpsetconstrER = $true )
& ( setukpairinjR1 = $true )
& ( binintersectEL = $true )
& ( in__Cong = $true )
& ( theprop = $true )
& ( exu__Cong = $true )
& ( exuE2 = $true )
& ( cartprodfstin = $true )
& ( brelnall1 = $true )
& ( subsetemptysetimpeq = $true )
& ( complementSubsetComplementIntersect = $true )
& ( inPowerset = $true )
& ( dsetconstrEL = $true )
& ( lam2p = $true )
& ( vacuousDall = $true )
& ( funcext2 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( demorgan2a = $true )
& ( binunionT_lem = $true )
& ( funcGraphProp1 = $true )
& ( emptyInPowerset = $true )
& ( iffalseProp2 = $true )
& ( complementImpComplementIntersect = $true )
& ( setminusSubset1 = $true )
& ( nonemptyI1 = $true )
& ( complementTE1 = $true )
& ( powersetsubset = $true )
& ( iftrueorfalse = $true )
& ( setOfPairsIsBReln = $true )
& ( woz1_1 = $true )
& ( prop2setI = $true )
& ( upairequniteq = $true )
& ( descrp = $true )
& ( setadjoinSub2 = $true )
& ( setextAx = $true )
& ( sepInPowerset = $true )
& ( exuI2 = $true )
& ( doubleComplementSub1 = $true )
& ( breln1SetBreln1 = $true )
& ( complementTcontraSubset = $true )
& ( woz13rule1 = $true )
& ( emptysetimpfalse = $true )
& ( subbreln1 = $true )
& ( dpsetconstrEL2 = $true )
& ( notsubsetI = $true )
& ( setunionE2 = $true )
& ( contraSubsetComplement = $true )
& ( disjointsetsI1 = $true )
& ( bs114d = $true )
& ( binunionLsub = $true )
& ( setminusIRneg = $true )
& ( symdiffI1 = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( dsetconstrER = $true )
& ( upairinpowunion = $true )
& ( eqimpsubset1 = $true )
& ( setminusERneg = $true )
& ( setukpairinjR2 = $true )
& ( cartprodpairmemEL = $true )
& ( demorgan1 = $true )
& ( setunion__Cong = $true )
& ( setminusELneg = $true )
& ( setadjoinAx = $true )
& ( powersetE1 = $true )
& ( cartprodpairsurjEq = $true )
& ( eqinunit = $true )
& ( doubleComplementSub2 = $true )
& ( dsetconstr__Cong = $true )
& ( breln1compprop = $true )
& ( woz1_3 = $true )
& ( iffalseProp1 = $true )
& ( ifp = $true )
& ( setminusER = $true )
& ( upairsetIL = $true )
& ( setunionsingleton2 = $true )
& ( setadjoinSub = $true )
& ( ksndpairEq = $true )
& ( kpairsurjEq = $true )
& ( cartprodmempair1 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( kpairiskpair = $true )
& ( demorgan2b2 = $true )
& ( upairsetIR = $true )
& ( omega__Cong = $true )
& ( subsetI2 = $true )
& ( kfstsingleton = $true )
& ( kfstpairEq = $true )
& ( notequalI1 = $true )
& ( contrasubsetT = $true )
& ( breln1all1 = $true )
& ( choice2fnsingleton = $true )
& ( symdiffIneg2 = $true )
& ( theeq = $true )
& ( demorgan1a = $true )
& ( funcGraphProp3 = $true )
& ( secondinupair = $true )
& ( setminusILneg = $true )
& ( lamProp = $true )
& ( contrasubsetT2 = $true )
& ( powersetI = $true )
& ( breln1compE = $true )
& ( powerset__Cong = $true )
& ( setukpairIL = $true )
& ( setextsub = $true )
& ( binunionIL = $true )
& ( descr__Cong = $true )
& ( setminusEL = $true )
& ( eqbreln = $true )
& ( subsetTrans = $true )
& ( setbeta = $true )
& ( complementUnionInPowersetComplement = $true )
& ( powersetAx = $true )
& ( powersetT_lem = $true )
& ( cartprodsndin = $true )
& ( notdexE = $true )
& ( setukpairinjL1 = $true )
& ( woz13rule0 = $true )
& ( setadjoinIL = $true )
& ( emptyinPowerset = $true )
& ( demorgan2a1 = $true )
& ( iffalse = $true )
& ( ex1I = $true )
& ( quantDeMorgan2 = $true )
& ( powersetI1 = $true )
& ( omegaIndAx = $true )
& ( upairset2E = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjR12 = $true )
& ( ex1E1 = $true )
& ( emptyset__Cong = $true )
& ( doubleComplementI1 = $true )
& ( breln1compI = $true )
& ( prop2setE = $true )
& ( setunionsingleton1 = $true )
& ( woz1_4 = $true )
& ( infuncsetfunc = $true )
& ( setminusT_lem = $true )
& ( setukpairIR = $true )
& ( brelnall2 = $true )
& ( dpsetconstrSub = $true )
& ( woz13rule2 = $true )
& ( ubforcartprodlem2 = $true )
& ( setukpairinjL = $true )
& ( binintersectSubset4 = $true )
& ( singletonsswitch = $true )
& ( setminusSubset2 = $true )
& ( setunionAx = $true )
& ( binintersectI = $true )
& ( powersetE = $true )
& ( breln1invE = $true )
& ( quantDeMorgan1 = $true )
& ( dsetconstrI = $true )
& ( breln1all2 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( subset2powerset = $true )
& ( nonemptyImpWitness = $true )
& ( eqbreln1 = $true )
& ( complementTI1 = $true )
& ( cartprodpairmemER = $true )
& ( emptyI = $true )
& ( setadjoinIR = $true )
& ( eta1 = $true )
& ( quantDeMorgan3 = $true )
& ( binintersectRsub = $true )
& ( emptysetAx = $true )
& ( eqimpsubset2 = $true )
& ( binintersectTERcontra = $true )
& ( binunionTILcontra = $true )
& ( iftrue = $true )
& ( noeltsimpempty = $true )
& ( demorgan1b = $true )
& ( subsetE = $true )
& ( prop2set2propI = $true )
& ( binunionIR = $true )
& ( singletonsuniq = $true )
& ( dpsetconstrEL1 = $true )
& ( subsetRefl = $true )
& ( funcGraphProp4 = $true )
& ( binunionTEcontra = $true )
& ( binunionTIRcontra = $true )
& ( exuE3u = $true )
& ( notdallE = $true ) ),
inference(flattening,[status(thm)],[f1014]) ).
thf(f1014,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ? [X5: $o] :
( ( $true != X5 )
& ! [X6: $i] :
( ( $true = X5 )
| ( $true
!= ( in @ ( kpair @ X6 @ X4 ) @ X2 ) )
| ( $true
!= ( in @ ( kpair @ X3 @ X6 ) @ X0 ) )
| ( $true
!= ( in @ X6 @ X1 ) ) ) )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) ) )
& ( $true
= ( in @ X4 @ X1 ) ) )
& ( $true
= ( in @ X3 @ X1 ) ) )
& ( $true
= ( breln1 @ X1 @ X2 ) ) )
& ( $true
= ( breln1 @ X1 @ X0 ) ) )
& ( 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)],[f782]) ).
thf(f782,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 )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X1 @ X0 ) )
=> ! [X2: $i] :
( ( $true
= ( breln1 @ X1 @ X2 ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ! [X4: $i] :
( ( $true
= ( in @ X4 @ X1 ) )
=> ( ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) ) )
=> ! [X5: $o] :
( ! [X6: $i] :
( ( $true
= ( in @ X6 @ X1 ) )
=> ( ( $true
= ( in @ ( kpair @ X3 @ X6 ) @ X0 ) )
=> ( ( $true
= ( in @ ( kpair @ X6 @ X4 ) @ X2 ) )
=> ( $true = X5 ) ) ) )
=> ( $true = X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f781]) ).
thf(f781,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
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X1 @ X0 )
=> ! [X2: $i] :
( ( breln1 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) )
=> ! [X5: $o] :
( ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X6 ) @ X0 )
=> ( ( in @ ( kpair @ X6 @ X4 ) @ X2 )
=> X5 ) ) )
=> X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f303]) ).
thf(f303,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
=> ! [X13: $i,X3: $i] :
( ( breln1 @ X3 @ X13 )
=> ! [X15: $i] :
( ( breln1 @ X3 @ X15 )
=> ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X3 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ ( breln1compset @ X3 @ X13 @ X15 ) )
=> ! [X0: $o] :
( ! [X8: $i] :
( ( in @ X8 @ X3 )
=> ( ( in @ ( kpair @ X1 @ X8 ) @ X13 )
=> ( ( in @ ( kpair @ X8 @ X2 ) @ X15 )
=> X0 ) ) )
=> X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f302]) ).
thf(f302,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
=> ! [X13: $i,X3: $i] :
( ( breln1 @ X3 @ X13 )
=> ! [X15: $i] :
( ( breln1 @ X3 @ X15 )
=> ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X3 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ ( breln1compset @ X3 @ X13 @ X15 ) )
=> ! [X0: $o] :
( ! [X8: $i] :
( ( in @ X8 @ X3 )
=> ( ( in @ ( kpair @ X1 @ X8 ) @ X13 )
=> ( ( in @ ( kpair @ X8 @ X2 ) @ X15 )
=> X0 ) ) )
=> X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LcmRL7iW1w/DTF2THF_3905.p',breln1compEex) ).
thf(f16316,plain,
( ( $true
!= ( in @ sK641 @ sK638 ) )
| ( $true
= ( in @ ( kpair @ sK640 @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) ) @ sK637 ) )
| ~ spl1249_47 ),
inference(trivial_inequality_removal,[status(thm)],[f16315]) ).
thf(f16315,plain,
( ( $true
= ( in @ ( kpair @ sK640 @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) ) @ sK637 ) )
| ( $true != $true )
| ( $true
!= ( in @ sK641 @ sK638 ) )
| ~ spl1249_47 ),
inference(forward_demodulation,[status(thm)],[f16314,f6836]) ).
thf(f6836,plain,
( ( subset @ sK637 @ ( cartprod @ sK638 @ sK638 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f5284]) ).
thf(f5284,plain,
( $true
= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ sK638
@ sK637 ) ),
inference(definition_unfolding,[status(thm)],[f3893,f4484]) ).
thf(f4484,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 ) ) ),
inference(definition_unfolding,[status(thm)],[f4444,f2971]) ).
thf(f2971,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f730]) ).
thf(f730,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f729]) ).
thf(f729,plain,
( breln
= ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f184]) ).
thf(f184,axiom,
( breln
= ( ^ [X3: $i,X4: $i,X5: $i] : ( subset @ X5 @ ( cartprod @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LcmRL7iW1w/DTF2THF_3905.p',breln) ).
thf(f4444,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f726]) ).
thf(f726,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f725]) ).
thf(f725,plain,
( ( ^ [X0: $i,X1: $i] : ( breln @ X0 @ X0 @ X1 ) )
= breln1 ),
inference(rectify,[status(thm)],[f288]) ).
thf(f288,axiom,
( ( ^ [X3: $i,X13: $i] : ( breln @ X3 @ X3 @ X13 ) )
= breln1 ),
file('/export/starexec/sandbox/tmp/tmp.LcmRL7iW1w/DTF2THF_3905.p',breln1) ).
thf(f3893,plain,
( $true
= ( breln1 @ sK638 @ sK637 ) ),
inference(cnf_transformation,[status(thm)],[f2293]) ).
thf(f16314,plain,
( ( ( subset @ sK637 @ ( cartprod @ sK638 @ sK638 ) )
!= $true )
| ( $true
= ( in @ ( kpair @ sK640 @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) ) @ sK637 ) )
| ( $true
!= ( in @ sK641 @ sK638 ) )
| ~ spl1249_47 ),
inference(trivial_inequality_removal,[status(thm)],[f16313]) ).
thf(f16313,plain,
( ( $true
= ( in @ ( kpair @ sK640 @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) ) @ sK637 ) )
| ( $true
!= ( in @ sK641 @ sK638 ) )
| ( ( subset @ sK637 @ ( cartprod @ sK638 @ sK638 ) )
!= $true )
| ( $true != $true )
| ~ spl1249_47 ),
inference(forward_demodulation,[status(thm)],[f16312,f3894]) ).
thf(f3894,plain,
( $true
= ( in @ sK640 @ sK638 ) ),
inference(cnf_transformation,[status(thm)],[f2293]) ).
thf(f16312,plain,
( ( $true
!= ( in @ sK640 @ sK638 ) )
| ( ( subset @ sK637 @ ( cartprod @ sK638 @ sK638 ) )
!= $true )
| ( $true
= ( in @ ( kpair @ sK640 @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) ) @ sK637 ) )
| ( $true
!= ( in @ sK641 @ sK638 ) )
| ~ spl1249_47 ),
inference(trivial_inequality_removal,[status(thm)],[f16311]) ).
thf(f16311,plain,
( ( $true
= ( in @ ( kpair @ sK640 @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) ) @ sK637 ) )
| ( $true != $true )
| ( ( subset @ sK637 @ ( cartprod @ sK638 @ sK638 ) )
!= $true )
| ( $true
!= ( in @ sK641 @ sK638 ) )
| ( $true
!= ( in @ sK640 @ sK638 ) )
| ~ spl1249_47 ),
inference(forward_demodulation,[status(thm)],[f16307,f6327]) ).
thf(f6327,plain,
( $true
= ( subset @ sK639 @ ( cartprod @ sK638 @ sK638 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f5283]) ).
thf(f5283,plain,
( $true
= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ sK638
@ sK639 ) ),
inference(definition_unfolding,[status(thm)],[f3899,f4484]) ).
thf(f3899,plain,
( $true
= ( breln1 @ sK638 @ sK639 ) ),
inference(cnf_transformation,[status(thm)],[f2293]) ).
thf(f16307,plain,
( ( $true
= ( in @ ( kpair @ sK640 @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) ) @ sK637 ) )
| ( $true
!= ( subset @ sK639 @ ( cartprod @ sK638 @ sK638 ) ) )
| ( $true
!= ( in @ sK641 @ sK638 ) )
| ( ( subset @ sK637 @ ( cartprod @ sK638 @ sK638 ) )
!= $true )
| ( $true
!= ( in @ sK640 @ sK638 ) )
| ~ spl1249_47 ),
inference(trivial_inequality_removal,[status(thm)],[f16253]) ).
thf(f16253,plain,
( ( $true != $true )
| ( $true
!= ( subset @ sK639 @ ( cartprod @ sK638 @ sK638 ) ) )
| ( $true
!= ( in @ sK641 @ sK638 ) )
| ( $true
!= ( in @ sK640 @ sK638 ) )
| ( $true
= ( in @ ( kpair @ sK640 @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) ) @ sK637 ) )
| ( ( subset @ sK637 @ ( cartprod @ sK638 @ sK638 ) )
!= $true )
| ~ spl1249_47 ),
inference(superposition,[status(thm)],[f7387,f3895]) ).
thf(f3895,plain,
( $true
= ( in @ ( kpair @ sK640 @ sK641 ) @ ( breln1compset @ sK638 @ sK637 @ sK639 ) ) ),
inference(cnf_transformation,[status(thm)],[f2293]) ).
thf(f7387,plain,
( ! [X10: $i,X8: $i,X6: $i,X9: $i,X7: $i] :
( ( $true
!= ( in @ ( kpair @ X9 @ X10 ) @ ( breln1compset @ X6 @ X7 @ X8 ) ) )
| ( $true
!= ( in @ X10 @ X6 ) )
| ( $true
!= ( subset @ X7 @ ( cartprod @ X6 @ X6 ) ) )
| ( $true
!= ( subset @ X8 @ ( cartprod @ X6 @ X6 ) ) )
| ( $true
= ( in @ ( kpair @ X9 @ ( sK317 @ X10 @ X9 @ X8 @ X7 @ X6 ) ) @ X7 ) )
| ( $true
!= ( in @ X9 @ X6 ) ) )
| ~ spl1249_47 ),
inference(avatar_component_clause,[status(thm)],[f7386]) ).
thf(f7386,definition,
( spl1249_47
<=> ! [X10: $i,X9: $i,X7: $i,X6: $i,X8: $i] :
( ( $true
!= ( in @ X9 @ X6 ) )
| ( $true
= ( in @ ( kpair @ X9 @ ( sK317 @ X10 @ X9 @ X8 @ X7 @ X6 ) ) @ X7 ) )
| ( $true
!= ( subset @ X7 @ ( cartprod @ X6 @ X6 ) ) )
| ( $true
!= ( subset @ X8 @ ( cartprod @ X6 @ X6 ) ) )
| ( $true
!= ( in @ ( kpair @ X9 @ X10 ) @ ( breln1compset @ X6 @ X7 @ X8 ) ) )
| ( $true
!= ( in @ X10 @ X6 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1249_47])],[avatar_definition]) ).
thf(f22092,plain,
( ( ( in @ ( kpair @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) @ sK641 ) @ sK639 )
= $false )
| ( $false
= ( in @ ( kpair @ sK640 @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) ) @ sK637 ) )
| ~ spl1249_26
| ~ spl1249_56 ),
inference(trivial_inequality_removal,[status(thm)],[f22067]) ).
thf(f22067,plain,
( ( $false
= ( in @ ( kpair @ sK640 @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) ) @ sK637 ) )
| ( ( in @ ( kpair @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) @ sK641 ) @ sK639 )
= $false )
| ( $true != $true )
| ~ spl1249_26
| ~ spl1249_56 ),
inference(superposition,[status(thm)],[f8493,f16343]) ).
thf(f16343,plain,
( ( $true
= ( in @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) @ sK638 ) )
| ~ spl1249_26 ),
inference(trivial_inequality_removal,[status(thm)],[f16342]) ).
thf(f16342,plain,
( ( $true
= ( in @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) @ sK638 ) )
| ( $true != $true )
| ~ spl1249_26 ),
inference(forward_demodulation,[status(thm)],[f16341,f3894]) ).
thf(f16341,plain,
( ( $true
!= ( in @ sK640 @ sK638 ) )
| ( $true
= ( in @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) @ sK638 ) )
| ~ spl1249_26 ),
inference(trivial_inequality_removal,[status(thm)],[f16340]) ).
thf(f16340,plain,
( ( $true
!= ( in @ sK640 @ sK638 ) )
| ( $true
= ( in @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) @ sK638 ) )
| ( $true != $true )
| ~ spl1249_26 ),
inference(forward_demodulation,[status(thm)],[f16339,f6836]) ).
thf(f16339,plain,
( ( ( subset @ sK637 @ ( cartprod @ sK638 @ sK638 ) )
!= $true )
| ( $true
!= ( in @ sK640 @ sK638 ) )
| ( $true
= ( in @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) @ sK638 ) )
| ~ spl1249_26 ),
inference(trivial_inequality_removal,[status(thm)],[f16338]) ).
thf(f16338,plain,
( ( $true != $true )
| ( $true
= ( in @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) @ sK638 ) )
| ( ( subset @ sK637 @ ( cartprod @ sK638 @ sK638 ) )
!= $true )
| ( $true
!= ( in @ sK640 @ sK638 ) )
| ~ spl1249_26 ),
inference(forward_demodulation,[status(thm)],[f16337,f6327]) ).
thf(f16337,plain,
( ( $true
!= ( subset @ sK639 @ ( cartprod @ sK638 @ sK638 ) ) )
| ( ( subset @ sK637 @ ( cartprod @ sK638 @ sK638 ) )
!= $true )
| ( $true
!= ( in @ sK640 @ sK638 ) )
| ( $true
= ( in @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) @ sK638 ) )
| ~ spl1249_26 ),
inference(trivial_inequality_removal,[status(thm)],[f16336]) ).
thf(f16336,plain,
( ( $true != $true )
| ( $true
!= ( subset @ sK639 @ ( cartprod @ sK638 @ sK638 ) ) )
| ( $true
= ( in @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) @ sK638 ) )
| ( $true
!= ( in @ sK640 @ sK638 ) )
| ( ( subset @ sK637 @ ( cartprod @ sK638 @ sK638 ) )
!= $true )
| ~ spl1249_26 ),
inference(forward_demodulation,[status(thm)],[f16277,f3896]) ).
thf(f16277,plain,
( ( $true
= ( in @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) @ sK638 ) )
| ( $true
!= ( in @ sK641 @ sK638 ) )
| ( $true
!= ( in @ sK640 @ sK638 ) )
| ( $true
!= ( subset @ sK639 @ ( cartprod @ sK638 @ sK638 ) ) )
| ( ( subset @ sK637 @ ( cartprod @ sK638 @ sK638 ) )
!= $true )
| ~ spl1249_26 ),
inference(trivial_inequality_removal,[status(thm)],[f16255]) ).
thf(f16255,plain,
( ( ( subset @ sK637 @ ( cartprod @ sK638 @ sK638 ) )
!= $true )
| ( $true
!= ( in @ sK640 @ sK638 ) )
| ( $true != $true )
| ( $true
= ( in @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) @ sK638 ) )
| ( $true
!= ( in @ sK641 @ sK638 ) )
| ( $true
!= ( subset @ sK639 @ ( cartprod @ sK638 @ sK638 ) ) )
| ~ spl1249_26 ),
inference(superposition,[status(thm)],[f7284,f3895]) ).
thf(f7284,plain,
( ! [X10: $i,X8: $i,X6: $i,X9: $i,X7: $i] :
( ( $true
!= ( in @ ( kpair @ X9 @ X10 ) @ ( breln1compset @ X6 @ X7 @ X8 ) ) )
| ( $true
!= ( in @ X9 @ X6 ) )
| ( $true
= ( in @ ( sK317 @ X10 @ X9 @ X8 @ X7 @ X6 ) @ X6 ) )
| ( $true
!= ( subset @ X8 @ ( cartprod @ X6 @ X6 ) ) )
| ( $true
!= ( subset @ X7 @ ( cartprod @ X6 @ X6 ) ) )
| ( $true
!= ( in @ X10 @ X6 ) ) )
| ~ spl1249_26 ),
inference(avatar_component_clause,[status(thm)],[f7283]) ).
thf(f7283,definition,
( spl1249_26
<=> ! [X10: $i,X9: $i,X7: $i,X6: $i,X8: $i] :
( ( $true
!= ( in @ X9 @ X6 ) )
| ( $true
!= ( subset @ X8 @ ( cartprod @ X6 @ X6 ) ) )
| ( $true
!= ( subset @ X7 @ ( cartprod @ X6 @ X6 ) ) )
| ( $true
= ( in @ ( sK317 @ X10 @ X9 @ X8 @ X7 @ X6 ) @ X6 ) )
| ( $true
!= ( in @ X10 @ X6 ) )
| ( $true
!= ( in @ ( kpair @ X9 @ X10 ) @ ( breln1compset @ X6 @ X7 @ X8 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1249_26])],[avatar_definition]) ).
thf(f8493,plain,
( ! [X6: $i] :
( ( $true
!= ( in @ X6 @ sK638 ) )
| ( $false
= ( in @ ( kpair @ sK640 @ X6 ) @ sK637 ) )
| ( $false
= ( in @ ( kpair @ X6 @ sK641 ) @ sK639 ) ) )
| ~ spl1249_56 ),
inference(trivial_inequality_removal,[status(thm)],[f8492]) ).
thf(f8492,plain,
( ! [X6: $i] :
( ( $true != $true )
| ( $false
= ( in @ ( kpair @ X6 @ sK641 ) @ sK639 ) )
| ( $true
!= ( in @ X6 @ sK638 ) )
| ( $false
= ( in @ ( kpair @ sK640 @ X6 ) @ sK637 ) ) )
| ~ spl1249_56 ),
inference(fool_paramodulation,[status(thm)],[f8484]) ).
thf(f8484,plain,
( ! [X6: $i] :
( ( $true
!= ( in @ ( kpair @ X6 @ sK641 ) @ sK639 ) )
| ( $false
= ( in @ ( kpair @ sK640 @ X6 ) @ sK637 ) )
| ( $true
!= ( in @ X6 @ sK638 ) ) )
| ~ spl1249_56 ),
inference(trivial_inequality_removal,[status(thm)],[f8483]) ).
thf(f8483,plain,
( ! [X6: $i] :
( ( $true
!= ( in @ ( kpair @ X6 @ sK641 ) @ sK639 ) )
| ( $true
!= ( in @ X6 @ sK638 ) )
| ( $false
= ( in @ ( kpair @ sK640 @ X6 ) @ sK637 ) )
| ( $true != $true ) )
| ~ spl1249_56 ),
inference(fool_paramodulation,[status(thm)],[f7438]) ).
thf(f7438,plain,
( ! [X6: $i] :
( ( $true
!= ( in @ ( kpair @ sK640 @ X6 ) @ sK637 ) )
| ( $true
!= ( in @ ( kpair @ X6 @ sK641 ) @ sK639 ) )
| ( $true
!= ( in @ X6 @ sK638 ) ) )
| ~ spl1249_56 ),
inference(avatar_component_clause,[status(thm)],[f7437]) ).
thf(f7437,definition,
( spl1249_56
<=> ! [X6: $i] :
( ( $true
!= ( in @ ( kpair @ sK640 @ X6 ) @ sK637 ) )
| ( $true
!= ( in @ ( kpair @ X6 @ sK641 ) @ sK639 ) )
| ( $true
!= ( in @ X6 @ sK638 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1249_56])],[avatar_definition]) ).
thf(f16335,plain,
( ( ( in @ ( kpair @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) @ sK641 ) @ sK639 )
= $true )
| ~ spl1249_11 ),
inference(trivial_inequality_removal,[status(thm)],[f16334]) ).
thf(f16334,plain,
( ( $true != $true )
| ( ( in @ ( kpair @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) @ sK641 ) @ sK639 )
= $true )
| ~ spl1249_11 ),
inference(forward_demodulation,[status(thm)],[f16333,f6327]) ).
thf(f16333,plain,
( ( ( in @ ( kpair @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) @ sK641 ) @ sK639 )
= $true )
| ( $true
!= ( subset @ sK639 @ ( cartprod @ sK638 @ sK638 ) ) )
| ~ spl1249_11 ),
inference(trivial_inequality_removal,[status(thm)],[f16332]) ).
thf(f16332,plain,
( ( $true
!= ( subset @ sK639 @ ( cartprod @ sK638 @ sK638 ) ) )
| ( ( in @ ( kpair @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) @ sK641 ) @ sK639 )
= $true )
| ( $true != $true )
| ~ spl1249_11 ),
inference(forward_demodulation,[status(thm)],[f16331,f3894]) ).
thf(f16331,plain,
( ( ( in @ ( kpair @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) @ sK641 ) @ sK639 )
= $true )
| ( $true
!= ( in @ sK640 @ sK638 ) )
| ( $true
!= ( subset @ sK639 @ ( cartprod @ sK638 @ sK638 ) ) )
| ~ spl1249_11 ),
inference(trivial_inequality_removal,[status(thm)],[f16330]) ).
thf(f16330,plain,
( ( $true != $true )
| ( ( in @ ( kpair @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) @ sK641 ) @ sK639 )
= $true )
| ( $true
!= ( subset @ sK639 @ ( cartprod @ sK638 @ sK638 ) ) )
| ( $true
!= ( in @ sK640 @ sK638 ) )
| ~ spl1249_11 ),
inference(forward_demodulation,[status(thm)],[f16329,f6836]) ).
thf(f16329,plain,
( ( ( subset @ sK637 @ ( cartprod @ sK638 @ sK638 ) )
!= $true )
| ( $true
!= ( in @ sK640 @ sK638 ) )
| ( $true
!= ( subset @ sK639 @ ( cartprod @ sK638 @ sK638 ) ) )
| ( ( in @ ( kpair @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) @ sK641 ) @ sK639 )
= $true )
| ~ spl1249_11 ),
inference(trivial_inequality_removal,[status(thm)],[f16328]) ).
thf(f16328,plain,
( ( $true
!= ( in @ sK640 @ sK638 ) )
| ( $true != $true )
| ( ( in @ ( kpair @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) @ sK641 ) @ sK639 )
= $true )
| ( $true
!= ( subset @ sK639 @ ( cartprod @ sK638 @ sK638 ) ) )
| ( ( subset @ sK637 @ ( cartprod @ sK638 @ sK638 ) )
!= $true )
| ~ spl1249_11 ),
inference(forward_demodulation,[status(thm)],[f16287,f3896]) ).
thf(f16287,plain,
( ( ( in @ ( kpair @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) @ sK641 ) @ sK639 )
= $true )
| ( $true
!= ( in @ sK641 @ sK638 ) )
| ( ( subset @ sK637 @ ( cartprod @ sK638 @ sK638 ) )
!= $true )
| ( $true
!= ( in @ sK640 @ sK638 ) )
| ( $true
!= ( subset @ sK639 @ ( cartprod @ sK638 @ sK638 ) ) )
| ~ spl1249_11 ),
inference(trivial_inequality_removal,[status(thm)],[f16254]) ).
thf(f16254,plain,
( ( $true
!= ( subset @ sK639 @ ( cartprod @ sK638 @ sK638 ) ) )
| ( ( in @ ( kpair @ ( sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638 ) @ sK641 ) @ sK639 )
= $true )
| ( ( subset @ sK637 @ ( cartprod @ sK638 @ sK638 ) )
!= $true )
| ( $true
!= ( in @ sK640 @ sK638 ) )
| ( $true != $true )
| ( $true
!= ( in @ sK641 @ sK638 ) )
| ~ spl1249_11 ),
inference(superposition,[status(thm)],[f7218,f3895]) ).
thf(f7218,plain,
( ! [X10: $i,X8: $i,X6: $i,X9: $i,X7: $i] :
( ( $true
!= ( in @ ( kpair @ X9 @ X10 ) @ ( breln1compset @ X6 @ X7 @ X8 ) ) )
| ( $true
!= ( subset @ X8 @ ( cartprod @ X6 @ X6 ) ) )
| ( $true
!= ( subset @ X7 @ ( cartprod @ X6 @ X6 ) ) )
| ( $true
= ( in @ ( kpair @ ( sK317 @ X10 @ X9 @ X8 @ X7 @ X6 ) @ X10 ) @ X8 ) )
| ( $true
!= ( in @ X10 @ X6 ) )
| ( $true
!= ( in @ X9 @ X6 ) ) )
| ~ spl1249_11 ),
inference(avatar_component_clause,[status(thm)],[f7217]) ).
thf(f7217,definition,
( spl1249_11
<=> ! [X10: $i,X9: $i,X7: $i,X6: $i,X8: $i] :
( ( $true
!= ( subset @ X7 @ ( cartprod @ X6 @ X6 ) ) )
| ( $true
!= ( in @ ( kpair @ X9 @ X10 ) @ ( breln1compset @ X6 @ X7 @ X8 ) ) )
| ( $true
!= ( in @ X10 @ X6 ) )
| ( $true
!= ( subset @ X8 @ ( cartprod @ X6 @ X6 ) ) )
| ( $true
= ( in @ ( kpair @ ( sK317 @ X10 @ X9 @ X8 @ X7 @ X6 ) @ X10 ) @ X8 ) )
| ( $true
!= ( in @ X9 @ X6 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1249_11])],[avatar_definition]) ).
thf(f8392,plain,
~ spl1249_57,
inference(avatar_contradiction_clause,[status(thm)],[f8391]) ).
thf(f8391,plain,
( $false
| ~ spl1249_57 ),
inference(trivial_inequality_removal,[status(thm)],[f8390]) ).
thf(f8390,plain,
( ( $true = $false )
| ~ spl1249_57 ),
inference(forward_demodulation,[status(thm)],[f7442,f7559]) ).
thf(f7559,plain,
sK642 = $false,
inference(trivial_inequality_removal,[status(thm)],[f7558]) ).
thf(f7558,plain,
( ( sK642 = $false )
| ( $true != $true ) ),
inference(fool_paramodulation,[status(thm)],[f3898]) ).
thf(f3898,plain,
sK642 != $true,
inference(cnf_transformation,[status(thm)],[f2293]) ).
thf(f7442,plain,
( ( sK642 = $true )
| ~ spl1249_57 ),
inference(avatar_component_clause,[status(thm)],[f7440]) ).
thf(f7440,definition,
( spl1249_57
<=> ( sK642 = $true ) ),
introduced(definition,[new_symbols(naming,[spl1249_57])],[avatar_definition]) ).
thf(f7517,plain,
spl1249_10,
inference(avatar_split_clause,[status(thm)],[f6333,f7213]) ).
thf(f7213,definition,
( spl1249_10
<=> ( $true = sP3 ) ),
introduced(definition,[new_symbols(naming,[spl1249_10])],[avatar_definition]) ).
thf(f6333,plain,
$true = sP3,
inference(trivial_inequality_removal,[status(thm)],[f4860]) ).
thf(f4860,plain,
( ( $true = sP3 )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f3244,f3766]) ).
thf(f3766,plain,
breln1compE = $true,
inference(cnf_transformation,[status(thm)],[f2293]) ).
thf(f3244,plain,
( ( $true = sP3 )
| ( breln1compE != $true ) ),
inference(cnf_transformation,[status(thm)],[f1813]) ).
thf(f1813,plain,
( ( ( $true = sP3 )
| ( breln1compE != $true ) )
& ( ( breln1compE = $true )
| ( $true != sP3 ) ) ),
inference(nnf_transformation,[status(thm)],[f1326]) ).
thf(f1326,plain,
( ( $true = sP3 )
<=> ( breln1compE = $true ) ),
inference(definition_folding,[status(thm)],[f966,f1325]) ).
thf(f1325,plain,
( ( $true = sP3 )
<=> ! [X0: $i,X1: $i] :
( ( $true
!= ( breln1 @ X0 @ X1 ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ? [X5: $i] :
( ( ( in @ ( kpair @ X3 @ X5 ) @ X1 )
= $true )
& ( $true
= ( in @ X5 @ X0 ) )
& ( $true
= ( in @ ( kpair @ X5 @ X4 ) @ X2 ) ) )
| ( $true
!= ( in @ X4 @ X0 ) )
| ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) )
| ( $true
!= ( in @ X3 @ X0 ) ) )
| ( $true
!= ( breln1 @ X0 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f966,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( breln1 @ X0 @ X1 ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ? [X5: $i] :
( ( ( in @ ( kpair @ X3 @ X5 ) @ X1 )
= $true )
& ( $true
= ( in @ X5 @ X0 ) )
& ( $true
= ( in @ ( kpair @ X5 @ X4 ) @ X2 ) ) )
| ( $true
!= ( in @ X4 @ X0 ) )
| ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) )
| ( $true
!= ( in @ X3 @ X0 ) ) )
| ( $true
!= ( breln1 @ X0 @ X2 ) ) ) )
<=> ( breln1compE = $true ) ),
inference(flattening,[status(thm)],[f965]) ).
thf(f965,plain,
( ( breln1compE = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ? [X5: $i] :
( ( ( in @ ( kpair @ X3 @ X5 ) @ X1 )
= $true )
& ( $true
= ( in @ X5 @ X0 ) )
& ( $true
= ( in @ ( kpair @ X5 @ X4 ) @ X2 ) ) )
| ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X0 @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X4 @ X0 ) ) )
| ( $true
!= ( in @ X3 @ X0 ) ) )
| ( $true
!= ( breln1 @ X0 @ X2 ) ) )
| ( $true
!= ( breln1 @ X0 @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f760]) ).
thf(f760,plain,
( ( breln1compE = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
=> ! [X2: $i] :
( ( $true
= ( breln1 @ X0 @ X2 ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X0 ) )
=> ! [X4: $i] :
( ( $true
= ( in @ X4 @ X0 ) )
=> ( ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X0 @ X1 @ X2 ) ) )
=> ? [X5: $i] :
( ( ( in @ ( kpair @ X3 @ X5 ) @ X1 )
= $true )
& ( $true
= ( in @ X5 @ X0 ) )
& ( $true
= ( in @ ( kpair @ X5 @ X4 ) @ X2 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f759]) ).
thf(f759,plain,
( breln1compE
= ( ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X0 @ X1 @ X2 ) )
=> ? [X5: $i] :
( ( in @ X5 @ X0 )
& ( in @ ( kpair @ X5 @ X4 ) @ X2 )
& ( in @ ( kpair @ X3 @ X5 ) @ X1 ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f301]) ).
thf(f301,axiom,
( breln1compE
= ( ! [X3: $i,X13: $i] :
( ( breln1 @ X3 @ X13 )
=> ! [X15: $i] :
( ( breln1 @ X3 @ X15 )
=> ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X3 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ ( breln1compset @ X3 @ X13 @ X15 ) )
=> ? [X8: $i] :
( ( in @ X8 @ X3 )
& ( in @ ( kpair @ X8 @ X2 ) @ X15 )
& ( in @ ( kpair @ X1 @ X8 ) @ X13 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LcmRL7iW1w/DTF2THF_3905.p',breln1compE) ).
thf(f7443,plain,
( spl1249_56
| spl1249_57 ),
inference(avatar_split_clause,[status(thm)],[f3897,f7440,f7437]) ).
thf(f3897,plain,
! [X6: $i] :
( ( $true
!= ( in @ ( kpair @ sK640 @ X6 ) @ sK637 ) )
| ( $true
!= ( in @ X6 @ sK638 ) )
| ( $true
!= ( in @ ( kpair @ X6 @ sK641 ) @ sK639 ) )
| ( sK642 = $true ) ),
inference(cnf_transformation,[status(thm)],[f2293]) ).
thf(f7388,plain,
( spl1249_47
| ~ spl1249_10 ),
inference(avatar_split_clause,[status(thm)],[f6668,f7213,f7386]) ).
thf(f6668,plain,
! [X10: $i,X8: $i,X6: $i,X9: $i,X7: $i] :
( ( $true
!= ( in @ X9 @ X6 ) )
| ( $true
!= ( in @ X10 @ X6 ) )
| ( $true != sP3 )
| ( $true
!= ( in @ ( kpair @ X9 @ X10 ) @ ( breln1compset @ X6 @ X7 @ X8 ) ) )
| ( $true
!= ( subset @ X8 @ ( cartprod @ X6 @ X6 ) ) )
| ( $true
!= ( subset @ X7 @ ( cartprod @ X6 @ X6 ) ) )
| ( $true
= ( in @ ( kpair @ X9 @ ( sK317 @ X10 @ X9 @ X8 @ X7 @ X6 ) ) @ X7 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f4857]) ).
thf(f4857,plain,
! [X10: $i,X8: $i,X6: $i,X9: $i,X7: $i] :
( ( $true
= ( in @ ( kpair @ X9 @ ( sK317 @ X10 @ X9 @ X8 @ X7 @ X6 ) ) @ X7 ) )
| ( $true
!= ( in @ X10 @ X6 ) )
| ( $true
!= ( in @ ( kpair @ X9 @ X10 ) @ ( breln1compset @ X6 @ X7 @ X8 ) ) )
| ( $true
!= ( in @ X9 @ X6 ) )
| ( $true
!= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ X6
@ X7 ) )
| ( $true != sP3 )
| ( $true
!= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ X6
@ X8 ) ) ),
inference(definition_unfolding,[status(thm)],[f3236,f4484,f4484]) ).
thf(f3236,plain,
! [X10: $i,X8: $i,X6: $i,X9: $i,X7: $i] :
( ( $true
!= ( breln1 @ X6 @ X7 ) )
| ( $true
= ( in @ ( kpair @ X9 @ ( sK317 @ X10 @ X9 @ X8 @ X7 @ X6 ) ) @ X7 ) )
| ( $true
!= ( in @ X10 @ X6 ) )
| ( $true
!= ( in @ ( kpair @ X9 @ X10 ) @ ( breln1compset @ X6 @ X7 @ X8 ) ) )
| ( $true
!= ( in @ X9 @ X6 ) )
| ( ( breln1 @ X6 @ X8 )
!= $true )
| ( $true != sP3 ) ),
inference(cnf_transformation,[status(thm)],[f1812]) ).
thf(f1812,plain,
( ( ( $true = sP3 )
| ( ( $true
= ( breln1 @ sK312 @ sK313 ) )
& ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ sK315 @ X5 ) @ sK313 ) )
| ( $true
!= ( in @ X5 @ sK312 ) )
| ( $true
!= ( in @ ( kpair @ X5 @ sK316 ) @ sK314 ) ) )
& ( $true
= ( in @ sK316 @ sK312 ) )
& ( ( in @ ( kpair @ sK315 @ sK316 ) @ ( breln1compset @ sK312 @ sK313 @ sK314 ) )
= $true )
& ( $true
= ( in @ sK315 @ sK312 ) )
& ( $true
= ( breln1 @ sK312 @ sK314 ) ) ) )
& ( ! [X6: $i,X7: $i] :
( ( $true
!= ( breln1 @ X6 @ X7 ) )
| ! [X8: $i] :
( ! [X9: $i] :
( ! [X10: $i] :
( ( ( $true
= ( in @ ( kpair @ X9 @ ( sK317 @ X10 @ X9 @ X8 @ X7 @ X6 ) ) @ X7 ) )
& ( $true
= ( in @ ( sK317 @ X10 @ X9 @ X8 @ X7 @ X6 ) @ X6 ) )
& ( $true
= ( in @ ( kpair @ ( sK317 @ X10 @ X9 @ X8 @ X7 @ X6 ) @ X10 ) @ X8 ) ) )
| ( $true
!= ( in @ X10 @ X6 ) )
| ( $true
!= ( in @ ( kpair @ X9 @ X10 ) @ ( breln1compset @ X6 @ X7 @ X8 ) ) ) )
| ( $true
!= ( in @ X9 @ X6 ) ) )
| ( ( breln1 @ X6 @ X8 )
!= $true ) ) )
| ( $true != sP3 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK312,sK313,sK314,sK315,sK316,sK317])],[f1806,f1811,f1810,f1809,f1808,f1807]) ).
thf(f1807,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
& ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ! [X5: $i] :
( ( ( in @ ( kpair @ X3 @ X5 ) @ X1 )
!= $true )
| ( $true
!= ( in @ X5 @ X0 ) )
| ( $true
!= ( in @ ( kpair @ X5 @ X4 ) @ X2 ) ) )
& ( $true
= ( in @ X4 @ X0 ) )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ X0 ) ) )
& ( $true
= ( breln1 @ X0 @ X2 ) ) ) )
=> ( ( $true
= ( breln1 @ sK312 @ sK313 ) )
& ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ! [X5: $i] :
( ( ( in @ ( kpair @ X3 @ X5 ) @ sK313 )
!= $true )
| ( $true
!= ( in @ X5 @ sK312 ) )
| ( $true
!= ( in @ ( kpair @ X5 @ X4 ) @ X2 ) ) )
& ( $true
= ( in @ X4 @ sK312 ) )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK312 @ sK313 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ sK312 ) ) )
& ( $true
= ( breln1 @ sK312 @ X2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1808,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ! [X5: $i] :
( ( ( in @ ( kpair @ X3 @ X5 ) @ sK313 )
!= $true )
| ( $true
!= ( in @ X5 @ sK312 ) )
| ( $true
!= ( in @ ( kpair @ X5 @ X4 ) @ X2 ) ) )
& ( $true
= ( in @ X4 @ sK312 ) )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK312 @ sK313 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ sK312 ) ) )
& ( $true
= ( breln1 @ sK312 @ X2 ) ) )
=> ( ? [X3: $i] :
( ? [X4: $i] :
( ! [X5: $i] :
( ( ( in @ ( kpair @ X3 @ X5 ) @ sK313 )
!= $true )
| ( $true
!= ( in @ X5 @ sK312 ) )
| ( $true
!= ( in @ ( kpair @ X5 @ X4 ) @ sK314 ) ) )
& ( $true
= ( in @ X4 @ sK312 ) )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK312 @ sK313 @ sK314 ) ) ) )
& ( $true
= ( in @ X3 @ sK312 ) ) )
& ( $true
= ( breln1 @ sK312 @ sK314 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1809,plain,
( ? [X3: $i] :
( ? [X4: $i] :
( ! [X5: $i] :
( ( ( in @ ( kpair @ X3 @ X5 ) @ sK313 )
!= $true )
| ( $true
!= ( in @ X5 @ sK312 ) )
| ( $true
!= ( in @ ( kpair @ X5 @ X4 ) @ sK314 ) ) )
& ( $true
= ( in @ X4 @ sK312 ) )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK312 @ sK313 @ sK314 ) ) ) )
& ( $true
= ( in @ X3 @ sK312 ) ) )
=> ( ? [X4: $i] :
( ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ sK315 @ X5 ) @ sK313 ) )
| ( $true
!= ( in @ X5 @ sK312 ) )
| ( $true
!= ( in @ ( kpair @ X5 @ X4 ) @ sK314 ) ) )
& ( $true
= ( in @ X4 @ sK312 ) )
& ( $true
= ( in @ ( kpair @ sK315 @ X4 ) @ ( breln1compset @ sK312 @ sK313 @ sK314 ) ) ) )
& ( $true
= ( in @ sK315 @ sK312 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1810,plain,
( ? [X4: $i] :
( ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ sK315 @ X5 ) @ sK313 ) )
| ( $true
!= ( in @ X5 @ sK312 ) )
| ( $true
!= ( in @ ( kpair @ X5 @ X4 ) @ sK314 ) ) )
& ( $true
= ( in @ X4 @ sK312 ) )
& ( $true
= ( in @ ( kpair @ sK315 @ X4 ) @ ( breln1compset @ sK312 @ sK313 @ sK314 ) ) ) )
=> ( ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ sK315 @ X5 ) @ sK313 ) )
| ( $true
!= ( in @ X5 @ sK312 ) )
| ( $true
!= ( in @ ( kpair @ X5 @ sK316 ) @ sK314 ) ) )
& ( $true
= ( in @ sK316 @ sK312 ) )
& ( ( in @ ( kpair @ sK315 @ sK316 ) @ ( breln1compset @ sK312 @ sK313 @ sK314 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1811,plain,
! [X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
( ? [X11: $i] :
( ( $true
= ( in @ ( kpair @ X9 @ X11 ) @ X7 ) )
& ( $true
= ( in @ X11 @ X6 ) )
& ( $true
= ( in @ ( kpair @ X11 @ X10 ) @ X8 ) ) )
=> ( ( $true
= ( in @ ( kpair @ X9 @ ( sK317 @ X10 @ X9 @ X8 @ X7 @ X6 ) ) @ X7 ) )
& ( $true
= ( in @ ( sK317 @ X10 @ X9 @ X8 @ X7 @ X6 ) @ X6 ) )
& ( $true
= ( in @ ( kpair @ ( sK317 @ X10 @ X9 @ X8 @ X7 @ X6 ) @ X10 ) @ X8 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1806,plain,
( ( ( $true = sP3 )
| ? [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
& ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ! [X5: $i] :
( ( ( in @ ( kpair @ X3 @ X5 ) @ X1 )
!= $true )
| ( $true
!= ( in @ X5 @ X0 ) )
| ( $true
!= ( in @ ( kpair @ X5 @ X4 ) @ X2 ) ) )
& ( $true
= ( in @ X4 @ X0 ) )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ X0 ) ) )
& ( $true
= ( breln1 @ X0 @ X2 ) ) ) ) )
& ( ! [X6: $i,X7: $i] :
( ( $true
!= ( breln1 @ X6 @ X7 ) )
| ! [X8: $i] :
( ! [X9: $i] :
( ! [X10: $i] :
( ? [X11: $i] :
( ( $true
= ( in @ ( kpair @ X9 @ X11 ) @ X7 ) )
& ( $true
= ( in @ X11 @ X6 ) )
& ( $true
= ( in @ ( kpair @ X11 @ X10 ) @ X8 ) ) )
| ( $true
!= ( in @ X10 @ X6 ) )
| ( $true
!= ( in @ ( kpair @ X9 @ X10 ) @ ( breln1compset @ X6 @ X7 @ X8 ) ) ) )
| ( $true
!= ( in @ X9 @ X6 ) ) )
| ( ( breln1 @ X6 @ X8 )
!= $true ) ) )
| ( $true != sP3 ) ) ),
inference(rectify,[status(thm)],[f1805]) ).
thf(f1805,plain,
( ( ( $true = sP3 )
| ? [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
& ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ! [X5: $i] :
( ( ( in @ ( kpair @ X3 @ X5 ) @ X1 )
!= $true )
| ( $true
!= ( in @ X5 @ X0 ) )
| ( $true
!= ( in @ ( kpair @ X5 @ X4 ) @ X2 ) ) )
& ( $true
= ( in @ X4 @ X0 ) )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) )
& ( $true
= ( in @ X3 @ X0 ) ) )
& ( $true
= ( breln1 @ X0 @ X2 ) ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ( $true
!= ( breln1 @ X0 @ X1 ) )
| ! [X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ? [X5: $i] :
( ( ( in @ ( kpair @ X3 @ X5 ) @ X1 )
= $true )
& ( $true
= ( in @ X5 @ X0 ) )
& ( $true
= ( in @ ( kpair @ X5 @ X4 ) @ X2 ) ) )
| ( $true
!= ( in @ X4 @ X0 ) )
| ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) )
| ( $true
!= ( in @ X3 @ X0 ) ) )
| ( $true
!= ( breln1 @ X0 @ X2 ) ) ) )
| ( $true != sP3 ) ) ),
inference(nnf_transformation,[status(thm)],[f1325]) ).
thf(f7285,plain,
( ~ spl1249_10
| spl1249_26 ),
inference(avatar_split_clause,[status(thm)],[f6902,f7283,f7213]) ).
thf(f6902,plain,
! [X10: $i,X8: $i,X6: $i,X9: $i,X7: $i] :
( ( $true
!= ( in @ X9 @ X6 ) )
| ( $true
!= ( in @ ( kpair @ X9 @ X10 ) @ ( breln1compset @ X6 @ X7 @ X8 ) ) )
| ( $true
!= ( in @ X10 @ X6 ) )
| ( $true
= ( in @ ( sK317 @ X10 @ X9 @ X8 @ X7 @ X6 ) @ X6 ) )
| ( $true
!= ( subset @ X7 @ ( cartprod @ X6 @ X6 ) ) )
| ( $true != sP3 )
| ( $true
!= ( subset @ X8 @ ( cartprod @ X6 @ X6 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f4858]) ).
thf(f4858,plain,
! [X10: $i,X8: $i,X6: $i,X9: $i,X7: $i] :
( ( $true
!= ( in @ X10 @ X6 ) )
| ( $true
!= ( in @ ( kpair @ X9 @ X10 ) @ ( breln1compset @ X6 @ X7 @ X8 ) ) )
| ( $true
!= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ X6
@ X8 ) )
| ( $true
!= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ X6
@ X7 ) )
| ( $true
= ( in @ ( sK317 @ X10 @ X9 @ X8 @ X7 @ X6 ) @ X6 ) )
| ( $true
!= ( in @ X9 @ X6 ) )
| ( $true != sP3 ) ),
inference(definition_unfolding,[status(thm)],[f3235,f4484,f4484]) ).
thf(f3235,plain,
! [X10: $i,X8: $i,X6: $i,X9: $i,X7: $i] :
( ( $true
!= ( breln1 @ X6 @ X7 ) )
| ( $true
= ( in @ ( sK317 @ X10 @ X9 @ X8 @ X7 @ X6 ) @ X6 ) )
| ( $true
!= ( in @ X10 @ X6 ) )
| ( $true
!= ( in @ ( kpair @ X9 @ X10 ) @ ( breln1compset @ X6 @ X7 @ X8 ) ) )
| ( $true
!= ( in @ X9 @ X6 ) )
| ( ( breln1 @ X6 @ X8 )
!= $true )
| ( $true != sP3 ) ),
inference(cnf_transformation,[status(thm)],[f1812]) ).
thf(f7219,plain,
( ~ spl1249_10
| spl1249_11 ),
inference(avatar_split_clause,[status(thm)],[f7038,f7217,f7213]) ).
thf(f7038,plain,
! [X10: $i,X8: $i,X6: $i,X9: $i,X7: $i] :
( ( $true
!= ( subset @ X7 @ ( cartprod @ X6 @ X6 ) ) )
| ( $true
!= ( in @ X9 @ X6 ) )
| ( $true != sP3 )
| ( $true
= ( in @ ( kpair @ ( sK317 @ X10 @ X9 @ X8 @ X7 @ X6 ) @ X10 ) @ X8 ) )
| ( $true
!= ( subset @ X8 @ ( cartprod @ X6 @ X6 ) ) )
| ( $true
!= ( in @ X10 @ X6 ) )
| ( $true
!= ( in @ ( kpair @ X9 @ X10 ) @ ( breln1compset @ X6 @ X7 @ X8 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f4859]) ).
thf(f4859,plain,
! [X10: $i,X8: $i,X6: $i,X9: $i,X7: $i] :
( ( $true
!= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ X6
@ X7 ) )
| ( $true
!= ( in @ X9 @ X6 ) )
| ( $true
!= ( in @ ( kpair @ X9 @ X10 ) @ ( breln1compset @ X6 @ X7 @ X8 ) ) )
| ( $true
!= ( in @ X10 @ X6 ) )
| ( $true
!= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ X6
@ X8 ) )
| ( $true != sP3 )
| ( $true
= ( in @ ( kpair @ ( sK317 @ X10 @ X9 @ X8 @ X7 @ X6 ) @ X10 ) @ X8 ) ) ),
inference(definition_unfolding,[status(thm)],[f3234,f4484,f4484]) ).
thf(f3234,plain,
! [X10: $i,X8: $i,X6: $i,X9: $i,X7: $i] :
( ( $true
!= ( breln1 @ X6 @ X7 ) )
| ( $true
= ( in @ ( kpair @ ( sK317 @ X10 @ X9 @ X8 @ X7 @ X6 ) @ X10 ) @ X8 ) )
| ( $true
!= ( in @ X10 @ X6 ) )
| ( $true
!= ( in @ ( kpair @ X9 @ X10 ) @ ( breln1compset @ X6 @ X7 @ X8 ) ) )
| ( $true
!= ( in @ X9 @ X6 ) )
| ( ( breln1 @ X6 @ X8 )
!= $true )
| ( $true != sP3 ) ),
inference(cnf_transformation,[status(thm)],[f1812]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU781^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n031.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:34:48 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.32/0.48 ---- Original DTF file ---
% 0.32/0.48 thf(spec,logic,$$dhol).
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 % File : SEU781^1 : TPTP v9.2.1. Released v3.7.0.
% 0.32/0.48 % Domain : Set Theory
% 0.32/0.48 % Problem : Binary Relations on a Set
% 0.32/0.48 % Version : Especial.
% 0.32/0.48 % English : (! A:i.! R:i.breln1 A R -> (! S:i.breln1 A S -> (! x:i.in x A ->
% 0.32/0.48 % (! y:i.in y A -> in (kpair x y) (breln1compset A R S) ->
% 0.32/0.48 % (! phi:o.(! z:i.in z A -> in (kpair x z) R -> in (kpair z y) S ->
% 0.32/0.48 % phi) -> phi)))))
% 0.32/0.48
% 0.32/0.48 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.32/0.48 % Source : [Bro08]
% 0.32/0.48 % Names : ZFC283g [Bro08]
% 0.32/0.48
% 0.32/0.48 % Status : Theorem
% 0.32/0.48 % Rating : 0.44 v9.1.0, 0.38 v9.0.0, 0.40 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.71 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.80 v6.2.0, 0.86 v5.5.0, 0.83 v5.4.0, 0.80 v5.2.0, 1.00 v3.7.0
% 0.32/0.48 % Syntax : Number of formulae : 647 ( 301 unt; 345 typ; 301 def)
% 0.32/0.48 % Number of atoms : 1838 ( 431 equ; 0 cnn)
% 0.32/0.48 % Maximal formula atoms : 305 ( 6 avg)
% 0.32/0.48 % Number of connectives : 3998 ( 73 ~; 12 |; 48 &;2900 @)
% 0.32/0.48 % ( 14 <=>; 951 =>; 0 <=; 0 <~>)
% 0.32/0.48 % Maximal formula depth : 318 ( 2 avg)
% 0.32/0.48 % Number of types : 2 ( 0 usr)
% 0.32/0.48 % Number of type conns : 157 ( 157 >; 0 *; 0 +; 0 <<)
% 0.32/0.48 % Number of symbols : 348 ( 345 usr; 301 con; 0-4 aty)
% 0.32/0.48 % Number of variables : 1053 ( 76 ^; 940 !; 37 ?;1053 :)
% 0.32/0.48 % SPC : TH0_THM_EQU_NAR
% 0.32/0.48
% 0.32/0.48 % Comments : http://mathgate.info/detsetitem.php?id=376
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 thf(in_type,type,
% 0.32/0.48 in: $i > $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(exu_type,type,
% 0.32/0.48 exu: ( $i > $o ) > $o ).
% 0.32/0.48
% 0.32/0.48 thf(exu,definition,
% 0.32/0.48 ( exu
% 0.32/0.48 = ( ^ [Xphi: $i > $o] :
% 0.32/0.48 ? [Xx: $i] :
% 0.32/0.48 ( ( Xphi @ Xx )
% 0.32/0.48 & ! [Xy: $i] :
% 0.32/0.48 ( ( Xphi @ Xy )
% 0.32/0.48 => ( Xx = Xy ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setextAx_type,type,
% 0.32/0.48 setextAx: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setextAx,definition,
% 0.32/0.48 ( setextAx
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 <=> ( in @ Xx @ B ) )
% 0.32/0.48 => ( A = B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(emptyset_type,type,
% 0.32/0.48 emptyset: $i ).
% 0.32/0.48
% 0.32/0.48 thf(emptysetAx_type,type,
% 0.32/0.48 emptysetAx: $o ).
% 0.32/0.48
% 0.32/0.48 thf(emptysetAx,definition,
% 0.32/0.48 ( emptysetAx
% 0.32/0.48 = ( ! [Xx: $i] :
% 0.32/0.48 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setadjoin_type,type,
% 0.32/0.48 setadjoin: $i > $i > $i ).
% 0.32/0.48
% 0.32/0.48 thf(setadjoinAx_type,type,
% 0.32/0.48 setadjoinAx: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setadjoinAx,definition,
% 0.32/0.48 ( setadjoinAx
% 0.32/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.32/0.48 <=> ( ( Xy = Xx )
% 0.32/0.48 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(powerset_type,type,
% 0.32/0.48 powerset: $i > $i ).
% 0.32/0.48
% 0.32/0.48 thf(powersetAx_type,type,
% 0.32/0.48 powersetAx: $o ).
% 0.32/0.48
% 0.32/0.48 thf(powersetAx,definition,
% 0.32/0.48 ( powersetAx
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( in @ B @ ( powerset @ A ) )
% 0.32/0.48 <=> ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ B )
% 0.32/0.48 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setunion_type,type,
% 0.32/0.48 setunion: $i > $i ).
% 0.32/0.48
% 0.32/0.48 thf(setunionAx_type,type,
% 0.32/0.48 setunionAx: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setunionAx,definition,
% 0.32/0.48 ( setunionAx
% 0.32/0.48 = ( ! [A: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ ( setunion @ A ) )
% 0.32/0.48 <=> ? [B: $i] :
% 0.32/0.48 ( ( in @ Xx @ B )
% 0.32/0.48 & ( in @ B @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(omega_type,type,
% 0.32/0.48 omega: $i ).
% 0.32/0.48
% 0.32/0.48 thf(omega0Ax_type,type,
% 0.32/0.48 omega0Ax: $o ).
% 0.32/0.48
% 0.32/0.48 thf(omega0Ax,definition,
% 0.32/0.48 ( omega0Ax
% 0.32/0.48 = ( in @ emptyset @ omega ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(omegaSAx_type,type,
% 0.32/0.48 omegaSAx: $o ).
% 0.32/0.48
% 0.32/0.48 thf(omegaSAx,definition,
% 0.32/0.48 ( omegaSAx
% 0.32/0.48 = ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ omega )
% 0.32/0.48 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(omegaIndAx_type,type,
% 0.32/0.48 omegaIndAx: $o ).
% 0.32/0.48
% 0.32/0.48 thf(omegaIndAx,definition,
% 0.32/0.48 ( omegaIndAx
% 0.32/0.48 = ( ! [A: $i] :
% 0.32/0.48 ( ( ( in @ emptyset @ A )
% 0.32/0.48 & ! [Xx: $i] :
% 0.32/0.48 ( ( ( in @ Xx @ omega )
% 0.32/0.48 & ( in @ Xx @ A ) )
% 0.32/0.48 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.32/0.48 => ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ omega )
% 0.32/0.48 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(replAx_type,type,
% 0.32/0.48 replAx: $o ).
% 0.32/0.48
% 0.32/0.48 thf(replAx,definition,
% 0.32/0.48 ( replAx
% 0.32/0.48 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.32/0.48 ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( exu
% 0.32/0.48 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.32/0.48 => ? [B: $i] :
% 0.32/0.48 ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ B )
% 0.32/0.48 <=> ? [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ A )
% 0.32/0.48 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(foundationAx_type,type,
% 0.32/0.48 foundationAx: $o ).
% 0.32/0.48
% 0.32/0.48 thf(foundationAx,definition,
% 0.32/0.48 ( foundationAx
% 0.32/0.48 = ( ! [A: $i] :
% 0.32/0.48 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.32/0.48 => ? [B: $i] :
% 0.32/0.48 ( ( in @ B @ A )
% 0.32/0.48 & ~ ? [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ B )
% 0.32/0.48 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(wellorderingAx_type,type,
% 0.32/0.48 wellorderingAx: $o ).
% 0.32/0.48
% 0.32/0.48 thf(wellorderingAx,definition,
% 0.32/0.48 ( wellorderingAx
% 0.32/0.48 = ( ! [A: $i] :
% 0.32/0.48 ? [B: $i] :
% 0.32/0.48 ( ! [C: $i] :
% 0.32/0.48 ( ( in @ C @ B )
% 0.32/0.48 => ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ C )
% 0.32/0.48 => ( in @ Xx @ A ) ) )
% 0.32/0.48 & ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( ( in @ Xx @ A )
% 0.32/0.48 & ( in @ Xy @ A ) )
% 0.32/0.48 => ( ! [C: $i] :
% 0.32/0.48 ( ( in @ C @ B )
% 0.32/0.48 => ( ( in @ Xx @ C )
% 0.32/0.48 <=> ( in @ Xy @ C ) ) )
% 0.32/0.48 => ( Xx = Xy ) ) )
% 0.32/0.48 & ! [C: $i,D: $i] :
% 0.32/0.48 ( ( ( in @ C @ B )
% 0.32/0.48 & ( in @ D @ B ) )
% 0.32/0.48 => ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ C )
% 0.32/0.48 => ( in @ Xx @ D ) )
% 0.32/0.48 | ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ D )
% 0.32/0.48 => ( in @ Xx @ C ) ) ) )
% 0.32/0.48 & ! [C: $i] :
% 0.32/0.48 ( ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ C )
% 0.32/0.48 => ( in @ Xx @ A ) )
% 0.32/0.48 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.32/0.48 => ? [D: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ D @ B )
% 0.32/0.48 & ( in @ Xx @ C )
% 0.32/0.48 & ~ ? [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ D )
% 0.32/0.48 & ( in @ Xy @ C ) )
% 0.32/0.48 & ! [E: $i] :
% 0.32/0.48 ( ( in @ E @ B )
% 0.32/0.48 => ( ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ E )
% 0.32/0.48 => ( in @ Xy @ D ) )
% 0.32/0.48 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(descr_type,type,
% 0.32/0.48 descr: ( $i > $o ) > $i ).
% 0.32/0.48
% 0.32/0.48 thf(descrp_type,type,
% 0.32/0.48 descrp: $o ).
% 0.32/0.48
% 0.32/0.48 thf(descrp,definition,
% 0.32/0.48 ( descrp
% 0.32/0.48 = ( ! [Xphi: $i > $o] :
% 0.32/0.48 ( ( exu
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/0.48 => ( Xphi
% 0.32/0.48 @ ( descr
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(dsetconstr_type,type,
% 0.32/0.48 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.32/0.48
% 0.32/0.48 thf(dsetconstrI_type,type,
% 0.32/0.48 dsetconstrI: $o ).
% 0.32/0.48
% 0.32/0.48 thf(dsetconstrI,definition,
% 0.32/0.48 ( dsetconstrI
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( ( Xphi @ Xx )
% 0.32/0.48 => ( in @ Xx
% 0.32/0.48 @ ( dsetconstr @ A
% 0.32/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(dsetconstrEL_type,type,
% 0.32/0.48 dsetconstrEL: $o ).
% 0.32/0.48
% 0.32/0.48 thf(dsetconstrEL,definition,
% 0.32/0.48 ( dsetconstrEL
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx
% 0.32/0.48 @ ( dsetconstr @ A
% 0.32/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.32/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(dsetconstrER_type,type,
% 0.32/0.48 dsetconstrER: $o ).
% 0.32/0.48
% 0.32/0.48 thf(dsetconstrER,definition,
% 0.32/0.48 ( dsetconstrER
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx
% 0.32/0.48 @ ( dsetconstr @ A
% 0.32/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.32/0.48 => ( Xphi @ Xx ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(exuE1_type,type,
% 0.32/0.48 exuE1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(exuE1,definition,
% 0.32/0.48 ( exuE1
% 0.32/0.48 = ( ! [Xphi: $i > $o] :
% 0.32/0.48 ( ( exu
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/0.48 => ? [Xx: $i] :
% 0.32/0.48 ( ( Xphi @ Xx )
% 0.32/0.48 & ! [Xy: $i] :
% 0.32/0.48 ( ( Xphi @ Xy )
% 0.32/0.48 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(prop2set_type,type,
% 0.32/0.48 prop2set: $o > $i ).
% 0.32/0.48
% 0.32/0.48 thf(prop2setE_type,type,
% 0.32/0.48 prop2setE: $o ).
% 0.32/0.48
% 0.32/0.48 thf(prop2setE,definition,
% 0.32/0.48 ( prop2setE
% 0.32/0.48 = ( ! [Xphi: $o,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.32/0.48 => Xphi ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(emptysetE_type,type,
% 0.32/0.48 emptysetE: $o ).
% 0.32/0.48
% 0.32/0.48 thf(emptysetE,definition,
% 0.32/0.48 ( emptysetE
% 0.32/0.48 = ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ emptyset )
% 0.32/0.48 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(emptysetimpfalse_type,type,
% 0.32/0.48 emptysetimpfalse: $o ).
% 0.32/0.48
% 0.32/0.48 thf(emptysetimpfalse,definition,
% 0.32/0.48 ( emptysetimpfalse
% 0.32/0.48 = ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ emptyset )
% 0.32/0.48 => $false ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(notinemptyset_type,type,
% 0.32/0.48 notinemptyset: $o ).
% 0.32/0.48
% 0.32/0.48 thf(notinemptyset,definition,
% 0.32/0.48 ( notinemptyset
% 0.32/0.48 = ( ! [Xx: $i] :
% 0.32/0.48 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(exuE3e_type,type,
% 0.32/0.48 exuE3e: $o ).
% 0.32/0.48
% 0.32/0.48 thf(exuE3e,definition,
% 0.32/0.48 ( exuE3e
% 0.32/0.48 = ( ! [Xphi: $i > $o] :
% 0.32/0.48 ( ( exu
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/0.48 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setext_type,type,
% 0.32/0.48 setext: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setext,definition,
% 0.32/0.48 ( setext
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ Xx @ B ) )
% 0.32/0.48 => ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ B )
% 0.32/0.48 => ( in @ Xx @ A ) )
% 0.32/0.48 => ( A = B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(emptyI_type,type,
% 0.32/0.48 emptyI: $o ).
% 0.32/0.48
% 0.32/0.48 thf(emptyI,definition,
% 0.32/0.48 ( emptyI
% 0.32/0.48 = ( ! [A: $i] :
% 0.32/0.48 ( ! [Xx: $i] :
% 0.32/0.48 ~ ( in @ Xx @ A )
% 0.32/0.48 => ( A = emptyset ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(noeltsimpempty_type,type,
% 0.32/0.48 noeltsimpempty: $o ).
% 0.32/0.48
% 0.32/0.48 thf(noeltsimpempty,definition,
% 0.32/0.48 ( noeltsimpempty
% 0.32/0.48 = ( ! [A: $i] :
% 0.32/0.48 ( ! [Xx: $i] :
% 0.32/0.48 ~ ( in @ Xx @ A )
% 0.32/0.48 => ( A = emptyset ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setbeta_type,type,
% 0.32/0.48 setbeta: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setbeta,definition,
% 0.32/0.48 ( setbeta
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( ( in @ Xx
% 0.32/0.48 @ ( dsetconstr @ A
% 0.32/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.32/0.48 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(nonempty_type,type,
% 0.32/0.48 nonempty: $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(nonempty,definition,
% 0.32/0.48 ( nonempty
% 0.32/0.48 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(nonemptyE1_type,type,
% 0.32/0.48 nonemptyE1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(nonemptyE1,definition,
% 0.32/0.48 ( nonemptyE1
% 0.32/0.48 = ( ! [A: $i] :
% 0.32/0.48 ( ( nonempty @ A )
% 0.32/0.48 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(nonemptyI_type,type,
% 0.32/0.48 nonemptyI: $o ).
% 0.32/0.48
% 0.32/0.48 thf(nonemptyI,definition,
% 0.32/0.48 ( nonemptyI
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( ( Xphi @ Xx )
% 0.32/0.48 => ( nonempty
% 0.32/0.48 @ ( dsetconstr @ A
% 0.32/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(nonemptyI1_type,type,
% 0.32/0.48 nonemptyI1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(nonemptyI1,definition,
% 0.32/0.48 ( nonemptyI1
% 0.32/0.48 = ( ! [A: $i] :
% 0.32/0.48 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.32/0.48 => ( nonempty @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setadjoinIL_type,type,
% 0.32/0.48 setadjoinIL: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setadjoinIL,definition,
% 0.32/0.48 ( setadjoinIL
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(emptyinunitempty_type,type,
% 0.32/0.48 emptyinunitempty: $o ).
% 0.32/0.48
% 0.32/0.48 thf(emptyinunitempty,definition,
% 0.32/0.48 ( emptyinunitempty
% 0.32/0.48 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setadjoinIR_type,type,
% 0.32/0.48 setadjoinIR: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setadjoinIR,definition,
% 0.32/0.48 ( setadjoinIR
% 0.32/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ A )
% 0.32/0.48 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setadjoinE_type,type,
% 0.32/0.48 setadjoinE: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setadjoinE,definition,
% 0.32/0.48 ( setadjoinE
% 0.32/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.32/0.48 => ! [Xphi: $o] :
% 0.32/0.48 ( ( ( Xy = Xx )
% 0.32/0.48 => Xphi )
% 0.32/0.48 => ( ( ( in @ Xy @ A )
% 0.32/0.48 => Xphi )
% 0.32/0.48 => Xphi ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setadjoinOr_type,type,
% 0.32/0.48 setadjoinOr: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setadjoinOr,definition,
% 0.32/0.48 ( setadjoinOr
% 0.32/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.32/0.48 => ( ( Xy = Xx )
% 0.32/0.48 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setoftrueEq_type,type,
% 0.32/0.48 setoftrueEq: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setoftrueEq,definition,
% 0.32/0.48 ( setoftrueEq
% 0.32/0.48 = ( ! [A: $i] :
% 0.32/0.48 ( ( dsetconstr @ A
% 0.32/0.48 @ ^ [Xx: $i] : $true )
% 0.32/0.48 = A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(powersetI_type,type,
% 0.32/0.48 powersetI: $o ).
% 0.32/0.48
% 0.32/0.48 thf(powersetI,definition,
% 0.32/0.48 ( powersetI
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ B )
% 0.32/0.48 => ( in @ Xx @ A ) )
% 0.32/0.48 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(emptyinPowerset_type,type,
% 0.32/0.48 emptyinPowerset: $o ).
% 0.32/0.48
% 0.32/0.48 thf(emptyinPowerset,definition,
% 0.32/0.48 ( emptyinPowerset
% 0.32/0.48 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(emptyInPowerset_type,type,
% 0.32/0.48 emptyInPowerset: $o ).
% 0.32/0.48
% 0.32/0.48 thf(emptyInPowerset,definition,
% 0.32/0.48 ( emptyInPowerset
% 0.32/0.48 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(powersetE_type,type,
% 0.32/0.48 powersetE: $o ).
% 0.32/0.48
% 0.32/0.48 thf(powersetE,definition,
% 0.32/0.48 ( powersetE
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ B @ ( powerset @ A ) )
% 0.32/0.48 => ( ( in @ Xx @ B )
% 0.32/0.48 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setunionI_type,type,
% 0.32/0.48 setunionI: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setunionI,definition,
% 0.32/0.48 ( setunionI
% 0.32/0.48 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.32/0.48 ( ( in @ Xx @ B )
% 0.32/0.48 => ( ( in @ B @ A )
% 0.32/0.48 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setunionE_type,type,
% 0.32/0.48 setunionE: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setunionE,definition,
% 0.32/0.48 ( setunionE
% 0.32/0.48 = ( ! [A: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ ( setunion @ A ) )
% 0.32/0.48 => ! [Xphi: $o] :
% 0.32/0.48 ( ! [B: $i] :
% 0.32/0.48 ( ( in @ Xx @ B )
% 0.32/0.48 => ( ( in @ B @ A )
% 0.32/0.48 => Xphi ) )
% 0.32/0.48 => Xphi ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(subPowSU_type,type,
% 0.32/0.48 subPowSU: $o ).
% 0.32/0.48
% 0.32/0.48 thf(subPowSU,definition,
% 0.32/0.48 ( subPowSU
% 0.32/0.48 = ( ! [A: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(exuE2_type,type,
% 0.32/0.48 exuE2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(exuE2,definition,
% 0.32/0.48 ( exuE2
% 0.32/0.48 = ( ! [Xphi: $i > $o] :
% 0.32/0.48 ( ( exu
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/0.48 => ? [Xx: $i] :
% 0.32/0.48 ! [Xy: $i] :
% 0.32/0.48 ( ( Xphi @ Xy )
% 0.32/0.48 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(nonemptyImpWitness_type,type,
% 0.32/0.48 nonemptyImpWitness: $o ).
% 0.32/0.48
% 0.32/0.48 thf(nonemptyImpWitness,definition,
% 0.32/0.48 ( nonemptyImpWitness
% 0.32/0.48 = ( ! [A: $i] :
% 0.32/0.48 ( ( nonempty @ A )
% 0.32/0.48 => ? [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 & $true ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(uniqinunit_type,type,
% 0.32/0.48 uniqinunit: $o ).
% 0.32/0.48
% 0.32/0.48 thf(uniqinunit,definition,
% 0.32/0.48 ( uniqinunit
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.32/0.48 => ( Xx = Xy ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(notinsingleton_type,type,
% 0.32/0.48 notinsingleton: $o ).
% 0.32/0.48
% 0.32/0.48 thf(notinsingleton,definition,
% 0.32/0.48 ( notinsingleton
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( Xx != Xy )
% 0.32/0.48 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(eqinunit_type,type,
% 0.32/0.48 eqinunit: $o ).
% 0.32/0.48
% 0.32/0.48 thf(eqinunit,definition,
% 0.32/0.48 ( eqinunit
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( Xx = Xy )
% 0.32/0.48 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(singletonsswitch_type,type,
% 0.32/0.48 singletonsswitch: $o ).
% 0.32/0.48
% 0.32/0.48 thf(singletonsswitch,definition,
% 0.32/0.48 ( singletonsswitch
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.32/0.48 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(upairsetE_type,type,
% 0.32/0.48 upairsetE: $o ).
% 0.32/0.48
% 0.32/0.48 thf(upairsetE,definition,
% 0.32/0.48 ( upairsetE
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.32/0.48 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.32/0.48 => ( ( Xz = Xx )
% 0.32/0.48 | ( Xz = Xy ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(upairsetIL_type,type,
% 0.32/0.48 upairsetIL: $o ).
% 0.32/0.48
% 0.32/0.48 thf(upairsetIL,definition,
% 0.32/0.48 ( upairsetIL
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(upairsetIR_type,type,
% 0.32/0.48 upairsetIR: $o ).
% 0.32/0.48
% 0.32/0.48 thf(upairsetIR,definition,
% 0.32/0.48 ( upairsetIR
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(emptyE1_type,type,
% 0.32/0.48 emptyE1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(emptyE1,definition,
% 0.32/0.48 ( emptyE1
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/0.48 ( ? [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 & ( Xphi @ Xx ) )
% 0.32/0.48 => ( ( ( dsetconstr @ A
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/0.48 = emptyset )
% 0.32/0.48 => $false ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(vacuousDall_type,type,
% 0.32/0.48 vacuousDall: $o ).
% 0.32/0.48
% 0.32/0.48 thf(vacuousDall,definition,
% 0.32/0.48 ( vacuousDall
% 0.32/0.48 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ emptyset )
% 0.32/0.48 => ( Xphi @ Xx ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(quantDeMorgan1_type,type,
% 0.32/0.48 quantDeMorgan1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(quantDeMorgan1,definition,
% 0.32/0.48 ( quantDeMorgan1
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/0.48 ( ~ ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( Xphi @ Xx ) )
% 0.32/0.48 => ? [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(quantDeMorgan2_type,type,
% 0.32/0.48 quantDeMorgan2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(quantDeMorgan2,definition,
% 0.32/0.48 ( quantDeMorgan2
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/0.48 ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ~ ( Xphi @ Xx ) )
% 0.32/0.48 => ~ ? [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(quantDeMorgan3_type,type,
% 0.32/0.48 quantDeMorgan3: $o ).
% 0.32/0.48
% 0.32/0.48 thf(quantDeMorgan3,definition,
% 0.32/0.48 ( quantDeMorgan3
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/0.48 ( ~ ? [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 & ( Xphi @ Xx ) )
% 0.32/0.48 => ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(quantDeMorgan4_type,type,
% 0.32/0.48 quantDeMorgan4: $o ).
% 0.32/0.48
% 0.32/0.48 thf(quantDeMorgan4,definition,
% 0.32/0.48 ( quantDeMorgan4
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/0.48 ( ? [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 & ~ ( Xphi @ Xx ) )
% 0.32/0.48 => ~ ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(prop2setI_type,type,
% 0.32/0.48 prop2setI: $o ).
% 0.32/0.48
% 0.32/0.48 thf(prop2setI,definition,
% 0.32/0.48 ( prop2setI
% 0.32/0.48 = ( ! [Xphi: $o] :
% 0.32/0.48 ( Xphi
% 0.32/0.48 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(set2prop_type,type,
% 0.32/0.48 set2prop: $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(prop2set2propI_type,type,
% 0.32/0.48 prop2set2propI: $o ).
% 0.32/0.48
% 0.32/0.48 thf(prop2set2propI,definition,
% 0.32/0.48 ( prop2set2propI
% 0.32/0.48 = ( ! [Xphi: $o] :
% 0.32/0.48 ( Xphi
% 0.32/0.48 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(notdexE_type,type,
% 0.32/0.48 notdexE: $o ).
% 0.32/0.48
% 0.32/0.48 thf(notdexE,definition,
% 0.32/0.48 ( notdexE
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/0.48 ( ~ ? [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 & ( Xphi @ Xx ) )
% 0.32/0.48 => ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(notdallE_type,type,
% 0.32/0.48 notdallE: $o ).
% 0.32/0.48
% 0.32/0.48 thf(notdallE,definition,
% 0.32/0.48 ( notdallE
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/0.48 ( ~ ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( Xphi @ Xx ) )
% 0.32/0.48 => ? [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(exuI1_type,type,
% 0.32/0.48 exuI1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(exuI1,definition,
% 0.32/0.48 ( exuI1
% 0.32/0.48 = ( ! [Xphi: $i > $o] :
% 0.32/0.48 ( ? [Xx: $i] :
% 0.32/0.48 ( ( Xphi @ Xx )
% 0.32/0.48 & ! [Xy: $i] :
% 0.32/0.48 ( ( Xphi @ Xy )
% 0.32/0.48 => ( Xx = Xy ) ) )
% 0.32/0.48 => ( exu
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(exuI3_type,type,
% 0.32/0.48 exuI3: $o ).
% 0.32/0.48
% 0.32/0.48 thf(exuI3,definition,
% 0.32/0.48 ( exuI3
% 0.32/0.48 = ( ! [Xphi: $i > $o] :
% 0.32/0.48 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.32/0.48 => ( ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( Xphi @ Xx )
% 0.32/0.48 => ( ( Xphi @ Xy )
% 0.32/0.48 => ( Xx = Xy ) ) )
% 0.32/0.48 => ( exu
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(exuI2_type,type,
% 0.32/0.48 exuI2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(exuI2,definition,
% 0.32/0.48 ( exuI2
% 0.32/0.48 = ( ! [Xphi: $i > $o] :
% 0.32/0.48 ( ? [Xx: $i] :
% 0.32/0.48 ! [Xy: $i] :
% 0.32/0.48 ( ( Xphi @ Xy )
% 0.32/0.48 <=> ( Xy = Xx ) )
% 0.32/0.48 => ( exu
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(inCongP_type,type,
% 0.32/0.48 inCongP: $o ).
% 0.32/0.48
% 0.32/0.48 thf(inCongP,definition,
% 0.32/0.48 ( inCongP
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( A = B )
% 0.32/0.48 => ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( Xx = Xy )
% 0.32/0.48 => ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(in__Cong_type,type,
% 0.32/0.48 in__Cong: $o ).
% 0.32/0.48
% 0.32/0.48 thf(in__Cong,definition,
% 0.32/0.48 ( in__Cong
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( A = B )
% 0.32/0.48 => ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( Xx = Xy )
% 0.32/0.48 => ( ( in @ Xx @ A )
% 0.32/0.48 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(exuE3u_type,type,
% 0.32/0.48 exuE3u: $o ).
% 0.32/0.48
% 0.32/0.48 thf(exuE3u,definition,
% 0.32/0.48 ( exuE3u
% 0.32/0.48 = ( ! [Xphi: $i > $o] :
% 0.32/0.48 ( ( exu
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/0.48 => ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( Xphi @ Xx )
% 0.32/0.48 => ( ( Xphi @ Xy )
% 0.32/0.48 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(exu__Cong_type,type,
% 0.32/0.48 exu__Cong: $o ).
% 0.32/0.48
% 0.32/0.48 thf(exu__Cong,definition,
% 0.32/0.48 ( exu__Cong
% 0.32/0.48 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.32/0.48 ( ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( Xx = Xy )
% 0.32/0.48 => ( ( Xphi @ Xx )
% 0.32/0.48 <=> ( Xpsi @ Xy ) ) )
% 0.32/0.48 => ( ( exu
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/0.48 <=> ( exu
% 0.32/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(emptyset__Cong_type,type,
% 0.32/0.48 emptyset__Cong: $o ).
% 0.32/0.48
% 0.32/0.48 thf(emptyset__Cong,definition,
% 0.32/0.48 ( emptyset__Cong
% 0.32/0.48 = ( emptyset = emptyset ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setadjoin__Cong_type,type,
% 0.32/0.48 setadjoin__Cong: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setadjoin__Cong,definition,
% 0.32/0.48 ( setadjoin__Cong
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( Xx = Xy )
% 0.32/0.48 => ! [Xz: $i,Xu: $i] :
% 0.32/0.48 ( ( Xz = Xu )
% 0.32/0.48 => ( ( setadjoin @ Xx @ Xz )
% 0.32/0.48 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(powerset__Cong_type,type,
% 0.32/0.48 powerset__Cong: $o ).
% 0.32/0.48
% 0.32/0.48 thf(powerset__Cong,definition,
% 0.32/0.48 ( powerset__Cong
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( A = B )
% 0.32/0.48 => ( ( powerset @ A )
% 0.32/0.48 = ( powerset @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setunion__Cong_type,type,
% 0.32/0.48 setunion__Cong: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setunion__Cong,definition,
% 0.32/0.48 ( setunion__Cong
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( A = B )
% 0.32/0.48 => ( ( setunion @ A )
% 0.32/0.48 = ( setunion @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(omega__Cong_type,type,
% 0.32/0.48 omega__Cong: $o ).
% 0.32/0.48
% 0.32/0.48 thf(omega__Cong,definition,
% 0.32/0.48 ( omega__Cong
% 0.32/0.48 = ( omega = omega ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(exuEu_type,type,
% 0.32/0.48 exuEu: $o ).
% 0.32/0.48
% 0.32/0.48 thf(exuEu,definition,
% 0.32/0.48 ( exuEu
% 0.32/0.48 = ( ! [Xphi: $i > $o] :
% 0.32/0.48 ( ( exu
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/0.48 => ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( Xphi @ Xx )
% 0.32/0.48 => ( ( Xphi @ Xy )
% 0.32/0.48 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(descr__Cong_type,type,
% 0.32/0.48 descr__Cong: $o ).
% 0.32/0.48
% 0.32/0.48 thf(descr__Cong,definition,
% 0.32/0.48 ( descr__Cong
% 0.32/0.48 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.32/0.48 ( ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( Xx = Xy )
% 0.32/0.48 => ( ( Xphi @ Xx )
% 0.32/0.48 <=> ( Xpsi @ Xy ) ) )
% 0.32/0.48 => ( ( exu
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/0.48 => ( ( exu
% 0.32/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.32/0.48 => ( ( descr
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/0.48 = ( descr
% 0.32/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(dsetconstr__Cong_type,type,
% 0.32/0.48 dsetconstr__Cong: $o ).
% 0.32/0.48
% 0.32/0.48 thf(dsetconstr__Cong,definition,
% 0.32/0.48 ( dsetconstr__Cong
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( A = B )
% 0.32/0.48 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.32/0.48 ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( ( Xx = Xy )
% 0.32/0.48 => ( ( Xphi @ Xx )
% 0.32/0.48 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.32/0.48 => ( ( dsetconstr @ A
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/0.48 = ( dsetconstr @ B
% 0.32/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(subset_type,type,
% 0.32/0.48 subset: $i > $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(disjoint_type,type,
% 0.32/0.48 disjoint: $i > $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(setsmeet_type,type,
% 0.32/0.48 setsmeet: $i > $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(subsetI1_type,type,
% 0.32/0.48 subsetI1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(subsetI1,definition,
% 0.32/0.48 ( subsetI1
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ Xx @ B ) )
% 0.32/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(eqimpsubset2_type,type,
% 0.32/0.48 eqimpsubset2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(eqimpsubset2,definition,
% 0.32/0.48 ( eqimpsubset2
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( A = B )
% 0.32/0.48 => ( subset @ B @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(eqimpsubset1_type,type,
% 0.32/0.48 eqimpsubset1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(eqimpsubset1,definition,
% 0.32/0.48 ( eqimpsubset1
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( A = B )
% 0.32/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(subsetI2_type,type,
% 0.32/0.48 subsetI2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(subsetI2,definition,
% 0.32/0.48 ( subsetI2
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ Xx @ B ) )
% 0.32/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(emptysetsubset_type,type,
% 0.32/0.48 emptysetsubset: $o ).
% 0.32/0.48
% 0.32/0.48 thf(emptysetsubset,definition,
% 0.32/0.48 ( emptysetsubset
% 0.32/0.48 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(subsetE_type,type,
% 0.32/0.48 subsetE: $o ).
% 0.32/0.48
% 0.32/0.48 thf(subsetE,definition,
% 0.32/0.48 ( subsetE
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( subset @ A @ B )
% 0.32/0.48 => ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(subsetE2_type,type,
% 0.32/0.48 subsetE2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(subsetE2,definition,
% 0.32/0.48 ( subsetE2
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( subset @ A @ B )
% 0.32/0.48 => ( ~ ( in @ Xx @ B )
% 0.32/0.48 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(notsubsetI_type,type,
% 0.32/0.48 notsubsetI: $o ).
% 0.32/0.48
% 0.32/0.48 thf(notsubsetI,definition,
% 0.32/0.48 ( notsubsetI
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( ~ ( in @ Xx @ B )
% 0.32/0.48 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(notequalI1_type,type,
% 0.32/0.48 notequalI1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(notequalI1,definition,
% 0.32/0.48 ( notequalI1
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ~ ( subset @ A @ B )
% 0.32/0.48 => ( A != B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(notequalI2_type,type,
% 0.32/0.48 notequalI2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(notequalI2,definition,
% 0.32/0.48 ( notequalI2
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( ~ ( in @ Xx @ B )
% 0.32/0.48 => ( A != B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(subsetRefl_type,type,
% 0.32/0.48 subsetRefl: $o ).
% 0.32/0.48
% 0.32/0.48 thf(subsetRefl,definition,
% 0.32/0.48 ( subsetRefl
% 0.32/0.48 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(subsetTrans_type,type,
% 0.32/0.48 subsetTrans: $o ).
% 0.32/0.48
% 0.32/0.48 thf(subsetTrans,definition,
% 0.32/0.48 ( subsetTrans
% 0.32/0.48 = ( ! [A: $i,B: $i,C: $i] :
% 0.32/0.48 ( ( subset @ A @ B )
% 0.32/0.48 => ( ( subset @ B @ C )
% 0.32/0.48 => ( subset @ A @ C ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setadjoinSub_type,type,
% 0.32/0.48 setadjoinSub: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setadjoinSub,definition,
% 0.32/0.48 ( setadjoinSub
% 0.32/0.48 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setadjoinSub2_type,type,
% 0.32/0.48 setadjoinSub2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setadjoinSub2,definition,
% 0.32/0.48 ( setadjoinSub2
% 0.32/0.48 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.32/0.48 ( ( subset @ A @ B )
% 0.32/0.48 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(subset2powerset_type,type,
% 0.32/0.48 subset2powerset: $o ).
% 0.32/0.48
% 0.32/0.48 thf(subset2powerset,definition,
% 0.32/0.48 ( subset2powerset
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( subset @ A @ B )
% 0.32/0.48 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setextsub_type,type,
% 0.32/0.48 setextsub: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setextsub,definition,
% 0.32/0.48 ( setextsub
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( subset @ A @ B )
% 0.32/0.48 => ( ( subset @ B @ A )
% 0.32/0.48 => ( A = B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(subsetemptysetimpeq_type,type,
% 0.32/0.48 subsetemptysetimpeq: $o ).
% 0.32/0.48
% 0.32/0.48 thf(subsetemptysetimpeq,definition,
% 0.32/0.48 ( subsetemptysetimpeq
% 0.32/0.48 = ( ! [A: $i] :
% 0.32/0.48 ( ( subset @ A @ emptyset )
% 0.32/0.48 => ( A = emptyset ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(powersetI1_type,type,
% 0.32/0.48 powersetI1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(powersetI1,definition,
% 0.32/0.48 ( powersetI1
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( subset @ B @ A )
% 0.32/0.48 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(powersetE1_type,type,
% 0.32/0.48 powersetE1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(powersetE1,definition,
% 0.32/0.48 ( powersetE1
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( in @ B @ ( powerset @ A ) )
% 0.32/0.48 => ( subset @ B @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(inPowerset_type,type,
% 0.32/0.48 inPowerset: $o ).
% 0.32/0.48
% 0.32/0.48 thf(inPowerset,definition,
% 0.32/0.48 ( inPowerset
% 0.32/0.48 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(powersetsubset_type,type,
% 0.32/0.48 powersetsubset: $o ).
% 0.32/0.48
% 0.32/0.48 thf(powersetsubset,definition,
% 0.32/0.48 ( powersetsubset
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( subset @ A @ B )
% 0.32/0.48 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(sepInPowerset_type,type,
% 0.32/0.48 sepInPowerset: $o ).
% 0.32/0.48
% 0.32/0.48 thf(sepInPowerset,definition,
% 0.32/0.48 ( sepInPowerset
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/0.48 ( in
% 0.32/0.48 @ ( dsetconstr @ A
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/0.48 @ ( powerset @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(sepSubset_type,type,
% 0.32/0.48 sepSubset: $o ).
% 0.32/0.48
% 0.32/0.48 thf(sepSubset,definition,
% 0.32/0.48 ( sepSubset
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/0.48 ( subset
% 0.32/0.48 @ ( dsetconstr @ A
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/0.48 @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binunion_type,type,
% 0.32/0.48 binunion: $i > $i > $i ).
% 0.32/0.48
% 0.32/0.48 thf(binunionIL_type,type,
% 0.32/0.48 binunionIL: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binunionIL,definition,
% 0.32/0.48 ( binunionIL
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(upairset2IR_type,type,
% 0.32/0.48 upairset2IR: $o ).
% 0.32/0.48
% 0.32/0.48 thf(upairset2IR,definition,
% 0.32/0.48 ( upairset2IR
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binunionIR_type,type,
% 0.32/0.48 binunionIR: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binunionIR,definition,
% 0.32/0.48 ( binunionIR
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ B )
% 0.32/0.48 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binunionEcases_type,type,
% 0.32/0.48 binunionEcases: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binunionEcases,definition,
% 0.32/0.48 ( binunionEcases
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.32/0.48 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.32/0.48 => ( ( ( in @ Xx @ A )
% 0.32/0.48 => Xphi )
% 0.32/0.48 => ( ( ( in @ Xx @ B )
% 0.32/0.48 => Xphi )
% 0.32/0.48 => Xphi ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binunionE_type,type,
% 0.32/0.48 binunionE: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binunionE,definition,
% 0.32/0.48 ( binunionE
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.32/0.48 => ( ( in @ Xx @ A )
% 0.32/0.48 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binunionLsub_type,type,
% 0.32/0.48 binunionLsub: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binunionLsub,definition,
% 0.32/0.48 ( binunionLsub
% 0.32/0.48 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binunionRsub_type,type,
% 0.32/0.48 binunionRsub: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binunionRsub,definition,
% 0.32/0.48 ( binunionRsub
% 0.32/0.48 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binintersect_type,type,
% 0.32/0.48 binintersect: $i > $i > $i ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectI_type,type,
% 0.32/0.48 binintersectI: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectI,definition,
% 0.32/0.48 ( binintersectI
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( ( in @ Xx @ B )
% 0.32/0.48 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectSubset5_type,type,
% 0.32/0.48 binintersectSubset5: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectSubset5,definition,
% 0.32/0.48 ( binintersectSubset5
% 0.32/0.48 = ( ! [A: $i,B: $i,C: $i] :
% 0.32/0.48 ( ( subset @ C @ A )
% 0.32/0.48 => ( ( subset @ C @ B )
% 0.32/0.48 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectEL_type,type,
% 0.32/0.48 binintersectEL: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectEL,definition,
% 0.32/0.48 ( binintersectEL
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.32/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectLsub_type,type,
% 0.32/0.48 binintersectLsub: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectLsub,definition,
% 0.32/0.48 ( binintersectLsub
% 0.32/0.48 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectSubset2_type,type,
% 0.32/0.48 binintersectSubset2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectSubset2,definition,
% 0.32/0.48 ( binintersectSubset2
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( subset @ A @ B )
% 0.32/0.48 => ( ( binintersect @ A @ B )
% 0.32/0.48 = A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectSubset3_type,type,
% 0.32/0.48 binintersectSubset3: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectSubset3,definition,
% 0.32/0.48 ( binintersectSubset3
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( ( binintersect @ A @ B )
% 0.32/0.48 = B )
% 0.32/0.48 => ( subset @ B @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectER_type,type,
% 0.32/0.48 binintersectER: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectER,definition,
% 0.32/0.48 ( binintersectER
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.32/0.48 => ( in @ Xx @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(disjointsetsI1_type,type,
% 0.32/0.48 disjointsetsI1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(disjointsetsI1,definition,
% 0.32/0.48 ( disjointsetsI1
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ~ ? [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 & ( in @ Xx @ B ) )
% 0.32/0.48 => ( ( binintersect @ A @ B )
% 0.32/0.48 = emptyset ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectRsub_type,type,
% 0.32/0.48 binintersectRsub: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectRsub,definition,
% 0.32/0.48 ( binintersectRsub
% 0.32/0.48 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectSubset4_type,type,
% 0.32/0.48 binintersectSubset4: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectSubset4,definition,
% 0.32/0.48 ( binintersectSubset4
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( subset @ B @ A )
% 0.32/0.48 => ( ( binintersect @ A @ B )
% 0.32/0.48 = B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectSubset1_type,type,
% 0.32/0.48 binintersectSubset1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectSubset1,definition,
% 0.32/0.48 ( binintersectSubset1
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( ( binintersect @ A @ B )
% 0.32/0.48 = A )
% 0.32/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(bs114d_type,type,
% 0.32/0.48 bs114d: $o ).
% 0.32/0.48
% 0.32/0.48 thf(bs114d,definition,
% 0.32/0.48 ( bs114d
% 0.32/0.48 = ( ! [A: $i,B: $i,C: $i] :
% 0.32/0.48 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.32/0.48 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(regular_type,type,
% 0.32/0.48 regular: $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(setminus_type,type,
% 0.32/0.48 setminus: $i > $i > $i ).
% 0.32/0.48
% 0.32/0.48 thf(setminusI_type,type,
% 0.32/0.48 setminusI: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setminusI,definition,
% 0.32/0.48 ( setminusI
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( ~ ( in @ Xx @ B )
% 0.32/0.48 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setminusEL_type,type,
% 0.32/0.48 setminusEL: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setminusEL,definition,
% 0.32/0.48 ( setminusEL
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.32/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setminusER_type,type,
% 0.32/0.48 setminusER: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setminusER,definition,
% 0.32/0.48 ( setminusER
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.32/0.48 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setminusSubset2_type,type,
% 0.32/0.48 setminusSubset2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setminusSubset2,definition,
% 0.32/0.48 ( setminusSubset2
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( subset @ A @ B )
% 0.32/0.48 => ( ( setminus @ A @ B )
% 0.32/0.48 = emptyset ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setminusERneg_type,type,
% 0.32/0.48 setminusERneg: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setminusERneg,definition,
% 0.32/0.48 ( setminusERneg
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.32/0.48 => ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setminusELneg_type,type,
% 0.32/0.48 setminusELneg: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setminusELneg,definition,
% 0.32/0.48 ( setminusELneg
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.32/0.48 => ( ~ ( in @ Xx @ B )
% 0.32/0.48 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setminusILneg_type,type,
% 0.32/0.48 setminusILneg: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setminusILneg,definition,
% 0.32/0.48 ( setminusILneg
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ~ ( in @ Xx @ A )
% 0.32/0.48 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setminusIRneg_type,type,
% 0.32/0.48 setminusIRneg: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setminusIRneg,definition,
% 0.32/0.48 ( setminusIRneg
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ B )
% 0.32/0.48 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setminusLsub_type,type,
% 0.32/0.48 setminusLsub: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setminusLsub,definition,
% 0.32/0.48 ( setminusLsub
% 0.32/0.48 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setminusSubset1_type,type,
% 0.32/0.48 setminusSubset1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setminusSubset1,definition,
% 0.32/0.48 ( setminusSubset1
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ( ( setminus @ A @ B )
% 0.32/0.48 = emptyset )
% 0.32/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(symdiff_type,type,
% 0.32/0.48 symdiff: $i > $i > $i ).
% 0.32/0.48
% 0.32/0.48 thf(symdiffE_type,type,
% 0.32/0.48 symdiffE: $o ).
% 0.32/0.48
% 0.32/0.48 thf(symdiffE,definition,
% 0.32/0.48 ( symdiffE
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.32/0.48 => ! [Xphi: $o] :
% 0.32/0.48 ( ( ( in @ Xx @ A )
% 0.32/0.48 => ( ~ ( in @ Xx @ B )
% 0.32/0.48 => Xphi ) )
% 0.32/0.48 => ( ( ~ ( in @ Xx @ A )
% 0.32/0.48 => ( ( in @ Xx @ B )
% 0.32/0.48 => Xphi ) )
% 0.32/0.48 => Xphi ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(symdiffI1_type,type,
% 0.32/0.48 symdiffI1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(symdiffI1,definition,
% 0.32/0.48 ( symdiffI1
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( ~ ( in @ Xx @ B )
% 0.32/0.48 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(symdiffI2_type,type,
% 0.32/0.48 symdiffI2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(symdiffI2,definition,
% 0.32/0.48 ( symdiffI2
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ~ ( in @ Xx @ A )
% 0.32/0.48 => ( ( in @ Xx @ B )
% 0.32/0.48 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(symdiffIneg1_type,type,
% 0.32/0.48 symdiffIneg1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(symdiffIneg1,definition,
% 0.32/0.48 ( symdiffIneg1
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( ( in @ Xx @ B )
% 0.32/0.48 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(symdiffIneg2_type,type,
% 0.32/0.48 symdiffIneg2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(symdiffIneg2,definition,
% 0.32/0.48 ( symdiffIneg2
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ~ ( in @ Xx @ A )
% 0.32/0.48 => ( ~ ( in @ Xx @ B )
% 0.32/0.48 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(iskpair_type,type,
% 0.32/0.48 iskpair: $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(secondinupair_type,type,
% 0.32/0.48 secondinupair: $o ).
% 0.32/0.48
% 0.32/0.48 thf(secondinupair,definition,
% 0.32/0.48 ( secondinupair
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairIL_type,type,
% 0.32/0.48 setukpairIL: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairIL,definition,
% 0.32/0.48 ( setukpairIL
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairIR_type,type,
% 0.32/0.48 setukpairIR: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairIR,definition,
% 0.32/0.48 ( setukpairIR
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(kpairiskpair_type,type,
% 0.32/0.48 kpairiskpair: $o ).
% 0.32/0.48
% 0.32/0.48 thf(kpairiskpair,definition,
% 0.32/0.48 ( kpairiskpair
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(kpair_type,type,
% 0.32/0.48 kpair: $i > $i > $i ).
% 0.32/0.48
% 0.32/0.48 thf(kpairp_type,type,
% 0.32/0.48 kpairp: $o ).
% 0.32/0.48
% 0.32/0.48 thf(kpairp,definition,
% 0.32/0.48 ( kpairp
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(cartprod_type,type,
% 0.32/0.48 cartprod: $i > $i > $i ).
% 0.32/0.48
% 0.32/0.48 thf(singletonsubset_type,type,
% 0.32/0.48 singletonsubset: $o ).
% 0.32/0.48
% 0.32/0.48 thf(singletonsubset,definition,
% 0.32/0.48 ( singletonsubset
% 0.32/0.48 = ( ! [A: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(singletoninpowerset_type,type,
% 0.32/0.48 singletoninpowerset: $o ).
% 0.32/0.48
% 0.32/0.48 thf(singletoninpowerset,definition,
% 0.32/0.48 ( singletoninpowerset
% 0.32/0.48 = ( ! [A: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(singletoninpowunion_type,type,
% 0.32/0.48 singletoninpowunion: $o ).
% 0.32/0.48
% 0.32/0.48 thf(singletoninpowunion,definition,
% 0.32/0.48 ( singletoninpowunion
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(upairset2E_type,type,
% 0.32/0.48 upairset2E: $o ).
% 0.32/0.48
% 0.32/0.48 thf(upairset2E,definition,
% 0.32/0.48 ( upairset2E
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.32/0.48 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.32/0.48 => ( ( Xz = Xx )
% 0.32/0.48 | ( Xz = Xy ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(upairsubunion_type,type,
% 0.32/0.48 upairsubunion: $o ).
% 0.32/0.48
% 0.32/0.48 thf(upairsubunion,definition,
% 0.32/0.48 ( upairsubunion
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(upairinpowunion_type,type,
% 0.32/0.48 upairinpowunion: $o ).
% 0.32/0.48
% 0.32/0.48 thf(upairinpowunion,definition,
% 0.32/0.48 ( upairinpowunion
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(ubforcartprodlem1_type,type,
% 0.32/0.48 ubforcartprodlem1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(ubforcartprodlem1,definition,
% 0.32/0.48 ( ubforcartprodlem1
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(ubforcartprodlem2_type,type,
% 0.32/0.48 ubforcartprodlem2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(ubforcartprodlem2,definition,
% 0.32/0.48 ( ubforcartprodlem2
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(ubforcartprodlem3_type,type,
% 0.32/0.48 ubforcartprodlem3: $o ).
% 0.32/0.48
% 0.32/0.48 thf(ubforcartprodlem3,definition,
% 0.32/0.48 ( ubforcartprodlem3
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodpairin_type,type,
% 0.32/0.48 cartprodpairin: $o ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodpairin,definition,
% 0.32/0.48 ( cartprodpairin
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodmempair1_type,type,
% 0.32/0.48 cartprodmempair1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodmempair1,definition,
% 0.32/0.48 ( cartprodmempair1
% 0.32/0.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.32/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.32/0.48 => ? [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 & ? [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 & ( Xu
% 0.32/0.48 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodmempair_type,type,
% 0.32/0.48 cartprodmempair: $o ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodmempair,definition,
% 0.32/0.48 ( cartprodmempair
% 0.32/0.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.32/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.32/0.48 => ( iskpair @ Xu ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setunionE2_type,type,
% 0.32/0.48 setunionE2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setunionE2,definition,
% 0.32/0.48 ( setunionE2
% 0.32/0.48 = ( ! [A: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ ( setunion @ A ) )
% 0.32/0.48 => ? [X: $i] :
% 0.32/0.48 ( ( in @ X @ A )
% 0.32/0.48 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setunionsingleton1_type,type,
% 0.32/0.48 setunionsingleton1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setunionsingleton1,definition,
% 0.32/0.48 ( setunionsingleton1
% 0.32/0.48 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setunionsingleton2_type,type,
% 0.32/0.48 setunionsingleton2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setunionsingleton2,definition,
% 0.32/0.48 ( setunionsingleton2
% 0.32/0.48 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setunionsingleton_type,type,
% 0.32/0.48 setunionsingleton: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setunionsingleton,definition,
% 0.32/0.48 ( setunionsingleton
% 0.32/0.48 = ( ! [Xx: $i] :
% 0.32/0.48 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.32/0.48 = Xx ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(singleton_type,type,
% 0.32/0.48 singleton: $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(singletonprop_type,type,
% 0.32/0.48 singletonprop: $o ).
% 0.32/0.48
% 0.32/0.48 thf(singletonprop,definition,
% 0.32/0.48 ( singletonprop
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/0.48 ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ A )
% 0.32/0.48 => ( ( Xphi @ Xx )
% 0.32/0.48 => ( ( Xphi @ Xy )
% 0.32/0.48 => ( Xx = Xy ) ) ) ) )
% 0.32/0.48 => ( ? [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 & ( Xphi @ Xx ) )
% 0.32/0.48 => ( singleton
% 0.32/0.48 @ ( dsetconstr @ A
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(ex1_type,type,
% 0.32/0.48 ex1: $i > ( $i > $o ) > $o ).
% 0.32/0.48
% 0.32/0.48 thf(ex1E1_type,type,
% 0.32/0.48 ex1E1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(ex1E1,definition,
% 0.32/0.48 ( ex1E1
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/0.48 ( ( ex1 @ A
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/0.48 => ? [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(ex1I_type,type,
% 0.32/0.48 ex1I: $o ).
% 0.32/0.48
% 0.32/0.48 thf(ex1I,definition,
% 0.32/0.48 ( ex1I
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( ( Xphi @ Xx )
% 0.32/0.48 => ( ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ A )
% 0.32/0.48 => ( ( Xphi @ Xy )
% 0.32/0.48 => ( Xy = Xx ) ) )
% 0.32/0.48 => ( ex1 @ A
% 0.32/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(ex1I2_type,type,
% 0.32/0.48 ex1I2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(ex1I2,definition,
% 0.32/0.48 ( ex1I2
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/0.48 ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ A )
% 0.32/0.48 => ( ( Xphi @ Xx )
% 0.32/0.48 => ( ( Xphi @ Xy )
% 0.32/0.48 => ( Xx = Xy ) ) ) ) )
% 0.32/0.48 => ( ? [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 & ( Xphi @ Xx ) )
% 0.32/0.48 => ( ex1 @ A
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(singletonsuniq_type,type,
% 0.32/0.48 singletonsuniq: $o ).
% 0.32/0.48
% 0.32/0.48 thf(singletonsuniq,definition,
% 0.32/0.48 ( singletonsuniq
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( ( setadjoin @ Xx @ emptyset )
% 0.32/0.48 = ( setadjoin @ Xy @ emptyset ) )
% 0.32/0.48 => ( Xx = Xy ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(atmost1p_type,type,
% 0.32/0.48 atmost1p: $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(atleast2p_type,type,
% 0.32/0.48 atleast2p: $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(atmost2p_type,type,
% 0.32/0.48 atmost2p: $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(upairsetp_type,type,
% 0.32/0.48 upairsetp: $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjL1_type,type,
% 0.32/0.48 setukpairinjL1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjL1,definition,
% 0.32/0.48 ( setukpairinjL1
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.32/0.48 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.32/0.48 => ( Xx = Xz ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(kfstsingleton_type,type,
% 0.32/0.48 kfstsingleton: $o ).
% 0.32/0.48
% 0.32/0.48 thf(kfstsingleton,definition,
% 0.32/0.48 ( kfstsingleton
% 0.32/0.48 = ( ! [Xu: $i] :
% 0.32/0.48 ( ( iskpair @ Xu )
% 0.32/0.48 => ( singleton
% 0.32/0.48 @ ( dsetconstr @ ( setunion @ Xu )
% 0.32/0.48 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(theprop_type,type,
% 0.32/0.48 theprop: $o ).
% 0.32/0.48
% 0.32/0.48 thf(theprop,definition,
% 0.32/0.48 ( theprop
% 0.32/0.48 = ( ! [X: $i] :
% 0.32/0.48 ( ( singleton @ X )
% 0.32/0.48 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(kfst_type,type,
% 0.32/0.48 kfst: $i > $i ).
% 0.32/0.48
% 0.32/0.48 thf(kfstpairEq_type,type,
% 0.32/0.48 kfstpairEq: $o ).
% 0.32/0.48
% 0.32/0.48 thf(kfstpairEq,definition,
% 0.32/0.48 ( kfstpairEq
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.32/0.48 = Xx ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodfstin_type,type,
% 0.32/0.48 cartprodfstin: $o ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodfstin,definition,
% 0.32/0.48 ( cartprodfstin
% 0.32/0.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.32/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.32/0.48 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjL2_type,type,
% 0.32/0.48 setukpairinjL2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjL2,definition,
% 0.32/0.48 ( setukpairinjL2
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.32/0.48 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.32/0.48 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.32/0.48 => ( Xx = Xz ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjL_type,type,
% 0.32/0.48 setukpairinjL: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjL,definition,
% 0.32/0.48 ( setukpairinjL
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.32/0.48 ( ( ( kpair @ Xx @ Xy )
% 0.32/0.48 = ( kpair @ Xz @ Xu ) )
% 0.32/0.48 => ( Xx = Xz ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjR11_type,type,
% 0.32/0.48 setukpairinjR11: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjR11,definition,
% 0.32/0.48 ( setukpairinjR11
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( Xx = Xy )
% 0.32/0.48 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.32/0.48 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjR12_type,type,
% 0.32/0.48 setukpairinjR12: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjR12,definition,
% 0.32/0.48 ( setukpairinjR12
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( Xx = Xy )
% 0.32/0.48 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.32/0.48 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjR1_type,type,
% 0.32/0.48 setukpairinjR1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjR1,definition,
% 0.32/0.48 ( setukpairinjR1
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.32/0.48 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.32/0.48 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.32/0.48 => ( ( Xz = Xu )
% 0.32/0.48 => ( Xy = Xu ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(upairequniteq_type,type,
% 0.32/0.48 upairequniteq: $o ).
% 0.32/0.48
% 0.32/0.48 thf(upairequniteq,definition,
% 0.32/0.48 ( upairequniteq
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.32/0.48 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.32/0.48 = ( setadjoin @ Xz @ emptyset ) )
% 0.32/0.48 => ( Xx = Xy ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjR2_type,type,
% 0.32/0.48 setukpairinjR2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjR2,definition,
% 0.32/0.48 ( setukpairinjR2
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.32/0.48 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.32/0.48 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.32/0.48 => ( Xy = Xu ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjR_type,type,
% 0.32/0.48 setukpairinjR: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setukpairinjR,definition,
% 0.32/0.48 ( setukpairinjR
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.32/0.48 ( ( ( kpair @ Xx @ Xy )
% 0.32/0.48 = ( kpair @ Xz @ Xu ) )
% 0.32/0.48 => ( Xy = Xu ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(ksndsingleton_type,type,
% 0.32/0.48 ksndsingleton: $o ).
% 0.32/0.48
% 0.32/0.48 thf(ksndsingleton,definition,
% 0.32/0.48 ( ksndsingleton
% 0.32/0.48 = ( ! [Xu: $i] :
% 0.32/0.48 ( ( iskpair @ Xu )
% 0.32/0.48 => ( singleton
% 0.32/0.48 @ ( dsetconstr @ ( setunion @ Xu )
% 0.32/0.48 @ ^ [Xx: $i] :
% 0.32/0.48 ( Xu
% 0.32/0.48 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(ksnd_type,type,
% 0.32/0.48 ksnd: $i > $i ).
% 0.32/0.48
% 0.32/0.48 thf(ksndpairEq_type,type,
% 0.32/0.48 ksndpairEq: $o ).
% 0.32/0.48
% 0.32/0.48 thf(ksndpairEq,definition,
% 0.32/0.48 ( ksndpairEq
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.32/0.48 = Xy ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(kpairsurjEq_type,type,
% 0.32/0.48 kpairsurjEq: $o ).
% 0.32/0.48
% 0.32/0.48 thf(kpairsurjEq,definition,
% 0.32/0.48 ( kpairsurjEq
% 0.32/0.48 = ( ! [Xu: $i] :
% 0.32/0.48 ( ( iskpair @ Xu )
% 0.32/0.48 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.32/0.48 = Xu ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodsndin_type,type,
% 0.32/0.48 cartprodsndin: $o ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodsndin,definition,
% 0.32/0.48 ( cartprodsndin
% 0.32/0.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.32/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.32/0.48 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodpairmemEL_type,type,
% 0.32/0.48 cartprodpairmemEL: $o ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodpairmemEL,definition,
% 0.32/0.48 ( cartprodpairmemEL
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.32/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodpairmemER_type,type,
% 0.32/0.48 cartprodpairmemER: $o ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodpairmemER,definition,
% 0.32/0.48 ( cartprodpairmemER
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.32/0.48 => ( in @ Xy @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodmempaircEq_type,type,
% 0.32/0.48 cartprodmempaircEq: $o ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodmempaircEq,definition,
% 0.32/0.48 ( cartprodmempaircEq
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( ( kpair @ Xx @ Xy )
% 0.32/0.48 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodfstpairEq_type,type,
% 0.32/0.48 cartprodfstpairEq: $o ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodfstpairEq,definition,
% 0.32/0.48 ( cartprodfstpairEq
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.32/0.48 = Xx ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodsndpairEq_type,type,
% 0.32/0.48 cartprodsndpairEq: $o ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodsndpairEq,definition,
% 0.32/0.48 ( cartprodsndpairEq
% 0.32/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.32/0.48 = Xy ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodpairsurjEq_type,type,
% 0.32/0.48 cartprodpairsurjEq: $o ).
% 0.32/0.48
% 0.32/0.48 thf(cartprodpairsurjEq,definition,
% 0.32/0.48 ( cartprodpairsurjEq
% 0.32/0.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.32/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.32/0.48 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.32/0.48 = Xu ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(breln_type,type,
% 0.32/0.48 breln: $i > $i > $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(breln,definition,
% 0.32/0.48 ( breln
% 0.32/0.48 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(dpsetconstr_type,type,
% 0.32/0.48 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.32/0.48
% 0.32/0.48 thf(dpsetconstrI_type,type,
% 0.32/0.48 dpsetconstrI: $o ).
% 0.32/0.48
% 0.32/0.48 thf(dpsetconstrI,definition,
% 0.32/0.48 ( dpsetconstrI
% 0.32/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( ( Xphi @ Xx @ Xy )
% 0.32/0.48 => ( in @ ( kpair @ Xx @ Xy )
% 0.32/0.48 @ ( dpsetconstr @ A @ B
% 0.32/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(dpsetconstrSub_type,type,
% 0.32/0.48 dpsetconstrSub: $o ).
% 0.32/0.48
% 0.32/0.48 thf(dpsetconstrSub,definition,
% 0.32/0.48 ( dpsetconstrSub
% 0.32/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.32/0.48 ( subset
% 0.32/0.48 @ ( dpsetconstr @ A @ B
% 0.32/0.48 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.32/0.48 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setOfPairsIsBReln_type,type,
% 0.32/0.48 setOfPairsIsBReln: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setOfPairsIsBReln,definition,
% 0.32/0.48 ( setOfPairsIsBReln
% 0.32/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.32/0.48 ( breln @ A @ B
% 0.32/0.48 @ ( dpsetconstr @ A @ B
% 0.32/0.48 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(dpsetconstrERa_type,type,
% 0.32/0.48 dpsetconstrERa: $o ).
% 0.32/0.48
% 0.32/0.48 thf(dpsetconstrERa,definition,
% 0.32/0.48 ( dpsetconstrERa
% 0.32/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.32/0.48 @ ( dpsetconstr @ A @ B
% 0.32/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.32/0.48 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(dpsetconstrEL1_type,type,
% 0.32/0.48 dpsetconstrEL1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(dpsetconstrEL1,definition,
% 0.32/0.48 ( dpsetconstrEL1
% 0.32/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( in @ ( kpair @ Xx @ Xy )
% 0.32/0.48 @ ( dpsetconstr @ A @ B
% 0.32/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.32/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(dpsetconstrEL2_type,type,
% 0.32/0.48 dpsetconstrEL2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(dpsetconstrEL2,definition,
% 0.32/0.48 ( dpsetconstrEL2
% 0.32/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( in @ ( kpair @ Xx @ Xy )
% 0.32/0.48 @ ( dpsetconstr @ A @ B
% 0.32/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.32/0.48 => ( in @ Xy @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(dpsetconstrER_type,type,
% 0.32/0.48 dpsetconstrER: $o ).
% 0.32/0.48
% 0.32/0.48 thf(dpsetconstrER,definition,
% 0.32/0.48 ( dpsetconstrER
% 0.32/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( in @ ( kpair @ Xx @ Xy )
% 0.32/0.48 @ ( dpsetconstr @ A @ B
% 0.32/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.32/0.48 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(func_type,type,
% 0.32/0.48 func: $i > $i > $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(funcSet_type,type,
% 0.32/0.48 funcSet: $i > $i > $i ).
% 0.32/0.48
% 0.32/0.48 thf(funcImageSingleton_type,type,
% 0.32/0.48 funcImageSingleton: $o ).
% 0.32/0.48
% 0.32/0.48 thf(funcImageSingleton,definition,
% 0.32/0.48 ( funcImageSingleton
% 0.32/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.48 ( ( func @ A @ B @ Xf )
% 0.32/0.48 => ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( singleton
% 0.32/0.48 @ ( dsetconstr @ B
% 0.32/0.48 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(apProp_type,type,
% 0.32/0.48 apProp: $o ).
% 0.32/0.48
% 0.32/0.48 thf(apProp,definition,
% 0.32/0.48 ( apProp
% 0.32/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.48 ( ( func @ A @ B @ Xf )
% 0.32/0.48 => ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( in
% 0.32/0.48 @ ( setunion
% 0.32/0.48 @ ( dsetconstr @ B
% 0.32/0.48 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.32/0.48 @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(ap_type,type,
% 0.32/0.48 ap: $i > $i > $i > $i > $i ).
% 0.32/0.48
% 0.32/0.48 thf(app_type,type,
% 0.32/0.48 app: $o ).
% 0.32/0.48
% 0.32/0.48 thf(app,definition,
% 0.32/0.48 ( app
% 0.32/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.48 ( ( func @ A @ B @ Xf )
% 0.32/0.48 => ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(infuncsetfunc_type,type,
% 0.32/0.48 infuncsetfunc: $o ).
% 0.32/0.48
% 0.32/0.48 thf(infuncsetfunc,definition,
% 0.32/0.48 ( infuncsetfunc
% 0.32/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.32/0.48 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(ap2p_type,type,
% 0.32/0.48 ap2p: $o ).
% 0.32/0.48
% 0.32/0.48 thf(ap2p,definition,
% 0.32/0.48 ( ap2p
% 0.32/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.32/0.48 => ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(funcinfuncset_type,type,
% 0.32/0.48 funcinfuncset: $o ).
% 0.32/0.48
% 0.32/0.48 thf(funcinfuncset,definition,
% 0.32/0.48 ( funcinfuncset
% 0.32/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.48 ( ( func @ A @ B @ Xf )
% 0.32/0.48 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(lamProp_type,type,
% 0.32/0.48 lamProp: $o ).
% 0.32/0.48
% 0.32/0.48 thf(lamProp,definition,
% 0.32/0.48 ( lamProp
% 0.32/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.32/0.48 ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.32/0.48 => ( func @ A @ B
% 0.32/0.48 @ ( dpsetconstr @ A @ B
% 0.32/0.48 @ ^ [Xx: $i,Xy: $i] :
% 0.32/0.48 ( ( Xf @ Xx )
% 0.32/0.48 = Xy ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(lam_type,type,
% 0.32/0.48 lam: $i > $i > ( $i > $i ) > $i ).
% 0.32/0.48
% 0.32/0.48 thf(lamp_type,type,
% 0.32/0.48 lamp: $o ).
% 0.32/0.48
% 0.32/0.48 thf(lamp,definition,
% 0.32/0.48 ( lamp
% 0.32/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.32/0.48 ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.32/0.48 => ( func @ A @ B
% 0.32/0.48 @ ( lam @ A @ B
% 0.32/0.48 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(lam2p_type,type,
% 0.32/0.48 lam2p: $o ).
% 0.32/0.48
% 0.32/0.48 thf(lam2p,definition,
% 0.32/0.48 ( lam2p
% 0.32/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.32/0.48 ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.32/0.48 => ( in
% 0.32/0.48 @ ( lam @ A @ B
% 0.32/0.48 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.32/0.48 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(brelnall1_type,type,
% 0.32/0.48 brelnall1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(brelnall1,definition,
% 0.32/0.48 ( brelnall1
% 0.32/0.48 = ( ! [A: $i,B: $i,R: $i] :
% 0.32/0.48 ( ( breln @ A @ B @ R )
% 0.32/0.48 => ! [Xphi: $i > $o] :
% 0.32/0.48 ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.32/0.48 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.32/0.48 => ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ R )
% 0.32/0.48 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(brelnall2_type,type,
% 0.32/0.48 brelnall2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(brelnall2,definition,
% 0.32/0.48 ( brelnall2
% 0.32/0.48 = ( ! [A: $i,B: $i,R: $i] :
% 0.32/0.48 ( ( breln @ A @ B @ R )
% 0.32/0.48 => ! [Xphi: $i > $o] :
% 0.32/0.48 ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.32/0.48 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.32/0.48 => ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ R )
% 0.32/0.48 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(ex1E2_type,type,
% 0.32/0.48 ex1E2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(ex1E2,definition,
% 0.32/0.48 ( ex1E2
% 0.32/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/0.48 ( ( ex1 @ A
% 0.32/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/0.48 => ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ A )
% 0.32/0.48 => ( ( Xphi @ Xx )
% 0.32/0.48 => ( ( Xphi @ Xy )
% 0.32/0.48 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(funcGraphProp1_type,type,
% 0.32/0.48 funcGraphProp1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(funcGraphProp1,definition,
% 0.32/0.48 ( funcGraphProp1
% 0.32/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.48 ( ( func @ A @ B @ Xf )
% 0.32/0.48 => ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(funcGraphProp3_type,type,
% 0.32/0.48 funcGraphProp3: $o ).
% 0.32/0.48
% 0.32/0.48 thf(funcGraphProp3,definition,
% 0.32/0.48 ( funcGraphProp3
% 0.32/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.32/0.48 => ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(funcGraphProp2_type,type,
% 0.32/0.48 funcGraphProp2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(funcGraphProp2,definition,
% 0.32/0.48 ( funcGraphProp2
% 0.32/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.48 ( ( func @ A @ B @ Xf )
% 0.32/0.48 => ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.32/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.32/0.48 = Xy ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(funcextLem_type,type,
% 0.32/0.48 funcextLem: $o ).
% 0.32/0.48
% 0.32/0.48 thf(funcextLem,definition,
% 0.32/0.48 ( funcextLem
% 0.32/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.48 ( ( func @ A @ B @ Xf )
% 0.32/0.48 => ! [Xg: $i] :
% 0.32/0.48 ( ( func @ A @ B @ Xg )
% 0.32/0.48 => ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.32/0.48 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.32/0.48 => ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 0.32/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(funcGraphProp4_type,type,
% 0.32/0.48 funcGraphProp4: $o ).
% 0.32/0.48
% 0.32/0.48 thf(funcGraphProp4,definition,
% 0.32/0.48 ( funcGraphProp4
% 0.32/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.32/0.48 => ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.32/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.32/0.48 = Xy ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(subbreln_type,type,
% 0.32/0.48 subbreln: $o ).
% 0.32/0.48
% 0.32/0.48 thf(subbreln,definition,
% 0.32/0.48 ( subbreln
% 0.32/0.48 = ( ! [A: $i,B: $i,R: $i] :
% 0.32/0.48 ( ( breln @ A @ B @ R )
% 0.32/0.48 => ! [S: $i] :
% 0.32/0.48 ( ( breln @ A @ B @ S )
% 0.32/0.48 => ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.32/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.32/0.48 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(eqbreln_type,type,
% 0.32/0.48 eqbreln: $o ).
% 0.32/0.48
% 0.32/0.48 thf(eqbreln,definition,
% 0.32/0.48 ( eqbreln
% 0.32/0.48 = ( ! [A: $i,B: $i,R: $i] :
% 0.32/0.48 ( ( breln @ A @ B @ R )
% 0.32/0.48 => ! [S: $i] :
% 0.32/0.48 ( ( breln @ A @ B @ S )
% 0.32/0.48 => ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.32/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.32/0.48 => ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ B )
% 0.32/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.32/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.32/0.48 => ( R = S ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(funcext_type,type,
% 0.32/0.48 funcext: $o ).
% 0.32/0.48
% 0.32/0.48 thf(funcext,definition,
% 0.32/0.48 ( funcext
% 0.32/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.48 ( ( func @ A @ B @ Xf )
% 0.32/0.48 => ! [Xg: $i] :
% 0.32/0.48 ( ( func @ A @ B @ Xg )
% 0.32/0.48 => ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.32/0.48 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.32/0.48 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(funcext2_type,type,
% 0.32/0.48 funcext2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(funcext2,definition,
% 0.32/0.48 ( funcext2
% 0.32/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.32/0.48 => ! [Xg: $i] :
% 0.32/0.48 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 0.32/0.48 => ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.32/0.48 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.32/0.48 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(ap2apEq1_type,type,
% 0.32/0.48 ap2apEq1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(ap2apEq1,definition,
% 0.32/0.48 ( ap2apEq1
% 0.32/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.32/0.48 => ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.32/0.48 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(ap2apEq2_type,type,
% 0.32/0.48 ap2apEq2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(ap2apEq2,definition,
% 0.32/0.48 ( ap2apEq2
% 0.32/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.48 ( ( func @ A @ B @ Xf )
% 0.32/0.48 => ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.32/0.48 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(beta1_type,type,
% 0.32/0.48 beta1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(beta1,definition,
% 0.32/0.48 ( beta1
% 0.32/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.32/0.48 ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.32/0.48 => ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( ( ap @ A @ B
% 0.32/0.48 @ ( lam @ A @ B
% 0.32/0.48 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.32/0.48 @ Xx )
% 0.32/0.48 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(eta1_type,type,
% 0.32/0.48 eta1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(eta1,definition,
% 0.32/0.48 ( eta1
% 0.32/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.48 ( ( func @ A @ B @ Xf )
% 0.32/0.48 => ( ( lam @ A @ B
% 0.32/0.48 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.32/0.48 = Xf ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(lam2lamEq_type,type,
% 0.32/0.48 lam2lamEq: $o ).
% 0.32/0.48
% 0.32/0.48 thf(lam2lamEq,definition,
% 0.32/0.48 ( lam2lamEq
% 0.32/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.32/0.48 ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.32/0.48 => ( ( lam @ A @ B
% 0.32/0.48 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.32/0.48 = ( lam @ A @ B
% 0.32/0.48 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(beta2_type,type,
% 0.32/0.48 beta2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(beta2,definition,
% 0.32/0.48 ( beta2
% 0.32/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.32/0.48 ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.32/0.48 => ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( ( ap @ A @ B
% 0.32/0.48 @ ( lam @ A @ B
% 0.32/0.48 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.32/0.48 @ Xx )
% 0.32/0.48 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(eta2_type,type,
% 0.32/0.48 eta2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(eta2,definition,
% 0.32/0.48 ( eta2
% 0.32/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.32/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.32/0.48 => ( ( lam @ A @ B
% 0.32/0.48 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.32/0.48 = Xf ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(iffalseProp1_type,type,
% 0.32/0.48 iffalseProp1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(iffalseProp1,definition,
% 0.32/0.48 ( iffalseProp1
% 0.32/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ A )
% 0.32/0.48 => ( ~ Xphi
% 0.32/0.48 => ( in @ Xy
% 0.32/0.48 @ ( dsetconstr @ A
% 0.32/0.48 @ ^ [Xz: $i] :
% 0.32/0.48 ( ( Xphi
% 0.32/0.48 & ( Xz = Xx ) )
% 0.32/0.48 | ( ~ Xphi
% 0.32/0.48 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(iffalseProp2_type,type,
% 0.32/0.48 iffalseProp2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(iffalseProp2,definition,
% 0.32/0.48 ( iffalseProp2
% 0.32/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ A )
% 0.32/0.48 => ( ~ Xphi
% 0.32/0.48 => ( ( dsetconstr @ A
% 0.32/0.48 @ ^ [Xz: $i] :
% 0.32/0.48 ( ( Xphi
% 0.32/0.48 & ( Xz = Xx ) )
% 0.32/0.48 | ( ~ Xphi
% 0.32/0.48 & ( Xz = Xy ) ) ) )
% 0.32/0.48 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(iftrueProp1_type,type,
% 0.32/0.48 iftrueProp1: $o ).
% 0.32/0.48
% 0.32/0.48 thf(iftrueProp1,definition,
% 0.32/0.48 ( iftrueProp1
% 0.32/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ A )
% 0.32/0.48 => ( Xphi
% 0.32/0.48 => ( in @ Xx
% 0.32/0.48 @ ( dsetconstr @ A
% 0.32/0.48 @ ^ [Xz: $i] :
% 0.32/0.48 ( ( Xphi
% 0.32/0.48 & ( Xz = Xx ) )
% 0.32/0.48 | ( ~ Xphi
% 0.32/0.48 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(iftrueProp2_type,type,
% 0.32/0.48 iftrueProp2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(iftrueProp2,definition,
% 0.32/0.48 ( iftrueProp2
% 0.32/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ A )
% 0.32/0.48 => ( Xphi
% 0.32/0.48 => ( ( dsetconstr @ A
% 0.32/0.48 @ ^ [Xz: $i] :
% 0.32/0.48 ( ( Xphi
% 0.32/0.48 & ( Xz = Xx ) )
% 0.32/0.48 | ( ~ Xphi
% 0.32/0.48 & ( Xz = Xy ) ) ) )
% 0.32/0.48 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(ifSingleton_type,type,
% 0.32/0.48 ifSingleton: $o ).
% 0.32/0.48
% 0.32/0.48 thf(ifSingleton,definition,
% 0.32/0.48 ( ifSingleton
% 0.32/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ A )
% 0.32/0.48 => ( singleton
% 0.32/0.48 @ ( dsetconstr @ A
% 0.32/0.48 @ ^ [Xz: $i] :
% 0.32/0.48 ( ( Xphi
% 0.32/0.48 & ( Xz = Xx ) )
% 0.32/0.48 | ( ~ Xphi
% 0.32/0.48 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(if_type,type,
% 0.32/0.48 if: $i > $o > $i > $i > $i ).
% 0.32/0.48
% 0.32/0.48 thf(ifp_type,type,
% 0.32/0.48 ifp: $o ).
% 0.32/0.48
% 0.32/0.48 thf(ifp,definition,
% 0.32/0.48 ( ifp
% 0.32/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ A )
% 0.32/0.48 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(theeq_type,type,
% 0.32/0.48 theeq: $o ).
% 0.32/0.48
% 0.32/0.48 thf(theeq,definition,
% 0.32/0.48 ( theeq
% 0.32/0.48 = ( ! [X: $i] :
% 0.32/0.48 ( ( singleton @ X )
% 0.32/0.48 => ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ X )
% 0.32/0.48 => ( ( setunion @ X )
% 0.32/0.48 = Xx ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(iftrue_type,type,
% 0.32/0.48 iftrue: $o ).
% 0.32/0.48
% 0.32/0.48 thf(iftrue,definition,
% 0.32/0.48 ( iftrue
% 0.32/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ A )
% 0.32/0.48 => ( Xphi
% 0.32/0.48 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.32/0.48 = Xx ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(iffalse_type,type,
% 0.32/0.48 iffalse: $o ).
% 0.32/0.48
% 0.32/0.48 thf(iffalse,definition,
% 0.32/0.48 ( iffalse
% 0.32/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ A )
% 0.32/0.48 => ( ~ Xphi
% 0.32/0.48 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.32/0.48 = Xy ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(iftrueorfalse_type,type,
% 0.32/0.48 iftrueorfalse: $o ).
% 0.32/0.48
% 0.32/0.48 thf(iftrueorfalse,definition,
% 0.32/0.48 ( iftrueorfalse
% 0.32/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ! [Xy: $i] :
% 0.32/0.48 ( ( in @ Xy @ A )
% 0.32/0.48 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectT_lem_type,type,
% 0.32/0.48 binintersectT_lem: $o ).
% 0.32/0.48
% 0.32/0.48 thf(binintersectT_lem,definition,
% 0.32/0.48 ( binintersectT_lem
% 0.32/0.48 = ( ! [A: $i,X: $i] :
% 0.32/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.48 => ! [Y: $i] :
% 0.32/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.48 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(binunionT_lem_type,type,
% 0.32/0.49 binunionT_lem: $o ).
% 0.32/0.49
% 0.32/0.49 thf(binunionT_lem,definition,
% 0.32/0.49 ( binunionT_lem
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(powersetT_lem_type,type,
% 0.32/0.49 powersetT_lem: $o ).
% 0.32/0.49
% 0.32/0.49 thf(powersetT_lem,definition,
% 0.32/0.49 ( powersetT_lem
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(setminusT_lem_type,type,
% 0.32/0.49 setminusT_lem: $o ).
% 0.32/0.49
% 0.32/0.49 thf(setminusT_lem,definition,
% 0.32/0.49 ( setminusT_lem
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(complementT_lem_type,type,
% 0.32/0.49 complementT_lem: $o ).
% 0.32/0.49
% 0.32/0.49 thf(complementT_lem,definition,
% 0.32/0.49 ( complementT_lem
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(setextT_type,type,
% 0.32/0.49 setextT: $o ).
% 0.32/0.49
% 0.32/0.49 thf(setextT,definition,
% 0.32/0.49 ( setextT
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ X )
% 0.32/0.49 => ( in @ Xx @ Y ) ) )
% 0.32/0.49 => ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ Y )
% 0.32/0.49 => ( in @ Xx @ X ) ) )
% 0.32/0.49 => ( X = Y ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(subsetTI_type,type,
% 0.32/0.49 subsetTI: $o ).
% 0.32/0.49
% 0.32/0.49 thf(subsetTI,definition,
% 0.32/0.49 ( subsetTI
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ X )
% 0.32/0.49 => ( in @ Xx @ Y ) ) )
% 0.32/0.49 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(powersetTI1_type,type,
% 0.32/0.49 powersetTI1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(powersetTI1,definition,
% 0.32/0.49 ( powersetTI1
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ X )
% 0.32/0.49 => ( in @ Xx @ Y ) ) )
% 0.32/0.49 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(powersetTE1_type,type,
% 0.32/0.49 powersetTE1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(powersetTE1,definition,
% 0.32/0.49 ( powersetTE1
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ X @ ( powerset @ Y ) )
% 0.32/0.49 => ( ( in @ Xx @ X )
% 0.32/0.49 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(complementTI1_type,type,
% 0.32/0.49 complementTI1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(complementTI1,definition,
% 0.32/0.49 ( complementTI1
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ X )
% 0.32/0.49 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(complementTE1_type,type,
% 0.32/0.49 complementTE1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(complementTE1,definition,
% 0.32/0.49 ( complementTE1
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 0.32/0.49 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(binintersectTELcontra_type,type,
% 0.32/0.49 binintersectTELcontra: $o ).
% 0.32/0.49
% 0.32/0.49 thf(binintersectTELcontra,definition,
% 0.32/0.49 ( binintersectTELcontra
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ~ ( in @ Xx @ X )
% 0.32/0.49 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(binintersectTERcontra_type,type,
% 0.32/0.49 binintersectTERcontra: $o ).
% 0.32/0.49
% 0.32/0.49 thf(binintersectTERcontra,definition,
% 0.32/0.49 ( binintersectTERcontra
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ~ ( in @ Xx @ Y )
% 0.32/0.49 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(contrasubsetT_type,type,
% 0.32/0.49 contrasubsetT: $o ).
% 0.32/0.49
% 0.32/0.49 thf(contrasubsetT,definition,
% 0.32/0.49 ( contrasubsetT
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.32/0.49 => ( ( in @ Xx @ Y )
% 0.32/0.49 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(contrasubsetT1_type,type,
% 0.32/0.49 contrasubsetT1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(contrasubsetT1,definition,
% 0.32/0.49 ( contrasubsetT1
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( subset @ X @ Y )
% 0.32/0.49 => ( ~ ( in @ Xx @ Y )
% 0.32/0.49 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(contrasubsetT2_type,type,
% 0.32/0.49 contrasubsetT2: $o ).
% 0.32/0.49
% 0.32/0.49 thf(contrasubsetT2,definition,
% 0.32/0.49 ( contrasubsetT2
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( ( subset @ X @ Y )
% 0.32/0.49 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(contrasubsetT3_type,type,
% 0.32/0.49 contrasubsetT3: $o ).
% 0.32/0.49
% 0.32/0.49 thf(contrasubsetT3,definition,
% 0.32/0.49 ( contrasubsetT3
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 0.32/0.49 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(doubleComplementI1_type,type,
% 0.32/0.49 doubleComplementI1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(doubleComplementI1,definition,
% 0.32/0.49 ( doubleComplementI1
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ X )
% 0.32/0.49 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(doubleComplementE1_type,type,
% 0.32/0.49 doubleComplementE1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(doubleComplementE1,definition,
% 0.32/0.49 ( doubleComplementE1
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 0.32/0.49 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(doubleComplementSub1_type,type,
% 0.32/0.49 doubleComplementSub1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(doubleComplementSub1,definition,
% 0.32/0.49 ( doubleComplementSub1
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(doubleComplementSub2_type,type,
% 0.32/0.49 doubleComplementSub2: $o ).
% 0.32/0.49
% 0.32/0.49 thf(doubleComplementSub2,definition,
% 0.32/0.49 ( doubleComplementSub2
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(doubleComplementEq_type,type,
% 0.32/0.49 doubleComplementEq: $o ).
% 0.32/0.49
% 0.32/0.49 thf(doubleComplementEq,definition,
% 0.32/0.49 ( doubleComplementEq
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ( X
% 0.32/0.49 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(complementTnotintersectT_type,type,
% 0.32/0.49 complementTnotintersectT: $o ).
% 0.32/0.49
% 0.32/0.49 thf(complementTnotintersectT,definition,
% 0.32/0.49 ( complementTnotintersectT
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.32/0.49 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(complementImpComplementIntersect_type,type,
% 0.32/0.49 complementImpComplementIntersect: $o ).
% 0.32/0.49
% 0.32/0.49 thf(complementImpComplementIntersect,definition,
% 0.32/0.49 ( complementImpComplementIntersect
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.32/0.49 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(complementSubsetComplementIntersect_type,type,
% 0.32/0.49 complementSubsetComplementIntersect: $o ).
% 0.32/0.49
% 0.32/0.49 thf(complementSubsetComplementIntersect,definition,
% 0.32/0.49 ( complementSubsetComplementIntersect
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(complementInPowersetComplementIntersect_type,type,
% 0.32/0.49 complementInPowersetComplementIntersect: $o ).
% 0.32/0.49
% 0.32/0.49 thf(complementInPowersetComplementIntersect,definition,
% 0.32/0.49 ( complementInPowersetComplementIntersect
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(contraSubsetComplement_type,type,
% 0.32/0.49 contraSubsetComplement: $o ).
% 0.32/0.49
% 0.32/0.49 thf(contraSubsetComplement,definition,
% 0.32/0.49 ( contraSubsetComplement
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ Y )
% 0.32/0.49 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(complementTcontraSubset_type,type,
% 0.32/0.49 complementTcontraSubset: $o ).
% 0.32/0.49
% 0.32/0.49 thf(complementTcontraSubset,definition,
% 0.32/0.49 ( complementTcontraSubset
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.32/0.49 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(binunionTILcontra_type,type,
% 0.32/0.49 binunionTILcontra: $o ).
% 0.32/0.49
% 0.32/0.49 thf(binunionTILcontra,definition,
% 0.32/0.49 ( binunionTILcontra
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.32/0.49 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(binunionTIRcontra_type,type,
% 0.32/0.49 binunionTIRcontra: $o ).
% 0.32/0.49
% 0.32/0.49 thf(binunionTIRcontra,definition,
% 0.32/0.49 ( binunionTIRcontra
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.32/0.49 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(inIntersectImpInUnion_type,type,
% 0.32/0.49 inIntersectImpInUnion: $o ).
% 0.32/0.49
% 0.32/0.49 thf(inIntersectImpInUnion,definition,
% 0.32/0.49 ( inIntersectImpInUnion
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Z: $i] :
% 0.32/0.49 ( ( in @ Z @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.32/0.49 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(inIntersectImpInUnion2_type,type,
% 0.32/0.49 inIntersectImpInUnion2: $o ).
% 0.32/0.49
% 0.32/0.49 thf(inIntersectImpInUnion2,definition,
% 0.32/0.49 ( inIntersectImpInUnion2
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Z: $i] :
% 0.32/0.49 ( ( in @ Z @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.32/0.49 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(inIntersectImpInIntersectUnions_type,type,
% 0.32/0.49 inIntersectImpInIntersectUnions: $o ).
% 0.32/0.49
% 0.32/0.49 thf(inIntersectImpInIntersectUnions,definition,
% 0.32/0.49 ( inIntersectImpInIntersectUnions
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Z: $i] :
% 0.32/0.49 ( ( in @ Z @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.32/0.49 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(intersectInPowersetIntersectUnions_type,type,
% 0.32/0.49 intersectInPowersetIntersectUnions: $o ).
% 0.32/0.49
% 0.32/0.49 thf(intersectInPowersetIntersectUnions,definition,
% 0.32/0.49 ( intersectInPowersetIntersectUnions
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Z: $i] :
% 0.32/0.49 ( ( in @ Z @ ( powerset @ A ) )
% 0.32/0.49 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(inComplementUnionImpNotIn1_type,type,
% 0.32/0.49 inComplementUnionImpNotIn1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(inComplementUnionImpNotIn1,definition,
% 0.32/0.49 ( inComplementUnionImpNotIn1
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.32/0.49 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(inComplementUnionImpInComplement1_type,type,
% 0.32/0.49 inComplementUnionImpInComplement1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(inComplementUnionImpInComplement1,definition,
% 0.32/0.49 ( inComplementUnionImpInComplement1
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.32/0.49 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(binunionTE_type,type,
% 0.32/0.49 binunionTE: $o ).
% 0.32/0.49
% 0.32/0.49 thf(binunionTE,definition,
% 0.32/0.49 ( binunionTE
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xphi: $o,Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.32/0.49 => ( ( ( in @ Xx @ X )
% 0.32/0.49 => Xphi )
% 0.32/0.49 => ( ( ( in @ Xx @ Y )
% 0.32/0.49 => Xphi )
% 0.32/0.49 => Xphi ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(binunionTEcontra_type,type,
% 0.32/0.49 binunionTEcontra: $o ).
% 0.32/0.49
% 0.32/0.49 thf(binunionTEcontra,definition,
% 0.32/0.49 ( binunionTEcontra
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ~ ( in @ Xx @ X )
% 0.32/0.49 => ( ~ ( in @ Xx @ Y )
% 0.32/0.49 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan2a1_type,type,
% 0.32/0.49 demorgan2a1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan2a1,definition,
% 0.32/0.49 ( demorgan2a1
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.32/0.49 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(complementUnionInPowersetComplement_type,type,
% 0.32/0.49 complementUnionInPowersetComplement: $o ).
% 0.32/0.49
% 0.32/0.49 thf(complementUnionInPowersetComplement,definition,
% 0.32/0.49 ( complementUnionInPowersetComplement
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan2a2_type,type,
% 0.32/0.49 demorgan2a2: $o ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan2a2,definition,
% 0.32/0.49 ( demorgan2a2
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.32/0.49 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan1a_type,type,
% 0.32/0.49 demorgan1a: $o ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan1a,definition,
% 0.32/0.49 ( demorgan1a
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 0.32/0.49 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan1b_type,type,
% 0.32/0.49 demorgan1b: $o ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan1b,definition,
% 0.32/0.49 ( demorgan1b
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.32/0.49 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan1_type,type,
% 0.32/0.49 demorgan1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan1,definition,
% 0.32/0.49 ( demorgan1
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 0.32/0.49 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan2a_type,type,
% 0.32/0.49 demorgan2a: $o ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan2a,definition,
% 0.32/0.49 ( demorgan2a
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.32/0.49 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan2b2_type,type,
% 0.32/0.49 demorgan2b2: $o ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan2b2,definition,
% 0.32/0.49 ( demorgan2b2
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.32/0.49 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 0.32/0.49 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan2b_type,type,
% 0.32/0.49 demorgan2b: $o ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan2b,definition,
% 0.32/0.49 ( demorgan2b
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.32/0.49 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan2_type,type,
% 0.32/0.49 demorgan2: $o ).
% 0.32/0.49
% 0.32/0.49 thf(demorgan2,definition,
% 0.32/0.49 ( demorgan2
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 0.32/0.49 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(woz13rule0_type,type,
% 0.32/0.49 woz13rule0: $o ).
% 0.32/0.49
% 0.32/0.49 thf(woz13rule0,definition,
% 0.32/0.49 ( woz13rule0
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.32/0.49 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(woz13rule1_type,type,
% 0.32/0.49 woz13rule1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(woz13rule1,definition,
% 0.32/0.49 ( woz13rule1
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Z: $i] :
% 0.32/0.49 ( ( in @ Z @ ( powerset @ A ) )
% 0.32/0.49 => ( ( subset @ X @ Z )
% 0.32/0.49 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(woz13rule2_type,type,
% 0.32/0.49 woz13rule2: $o ).
% 0.32/0.49
% 0.32/0.49 thf(woz13rule2,definition,
% 0.32/0.49 ( woz13rule2
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Z: $i] :
% 0.32/0.49 ( ( in @ Z @ ( powerset @ A ) )
% 0.32/0.49 => ( ( subset @ Y @ Z )
% 0.32/0.49 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(woz13rule3_type,type,
% 0.32/0.49 woz13rule3: $o ).
% 0.32/0.49
% 0.32/0.49 thf(woz13rule3,definition,
% 0.32/0.49 ( woz13rule3
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Z: $i] :
% 0.32/0.49 ( ( in @ Z @ ( powerset @ A ) )
% 0.32/0.49 => ( ( subset @ X @ Y )
% 0.32/0.49 => ( ( subset @ X @ Z )
% 0.32/0.49 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(woz13rule4_type,type,
% 0.32/0.49 woz13rule4: $o ).
% 0.32/0.49
% 0.32/0.49 thf(woz13rule4,definition,
% 0.32/0.49 ( woz13rule4
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Z: $i] :
% 0.32/0.49 ( ( in @ Z @ ( powerset @ A ) )
% 0.32/0.49 => ! [W: $i] :
% 0.32/0.49 ( ( in @ W @ ( powerset @ A ) )
% 0.32/0.49 => ( ( subset @ X @ Z )
% 0.32/0.49 => ( ( subset @ Y @ W )
% 0.32/0.49 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(woz1_1_type,type,
% 0.32/0.49 woz1_1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(woz1_1,definition,
% 0.32/0.49 ( woz1_1
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(woz1_2_type,type,
% 0.32/0.49 woz1_2: $o ).
% 0.32/0.49
% 0.32/0.49 thf(woz1_2,definition,
% 0.32/0.49 ( woz1_2
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Z: $i] :
% 0.32/0.49 ( ( in @ Z @ ( powerset @ A ) )
% 0.32/0.49 => ! [W: $i] :
% 0.32/0.49 ( ( in @ W @ ( powerset @ A ) )
% 0.32/0.49 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 0.32/0.49 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(woz1_3_type,type,
% 0.32/0.49 woz1_3: $o ).
% 0.32/0.49
% 0.32/0.49 thf(woz1_3,definition,
% 0.32/0.49 ( woz1_3
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ! [Z: $i] :
% 0.32/0.49 ( ( in @ Z @ ( powerset @ A ) )
% 0.32/0.49 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(woz1_4_type,type,
% 0.32/0.49 woz1_4: $o ).
% 0.32/0.49
% 0.32/0.49 thf(woz1_4,definition,
% 0.32/0.49 ( woz1_4
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.32/0.49 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(woz1_5_type,type,
% 0.32/0.49 woz1_5: $o ).
% 0.32/0.49
% 0.32/0.49 thf(woz1_5,definition,
% 0.32/0.49 ( woz1_5
% 0.32/0.49 = ( ! [A: $i,X: $i] :
% 0.32/0.49 ( ( in @ X @ ( powerset @ A ) )
% 0.32/0.49 => ! [Y: $i] :
% 0.32/0.49 ( ( in @ Y @ ( powerset @ A ) )
% 0.32/0.49 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(breln1_type,type,
% 0.32/0.49 breln1: $i > $i > $o ).
% 0.32/0.49
% 0.32/0.49 thf(breln1,definition,
% 0.32/0.49 ( breln1
% 0.32/0.49 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(breln1all2_type,type,
% 0.32/0.49 breln1all2: $o ).
% 0.32/0.49
% 0.32/0.49 thf(breln1all2,definition,
% 0.32/0.49 ( breln1all2
% 0.32/0.49 = ( ! [A: $i,R: $i] :
% 0.32/0.49 ( ( breln1 @ A @ R )
% 0.32/0.49 => ! [Xphi: $i > $o] :
% 0.32/0.49 ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ A )
% 0.32/0.49 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.32/0.49 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ R )
% 0.32/0.49 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(breln1Set_type,type,
% 0.32/0.49 breln1Set: $i > $i ).
% 0.32/0.49
% 0.32/0.49 thf(breln1SetBreln1_type,type,
% 0.32/0.49 breln1SetBreln1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(breln1SetBreln1,definition,
% 0.32/0.49 ( breln1SetBreln1
% 0.32/0.49 = ( ! [A: $i,R: $i] :
% 0.32/0.49 ( ( in @ R @ ( breln1Set @ A ) )
% 0.32/0.49 => ( breln1 @ A @ R ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(transitive_type,type,
% 0.32/0.49 transitive: $i > $i > $o ).
% 0.32/0.49
% 0.32/0.49 thf(antisymmetric_type,type,
% 0.32/0.49 antisymmetric: $i > $i > $o ).
% 0.32/0.49
% 0.32/0.49 thf(reflexive_type,type,
% 0.32/0.49 reflexive: $i > $i > $o ).
% 0.32/0.49
% 0.32/0.49 thf(refltransitive_type,type,
% 0.32/0.49 refltransitive: $i > $i > $o ).
% 0.32/0.49
% 0.32/0.49 thf(refllinearorder_type,type,
% 0.32/0.49 refllinearorder: $i > $i > $o ).
% 0.32/0.49
% 0.32/0.49 thf(reflwellordering_type,type,
% 0.32/0.49 reflwellordering: $i > $i > $o ).
% 0.32/0.49
% 0.32/0.49 thf(choice2fnsingleton_type,type,
% 0.32/0.49 choice2fnsingleton: $o ).
% 0.32/0.49
% 0.32/0.49 thf(choice2fnsingleton,definition,
% 0.32/0.49 ( choice2fnsingleton
% 0.32/0.49 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.32/0.49 ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ? [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ B )
% 0.32/0.49 & ( Xphi @ Xx @ Xy ) ) )
% 0.32/0.49 => ! [R: $i] :
% 0.32/0.49 ( ( in @ R @ ( breln1Set @ B ) )
% 0.32/0.49 => ( ( reflwellordering @ B @ R )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ( singleton
% 0.32/0.49 @ ( dsetconstr @ B
% 0.32/0.49 @ ^ [Xy: $i] :
% 0.32/0.49 ( ( Xphi @ Xx @ Xy )
% 0.32/0.49 & ! [Xz: $i] :
% 0.32/0.49 ( ( in @ Xz @ B )
% 0.32/0.49 => ( ( Xphi @ Xx @ Xz )
% 0.32/0.49 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(setOfPairsIsBReln1_type,type,
% 0.32/0.49 setOfPairsIsBReln1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(setOfPairsIsBReln1,definition,
% 0.32/0.49 ( setOfPairsIsBReln1
% 0.32/0.49 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 0.32/0.49 ( breln1 @ A
% 0.32/0.49 @ ( dpsetconstr @ A @ A
% 0.32/0.49 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(breln1all1_type,type,
% 0.32/0.49 breln1all1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(breln1all1,definition,
% 0.32/0.49 ( breln1all1
% 0.32/0.49 = ( ! [A: $i,R: $i] :
% 0.32/0.49 ( ( breln1 @ A @ R )
% 0.32/0.49 => ! [Xphi: $i > $o] :
% 0.32/0.49 ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ A )
% 0.32/0.49 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.32/0.49 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ R )
% 0.32/0.49 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(subbreln1_type,type,
% 0.32/0.49 subbreln1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(subbreln1,definition,
% 0.32/0.49 ( subbreln1
% 0.32/0.49 = ( ! [A: $i,R: $i] :
% 0.32/0.49 ( ( breln1 @ A @ R )
% 0.32/0.49 => ! [S: $i] :
% 0.32/0.49 ( ( breln1 @ A @ S )
% 0.32/0.49 => ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ A )
% 0.32/0.49 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.32/0.49 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.32/0.49 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(eqbreln1_type,type,
% 0.32/0.49 eqbreln1: $o ).
% 0.32/0.49
% 0.32/0.49 thf(eqbreln1,definition,
% 0.32/0.49 ( eqbreln1
% 0.32/0.49 = ( ! [A: $i,R: $i] :
% 0.32/0.49 ( ( breln1 @ A @ R )
% 0.32/0.49 => ! [S: $i] :
% 0.32/0.49 ( ( breln1 @ A @ S )
% 0.32/0.49 => ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ A )
% 0.32/0.49 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.32/0.49 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.32/0.49 => ( ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ A )
% 0.32/0.49 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.32/0.49 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.32/0.49 => ( R = S ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(breln1invset_type,type,
% 0.32/0.49 breln1invset: $i > $i > $i ).
% 0.32/0.49
% 0.32/0.49 thf(breln1invprop_type,type,
% 0.32/0.49 breln1invprop: $o ).
% 0.32/0.49
% 0.32/0.49 thf(breln1invprop,definition,
% 0.32/0.49 ( breln1invprop
% 0.32/0.49 = ( ! [A: $i,R: $i] :
% 0.32/0.49 ( ( breln1 @ A @ R )
% 0.32/0.49 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(breln1invI_type,type,
% 0.32/0.49 breln1invI: $o ).
% 0.32/0.49
% 0.32/0.49 thf(breln1invI,definition,
% 0.32/0.49 ( breln1invI
% 0.32/0.49 = ( ! [A: $i,R: $i] :
% 0.32/0.49 ( ( breln1 @ A @ R )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ A )
% 0.32/0.49 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.32/0.49 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(breln1invE_type,type,
% 0.32/0.49 breln1invE: $o ).
% 0.32/0.49
% 0.32/0.49 thf(breln1invE,definition,
% 0.32/0.49 ( breln1invE
% 0.32/0.49 = ( ! [A: $i,R: $i] :
% 0.32/0.49 ( ( breln1 @ A @ R )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ A )
% 0.32/0.49 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 0.32/0.49 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(breln1compset_type,type,
% 0.32/0.49 breln1compset: $i > $i > $i > $i ).
% 0.32/0.49
% 0.32/0.49 thf(breln1compprop_type,type,
% 0.32/0.49 breln1compprop: $o ).
% 0.32/0.49
% 0.32/0.49 thf(breln1compprop,definition,
% 0.32/0.49 ( breln1compprop
% 0.32/0.49 = ( ! [A: $i,R: $i] :
% 0.32/0.49 ( ( breln1 @ A @ R )
% 0.32/0.49 => ! [S: $i] :
% 0.32/0.49 ( ( breln1 @ A @ S )
% 0.32/0.49 => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(breln1compI_type,type,
% 0.32/0.49 breln1compI: $o ).
% 0.32/0.49
% 0.32/0.49 thf(breln1compI,definition,
% 0.32/0.49 ( breln1compI
% 0.32/0.49 = ( ! [A: $i,R: $i] :
% 0.32/0.49 ( ( breln1 @ A @ R )
% 0.32/0.49 => ! [S: $i] :
% 0.32/0.49 ( ( breln1 @ A @ S )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ A )
% 0.32/0.49 => ! [Xz: $i] :
% 0.32/0.49 ( ( in @ Xz @ A )
% 0.32/0.49 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.32/0.49 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 0.32/0.49 => ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(breln1compE_type,type,
% 0.32/0.49 breln1compE: $o ).
% 0.32/0.49
% 0.32/0.49 thf(breln1compE,definition,
% 0.32/0.49 ( breln1compE
% 0.32/0.49 = ( ! [A: $i,R: $i] :
% 0.32/0.49 ( ( breln1 @ A @ R )
% 0.32/0.49 => ! [S: $i] :
% 0.32/0.49 ( ( breln1 @ A @ S )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ A )
% 0.32/0.49 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 0.32/0.49 => ? [Xz: $i] :
% 0.32/0.49 ( ( in @ Xz @ A )
% 0.32/0.49 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.32/0.49 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 thf(breln1compEex,conjecture,
% 0.32/0.49 ( setextAx
% 0.32/0.49 => ( emptysetAx
% 0.32/0.49 => ( setadjoinAx
% 0.32/0.49 => ( powersetAx
% 0.32/0.49 => ( setunionAx
% 0.32/0.49 => ( omega0Ax
% 0.32/0.49 => ( omegaSAx
% 0.32/0.49 => ( omegaIndAx
% 0.32/0.49 => ( replAx
% 0.32/0.49 => ( foundationAx
% 0.32/0.49 => ( wellorderingAx
% 0.32/0.49 => ( descrp
% 0.32/0.49 => ( dsetconstrI
% 0.32/0.49 => ( dsetconstrEL
% 0.32/0.49 => ( dsetconstrER
% 0.32/0.49 => ( exuE1
% 0.32/0.49 => ( prop2setE
% 0.32/0.49 => ( emptysetE
% 0.32/0.49 => ( emptysetimpfalse
% 0.32/0.49 => ( notinemptyset
% 0.32/0.49 => ( exuE3e
% 0.32/0.49 => ( setext
% 0.32/0.49 => ( emptyI
% 0.32/0.49 => ( noeltsimpempty
% 0.32/0.49 => ( setbeta
% 0.32/0.49 => ( nonemptyE1
% 0.32/0.49 => ( nonemptyI
% 0.32/0.49 => ( nonemptyI1
% 0.32/0.49 => ( setadjoinIL
% 0.32/0.49 => ( emptyinunitempty
% 0.32/0.49 => ( setadjoinIR
% 0.32/0.49 => ( setadjoinE
% 0.32/0.49 => ( setadjoinOr
% 0.32/0.49 => ( setoftrueEq
% 0.32/0.49 => ( powersetI
% 0.32/0.49 => ( emptyinPowerset
% 0.32/0.49 => ( emptyInPowerset
% 0.32/0.49 => ( powersetE
% 0.32/0.49 => ( setunionI
% 0.32/0.49 => ( setunionE
% 0.32/0.49 => ( subPowSU
% 0.32/0.49 => ( exuE2
% 0.32/0.49 => ( nonemptyImpWitness
% 0.32/0.49 => ( uniqinunit
% 0.32/0.49 => ( notinsingleton
% 0.32/0.49 => ( eqinunit
% 0.32/0.49 => ( singletonsswitch
% 0.32/0.49 => ( upairsetE
% 0.32/0.49 => ( upairsetIL
% 0.32/0.49 => ( upairsetIR
% 0.32/0.49 => ( emptyE1
% 0.32/0.49 => ( vacuousDall
% 0.32/0.49 => ( quantDeMorgan1
% 0.32/0.49 => ( quantDeMorgan2
% 0.32/0.49 => ( quantDeMorgan3
% 0.32/0.49 => ( quantDeMorgan4
% 0.32/0.49 => ( prop2setI
% 0.32/0.49 => ( prop2set2propI
% 0.32/0.49 => ( notdexE
% 0.32/0.49 => ( notdallE
% 0.32/0.49 => ( exuI1
% 0.32/0.49 => ( exuI3
% 0.32/0.49 => ( exuI2
% 0.32/0.49 => ( inCongP
% 0.32/0.49 => ( in__Cong
% 0.32/0.49 => ( exuE3u
% 0.32/0.49 => ( exu__Cong
% 0.32/0.49 => ( emptyset__Cong
% 0.32/0.49 => ( setadjoin__Cong
% 0.32/0.49 => ( powerset__Cong
% 0.32/0.49 => ( setunion__Cong
% 0.32/0.49 => ( omega__Cong
% 0.32/0.49 => ( exuEu
% 0.32/0.49 => ( descr__Cong
% 0.32/0.49 => ( dsetconstr__Cong
% 0.32/0.49 => ( subsetI1
% 0.32/0.49 => ( eqimpsubset2
% 0.32/0.49 => ( eqimpsubset1
% 0.32/0.49 => ( subsetI2
% 0.32/0.49 => ( emptysetsubset
% 0.32/0.49 => ( subsetE
% 0.32/0.49 => ( subsetE2
% 0.32/0.49 => ( notsubsetI
% 0.32/0.49 => ( notequalI1
% 0.32/0.49 => ( notequalI2
% 0.32/0.49 => ( subsetRefl
% 0.32/0.49 => ( subsetTrans
% 0.32/0.49 => ( setadjoinSub
% 0.32/0.49 => ( setadjoinSub2
% 0.32/0.49 => ( subset2powerset
% 0.32/0.49 => ( setextsub
% 0.32/0.49 => ( subsetemptysetimpeq
% 0.32/0.49 => ( powersetI1
% 0.32/0.49 => ( powersetE1
% 0.32/0.49 => ( inPowerset
% 0.32/0.49 => ( powersetsubset
% 0.32/0.49 => ( sepInPowerset
% 0.32/0.49 => ( sepSubset
% 0.32/0.49 => ( binunionIL
% 0.32/0.49 => ( upairset2IR
% 0.32/0.49 => ( binunionIR
% 0.32/0.49 => ( binunionEcases
% 0.32/0.49 => ( binunionE
% 0.32/0.49 => ( binunionLsub
% 0.32/0.49 => ( binunionRsub
% 0.32/0.49 => ( binintersectI
% 0.32/0.49 => ( binintersectSubset5
% 0.32/0.49 => ( binintersectEL
% 0.32/0.49 => ( binintersectLsub
% 0.32/0.49 => ( binintersectSubset2
% 0.32/0.49 => ( binintersectSubset3
% 0.32/0.49 => ( binintersectER
% 0.32/0.49 => ( disjointsetsI1
% 0.32/0.49 => ( binintersectRsub
% 0.32/0.49 => ( binintersectSubset4
% 0.32/0.49 => ( binintersectSubset1
% 0.32/0.49 => ( bs114d
% 0.32/0.49 => ( setminusI
% 0.32/0.49 => ( setminusEL
% 0.32/0.49 => ( setminusER
% 0.32/0.49 => ( setminusSubset2
% 0.32/0.49 => ( setminusERneg
% 0.32/0.49 => ( setminusELneg
% 0.32/0.49 => ( setminusILneg
% 0.32/0.49 => ( setminusIRneg
% 0.32/0.49 => ( setminusLsub
% 0.32/0.49 => ( setminusSubset1
% 0.32/0.49 => ( symdiffE
% 0.32/0.49 => ( symdiffI1
% 0.32/0.49 => ( symdiffI2
% 0.32/0.49 => ( symdiffIneg1
% 0.32/0.49 => ( symdiffIneg2
% 0.32/0.49 => ( secondinupair
% 0.32/0.49 => ( setukpairIL
% 0.32/0.49 => ( setukpairIR
% 0.32/0.49 => ( kpairiskpair
% 0.32/0.49 => ( kpairp
% 0.32/0.49 => ( singletonsubset
% 0.32/0.49 => ( singletoninpowerset
% 0.32/0.49 => ( singletoninpowunion
% 0.32/0.49 => ( upairset2E
% 0.32/0.49 => ( upairsubunion
% 0.32/0.49 => ( upairinpowunion
% 0.32/0.49 => ( ubforcartprodlem1
% 0.32/0.49 => ( ubforcartprodlem2
% 0.32/0.49 => ( ubforcartprodlem3
% 0.32/0.49 => ( cartprodpairin
% 0.32/0.49 => ( cartprodmempair1
% 0.32/0.49 => ( cartprodmempair
% 0.32/0.49 => ( setunionE2
% 0.32/0.49 => ( setunionsingleton1
% 0.32/0.49 => ( setunionsingleton2
% 0.32/0.49 => ( setunionsingleton
% 0.32/0.49 => ( singletonprop
% 0.32/0.49 => ( ex1E1
% 0.32/0.49 => ( ex1I
% 0.32/0.49 => ( ex1I2
% 0.32/0.49 => ( singletonsuniq
% 0.32/0.49 => ( setukpairinjL1
% 0.32/0.49 => ( kfstsingleton
% 0.32/0.49 => ( theprop
% 0.32/0.49 => ( kfstpairEq
% 0.32/0.49 => ( cartprodfstin
% 0.32/0.49 => ( setukpairinjL2
% 0.32/0.49 => ( setukpairinjL
% 0.32/0.49 => ( setukpairinjR11
% 0.32/0.49 => ( setukpairinjR12
% 0.32/0.49 => ( setukpairinjR1
% 0.32/0.49 => ( upairequniteq
% 0.32/0.49 => ( setukpairinjR2
% 0.32/0.49 => ( setukpairinjR
% 0.32/0.49 => ( ksndsingleton
% 0.32/0.49 => ( ksndpairEq
% 0.32/0.49 => ( kpairsurjEq
% 0.32/0.49 => ( cartprodsndin
% 0.32/0.49 => ( cartprodpairmemEL
% 0.32/0.49 => ( cartprodpairmemER
% 0.32/0.49 => ( cartprodmempaircEq
% 0.32/0.49 => ( cartprodfstpairEq
% 0.32/0.49 => ( cartprodsndpairEq
% 0.32/0.49 => ( cartprodpairsurjEq
% 0.32/0.49 => ( dpsetconstrI
% 0.32/0.49 => ( dpsetconstrSub
% 0.32/0.49 => ( setOfPairsIsBReln
% 0.32/0.49 => ( dpsetconstrERa
% 0.32/0.49 => ( dpsetconstrEL1
% 0.32/0.49 => ( dpsetconstrEL2
% 0.32/0.49 => ( dpsetconstrER
% 0.32/0.49 => ( funcImageSingleton
% 0.32/0.49 => ( apProp
% 0.32/0.49 => ( app
% 0.32/0.49 => ( infuncsetfunc
% 0.32/0.49 => ( ap2p
% 0.32/0.49 => ( funcinfuncset
% 0.32/0.49 => ( lamProp
% 0.32/0.49 => ( lamp
% 0.32/0.49 => ( lam2p
% 0.32/0.49 => ( brelnall1
% 0.32/0.49 => ( brelnall2
% 0.32/0.49 => ( ex1E2
% 0.32/0.49 => ( funcGraphProp1
% 0.32/0.49 => ( funcGraphProp3
% 0.32/0.49 => ( funcGraphProp2
% 0.32/0.49 => ( funcextLem
% 0.32/0.49 => ( funcGraphProp4
% 0.32/0.49 => ( subbreln
% 0.32/0.49 => ( eqbreln
% 0.32/0.49 => ( funcext
% 0.32/0.49 => ( funcext2
% 0.32/0.49 => ( ap2apEq1
% 0.32/0.49 => ( ap2apEq2
% 0.32/0.49 => ( beta1
% 0.32/0.49 => ( eta1
% 0.32/0.49 => ( lam2lamEq
% 0.32/0.49 => ( beta2
% 0.32/0.49 => ( eta2
% 0.32/0.49 => ( iffalseProp1
% 0.32/0.49 => ( iffalseProp2
% 0.32/0.49 => ( iftrueProp1
% 0.32/0.49 => ( iftrueProp2
% 0.32/0.49 => ( ifSingleton
% 0.32/0.49 => ( ifp
% 0.32/0.49 => ( theeq
% 0.32/0.49 => ( iftrue
% 0.32/0.49 => ( iffalse
% 0.32/0.49 => ( iftrueorfalse
% 0.32/0.49 => ( binintersectT_lem
% 0.32/0.49 => ( binunionT_lem
% 0.32/0.49 => ( powersetT_lem
% 0.32/0.49 => ( setminusT_lem
% 0.32/0.49 => ( complementT_lem
% 0.32/0.49 => ( setextT
% 0.32/0.49 => ( subsetTI
% 0.32/0.49 => ( powersetTI1
% 0.32/0.49 => ( powersetTE1
% 0.32/0.49 => ( complementTI1
% 0.32/0.49 => ( complementTE1
% 0.32/0.49 => ( binintersectTELcontra
% 0.32/0.49 => ( binintersectTERcontra
% 0.32/0.49 => ( contrasubsetT
% 0.32/0.49 => ( contrasubsetT1
% 0.32/0.49 => ( contrasubsetT2
% 0.32/0.49 => ( contrasubsetT3
% 0.32/0.49 => ( doubleComplementI1
% 0.32/0.49 => ( doubleComplementE1
% 0.32/0.49 => ( doubleComplementSub1
% 0.32/0.49 => ( doubleComplementSub2
% 0.32/0.49 => ( doubleComplementEq
% 0.32/0.49 => ( complementTnotintersectT
% 0.32/0.49 => ( complementImpComplementIntersect
% 0.32/0.49 => ( complementSubsetComplementIntersect
% 0.32/0.49 => ( complementInPowersetComplementIntersect
% 0.32/0.49 => ( contraSubsetComplement
% 0.32/0.49 => ( complementTcontraSubset
% 0.32/0.49 => ( binunionTILcontra
% 0.32/0.49 => ( binunionTIRcontra
% 0.32/0.49 => ( inIntersectImpInUnion
% 0.32/0.49 => ( inIntersectImpInUnion2
% 0.32/0.49 => ( inIntersectImpInIntersectUnions
% 0.32/0.49 => ( intersectInPowersetIntersectUnions
% 0.32/0.49 => ( inComplementUnionImpNotIn1
% 0.32/0.49 => ( inComplementUnionImpInComplement1
% 0.32/0.49 => ( binunionTE
% 0.32/0.49 => ( binunionTEcontra
% 0.32/0.49 => ( demorgan2a1
% 0.32/0.49 => ( complementUnionInPowersetComplement
% 0.32/0.49 => ( demorgan2a2
% 0.32/0.49 => ( demorgan1a
% 0.32/0.49 => ( demorgan1b
% 0.32/0.49 => ( demorgan1
% 0.32/0.49 => ( demorgan2a
% 0.32/0.49 => ( demorgan2b2
% 0.32/0.49 => ( demorgan2b
% 0.32/0.49 => ( demorgan2
% 0.32/0.49 => ( woz13rule0
% 0.32/0.49 => ( woz13rule1
% 0.32/0.49 => ( woz13rule2
% 0.32/0.49 => ( woz13rule3
% 0.32/0.49 => ( woz13rule4
% 0.32/0.49 => ( woz1_1
% 0.32/0.49 => ( woz1_2
% 0.32/0.49 => ( woz1_3
% 0.32/0.49 => ( woz1_4
% 0.32/0.49 => ( woz1_5
% 0.32/0.49 => ( breln1all2
% 0.32/0.49 => ( breln1SetBreln1
% 0.32/0.49 => ( choice2fnsingleton
% 0.32/0.49 => ( setOfPairsIsBReln1
% 0.32/0.49 => ( breln1all1
% 0.32/0.49 => ( subbreln1
% 0.32/0.49 => ( eqbreln1
% 0.32/0.49 => ( breln1invprop
% 0.32/0.49 => ( breln1invI
% 0.32/0.49 => ( breln1invE
% 0.32/0.49 => ( breln1compprop
% 0.32/0.49 => ( breln1compI
% 0.32/0.49 => ( breln1compE
% 0.32/0.49 => ! [A: $i,R: $i] :
% 0.32/0.49 ( ( breln1 @ A @ R )
% 0.32/0.49 => ! [S: $i] :
% 0.32/0.49 ( ( breln1 @ A @ S )
% 0.32/0.49 => ! [Xx: $i] :
% 0.32/0.49 ( ( in @ Xx @ A )
% 0.32/0.49 => ! [Xy: $i] :
% 0.32/0.49 ( ( in @ Xy @ A )
% 0.32/0.49 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 0.32/0.49 => ! [Xphi: $o] :
% 0.32/0.49 ( ! [Xz: $i] :
% 0.32/0.49 ( ( in @ Xz @ A )
% 0.32/0.49 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.32/0.49 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 0.32/0.49 => Xphi ) ) )
% 0.32/0.49 => Xphi ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 ------------------------
% 2.84/1.58 ---- Embedded in THF ---
% 2.84/1.58 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.84/1.58 %%% Generated on Tue Feb 24 12:34:49 EST 2026
% 2.84/1.58 %%% using '$$dhol' embedding, version 1.3.0.
% 2.84/1.58 %%% Logic specification used:
% 2.84/1.58 %%% thf(spec, logic, $$dhol).
% 2.84/1.58
% 2.84/1.58 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.LcmRL7iW1w/DTF2DTF3905.p
% See solution above
% 2.84/1.58 ------------------------
% 3.08/1.61 ---- Cleaned THF ---
% 3.08/1.62 thf(in_type,type,
% 3.08/1.62 in: $i > $i > $o ).
% 3.08/1.62
% 3.08/1.62 thf(exu_type,type,
% 3.08/1.62 exu: ( $i > $o ) > $o ).
% 3.08/1.62
% 3.08/1.62 thf(exu,definition,
% 3.08/1.62 ( exu
% 3.08/1.62 = ( ^ [Xphi: $i > $o] :
% 3.08/1.62 ? [Xx: $i] :
% 3.08/1.62 ( ( Xphi @ Xx )
% 3.08/1.62 & ! [Xy: $i] :
% 3.08/1.62 ( ( Xphi @ Xy )
% 3.08/1.62 => ( Xx = Xy ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setextAx_type,type,
% 3.08/1.62 setextAx: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setextAx,definition,
% 3.08/1.62 ( setextAx
% 3.08/1.62 = ( ! [A: $i,B: $i] :
% 3.08/1.62 ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 <=> ( in @ Xx @ B ) )
% 3.08/1.62 => ( A = B ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(emptyset_type,type,
% 3.08/1.62 emptyset: $i ).
% 3.08/1.62
% 3.08/1.62 thf(emptysetAx_type,type,
% 3.08/1.62 emptysetAx: $o ).
% 3.08/1.62
% 3.08/1.62 thf(emptysetAx,definition,
% 3.08/1.62 ( emptysetAx
% 3.08/1.62 = ( ! [Xx: $i] :
% 3.08/1.62 ~ ( in @ Xx @ emptyset ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setadjoin_type,type,
% 3.08/1.62 setadjoin: $i > $i > $i ).
% 3.08/1.62
% 3.08/1.62 thf(setadjoinAx_type,type,
% 3.08/1.62 setadjoinAx: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setadjoinAx,definition,
% 3.08/1.62 ( setadjoinAx
% 3.08/1.62 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.08/1.62 <=> ( ( Xy = Xx )
% 3.08/1.62 | ( in @ Xy @ A ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(powerset_type,type,
% 3.08/1.62 powerset: $i > $i ).
% 3.08/1.62
% 3.08/1.62 thf(powersetAx_type,type,
% 3.08/1.62 powersetAx: $o ).
% 3.08/1.62
% 3.08/1.62 thf(powersetAx,definition,
% 3.08/1.62 ( powersetAx
% 3.08/1.62 = ( ! [A: $i,B: $i] :
% 3.08/1.62 ( ( in @ B @ ( powerset @ A ) )
% 3.08/1.62 <=> ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ B )
% 3.08/1.62 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setunion_type,type,
% 3.08/1.62 setunion: $i > $i ).
% 3.08/1.62
% 3.08/1.62 thf(setunionAx_type,type,
% 3.08/1.62 setunionAx: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setunionAx,definition,
% 3.08/1.62 ( setunionAx
% 3.08/1.62 = ( ! [A: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ ( setunion @ A ) )
% 3.08/1.62 <=> ? [B: $i] :
% 3.08/1.62 ( ( in @ Xx @ B )
% 3.08/1.62 & ( in @ B @ A ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(omega_type,type,
% 3.08/1.62 omega: $i ).
% 3.08/1.62
% 3.08/1.62 thf(omega0Ax_type,type,
% 3.08/1.62 omega0Ax: $o ).
% 3.08/1.62
% 3.08/1.62 thf(omega0Ax,definition,
% 3.08/1.62 ( omega0Ax
% 3.08/1.62 = ( in @ emptyset @ omega ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(omegaSAx_type,type,
% 3.08/1.62 omegaSAx: $o ).
% 3.08/1.62
% 3.08/1.62 thf(omegaSAx,definition,
% 3.08/1.62 ( omegaSAx
% 3.08/1.62 = ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ omega )
% 3.08/1.62 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(omegaIndAx_type,type,
% 3.08/1.62 omegaIndAx: $o ).
% 3.08/1.62
% 3.08/1.62 thf(omegaIndAx,definition,
% 3.08/1.62 ( omegaIndAx
% 3.08/1.62 = ( ! [A: $i] :
% 3.08/1.62 ( ( ( in @ emptyset @ A )
% 3.08/1.62 & ! [Xx: $i] :
% 3.08/1.62 ( ( ( in @ Xx @ omega )
% 3.08/1.62 & ( in @ Xx @ A ) )
% 3.08/1.62 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ omega )
% 3.08/1.62 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(replAx_type,type,
% 3.08/1.62 replAx: $o ).
% 3.08/1.62
% 3.08/1.62 thf(replAx,definition,
% 3.08/1.62 ( replAx
% 3.08/1.62 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 3.08/1.62 ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( exu
% 3.08/1.62 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 3.08/1.62 => ? [B: $i] :
% 3.08/1.62 ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ B )
% 3.08/1.62 <=> ? [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ A )
% 3.08/1.62 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(foundationAx_type,type,
% 3.08/1.62 foundationAx: $o ).
% 3.08/1.62
% 3.08/1.62 thf(foundationAx,definition,
% 3.08/1.62 ( foundationAx
% 3.08/1.62 = ( ! [A: $i] :
% 3.08/1.62 ( ? [Xx: $i] : ( in @ Xx @ A )
% 3.08/1.62 => ? [B: $i] :
% 3.08/1.62 ( ( in @ B @ A )
% 3.08/1.62 & ~ ? [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ B )
% 3.08/1.62 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(wellorderingAx_type,type,
% 3.08/1.62 wellorderingAx: $o ).
% 3.08/1.62
% 3.08/1.62 thf(wellorderingAx,definition,
% 3.08/1.62 ( wellorderingAx
% 3.08/1.62 = ( ! [A: $i] :
% 3.08/1.62 ? [B: $i] :
% 3.08/1.62 ( ! [C: $i] :
% 3.08/1.62 ( ( in @ C @ B )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ C )
% 3.08/1.62 => ( in @ Xx @ A ) ) )
% 3.08/1.62 & ! [Xx: $i,Xy: $i] :
% 3.08/1.62 ( ( ( in @ Xx @ A )
% 3.08/1.62 & ( in @ Xy @ A ) )
% 3.08/1.62 => ( ! [C: $i] :
% 3.08/1.62 ( ( in @ C @ B )
% 3.08/1.62 => ( ( in @ Xx @ C )
% 3.08/1.62 <=> ( in @ Xy @ C ) ) )
% 3.08/1.62 => ( Xx = Xy ) ) )
% 3.08/1.62 & ! [C: $i,D: $i] :
% 3.08/1.62 ( ( ( in @ C @ B )
% 3.08/1.62 & ( in @ D @ B ) )
% 3.08/1.62 => ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ C )
% 3.08/1.62 => ( in @ Xx @ D ) )
% 3.08/1.62 | ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ D )
% 3.08/1.62 => ( in @ Xx @ C ) ) ) )
% 3.08/1.62 & ! [C: $i] :
% 3.08/1.62 ( ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ C )
% 3.08/1.62 => ( in @ Xx @ A ) )
% 3.08/1.62 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 3.08/1.62 => ? [D: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ D @ B )
% 3.08/1.62 & ( in @ Xx @ C )
% 3.08/1.62 & ~ ? [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ D )
% 3.08/1.62 & ( in @ Xy @ C ) )
% 3.08/1.62 & ! [E: $i] :
% 3.08/1.62 ( ( in @ E @ B )
% 3.08/1.62 => ( ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ E )
% 3.08/1.62 => ( in @ Xy @ D ) )
% 3.08/1.62 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(descr_type,type,
% 3.08/1.62 descr: ( $i > $o ) > $i ).
% 3.08/1.62
% 3.08/1.62 thf(descrp_type,type,
% 3.08/1.62 descrp: $o ).
% 3.08/1.62
% 3.08/1.62 thf(descrp,definition,
% 3.08/1.62 ( descrp
% 3.08/1.62 = ( ! [Xphi: $i > $o] :
% 3.08/1.62 ( ( exu
% 3.08/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.62 => ( Xphi
% 3.08/1.62 @ ( descr
% 3.08/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(dsetconstr_type,type,
% 3.08/1.62 dsetconstr: $i > ( $i > $o ) > $i ).
% 3.08/1.62
% 3.08/1.62 thf(dsetconstrI_type,type,
% 3.08/1.62 dsetconstrI: $o ).
% 3.08/1.62
% 3.08/1.62 thf(dsetconstrI,definition,
% 3.08/1.62 ( dsetconstrI
% 3.08/1.62 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ( Xphi @ Xx )
% 3.08/1.62 => ( in @ Xx
% 3.08/1.62 @ ( dsetconstr @ A
% 3.08/1.62 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(dsetconstrEL_type,type,
% 3.08/1.62 dsetconstrEL: $o ).
% 3.08/1.62
% 3.08/1.62 thf(dsetconstrEL,definition,
% 3.08/1.62 ( dsetconstrEL
% 3.08/1.62 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx
% 3.08/1.62 @ ( dsetconstr @ A
% 3.08/1.62 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.08/1.62 => ( in @ Xx @ A ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(dsetconstrER_type,type,
% 3.08/1.62 dsetconstrER: $o ).
% 3.08/1.62
% 3.08/1.62 thf(dsetconstrER,definition,
% 3.08/1.62 ( dsetconstrER
% 3.08/1.62 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx
% 3.08/1.62 @ ( dsetconstr @ A
% 3.08/1.62 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.08/1.62 => ( Xphi @ Xx ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(exuE1_type,type,
% 3.08/1.62 exuE1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(exuE1,definition,
% 3.08/1.62 ( exuE1
% 3.08/1.62 = ( ! [Xphi: $i > $o] :
% 3.08/1.62 ( ( exu
% 3.08/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.62 => ? [Xx: $i] :
% 3.08/1.62 ( ( Xphi @ Xx )
% 3.08/1.62 & ! [Xy: $i] :
% 3.08/1.62 ( ( Xphi @ Xy )
% 3.08/1.62 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(prop2set_type,type,
% 3.08/1.62 prop2set: $o > $i ).
% 3.08/1.62
% 3.08/1.62 thf(prop2setE_type,type,
% 3.08/1.62 prop2setE: $o ).
% 3.08/1.62
% 3.08/1.62 thf(prop2setE,definition,
% 3.08/1.62 ( prop2setE
% 3.08/1.62 = ( ! [Xphi: $o,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 3.08/1.62 => Xphi ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(emptysetE_type,type,
% 3.08/1.62 emptysetE: $o ).
% 3.08/1.62
% 3.08/1.62 thf(emptysetE,definition,
% 3.08/1.62 ( emptysetE
% 3.08/1.62 = ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ emptyset )
% 3.08/1.62 => ! [Xphi: $o] : Xphi ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(emptysetimpfalse_type,type,
% 3.08/1.62 emptysetimpfalse: $o ).
% 3.08/1.62
% 3.08/1.62 thf(emptysetimpfalse,definition,
% 3.08/1.62 ( emptysetimpfalse
% 3.08/1.62 = ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ emptyset )
% 3.08/1.62 => $false ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(notinemptyset_type,type,
% 3.08/1.62 notinemptyset: $o ).
% 3.08/1.62
% 3.08/1.62 thf(notinemptyset,definition,
% 3.08/1.62 ( notinemptyset
% 3.08/1.62 = ( ! [Xx: $i] :
% 3.08/1.62 ~ ( in @ Xx @ emptyset ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(exuE3e_type,type,
% 3.08/1.62 exuE3e: $o ).
% 3.08/1.62
% 3.08/1.62 thf(exuE3e,definition,
% 3.08/1.62 ( exuE3e
% 3.08/1.62 = ( ! [Xphi: $i > $o] :
% 3.08/1.62 ( ( exu
% 3.08/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.62 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setext_type,type,
% 3.08/1.62 setext: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setext,definition,
% 3.08/1.62 ( setext
% 3.08/1.62 = ( ! [A: $i,B: $i] :
% 3.08/1.62 ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( in @ Xx @ B ) )
% 3.08/1.62 => ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ B )
% 3.08/1.62 => ( in @ Xx @ A ) )
% 3.08/1.62 => ( A = B ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(emptyI_type,type,
% 3.08/1.62 emptyI: $o ).
% 3.08/1.62
% 3.08/1.62 thf(emptyI,definition,
% 3.08/1.62 ( emptyI
% 3.08/1.62 = ( ! [A: $i] :
% 3.08/1.62 ( ! [Xx: $i] :
% 3.08/1.62 ~ ( in @ Xx @ A )
% 3.08/1.62 => ( A = emptyset ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(noeltsimpempty_type,type,
% 3.08/1.62 noeltsimpempty: $o ).
% 3.08/1.62
% 3.08/1.62 thf(noeltsimpempty,definition,
% 3.08/1.62 ( noeltsimpempty
% 3.08/1.62 = ( ! [A: $i] :
% 3.08/1.62 ( ! [Xx: $i] :
% 3.08/1.62 ~ ( in @ Xx @ A )
% 3.08/1.62 => ( A = emptyset ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setbeta_type,type,
% 3.08/1.62 setbeta: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setbeta,definition,
% 3.08/1.62 ( setbeta
% 3.08/1.62 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ( in @ Xx
% 3.08/1.62 @ ( dsetconstr @ A
% 3.08/1.62 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.08/1.62 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(nonempty_type,type,
% 3.08/1.62 nonempty: $i > $o ).
% 3.08/1.62
% 3.08/1.62 thf(nonempty,definition,
% 3.08/1.62 ( nonempty
% 3.08/1.62 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(nonemptyE1_type,type,
% 3.08/1.62 nonemptyE1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(nonemptyE1,definition,
% 3.08/1.62 ( nonemptyE1
% 3.08/1.62 = ( ! [A: $i] :
% 3.08/1.62 ( ( nonempty @ A )
% 3.08/1.62 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(nonemptyI_type,type,
% 3.08/1.62 nonemptyI: $o ).
% 3.08/1.62
% 3.08/1.62 thf(nonemptyI,definition,
% 3.08/1.62 ( nonemptyI
% 3.08/1.62 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ( Xphi @ Xx )
% 3.08/1.62 => ( nonempty
% 3.08/1.62 @ ( dsetconstr @ A
% 3.08/1.62 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(nonemptyI1_type,type,
% 3.08/1.62 nonemptyI1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(nonemptyI1,definition,
% 3.08/1.62 ( nonemptyI1
% 3.08/1.62 = ( ! [A: $i] :
% 3.08/1.62 ( ? [Xx: $i] : ( in @ Xx @ A )
% 3.08/1.62 => ( nonempty @ A ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setadjoinIL_type,type,
% 3.08/1.62 setadjoinIL: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setadjoinIL,definition,
% 3.08/1.62 ( setadjoinIL
% 3.08/1.62 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(emptyinunitempty_type,type,
% 3.08/1.62 emptyinunitempty: $o ).
% 3.08/1.62
% 3.08/1.62 thf(emptyinunitempty,definition,
% 3.08/1.62 ( emptyinunitempty
% 3.08/1.62 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setadjoinIR_type,type,
% 3.08/1.62 setadjoinIR: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setadjoinIR,definition,
% 3.08/1.62 ( setadjoinIR
% 3.08/1.62 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ A )
% 3.08/1.62 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setadjoinE_type,type,
% 3.08/1.62 setadjoinE: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setadjoinE,definition,
% 3.08/1.62 ( setadjoinE
% 3.08/1.62 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.08/1.62 => ! [Xphi: $o] :
% 3.08/1.62 ( ( ( Xy = Xx )
% 3.08/1.62 => Xphi )
% 3.08/1.62 => ( ( ( in @ Xy @ A )
% 3.08/1.62 => Xphi )
% 3.08/1.62 => Xphi ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setadjoinOr_type,type,
% 3.08/1.62 setadjoinOr: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setadjoinOr,definition,
% 3.08/1.62 ( setadjoinOr
% 3.08/1.62 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.08/1.62 => ( ( Xy = Xx )
% 3.08/1.62 | ( in @ Xy @ A ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setoftrueEq_type,type,
% 3.08/1.62 setoftrueEq: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setoftrueEq,definition,
% 3.08/1.62 ( setoftrueEq
% 3.08/1.62 = ( ! [A: $i] :
% 3.08/1.62 ( ( dsetconstr @ A
% 3.08/1.62 @ ^ [Xx: $i] : $true )
% 3.08/1.62 = A ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(powersetI_type,type,
% 3.08/1.62 powersetI: $o ).
% 3.08/1.62
% 3.08/1.62 thf(powersetI,definition,
% 3.08/1.62 ( powersetI
% 3.08/1.62 = ( ! [A: $i,B: $i] :
% 3.08/1.62 ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ B )
% 3.08/1.62 => ( in @ Xx @ A ) )
% 3.08/1.62 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(emptyinPowerset_type,type,
% 3.08/1.62 emptyinPowerset: $o ).
% 3.08/1.62
% 3.08/1.62 thf(emptyinPowerset,definition,
% 3.08/1.62 ( emptyinPowerset
% 3.08/1.62 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(emptyInPowerset_type,type,
% 3.08/1.62 emptyInPowerset: $o ).
% 3.08/1.62
% 3.08/1.62 thf(emptyInPowerset,definition,
% 3.08/1.62 ( emptyInPowerset
% 3.08/1.62 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(powersetE_type,type,
% 3.08/1.62 powersetE: $o ).
% 3.08/1.62
% 3.08/1.62 thf(powersetE,definition,
% 3.08/1.62 ( powersetE
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ B @ ( powerset @ A ) )
% 3.08/1.62 => ( ( in @ Xx @ B )
% 3.08/1.62 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setunionI_type,type,
% 3.08/1.62 setunionI: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setunionI,definition,
% 3.08/1.62 ( setunionI
% 3.08/1.62 = ( ! [A: $i,Xx: $i,B: $i] :
% 3.08/1.62 ( ( in @ Xx @ B )
% 3.08/1.62 => ( ( in @ B @ A )
% 3.08/1.62 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setunionE_type,type,
% 3.08/1.62 setunionE: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setunionE,definition,
% 3.08/1.62 ( setunionE
% 3.08/1.62 = ( ! [A: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ ( setunion @ A ) )
% 3.08/1.62 => ! [Xphi: $o] :
% 3.08/1.62 ( ! [B: $i] :
% 3.08/1.62 ( ( in @ Xx @ B )
% 3.08/1.62 => ( ( in @ B @ A )
% 3.08/1.62 => Xphi ) )
% 3.08/1.62 => Xphi ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(subPowSU_type,type,
% 3.08/1.62 subPowSU: $o ).
% 3.08/1.62
% 3.08/1.62 thf(subPowSU,definition,
% 3.08/1.62 ( subPowSU
% 3.08/1.62 = ( ! [A: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(exuE2_type,type,
% 3.08/1.62 exuE2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(exuE2,definition,
% 3.08/1.62 ( exuE2
% 3.08/1.62 = ( ! [Xphi: $i > $o] :
% 3.08/1.62 ( ( exu
% 3.08/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.62 => ? [Xx: $i] :
% 3.08/1.62 ! [Xy: $i] :
% 3.08/1.62 ( ( Xphi @ Xy )
% 3.08/1.62 <=> ( Xy = Xx ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(nonemptyImpWitness_type,type,
% 3.08/1.62 nonemptyImpWitness: $o ).
% 3.08/1.62
% 3.08/1.62 thf(nonemptyImpWitness,definition,
% 3.08/1.62 ( nonemptyImpWitness
% 3.08/1.62 = ( ! [A: $i] :
% 3.08/1.62 ( ( nonempty @ A )
% 3.08/1.62 => ? [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 & $true ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(uniqinunit_type,type,
% 3.08/1.62 uniqinunit: $o ).
% 3.08/1.62
% 3.08/1.62 thf(uniqinunit,definition,
% 3.08/1.62 ( uniqinunit
% 3.08/1.62 = ( ! [Xx: $i,Xy: $i] :
% 3.08/1.62 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.08/1.62 => ( Xx = Xy ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(notinsingleton_type,type,
% 3.08/1.62 notinsingleton: $o ).
% 3.08/1.62
% 3.08/1.62 thf(notinsingleton,definition,
% 3.08/1.62 ( notinsingleton
% 3.08/1.62 = ( ! [Xx: $i,Xy: $i] :
% 3.08/1.62 ( ( Xx != Xy )
% 3.08/1.62 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(eqinunit_type,type,
% 3.08/1.62 eqinunit: $o ).
% 3.08/1.62
% 3.08/1.62 thf(eqinunit,definition,
% 3.08/1.62 ( eqinunit
% 3.08/1.62 = ( ! [Xx: $i,Xy: $i] :
% 3.08/1.62 ( ( Xx = Xy )
% 3.08/1.62 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(singletonsswitch_type,type,
% 3.08/1.62 singletonsswitch: $o ).
% 3.08/1.62
% 3.08/1.62 thf(singletonsswitch,definition,
% 3.08/1.62 ( singletonsswitch
% 3.08/1.62 = ( ! [Xx: $i,Xy: $i] :
% 3.08/1.62 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.08/1.62 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(upairsetE_type,type,
% 3.08/1.62 upairsetE: $o ).
% 3.08/1.62
% 3.08/1.62 thf(upairsetE,definition,
% 3.08/1.62 ( upairsetE
% 3.08/1.62 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.08/1.62 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 3.08/1.62 => ( ( Xz = Xx )
% 3.08/1.62 | ( Xz = Xy ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(upairsetIL_type,type,
% 3.08/1.62 upairsetIL: $o ).
% 3.08/1.62
% 3.08/1.62 thf(upairsetIL,definition,
% 3.08/1.62 ( upairsetIL
% 3.08/1.62 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(upairsetIR_type,type,
% 3.08/1.62 upairsetIR: $o ).
% 3.08/1.62
% 3.08/1.62 thf(upairsetIR,definition,
% 3.08/1.62 ( upairsetIR
% 3.08/1.62 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(emptyE1_type,type,
% 3.08/1.62 emptyE1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(emptyE1,definition,
% 3.08/1.62 ( emptyE1
% 3.08/1.62 = ( ! [A: $i,Xphi: $i > $o] :
% 3.08/1.62 ( ? [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 & ( Xphi @ Xx ) )
% 3.08/1.62 => ( ( ( dsetconstr @ A
% 3.08/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.62 = emptyset )
% 3.08/1.62 => $false ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(vacuousDall_type,type,
% 3.08/1.62 vacuousDall: $o ).
% 3.08/1.62
% 3.08/1.62 thf(vacuousDall,definition,
% 3.08/1.62 ( vacuousDall
% 3.08/1.62 = ( ! [Xphi: $i > $o,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ emptyset )
% 3.08/1.62 => ( Xphi @ Xx ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(quantDeMorgan1_type,type,
% 3.08/1.62 quantDeMorgan1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(quantDeMorgan1,definition,
% 3.08/1.62 ( quantDeMorgan1
% 3.08/1.62 = ( ! [A: $i,Xphi: $i > $o] :
% 3.08/1.62 ( ~ ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( Xphi @ Xx ) )
% 3.08/1.62 => ? [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(quantDeMorgan2_type,type,
% 3.08/1.62 quantDeMorgan2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(quantDeMorgan2,definition,
% 3.08/1.62 ( quantDeMorgan2
% 3.08/1.62 = ( ! [A: $i,Xphi: $i > $o] :
% 3.08/1.62 ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ~ ( Xphi @ Xx ) )
% 3.08/1.62 => ~ ? [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 & ( Xphi @ Xx ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(quantDeMorgan3_type,type,
% 3.08/1.62 quantDeMorgan3: $o ).
% 3.08/1.62
% 3.08/1.62 thf(quantDeMorgan3,definition,
% 3.08/1.62 ( quantDeMorgan3
% 3.08/1.62 = ( ! [A: $i,Xphi: $i > $o] :
% 3.08/1.62 ( ~ ? [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 & ( Xphi @ Xx ) )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(quantDeMorgan4_type,type,
% 3.08/1.62 quantDeMorgan4: $o ).
% 3.08/1.62
% 3.08/1.62 thf(quantDeMorgan4,definition,
% 3.08/1.62 ( quantDeMorgan4
% 3.08/1.62 = ( ! [A: $i,Xphi: $i > $o] :
% 3.08/1.62 ( ? [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 & ~ ( Xphi @ Xx ) )
% 3.08/1.62 => ~ ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( Xphi @ Xx ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(prop2setI_type,type,
% 3.08/1.62 prop2setI: $o ).
% 3.08/1.62
% 3.08/1.62 thf(prop2setI,definition,
% 3.08/1.62 ( prop2setI
% 3.08/1.62 = ( ! [Xphi: $o] :
% 3.08/1.62 ( Xphi
% 3.08/1.62 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(set2prop_type,type,
% 3.08/1.62 set2prop: $i > $o ).
% 3.08/1.62
% 3.08/1.62 thf(prop2set2propI_type,type,
% 3.08/1.62 prop2set2propI: $o ).
% 3.08/1.62
% 3.08/1.62 thf(prop2set2propI,definition,
% 3.08/1.62 ( prop2set2propI
% 3.08/1.62 = ( ! [Xphi: $o] :
% 3.08/1.62 ( Xphi
% 3.08/1.62 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(notdexE_type,type,
% 3.08/1.62 notdexE: $o ).
% 3.08/1.62
% 3.08/1.62 thf(notdexE,definition,
% 3.08/1.62 ( notdexE
% 3.08/1.62 = ( ! [A: $i,Xphi: $i > $o] :
% 3.08/1.62 ( ~ ? [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 & ( Xphi @ Xx ) )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(notdallE_type,type,
% 3.08/1.62 notdallE: $o ).
% 3.08/1.62
% 3.08/1.62 thf(notdallE,definition,
% 3.08/1.62 ( notdallE
% 3.08/1.62 = ( ! [A: $i,Xphi: $i > $o] :
% 3.08/1.62 ( ~ ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( Xphi @ Xx ) )
% 3.08/1.62 => ? [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(exuI1_type,type,
% 3.08/1.62 exuI1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(exuI1,definition,
% 3.08/1.62 ( exuI1
% 3.08/1.62 = ( ! [Xphi: $i > $o] :
% 3.08/1.62 ( ? [Xx: $i] :
% 3.08/1.62 ( ( Xphi @ Xx )
% 3.08/1.62 & ! [Xy: $i] :
% 3.08/1.62 ( ( Xphi @ Xy )
% 3.08/1.62 => ( Xx = Xy ) ) )
% 3.08/1.62 => ( exu
% 3.08/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(exuI3_type,type,
% 3.08/1.62 exuI3: $o ).
% 3.08/1.62
% 3.08/1.62 thf(exuI3,definition,
% 3.08/1.62 ( exuI3
% 3.08/1.62 = ( ! [Xphi: $i > $o] :
% 3.08/1.62 ( ? [Xx: $i] : ( Xphi @ Xx )
% 3.08/1.62 => ( ! [Xx: $i,Xy: $i] :
% 3.08/1.62 ( ( Xphi @ Xx )
% 3.08/1.62 => ( ( Xphi @ Xy )
% 3.08/1.62 => ( Xx = Xy ) ) )
% 3.08/1.62 => ( exu
% 3.08/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(exuI2_type,type,
% 3.08/1.62 exuI2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(exuI2,definition,
% 3.08/1.62 ( exuI2
% 3.08/1.62 = ( ! [Xphi: $i > $o] :
% 3.08/1.62 ( ? [Xx: $i] :
% 3.08/1.62 ! [Xy: $i] :
% 3.08/1.62 ( ( Xphi @ Xy )
% 3.08/1.62 <=> ( Xy = Xx ) )
% 3.08/1.62 => ( exu
% 3.08/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(inCongP_type,type,
% 3.08/1.62 inCongP: $o ).
% 3.08/1.62
% 3.08/1.62 thf(inCongP,definition,
% 3.08/1.62 ( inCongP
% 3.08/1.62 = ( ! [A: $i,B: $i] :
% 3.08/1.62 ( ( A = B )
% 3.08/1.62 => ! [Xx: $i,Xy: $i] :
% 3.08/1.62 ( ( Xx = Xy )
% 3.08/1.62 => ( ( in @ Xx @ A )
% 3.08/1.62 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(in__Cong_type,type,
% 3.08/1.62 in__Cong: $o ).
% 3.08/1.62
% 3.08/1.62 thf(in__Cong,definition,
% 3.08/1.62 ( in__Cong
% 3.08/1.62 = ( ! [A: $i,B: $i] :
% 3.08/1.62 ( ( A = B )
% 3.08/1.62 => ! [Xx: $i,Xy: $i] :
% 3.08/1.62 ( ( Xx = Xy )
% 3.08/1.62 => ( ( in @ Xx @ A )
% 3.08/1.62 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(exuE3u_type,type,
% 3.08/1.62 exuE3u: $o ).
% 3.08/1.62
% 3.08/1.62 thf(exuE3u,definition,
% 3.08/1.62 ( exuE3u
% 3.08/1.62 = ( ! [Xphi: $i > $o] :
% 3.08/1.62 ( ( exu
% 3.08/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.62 => ! [Xx: $i,Xy: $i] :
% 3.08/1.62 ( ( Xphi @ Xx )
% 3.08/1.62 => ( ( Xphi @ Xy )
% 3.08/1.62 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(exu__Cong_type,type,
% 3.08/1.62 exu__Cong: $o ).
% 3.08/1.62
% 3.08/1.62 thf(exu__Cong,definition,
% 3.08/1.62 ( exu__Cong
% 3.08/1.62 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.08/1.62 ( ! [Xx: $i,Xy: $i] :
% 3.08/1.62 ( ( Xx = Xy )
% 3.08/1.62 => ( ( Xphi @ Xx )
% 3.08/1.62 <=> ( Xpsi @ Xy ) ) )
% 3.08/1.62 => ( ( exu
% 3.08/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.62 <=> ( exu
% 3.08/1.62 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(emptyset__Cong_type,type,
% 3.08/1.62 emptyset__Cong: $o ).
% 3.08/1.62
% 3.08/1.62 thf(emptyset__Cong,definition,
% 3.08/1.62 ( emptyset__Cong
% 3.08/1.62 = ( emptyset = emptyset ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setadjoin__Cong_type,type,
% 3.08/1.62 setadjoin__Cong: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setadjoin__Cong,definition,
% 3.08/1.62 ( setadjoin__Cong
% 3.08/1.62 = ( ! [Xx: $i,Xy: $i] :
% 3.08/1.62 ( ( Xx = Xy )
% 3.08/1.62 => ! [Xz: $i,Xu: $i] :
% 3.08/1.62 ( ( Xz = Xu )
% 3.08/1.62 => ( ( setadjoin @ Xx @ Xz )
% 3.08/1.62 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(powerset__Cong_type,type,
% 3.08/1.62 powerset__Cong: $o ).
% 3.08/1.62
% 3.08/1.62 thf(powerset__Cong,definition,
% 3.08/1.62 ( powerset__Cong
% 3.08/1.62 = ( ! [A: $i,B: $i] :
% 3.08/1.62 ( ( A = B )
% 3.08/1.62 => ( ( powerset @ A )
% 3.08/1.62 = ( powerset @ B ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setunion__Cong_type,type,
% 3.08/1.62 setunion__Cong: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setunion__Cong,definition,
% 3.08/1.62 ( setunion__Cong
% 3.08/1.62 = ( ! [A: $i,B: $i] :
% 3.08/1.62 ( ( A = B )
% 3.08/1.62 => ( ( setunion @ A )
% 3.08/1.62 = ( setunion @ B ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(omega__Cong_type,type,
% 3.08/1.62 omega__Cong: $o ).
% 3.08/1.62
% 3.08/1.62 thf(omega__Cong,definition,
% 3.08/1.62 ( omega__Cong
% 3.08/1.62 = ( omega = omega ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(exuEu_type,type,
% 3.08/1.62 exuEu: $o ).
% 3.08/1.62
% 3.08/1.62 thf(exuEu,definition,
% 3.08/1.62 ( exuEu
% 3.08/1.62 = ( ! [Xphi: $i > $o] :
% 3.08/1.62 ( ( exu
% 3.08/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.62 => ! [Xx: $i,Xy: $i] :
% 3.08/1.62 ( ( Xphi @ Xx )
% 3.08/1.62 => ( ( Xphi @ Xy )
% 3.08/1.62 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(descr__Cong_type,type,
% 3.08/1.62 descr__Cong: $o ).
% 3.08/1.62
% 3.08/1.62 thf(descr__Cong,definition,
% 3.08/1.62 ( descr__Cong
% 3.08/1.62 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.08/1.62 ( ! [Xx: $i,Xy: $i] :
% 3.08/1.62 ( ( Xx = Xy )
% 3.08/1.62 => ( ( Xphi @ Xx )
% 3.08/1.62 <=> ( Xpsi @ Xy ) ) )
% 3.08/1.62 => ( ( exu
% 3.08/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.62 => ( ( exu
% 3.08/1.62 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 3.08/1.62 => ( ( descr
% 3.08/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.62 = ( descr
% 3.08/1.62 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(dsetconstr__Cong_type,type,
% 3.08/1.62 dsetconstr__Cong: $o ).
% 3.08/1.62
% 3.08/1.62 thf(dsetconstr__Cong,definition,
% 3.08/1.62 ( dsetconstr__Cong
% 3.08/1.62 = ( ! [A: $i,B: $i] :
% 3.08/1.62 ( ( A = B )
% 3.08/1.62 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.08/1.62 ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ B )
% 3.08/1.62 => ( ( Xx = Xy )
% 3.08/1.62 => ( ( Xphi @ Xx )
% 3.08/1.62 <=> ( Xpsi @ Xy ) ) ) ) )
% 3.08/1.62 => ( ( dsetconstr @ A
% 3.08/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.62 = ( dsetconstr @ B
% 3.08/1.62 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(subset_type,type,
% 3.08/1.62 subset: $i > $i > $o ).
% 3.08/1.62
% 3.08/1.62 thf(disjoint_type,type,
% 3.08/1.62 disjoint: $i > $i > $o ).
% 3.08/1.62
% 3.08/1.62 thf(setsmeet_type,type,
% 3.08/1.62 setsmeet: $i > $i > $o ).
% 3.08/1.62
% 3.08/1.62 thf(subsetI1_type,type,
% 3.08/1.62 subsetI1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(subsetI1,definition,
% 3.08/1.62 ( subsetI1
% 3.08/1.62 = ( ! [A: $i,B: $i] :
% 3.08/1.62 ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( in @ Xx @ B ) )
% 3.08/1.62 => ( subset @ A @ B ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(eqimpsubset2_type,type,
% 3.08/1.62 eqimpsubset2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(eqimpsubset2,definition,
% 3.08/1.62 ( eqimpsubset2
% 3.08/1.62 = ( ! [A: $i,B: $i] :
% 3.08/1.62 ( ( A = B )
% 3.08/1.62 => ( subset @ B @ A ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(eqimpsubset1_type,type,
% 3.08/1.62 eqimpsubset1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(eqimpsubset1,definition,
% 3.08/1.62 ( eqimpsubset1
% 3.08/1.62 = ( ! [A: $i,B: $i] :
% 3.08/1.62 ( ( A = B )
% 3.08/1.62 => ( subset @ A @ B ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(subsetI2_type,type,
% 3.08/1.62 subsetI2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(subsetI2,definition,
% 3.08/1.62 ( subsetI2
% 3.08/1.62 = ( ! [A: $i,B: $i] :
% 3.08/1.62 ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( in @ Xx @ B ) )
% 3.08/1.62 => ( subset @ A @ B ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(emptysetsubset_type,type,
% 3.08/1.62 emptysetsubset: $o ).
% 3.08/1.62
% 3.08/1.62 thf(emptysetsubset,definition,
% 3.08/1.62 ( emptysetsubset
% 3.08/1.62 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(subsetE_type,type,
% 3.08/1.62 subsetE: $o ).
% 3.08/1.62
% 3.08/1.62 thf(subsetE,definition,
% 3.08/1.62 ( subsetE
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ( subset @ A @ B )
% 3.08/1.62 => ( ( in @ Xx @ A )
% 3.08/1.62 => ( in @ Xx @ B ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(subsetE2_type,type,
% 3.08/1.62 subsetE2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(subsetE2,definition,
% 3.08/1.62 ( subsetE2
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ( subset @ A @ B )
% 3.08/1.62 => ( ~ ( in @ Xx @ B )
% 3.08/1.62 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(notsubsetI_type,type,
% 3.08/1.62 notsubsetI: $o ).
% 3.08/1.62
% 3.08/1.62 thf(notsubsetI,definition,
% 3.08/1.62 ( notsubsetI
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ~ ( in @ Xx @ B )
% 3.08/1.62 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(notequalI1_type,type,
% 3.08/1.62 notequalI1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(notequalI1,definition,
% 3.08/1.62 ( notequalI1
% 3.08/1.62 = ( ! [A: $i,B: $i] :
% 3.08/1.62 ( ~ ( subset @ A @ B )
% 3.08/1.62 => ( A != B ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(notequalI2_type,type,
% 3.08/1.62 notequalI2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(notequalI2,definition,
% 3.08/1.62 ( notequalI2
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ~ ( in @ Xx @ B )
% 3.08/1.62 => ( A != B ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(subsetRefl_type,type,
% 3.08/1.62 subsetRefl: $o ).
% 3.08/1.62
% 3.08/1.62 thf(subsetRefl,definition,
% 3.08/1.62 ( subsetRefl
% 3.08/1.62 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(subsetTrans_type,type,
% 3.08/1.62 subsetTrans: $o ).
% 3.08/1.62
% 3.08/1.62 thf(subsetTrans,definition,
% 3.08/1.62 ( subsetTrans
% 3.08/1.62 = ( ! [A: $i,B: $i,C: $i] :
% 3.08/1.62 ( ( subset @ A @ B )
% 3.08/1.62 => ( ( subset @ B @ C )
% 3.08/1.62 => ( subset @ A @ C ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setadjoinSub_type,type,
% 3.08/1.62 setadjoinSub: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setadjoinSub,definition,
% 3.08/1.62 ( setadjoinSub
% 3.08/1.62 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setadjoinSub2_type,type,
% 3.08/1.62 setadjoinSub2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setadjoinSub2,definition,
% 3.08/1.62 ( setadjoinSub2
% 3.08/1.62 = ( ! [A: $i,Xx: $i,B: $i] :
% 3.08/1.62 ( ( subset @ A @ B )
% 3.08/1.62 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(subset2powerset_type,type,
% 3.08/1.62 subset2powerset: $o ).
% 3.08/1.62
% 3.08/1.62 thf(subset2powerset,definition,
% 3.08/1.62 ( subset2powerset
% 3.08/1.62 = ( ! [A: $i,B: $i] :
% 3.08/1.62 ( ( subset @ A @ B )
% 3.08/1.62 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setextsub_type,type,
% 3.08/1.62 setextsub: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setextsub,definition,
% 3.08/1.62 ( setextsub
% 3.08/1.62 = ( ! [A: $i,B: $i] :
% 3.08/1.62 ( ( subset @ A @ B )
% 3.08/1.62 => ( ( subset @ B @ A )
% 3.08/1.62 => ( A = B ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(subsetemptysetimpeq_type,type,
% 3.08/1.62 subsetemptysetimpeq: $o ).
% 3.08/1.62
% 3.08/1.62 thf(subsetemptysetimpeq,definition,
% 3.08/1.62 ( subsetemptysetimpeq
% 3.08/1.62 = ( ! [A: $i] :
% 3.08/1.62 ( ( subset @ A @ emptyset )
% 3.08/1.62 => ( A = emptyset ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(powersetI1_type,type,
% 3.08/1.62 powersetI1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(powersetI1,definition,
% 3.08/1.62 ( powersetI1
% 3.08/1.62 = ( ! [A: $i,B: $i] :
% 3.08/1.62 ( ( subset @ B @ A )
% 3.08/1.62 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(powersetE1_type,type,
% 3.08/1.62 powersetE1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(powersetE1,definition,
% 3.08/1.62 ( powersetE1
% 3.08/1.62 = ( ! [A: $i,B: $i] :
% 3.08/1.62 ( ( in @ B @ ( powerset @ A ) )
% 3.08/1.62 => ( subset @ B @ A ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(inPowerset_type,type,
% 3.08/1.62 inPowerset: $o ).
% 3.08/1.62
% 3.08/1.62 thf(inPowerset,definition,
% 3.08/1.62 ( inPowerset
% 3.08/1.62 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(powersetsubset_type,type,
% 3.08/1.62 powersetsubset: $o ).
% 3.08/1.62
% 3.08/1.62 thf(powersetsubset,definition,
% 3.08/1.62 ( powersetsubset
% 3.08/1.62 = ( ! [A: $i,B: $i] :
% 3.08/1.62 ( ( subset @ A @ B )
% 3.08/1.62 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(sepInPowerset_type,type,
% 3.08/1.62 sepInPowerset: $o ).
% 3.08/1.62
% 3.08/1.62 thf(sepInPowerset,definition,
% 3.08/1.62 ( sepInPowerset
% 3.08/1.62 = ( ! [A: $i,Xphi: $i > $o] :
% 3.08/1.62 ( in
% 3.08/1.62 @ ( dsetconstr @ A
% 3.08/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.62 @ ( powerset @ A ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(sepSubset_type,type,
% 3.08/1.62 sepSubset: $o ).
% 3.08/1.62
% 3.08/1.62 thf(sepSubset,definition,
% 3.08/1.62 ( sepSubset
% 3.08/1.62 = ( ! [A: $i,Xphi: $i > $o] :
% 3.08/1.62 ( subset
% 3.08/1.62 @ ( dsetconstr @ A
% 3.08/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.62 @ A ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(binunion_type,type,
% 3.08/1.62 binunion: $i > $i > $i ).
% 3.08/1.62
% 3.08/1.62 thf(binunionIL_type,type,
% 3.08/1.62 binunionIL: $o ).
% 3.08/1.62
% 3.08/1.62 thf(binunionIL,definition,
% 3.08/1.62 ( binunionIL
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(upairset2IR_type,type,
% 3.08/1.62 upairset2IR: $o ).
% 3.08/1.62
% 3.08/1.62 thf(upairset2IR,definition,
% 3.08/1.62 ( upairset2IR
% 3.08/1.62 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(binunionIR_type,type,
% 3.08/1.62 binunionIR: $o ).
% 3.08/1.62
% 3.08/1.62 thf(binunionIR,definition,
% 3.08/1.62 ( binunionIR
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ B )
% 3.08/1.62 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(binunionEcases_type,type,
% 3.08/1.62 binunionEcases: $o ).
% 3.08/1.62
% 3.08/1.62 thf(binunionEcases,definition,
% 3.08/1.62 ( binunionEcases
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 3.08/1.62 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 3.08/1.62 => ( ( ( in @ Xx @ A )
% 3.08/1.62 => Xphi )
% 3.08/1.62 => ( ( ( in @ Xx @ B )
% 3.08/1.62 => Xphi )
% 3.08/1.62 => Xphi ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(binunionE_type,type,
% 3.08/1.62 binunionE: $o ).
% 3.08/1.62
% 3.08/1.62 thf(binunionE,definition,
% 3.08/1.62 ( binunionE
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 3.08/1.62 => ( ( in @ Xx @ A )
% 3.08/1.62 | ( in @ Xx @ B ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(binunionLsub_type,type,
% 3.08/1.62 binunionLsub: $o ).
% 3.08/1.62
% 3.08/1.62 thf(binunionLsub,definition,
% 3.08/1.62 ( binunionLsub
% 3.08/1.62 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(binunionRsub_type,type,
% 3.08/1.62 binunionRsub: $o ).
% 3.08/1.62
% 3.08/1.62 thf(binunionRsub,definition,
% 3.08/1.62 ( binunionRsub
% 3.08/1.62 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(binintersect_type,type,
% 3.08/1.62 binintersect: $i > $i > $i ).
% 3.08/1.62
% 3.08/1.62 thf(binintersectI_type,type,
% 3.08/1.62 binintersectI: $o ).
% 3.08/1.62
% 3.08/1.62 thf(binintersectI,definition,
% 3.08/1.62 ( binintersectI
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ( in @ Xx @ B )
% 3.08/1.62 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(binintersectSubset5_type,type,
% 3.08/1.62 binintersectSubset5: $o ).
% 3.08/1.62
% 3.08/1.62 thf(binintersectSubset5,definition,
% 3.08/1.62 ( binintersectSubset5
% 3.08/1.62 = ( ! [A: $i,B: $i,C: $i] :
% 3.08/1.62 ( ( subset @ C @ A )
% 3.08/1.62 => ( ( subset @ C @ B )
% 3.08/1.62 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(binintersectEL_type,type,
% 3.08/1.62 binintersectEL: $o ).
% 3.08/1.62
% 3.08/1.62 thf(binintersectEL,definition,
% 3.08/1.62 ( binintersectEL
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 3.08/1.62 => ( in @ Xx @ A ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(binintersectLsub_type,type,
% 3.08/1.62 binintersectLsub: $o ).
% 3.08/1.62
% 3.08/1.62 thf(binintersectLsub,definition,
% 3.08/1.62 ( binintersectLsub
% 3.08/1.62 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(binintersectSubset2_type,type,
% 3.08/1.62 binintersectSubset2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(binintersectSubset2,definition,
% 3.08/1.62 ( binintersectSubset2
% 3.08/1.62 = ( ! [A: $i,B: $i] :
% 3.08/1.62 ( ( subset @ A @ B )
% 3.08/1.62 => ( ( binintersect @ A @ B )
% 3.08/1.62 = A ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(binintersectSubset3_type,type,
% 3.08/1.62 binintersectSubset3: $o ).
% 3.08/1.62
% 3.08/1.62 thf(binintersectSubset3,definition,
% 3.08/1.62 ( binintersectSubset3
% 3.08/1.62 = ( ! [A: $i,B: $i] :
% 3.08/1.62 ( ( ( binintersect @ A @ B )
% 3.08/1.62 = B )
% 3.08/1.62 => ( subset @ B @ A ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(binintersectER_type,type,
% 3.08/1.62 binintersectER: $o ).
% 3.08/1.62
% 3.08/1.62 thf(binintersectER,definition,
% 3.08/1.62 ( binintersectER
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 3.08/1.62 => ( in @ Xx @ B ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(disjointsetsI1_type,type,
% 3.08/1.62 disjointsetsI1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(disjointsetsI1,definition,
% 3.08/1.62 ( disjointsetsI1
% 3.08/1.62 = ( ! [A: $i,B: $i] :
% 3.08/1.62 ( ~ ? [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 & ( in @ Xx @ B ) )
% 3.08/1.62 => ( ( binintersect @ A @ B )
% 3.08/1.62 = emptyset ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(binintersectRsub_type,type,
% 3.08/1.62 binintersectRsub: $o ).
% 3.08/1.62
% 3.08/1.62 thf(binintersectRsub,definition,
% 3.08/1.62 ( binintersectRsub
% 3.08/1.62 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(binintersectSubset4_type,type,
% 3.08/1.62 binintersectSubset4: $o ).
% 3.08/1.62
% 3.08/1.62 thf(binintersectSubset4,definition,
% 3.08/1.62 ( binintersectSubset4
% 3.08/1.62 = ( ! [A: $i,B: $i] :
% 3.08/1.62 ( ( subset @ B @ A )
% 3.08/1.62 => ( ( binintersect @ A @ B )
% 3.08/1.62 = B ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(binintersectSubset1_type,type,
% 3.08/1.62 binintersectSubset1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(binintersectSubset1,definition,
% 3.08/1.62 ( binintersectSubset1
% 3.08/1.62 = ( ! [A: $i,B: $i] :
% 3.08/1.62 ( ( ( binintersect @ A @ B )
% 3.08/1.62 = A )
% 3.08/1.62 => ( subset @ A @ B ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(bs114d_type,type,
% 3.08/1.62 bs114d: $o ).
% 3.08/1.62
% 3.08/1.62 thf(bs114d,definition,
% 3.08/1.62 ( bs114d
% 3.08/1.62 = ( ! [A: $i,B: $i,C: $i] :
% 3.08/1.62 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 3.08/1.62 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(regular_type,type,
% 3.08/1.62 regular: $i > $o ).
% 3.08/1.62
% 3.08/1.62 thf(setminus_type,type,
% 3.08/1.62 setminus: $i > $i > $i ).
% 3.08/1.62
% 3.08/1.62 thf(setminusI_type,type,
% 3.08/1.62 setminusI: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setminusI,definition,
% 3.08/1.62 ( setminusI
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ~ ( in @ Xx @ B )
% 3.08/1.62 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setminusEL_type,type,
% 3.08/1.62 setminusEL: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setminusEL,definition,
% 3.08/1.62 ( setminusEL
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 3.08/1.62 => ( in @ Xx @ A ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setminusER_type,type,
% 3.08/1.62 setminusER: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setminusER,definition,
% 3.08/1.62 ( setminusER
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 3.08/1.62 => ~ ( in @ Xx @ B ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setminusSubset2_type,type,
% 3.08/1.62 setminusSubset2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setminusSubset2,definition,
% 3.08/1.62 ( setminusSubset2
% 3.08/1.62 = ( ! [A: $i,B: $i] :
% 3.08/1.62 ( ( subset @ A @ B )
% 3.08/1.62 => ( ( setminus @ A @ B )
% 3.08/1.62 = emptyset ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setminusERneg_type,type,
% 3.08/1.62 setminusERneg: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setminusERneg,definition,
% 3.08/1.62 ( setminusERneg
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 3.08/1.62 => ( ( in @ Xx @ A )
% 3.08/1.62 => ( in @ Xx @ B ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setminusELneg_type,type,
% 3.08/1.62 setminusELneg: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setminusELneg,definition,
% 3.08/1.62 ( setminusELneg
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 3.08/1.62 => ( ~ ( in @ Xx @ B )
% 3.08/1.62 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setminusILneg_type,type,
% 3.08/1.62 setminusILneg: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setminusILneg,definition,
% 3.08/1.62 ( setminusILneg
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ~ ( in @ Xx @ A )
% 3.08/1.62 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setminusIRneg_type,type,
% 3.08/1.62 setminusIRneg: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setminusIRneg,definition,
% 3.08/1.62 ( setminusIRneg
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ B )
% 3.08/1.62 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setminusLsub_type,type,
% 3.08/1.62 setminusLsub: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setminusLsub,definition,
% 3.08/1.62 ( setminusLsub
% 3.08/1.62 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setminusSubset1_type,type,
% 3.08/1.62 setminusSubset1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setminusSubset1,definition,
% 3.08/1.62 ( setminusSubset1
% 3.08/1.62 = ( ! [A: $i,B: $i] :
% 3.08/1.62 ( ( ( setminus @ A @ B )
% 3.08/1.62 = emptyset )
% 3.08/1.62 => ( subset @ A @ B ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(symdiff_type,type,
% 3.08/1.62 symdiff: $i > $i > $i ).
% 3.08/1.62
% 3.08/1.62 thf(symdiffE_type,type,
% 3.08/1.62 symdiffE: $o ).
% 3.08/1.62
% 3.08/1.62 thf(symdiffE,definition,
% 3.08/1.62 ( symdiffE
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 3.08/1.62 => ! [Xphi: $o] :
% 3.08/1.62 ( ( ( in @ Xx @ A )
% 3.08/1.62 => ( ~ ( in @ Xx @ B )
% 3.08/1.62 => Xphi ) )
% 3.08/1.62 => ( ( ~ ( in @ Xx @ A )
% 3.08/1.62 => ( ( in @ Xx @ B )
% 3.08/1.62 => Xphi ) )
% 3.08/1.62 => Xphi ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(symdiffI1_type,type,
% 3.08/1.62 symdiffI1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(symdiffI1,definition,
% 3.08/1.62 ( symdiffI1
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ~ ( in @ Xx @ B )
% 3.08/1.62 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(symdiffI2_type,type,
% 3.08/1.62 symdiffI2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(symdiffI2,definition,
% 3.08/1.62 ( symdiffI2
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ~ ( in @ Xx @ A )
% 3.08/1.62 => ( ( in @ Xx @ B )
% 3.08/1.62 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(symdiffIneg1_type,type,
% 3.08/1.62 symdiffIneg1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(symdiffIneg1,definition,
% 3.08/1.62 ( symdiffIneg1
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ( in @ Xx @ B )
% 3.08/1.62 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(symdiffIneg2_type,type,
% 3.08/1.62 symdiffIneg2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(symdiffIneg2,definition,
% 3.08/1.62 ( symdiffIneg2
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ~ ( in @ Xx @ A )
% 3.08/1.62 => ( ~ ( in @ Xx @ B )
% 3.08/1.62 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(iskpair_type,type,
% 3.08/1.62 iskpair: $i > $o ).
% 3.08/1.62
% 3.08/1.62 thf(secondinupair_type,type,
% 3.08/1.62 secondinupair: $o ).
% 3.08/1.62
% 3.08/1.62 thf(secondinupair,definition,
% 3.08/1.62 ( secondinupair
% 3.08/1.62 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setukpairIL_type,type,
% 3.08/1.62 setukpairIL: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setukpairIL,definition,
% 3.08/1.62 ( setukpairIL
% 3.08/1.62 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setukpairIR_type,type,
% 3.08/1.62 setukpairIR: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setukpairIR,definition,
% 3.08/1.62 ( setukpairIR
% 3.08/1.62 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(kpairiskpair_type,type,
% 3.08/1.62 kpairiskpair: $o ).
% 3.08/1.62
% 3.08/1.62 thf(kpairiskpair,definition,
% 3.08/1.62 ( kpairiskpair
% 3.08/1.62 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(kpair_type,type,
% 3.08/1.62 kpair: $i > $i > $i ).
% 3.08/1.62
% 3.08/1.62 thf(kpairp_type,type,
% 3.08/1.62 kpairp: $o ).
% 3.08/1.62
% 3.08/1.62 thf(kpairp,definition,
% 3.08/1.62 ( kpairp
% 3.08/1.62 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(cartprod_type,type,
% 3.08/1.62 cartprod: $i > $i > $i ).
% 3.08/1.62
% 3.08/1.62 thf(singletonsubset_type,type,
% 3.08/1.62 singletonsubset: $o ).
% 3.08/1.62
% 3.08/1.62 thf(singletonsubset,definition,
% 3.08/1.62 ( singletonsubset
% 3.08/1.62 = ( ! [A: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(singletoninpowerset_type,type,
% 3.08/1.62 singletoninpowerset: $o ).
% 3.08/1.62
% 3.08/1.62 thf(singletoninpowerset,definition,
% 3.08/1.62 ( singletoninpowerset
% 3.08/1.62 = ( ! [A: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(singletoninpowunion_type,type,
% 3.08/1.62 singletoninpowunion: $o ).
% 3.08/1.62
% 3.08/1.62 thf(singletoninpowunion,definition,
% 3.08/1.62 ( singletoninpowunion
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(upairset2E_type,type,
% 3.08/1.62 upairset2E: $o ).
% 3.08/1.62
% 3.08/1.62 thf(upairset2E,definition,
% 3.08/1.62 ( upairset2E
% 3.08/1.62 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.08/1.62 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 3.08/1.62 => ( ( Xz = Xx )
% 3.08/1.62 | ( Xz = Xy ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(upairsubunion_type,type,
% 3.08/1.62 upairsubunion: $o ).
% 3.08/1.62
% 3.08/1.62 thf(upairsubunion,definition,
% 3.08/1.62 ( upairsubunion
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ B )
% 3.08/1.62 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(upairinpowunion_type,type,
% 3.08/1.62 upairinpowunion: $o ).
% 3.08/1.62
% 3.08/1.62 thf(upairinpowunion,definition,
% 3.08/1.62 ( upairinpowunion
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ B )
% 3.08/1.62 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(ubforcartprodlem1_type,type,
% 3.08/1.62 ubforcartprodlem1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(ubforcartprodlem1,definition,
% 3.08/1.62 ( ubforcartprodlem1
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ B )
% 3.08/1.62 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(ubforcartprodlem2_type,type,
% 3.08/1.62 ubforcartprodlem2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(ubforcartprodlem2,definition,
% 3.08/1.62 ( ubforcartprodlem2
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ B )
% 3.08/1.62 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(ubforcartprodlem3_type,type,
% 3.08/1.62 ubforcartprodlem3: $o ).
% 3.08/1.62
% 3.08/1.62 thf(ubforcartprodlem3,definition,
% 3.08/1.62 ( ubforcartprodlem3
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ B )
% 3.08/1.62 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(cartprodpairin_type,type,
% 3.08/1.62 cartprodpairin: $o ).
% 3.08/1.62
% 3.08/1.62 thf(cartprodpairin,definition,
% 3.08/1.62 ( cartprodpairin
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ B )
% 3.08/1.62 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(cartprodmempair1_type,type,
% 3.08/1.62 cartprodmempair1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(cartprodmempair1,definition,
% 3.08/1.62 ( cartprodmempair1
% 3.08/1.62 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.08/1.62 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.08/1.62 => ? [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 & ? [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ B )
% 3.08/1.62 & ( Xu
% 3.08/1.62 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(cartprodmempair_type,type,
% 3.08/1.62 cartprodmempair: $o ).
% 3.08/1.62
% 3.08/1.62 thf(cartprodmempair,definition,
% 3.08/1.62 ( cartprodmempair
% 3.08/1.62 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.08/1.62 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.08/1.62 => ( iskpair @ Xu ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setunionE2_type,type,
% 3.08/1.62 setunionE2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setunionE2,definition,
% 3.08/1.62 ( setunionE2
% 3.08/1.62 = ( ! [A: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ ( setunion @ A ) )
% 3.08/1.62 => ? [X: $i] :
% 3.08/1.62 ( ( in @ X @ A )
% 3.08/1.62 & ( in @ Xx @ X ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setunionsingleton1_type,type,
% 3.08/1.62 setunionsingleton1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setunionsingleton1,definition,
% 3.08/1.62 ( setunionsingleton1
% 3.08/1.62 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setunionsingleton2_type,type,
% 3.08/1.62 setunionsingleton2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setunionsingleton2,definition,
% 3.08/1.62 ( setunionsingleton2
% 3.08/1.62 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setunionsingleton_type,type,
% 3.08/1.62 setunionsingleton: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setunionsingleton,definition,
% 3.08/1.62 ( setunionsingleton
% 3.08/1.62 = ( ! [Xx: $i] :
% 3.08/1.62 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 3.08/1.62 = Xx ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(singleton_type,type,
% 3.08/1.62 singleton: $i > $o ).
% 3.08/1.62
% 3.08/1.62 thf(singletonprop_type,type,
% 3.08/1.62 singletonprop: $o ).
% 3.08/1.62
% 3.08/1.62 thf(singletonprop,definition,
% 3.08/1.62 ( singletonprop
% 3.08/1.62 = ( ! [A: $i,Xphi: $i > $o] :
% 3.08/1.62 ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ A )
% 3.08/1.62 => ( ( Xphi @ Xx )
% 3.08/1.62 => ( ( Xphi @ Xy )
% 3.08/1.62 => ( Xx = Xy ) ) ) ) )
% 3.08/1.62 => ( ? [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 & ( Xphi @ Xx ) )
% 3.08/1.62 => ( singleton
% 3.08/1.62 @ ( dsetconstr @ A
% 3.08/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(ex1_type,type,
% 3.08/1.62 ex1: $i > ( $i > $o ) > $o ).
% 3.08/1.62
% 3.08/1.62 thf(ex1E1_type,type,
% 3.08/1.62 ex1E1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(ex1E1,definition,
% 3.08/1.62 ( ex1E1
% 3.08/1.62 = ( ! [A: $i,Xphi: $i > $o] :
% 3.08/1.62 ( ( ex1 @ A
% 3.08/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.62 => ? [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 & ( Xphi @ Xx ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(ex1I_type,type,
% 3.08/1.62 ex1I: $o ).
% 3.08/1.62
% 3.08/1.62 thf(ex1I,definition,
% 3.08/1.62 ( ex1I
% 3.08/1.62 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ( Xphi @ Xx )
% 3.08/1.62 => ( ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ A )
% 3.08/1.62 => ( ( Xphi @ Xy )
% 3.08/1.62 => ( Xy = Xx ) ) )
% 3.08/1.62 => ( ex1 @ A
% 3.08/1.62 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(ex1I2_type,type,
% 3.08/1.62 ex1I2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(ex1I2,definition,
% 3.08/1.62 ( ex1I2
% 3.08/1.62 = ( ! [A: $i,Xphi: $i > $o] :
% 3.08/1.62 ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ A )
% 3.08/1.62 => ( ( Xphi @ Xx )
% 3.08/1.62 => ( ( Xphi @ Xy )
% 3.08/1.62 => ( Xx = Xy ) ) ) ) )
% 3.08/1.62 => ( ? [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 & ( Xphi @ Xx ) )
% 3.08/1.62 => ( ex1 @ A
% 3.08/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(singletonsuniq_type,type,
% 3.08/1.62 singletonsuniq: $o ).
% 3.08/1.62
% 3.08/1.62 thf(singletonsuniq,definition,
% 3.08/1.62 ( singletonsuniq
% 3.08/1.62 = ( ! [Xx: $i,Xy: $i] :
% 3.08/1.62 ( ( ( setadjoin @ Xx @ emptyset )
% 3.08/1.62 = ( setadjoin @ Xy @ emptyset ) )
% 3.08/1.62 => ( Xx = Xy ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(atmost1p_type,type,
% 3.08/1.62 atmost1p: $i > $o ).
% 3.08/1.62
% 3.08/1.62 thf(atleast2p_type,type,
% 3.08/1.62 atleast2p: $i > $o ).
% 3.08/1.62
% 3.08/1.62 thf(atmost2p_type,type,
% 3.08/1.62 atmost2p: $i > $o ).
% 3.08/1.62
% 3.08/1.62 thf(upairsetp_type,type,
% 3.08/1.62 upairsetp: $i > $o ).
% 3.08/1.62
% 3.08/1.62 thf(setukpairinjL1_type,type,
% 3.08/1.62 setukpairinjL1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setukpairinjL1,definition,
% 3.08/1.62 ( setukpairinjL1
% 3.08/1.62 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.08/1.62 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 3.08/1.62 => ( Xx = Xz ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(kfstsingleton_type,type,
% 3.08/1.62 kfstsingleton: $o ).
% 3.08/1.62
% 3.08/1.62 thf(kfstsingleton,definition,
% 3.08/1.62 ( kfstsingleton
% 3.08/1.62 = ( ! [Xu: $i] :
% 3.08/1.62 ( ( iskpair @ Xu )
% 3.08/1.62 => ( singleton
% 3.08/1.62 @ ( dsetconstr @ ( setunion @ Xu )
% 3.08/1.62 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(theprop_type,type,
% 3.08/1.62 theprop: $o ).
% 3.08/1.62
% 3.08/1.62 thf(theprop,definition,
% 3.08/1.62 ( theprop
% 3.08/1.62 = ( ! [X: $i] :
% 3.08/1.62 ( ( singleton @ X )
% 3.08/1.62 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(kfst_type,type,
% 3.08/1.62 kfst: $i > $i ).
% 3.08/1.62
% 3.08/1.62 thf(kfstpairEq_type,type,
% 3.08/1.62 kfstpairEq: $o ).
% 3.08/1.62
% 3.08/1.62 thf(kfstpairEq,definition,
% 3.08/1.62 ( kfstpairEq
% 3.08/1.62 = ( ! [Xx: $i,Xy: $i] :
% 3.08/1.62 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 3.08/1.62 = Xx ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(cartprodfstin_type,type,
% 3.08/1.62 cartprodfstin: $o ).
% 3.08/1.62
% 3.08/1.62 thf(cartprodfstin,definition,
% 3.08/1.62 ( cartprodfstin
% 3.08/1.62 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.08/1.62 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.08/1.62 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setukpairinjL2_type,type,
% 3.08/1.62 setukpairinjL2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setukpairinjL2,definition,
% 3.08/1.62 ( setukpairinjL2
% 3.08/1.62 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.08/1.62 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.08/1.62 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.08/1.62 => ( Xx = Xz ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setukpairinjL_type,type,
% 3.08/1.62 setukpairinjL: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setukpairinjL,definition,
% 3.08/1.62 ( setukpairinjL
% 3.08/1.62 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.08/1.62 ( ( ( kpair @ Xx @ Xy )
% 3.08/1.62 = ( kpair @ Xz @ Xu ) )
% 3.08/1.62 => ( Xx = Xz ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setukpairinjR11_type,type,
% 3.08/1.62 setukpairinjR11: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setukpairinjR11,definition,
% 3.08/1.62 ( setukpairinjR11
% 3.08/1.62 = ( ! [Xx: $i,Xy: $i] :
% 3.08/1.62 ( ( Xx = Xy )
% 3.08/1.62 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.08/1.62 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setukpairinjR12_type,type,
% 3.08/1.62 setukpairinjR12: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setukpairinjR12,definition,
% 3.08/1.62 ( setukpairinjR12
% 3.08/1.62 = ( ! [Xx: $i,Xy: $i] :
% 3.08/1.62 ( ( Xx = Xy )
% 3.08/1.62 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.08/1.62 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setukpairinjR1_type,type,
% 3.08/1.62 setukpairinjR1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setukpairinjR1,definition,
% 3.08/1.62 ( setukpairinjR1
% 3.08/1.62 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.08/1.62 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.08/1.62 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.08/1.62 => ( ( Xz = Xu )
% 3.08/1.62 => ( Xy = Xu ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(upairequniteq_type,type,
% 3.08/1.62 upairequniteq: $o ).
% 3.08/1.62
% 3.08/1.62 thf(upairequniteq,definition,
% 3.08/1.62 ( upairequniteq
% 3.08/1.62 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.08/1.62 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.08/1.62 = ( setadjoin @ Xz @ emptyset ) )
% 3.08/1.62 => ( Xx = Xy ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setukpairinjR2_type,type,
% 3.08/1.62 setukpairinjR2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setukpairinjR2,definition,
% 3.08/1.62 ( setukpairinjR2
% 3.08/1.62 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.08/1.62 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.08/1.62 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.08/1.62 => ( Xy = Xu ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setukpairinjR_type,type,
% 3.08/1.62 setukpairinjR: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setukpairinjR,definition,
% 3.08/1.62 ( setukpairinjR
% 3.08/1.62 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.08/1.62 ( ( ( kpair @ Xx @ Xy )
% 3.08/1.62 = ( kpair @ Xz @ Xu ) )
% 3.08/1.62 => ( Xy = Xu ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(ksndsingleton_type,type,
% 3.08/1.62 ksndsingleton: $o ).
% 3.08/1.62
% 3.08/1.62 thf(ksndsingleton,definition,
% 3.08/1.62 ( ksndsingleton
% 3.08/1.62 = ( ! [Xu: $i] :
% 3.08/1.62 ( ( iskpair @ Xu )
% 3.08/1.62 => ( singleton
% 3.08/1.62 @ ( dsetconstr @ ( setunion @ Xu )
% 3.08/1.62 @ ^ [Xx: $i] :
% 3.08/1.62 ( Xu
% 3.08/1.62 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(ksnd_type,type,
% 3.08/1.62 ksnd: $i > $i ).
% 3.08/1.62
% 3.08/1.62 thf(ksndpairEq_type,type,
% 3.08/1.62 ksndpairEq: $o ).
% 3.08/1.62
% 3.08/1.62 thf(ksndpairEq,definition,
% 3.08/1.62 ( ksndpairEq
% 3.08/1.62 = ( ! [Xx: $i,Xy: $i] :
% 3.08/1.62 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 3.08/1.62 = Xy ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(kpairsurjEq_type,type,
% 3.08/1.62 kpairsurjEq: $o ).
% 3.08/1.62
% 3.08/1.62 thf(kpairsurjEq,definition,
% 3.08/1.62 ( kpairsurjEq
% 3.08/1.62 = ( ! [Xu: $i] :
% 3.08/1.62 ( ( iskpair @ Xu )
% 3.08/1.62 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 3.08/1.62 = Xu ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(cartprodsndin_type,type,
% 3.08/1.62 cartprodsndin: $o ).
% 3.08/1.62
% 3.08/1.62 thf(cartprodsndin,definition,
% 3.08/1.62 ( cartprodsndin
% 3.08/1.62 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.08/1.62 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.08/1.62 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(cartprodpairmemEL_type,type,
% 3.08/1.62 cartprodpairmemEL: $o ).
% 3.08/1.62
% 3.08/1.62 thf(cartprodpairmemEL,definition,
% 3.08/1.62 ( cartprodpairmemEL
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 3.08/1.62 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 3.08/1.62 => ( in @ Xx @ A ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(cartprodpairmemER_type,type,
% 3.08/1.62 cartprodpairmemER: $o ).
% 3.08/1.62
% 3.08/1.62 thf(cartprodpairmemER,definition,
% 3.08/1.62 ( cartprodpairmemER
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 3.08/1.62 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 3.08/1.62 => ( in @ Xy @ B ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(cartprodmempaircEq_type,type,
% 3.08/1.62 cartprodmempaircEq: $o ).
% 3.08/1.62
% 3.08/1.62 thf(cartprodmempaircEq,definition,
% 3.08/1.62 ( cartprodmempaircEq
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ B )
% 3.08/1.62 => ( ( kpair @ Xx @ Xy )
% 3.08/1.62 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(cartprodfstpairEq_type,type,
% 3.08/1.62 cartprodfstpairEq: $o ).
% 3.08/1.62
% 3.08/1.62 thf(cartprodfstpairEq,definition,
% 3.08/1.62 ( cartprodfstpairEq
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ B )
% 3.08/1.62 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 3.08/1.62 = Xx ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(cartprodsndpairEq_type,type,
% 3.08/1.62 cartprodsndpairEq: $o ).
% 3.08/1.62
% 3.08/1.62 thf(cartprodsndpairEq,definition,
% 3.08/1.62 ( cartprodsndpairEq
% 3.08/1.62 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ B )
% 3.08/1.62 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 3.08/1.62 = Xy ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(cartprodpairsurjEq_type,type,
% 3.08/1.62 cartprodpairsurjEq: $o ).
% 3.08/1.62
% 3.08/1.62 thf(cartprodpairsurjEq,definition,
% 3.08/1.62 ( cartprodpairsurjEq
% 3.08/1.62 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.08/1.62 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.08/1.62 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 3.08/1.62 = Xu ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(breln_type,type,
% 3.08/1.62 breln: $i > $i > $i > $o ).
% 3.08/1.62
% 3.08/1.62 thf(breln,definition,
% 3.08/1.62 ( breln
% 3.08/1.62 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(dpsetconstr_type,type,
% 3.08/1.62 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 3.08/1.62
% 3.08/1.62 thf(dpsetconstrI_type,type,
% 3.08/1.62 dpsetconstrI: $o ).
% 3.08/1.62
% 3.08/1.62 thf(dpsetconstrI,definition,
% 3.08/1.62 ( dpsetconstrI
% 3.08/1.62 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ B )
% 3.08/1.62 => ( ( Xphi @ Xx @ Xy )
% 3.08/1.62 => ( in @ ( kpair @ Xx @ Xy )
% 3.08/1.62 @ ( dpsetconstr @ A @ B
% 3.08/1.62 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(dpsetconstrSub_type,type,
% 3.08/1.62 dpsetconstrSub: $o ).
% 3.08/1.62
% 3.08/1.62 thf(dpsetconstrSub,definition,
% 3.08/1.62 ( dpsetconstrSub
% 3.08/1.62 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.08/1.62 ( subset
% 3.08/1.62 @ ( dpsetconstr @ A @ B
% 3.08/1.62 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 3.08/1.62 @ ( cartprod @ A @ B ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setOfPairsIsBReln_type,type,
% 3.08/1.62 setOfPairsIsBReln: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setOfPairsIsBReln,definition,
% 3.08/1.62 ( setOfPairsIsBReln
% 3.08/1.62 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.08/1.62 ( breln @ A @ B
% 3.08/1.62 @ ( dpsetconstr @ A @ B
% 3.08/1.62 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(dpsetconstrERa_type,type,
% 3.08/1.62 dpsetconstrERa: $o ).
% 3.08/1.62
% 3.08/1.62 thf(dpsetconstrERa,definition,
% 3.08/1.62 ( dpsetconstrERa
% 3.08/1.62 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ B )
% 3.08/1.62 => ( ( in @ ( kpair @ Xx @ Xy )
% 3.08/1.62 @ ( dpsetconstr @ A @ B
% 3.08/1.62 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.08/1.62 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(dpsetconstrEL1_type,type,
% 3.08/1.62 dpsetconstrEL1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(dpsetconstrEL1,definition,
% 3.08/1.62 ( dpsetconstrEL1
% 3.08/1.62 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.08/1.62 ( ( in @ ( kpair @ Xx @ Xy )
% 3.08/1.62 @ ( dpsetconstr @ A @ B
% 3.08/1.62 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.08/1.62 => ( in @ Xx @ A ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(dpsetconstrEL2_type,type,
% 3.08/1.62 dpsetconstrEL2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(dpsetconstrEL2,definition,
% 3.08/1.62 ( dpsetconstrEL2
% 3.08/1.62 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.08/1.62 ( ( in @ ( kpair @ Xx @ Xy )
% 3.08/1.62 @ ( dpsetconstr @ A @ B
% 3.08/1.62 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.08/1.62 => ( in @ Xy @ B ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(dpsetconstrER_type,type,
% 3.08/1.62 dpsetconstrER: $o ).
% 3.08/1.62
% 3.08/1.62 thf(dpsetconstrER,definition,
% 3.08/1.62 ( dpsetconstrER
% 3.08/1.62 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.08/1.62 ( ( in @ ( kpair @ Xx @ Xy )
% 3.08/1.62 @ ( dpsetconstr @ A @ B
% 3.08/1.62 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.08/1.62 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(func_type,type,
% 3.08/1.62 func: $i > $i > $i > $o ).
% 3.08/1.62
% 3.08/1.62 thf(funcSet_type,type,
% 3.08/1.62 funcSet: $i > $i > $i ).
% 3.08/1.62
% 3.08/1.62 thf(funcImageSingleton_type,type,
% 3.08/1.62 funcImageSingleton: $o ).
% 3.08/1.62
% 3.08/1.62 thf(funcImageSingleton,definition,
% 3.08/1.62 ( funcImageSingleton
% 3.08/1.62 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.62 ( ( func @ A @ B @ Xf )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( singleton
% 3.08/1.62 @ ( dsetconstr @ B
% 3.08/1.62 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(apProp_type,type,
% 3.08/1.62 apProp: $o ).
% 3.08/1.62
% 3.08/1.62 thf(apProp,definition,
% 3.08/1.62 ( apProp
% 3.08/1.62 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.62 ( ( func @ A @ B @ Xf )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( in
% 3.08/1.62 @ ( setunion
% 3.08/1.62 @ ( dsetconstr @ B
% 3.08/1.62 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 3.08/1.62 @ B ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(ap_type,type,
% 3.08/1.62 ap: $i > $i > $i > $i > $i ).
% 3.08/1.62
% 3.08/1.62 thf(app_type,type,
% 3.08/1.62 app: $o ).
% 3.08/1.62
% 3.08/1.62 thf(app,definition,
% 3.08/1.62 ( app
% 3.08/1.62 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.62 ( ( func @ A @ B @ Xf )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(infuncsetfunc_type,type,
% 3.08/1.62 infuncsetfunc: $o ).
% 3.08/1.62
% 3.08/1.62 thf(infuncsetfunc,definition,
% 3.08/1.62 ( infuncsetfunc
% 3.08/1.62 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.62 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.08/1.62 => ( func @ A @ B @ Xf ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(ap2p_type,type,
% 3.08/1.62 ap2p: $o ).
% 3.08/1.62
% 3.08/1.62 thf(ap2p,definition,
% 3.08/1.62 ( ap2p
% 3.08/1.62 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.62 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(funcinfuncset_type,type,
% 3.08/1.62 funcinfuncset: $o ).
% 3.08/1.62
% 3.08/1.62 thf(funcinfuncset,definition,
% 3.08/1.62 ( funcinfuncset
% 3.08/1.62 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.62 ( ( func @ A @ B @ Xf )
% 3.08/1.62 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(lamProp_type,type,
% 3.08/1.62 lamProp: $o ).
% 3.08/1.62
% 3.08/1.62 thf(lamProp,definition,
% 3.08/1.62 ( lamProp
% 3.08/1.62 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.08/1.62 ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.08/1.62 => ( func @ A @ B
% 3.08/1.62 @ ( dpsetconstr @ A @ B
% 3.08/1.62 @ ^ [Xx: $i,Xy: $i] :
% 3.08/1.62 ( ( Xf @ Xx )
% 3.08/1.62 = Xy ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(lam_type,type,
% 3.08/1.62 lam: $i > $i > ( $i > $i ) > $i ).
% 3.08/1.62
% 3.08/1.62 thf(lamp_type,type,
% 3.08/1.62 lamp: $o ).
% 3.08/1.62
% 3.08/1.62 thf(lamp,definition,
% 3.08/1.62 ( lamp
% 3.08/1.62 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.08/1.62 ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.08/1.62 => ( func @ A @ B
% 3.08/1.62 @ ( lam @ A @ B
% 3.08/1.62 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(lam2p_type,type,
% 3.08/1.62 lam2p: $o ).
% 3.08/1.62
% 3.08/1.62 thf(lam2p,definition,
% 3.08/1.62 ( lam2p
% 3.08/1.62 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.08/1.62 ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.08/1.62 => ( in
% 3.08/1.62 @ ( lam @ A @ B
% 3.08/1.62 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 3.08/1.62 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(brelnall1_type,type,
% 3.08/1.62 brelnall1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(brelnall1,definition,
% 3.08/1.62 ( brelnall1
% 3.08/1.62 = ( ! [A: $i,B: $i,R: $i] :
% 3.08/1.62 ( ( breln @ A @ B @ R )
% 3.08/1.62 => ! [Xphi: $i > $o] :
% 3.08/1.62 ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ B )
% 3.08/1.62 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.08/1.62 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ R )
% 3.08/1.62 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(brelnall2_type,type,
% 3.08/1.62 brelnall2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(brelnall2,definition,
% 3.08/1.62 ( brelnall2
% 3.08/1.62 = ( ! [A: $i,B: $i,R: $i] :
% 3.08/1.62 ( ( breln @ A @ B @ R )
% 3.08/1.62 => ! [Xphi: $i > $o] :
% 3.08/1.62 ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ B )
% 3.08/1.62 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.08/1.62 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ R )
% 3.08/1.62 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(ex1E2_type,type,
% 3.08/1.62 ex1E2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(ex1E2,definition,
% 3.08/1.62 ( ex1E2
% 3.08/1.62 = ( ! [A: $i,Xphi: $i > $o] :
% 3.08/1.62 ( ( ex1 @ A
% 3.08/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ A )
% 3.08/1.62 => ( ( Xphi @ Xx )
% 3.08/1.62 => ( ( Xphi @ Xy )
% 3.08/1.62 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(funcGraphProp1_type,type,
% 3.08/1.62 funcGraphProp1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(funcGraphProp1,definition,
% 3.08/1.62 ( funcGraphProp1
% 3.08/1.62 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.62 ( ( func @ A @ B @ Xf )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(funcGraphProp3_type,type,
% 3.08/1.62 funcGraphProp3: $o ).
% 3.08/1.62
% 3.08/1.62 thf(funcGraphProp3,definition,
% 3.08/1.62 ( funcGraphProp3
% 3.08/1.62 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.62 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(funcGraphProp2_type,type,
% 3.08/1.62 funcGraphProp2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(funcGraphProp2,definition,
% 3.08/1.62 ( funcGraphProp2
% 3.08/1.62 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.62 ( ( func @ A @ B @ Xf )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ B )
% 3.08/1.62 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 3.08/1.62 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.08/1.62 = Xy ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(funcextLem_type,type,
% 3.08/1.62 funcextLem: $o ).
% 3.08/1.62
% 3.08/1.62 thf(funcextLem,definition,
% 3.08/1.62 ( funcextLem
% 3.08/1.62 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.62 ( ( func @ A @ B @ Xf )
% 3.08/1.62 => ! [Xg: $i] :
% 3.08/1.62 ( ( func @ A @ B @ Xg )
% 3.08/1.62 => ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.08/1.62 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ B )
% 3.08/1.62 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 3.08/1.62 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(funcGraphProp4_type,type,
% 3.08/1.62 funcGraphProp4: $o ).
% 3.08/1.62
% 3.08/1.62 thf(funcGraphProp4,definition,
% 3.08/1.62 ( funcGraphProp4
% 3.08/1.62 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.62 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ B )
% 3.08/1.62 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 3.08/1.62 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.08/1.62 = Xy ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(subbreln_type,type,
% 3.08/1.62 subbreln: $o ).
% 3.08/1.62
% 3.08/1.62 thf(subbreln,definition,
% 3.08/1.62 ( subbreln
% 3.08/1.62 = ( ! [A: $i,B: $i,R: $i] :
% 3.08/1.62 ( ( breln @ A @ B @ R )
% 3.08/1.62 => ! [S: $i] :
% 3.08/1.62 ( ( breln @ A @ B @ S )
% 3.08/1.62 => ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ B )
% 3.08/1.62 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.08/1.62 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.08/1.62 => ( subset @ R @ S ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(eqbreln_type,type,
% 3.08/1.62 eqbreln: $o ).
% 3.08/1.62
% 3.08/1.62 thf(eqbreln,definition,
% 3.08/1.62 ( eqbreln
% 3.08/1.62 = ( ! [A: $i,B: $i,R: $i] :
% 3.08/1.62 ( ( breln @ A @ B @ R )
% 3.08/1.62 => ! [S: $i] :
% 3.08/1.62 ( ( breln @ A @ B @ S )
% 3.08/1.62 => ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ B )
% 3.08/1.62 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.08/1.62 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.08/1.62 => ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ B )
% 3.08/1.62 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.08/1.62 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 3.08/1.62 => ( R = S ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(funcext_type,type,
% 3.08/1.62 funcext: $o ).
% 3.08/1.62
% 3.08/1.62 thf(funcext,definition,
% 3.08/1.62 ( funcext
% 3.08/1.62 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.62 ( ( func @ A @ B @ Xf )
% 3.08/1.62 => ! [Xg: $i] :
% 3.08/1.62 ( ( func @ A @ B @ Xg )
% 3.08/1.62 => ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.08/1.62 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.08/1.62 => ( Xf = Xg ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(funcext2_type,type,
% 3.08/1.62 funcext2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(funcext2,definition,
% 3.08/1.62 ( funcext2
% 3.08/1.62 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.62 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.08/1.62 => ! [Xg: $i] :
% 3.08/1.62 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 3.08/1.62 => ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.08/1.62 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.08/1.62 => ( Xf = Xg ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(ap2apEq1_type,type,
% 3.08/1.62 ap2apEq1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(ap2apEq1,definition,
% 3.08/1.62 ( ap2apEq1
% 3.08/1.62 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.62 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.08/1.62 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(ap2apEq2_type,type,
% 3.08/1.62 ap2apEq2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(ap2apEq2,definition,
% 3.08/1.62 ( ap2apEq2
% 3.08/1.62 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.62 ( ( func @ A @ B @ Xf )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.08/1.62 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(beta1_type,type,
% 3.08/1.62 beta1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(beta1,definition,
% 3.08/1.62 ( beta1
% 3.08/1.62 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.08/1.62 ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ( ap @ A @ B
% 3.08/1.62 @ ( lam @ A @ B
% 3.08/1.62 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 3.08/1.62 @ Xx )
% 3.08/1.62 = ( Xf @ Xx ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(eta1_type,type,
% 3.08/1.62 eta1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(eta1,definition,
% 3.08/1.62 ( eta1
% 3.08/1.62 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.62 ( ( func @ A @ B @ Xf )
% 3.08/1.62 => ( ( lam @ A @ B
% 3.08/1.62 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 3.08/1.62 = Xf ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(lam2lamEq_type,type,
% 3.08/1.62 lam2lamEq: $o ).
% 3.08/1.62
% 3.08/1.62 thf(lam2lamEq,definition,
% 3.08/1.62 ( lam2lamEq
% 3.08/1.62 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.08/1.62 ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.08/1.62 => ( ( lam @ A @ B
% 3.08/1.62 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 3.08/1.62 = ( lam @ A @ B
% 3.08/1.62 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(beta2_type,type,
% 3.08/1.62 beta2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(beta2,definition,
% 3.08/1.62 ( beta2
% 3.08/1.62 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.08/1.62 ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ( ap @ A @ B
% 3.08/1.62 @ ( lam @ A @ B
% 3.08/1.62 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 3.08/1.62 @ Xx )
% 3.08/1.62 = ( Xf @ Xx ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(eta2_type,type,
% 3.08/1.62 eta2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(eta2,definition,
% 3.08/1.62 ( eta2
% 3.08/1.62 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.62 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.08/1.62 => ( ( lam @ A @ B
% 3.08/1.62 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 3.08/1.62 = Xf ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(iffalseProp1_type,type,
% 3.08/1.62 iffalseProp1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(iffalseProp1,definition,
% 3.08/1.62 ( iffalseProp1
% 3.08/1.62 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ A )
% 3.08/1.62 => ( ~ Xphi
% 3.08/1.62 => ( in @ Xy
% 3.08/1.62 @ ( dsetconstr @ A
% 3.08/1.62 @ ^ [Xz: $i] :
% 3.08/1.62 ( ( Xphi
% 3.08/1.62 & ( Xz = Xx ) )
% 3.08/1.62 | ( ~ Xphi
% 3.08/1.62 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(iffalseProp2_type,type,
% 3.08/1.62 iffalseProp2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(iffalseProp2,definition,
% 3.08/1.62 ( iffalseProp2
% 3.08/1.62 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ A )
% 3.08/1.62 => ( ~ Xphi
% 3.08/1.62 => ( ( dsetconstr @ A
% 3.08/1.62 @ ^ [Xz: $i] :
% 3.08/1.62 ( ( Xphi
% 3.08/1.62 & ( Xz = Xx ) )
% 3.08/1.62 | ( ~ Xphi
% 3.08/1.62 & ( Xz = Xy ) ) ) )
% 3.08/1.62 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(iftrueProp1_type,type,
% 3.08/1.62 iftrueProp1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(iftrueProp1,definition,
% 3.08/1.62 ( iftrueProp1
% 3.08/1.62 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ A )
% 3.08/1.62 => ( Xphi
% 3.08/1.62 => ( in @ Xx
% 3.08/1.62 @ ( dsetconstr @ A
% 3.08/1.62 @ ^ [Xz: $i] :
% 3.08/1.62 ( ( Xphi
% 3.08/1.62 & ( Xz = Xx ) )
% 3.08/1.62 | ( ~ Xphi
% 3.08/1.62 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(iftrueProp2_type,type,
% 3.08/1.62 iftrueProp2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(iftrueProp2,definition,
% 3.08/1.62 ( iftrueProp2
% 3.08/1.62 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ A )
% 3.08/1.62 => ( Xphi
% 3.08/1.62 => ( ( dsetconstr @ A
% 3.08/1.62 @ ^ [Xz: $i] :
% 3.08/1.62 ( ( Xphi
% 3.08/1.62 & ( Xz = Xx ) )
% 3.08/1.62 | ( ~ Xphi
% 3.08/1.62 & ( Xz = Xy ) ) ) )
% 3.08/1.62 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(ifSingleton_type,type,
% 3.08/1.62 ifSingleton: $o ).
% 3.08/1.62
% 3.08/1.62 thf(ifSingleton,definition,
% 3.08/1.62 ( ifSingleton
% 3.08/1.62 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ A )
% 3.08/1.62 => ( singleton
% 3.08/1.62 @ ( dsetconstr @ A
% 3.08/1.62 @ ^ [Xz: $i] :
% 3.08/1.62 ( ( Xphi
% 3.08/1.62 & ( Xz = Xx ) )
% 3.08/1.62 | ( ~ Xphi
% 3.08/1.62 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(if_type,type,
% 3.08/1.62 if: $i > $o > $i > $i > $i ).
% 3.08/1.62
% 3.08/1.62 thf(ifp_type,type,
% 3.08/1.62 ifp: $o ).
% 3.08/1.62
% 3.08/1.62 thf(ifp,definition,
% 3.08/1.62 ( ifp
% 3.08/1.62 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ A )
% 3.08/1.62 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(theeq_type,type,
% 3.08/1.62 theeq: $o ).
% 3.08/1.62
% 3.08/1.62 thf(theeq,definition,
% 3.08/1.62 ( theeq
% 3.08/1.62 = ( ! [X: $i] :
% 3.08/1.62 ( ( singleton @ X )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ X )
% 3.08/1.62 => ( ( setunion @ X )
% 3.08/1.62 = Xx ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(iftrue_type,type,
% 3.08/1.62 iftrue: $o ).
% 3.08/1.62
% 3.08/1.62 thf(iftrue,definition,
% 3.08/1.62 ( iftrue
% 3.08/1.62 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ A )
% 3.08/1.62 => ( Xphi
% 3.08/1.62 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 3.08/1.62 = Xx ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(iffalse_type,type,
% 3.08/1.62 iffalse: $o ).
% 3.08/1.62
% 3.08/1.62 thf(iffalse,definition,
% 3.08/1.62 ( iffalse
% 3.08/1.62 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ A )
% 3.08/1.62 => ( ~ Xphi
% 3.08/1.62 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 3.08/1.62 = Xy ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(iftrueorfalse_type,type,
% 3.08/1.62 iftrueorfalse: $o ).
% 3.08/1.62
% 3.08/1.62 thf(iftrueorfalse,definition,
% 3.08/1.62 ( iftrueorfalse
% 3.08/1.62 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ A )
% 3.08/1.62 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(binintersectT_lem_type,type,
% 3.08/1.62 binintersectT_lem: $o ).
% 3.08/1.62
% 3.08/1.62 thf(binintersectT_lem,definition,
% 3.08/1.62 ( binintersectT_lem
% 3.08/1.62 = ( ! [A: $i,X: $i] :
% 3.08/1.62 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.62 => ! [Y: $i] :
% 3.08/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.62 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(binunionT_lem_type,type,
% 3.08/1.62 binunionT_lem: $o ).
% 3.08/1.62
% 3.08/1.62 thf(binunionT_lem,definition,
% 3.08/1.62 ( binunionT_lem
% 3.08/1.62 = ( ! [A: $i,X: $i] :
% 3.08/1.62 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.62 => ! [Y: $i] :
% 3.08/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.62 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(powersetT_lem_type,type,
% 3.08/1.62 powersetT_lem: $o ).
% 3.08/1.62
% 3.08/1.62 thf(powersetT_lem,definition,
% 3.08/1.62 ( powersetT_lem
% 3.08/1.62 = ( ! [A: $i,X: $i] :
% 3.08/1.62 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.62 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setminusT_lem_type,type,
% 3.08/1.62 setminusT_lem: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setminusT_lem,definition,
% 3.08/1.62 ( setminusT_lem
% 3.08/1.62 = ( ! [A: $i,X: $i] :
% 3.08/1.62 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.62 => ! [Y: $i] :
% 3.08/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.62 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(complementT_lem_type,type,
% 3.08/1.62 complementT_lem: $o ).
% 3.08/1.62
% 3.08/1.62 thf(complementT_lem,definition,
% 3.08/1.62 ( complementT_lem
% 3.08/1.62 = ( ! [A: $i,X: $i] :
% 3.08/1.62 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.62 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(setextT_type,type,
% 3.08/1.62 setextT: $o ).
% 3.08/1.62
% 3.08/1.62 thf(setextT,definition,
% 3.08/1.62 ( setextT
% 3.08/1.62 = ( ! [A: $i,X: $i] :
% 3.08/1.62 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.62 => ! [Y: $i] :
% 3.08/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.62 => ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ( in @ Xx @ X )
% 3.08/1.62 => ( in @ Xx @ Y ) ) )
% 3.08/1.62 => ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ( in @ Xx @ Y )
% 3.08/1.62 => ( in @ Xx @ X ) ) )
% 3.08/1.62 => ( X = Y ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(subsetTI_type,type,
% 3.08/1.62 subsetTI: $o ).
% 3.08/1.62
% 3.08/1.62 thf(subsetTI,definition,
% 3.08/1.62 ( subsetTI
% 3.08/1.62 = ( ! [A: $i,X: $i] :
% 3.08/1.62 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.62 => ! [Y: $i] :
% 3.08/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.62 => ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ( in @ Xx @ X )
% 3.08/1.62 => ( in @ Xx @ Y ) ) )
% 3.08/1.62 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(powersetTI1_type,type,
% 3.08/1.62 powersetTI1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(powersetTI1,definition,
% 3.08/1.62 ( powersetTI1
% 3.08/1.62 = ( ! [A: $i,X: $i] :
% 3.08/1.62 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.62 => ! [Y: $i] :
% 3.08/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.62 => ( ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ( in @ Xx @ X )
% 3.08/1.62 => ( in @ Xx @ Y ) ) )
% 3.08/1.62 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(powersetTE1_type,type,
% 3.08/1.62 powersetTE1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(powersetTE1,definition,
% 3.08/1.62 ( powersetTE1
% 3.08/1.62 = ( ! [A: $i,X: $i] :
% 3.08/1.62 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.62 => ! [Y: $i] :
% 3.08/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ( in @ X @ ( powerset @ Y ) )
% 3.08/1.62 => ( ( in @ Xx @ X )
% 3.08/1.62 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(complementTI1_type,type,
% 3.08/1.62 complementTI1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(complementTI1,definition,
% 3.08/1.62 ( complementTI1
% 3.08/1.62 = ( ! [A: $i,X: $i] :
% 3.08/1.62 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ( in @ Xx @ X )
% 3.08/1.62 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(complementTE1_type,type,
% 3.08/1.62 complementTE1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(complementTE1,definition,
% 3.08/1.62 ( complementTE1
% 3.08/1.62 = ( ! [A: $i,X: $i] :
% 3.08/1.62 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 3.08/1.62 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(binintersectTELcontra_type,type,
% 3.08/1.62 binintersectTELcontra: $o ).
% 3.08/1.62
% 3.08/1.62 thf(binintersectTELcontra,definition,
% 3.08/1.62 ( binintersectTELcontra
% 3.08/1.62 = ( ! [A: $i,X: $i] :
% 3.08/1.62 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.62 => ! [Y: $i] :
% 3.08/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ~ ( in @ Xx @ X )
% 3.08/1.62 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(binintersectTERcontra_type,type,
% 3.08/1.62 binintersectTERcontra: $o ).
% 3.08/1.62
% 3.08/1.62 thf(binintersectTERcontra,definition,
% 3.08/1.62 ( binintersectTERcontra
% 3.08/1.62 = ( ! [A: $i,X: $i] :
% 3.08/1.62 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.62 => ! [Y: $i] :
% 3.08/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ~ ( in @ Xx @ Y )
% 3.08/1.62 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(contrasubsetT_type,type,
% 3.08/1.62 contrasubsetT: $o ).
% 3.08/1.62
% 3.08/1.62 thf(contrasubsetT,definition,
% 3.08/1.62 ( contrasubsetT
% 3.08/1.62 = ( ! [A: $i,X: $i] :
% 3.08/1.62 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.62 => ! [Y: $i] :
% 3.08/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.08/1.62 => ( ( in @ Xx @ Y )
% 3.08/1.62 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(contrasubsetT1_type,type,
% 3.08/1.62 contrasubsetT1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(contrasubsetT1,definition,
% 3.08/1.62 ( contrasubsetT1
% 3.08/1.62 = ( ! [A: $i,X: $i] :
% 3.08/1.62 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.62 => ! [Y: $i] :
% 3.08/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ( subset @ X @ Y )
% 3.08/1.62 => ( ~ ( in @ Xx @ Y )
% 3.08/1.62 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(contrasubsetT2_type,type,
% 3.08/1.62 contrasubsetT2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(contrasubsetT2,definition,
% 3.08/1.62 ( contrasubsetT2
% 3.08/1.62 = ( ! [A: $i,X: $i] :
% 3.08/1.62 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.62 => ! [Y: $i] :
% 3.08/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.62 => ( ( subset @ X @ Y )
% 3.08/1.62 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(contrasubsetT3_type,type,
% 3.08/1.62 contrasubsetT3: $o ).
% 3.08/1.62
% 3.08/1.62 thf(contrasubsetT3,definition,
% 3.08/1.62 ( contrasubsetT3
% 3.08/1.62 = ( ! [A: $i,X: $i] :
% 3.08/1.62 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.62 => ! [Y: $i] :
% 3.08/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.62 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 3.08/1.62 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(doubleComplementI1_type,type,
% 3.08/1.62 doubleComplementI1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(doubleComplementI1,definition,
% 3.08/1.62 ( doubleComplementI1
% 3.08/1.62 = ( ! [A: $i,X: $i] :
% 3.08/1.62 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ( in @ Xx @ X )
% 3.08/1.62 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(doubleComplementE1_type,type,
% 3.08/1.62 doubleComplementE1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(doubleComplementE1,definition,
% 3.08/1.62 ( doubleComplementE1
% 3.08/1.62 = ( ! [A: $i,X: $i] :
% 3.08/1.62 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 3.08/1.62 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(doubleComplementSub1_type,type,
% 3.08/1.62 doubleComplementSub1: $o ).
% 3.08/1.62
% 3.08/1.62 thf(doubleComplementSub1,definition,
% 3.08/1.62 ( doubleComplementSub1
% 3.08/1.62 = ( ! [A: $i,X: $i] :
% 3.08/1.62 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.62 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(doubleComplementSub2_type,type,
% 3.08/1.62 doubleComplementSub2: $o ).
% 3.08/1.62
% 3.08/1.62 thf(doubleComplementSub2,definition,
% 3.08/1.62 ( doubleComplementSub2
% 3.08/1.62 = ( ! [A: $i,X: $i] :
% 3.08/1.62 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.62 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(doubleComplementEq_type,type,
% 3.08/1.62 doubleComplementEq: $o ).
% 3.08/1.62
% 3.08/1.62 thf(doubleComplementEq,definition,
% 3.08/1.62 ( doubleComplementEq
% 3.08/1.62 = ( ! [A: $i,X: $i] :
% 3.08/1.62 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.62 => ( X
% 3.08/1.62 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(complementTnotintersectT_type,type,
% 3.08/1.62 complementTnotintersectT: $o ).
% 3.08/1.62
% 3.08/1.62 thf(complementTnotintersectT,definition,
% 3.08/1.62 ( complementTnotintersectT
% 3.08/1.62 = ( ! [A: $i,X: $i] :
% 3.08/1.62 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.62 => ! [Y: $i] :
% 3.08/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.08/1.62 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(complementImpComplementIntersect_type,type,
% 3.08/1.62 complementImpComplementIntersect: $o ).
% 3.08/1.62
% 3.08/1.62 thf(complementImpComplementIntersect,definition,
% 3.08/1.62 ( complementImpComplementIntersect
% 3.08/1.62 = ( ! [A: $i,X: $i] :
% 3.08/1.62 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.62 => ! [Y: $i] :
% 3.08/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.08/1.62 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(complementSubsetComplementIntersect_type,type,
% 3.08/1.62 complementSubsetComplementIntersect: $o ).
% 3.08/1.62
% 3.08/1.62 thf(complementSubsetComplementIntersect,definition,
% 3.08/1.62 ( complementSubsetComplementIntersect
% 3.08/1.62 = ( ! [A: $i,X: $i] :
% 3.08/1.62 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.62 => ! [Y: $i] :
% 3.08/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.62 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(complementInPowersetComplementIntersect_type,type,
% 3.08/1.62 complementInPowersetComplementIntersect: $o ).
% 3.08/1.62
% 3.08/1.62 thf(complementInPowersetComplementIntersect,definition,
% 3.08/1.62 ( complementInPowersetComplementIntersect
% 3.08/1.62 = ( ! [A: $i,X: $i] :
% 3.08/1.62 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.62 => ! [Y: $i] :
% 3.08/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.62 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(contraSubsetComplement_type,type,
% 3.08/1.62 contraSubsetComplement: $o ).
% 3.08/1.62
% 3.08/1.62 thf(contraSubsetComplement,definition,
% 3.08/1.62 ( contraSubsetComplement
% 3.08/1.62 = ( ! [A: $i,X: $i] :
% 3.08/1.62 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.62 => ! [Y: $i] :
% 3.08/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.62 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ( ( in @ Xx @ Y )
% 3.08/1.62 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(complementTcontraSubset_type,type,
% 3.08/1.62 complementTcontraSubset: $o ).
% 3.08/1.62
% 3.08/1.62 thf(complementTcontraSubset,definition,
% 3.08/1.62 ( complementTcontraSubset
% 3.08/1.62 = ( ! [A: $i,X: $i] :
% 3.08/1.62 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.62 => ! [Y: $i] :
% 3.08/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.62 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.08/1.62 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.08/1.62
% 3.08/1.62 thf(binunionTILcontra_type,type,
% 3.08/1.62 binunionTILcontra: $o ).
% 3.08/1.62
% 3.08/1.62 thf(binunionTILcontra,definition,
% 3.08/1.62 ( binunionTILcontra
% 3.08/1.62 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ A )
% 3.08/1.63 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.08/1.63 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(binunionTIRcontra_type,type,
% 3.08/1.63 binunionTIRcontra: $o ).
% 3.08/1.63
% 3.08/1.63 thf(binunionTIRcontra,definition,
% 3.08/1.63 ( binunionTIRcontra
% 3.08/1.63 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ A )
% 3.08/1.63 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.08/1.63 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(inIntersectImpInUnion_type,type,
% 3.08/1.63 inIntersectImpInUnion: $o ).
% 3.08/1.63
% 3.08/1.63 thf(inIntersectImpInUnion,definition,
% 3.08/1.63 ( inIntersectImpInUnion
% 3.08/1.63 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ! [Z: $i] :
% 3.08/1.63 ( ( in @ Z @ ( powerset @ A ) )
% 3.08/1.63 => ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ A )
% 3.08/1.63 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.08/1.63 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(inIntersectImpInUnion2_type,type,
% 3.08/1.63 inIntersectImpInUnion2: $o ).
% 3.08/1.63
% 3.08/1.63 thf(inIntersectImpInUnion2,definition,
% 3.08/1.63 ( inIntersectImpInUnion2
% 3.08/1.63 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ! [Z: $i] :
% 3.08/1.63 ( ( in @ Z @ ( powerset @ A ) )
% 3.08/1.63 => ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ A )
% 3.08/1.63 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.08/1.63 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(inIntersectImpInIntersectUnions_type,type,
% 3.08/1.63 inIntersectImpInIntersectUnions: $o ).
% 3.08/1.63
% 3.08/1.63 thf(inIntersectImpInIntersectUnions,definition,
% 3.08/1.63 ( inIntersectImpInIntersectUnions
% 3.08/1.63 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ! [Z: $i] :
% 3.08/1.63 ( ( in @ Z @ ( powerset @ A ) )
% 3.08/1.63 => ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ A )
% 3.08/1.63 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.08/1.63 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(intersectInPowersetIntersectUnions_type,type,
% 3.08/1.63 intersectInPowersetIntersectUnions: $o ).
% 3.08/1.63
% 3.08/1.63 thf(intersectInPowersetIntersectUnions,definition,
% 3.08/1.63 ( intersectInPowersetIntersectUnions
% 3.08/1.63 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ! [Z: $i] :
% 3.08/1.63 ( ( in @ Z @ ( powerset @ A ) )
% 3.08/1.63 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(inComplementUnionImpNotIn1_type,type,
% 3.08/1.63 inComplementUnionImpNotIn1: $o ).
% 3.08/1.63
% 3.08/1.63 thf(inComplementUnionImpNotIn1,definition,
% 3.08/1.63 ( inComplementUnionImpNotIn1
% 3.08/1.63 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ A )
% 3.08/1.63 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.08/1.63 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(inComplementUnionImpInComplement1_type,type,
% 3.08/1.63 inComplementUnionImpInComplement1: $o ).
% 3.08/1.63
% 3.08/1.63 thf(inComplementUnionImpInComplement1,definition,
% 3.08/1.63 ( inComplementUnionImpInComplement1
% 3.08/1.63 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ A )
% 3.08/1.63 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.08/1.63 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(binunionTE_type,type,
% 3.08/1.63 binunionTE: $o ).
% 3.08/1.63
% 3.08/1.63 thf(binunionTE,definition,
% 3.08/1.63 ( binunionTE
% 3.08/1.63 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ! [Xphi: $o,Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ A )
% 3.08/1.63 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.08/1.63 => ( ( ( in @ Xx @ X )
% 3.08/1.63 => Xphi )
% 3.08/1.63 => ( ( ( in @ Xx @ Y )
% 3.08/1.63 => Xphi )
% 3.08/1.63 => Xphi ) ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(binunionTEcontra_type,type,
% 3.08/1.63 binunionTEcontra: $o ).
% 3.08/1.63
% 3.08/1.63 thf(binunionTEcontra,definition,
% 3.08/1.63 ( binunionTEcontra
% 3.08/1.63 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ A )
% 3.08/1.63 => ( ~ ( in @ Xx @ X )
% 3.08/1.63 => ( ~ ( in @ Xx @ Y )
% 3.08/1.63 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(demorgan2a1_type,type,
% 3.08/1.63 demorgan2a1: $o ).
% 3.08/1.63
% 3.08/1.63 thf(demorgan2a1,definition,
% 3.08/1.63 ( demorgan2a1
% 3.08/1.63 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ A )
% 3.08/1.63 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.08/1.63 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(complementUnionInPowersetComplement_type,type,
% 3.08/1.63 complementUnionInPowersetComplement: $o ).
% 3.08/1.63
% 3.08/1.63 thf(complementUnionInPowersetComplement,definition,
% 3.08/1.63 ( complementUnionInPowersetComplement
% 3.08/1.63 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(demorgan2a2_type,type,
% 3.08/1.63 demorgan2a2: $o ).
% 3.08/1.63
% 3.08/1.63 thf(demorgan2a2,definition,
% 3.08/1.63 ( demorgan2a2
% 3.08/1.63 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ A )
% 3.08/1.63 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.08/1.63 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(demorgan1a_type,type,
% 3.08/1.63 demorgan1a: $o ).
% 3.08/1.63
% 3.08/1.63 thf(demorgan1a,definition,
% 3.08/1.63 ( demorgan1a
% 3.08/1.63 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ A )
% 3.08/1.63 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 3.08/1.63 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(demorgan1b_type,type,
% 3.08/1.63 demorgan1b: $o ).
% 3.08/1.63
% 3.08/1.63 thf(demorgan1b,definition,
% 3.08/1.63 ( demorgan1b
% 3.08/1.63 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ A )
% 3.08/1.63 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 3.08/1.63 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(demorgan1_type,type,
% 3.08/1.63 demorgan1: $o ).
% 3.08/1.63
% 3.08/1.63 thf(demorgan1,definition,
% 3.08/1.63 ( demorgan1
% 3.08/1.63 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 3.08/1.63 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(demorgan2a_type,type,
% 3.08/1.63 demorgan2a: $o ).
% 3.08/1.63
% 3.08/1.63 thf(demorgan2a,definition,
% 3.08/1.63 ( demorgan2a
% 3.08/1.63 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ A )
% 3.08/1.63 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.08/1.63 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(demorgan2b2_type,type,
% 3.08/1.63 demorgan2b2: $o ).
% 3.08/1.63
% 3.08/1.63 thf(demorgan2b2,definition,
% 3.08/1.63 ( demorgan2b2
% 3.08/1.63 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ A )
% 3.08/1.63 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.08/1.63 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 3.08/1.63 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(demorgan2b_type,type,
% 3.08/1.63 demorgan2b: $o ).
% 3.08/1.63
% 3.08/1.63 thf(demorgan2b,definition,
% 3.08/1.63 ( demorgan2b
% 3.08/1.63 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ A )
% 3.08/1.63 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 3.08/1.63 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(demorgan2_type,type,
% 3.08/1.63 demorgan2: $o ).
% 3.08/1.63
% 3.08/1.63 thf(demorgan2,definition,
% 3.08/1.63 ( demorgan2
% 3.08/1.63 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 3.08/1.63 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(woz13rule0_type,type,
% 3.08/1.63 woz13rule0: $o ).
% 3.08/1.63
% 3.08/1.63 thf(woz13rule0,definition,
% 3.08/1.63 ( woz13rule0
% 3.08/1.63 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.08/1.63 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(woz13rule1_type,type,
% 3.08/1.63 woz13rule1: $o ).
% 3.08/1.63
% 3.08/1.63 thf(woz13rule1,definition,
% 3.08/1.63 ( woz13rule1
% 3.08/1.63 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ! [Z: $i] :
% 3.08/1.63 ( ( in @ Z @ ( powerset @ A ) )
% 3.08/1.63 => ( ( subset @ X @ Z )
% 3.08/1.63 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(woz13rule2_type,type,
% 3.08/1.63 woz13rule2: $o ).
% 3.08/1.63
% 3.08/1.63 thf(woz13rule2,definition,
% 3.08/1.63 ( woz13rule2
% 3.08/1.63 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ! [Z: $i] :
% 3.08/1.63 ( ( in @ Z @ ( powerset @ A ) )
% 3.08/1.63 => ( ( subset @ Y @ Z )
% 3.08/1.63 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(woz13rule3_type,type,
% 3.08/1.63 woz13rule3: $o ).
% 3.08/1.63
% 3.08/1.63 thf(woz13rule3,definition,
% 3.08/1.63 ( woz13rule3
% 3.08/1.63 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ! [Z: $i] :
% 3.08/1.63 ( ( in @ Z @ ( powerset @ A ) )
% 3.08/1.63 => ( ( subset @ X @ Y )
% 3.08/1.63 => ( ( subset @ X @ Z )
% 3.08/1.63 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(woz13rule4_type,type,
% 3.08/1.63 woz13rule4: $o ).
% 3.08/1.63
% 3.08/1.63 thf(woz13rule4,definition,
% 3.08/1.63 ( woz13rule4
% 3.08/1.63 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ! [Z: $i] :
% 3.08/1.63 ( ( in @ Z @ ( powerset @ A ) )
% 3.08/1.63 => ! [W: $i] :
% 3.08/1.63 ( ( in @ W @ ( powerset @ A ) )
% 3.08/1.63 => ( ( subset @ X @ Z )
% 3.08/1.63 => ( ( subset @ Y @ W )
% 3.08/1.63 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(woz1_1_type,type,
% 3.08/1.63 woz1_1: $o ).
% 3.08/1.63
% 3.08/1.63 thf(woz1_1,definition,
% 3.08/1.63 ( woz1_1
% 3.08/1.63 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(woz1_2_type,type,
% 3.08/1.63 woz1_2: $o ).
% 3.08/1.63
% 3.08/1.63 thf(woz1_2,definition,
% 3.08/1.63 ( woz1_2
% 3.08/1.63 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ! [Z: $i] :
% 3.08/1.63 ( ( in @ Z @ ( powerset @ A ) )
% 3.08/1.63 => ! [W: $i] :
% 3.08/1.63 ( ( in @ W @ ( powerset @ A ) )
% 3.08/1.63 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 3.08/1.63 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(woz1_3_type,type,
% 3.08/1.63 woz1_3: $o ).
% 3.08/1.63
% 3.08/1.63 thf(woz1_3,definition,
% 3.08/1.63 ( woz1_3
% 3.08/1.63 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ! [Z: $i] :
% 3.08/1.63 ( ( in @ Z @ ( powerset @ A ) )
% 3.08/1.63 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(woz1_4_type,type,
% 3.08/1.63 woz1_4: $o ).
% 3.08/1.63
% 3.08/1.63 thf(woz1_4,definition,
% 3.08/1.63 ( woz1_4
% 3.08/1.63 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.08/1.63 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(woz1_5_type,type,
% 3.08/1.63 woz1_5: $o ).
% 3.08/1.63
% 3.08/1.63 thf(woz1_5,definition,
% 3.08/1.63 ( woz1_5
% 3.08/1.63 = ( ! [A: $i,X: $i] :
% 3.08/1.63 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.63 => ! [Y: $i] :
% 3.08/1.63 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.63 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(breln1_type,type,
% 3.08/1.63 breln1: $i > $i > $o ).
% 3.08/1.63
% 3.08/1.63 thf(breln1,definition,
% 3.08/1.63 ( breln1
% 3.08/1.63 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(breln1all2_type,type,
% 3.08/1.63 breln1all2: $o ).
% 3.08/1.63
% 3.08/1.63 thf(breln1all2,definition,
% 3.08/1.63 ( breln1all2
% 3.08/1.63 = ( ! [A: $i,R: $i] :
% 3.08/1.63 ( ( breln1 @ A @ R )
% 3.08/1.63 => ! [Xphi: $i > $o] :
% 3.08/1.63 ( ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ A )
% 3.08/1.63 => ! [Xy: $i] :
% 3.08/1.63 ( ( in @ Xy @ A )
% 3.08/1.63 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.08/1.63 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.08/1.63 => ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ R )
% 3.08/1.63 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(breln1Set_type,type,
% 3.08/1.63 breln1Set: $i > $i ).
% 3.08/1.63
% 3.08/1.63 thf(breln1SetBreln1_type,type,
% 3.08/1.63 breln1SetBreln1: $o ).
% 3.08/1.63
% 3.08/1.63 thf(breln1SetBreln1,definition,
% 3.08/1.63 ( breln1SetBreln1
% 3.08/1.63 = ( ! [A: $i,R: $i] :
% 3.08/1.63 ( ( in @ R @ ( breln1Set @ A ) )
% 3.08/1.63 => ( breln1 @ A @ R ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(transitive_type,type,
% 3.08/1.63 transitive: $i > $i > $o ).
% 3.08/1.63
% 3.08/1.63 thf(antisymmetric_type,type,
% 3.08/1.63 antisymmetric: $i > $i > $o ).
% 3.08/1.63
% 3.08/1.63 thf(reflexive_type,type,
% 3.08/1.63 reflexive: $i > $i > $o ).
% 3.08/1.63
% 3.08/1.63 thf(refltransitive_type,type,
% 3.08/1.63 refltransitive: $i > $i > $o ).
% 3.08/1.63
% 3.08/1.63 thf(refllinearorder_type,type,
% 3.08/1.63 refllinearorder: $i > $i > $o ).
% 3.08/1.63
% 3.08/1.63 thf(reflwellordering_type,type,
% 3.08/1.63 reflwellordering: $i > $i > $o ).
% 3.08/1.63
% 3.08/1.63 thf(choice2fnsingleton_type,type,
% 3.08/1.63 choice2fnsingleton: $o ).
% 3.08/1.63
% 3.08/1.63 thf(choice2fnsingleton,definition,
% 3.08/1.63 ( choice2fnsingleton
% 3.08/1.63 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.08/1.63 ( ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ A )
% 3.08/1.63 => ? [Xy: $i] :
% 3.08/1.63 ( ( in @ Xy @ B )
% 3.08/1.63 & ( Xphi @ Xx @ Xy ) ) )
% 3.08/1.63 => ! [R: $i] :
% 3.08/1.63 ( ( in @ R @ ( breln1Set @ B ) )
% 3.08/1.63 => ( ( reflwellordering @ B @ R )
% 3.08/1.63 => ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ A )
% 3.08/1.63 => ( singleton
% 3.08/1.63 @ ( dsetconstr @ B
% 3.08/1.63 @ ^ [Xy: $i] :
% 3.08/1.63 ( ( Xphi @ Xx @ Xy )
% 3.08/1.63 & ! [Xz: $i] :
% 3.08/1.63 ( ( in @ Xz @ B )
% 3.08/1.63 => ( ( Xphi @ Xx @ Xz )
% 3.08/1.63 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(setOfPairsIsBReln1_type,type,
% 3.08/1.63 setOfPairsIsBReln1: $o ).
% 3.08/1.63
% 3.08/1.63 thf(setOfPairsIsBReln1,definition,
% 3.08/1.63 ( setOfPairsIsBReln1
% 3.08/1.63 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 3.08/1.63 ( breln1 @ A
% 3.08/1.63 @ ( dpsetconstr @ A @ A
% 3.08/1.63 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(breln1all1_type,type,
% 3.08/1.63 breln1all1: $o ).
% 3.08/1.63
% 3.08/1.63 thf(breln1all1,definition,
% 3.08/1.63 ( breln1all1
% 3.08/1.63 = ( ! [A: $i,R: $i] :
% 3.08/1.63 ( ( breln1 @ A @ R )
% 3.08/1.63 => ! [Xphi: $i > $o] :
% 3.08/1.63 ( ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ A )
% 3.08/1.63 => ! [Xy: $i] :
% 3.08/1.63 ( ( in @ Xy @ A )
% 3.08/1.63 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.08/1.63 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.08/1.63 => ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ R )
% 3.08/1.63 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(subbreln1_type,type,
% 3.08/1.63 subbreln1: $o ).
% 3.08/1.63
% 3.08/1.63 thf(subbreln1,definition,
% 3.08/1.63 ( subbreln1
% 3.08/1.63 = ( ! [A: $i,R: $i] :
% 3.08/1.63 ( ( breln1 @ A @ R )
% 3.08/1.63 => ! [S: $i] :
% 3.08/1.63 ( ( breln1 @ A @ S )
% 3.08/1.63 => ( ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ A )
% 3.08/1.63 => ! [Xy: $i] :
% 3.08/1.63 ( ( in @ Xy @ A )
% 3.08/1.63 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.08/1.63 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.08/1.63 => ( subset @ R @ S ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(eqbreln1_type,type,
% 3.08/1.63 eqbreln1: $o ).
% 3.08/1.63
% 3.08/1.63 thf(eqbreln1,definition,
% 3.08/1.63 ( eqbreln1
% 3.08/1.63 = ( ! [A: $i,R: $i] :
% 3.08/1.63 ( ( breln1 @ A @ R )
% 3.08/1.63 => ! [S: $i] :
% 3.08/1.63 ( ( breln1 @ A @ S )
% 3.08/1.63 => ( ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ A )
% 3.08/1.63 => ! [Xy: $i] :
% 3.08/1.63 ( ( in @ Xy @ A )
% 3.08/1.63 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.08/1.63 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.08/1.63 => ( ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ A )
% 3.08/1.63 => ! [Xy: $i] :
% 3.08/1.63 ( ( in @ Xy @ A )
% 3.08/1.63 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.08/1.63 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 3.08/1.63 => ( R = S ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(breln1invset_type,type,
% 3.08/1.63 breln1invset: $i > $i > $i ).
% 3.08/1.63
% 3.08/1.63 thf(breln1invprop_type,type,
% 3.08/1.63 breln1invprop: $o ).
% 3.08/1.63
% 3.08/1.63 thf(breln1invprop,definition,
% 3.08/1.63 ( breln1invprop
% 3.08/1.63 = ( ! [A: $i,R: $i] :
% 3.08/1.63 ( ( breln1 @ A @ R )
% 3.08/1.63 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(breln1invI_type,type,
% 3.08/1.63 breln1invI: $o ).
% 3.08/1.63
% 3.08/1.63 thf(breln1invI,definition,
% 3.08/1.63 ( breln1invI
% 3.08/1.63 = ( ! [A: $i,R: $i] :
% 3.08/1.63 ( ( breln1 @ A @ R )
% 3.08/1.63 => ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ A )
% 3.08/1.63 => ! [Xy: $i] :
% 3.08/1.63 ( ( in @ Xy @ A )
% 3.08/1.63 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.08/1.63 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(breln1invE_type,type,
% 3.08/1.63 breln1invE: $o ).
% 3.08/1.63
% 3.08/1.63 thf(breln1invE,definition,
% 3.08/1.63 ( breln1invE
% 3.08/1.63 = ( ! [A: $i,R: $i] :
% 3.08/1.63 ( ( breln1 @ A @ R )
% 3.08/1.63 => ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ A )
% 3.08/1.63 => ! [Xy: $i] :
% 3.08/1.63 ( ( in @ Xy @ A )
% 3.08/1.63 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 3.08/1.63 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(breln1compset_type,type,
% 3.08/1.63 breln1compset: $i > $i > $i > $i ).
% 3.08/1.63
% 3.08/1.63 thf(breln1compprop_type,type,
% 3.08/1.63 breln1compprop: $o ).
% 3.08/1.63
% 3.08/1.63 thf(breln1compprop,definition,
% 3.08/1.63 ( breln1compprop
% 3.08/1.63 = ( ! [A: $i,R: $i] :
% 3.08/1.63 ( ( breln1 @ A @ R )
% 3.08/1.63 => ! [S: $i] :
% 3.08/1.63 ( ( breln1 @ A @ S )
% 3.08/1.63 => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(breln1compI_type,type,
% 3.08/1.63 breln1compI: $o ).
% 3.08/1.63
% 3.08/1.63 thf(breln1compI,definition,
% 3.08/1.63 ( breln1compI
% 3.08/1.63 = ( ! [A: $i,R: $i] :
% 3.08/1.63 ( ( breln1 @ A @ R )
% 3.08/1.63 => ! [S: $i] :
% 3.08/1.63 ( ( breln1 @ A @ S )
% 3.08/1.63 => ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ A )
% 3.08/1.63 => ! [Xy: $i] :
% 3.08/1.63 ( ( in @ Xy @ A )
% 3.08/1.63 => ! [Xz: $i] :
% 3.08/1.63 ( ( in @ Xz @ A )
% 3.08/1.63 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 3.08/1.63 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 3.08/1.63 => ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(breln1compE_type,type,
% 3.08/1.63 breln1compE: $o ).
% 3.08/1.63
% 3.08/1.63 thf(breln1compE,definition,
% 3.08/1.63 ( breln1compE
% 3.08/1.63 = ( ! [A: $i,R: $i] :
% 3.08/1.63 ( ( breln1 @ A @ R )
% 3.08/1.63 => ! [S: $i] :
% 3.08/1.63 ( ( breln1 @ A @ S )
% 3.08/1.63 => ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ A )
% 3.08/1.63 => ! [Xy: $i] :
% 3.08/1.63 ( ( in @ Xy @ A )
% 3.08/1.63 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 3.08/1.63 => ? [Xz: $i] :
% 3.08/1.63 ( ( in @ Xz @ A )
% 3.08/1.63 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 3.08/1.63 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 3.08/1.63
% 3.08/1.63 thf(breln1compEex,conjecture,
% 3.08/1.63 ( setextAx
% 3.08/1.63 => ( emptysetAx
% 3.08/1.63 => ( setadjoinAx
% 3.08/1.63 => ( powersetAx
% 3.08/1.63 => ( setunionAx
% 3.08/1.63 => ( omega0Ax
% 3.08/1.63 => ( omegaSAx
% 3.08/1.63 => ( omegaIndAx
% 3.08/1.63 => ( replAx
% 3.08/1.63 => ( foundationAx
% 3.08/1.63 => ( wellorderingAx
% 3.08/1.63 => ( descrp
% 3.08/1.63 => ( dsetconstrI
% 3.08/1.63 => ( dsetconstrEL
% 3.08/1.63 => ( dsetconstrER
% 3.08/1.63 => ( exuE1
% 3.08/1.63 => ( prop2setE
% 3.08/1.63 => ( emptysetE
% 3.08/1.63 => ( emptysetimpfalse
% 3.08/1.63 => ( notinemptyset
% 3.08/1.63 => ( exuE3e
% 3.08/1.63 => ( setext
% 3.08/1.63 => ( emptyI
% 3.08/1.63 => ( noeltsimpempty
% 3.08/1.63 => ( setbeta
% 3.08/1.63 => ( nonemptyE1
% 3.08/1.63 => ( nonemptyI
% 3.08/1.63 => ( nonemptyI1
% 3.08/1.63 => ( setadjoinIL
% 3.08/1.63 => ( emptyinunitempty
% 3.08/1.63 => ( setadjoinIR
% 3.08/1.63 => ( setadjoinE
% 3.08/1.63 => ( setadjoinOr
% 3.08/1.63 => ( setoftrueEq
% 3.08/1.63 => ( powersetI
% 3.08/1.63 => ( emptyinPowerset
% 3.08/1.63 => ( emptyInPowerset
% 3.08/1.63 => ( powersetE
% 3.08/1.63 => ( setunionI
% 3.08/1.63 => ( setunionE
% 3.08/1.63 => ( subPowSU
% 3.08/1.63 => ( exuE2
% 3.08/1.63 => ( nonemptyImpWitness
% 3.08/1.63 => ( uniqinunit
% 3.08/1.63 => ( notinsingleton
% 3.08/1.63 => ( eqinunit
% 3.08/1.63 => ( singletonsswitch
% 3.08/1.63 => ( upairsetE
% 3.08/1.63 => ( upairsetIL
% 3.08/1.63 => ( upairsetIR
% 3.08/1.63 => ( emptyE1
% 3.08/1.63 => ( vacuousDall
% 3.08/1.63 => ( quantDeMorgan1
% 3.08/1.63 => ( quantDeMorgan2
% 3.08/1.63 => ( quantDeMorgan3
% 3.08/1.63 => ( quantDeMorgan4
% 3.08/1.63 => ( prop2setI
% 3.08/1.63 => ( prop2set2propI
% 3.08/1.63 => ( notdexE
% 3.08/1.63 => ( notdallE
% 3.08/1.63 => ( exuI1
% 3.08/1.63 => ( exuI3
% 3.08/1.63 => ( exuI2
% 3.08/1.63 => ( inCongP
% 3.08/1.63 => ( in__Cong
% 3.08/1.63 => ( exuE3u
% 3.08/1.63 => ( exu__Cong
% 3.08/1.63 => ( emptyset__Cong
% 3.08/1.63 => ( setadjoin__Cong
% 3.08/1.63 => ( powerset__Cong
% 3.08/1.63 => ( setunion__Cong
% 3.08/1.63 => ( omega__Cong
% 3.08/1.63 => ( exuEu
% 3.08/1.63 => ( descr__Cong
% 3.08/1.63 => ( dsetconstr__Cong
% 3.08/1.63 => ( subsetI1
% 3.08/1.63 => ( eqimpsubset2
% 3.08/1.63 => ( eqimpsubset1
% 3.08/1.63 => ( subsetI2
% 3.08/1.63 => ( emptysetsubset
% 3.08/1.63 => ( subsetE
% 3.08/1.63 => ( subsetE2
% 3.08/1.63 => ( notsubsetI
% 3.08/1.63 => ( notequalI1
% 3.08/1.63 => ( notequalI2
% 3.08/1.63 => ( subsetRefl
% 3.08/1.63 => ( subsetTrans
% 3.08/1.63 => ( setadjoinSub
% 3.08/1.63 => ( setadjoinSub2
% 3.08/1.63 => ( subset2powerset
% 3.08/1.63 => ( setextsub
% 3.08/1.63 => ( subsetemptysetimpeq
% 3.08/1.63 => ( powersetI1
% 3.08/1.63 => ( powersetE1
% 3.08/1.63 => ( inPowerset
% 3.08/1.63 => ( powersetsubset
% 3.08/1.63 => ( sepInPowerset
% 3.08/1.63 => ( sepSubset
% 3.08/1.63 => ( binunionIL
% 3.08/1.63 => ( upairset2IR
% 3.08/1.63 => ( binunionIR
% 3.08/1.63 => ( binunionEcases
% 3.08/1.63 => ( binunionE
% 3.08/1.63 => ( binunionLsub
% 3.08/1.63 => ( binunionRsub
% 3.08/1.63 => ( binintersectI
% 3.08/1.63 => ( binintersectSubset5
% 3.08/1.63 => ( binintersectEL
% 3.08/1.63 => ( binintersectLsub
% 3.08/1.63 => ( binintersectSubset2
% 3.08/1.63 => ( binintersectSubset3
% 3.08/1.63 => ( binintersectER
% 3.08/1.63 => ( disjointsetsI1
% 3.08/1.63 => ( binintersectRsub
% 3.08/1.63 => ( binintersectSubset4
% 3.08/1.63 => ( binintersectSubset1
% 3.08/1.63 => ( bs114d
% 3.08/1.63 => ( setminusI
% 3.08/1.63 => ( setminusEL
% 3.08/1.63 => ( setminusER
% 3.08/1.63 => ( setminusSubset2
% 3.08/1.63 => ( setminusERneg
% 3.08/1.63 => ( setminusELneg
% 3.08/1.63 => ( setminusILneg
% 3.08/1.63 => ( setminusIRneg
% 3.08/1.63 => ( setminusLsub
% 3.08/1.63 => ( setminusSubset1
% 3.08/1.63 => ( symdiffE
% 3.08/1.63 => ( symdiffI1
% 3.08/1.63 => ( symdiffI2
% 3.08/1.63 => ( symdiffIneg1
% 3.08/1.63 => ( symdiffIneg2
% 3.08/1.63 => ( secondinupair
% 3.08/1.63 => ( setukpairIL
% 3.08/1.63 => ( setukpairIR
% 3.08/1.63 => ( kpairiskpair
% 3.08/1.63 => ( kpairp
% 3.08/1.63 => ( singletonsubset
% 3.08/1.63 => ( singletoninpowerset
% 3.08/1.63 => ( singletoninpowunion
% 3.08/1.63 => ( upairset2E
% 3.08/1.63 => ( upairsubunion
% 3.08/1.63 => ( upairinpowunion
% 3.08/1.63 => ( ubforcartprodlem1
% 3.08/1.63 => ( ubforcartprodlem2
% 3.08/1.63 => ( ubforcartprodlem3
% 3.08/1.63 => ( cartprodpairin
% 3.08/1.63 => ( cartprodmempair1
% 3.08/1.63 => ( cartprodmempair
% 3.08/1.63 => ( setunionE2
% 3.08/1.63 => ( setunionsingleton1
% 3.08/1.63 => ( setunionsingleton2
% 3.08/1.63 => ( setunionsingleton
% 3.08/1.63 => ( singletonprop
% 3.08/1.63 => ( ex1E1
% 3.08/1.63 => ( ex1I
% 3.08/1.63 => ( ex1I2
% 3.08/1.63 => ( singletonsuniq
% 3.08/1.63 => ( setukpairinjL1
% 3.08/1.63 => ( kfstsingleton
% 3.08/1.63 => ( theprop
% 3.08/1.63 => ( kfstpairEq
% 3.08/1.63 => ( cartprodfstin
% 3.08/1.63 => ( setukpairinjL2
% 3.08/1.63 => ( setukpairinjL
% 3.08/1.63 => ( setukpairinjR11
% 3.08/1.63 => ( setukpairinjR12
% 3.08/1.63 => ( setukpairinjR1
% 3.08/1.63 => ( upairequniteq
% 3.08/1.63 => ( setukpairinjR2
% 3.08/1.63 => ( setukpairinjR
% 3.08/1.63 => ( ksndsingleton
% 3.08/1.63 => ( ksndpairEq
% 3.08/1.63 => ( kpairsurjEq
% 3.08/1.63 => ( cartprodsndin
% 3.08/1.63 => ( cartprodpairmemEL
% 3.08/1.63 => ( cartprodpairmemER
% 3.08/1.63 => ( cartprodmempaircEq
% 3.08/1.63 => ( cartprodfstpairEq
% 3.08/1.63 => ( cartprodsndpairEq
% 3.08/1.63 => ( cartprodpairsurjEq
% 3.08/1.63 => ( dpsetconstrI
% 3.08/1.63 => ( dpsetconstrSub
% 3.08/1.63 => ( setOfPairsIsBReln
% 3.08/1.63 => ( dpsetconstrERa
% 3.08/1.63 => ( dpsetconstrEL1
% 3.08/1.63 => ( dpsetconstrEL2
% 3.08/1.63 => ( dpsetconstrER
% 3.08/1.63 => ( funcImageSingleton
% 3.08/1.63 => ( apProp
% 3.08/1.63 => ( app
% 3.08/1.63 => ( infuncsetfunc
% 3.08/1.63 => ( ap2p
% 3.08/1.63 => ( funcinfuncset
% 3.08/1.63 => ( lamProp
% 3.08/1.63 => ( lamp
% 3.08/1.63 => ( lam2p
% 3.08/1.63 => ( brelnall1
% 3.08/1.63 => ( brelnall2
% 3.08/1.63 => ( ex1E2
% 3.08/1.63 => ( funcGraphProp1
% 3.08/1.63 => ( funcGraphProp3
% 3.08/1.63 => ( funcGraphProp2
% 3.08/1.63 => ( funcextLem
% 3.08/1.63 => ( funcGraphProp4
% 3.08/1.63 => ( subbreln
% 3.08/1.63 => ( eqbreln
% 3.08/1.63 => ( funcext
% 3.08/1.63 => ( funcext2
% 3.08/1.63 => ( ap2apEq1
% 3.08/1.63 => ( ap2apEq2
% 3.08/1.63 => ( beta1
% 3.08/1.63 => ( eta1
% 3.08/1.63 => ( lam2lamEq
% 3.08/1.63 => ( beta2
% 3.08/1.63 => ( eta2
% 3.08/1.63 => ( iffalseProp1
% 3.08/1.63 => ( iffalseProp2
% 3.08/1.63 => ( iftrueProp1
% 3.08/1.63 => ( iftrueProp2
% 3.08/1.63 => ( ifSingleton
% 3.08/1.63 => ( ifp
% 3.08/1.63 => ( theeq
% 3.08/1.63 => ( iftrue
% 3.08/1.63 => ( iffalse
% 3.08/1.63 => ( iftrueorfalse
% 3.08/1.63 => ( binintersectT_lem
% 3.08/1.63 => ( binunionT_lem
% 3.08/1.63 => ( powersetT_lem
% 3.08/1.63 => ( setminusT_lem
% 3.08/1.63 => ( complementT_lem
% 3.08/1.63 => ( setextT
% 3.08/1.63 => ( subsetTI
% 3.08/1.63 => ( powersetTI1
% 3.08/1.63 => ( powersetTE1
% 3.08/1.63 => ( complementTI1
% 3.08/1.63 => ( complementTE1
% 3.08/1.63 => ( binintersectTELcontra
% 3.08/1.63 => ( binintersectTERcontra
% 3.08/1.63 => ( contrasubsetT
% 3.08/1.63 => ( contrasubsetT1
% 3.08/1.63 => ( contrasubsetT2
% 3.08/1.63 => ( contrasubsetT3
% 3.08/1.63 => ( doubleComplementI1
% 3.08/1.63 => ( doubleComplementE1
% 3.08/1.63 => ( doubleComplementSub1
% 3.08/1.63 => ( doubleComplementSub2
% 3.08/1.63 => ( doubleComplementEq
% 3.08/1.63 => ( complementTnotintersectT
% 3.08/1.63 => ( complementImpComplementIntersect
% 3.08/1.63 => ( complementSubsetComplementIntersect
% 3.08/1.63 => ( complementInPowersetComplementIntersect
% 3.08/1.63 => ( contraSubsetComplement
% 3.08/1.63 => ( complementTcontraSubset
% 3.08/1.63 => ( binunionTILcontra
% 3.08/1.63 => ( binunionTIRcontra
% 3.08/1.63 => ( inIntersectImpInUnion
% 3.08/1.63 => ( inIntersectImpInUnion2
% 3.08/1.63 => ( inIntersectImpInIntersectUnions
% 3.08/1.63 => ( intersectInPowersetIntersectUnions
% 3.08/1.63 => ( inComplementUnionImpNotIn1
% 3.08/1.63 => ( inComplementUnionImpInComplement1
% 3.08/1.63 => ( binunionTE
% 3.08/1.63 => ( binunionTEcontra
% 3.08/1.63 => ( demorgan2a1
% 3.08/1.63 => ( complementUnionInPowersetComplement
% 3.08/1.63 => ( demorgan2a2
% 3.08/1.63 => ( demorgan1a
% 3.08/1.63 => ( demorgan1b
% 3.08/1.63 => ( demorgan1
% 3.08/1.63 => ( demorgan2a
% 3.08/1.63 => ( demorgan2b2
% 3.08/1.63 => ( demorgan2b
% 3.08/1.63 => ( demorgan2
% 3.08/1.63 => ( woz13rule0
% 3.08/1.63 => ( woz13rule1
% 3.08/1.63 => ( woz13rule2
% 3.08/1.63 => ( woz13rule3
% 3.08/1.63 => ( woz13rule4
% 3.08/1.63 => ( woz1_1
% 3.08/1.63 => ( woz1_2
% 3.08/1.63 => ( woz1_3
% 3.08/1.63 => ( woz1_4
% 3.08/1.63 => ( woz1_5
% 3.08/1.63 => ( breln1all2
% 3.08/1.63 => ( breln1SetBreln1
% 3.08/1.63 => ( choice2fnsingleton
% 3.08/1.63 => ( setOfPairsIsBReln1
% 3.08/1.63 => ( breln1all1
% 3.08/1.63 => ( subbreln1
% 3.08/1.63 => ( eqbreln1
% 3.08/1.63 => ( breln1invprop
% 3.08/1.63 => ( breln1invI
% 3.08/1.63 => ( breln1invE
% 3.08/1.63 => ( breln1compprop
% 3.08/1.63 => ( breln1compI
% 3.08/1.63 => ( breln1compE
% 3.08/1.63 => ! [A: $i,R: $i] :
% 3.08/1.63 ( ( breln1 @ A @ R )
% 3.08/1.63 => ! [S: $i] :
% 3.08/1.63 ( ( breln1 @ A @ S )
% 3.08/1.63 => ! [Xx: $i] :
% 3.08/1.63 ( ( in @ Xx @ A )
% 3.08/1.63 => ! [Xy: $i] :
% 3.08/1.63 ( ( in @ Xy @ A )
% 3.08/1.63 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 3.08/1.63 => ! [Xphi: $o] :
% 3.08/1.63 ( ! [Xz: $i] :
% 3.08/1.63 ( ( in @ Xz @ A )
% 3.08/1.63 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 3.08/1.63 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 3.08/1.63 => Xphi ) ) )
% 3.08/1.63 => Xphi ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.08/1.63 ------------------------
% 3.08/1.67 % (4229)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3905 for (2999ds/183Mi)
% 3.08/1.67 % (4231)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_3905 for (2999ds/27Mi)
% 3.08/1.67 % (4230)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_3905 for (2999ds/4Mi)
% 3.08/1.67 % (4230)Instruction limit reached!
% 3.08/1.67 % (4230)------------------------------
% 3.08/1.67 % (4230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.67 % (4230)Termination reason: Unknown
% 3.08/1.67 % (4230)Termination phase: shuffling
% 3.08/1.67
% 3.08/1.67 % (4230)Memory used [KB]: 1535
% 3.08/1.67 % (4230)Time elapsed: 0.004 s
% 3.08/1.67 % (4230)Instructions burned: 5 (million)
% 3.08/1.67 % (4230)------------------------------
% 3.08/1.67 % (4230)------------------------------
% 3.08/1.68 % (4232)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3905 for (2999ds/2Mi)
% 3.08/1.68 % (4233)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_3905 for (2999ds/2Mi)
% 3.08/1.68 % (4234)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_3905 for (2999ds/275Mi)
% 3.08/1.68 % (4231)Instruction limit reached!
% 3.08/1.68 % (4231)------------------------------
% 3.08/1.68 % (4231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.68 % (4231)Termination reason: Unknown
% 3.08/1.68 % (4231)Termination phase: shuffling
% 3.08/1.68
% 3.08/1.68 % (4231)Memory used [KB]: 2046
% 3.08/1.68 % (4231)Time elapsed: 0.009 s
% 3.08/1.68 % (4231)Instructions burned: 28 (million)
% 3.08/1.68 % (4231)------------------------------
% 3.08/1.68 % (4231)------------------------------
% 3.08/1.68 % (4235)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3905 for (2999ds/18Mi)
% 3.08/1.68 % (4232)Instruction limit reached!
% 3.08/1.68 % (4232)------------------------------
% 3.08/1.68 % (4232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.68 % (4232)Termination reason: Unknown
% 3.08/1.68 % (4232)Termination phase: shuffling
% 3.08/1.68
% 3.08/1.68 % (4232)Memory used [KB]: 1535
% 3.08/1.68 % (4232)Time elapsed: 0.004 s
% 3.08/1.68 % (4232)Instructions burned: 3 (million)
% 3.08/1.68 % (4232)------------------------------
% 3.08/1.68 % (4232)------------------------------
% 3.08/1.68 % (4233)Instruction limit reached!
% 3.08/1.68 % (4233)------------------------------
% 3.08/1.68 % (4233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.68 % (4233)Termination reason: Unknown
% 3.08/1.68 % (4233)Termination phase: shuffling
% 3.08/1.68
% 3.08/1.68 % (4233)Memory used [KB]: 1535
% 3.08/1.68 % (4233)Time elapsed: 0.003 s
% 3.08/1.68 % (4233)Instructions burned: 3 (million)
% 3.08/1.68 % (4233)------------------------------
% 3.08/1.68 % (4233)------------------------------
% 3.08/1.69 % (4236)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3905 for (2999ds/3Mi)
% 3.08/1.69 % (4237)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_3905 for (2999ds/37Mi)
% 3.08/1.69 % (4236)Instruction limit reached!
% 3.08/1.69 % (4236)------------------------------
% 3.08/1.69 % (4236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.69 % (4236)Termination reason: Unknown
% 3.08/1.69 % (4236)Termination phase: shuffling
% 3.08/1.69
% 3.08/1.69 % (4236)Memory used [KB]: 1535
% 3.08/1.69 % (4236)Time elapsed: 0.004 s
% 3.08/1.69 % (4236)Instructions burned: 5 (million)
% 3.08/1.69 % (4236)------------------------------
% 3.08/1.69 % (4236)------------------------------
% 3.08/1.69 % (4235)Instruction limit reached!
% 3.08/1.69 % (4235)------------------------------
% 3.08/1.69 % (4235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.69 % (4235)Termination reason: Unknown
% 3.08/1.69 % (4235)Termination phase: shuffling
% 3.08/1.69
% 3.08/1.69 % (4235)Memory used [KB]: 1791
% 3.08/1.69 % (4235)Time elapsed: 0.014 s
% 3.08/1.69 % (4235)Instructions burned: 19 (million)
% 3.08/1.69 % (4235)------------------------------
% 3.08/1.69 % (4235)------------------------------
% 3.11/1.70 % (4239)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_3905 for (2999ds/3Mi)
% 3.11/1.70 % (4238)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_3905 for (2999ds/15Mi)
% 3.11/1.70 % (4237)Instruction limit reached!
% 3.11/1.70 % (4237)------------------------------
% 3.11/1.70 % (4237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.70 % (4237)Termination reason: Unknown
% 3.11/1.70 % (4237)Termination phase: shuffling
% 3.11/1.70
% 3.11/1.70 % (4237)Memory used [KB]: 2302
% 3.11/1.70 % (4237)Time elapsed: 0.011 s
% 3.11/1.70 % (4237)Instructions burned: 38 (million)
% 3.11/1.70 % (4237)------------------------------
% 3.11/1.70 % (4237)------------------------------
% 3.11/1.70 % (4239)Instruction limit reached!
% 3.11/1.70 % (4239)------------------------------
% 3.11/1.70 % (4239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.70 % (4239)Termination reason: Unknown
% 3.11/1.70 % (4239)Termination phase: shuffling
% 3.11/1.70
% 3.11/1.70 % (4239)Memory used [KB]: 1535
% 3.11/1.70 % (4239)Time elapsed: 0.004 s
% 3.11/1.70 % (4239)Instructions burned: 3 (million)
% 3.11/1.70 % (4239)------------------------------
% 3.11/1.70 % (4239)------------------------------
% 3.11/1.70 % (4240)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_3905 for (2999ds/1041Mi)
% 3.11/1.71 % (4241)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3905 for (2999ds/7Mi)
% 3.11/1.71 % (4238)Instruction limit reached!
% 3.11/1.71 % (4238)------------------------------
% 3.11/1.71 % (4238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.71 % (4238)Termination reason: Unknown
% 3.11/1.71 % (4238)Termination phase: shuffling
% 3.11/1.71
% 3.11/1.71 % (4238)Memory used [KB]: 1791
% 3.11/1.71 % (4238)Time elapsed: 0.012 s
% 3.11/1.71 % (4238)Instructions burned: 16 (million)
% 3.11/1.71 % (4238)------------------------------
% 3.11/1.71 % (4238)------------------------------
% 3.11/1.71 % (4242)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3905 for (2999ds/16Mi)
% 3.11/1.71 % (4241)Instruction limit reached!
% 3.11/1.71 % (4241)------------------------------
% 3.11/1.71 % (4241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.71 % (4241)Termination reason: Unknown
% 3.11/1.71 % (4241)Termination phase: shuffling
% 3.11/1.71
% 3.11/1.71 % (4241)Memory used [KB]: 1663
% 3.11/1.71 % (4241)Time elapsed: 0.006 s
% 3.11/1.71 % (4241)Instructions burned: 9 (million)
% 3.11/1.71 % (4241)------------------------------
% 3.11/1.71 % (4241)------------------------------
% 3.11/1.71 % (4242)Instruction limit reached!
% 3.11/1.71 % (4242)------------------------------
% 3.11/1.71 % (4242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.71 % (4242)Termination reason: Unknown
% 3.11/1.71 % (4242)Termination phase: shuffling
% 3.11/1.71
% 3.11/1.71 % (4242)Memory used [KB]: 1918
% 3.11/1.71 % (4242)Time elapsed: 0.006 s
% 3.11/1.71 % (4242)Instructions burned: 17 (million)
% 3.11/1.71 % (4242)------------------------------
% 3.11/1.71 % (4242)------------------------------
% 3.11/1.72 % (4229)Instruction limit reached!
% 3.11/1.72 % (4229)------------------------------
% 3.11/1.72 % (4229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.72 % (4229)Termination reason: Unknown
% 3.11/1.72 % (4229)Termination phase: Saturation
% 3.11/1.72
% 3.11/1.72 % (4229)Memory used [KB]: 7419
% 3.11/1.72 % (4229)Time elapsed: 0.048 s
% 3.11/1.72 % (4229)Instructions burned: 183 (million)
% 3.11/1.72 % (4229)------------------------------
% 3.11/1.72 % (4229)------------------------------
% 3.11/1.72 % (4243)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_3905 for (2999ds/3Mi)
% 3.11/1.72 % (4243)Instruction limit reached!
% 3.11/1.72 % (4243)------------------------------
% 3.11/1.72 % (4243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.72 % (4243)Termination reason: Unknown
% 3.11/1.72 % (4243)Termination phase: shuffling
% 3.11/1.72
% 3.11/1.72 % (4243)Memory used [KB]: 1535
% 3.11/1.72 % (4243)Time elapsed: 0.004 s
% 3.11/1.72 % (4243)Instructions burned: 5 (million)
% 3.11/1.72 % (4243)------------------------------
% 3.11/1.72 % (4243)------------------------------
% 3.11/1.72 % (4246)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3905 for (2999ds/3Mi)
% 3.11/1.72 % (4245)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3905 for (2999ds/7Mi)
% 3.11/1.72 % (4246)Instruction limit reached!
% 3.11/1.72 % (4246)------------------------------
% 3.11/1.72 % (4246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.72 % (4246)Termination reason: Unknown
% 3.11/1.72 % (4246)Termination phase: shuffling
% 3.11/1.72
% 3.11/1.72 % (4246)Memory used [KB]: 1535
% 3.11/1.72 % (4246)Time elapsed: 0.002 s
% 3.11/1.72 % (4246)Instructions burned: 3 (million)
% 3.11/1.72 % (4246)------------------------------
% 3.11/1.72 % (4246)------------------------------
% 3.11/1.72 % (4245)Instruction limit reached!
% 3.11/1.72 % (4245)------------------------------
% 3.11/1.72 % (4245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.72 % (4245)Termination reason: Unknown
% 3.11/1.72 % (4245)Termination phase: shuffling
% 3.11/1.72
% 3.11/1.72 % (4245)Memory used [KB]: 1663
% 3.11/1.72 % (4245)Time elapsed: 0.004 s
% 3.11/1.72 % (4245)Instructions burned: 8 (million)
% 3.11/1.72 % (4245)------------------------------
% 3.11/1.72 % (4245)------------------------------
% 3.11/1.72 % (4244)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_3905 for (2999ds/3Mi)
% 3.11/1.73 % (4247)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_3905 for (2999ds/4Mi)
% 3.11/1.73 % (4244)Instruction limit reached!
% 3.11/1.73 % (4244)------------------------------
% 3.11/1.73 % (4244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.73 % (4244)Termination reason: Unknown
% 3.11/1.73 % (4244)Termination phase: shuffling
% 3.11/1.73
% 3.11/1.73 % (4244)Memory used [KB]: 1535
% 3.11/1.73 % (4244)Time elapsed: 0.004 s
% 3.11/1.73 % (4244)Instructions burned: 3 (million)
% 3.11/1.73 % (4244)------------------------------
% 3.11/1.73 % (4244)------------------------------
% 3.11/1.73 % (4247)Instruction limit reached!
% 3.11/1.73 % (4247)------------------------------
% 3.11/1.73 % (4247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.73 % (4247)Termination reason: Unknown
% 3.11/1.73 % (4247)Termination phase: shuffling
% 3.11/1.73
% 3.11/1.73 % (4247)Memory used [KB]: 1535
% 3.11/1.73 % (4247)Time elapsed: 0.003 s
% 3.11/1.73 % (4247)Instructions burned: 6 (million)
% 3.11/1.73 % (4247)------------------------------
% 3.11/1.73 % (4247)------------------------------
% 3.11/1.73 % (4248)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_3905 for (2999ds/18Mi)
% 3.11/1.73 % (4249)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_3905 for (2999ds/710Mi)
% 3.11/1.73 % (4250)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3905 for (2999ds/6Mi)
% 3.11/1.73 % (4248)Instruction limit reached!
% 3.11/1.73 % (4248)------------------------------
% 3.11/1.73 % (4248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.73 % (4248)Termination reason: Unknown
% 3.11/1.73 % (4248)Termination phase: shuffling
% 3.11/1.73
% 3.11/1.73 % (4248)Memory used [KB]: 1791
% 3.11/1.73 % (4248)Time elapsed: 0.006 s
% 3.11/1.73 % (4248)Instructions burned: 19 (million)
% 3.11/1.73 % (4248)------------------------------
% 3.11/1.73 % (4248)------------------------------
% 3.11/1.74 % (4250)Instruction limit reached!
% 3.11/1.74 % (4250)------------------------------
% 3.11/1.74 % (4250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.74 % (4250)Termination reason: Unknown
% 3.11/1.74 % (4250)Termination phase: shuffling
% 3.11/1.74
% 3.11/1.74 % (4250)Memory used [KB]: 1663
% 3.11/1.74 % (4250)Time elapsed: 0.003 s
% 3.11/1.74 % (4250)Instructions burned: 7 (million)
% 3.11/1.74 % (4250)------------------------------
% 3.11/1.74 % (4250)------------------------------
% 3.11/1.74 % (4252)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_3905 for (2999ds/21Mi)
% 3.11/1.74 % (4252)Instruction limit reached!
% 3.11/1.74 % (4252)------------------------------
% 3.11/1.74 % (4252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.74 % (4252)Termination reason: Unknown
% 3.11/1.74 % (4252)Termination phase: shuffling
% 3.11/1.74
% 3.11/1.74 % (4252)Memory used [KB]: 1918
% 3.11/1.74 % (4252)Time elapsed: 0.007 s
% 3.11/1.74 % (4252)Instructions burned: 22 (million)
% 3.11/1.74 % (4252)------------------------------
% 3.11/1.74 % (4252)------------------------------
% 3.11/1.74 % (4251)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_3905 for (2999ds/902Mi)
% 3.11/1.74 % (4253)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_3905 for (2999ds/5Mi)
% 3.11/1.75 % (4253)Instruction limit reached!
% 3.11/1.75 % (4253)------------------------------
% 3.11/1.75 % (4253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.75 % (4253)Termination reason: Unknown
% 3.11/1.75 % (4253)Termination phase: shuffling
% 3.11/1.75
% 3.11/1.75 % (4253)Memory used [KB]: 1663
% 3.11/1.75 % (4253)Time elapsed: 0.003 s
% 3.11/1.75 % (4253)Instructions burned: 7 (million)
% 3.11/1.75 % (4253)------------------------------
% 3.11/1.75 % (4253)------------------------------
% 3.11/1.75 % (4254)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_3905 for (2999ds/6Mi)
% 3.11/1.75 % (4254)Instruction limit reached!
% 3.11/1.75 % (4254)------------------------------
% 3.11/1.75 % (4254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.75 % (4254)Termination reason: Unknown
% 3.11/1.75 % (4254)Termination phase: shuffling
% 3.11/1.75
% 3.11/1.75 % (4254)Memory used [KB]: 1663
% 3.11/1.75 % (4254)Time elapsed: 0.003 s
% 3.11/1.75 % (4254)Instructions burned: 7 (million)
% 3.11/1.75 % (4254)------------------------------
% 3.11/1.75 % (4254)------------------------------
% 3.11/1.75 % (4255)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_3905 for (2998ds/377Mi)
% 3.11/1.76 % (4256)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_3905 for (2998ds/779Mi)
% 3.11/1.76 % (4257)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_3905 for (2998ds/19Mi)
% 3.11/1.77 % (4257)Instruction limit reached!
% 3.11/1.77 % (4257)------------------------------
% 3.11/1.77 % (4257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.77 % (4257)Termination reason: Unknown
% 3.11/1.77 % (4257)Termination phase: shuffling
% 3.11/1.77
% 3.11/1.77 % (4257)Memory used [KB]: 1918
% 3.11/1.77 % (4257)Time elapsed: 0.007 s
% 3.11/1.77 % (4257)Instructions burned: 21 (million)
% 3.11/1.77 % (4257)------------------------------
% 3.11/1.77 % (4257)------------------------------
% 3.11/1.78 % (4258)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_3905 for (2998ds/879Mi)
% 3.11/1.80 % (4234)Instruction limit reached!
% 3.11/1.80 % (4234)------------------------------
% 3.11/1.80 % (4234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.80 % (4234)Termination reason: Unknown
% 3.11/1.80 % (4234)Termination phase: Saturation
% 3.11/1.80
% 3.11/1.80 % (4234)Memory used [KB]: 10362
% 3.11/1.80 % (4234)Time elapsed: 0.128 s
% 3.11/1.80 % (4234)Instructions burned: 275 (million)
% 3.11/1.80 % (4234)------------------------------
% 3.11/1.80 % (4234)------------------------------
% 3.11/1.82 % (4259)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_3905 for (2998ds/17Mi)
% 3.11/1.82 % (4259)Instruction limit reached!
% 3.11/1.82 % (4259)------------------------------
% 3.11/1.82 % (4259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.82 % (4259)Termination reason: Unknown
% 3.11/1.82 % (4259)Termination phase: shuffling
% 3.11/1.82
% 3.11/1.82 % (4259)Memory used [KB]: 1918
% 3.11/1.82 % (4259)Time elapsed: 0.007 s
% 3.11/1.82 % (4259)Instructions burned: 20 (million)
% 3.11/1.82 % (4259)------------------------------
% 3.11/1.82 % (4259)------------------------------
% 3.11/1.83 % (4260)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_3905 for (2998ds/3Mi)
% 3.11/1.83 % (4260)Instruction limit reached!
% 3.11/1.83 % (4260)------------------------------
% 3.11/1.83 % (4260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.83 % (4260)Termination reason: Unknown
% 3.11/1.83 % (4260)Termination phase: shuffling
% 3.11/1.83
% 3.11/1.83 % (4260)Memory used [KB]: 1535
% 3.11/1.83 % (4260)Time elapsed: 0.002 s
% 3.11/1.83 % (4260)Instructions burned: 3 (million)
% 3.11/1.83 % (4260)------------------------------
% 3.11/1.83 % (4260)------------------------------
% 3.11/1.84 % (4261)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_3905 for (2997ds/30Mi)
% 3.11/1.85 % (4255)Instruction limit reached!
% 3.11/1.85 % (4255)------------------------------
% 3.11/1.85 % (4255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.85 % (4255)Termination reason: Unknown
% 3.11/1.85 % (4255)Termination phase: Saturation
% 3.11/1.85
% 3.11/1.85 % (4255)Memory used [KB]: 9466
% 3.11/1.85 % (4255)Time elapsed: 0.100 s
% 3.11/1.85 % (4255)Instructions burned: 377 (million)
% 3.11/1.85 % (4255)------------------------------
% 3.11/1.85 % (4255)------------------------------
% 3.11/1.85 % (4261)Instruction limit reached!
% 3.11/1.85 % (4261)------------------------------
% 3.11/1.85 % (4261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.85 % (4261)Termination reason: Unknown
% 3.11/1.85 % (4261)Termination phase: shuffling
% 3.11/1.85
% 3.11/1.85 % (4261)Memory used [KB]: 2174
% 3.11/1.85 % (4261)Time elapsed: 0.010 s
% 3.11/1.85 % (4261)Instructions burned: 31 (million)
% 3.11/1.85 % (4261)------------------------------
% 3.11/1.85 % (4261)------------------------------
% 3.11/1.86 % (4262)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_3905 for (2997ds/127Mi)
% 3.11/1.86 % (4263)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_3905 for (2997ds/100Mi)
% 3.11/1.89 % (4263)Instruction limit reached!
% 3.11/1.89 % (4263)------------------------------
% 3.11/1.89 % (4263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.89 % (4263)Termination reason: Unknown
% 3.11/1.89 % (4263)Termination phase: Property scanning
% 3.11/1.89
% 3.11/1.89 % (4263)Memory used [KB]: 2814
% 3.11/1.89 % (4263)Time elapsed: 0.029 s
% 3.11/1.89 % (4263)Instructions burned: 101 (million)
% 3.11/1.89 % (4263)------------------------------
% 3.11/1.89 % (4263)------------------------------
% 3.11/1.89 % (4262)Instruction limit reached!
% 3.11/1.89 % (4262)------------------------------
% 3.11/1.89 % (4262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.89 % (4262)Termination reason: Unknown
% 3.11/1.89 % (4262)Termination phase: Property scanning
% 3.11/1.89
% 3.11/1.89 % (4262)Memory used [KB]: 2814
% 3.11/1.89 % (4262)Time elapsed: 0.035 s
% 3.11/1.89 % (4262)Instructions burned: 129 (million)
% 3.11/1.89 % (4262)------------------------------
% 3.11/1.89 % (4262)------------------------------
% 3.11/1.90 % (4264)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_3905 for (2997ds/3Mi)
% 3.11/1.90 % (4264)Instruction limit reached!
% 3.11/1.90 % (4264)------------------------------
% 3.11/1.90 % (4264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.90 % (4264)Termination reason: Unknown
% 3.11/1.90 % (4264)Termination phase: shuffling
% 3.11/1.90
% 3.11/1.90 % (4264)Memory used [KB]: 1535
% 3.11/1.90 % (4264)Time elapsed: 0.002 s
% 3.11/1.90 % (4264)Instructions burned: 3 (million)
% 3.11/1.90 % (4264)------------------------------
% 3.11/1.90 % (4264)------------------------------
% 3.11/1.90 % (4265)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_3905 for (2997ds/20Mi)
% 3.11/1.91 % (4265)Instruction limit reached!
% 3.11/1.91 % (4265)------------------------------
% 3.11/1.91 % (4265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.91 % (4265)Termination reason: Unknown
% 3.11/1.91 % (4265)Termination phase: shuffling
% 3.11/1.91
% 3.11/1.91 % (4265)Memory used [KB]: 1918
% 3.11/1.91 % (4265)Time elapsed: 0.008 s
% 3.11/1.91 % (4265)Instructions burned: 20 (million)
% 3.11/1.91 % (4265)------------------------------
% 3.11/1.91 % (4265)------------------------------
% 3.11/1.91 % (4266)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_3905 for (2997ds/86Mi)
% 3.11/1.92 % (4267)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_3905 for (2997ds/107Mi)
% 3.11/1.94 % (4266)Instruction limit reached!
% 3.11/1.94 % (4266)------------------------------
% 3.11/1.94 % (4266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.94 % (4266)Termination reason: Unknown
% 3.11/1.94 % (4266)Termination phase: Property scanning
% 3.11/1.94
% 3.11/1.94 % (4266)Memory used [KB]: 2558
% 3.11/1.94 % (4266)Time elapsed: 0.026 s
% 3.11/1.94 % (4266)Instructions burned: 89 (million)
% 3.11/1.94 % (4266)------------------------------
% 3.11/1.94 % (4266)------------------------------
% 3.11/1.95 % (4268)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_3905 for (2996ds/39Mi)
% 3.11/1.95 % (4267)Instruction limit reached!
% 3.11/1.95 % (4267)------------------------------
% 3.11/1.95 % (4267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.95 % (4267)Termination reason: Unknown
% 3.11/1.95 % (4267)Termination phase: SInE selection
% 3.11/1.95
% 3.11/1.95 % (4267)Memory used [KB]: 2686
% 3.11/1.95 % (4267)Time elapsed: 0.029 s
% 3.11/1.95 % (4267)Instructions burned: 111 (million)
% 3.11/1.95 % (4267)------------------------------
% 3.11/1.95 % (4267)------------------------------
% 3.11/1.95 % (4256)Instruction limit reached!
% 3.11/1.95 % (4256)------------------------------
% 3.11/1.95 % (4256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.95 % (4249)Instruction limit reached!
% 3.11/1.95 % (4249)------------------------------
% 3.11/1.95 % (4249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.95 % (4256)Termination reason: Unknown
% 3.11/1.95 % (4249)Termination reason: Unknown
% 3.11/1.95 % (4249)Termination phase: Saturation
% 3.11/1.95
% 3.11/1.95 % (4256)Termination phase: Saturation
% 3.11/1.95
% 3.11/1.95 % (4249)Memory used [KB]: 11641
% 3.11/1.95 % (4256)Memory used [KB]: 7803
% 3.11/1.95 % (4249)Time elapsed: 0.219 s
% 3.11/1.95 % (4256)Time elapsed: 0.195 s
% 3.11/1.95 % (4249)Instructions burned: 710 (million)
% 3.11/1.95 % (4256)Instructions burned: 781 (million)
% 3.11/1.95 % (4249)------------------------------
% 3.11/1.95 % (4249)------------------------------
% 3.11/1.95 % (4256)------------------------------
% 3.11/1.95 % (4256)------------------------------
% 3.11/1.96 % (4269)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_3905 for (2996ds/448Mi)
% 3.11/1.96 % (4268)Instruction limit reached!
% 3.11/1.96 % (4268)------------------------------
% 3.11/1.96 % (4268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.96 % (4268)Termination reason: Unknown
% 3.11/1.96 % (4268)Termination phase: shuffling
% 3.11/1.96
% 3.11/1.96 % (4268)Memory used [KB]: 2302
% 3.11/1.96 % (4268)Time elapsed: 0.012 s
% 3.11/1.96 % (4268)Instructions burned: 39 (million)
% 3.11/1.96 % (4268)------------------------------
% 3.11/1.96 % (4268)------------------------------
% 3.11/1.96 % (4270)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_3905 for (2996ds/46Mi)
% 3.11/1.96 % (4271)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_3905 for (2996ds/98Mi)
% 3.11/1.96 % (4240)Instruction limit reached!
% 3.11/1.96 % (4240)------------------------------
% 3.11/1.96 % (4240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.96 % (4240)Termination reason: Unknown
% 3.11/1.96 % (4240)Termination phase: Saturation
% 3.11/1.96
% 3.11/1.96 % (4240)Memory used [KB]: 17014
% 3.11/1.96 % (4240)Time elapsed: 0.262 s
% 3.11/1.96 % (4240)Instructions burned: 1042 (million)
% 3.11/1.96 % (4240)------------------------------
% 3.11/1.96 % (4240)------------------------------
% 3.11/1.97 % (4272)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_3905 for (2996ds/507Mi)
% 3.11/1.97 % (4273)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_3905 for (2996ds/149Mi)
% 3.11/1.97 % (4270)Instruction limit reached!
% 3.11/1.97 % (4270)------------------------------
% 3.11/1.97 % (4270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.97 % (4270)Termination reason: Unknown
% 3.11/1.97 % (4270)Termination phase: shuffling
% 3.11/1.97
% 3.11/1.97 % (4270)Memory used [KB]: 2430
% 3.11/1.97 % (4270)Time elapsed: 0.014 s
% 3.11/1.97 % (4270)Instructions burned: 47 (million)
% 3.11/1.97 % (4270)------------------------------
% 3.11/1.97 % (4270)------------------------------
% 3.11/1.98 % (4274)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_3905 for (2996ds/39Mi)
% 3.11/1.99 % (4271)Instruction limit reached!
% 3.11/1.99 % (4271)------------------------------
% 3.11/1.99 % (4271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.99 % (4271)Termination reason: Unknown
% 3.11/1.99 % (4271)Termination phase: Property scanning
% 3.11/1.99
% 3.11/1.99 % (4271)Memory used [KB]: 2686
% 3.11/1.99 % (4271)Time elapsed: 0.027 s
% 3.11/1.99 % (4271)Instructions burned: 100 (million)
% 3.11/1.99 % (4271)------------------------------
% 3.11/1.99 % (4271)------------------------------
% 3.11/1.99 % (4274)Instruction limit reached!
% 3.11/1.99 % (4274)------------------------------
% 3.11/1.99 % (4274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.99 % (4274)Termination reason: Unknown
% 3.11/1.99 % (4274)Termination phase: shuffling
% 3.11/1.99
% 3.11/1.99 % (4274)Memory used [KB]: 2302
% 3.11/1.99 % (4274)Time elapsed: 0.012 s
% 3.11/1.99 % (4274)Instructions burned: 40 (million)
% 3.11/1.99 % (4274)------------------------------
% 3.11/1.99 % (4274)------------------------------
% 3.11/2.00 % (4275)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_3905 for (2996ds/6Mi)
% 3.11/2.00 % (4275)Instruction limit reached!
% 3.11/2.00 % (4275)------------------------------
% 3.11/2.00 % (4275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/2.00 % (4275)Termination reason: Unknown
% 3.11/2.00 % (4275)Termination phase: shuffling
% 3.11/2.00
% 3.11/2.00 % (4275)Memory used [KB]: 1663
% 3.11/2.00 % (4275)Time elapsed: 0.003 s
% 3.11/2.00 % (4275)Instructions burned: 8 (million)
% 3.11/2.00 % (4275)------------------------------
% 3.11/2.00 % (4275)------------------------------
% 3.11/2.00 % (4276)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_3905 for (2996ds/1087Mi)
% 3.11/2.01 % (4277)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_3905 for (2996ds/47Mi)
% 3.11/2.01 % (4273)Instruction limit reached!
% 3.11/2.01 % (4273)------------------------------
% 3.11/2.01 % (4273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/2.01 % (4273)Termination reason: Unknown
% 3.11/2.01 % (4273)Termination phase: Twee Goal Transformation
% 3.11/2.01
% 3.11/2.01 % (4273)Memory used [KB]: 3070
% 3.11/2.01 % (4273)Time elapsed: 0.040 s
% 3.11/2.01 % (4273)Instructions burned: 152 (million)
% 3.11/2.01 % (4273)------------------------------
% 3.11/2.01 % (4273)------------------------------
% 3.11/2.02 % (4277)Instruction limit reached!
% 3.11/2.02 % (4277)------------------------------
% 3.11/2.02 % (4277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/2.02 % (4277)Termination reason: Unknown
% 3.11/2.02 % (4277)Termination phase: shuffling
% 3.11/2.02
% 3.11/2.02 % (4277)Memory used [KB]: 2430
% 3.11/2.02 % (4277)Time elapsed: 0.014 s
% 3.11/2.02 % (4277)Instructions burned: 48 (million)
% 3.11/2.02 % (4277)------------------------------
% 3.11/2.02 % (4277)------------------------------
% 3.11/2.02 % (4278)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_3905 for (2996ds/44Mi)
% 5.57/2.03 % (4279)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_3905 for (2996ds/432Mi)
% 5.57/2.03 % (4278)Instruction limit reached!
% 5.57/2.03 % (4278)------------------------------
% 5.57/2.03 % (4278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.03 % (4278)Termination reason: Unknown
% 5.57/2.03 % (4278)Termination phase: shuffling
% 5.57/2.03
% 5.57/2.03 % (4278)Memory used [KB]: 2430
% 5.57/2.03 % (4278)Time elapsed: 0.013 s
% 5.57/2.03 % (4278)Instructions burned: 46 (million)
% 5.57/2.03 % (4278)------------------------------
% 5.57/2.03 % (4278)------------------------------
% 5.57/2.04 % (4280)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_3905 for (2996ds/62Mi)
% 5.57/2.05 % (4258)Instruction limit reached!
% 5.57/2.05 % (4258)------------------------------
% 5.57/2.05 % (4258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.05 % (4258)Termination reason: Unknown
% 5.57/2.05 % (4258)Termination phase: Saturation
% 5.57/2.05
% 5.57/2.05 % (4258)Memory used [KB]: 10362
% 5.57/2.05 % (4258)Time elapsed: 0.279 s
% 5.57/2.05 % (4258)Instructions burned: 879 (million)
% 5.57/2.05 % (4258)------------------------------
% 5.57/2.05 % (4258)------------------------------
% 5.57/2.06 % (4280)Instruction limit reached!
% 5.57/2.06 % (4280)------------------------------
% 5.57/2.06 % (4280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.06 % (4280)Termination reason: Unknown
% 5.57/2.06 % (4280)Termination phase: Property scanning
% 5.57/2.06
% 5.57/2.06 % (4280)Memory used [KB]: 2558
% 5.57/2.06 % (4280)Time elapsed: 0.018 s
% 5.57/2.06 % (4280)Instructions burned: 63 (million)
% 5.57/2.06 % (4280)------------------------------
% 5.57/2.06 % (4280)------------------------------
% 5.57/2.06 % (4251)Instruction limit reached!
% 5.57/2.06 % (4251)------------------------------
% 5.57/2.06 % (4251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.06 % (4251)Termination reason: Unknown
% 5.57/2.06 % (4251)Termination phase: Saturation
% 5.57/2.06
% 5.57/2.06 % (4251)Memory used [KB]: 12153
% 5.57/2.06 % (4251)Time elapsed: 0.321 s
% 5.57/2.06 % (4251)Instructions burned: 904 (million)
% 5.57/2.06 % (4251)------------------------------
% 5.57/2.06 % (4251)------------------------------
% 5.57/2.07 % (4281)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_3905 for (2995ds/31Mi)
% 5.57/2.07 % (4282)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_3905 for (2995ds/96Mi)
% 5.57/2.07 % (4269)Instruction limit reached!
% 5.57/2.07 % (4269)------------------------------
% 5.57/2.07 % (4269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.07 % (4269)Termination reason: Unknown
% 5.57/2.07 % (4269)Termination phase: Saturation
% 5.57/2.07
% 5.57/2.07 % (4269)Memory used [KB]: 7675
% 5.57/2.07 % (4269)Time elapsed: 0.111 s
% 5.57/2.07 % (4269)Instructions burned: 449 (million)
% 5.57/2.07 % (4269)------------------------------
% 5.57/2.07 % (4269)------------------------------
% 5.57/2.07 % (4283)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_3905 for (2995ds/453Mi)
% 5.57/2.07 % (4281)Instruction limit reached!
% 5.57/2.07 % (4281)------------------------------
% 5.57/2.07 % (4281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.07 % (4281)Termination reason: Unknown
% 5.57/2.07 % (4281)Termination phase: shuffling
% 5.57/2.07
% 5.57/2.07 % (4281)Memory used [KB]: 2302
% 5.57/2.07 % (4281)Time elapsed: 0.011 s
% 5.57/2.07 % (4281)Instructions burned: 33 (million)
% 5.57/2.07 % (4281)------------------------------
% 5.57/2.07 % (4281)------------------------------
% 5.57/2.08 % (4284)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_3905 for (2995ds/71Mi)
% 5.57/2.09 % (4285)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_3905 for (2995ds/83Mi)
% 5.57/2.09 % (4282)Instruction limit reached!
% 5.57/2.09 % (4282)------------------------------
% 5.57/2.09 % (4282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.09 % (4282)Termination reason: Unknown
% 5.57/2.09 % (4282)Termination phase: Clausification
% 5.57/2.09
% 5.57/2.09 % (4282)Memory used [KB]: 2814
% 5.57/2.09 % (4282)Time elapsed: 0.026 s
% 5.57/2.09 % (4282)Instructions burned: 96 (million)
% 5.57/2.09 % (4282)------------------------------
% 5.57/2.09 % (4282)------------------------------
% 5.57/2.10 % (4284)Instruction limit reached!
% 5.57/2.10 % (4284)------------------------------
% 5.57/2.10 % (4284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.10 % (4284)Termination reason: Unknown
% 5.57/2.10 % (4284)Termination phase: Property scanning
% 5.57/2.10
% 5.57/2.10 % (4284)Memory used [KB]: 2558
% 5.57/2.10 % (4284)Time elapsed: 0.020 s
% 5.57/2.10 % (4284)Instructions burned: 71 (million)
% 5.57/2.10 % (4284)------------------------------
% 5.57/2.10 % (4284)------------------------------
% 5.57/2.10 % (4286)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_3905 for (2995ds/11Mi)
% 5.57/2.11 % (4286)Instruction limit reached!
% 5.57/2.11 % (4286)------------------------------
% 5.57/2.11 % (4286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.11 % (4286)Termination reason: Unknown
% 5.57/2.11 % (4286)Termination phase: shuffling
% 5.57/2.11
% 5.57/2.11 % (4286)Memory used [KB]: 1791
% 5.57/2.11 % (4286)Time elapsed: 0.004 s
% 5.57/2.11 % (4286)Instructions burned: 11 (million)
% 5.57/2.11 % (4286)------------------------------
% 5.57/2.11 % (4286)------------------------------
% 5.57/2.11 % (4287)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_3905 for (2995ds/41Mi)
% 5.57/2.11 % (4285)Instruction limit reached!
% 5.57/2.11 % (4285)------------------------------
% 5.57/2.11 % (4285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.11 % (4285)Termination reason: Unknown
% 5.57/2.11 % (4285)Termination phase: Property scanning
% 5.57/2.11
% 5.57/2.11 % (4285)Memory used [KB]: 2558
% 5.57/2.11 % (4285)Time elapsed: 0.024 s
% 5.57/2.11 % (4285)Instructions burned: 84 (million)
% 5.57/2.11 % (4285)------------------------------
% 5.57/2.11 % (4285)------------------------------
% 5.57/2.11 % (4288)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3905 for (2995ds/6Mi)
% 5.57/2.12 % (4288)Instruction limit reached!
% 5.57/2.12 % (4288)------------------------------
% 5.57/2.12 % (4288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.12 % (4288)Termination reason: Unknown
% 5.57/2.12 % (4288)Termination phase: shuffling
% 5.57/2.12
% 5.57/2.12 % (4288)Memory used [KB]: 1663
% 5.57/2.12 % (4288)Time elapsed: 0.003 s
% 5.57/2.12 % (4288)Instructions burned: 7 (million)
% 5.57/2.12 % (4288)------------------------------
% 5.57/2.12 % (4288)------------------------------
% 5.57/2.12 % (4287)Instruction limit reached!
% 5.57/2.12 % (4287)------------------------------
% 5.57/2.12 % (4287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.12 % (4287)Termination reason: Unknown
% 5.57/2.12 % (4287)Termination phase: shuffling
% 5.57/2.12
% 5.57/2.12 % (4287)Memory used [KB]: 2302
% 5.57/2.12 % (4287)Time elapsed: 0.012 s
% 5.57/2.12 % (4287)Instructions burned: 42 (million)
% 5.57/2.12 % (4287)------------------------------
% 5.57/2.12 % (4287)------------------------------
% 5.57/2.12 % (4289)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_3905 for (2995ds/150Mi)
% 5.57/2.12 % (4272)Instruction limit reached!
% 5.57/2.12 % (4272)------------------------------
% 5.57/2.12 % (4272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.57/2.12 % (4272)Termination reason: Unknown
% 5.57/2.12 % (4272)Termination phase: Saturation
% 5.57/2.12
% 5.57/2.12 % (4272)Memory used [KB]: 8187
% 5.57/2.12 % (4272)Time elapsed: 0.156 s
% 5.57/2.12 % (4272)Instructions burned: 507 (million)
% 5.57/2.12 % (4272)------------------------------
% 5.57/2.12 % (4272)------------------------------
% 6.18/2.13 % (4290)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_3905 for (2995ds/343Mi)
% 6.18/2.13 % (4291)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_3905 for (2995ds/109Mi)
% 6.18/2.13 % (4292)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_3905 for (2995ds/253Mi)
% 6.18/2.14 % (4279)Instruction limit reached!
% 6.18/2.14 % (4279)------------------------------
% 6.18/2.14 % (4279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.18/2.14 % (4279)Termination reason: Unknown
% 6.18/2.14 % (4279)Termination phase: Saturation
% 6.18/2.14
% 6.18/2.14 % (4279)Memory used [KB]: 3198
% 6.18/2.14 % (4279)Time elapsed: 0.108 s
% 6.18/2.14 % (4279)Instructions burned: 435 (million)
% 6.18/2.14 % (4279)------------------------------
% 6.18/2.14 % (4279)------------------------------
% 6.18/2.15 % (4293)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_3905 for (2995ds/140Mi)
% 6.18/2.15 % (4291)Instruction limit reached!
% 6.18/2.15 % (4291)------------------------------
% 6.18/2.15 % (4291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.18/2.15 % (4291)Termination reason: Unknown
% 6.18/2.15 % (4291)Termination phase: SInE selection
% 6.18/2.15
% 6.18/2.15 % (4291)Memory used [KB]: 2686
% 6.18/2.15 % (4291)Time elapsed: 0.029 s
% 6.18/2.15 % (4291)Instructions burned: 109 (million)
% 6.18/2.15 % (4291)------------------------------
% 6.18/2.15 % (4291)------------------------------
% 6.18/2.16 % (4289)Instruction limit reached!
% 6.18/2.16 % (4289)------------------------------
% 6.18/2.16 % (4289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.18/2.16 % (4289)Termination reason: Unknown
% 6.18/2.16 % (4289)Termination phase: Property scanning
% 6.18/2.16
% 6.18/2.16 % (4289)Memory used [KB]: 5245
% 6.18/2.16 % (4289)Time elapsed: 0.045 s
% 6.18/2.16 % (4289)Instructions burned: 150 (million)
% 6.18/2.16 % (4289)------------------------------
% 6.18/2.16 % (4289)------------------------------
% 6.18/2.16 % (4294)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_3905 for (2994ds/614Mi)
% 6.18/2.17 % (4295)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_3905 for (2994ds/202Mi)
% 6.18/2.18 % (4293)Instruction limit reached!
% 6.18/2.18 % (4293)------------------------------
% 6.18/2.18 % (4293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.18/2.18 % (4293)Termination reason: Unknown
% 6.18/2.18 % (4293)Termination phase: Property scanning
% 6.18/2.18
% 6.18/2.18 % (4293)Memory used [KB]: 2814
% 6.18/2.18 % (4293)Time elapsed: 0.038 s
% 6.18/2.18 % (4293)Instructions burned: 142 (million)
% 6.18/2.18 % (4293)------------------------------
% 6.18/2.18 % (4293)------------------------------
% 6.18/2.19 % (4296)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_3905 for (2994ds/339Mi)
% 6.18/2.19 % (4283)Instruction limit reached!
% 6.18/2.19 % (4283)------------------------------
% 6.18/2.19 % (4283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.18/2.19 % (4283)Termination reason: Unknown
% 6.18/2.19 % (4283)Termination phase: Saturation
% 6.18/2.19
% 6.18/2.19 % (4283)Memory used [KB]: 7675
% 6.18/2.19 % (4283)Time elapsed: 0.121 s
% 6.18/2.19 % (4283)Instructions burned: 453 (million)
% 6.18/2.19 % (4283)------------------------------
% 6.18/2.19 % (4283)------------------------------
% 6.63/2.20 % (4297)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_3905 for (2994ds/283Mi)
% 6.63/2.21 % (4292)Instruction limit reached!
% 6.63/2.21 % (4292)------------------------------
% 6.63/2.21 % (4292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.63/2.21 % (4292)Termination reason: Unknown
% 6.63/2.21 % (4292)Termination phase: Saturation
% 6.63/2.21
% 6.63/2.21 % (4292)Memory used [KB]: 5628
% 6.63/2.21 % (4292)Time elapsed: 0.074 s
% 6.63/2.21 % (4292)Instructions burned: 254 (million)
% 6.63/2.21 % (4292)------------------------------
% 6.63/2.21 % (4292)------------------------------
% 6.63/2.22 % (4290)Instruction limit reached!
% 6.63/2.22 % (4290)------------------------------
% 6.63/2.22 % (4290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.63/2.22 % (4290)Termination reason: Unknown
% 6.63/2.22 % (4290)Termination phase: Saturation
% 6.63/2.22
% 6.63/2.22 % (4290)Memory used [KB]: 8443
% 6.63/2.22 % (4290)Time elapsed: 0.090 s
% 6.63/2.22 % (4290)Instructions burned: 343 (million)
% 6.63/2.22 % (4290)------------------------------
% 6.63/2.22 % (4290)------------------------------
% 6.63/2.22 % (4298)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_3905 for (2994ds/134Mi)
% 6.63/2.22 % (4299)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_3905 for (2994ds/298Mi)
% 6.63/2.23 % (4295)Instruction limit reached!
% 6.63/2.23 % (4295)------------------------------
% 6.63/2.23 % (4295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.63/2.23 % (4295)Termination reason: Unknown
% 6.63/2.23 % (4295)Termination phase: Property scanning
% 6.63/2.23
% 6.63/2.23 % (4295)Memory used [KB]: 5373
% 6.63/2.23 % (4295)Time elapsed: 0.059 s
% 6.63/2.23 % (4295)Instructions burned: 204 (million)
% 6.63/2.23 % (4295)------------------------------
% 6.63/2.23 % (4295)------------------------------
% 6.63/2.24 % (4300)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_3905 for (2993ds/192Mi)
% 6.63/2.25 % (4298)Instruction limit reached!
% 6.63/2.25 % (4298)------------------------------
% 6.63/2.25 % (4298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.63/2.25 % (4298)Termination reason: Unknown
% 6.63/2.25 % (4298)Termination phase: Function definition elimination
% 6.63/2.25
% 6.63/2.25 % (4298)Memory used [KB]: 2814
% 6.63/2.25 % (4298)Time elapsed: 0.036 s
% 6.63/2.25 % (4298)Instructions burned: 136 (million)
% 6.63/2.25 % (4298)------------------------------
% 6.63/2.25 % (4298)------------------------------
% 6.63/2.26 % (4301)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_3905 for (2993ds/258Mi)
% 6.63/2.27 % (4297)Instruction limit reached!
% 6.63/2.27 % (4297)------------------------------
% 6.63/2.27 % (4297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.63/2.27 % (4297)Termination reason: Unknown
% 6.63/2.27 % (4297)Termination phase: Saturation
% 6.63/2.27
% 6.63/2.27 % (4297)Memory used [KB]: 7547
% 6.63/2.27 % (4297)Time elapsed: 0.072 s
% 6.63/2.27 % (4297)Instructions burned: 286 (million)
% 6.63/2.27 % (4297)------------------------------
% 6.63/2.27 % (4297)------------------------------
% 6.63/2.28 % (4296)Instruction limit reached!
% 6.63/2.28 % (4296)------------------------------
% 6.63/2.28 % (4296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.63/2.28 % (4296)Termination reason: Unknown
% 6.63/2.28 % (4296)Termination phase: Saturation
% 6.63/2.28
% 6.63/2.28 % (4296)Memory used [KB]: 7931
% 6.63/2.28 % (4296)Time elapsed: 0.092 s
% 6.63/2.28 % (4296)Instructions burned: 341 (million)
% 6.63/2.28 % (4296)------------------------------
% 6.63/2.28 % (4296)------------------------------
% 6.63/2.28 % (4302)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_3905 for (2993ds/90Mi)
% 6.63/2.29 % (4300)Instruction limit reached!
% 6.63/2.29 % (4300)------------------------------
% 6.63/2.29 % (4300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.63/2.29 % (4300)Termination reason: Unknown
% 6.63/2.29 % (4300)Termination phase: Saturation
% 6.63/2.29
% 6.63/2.29 % (4300)Memory used [KB]: 7547
% 6.63/2.29 % (4300)Time elapsed: 0.050 s
% 6.63/2.29 % (4300)Instructions burned: 192 (million)
% 6.63/2.29 % (4300)------------------------------
% 6.63/2.29 % (4300)------------------------------
% 6.63/2.29 % (4303)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_3905 for (2993ds/231Mi)
% 7.28/2.30 % (4304)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_3905 for (2993ds/458Mi)
% 7.28/2.30 % (4299)Instruction limit reached!
% 7.28/2.30 % (4299)------------------------------
% 7.28/2.30 % (4299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.30 % (4299)Termination reason: Unknown
% 7.28/2.30 % (4299)Termination phase: Saturation
% 7.28/2.30
% 7.28/2.30 % (4299)Memory used [KB]: 7547
% 7.28/2.30 % (4299)Time elapsed: 0.075 s
% 7.28/2.30 % (4299)Instructions burned: 300 (million)
% 7.28/2.30 % (4299)------------------------------
% 7.28/2.30 % (4299)------------------------------
% 7.28/2.31 % (4302)Instruction limit reached!
% 7.28/2.31 % (4302)------------------------------
% 7.28/2.31 % (4302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.31 % (4302)Termination reason: Unknown
% 7.28/2.31 % (4302)Termination phase: Property scanning
% 7.28/2.31
% 7.28/2.31 % (4302)Memory used [KB]: 2558
% 7.28/2.31 % (4302)Time elapsed: 0.025 s
% 7.28/2.31 % (4302)Instructions burned: 93 (million)
% 7.28/2.31 % (4302)------------------------------
% 7.28/2.31 % (4302)------------------------------
% 7.28/2.31 % (4305)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_3905 for (2993ds/31Mi)
% 7.28/2.32 % (4305)Instruction limit reached!
% 7.28/2.32 % (4305)------------------------------
% 7.28/2.32 % (4305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.32 % (4305)Termination reason: Unknown
% 7.28/2.32 % (4305)Termination phase: shuffling
% 7.28/2.32
% 7.28/2.32 % (4305)Memory used [KB]: 2174
% 7.28/2.32 % (4305)Time elapsed: 0.010 s
% 7.28/2.32 % (4305)Instructions burned: 32 (million)
% 7.28/2.32 % (4305)------------------------------
% 7.28/2.32 % (4305)------------------------------
% 7.28/2.32 % (4306)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_3905 for (2993ds/297Mi)
% 7.28/2.33 % (4307)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_3905 for (2993ds/987Mi)
% 7.28/2.33 % (4301)Instruction limit reached!
% 7.28/2.33 % (4301)------------------------------
% 7.28/2.33 % (4301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.33 % (4301)Termination reason: Unknown
% 7.28/2.33 % (4301)Termination phase: Saturation
% 7.28/2.33
% 7.28/2.33 % (4301)Memory used [KB]: 7931
% 7.28/2.33 % (4301)Time elapsed: 0.068 s
% 7.28/2.33 % (4301)Instructions burned: 259 (million)
% 7.28/2.33 % (4301)------------------------------
% 7.28/2.33 % (4301)------------------------------
% 7.28/2.34 % (4276)Instruction limit reached!
% 7.28/2.34 % (4276)------------------------------
% 7.28/2.34 % (4276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.34 % (4276)Termination reason: Unknown
% 7.28/2.34 % (4276)Termination phase: Saturation
% 7.28/2.34
% 7.28/2.34 % (4276)Memory used [KB]: 12792
% 7.28/2.34 % (4276)Time elapsed: 0.338 s
% 7.28/2.34 % (4276)Instructions burned: 1087 (million)
% 7.28/2.34 % (4276)------------------------------
% 7.28/2.34 % (4276)------------------------------
% 7.28/2.34 % (4308)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_3905 for (2993ds/182Mi)
% 7.28/2.34 % (4294)Instruction limit reached!
% 7.28/2.34 % (4294)------------------------------
% 7.28/2.34 % (4294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.34 % (4294)Termination reason: Unknown
% 7.28/2.34 % (4294)Termination phase: Saturation
% 7.28/2.34
% 7.28/2.34 % (4294)Memory used [KB]: 10234
% 7.28/2.34 % (4294)Time elapsed: 0.176 s
% 7.28/2.34 % (4294)Instructions burned: 614 (million)
% 7.28/2.34 % (4294)------------------------------
% 7.28/2.34 % (4294)------------------------------
% 7.28/2.35 % (4309)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_3905 for (2992ds/182Mi)
% 7.28/2.35 % (4310)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_3905 for (2992ds/154Mi)
% 7.28/2.35 % (4303)Instruction limit reached!
% 7.28/2.35 % (4303)------------------------------
% 7.28/2.35 % (4303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.35 % (4303)Termination reason: Unknown
% 7.28/2.35 % (4303)Termination phase: Saturation
% 7.28/2.35
% 7.28/2.35 % (4303)Memory used [KB]: 8443
% 7.28/2.35 % (4303)Time elapsed: 0.060 s
% 7.28/2.35 % (4303)Instructions burned: 231 (million)
% 7.28/2.35 % (4303)------------------------------
% 7.28/2.35 % (4303)------------------------------
% 7.28/2.36 % (4311)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_3905 for (2992ds/79Mi)
% 7.28/2.38 % (4311)Instruction limit reached!
% 7.28/2.38 % (4311)------------------------------
% 7.28/2.38 % (4311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.38 % (4311)Termination reason: Unknown
% 7.28/2.38 % (4311)Termination phase: Property scanning
% 7.28/2.38
% 7.28/2.38 % (4311)Memory used [KB]: 2558
% 7.28/2.38 % (4311)Time elapsed: 0.022 s
% 7.28/2.38 % (4311)Instructions burned: 80 (million)
% 7.28/2.38 % (4311)------------------------------
% 7.28/2.38 % (4311)------------------------------
% 7.28/2.38 % (4308)Instruction limit reached!
% 7.28/2.38 % (4308)------------------------------
% 7.28/2.38 % (4308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.38 % (4308)Termination reason: Unknown
% 7.28/2.38 % (4308)Termination phase: Saturation
% 7.28/2.38
% 7.28/2.38 % (4308)Memory used [KB]: 7419
% 7.28/2.38 % (4308)Time elapsed: 0.047 s
% 7.28/2.38 % (4308)Instructions burned: 182 (million)
% 7.28/2.38 % (4308)------------------------------
% 7.28/2.38 % (4308)------------------------------
% 7.28/2.39 % (4310)Instruction limit reached!
% 7.28/2.39 % (4310)------------------------------
% 7.28/2.39 % (4310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.39 % (4310)Termination reason: Unknown
% 7.28/2.39 % (4310)Termination phase: Property scanning
% 7.28/2.39
% 7.28/2.39 % (4310)Memory used [KB]: 3070
% 7.28/2.39 % (4310)Time elapsed: 0.040 s
% 7.28/2.39 % (4310)Instructions burned: 157 (million)
% 7.28/2.39 % (4310)------------------------------
% 7.28/2.39 % (4310)------------------------------
% 7.28/2.39 % (4306)Instruction limit reached!
% 7.28/2.39 % (4306)------------------------------
% 7.28/2.39 % (4306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.28/2.39 % (4306)Termination reason: Unknown
% 7.28/2.39 % (4306)Termination phase: Saturation
% 7.28/2.39
% 7.28/2.39 % (4306)Memory used [KB]: 7547
% 7.28/2.39 % (4306)Time elapsed: 0.074 s
% 7.28/2.39 % (4306)Instructions burned: 298 (million)
% 7.28/2.39 % (4306)------------------------------
% 7.28/2.39 % (4306)------------------------------
% 7.28/2.39 % (4312)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_3905 for (2992ds/216Mi)
% 7.28/2.39 % (4313)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_3905 for (2992ds/114Mi)
% 8.02/2.40 % (4314)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_3905 for (2992ds/922Mi)
% 8.02/2.40 % (4315)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_3905 for (2992ds/182Mi)
% 8.02/2.40 % (4309)Instruction limit reached!
% 8.02/2.40 % (4309)------------------------------
% 8.02/2.40 % (4309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.40 % (4309)Termination reason: Unknown
% 8.02/2.40 % (4309)Termination phase: Property scanning
% 8.02/2.40
% 8.02/2.40 % (4309)Memory used [KB]: 5245
% 8.02/2.40 % (4309)Time elapsed: 0.053 s
% 8.02/2.40 % (4309)Instructions burned: 185 (million)
% 8.02/2.40 % (4309)------------------------------
% 8.02/2.40 % (4309)------------------------------
% 8.02/2.41 % (4316)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_3905 for (2992ds/164Mi)
% 8.02/2.42 % (4304)Instruction limit reached!
% 8.02/2.42 % (4304)------------------------------
% 8.02/2.42 % (4304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.42 % (4304)Termination reason: Unknown
% 8.02/2.42 % (4304)Termination phase: Saturation
% 8.02/2.42
% 8.02/2.42 % (4304)Memory used [KB]: 9722
% 8.02/2.42 % (4304)Time elapsed: 0.123 s
% 8.02/2.42 % (4304)Instructions burned: 459 (million)
% 8.02/2.42 % (4304)------------------------------
% 8.02/2.42 % (4304)------------------------------
% 8.02/2.42 % (4313)Instruction limit reached!
% 8.02/2.42 % (4313)------------------------------
% 8.02/2.42 % (4313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.42 % (4313)Termination reason: Unknown
% 8.02/2.42 % (4313)Termination phase: Property scanning
% 8.02/2.42
% 8.02/2.42 % (4313)Memory used [KB]: 2814
% 8.02/2.42 % (4313)Time elapsed: 0.031 s
% 8.02/2.42 % (4313)Instructions burned: 116 (million)
% 8.02/2.42 % (4313)------------------------------
% 8.02/2.42 % (4313)------------------------------
% 8.02/2.43 % (4317)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_3905 for (2992ds/50Mi)
% 8.02/2.43 % (4318)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_3905 for (2992ds/368Mi)
% 8.02/2.44 % (4317)Instruction limit reached!
% 8.02/2.44 % (4317)------------------------------
% 8.02/2.44 % (4317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.44 % (4317)Termination reason: Unknown
% 8.02/2.44 % (4317)Termination phase: shuffling
% 8.02/2.44
% 8.02/2.44 % (4317)Memory used [KB]: 2558
% 8.02/2.44 % (4317)Time elapsed: 0.015 s
% 8.02/2.44 % (4317)Instructions burned: 53 (million)
% 8.02/2.44 % (4317)------------------------------
% 8.02/2.44 % (4317)------------------------------
% 8.02/2.44 % (4312)Instruction limit reached!
% 8.02/2.44 % (4312)------------------------------
% 8.02/2.44 % (4312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.44 % (4312)Termination reason: Unknown
% 8.02/2.44 % (4312)Termination phase: Property scanning
% 8.02/2.44
% 8.02/2.44 % (4312)Memory used [KB]: 3070
% 8.02/2.44 % (4312)Time elapsed: 0.054 s
% 8.02/2.44 % (4312)Instructions burned: 218 (million)
% 8.02/2.44 % (4312)------------------------------
% 8.02/2.44 % (4312)------------------------------
% 8.02/2.45 % (4315)Instruction limit reached!
% 8.02/2.45 % (4315)------------------------------
% 8.02/2.45 % (4315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.45 % (4315)Termination reason: Unknown
% 8.02/2.45 % (4315)Termination phase: Property scanning
% 8.02/2.45
% 8.02/2.45 % (4315)Memory used [KB]: 3070
% 8.02/2.45 % (4315)Time elapsed: 0.046 s
% 8.02/2.45 % (4315)Instructions burned: 184 (million)
% 8.02/2.45 % (4315)------------------------------
% 8.02/2.45 % (4315)------------------------------
% 8.02/2.45 % (4316)Instruction limit reached!
% 8.02/2.45 % (4316)------------------------------
% 8.02/2.45 % (4316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.45 % (4316)Termination reason: Unknown
% 8.02/2.45 % (4316)Termination phase: Function definition elimination
% 8.02/2.45
% 8.02/2.45 % (4316)Memory used [KB]: 2814
% 8.02/2.45 % (4316)Time elapsed: 0.042 s
% 8.02/2.45 % (4316)Instructions burned: 166 (million)
% 8.02/2.45 % (4316)------------------------------
% 8.02/2.45 % (4316)------------------------------
% 8.02/2.45 % (4320)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_3905 for (2991ds/1021Mi)
% 8.02/2.45 % (4321)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_3905 for (2991ds/267Mi)
% 8.02/2.45 % (4322)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_3905 for (2991ds/204Mi)
% 8.02/2.46 % (4323)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_3905 for (2991ds/26Mi)
% 8.02/2.47 % (4323)Instruction limit reached!
% 8.02/2.47 % (4323)------------------------------
% 8.02/2.47 % (4323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.47 % (4323)Termination reason: Unknown
% 8.02/2.47 % (4323)Termination phase: shuffling
% 8.02/2.47
% 8.02/2.47 % (4323)Memory used [KB]: 2046
% 8.02/2.47 % (4323)Time elapsed: 0.009 s
% 8.02/2.47 % (4323)Instructions burned: 29 (million)
% 8.02/2.47 % (4323)------------------------------
% 8.02/2.47 % (4323)------------------------------
% 8.02/2.48 % (4324)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_3905 for (2991ds/53Mi)
% 8.02/2.49 % (4324)Instruction limit reached!
% 8.02/2.49 % (4324)------------------------------
% 8.02/2.49 % (4324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.49 % (4324)Termination reason: Unknown
% 8.02/2.49 % (4324)Termination phase: shuffling
% 8.02/2.49
% 8.02/2.49 % (4324)Memory used [KB]: 2558
% 8.02/2.49 % (4324)Time elapsed: 0.016 s
% 8.02/2.49 % (4324)Instructions burned: 56 (million)
% 8.02/2.49 % (4324)------------------------------
% 8.02/2.49 % (4324)------------------------------
% 8.48/2.50 % (4325)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_3905 for (2991ds/4436Mi)
% 8.48/2.51 % (4322)Instruction limit reached!
% 8.48/2.51 % (4322)------------------------------
% 8.48/2.51 % (4322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.48/2.51 % (4322)Termination reason: Unknown
% 8.48/2.51 % (4322)Termination phase: Property scanning
% 8.48/2.51
% 8.48/2.51 % (4322)Memory used [KB]: 2942
% 8.48/2.51 % (4322)Time elapsed: 0.052 s
% 8.48/2.51 % (4322)Instructions burned: 206 (million)
% 8.48/2.51 % (4322)------------------------------
% 8.48/2.51 % (4322)------------------------------
% 8.48/2.52 % (4326)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_3905 for (2991ds/1539Mi)
% 8.48/2.52 % (4321)Instruction limit reached!
% 8.48/2.52 % (4321)------------------------------
% 8.48/2.52 % (4321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.48/2.52 % (4321)Termination reason: Unknown
% 8.48/2.52 % (4321)Termination phase: Saturation
% 8.48/2.52
% 8.48/2.52 % (4321)Memory used [KB]: 7547
% 8.48/2.52 % (4321)Time elapsed: 0.067 s
% 8.48/2.52 % (4321)Instructions burned: 267 (million)
% 8.48/2.52 % (4321)------------------------------
% 8.48/2.52 % (4321)------------------------------
% 8.48/2.53 % (4327)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_3905 for (2991ds/408Mi)
% 8.48/2.53 % (4318)Instruction limit reached!
% 8.48/2.53 % (4318)------------------------------
% 8.48/2.53 % (4318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.48/2.53 % (4318)Termination reason: Unknown
% 8.48/2.53 % (4318)Termination phase: Saturation
% 8.48/2.53
% 8.48/2.53 % (4318)Memory used [KB]: 9338
% 8.48/2.53 % (4318)Time elapsed: 0.098 s
% 8.48/2.53 % (4318)Instructions burned: 370 (million)
% 8.48/2.53 % (4318)------------------------------
% 8.48/2.53 % (4318)------------------------------
% 8.48/2.54 % (4328)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_3905 for (2991ds/5205Mi)
% 8.48/2.57 % (4307)Instruction limit reached!
% 8.48/2.57 % (4307)------------------------------
% 8.48/2.57 % (4307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.48/2.57 % (4307)Termination reason: Unknown
% 8.48/2.57 % (4307)Termination phase: Saturation
% 8.48/2.57
% 8.48/2.57 % (4307)Memory used [KB]: 17014
% 8.48/2.57 % (4307)Time elapsed: 0.247 s
% 8.48/2.57 % (4307)Instructions burned: 987 (million)
% 8.48/2.57 % (4307)------------------------------
% 8.48/2.57 % (4307)------------------------------
% 8.48/2.58 % (4329)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_3905 for (2990ds/1913Mi)
% 8.99/2.65 % (4327)Instruction limit reached!
% 8.99/2.65 % (4327)------------------------------
% 8.99/2.65 % (4327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.99/2.65 % (4327)Termination reason: Unknown
% 8.99/2.65 % (4327)Termination phase: Saturation
% 8.99/2.65
% 8.99/2.65 % (4327)Memory used [KB]: 11641
% 8.99/2.65 % (4327)Time elapsed: 0.118 s
% 8.99/2.65 % (4327)Instructions burned: 409 (million)
% 8.99/2.65 % (4327)------------------------------
% 8.99/2.65 % (4327)------------------------------
% 8.99/2.66 % (4330)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_3905 for (2989ds/4350Mi)
% 8.99/2.68 % (4314)Instruction limit reached!
% 8.99/2.68 % (4314)------------------------------
% 8.99/2.68 % (4314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.99/2.68 % (4314)Termination reason: Unknown
% 8.99/2.68 % (4314)Termination phase: Saturation
% 8.99/2.68
% 8.99/2.68 % (4314)Memory used [KB]: 12537
% 8.99/2.68 % (4314)Time elapsed: 0.283 s
% 8.99/2.68 % (4314)Instructions burned: 924 (million)
% 8.99/2.68 % (4314)------------------------------
% 8.99/2.68 % (4314)------------------------------
% 8.99/2.69 % (4331)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_3905 for (2989ds/68Mi)
% 9.41/2.71 % (4331)Instruction limit reached!
% 9.41/2.71 % (4331)------------------------------
% 9.41/2.71 % (4331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.41/2.71 % (4331)Termination reason: Unknown
% 9.41/2.71 % (4331)Termination phase: Property scanning
% 9.41/2.71
% 9.41/2.71 % (4331)Memory used [KB]: 2558
% 9.41/2.71 % (4331)Time elapsed: 0.020 s
% 9.41/2.71 % (4331)Instructions burned: 71 (million)
% 9.41/2.71 % (4331)------------------------------
% 9.41/2.71 % (4331)------------------------------
% 9.41/2.72 % (4332)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_3905 for (2989ds/358Mi)
% 9.41/2.77 % (4320)Instruction limit reached!
% 9.41/2.77 % (4320)------------------------------
% 9.41/2.77 % (4320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.41/2.77 % (4320)Termination reason: Unknown
% 9.41/2.77 % (4320)Termination phase: Saturation
% 9.41/2.77
% 9.41/2.77 % (4320)Memory used [KB]: 12792
% 9.41/2.77 % (4320)Time elapsed: 0.314 s
% 9.41/2.77 % (4320)Instructions burned: 1022 (million)
% 9.41/2.77 % (4320)------------------------------
% 9.41/2.77 % (4320)------------------------------
% 9.41/2.78 % (4333)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_3905 for (2988ds/31Mi)
% 9.41/2.79 % (4333)Instruction limit reached!
% 9.41/2.79 % (4333)------------------------------
% 9.41/2.79 % (4333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.41/2.79 % (4333)Termination reason: Unknown
% 9.41/2.79 % (4333)Termination phase: shuffling
% 9.41/2.79
% 9.41/2.79 % (4333)Memory used [KB]: 2174
% 9.41/2.79 % (4333)Time elapsed: 0.010 s
% 9.41/2.79 % (4333)Instructions burned: 31 (million)
% 9.41/2.79 % (4333)------------------------------
% 9.41/2.79 % (4333)------------------------------
% 9.41/2.80 % (4334)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_3905 for (2988ds/279Mi)
% 9.78/2.81 % (4332)Instruction limit reached!
% 9.78/2.81 % (4332)------------------------------
% 9.78/2.81 % (4332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.78/2.81 % (4332)Termination reason: Unknown
% 9.78/2.81 % (4332)Termination phase: Saturation
% 9.78/2.81
% 9.78/2.81 % (4332)Memory used [KB]: 8443
% 9.78/2.81 % (4332)Time elapsed: 0.093 s
% 9.78/2.81 % (4332)Instructions burned: 359 (million)
% 9.78/2.81 % (4332)------------------------------
% 9.78/2.81 % (4332)------------------------------
% 9.78/2.82 % (4335)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_3905 for (2988ds/258Mi)
% 9.78/2.86 % (4334)Instruction limit reached!
% 9.78/2.86 % (4334)------------------------------
% 9.78/2.86 % (4334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.78/2.86 % (4334)Termination reason: Unknown
% 9.78/2.86 % (4334)Termination phase: Saturation
% 9.78/2.86
% 9.78/2.86 % (4334)Memory used [KB]: 7547
% 9.78/2.86 % (4334)Time elapsed: 0.070 s
% 9.78/2.86 % (4334)Instructions burned: 279 (million)
% 9.78/2.86 % (4334)------------------------------
% 9.78/2.86 % (4334)------------------------------
% 9.78/2.87 % (4336)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_3905 for (2987ds/26Mi)
% 9.78/2.88 % (4336)Instruction limit reached!
% 9.78/2.88 % (4336)------------------------------
% 9.78/2.88 % (4336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.78/2.88 % (4336)Termination reason: Unknown
% 9.78/2.88 % (4336)Termination phase: shuffling
% 9.78/2.88
% 9.78/2.88 % (4336)Memory used [KB]: 2046
% 9.78/2.88 % (4336)Time elapsed: 0.008 s
% 9.78/2.88 % (4336)Instructions burned: 26 (million)
% 9.78/2.88 % (4336)------------------------------
% 9.78/2.88 % (4336)------------------------------
% 9.78/2.89 % (4335)Instruction limit reached!
% 9.78/2.89 % (4335)------------------------------
% 9.78/2.89 % (4335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.78/2.89 % (4335)Termination reason: Unknown
% 9.78/2.89 % (4335)Termination phase: Saturation
% 9.78/2.89
% 9.78/2.89 % (4335)Memory used [KB]: 8315
% 9.78/2.89 % (4335)Time elapsed: 0.068 s
% 9.78/2.89 % (4335)Instructions burned: 258 (million)
% 9.78/2.89 % (4335)------------------------------
% 9.78/2.89 % (4335)------------------------------
% 9.78/2.89 % (4337)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_3905 for (2987ds/995Mi)
% 10.05/2.90 % (4338)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_3905 for (2987ds/373Mi)
% 10.05/2.98 % (4326)Instruction limit reached!
% 10.05/2.98 % (4326)------------------------------
% 10.05/2.98 % (4326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.05/2.98 % (4326)Termination reason: Unknown
% 10.05/2.98 % (4326)Termination phase: Saturation
% 10.05/2.98
% 10.05/2.98 % (4326)Memory used [KB]: 11257
% 10.05/2.98 % (4326)Time elapsed: 0.467 s
% 10.05/2.98 % (4326)Instructions burned: 1541 (million)
% 10.05/2.98 % (4326)------------------------------
% 10.05/2.98 % (4326)------------------------------
% 10.05/2.99 % (4339)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_3905 for (2986ds/253Mi)
% 10.05/3.00 % (4338)Instruction limit reached!
% 10.05/3.00 % (4338)------------------------------
% 10.05/3.00 % (4338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.05/3.00 % (4338)Termination reason: Unknown
% 10.05/3.00 % (4338)Termination phase: Saturation
% 10.05/3.00
% 10.05/3.00 % (4338)Memory used [KB]: 9338
% 10.05/3.00 % (4338)Time elapsed: 0.101 s
% 10.05/3.00 % (4338)Instructions burned: 373 (million)
% 10.05/3.00 % (4338)------------------------------
% 10.05/3.00 % (4338)------------------------------
% 10.05/3.01 % (4340)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_3905 for (2986ds/832Mi)
% 12.58/3.05 % (4339)Instruction limit reached!
% 12.58/3.05 % (4339)------------------------------
% 12.58/3.05 % (4339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.58/3.05 % (4339)Termination reason: Unknown
% 12.58/3.05 % (4339)Termination phase: Saturation
% 12.58/3.05
% 12.58/3.05 % (4339)Memory used [KB]: 7547
% 12.58/3.05 % (4339)Time elapsed: 0.063 s
% 12.58/3.05 % (4339)Instructions burned: 253 (million)
% 12.58/3.05 % (4339)------------------------------
% 12.58/3.05 % (4339)------------------------------
% 12.58/3.06 % (4341)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_3905 for (2985ds/668Mi)
% 13.16/3.14 % (4337)Instruction limit reached!
% 13.16/3.14 % (4337)------------------------------
% 13.16/3.14 % (4337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.16/3.14 % (4337)Termination reason: Unknown
% 13.16/3.14 % (4337)Termination phase: Saturation
% 13.16/3.14
% 13.16/3.14 % (4337)Memory used [KB]: 16886
% 13.16/3.14 % (4337)Time elapsed: 0.250 s
% 13.16/3.14 % (4337)Instructions burned: 995 (million)
% 13.16/3.14 % (4337)------------------------------
% 13.16/3.14 % (4337)------------------------------
% 13.16/3.15 % (4342)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_3905 for (2984ds/40Mi)
% 13.16/3.16 % (4342)Instruction limit reached!
% 13.16/3.16 % (4342)------------------------------
% 13.16/3.16 % (4342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.16/3.16 % (4342)Termination reason: Unknown
% 13.16/3.16 % (4342)Termination phase: shuffling
% 13.16/3.16
% 13.16/3.16 % (4342)Memory used [KB]: 2302
% 13.16/3.16 % (4342)Time elapsed: 0.012 s
% 13.16/3.16 % (4342)Instructions burned: 40 (million)
% 13.16/3.16 % (4342)------------------------------
% 13.16/3.16 % (4342)------------------------------
% 13.16/3.16 % (4329)Instruction limit reached!
% 13.16/3.16 % (4329)------------------------------
% 13.16/3.16 % (4329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.16/3.16 % (4329)Termination reason: Unknown
% 13.16/3.16 % (4329)Termination phase: Saturation
% 13.16/3.16
% 13.16/3.16 % (4329)Memory used [KB]: 6396
% 13.16/3.16 % (4329)Time elapsed: 0.600 s
% 13.16/3.16 % (4329)Instructions burned: 1914 (million)
% 13.16/3.16 % (4329)------------------------------
% 13.16/3.16 % (4329)------------------------------
% 13.16/3.17 % (4343)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_3905 for (2984ds/294Mi)
% 13.16/3.17 % (4344)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_3905 for (2984ds/187Mi)
% 13.46/3.22 % (4344)Instruction limit reached!
% 13.46/3.22 % (4344)------------------------------
% 13.46/3.22 % (4344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.46/3.22 % (4344)Termination reason: Unknown
% 13.46/3.22 % (4344)Termination phase: Saturation
% 13.46/3.22
% 13.46/3.22 % (4344)Memory used [KB]: 7419
% 13.46/3.22 % (4344)Time elapsed: 0.048 s
% 13.46/3.22 % (4344)Instructions burned: 187 (million)
% 13.46/3.22 % (4344)------------------------------
% 13.46/3.22 % (4344)------------------------------
% 13.46/3.23 % (4341)Instruction limit reached!
% 13.46/3.23 % (4341)------------------------------
% 13.46/3.23 % (4341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.46/3.23 % (4341)Termination reason: Unknown
% 13.46/3.23 % (4341)Termination phase: Saturation
% 13.46/3.23
% 13.46/3.23 % (4341)Memory used [KB]: 13048
% 13.46/3.23 % (4341)Time elapsed: 0.165 s
% 13.46/3.23 % (4341)Instructions burned: 669 (million)
% 13.46/3.23 % (4341)------------------------------
% 13.46/3.23 % (4341)------------------------------
% 13.46/3.23 % (4345)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_3905 for (2984ds/371Mi)
% 13.46/3.24 % (4346)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_3905 for (2984ds/1827Mi)
% 13.46/3.24 % (4343)Instruction limit reached!
% 13.46/3.24 % (4343)------------------------------
% 13.46/3.24 % (4343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.46/3.24 % (4343)Termination reason: Unknown
% 13.46/3.24 % (4343)Termination phase: Saturation
% 13.46/3.24
% 13.46/3.24 % (4343)Memory used [KB]: 7547
% 13.46/3.24 % (4343)Time elapsed: 0.074 s
% 13.46/3.24 % (4343)Instructions burned: 295 (million)
% 13.46/3.24 % (4343)------------------------------
% 13.46/3.24 % (4343)------------------------------
% 13.46/3.25 % (4340)Instruction limit reached!
% 13.46/3.25 % (4340)------------------------------
% 13.46/3.25 % (4340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.46/3.25 % (4340)Termination reason: Unknown
% 13.46/3.25 % (4340)Termination phase: Saturation
% 13.46/3.25
% 13.46/3.25 % (4340)Memory used [KB]: 11897
% 13.46/3.25 % (4340)Time elapsed: 0.242 s
% 13.46/3.25 % (4340)Instructions burned: 832 (million)
% 13.46/3.25 % (4340)------------------------------
% 13.46/3.25 % (4340)------------------------------
% 13.46/3.25 % (4347)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_3905 for (2983ds/70Mi)
% 13.46/3.26 % (4348)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_3905 for (2983ds/316Mi)
% 13.46/3.27 % (4347)Instruction limit reached!
% 13.46/3.27 % (4347)------------------------------
% 13.46/3.27 % (4347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.46/3.27 % (4347)Termination reason: Unknown
% 13.46/3.27 % (4347)Termination phase: Property scanning
% 13.46/3.27
% 13.46/3.27 % (4347)Memory used [KB]: 2558
% 13.46/3.27 % (4347)Time elapsed: 0.020 s
% 13.46/3.27 % (4347)Instructions burned: 73 (million)
% 13.46/3.27 % (4347)------------------------------
% 13.46/3.27 % (4347)------------------------------
% 13.46/3.28 % (4349)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_3905 for (2983ds/932Mi)
% 14.35/3.33 % (4345)Instruction limit reached!
% 14.35/3.33 % (4345)------------------------------
% 14.35/3.33 % (4345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.35/3.33 % (4345)Termination reason: Unknown
% 14.35/3.33 % (4345)Termination phase: Saturation
% 14.35/3.33
% 14.35/3.33 % (4345)Memory used [KB]: 9210
% 14.35/3.33 % (4345)Time elapsed: 0.100 s
% 14.35/3.33 % (4345)Instructions burned: 371 (million)
% 14.35/3.33 % (4345)------------------------------
% 14.35/3.33 % (4345)------------------------------
% 14.35/3.34 % (4350)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_3905 for (2983ds/4714Mi)
% 14.35/3.34 % (4348)Instruction limit reached!
% 14.35/3.34 % (4348)------------------------------
% 14.35/3.34 % (4348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.35/3.34 % (4348)Termination reason: Unknown
% 14.35/3.34 % (4348)Termination phase: Saturation
% 14.35/3.34
% 14.35/3.34 % (4348)Memory used [KB]: 7547
% 14.35/3.34 % (4348)Time elapsed: 0.081 s
% 14.35/3.34 % (4348)Instructions burned: 317 (million)
% 14.35/3.34 % (4348)------------------------------
% 14.35/3.34 % (4348)------------------------------
% 14.35/3.35 % (4351)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_3905 for (2983ds/8250Mi)
% 15.16/3.52 % (4349)Instruction limit reached!
% 15.16/3.52 % (4349)------------------------------
% 15.16/3.52 % (4349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.16/3.52 % (4349)Termination reason: Unknown
% 15.16/3.52 % (4349)Termination phase: Saturation
% 15.16/3.52
% 15.16/3.52 % (4349)Memory used [KB]: 16630
% 15.16/3.52 % (4349)Time elapsed: 0.237 s
% 15.16/3.52 % (4349)Instructions burned: 933 (million)
% 15.16/3.52 % (4349)------------------------------
% 15.16/3.52 % (4349)------------------------------
% 15.16/3.53 % (4352)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_3905 for (2981ds/770Mi)
% 16.01/3.73 % (4352)Instruction limit reached!
% 16.01/3.73 % (4352)------------------------------
% 16.01/3.73 % (4352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.01/3.73 % (4352)Termination reason: Unknown
% 16.01/3.73 % (4352)Termination phase: Saturation
% 16.01/3.73
% 16.01/3.73 % (4352)Memory used [KB]: 7803
% 16.01/3.73 % (4352)Time elapsed: 0.208 s
% 16.01/3.73 % (4352)Instructions burned: 771 (million)
% 16.01/3.73 % (4352)------------------------------
% 16.01/3.73 % (4352)------------------------------
% 16.01/3.74 % (4346)Instruction limit reached!
% 16.01/3.74 % (4346)------------------------------
% 16.01/3.74 % (4346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.01/3.74 % (4346)Termination reason: Unknown
% 16.01/3.74 % (4346)Termination phase: Saturation
% 16.01/3.74
% 16.01/3.74 % (4346)Memory used [KB]: 21364
% 16.01/3.74 % (4346)Time elapsed: 0.503 s
% 16.01/3.74 % (4346)Instructions burned: 1829 (million)
% 16.01/3.74 % (4346)------------------------------
% 16.01/3.74 % (4346)------------------------------
% 16.01/3.74 % (4353)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_3905 for (2979ds/794Mi)
% 16.01/3.75 % (4354)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_3905 for (2979ds/464Mi)
% 17.05/3.82 % (4328)Instruction limit reached!
% 17.05/3.82 % (4328)------------------------------
% 17.05/3.82 % (4328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.05/3.82 % (4328)Termination reason: Unknown
% 17.05/3.82 % (4328)Termination phase: Saturation
% 17.05/3.82
% 17.05/3.82 % (4328)Memory used [KB]: 17910
% 17.05/3.82 % (4328)Time elapsed: 1.281 s
% 17.05/3.82 % (4328)Instructions burned: 5207 (million)
% 17.05/3.82 % (4328)------------------------------
% 17.05/3.82 % (4328)------------------------------
% 17.05/3.83 % (4355)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_3905 for (2978ds/1376Mi)
% 17.05/3.87 % (4354)Instruction limit reached!
% 17.05/3.87 % (4354)------------------------------
% 17.05/3.87 % (4354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.05/3.87 % (4354)Termination reason: Unknown
% 17.05/3.87 % (4354)Termination phase: Saturation
% 17.05/3.87
% 17.05/3.87 % (4354)Memory used [KB]: 9594
% 17.05/3.87 % (4354)Time elapsed: 0.125 s
% 17.05/3.87 % (4354)Instructions burned: 465 (million)
% 17.05/3.87 % (4354)------------------------------
% 17.05/3.87 % (4354)------------------------------
% 17.05/3.88 % (4356)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_3905 for (2977ds/906Mi)
% 17.05/3.89 % (4325)Instruction limit reached!
% 17.05/3.89 % (4325)------------------------------
% 17.05/3.89 % (4325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.05/3.89 % (4325)Termination reason: Unknown
% 17.05/3.89 % (4325)Termination phase: Saturation
% 17.05/3.89
% 17.05/3.89 % (4325)Memory used [KB]: 15351
% 17.05/3.89 % (4325)Time elapsed: 1.386 s
% 17.05/3.89 % (4325)Instructions burned: 4436 (million)
% 17.05/3.89 % (4325)------------------------------
% 17.05/3.89 % (4325)------------------------------
% 17.43/3.90 % (4357)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_3905 for (2977ds/434Mi)
% 17.43/3.98 % (4353)Instruction limit reached!
% 17.43/3.98 % (4353)------------------------------
% 17.43/3.98 % (4353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.43/3.98 % (4353)Termination reason: Unknown
% 17.43/3.98 % (4353)Termination phase: Saturation
% 17.43/3.98
% 17.43/3.98 % (4353)Memory used [KB]: 6140
% 17.43/3.98 % (4353)Time elapsed: 0.234 s
% 17.43/3.98 % (4353)Instructions burned: 794 (million)
% 17.43/3.98 % (4353)------------------------------
% 17.43/3.98 % (4353)------------------------------
% 17.43/3.99 % (4358)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_3905 for (2976ds/865Mi)
% 17.43/3.99 % (4330)Instruction limit reached!
% 17.43/3.99 % (4330)------------------------------
% 17.43/3.99 % (4330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.43/3.99 % (4330)Termination reason: Unknown
% 17.43/3.99 % (4330)Termination phase: Saturation
% 17.43/3.99
% 17.43/3.99 % (4330)Memory used [KB]: 14072
% 17.43/3.99 % (4330)Time elapsed: 1.360 s
% 17.43/3.99 % (4330)Instructions burned: 4350 (million)
% 17.43/3.99 % (4330)------------------------------
% 17.43/3.99 % (4330)------------------------------
% 17.43/4.00 % (4359)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_3905 for (2976ds/593Mi)
% 19.64/4.03 % (4357)Instruction limit reached!
% 19.64/4.03 % (4357)------------------------------
% 19.64/4.03 % (4357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.64/4.03 % (4357)Termination reason: Unknown
% 19.64/4.03 % (4357)Termination phase: Saturation
% 19.64/4.03
% 19.64/4.03 % (4357)Memory used [KB]: 11769
% 19.64/4.03 % (4357)Time elapsed: 0.129 s
% 19.64/4.03 % (4357)Instructions burned: 435 (million)
% 19.64/4.03 % (4357)------------------------------
% 19.64/4.03 % (4357)------------------------------
% 19.64/4.04 % (4360)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_3905 for (2976ds/443Mi)
% 20.28/4.16 % (4359)Instruction limit reached!
% 20.28/4.16 % (4359)------------------------------
% 20.28/4.16 % (4359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.28/4.16 % (4359)Termination reason: Unknown
% 20.28/4.16 % (4359)Termination phase: Saturation
% 20.28/4.16
% 20.28/4.16 % (4359)Memory used [KB]: 7675
% 20.28/4.16 % (4359)Time elapsed: 0.152 s
% 20.28/4.16 % (4359)Instructions burned: 595 (million)
% 20.28/4.16 % (4359)------------------------------
% 20.28/4.16 % (4359)------------------------------
% 20.28/4.16 % (4360)Instruction limit reached!
% 20.28/4.16 % (4360)------------------------------
% 20.28/4.16 % (4360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.28/4.16 % (4360)Termination reason: Unknown
% 20.28/4.16 % (4360)Termination phase: Saturation
% 20.28/4.16
% 20.28/4.16 % (4360)Memory used [KB]: 9594
% 20.28/4.16 % (4360)Time elapsed: 0.122 s
% 20.28/4.16 % (4360)Instructions burned: 445 (million)
% 20.28/4.16 % (4360)------------------------------
% 20.28/4.16 % (4360)------------------------------
% 20.28/4.17 % (4356)Instruction limit reached!
% 20.28/4.17 % (4356)------------------------------
% 20.28/4.17 % (4356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.28/4.17 % (4356)Termination reason: Unknown
% 20.28/4.17 % (4356)Termination phase: Saturation
% 20.28/4.17
% 20.28/4.17 % (4356)Memory used [KB]: 11513
% 20.28/4.17 % (4356)Time elapsed: 0.283 s
% 20.28/4.17 % (4356)Instructions burned: 906 (million)
% 20.28/4.17 % (4356)------------------------------
% 20.28/4.17 % (4356)------------------------------
% 20.28/4.17 % (4361)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_3905 for (2974ds/594Mi)
% 20.28/4.17 % (4362)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_3905 for (2974ds/327Mi)
% 20.28/4.18 % (4363)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_3905 for (2974ds/5411Mi)
% 20.28/4.18 % (4355)Instruction limit reached!
% 20.28/4.18 % (4355)------------------------------
% 20.28/4.18 % (4355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.28/4.18 % (4355)Termination reason: Unknown
% 20.28/4.18 % (4355)Termination phase: Saturation
% 20.28/4.18
% 20.28/4.18 % (4355)Memory used [KB]: 9210
% 20.28/4.18 % (4355)Time elapsed: 0.350 s
% 20.28/4.18 % (4355)Instructions burned: 1376 (million)
% 20.28/4.18 % (4355)------------------------------
% 20.28/4.18 % (4355)------------------------------
% 20.28/4.19 % (4364)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_3905 for (2974ds/1762Mi)
% 20.79/4.24 % (4358)Instruction limit reached!
% 20.79/4.24 % (4358)------------------------------
% 20.79/4.24 % (4358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.79/4.24 % (4358)Termination reason: Unknown
% 20.79/4.24 % (4358)Termination phase: Saturation
% 20.79/4.24
% 20.79/4.24 % (4358)Memory used [KB]: 9978
% 20.79/4.24 % (4358)Time elapsed: 0.256 s
% 20.79/4.24 % (4358)Instructions burned: 867 (million)
% 20.79/4.24 % (4358)------------------------------
% 20.79/4.24 % (4358)------------------------------
% 20.79/4.25 % (4365)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_3905 for (2973ds/96Mi)
% 20.79/4.26 % (4362)Instruction limit reached!
% 20.79/4.26 % (4362)------------------------------
% 20.79/4.26 % (4362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.79/4.26 % (4362)Termination reason: Unknown
% 20.79/4.26 % (4362)Termination phase: Saturation
% 20.79/4.26
% 20.79/4.26 % (4362)Memory used [KB]: 11385
% 20.79/4.26 % (4362)Time elapsed: 0.094 s
% 20.79/4.26 % (4362)Instructions burned: 327 (million)
% 20.79/4.26 % (4362)------------------------------
% 20.79/4.26 % (4362)------------------------------
% 20.79/4.27 % (4366)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_3905 for (2973ds/503Mi)
% 20.79/4.28 % (4365)Instruction limit reached!
% 20.79/4.28 % (4365)------------------------------
% 20.79/4.28 % (4365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.79/4.28 % (4365)Termination reason: Unknown
% 20.79/4.28 % (4365)Termination phase: Property scanning
% 20.79/4.28
% 20.79/4.28 % (4365)Memory used [KB]: 2686
% 20.79/4.28 % (4365)Time elapsed: 0.027 s
% 20.79/4.28 % (4365)Instructions burned: 99 (million)
% 20.79/4.28 % (4365)------------------------------
% 20.79/4.28 % (4365)------------------------------
% 20.79/4.29 % (4367)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_3905 for (2973ds/90Mi)
% 21.18/4.31 % (4367)Instruction limit reached!
% 21.18/4.31 % (4367)------------------------------
% 21.18/4.31 % (4367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.18/4.31 % (4367)Termination reason: Unknown
% 21.18/4.31 % (4367)Termination phase: Preprocessing 2
% 21.18/4.31
% 21.18/4.31 % (4367)Memory used [KB]: 2558
% 21.18/4.31 % (4367)Time elapsed: 0.025 s
% 21.18/4.31 % (4367)Instructions burned: 93 (million)
% 21.18/4.31 % (4367)------------------------------
% 21.18/4.31 % (4367)------------------------------
% 21.18/4.32 % (4368)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_3905 for (2973ds/593Mi)
% 21.18/4.33 % (4361)Instruction limit reached!
% 21.18/4.33 % (4361)------------------------------
% 21.18/4.33 % (4361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.18/4.33 % (4361)Termination reason: Unknown
% 21.18/4.33 % (4361)Termination phase: Saturation
% 21.18/4.33
% 21.18/4.33 % (4361)Memory used [KB]: 9850
% 21.18/4.33 % (4361)Time elapsed: 0.168 s
% 21.18/4.33 % (4361)Instructions burned: 596 (million)
% 21.18/4.33 % (4361)------------------------------
% 21.18/4.33 % (4361)------------------------------
% 21.18/4.34 % (4369)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_3905 for (2973ds/1512Mi)
% 21.59/4.41 % (4366)Instruction limit reached!
% 21.59/4.41 % (4366)------------------------------
% 21.59/4.41 % (4366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.59/4.41 % (4366)Termination reason: Unknown
% 21.59/4.41 % (4366)Termination phase: Saturation
% 21.59/4.41
% 21.59/4.41 % (4366)Memory used [KB]: 9978
% 21.59/4.41 % (4366)Time elapsed: 0.141 s
% 21.59/4.41 % (4366)Instructions burned: 503 (million)
% 21.59/4.41 % (4366)------------------------------
% 21.59/4.41 % (4366)------------------------------
% 21.59/4.42 % (4370)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_3905 for (2972ds/569Mi)
% 21.59/4.49 % (4368)Instruction limit reached!
% 21.59/4.49 % (4368)------------------------------
% 21.59/4.49 % (4368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.59/4.49 % (4368)Termination reason: Unknown
% 21.59/4.49 % (4368)Termination phase: Saturation
% 21.59/4.49
% 21.59/4.49 % (4368)Memory used [KB]: 10234
% 21.59/4.49 % (4368)Time elapsed: 0.170 s
% 21.59/4.49 % (4368)Instructions burned: 596 (million)
% 21.59/4.49 % (4368)------------------------------
% 21.59/4.49 % (4368)------------------------------
% 22.13/4.50 % (4371)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_3905 for (2971ds/501Mi)
% 22.13/4.52 % (4350)Instruction limit reached!
% 22.13/4.52 % (4350)------------------------------
% 22.13/4.52 % (4350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.13/4.52 % (4350)Termination reason: Unknown
% 22.13/4.52 % (4350)Termination phase: Saturation
% 22.13/4.52
% 22.13/4.52 % (4350)Memory used [KB]: 7803
% 22.13/4.52 % (4350)Time elapsed: 1.182 s
% 22.13/4.52 % (4350)Instructions burned: 4714 (million)
% 22.13/4.52 % (4350)------------------------------
% 22.13/4.52 % (4350)------------------------------
% 22.13/4.53 % (4372)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_3905 for (2971ds/562Mi)
% 22.13/4.56 % (4370)Instruction limit reached!
% 22.13/4.56 % (4370)------------------------------
% 22.13/4.56 % (4370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.13/4.56 % (4370)Termination reason: Unknown
% 22.13/4.56 % (4370)Termination phase: Saturation
% 22.13/4.56
% 22.13/4.56 % (4370)Memory used [KB]: 7675
% 22.13/4.56 % (4370)Time elapsed: 0.141 s
% 22.13/4.56 % (4370)Instructions burned: 569 (million)
% 22.13/4.56 % (4370)------------------------------
% 22.13/4.56 % (4370)------------------------------
% 22.13/4.57 % (4373)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_3905 for (2970ds/406Mi)
% 22.41/4.62 % (4364)Instruction limit reached!
% 22.41/4.62 % (4364)------------------------------
% 22.41/4.62 % (4364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.41/4.62 % (4364)Termination reason: Unknown
% 22.41/4.62 % (4364)Termination phase: Saturation
% 22.41/4.62
% 22.41/4.62 % (4364)Memory used [KB]: 20980
% 22.41/4.62 % (4364)Time elapsed: 0.430 s
% 22.41/4.62 % (4364)Instructions burned: 1764 (million)
% 22.41/4.62 % (4364)------------------------------
% 22.41/4.62 % (4364)------------------------------
% 22.41/4.63 % (4374)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_3905 for (2970ds/582Mi)
% 22.41/4.65 % (4371)Instruction limit reached!
% 22.41/4.65 % (4371)------------------------------
% 22.41/4.65 % (4371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.41/4.65 % (4371)Termination reason: Unknown
% 22.41/4.65 % (4371)Termination phase: Saturation
% 22.41/4.65
% 22.41/4.65 % (4371)Memory used [KB]: 10874
% 22.41/4.65 % (4371)Time elapsed: 0.149 s
% 22.41/4.65 % (4371)Instructions burned: 502 (million)
% 22.41/4.65 % (4371)------------------------------
% 22.41/4.65 % (4371)------------------------------
% 22.41/4.66 % (4375)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_3905 for (2969ds/456Mi)
% 22.41/4.68 % (4373)Instruction limit reached!
% 22.41/4.68 % (4373)------------------------------
% 22.41/4.68 % (4373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.41/4.68 % (4373)Termination reason: Unknown
% 22.41/4.68 % (4373)Termination phase: Saturation
% 22.41/4.68
% 22.41/4.68 % (4373)Memory used [KB]: 7931
% 22.41/4.68 % (4373)Time elapsed: 0.108 s
% 22.41/4.68 % (4373)Instructions burned: 407 (million)
% 22.41/4.68 % (4373)------------------------------
% 22.41/4.68 % (4373)------------------------------
% 22.41/4.69 % (4372)Instruction limit reached!
% 22.41/4.69 % (4372)------------------------------
% 22.41/4.69 % (4372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.41/4.69 % (4372)Termination reason: Unknown
% 22.41/4.69 % (4372)Termination phase: Saturation
% 22.41/4.69
% 22.41/4.69 % (4372)Memory used [KB]: 9338
% 22.41/4.69 % (4372)Time elapsed: 0.160 s
% 22.41/4.69 % (4372)Instructions burned: 563 (million)
% 22.41/4.69 % (4372)------------------------------
% 22.41/4.69 % (4372)------------------------------
% 22.41/4.69 % (4376)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_3905 for (2969ds/393Mi)
% 22.41/4.70 % (4377)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_3905 for (2969ds/1335Mi)
% 23.39/4.78 % (4375)Instruction limit reached!
% 23.39/4.78 % (4375)------------------------------
% 23.39/4.78 % (4375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.39/4.78 % (4375)Termination reason: Unknown
% 23.39/4.78 % (4375)Termination phase: Saturation
% 23.39/4.78
% 23.39/4.78 % (4375)Memory used [KB]: 9722
% 23.39/4.78 % (4375)Time elapsed: 0.124 s
% 23.39/4.78 % (4375)Instructions burned: 458 (million)
% 23.39/4.78 % (4375)------------------------------
% 23.39/4.78 % (4375)------------------------------
% 23.39/4.79 % (4378)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_3905 for (2968ds/3373Mi)
% 23.39/4.79 % (4376)Instruction limit reached!
% 23.39/4.79 % (4376)------------------------------
% 23.39/4.79 % (4376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.39/4.79 % (4376)Termination reason: Unknown
% 23.39/4.79 % (4376)Termination phase: Saturation
% 23.39/4.79
% 23.39/4.79 % (4376)Memory used [KB]: 10234
% 23.39/4.79 % (4376)Time elapsed: 0.108 s
% 23.39/4.79 % (4376)Instructions burned: 394 (million)
% 23.39/4.79 % (4376)------------------------------
% 23.39/4.79 % (4376)------------------------------
% 23.74/4.80 % (4369)Instruction limit reached!
% 23.74/4.80 % (4369)------------------------------
% 23.74/4.80 % (4369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.74/4.80 % (4369)Termination reason: Unknown
% 23.74/4.80 % (4369)Termination phase: Saturation
% 23.74/4.80
% 23.74/4.80 % (4369)Memory used [KB]: 12792
% 23.74/4.80 % (4369)Time elapsed: 0.459 s
% 23.74/4.80 % (4369)Instructions burned: 1515 (million)
% 23.74/4.80 % (4369)------------------------------
% 23.74/4.80 % (4369)------------------------------
% 23.74/4.80 % (4379)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_3905 for (2968ds/474Mi)
% 23.74/4.80 % (4374)Instruction limit reached!
% 23.74/4.80 % (4374)------------------------------
% 23.74/4.80 % (4374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.74/4.80 % (4374)Termination reason: Unknown
% 23.74/4.80 % (4374)Termination phase: Saturation
% 23.74/4.80
% 23.74/4.80 % (4374)Memory used [KB]: 11001
% 23.74/4.80 % (4374)Time elapsed: 0.175 s
% 23.74/4.80 % (4374)Instructions burned: 584 (million)
% 23.74/4.80 % (4374)------------------------------
% 23.74/4.80 % (4374)------------------------------
% 23.74/4.81 % (4380)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_3905 for (2968ds/157Mi)
% 23.74/4.81 % (4381)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_3905 for (2968ds/590Mi)
% 23.74/4.85 % (4380)Instruction limit reached!
% 23.74/4.85 % (4380)------------------------------
% 23.74/4.85 % (4380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.74/4.85 % (4380)Termination reason: Unknown
% 23.74/4.85 % (4380)Termination phase: Function definition elimination
% 23.74/4.85
% 23.74/4.85 % (4380)Memory used [KB]: 3070
% 23.74/4.85 % (4380)Time elapsed: 0.041 s
% 23.74/4.85 % (4380)Instructions burned: 161 (million)
% 23.74/4.85 % (4380)------------------------------
% 23.74/4.85 % (4380)------------------------------
% 23.74/4.86 % (4382)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_3905 for (2967ds/104Mi)
% 23.74/4.89 % (4382)Instruction limit reached!
% 23.74/4.89 % (4382)------------------------------
% 23.74/4.89 % (4382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.74/4.89 % (4382)Termination reason: Unknown
% 23.74/4.89 % (4382)Termination phase: Property scanning
% 23.74/4.89
% 23.74/4.89 % (4382)Memory used [KB]: 2814
% 23.74/4.89 % (4382)Time elapsed: 0.028 s
% 23.74/4.89 % (4382)Instructions burned: 105 (million)
% 23.74/4.89 % (4382)------------------------------
% 23.74/4.89 % (4382)------------------------------
% 23.74/4.90 % (4383)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_3905 for (2967ds/414Mi)
% 24.58/4.92 % (4379)Instruction limit reached!
% 24.58/4.92 % (4379)------------------------------
% 24.58/4.92 % (4379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.58/4.92 % (4379)Termination reason: Unknown
% 24.58/4.92 % (4379)Termination phase: Saturation
% 24.58/4.92
% 24.58/4.92 % (4379)Memory used [KB]: 7547
% 24.58/4.92 % (4379)Time elapsed: 0.118 s
% 24.58/4.92 % (4379)Instructions burned: 476 (million)
% 24.58/4.92 % (4379)------------------------------
% 24.58/4.92 % (4379)------------------------------
% 24.58/4.93 % (4384)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_3905 for (2967ds/715Mi)
% 24.58/4.98 % (4381)Instruction limit reached!
% 24.58/4.98 % (4381)------------------------------
% 24.58/4.98 % (4381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.58/4.98 % (4381)Termination reason: Unknown
% 24.58/4.98 % (4381)Termination phase: Saturation
% 24.58/4.98
% 24.58/4.98 % (4381)Memory used [KB]: 8699
% 24.58/4.98 % (4381)Time elapsed: 0.164 s
% 24.58/4.98 % (4381)Instructions burned: 590 (million)
% 24.58/4.98 % (4381)------------------------------
% 24.58/4.98 % (4381)------------------------------
% 24.58/4.99 % (4385)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_3905 for (2966ds/961Mi)
% 24.58/5.00 % (4383)Instruction limit reached!
% 24.58/5.00 % (4383)------------------------------
% 24.58/5.00 % (4383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.58/5.00 % (4383)Termination reason: Unknown
% 24.58/5.00 % (4383)Termination phase: Saturation
% 24.58/5.00
% 24.58/5.00 % (4383)Memory used [KB]: 7675
% 24.58/5.00 % (4383)Time elapsed: 0.103 s
% 24.58/5.00 % (4383)Instructions burned: 415 (million)
% 24.58/5.00 % (4383)------------------------------
% 24.58/5.00 % (4383)------------------------------
% 24.58/5.01 % (4386)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_3905 for (2966ds/1213Mi)
% 26.63/5.05 % (4377)Instruction limit reached!
% 26.63/5.05 % (4377)------------------------------
% 26.63/5.05 % (4377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.63/5.05 % (4377)Termination reason: Unknown
% 26.63/5.05 % (4377)Termination phase: Saturation
% 26.63/5.05
% 26.63/5.05 % (4377)Memory used [KB]: 9594
% 26.63/5.05 % (4377)Time elapsed: 0.360 s
% 26.63/5.05 % (4377)Instructions burned: 1335 (million)
% 26.63/5.05 % (4377)------------------------------
% 26.63/5.05 % (4377)------------------------------
% 26.63/5.07 % (4387)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_3905 for (2965ds/1979Mi)
% 27.22/5.14 % (4384)Instruction limit reached!
% 27.22/5.14 % (4384)------------------------------
% 27.22/5.14 % (4384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.22/5.14 % (4384)Termination reason: Unknown
% 27.22/5.14 % (4384)Termination phase: Saturation
% 27.22/5.14
% 27.22/5.14 % (4384)Memory used [KB]: 5628
% 27.22/5.14 % (4384)Time elapsed: 0.232 s
% 27.22/5.14 % (4384)Instructions burned: 717 (million)
% 27.22/5.14 % (4384)------------------------------
% 27.22/5.14 % (4384)------------------------------
% 27.22/5.15 % (4388)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_3905 for (2964ds/481Mi)
% 27.52/5.27 % (4388)Instruction limit reached!
% 27.52/5.27 % (4388)------------------------------
% 27.52/5.27 % (4388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.52/5.27 % (4388)Termination reason: Unknown
% 27.52/5.27 % (4388)Termination phase: Saturation
% 27.52/5.27
% 27.52/5.27 % (4388)Memory used [KB]: 7675
% 27.52/5.27 % (4388)Time elapsed: 0.120 s
% 27.52/5.27 % (4388)Instructions burned: 481 (million)
% 27.52/5.27 % (4388)------------------------------
% 27.52/5.27 % (4388)------------------------------
% 27.52/5.27 % (4385)Instruction limit reached!
% 27.52/5.27 % (4385)------------------------------
% 27.52/5.27 % (4385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.52/5.27 % (4385)Termination reason: Unknown
% 27.52/5.27 % (4385)Termination phase: Saturation
% 27.52/5.27
% 27.52/5.27 % (4385)Memory used [KB]: 10490
% 27.52/5.27 % (4385)Time elapsed: 0.310 s
% 27.52/5.27 % (4385)Instructions burned: 963 (million)
% 27.52/5.27 % (4385)------------------------------
% 27.52/5.27 % (4385)------------------------------
% 27.52/5.28 % (4389)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_3905 for (2963ds/783Mi)
% 27.52/5.28 % (4390)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_3905 for (2963ds/432Mi)
% 28.05/5.38 % (4386)Instruction limit reached!
% 28.05/5.38 % (4386)------------------------------
% 28.05/5.38 % (4386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.05/5.38 % (4386)Termination reason: Unknown
% 28.05/5.38 % (4386)Termination phase: Saturation
% 28.05/5.38
% 28.05/5.38 % (4386)Memory used [KB]: 15351
% 28.05/5.38 % (4386)Time elapsed: 0.400 s
% 28.05/5.38 % (4386)Instructions burned: 1216 (million)
% 28.05/5.38 % (4386)------------------------------
% 28.05/5.38 % (4386)------------------------------
% 28.05/5.40 % (4391)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_3905 for (2962ds/1670Mi)
% 28.74/5.40 % (4390)Instruction limit reached!
% 28.74/5.40 % (4390)------------------------------
% 28.74/5.40 % (4390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.74/5.40 % (4390)Termination reason: Unknown
% 28.74/5.40 % (4390)Termination phase: Saturation
% 28.74/5.40
% 28.74/5.40 % (4390)Memory used [KB]: 9722
% 28.74/5.40 % (4390)Time elapsed: 0.118 s
% 28.74/5.40 % (4390)Instructions burned: 434 (million)
% 28.74/5.40 % (4390)------------------------------
% 28.74/5.40 % (4390)------------------------------
% 28.74/5.41 % (4392)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_3905 for (2962ds/90Mi)
% 28.74/5.43 % (4392)Instruction limit reached!
% 28.74/5.43 % (4392)------------------------------
% 28.74/5.43 % (4392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.74/5.43 % (4392)Termination reason: Unknown
% 28.74/5.43 % (4392)Termination phase: Preprocessing 1
% 28.74/5.43
% 28.74/5.43 % (4392)Memory used [KB]: 2558
% 28.74/5.43 % (4392)Time elapsed: 0.025 s
% 28.74/5.43 % (4392)Instructions burned: 93 (million)
% 28.74/5.43 % (4392)------------------------------
% 28.74/5.43 % (4392)------------------------------
% 28.74/5.44 % (4393)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_3905 for (2961ds/346Mi)
% 29.20/5.52 % (4389)Instruction limit reached!
% 29.20/5.52 % (4389)------------------------------
% 29.20/5.52 % (4389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.20/5.52 % (4389)Termination reason: Unknown
% 29.20/5.52 % (4389)Termination phase: Saturation
% 29.20/5.52
% 29.20/5.52 % (4389)Memory used [KB]: 12025
% 29.20/5.52 % (4389)Time elapsed: 0.241 s
% 29.20/5.52 % (4389)Instructions burned: 784 (million)
% 29.20/5.52 % (4389)------------------------------
% 29.20/5.52 % (4389)------------------------------
% 29.20/5.53 % (4394)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_3905 for (2961ds/401Mi)
% 29.20/5.53 % (4393)Instruction limit reached!
% 29.20/5.53 % (4393)------------------------------
% 29.20/5.53 % (4393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.20/5.53 % (4393)Termination reason: Unknown
% 29.20/5.53 % (4393)Termination phase: Saturation
% 29.20/5.53
% 29.20/5.53 % (4393)Memory used [KB]: 7547
% 29.20/5.53 % (4393)Time elapsed: 0.089 s
% 29.20/5.53 % (4393)Instructions burned: 349 (million)
% 29.20/5.53 % (4393)------------------------------
% 29.20/5.53 % (4393)------------------------------
% 29.20/5.54 % (4395)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_3905 for (2960ds/6454Mi)
% 29.85/5.63 % (4394)Instruction limit reached!
% 29.85/5.63 % (4394)------------------------------
% 29.85/5.63 % (4394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.85/5.63 % (4394)Termination reason: Unknown
% 29.85/5.63 % (4394)Termination phase: Saturation
% 29.85/5.63
% 29.85/5.63 % (4394)Memory used [KB]: 7675
% 29.85/5.63 % (4394)Time elapsed: 0.100 s
% 29.85/5.63 % (4394)Instructions burned: 401 (million)
% 29.85/5.63 % (4394)------------------------------
% 29.85/5.63 % (4394)------------------------------
% 29.85/5.64 % (4396)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_3905 for (2960ds/283Mi)
% 29.85/5.66 % (4387)Instruction limit reached!
% 29.85/5.66 % (4387)------------------------------
% 29.85/5.66 % (4387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.85/5.66 % (4387)Termination reason: Unknown
% 29.85/5.66 % (4387)Termination phase: Saturation
% 29.85/5.66
% 29.85/5.66 % (4387)Memory used [KB]: 10618
% 29.85/5.66 % (4387)Time elapsed: 0.599 s
% 29.85/5.66 % (4387)Instructions burned: 1981 (million)
% 29.85/5.66 % (4387)------------------------------
% 29.85/5.66 % (4387)------------------------------
% 29.85/5.67 % (4397)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_3905 for (2959ds/865Mi)
% 30.88/5.71 % (4396)Instruction limit reached!
% 30.88/5.71 % (4396)------------------------------
% 30.88/5.71 % (4396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.88/5.71 % (4396)Termination reason: Unknown
% 30.88/5.71 % (4396)Termination phase: Saturation
% 30.88/5.71
% 30.88/5.71 % (4396)Memory used [KB]: 8187
% 30.88/5.71 % (4396)Time elapsed: 0.076 s
% 30.88/5.71 % (4396)Instructions burned: 285 (million)
% 30.88/5.71 % (4396)------------------------------
% 30.88/5.71 % (4396)------------------------------
% 30.88/5.72 % (4398)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_3905 for (2959ds/4528Mi)
% 31.25/5.82 % (4378)Instruction limit reached!
% 31.25/5.82 % (4378)------------------------------
% 31.25/5.82 % (4378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.25/5.82 % (4378)Termination reason: Unknown
% 31.25/5.82 % (4378)Termination phase: Saturation
% 31.25/5.82
% 31.25/5.82 % (4378)Memory used [KB]: 13304
% 31.25/5.82 % (4378)Time elapsed: 1.026 s
% 31.25/5.82 % (4378)Instructions burned: 3374 (million)
% 31.25/5.82 % (4378)------------------------------
% 31.25/5.82 % (4378)------------------------------
% 31.25/5.82 % (4391)Instruction limit reached!
% 31.25/5.82 % (4391)------------------------------
% 31.25/5.82 % (4391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.25/5.82 % (4391)Termination reason: Unknown
% 31.25/5.82 % (4391)Termination phase: Saturation
% 31.25/5.82
% 31.25/5.82 % (4391)Memory used [KB]: 18166
% 31.25/5.82 % (4391)Time elapsed: 0.428 s
% 31.25/5.82 % (4391)Instructions burned: 1672 (million)
% 31.25/5.82 % (4391)------------------------------
% 31.25/5.82 % (4391)------------------------------
% 31.25/5.83 % (4399)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_3905 for (2958ds/1001Mi)
% 31.25/5.83 % (4400)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_3905 for (2958ds/102Mi)
% 31.25/5.86 % (4400)Instruction limit reached!
% 31.25/5.86 % (4400)------------------------------
% 31.25/5.86 % (4400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.25/5.86 % (4400)Termination reason: Unknown
% 31.25/5.86 % (4400)Termination phase: Property scanning
% 31.25/5.86
% 31.25/5.86 % (4400)Memory used [KB]: 2814
% 31.25/5.86 % (4400)Time elapsed: 0.027 s
% 31.25/5.86 % (4400)Instructions burned: 102 (million)
% 31.25/5.86 % (4400)------------------------------
% 31.25/5.86 % (4400)------------------------------
% 31.25/5.86 % (4363)Instruction limit reached!
% 31.25/5.86 % (4363)------------------------------
% 31.25/5.86 % (4363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.25/5.86 % (4363)Termination reason: Unknown
% 31.25/5.86 % (4363)Termination phase: Saturation
% 31.25/5.86
% 31.25/5.86 % (4363)Memory used [KB]: 17014
% 31.25/5.86 % (4363)Time elapsed: 1.685 s
% 31.25/5.86 % (4363)Instructions burned: 5413 (million)
% 31.25/5.86 % (4363)------------------------------
% 31.25/5.86 % (4363)------------------------------
% 31.25/5.87 % (4401)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_3905 for (2957ds/952Mi)
% 31.25/5.87 % (4402)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_3905 for (2957ds/578Mi)
% 31.93/5.91 % (4397)Instruction limit reached!
% 31.93/5.91 % (4397)------------------------------
% 31.93/5.91 % (4397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.93/5.91 % (4397)Termination reason: Unknown
% 31.93/5.91 % (4397)Termination phase: Saturation
% 31.93/5.91
% 31.93/5.91 % (4397)Memory used [KB]: 8443
% 31.93/5.91 % (4397)Time elapsed: 0.235 s
% 31.93/5.91 % (4397)Instructions burned: 867 (million)
% 31.93/5.91 % (4397)------------------------------
% 31.93/5.91 % (4397)------------------------------
% 31.93/5.92 % (4403)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_3905 for (2957ds/643Mi)
% 31.93/5.93 % (4398)Refutation not found, incomplete strategy
% 31.93/5.93 % (4398)------------------------------
% 31.93/5.93 % (4398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.93/5.93 % (4398)Termination reason: Refutation not found, incomplete strategy
% 31.93/5.93
% 31.93/5.93
% 31.93/5.93 % (4398)Memory used [KB]: 3198
% 31.93/5.93 % (4398)Time elapsed: 0.205 s
% 31.93/5.93 % (4398)Instructions burned: 796 (million)
% 31.93/5.93 % (4398)------------------------------
% 31.93/5.93 % (4398)------------------------------
% 31.93/5.94 % (4404)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_3905 for (2957ds/865Mi)
% 31.93/5.98 % (4351)Instruction limit reached!
% 31.93/5.98 % (4351)------------------------------
% 31.93/5.98 % (4351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.93/5.98 % (4351)Termination reason: Unknown
% 31.93/5.98 % (4351)Termination phase: Saturation
% 31.93/5.98
% 31.93/5.98 % (4351)Memory used [KB]: 29423
% 31.93/5.98 % (4351)Time elapsed: 2.636 s
% 31.93/5.98 % (4351)Instructions burned: 8251 (million)
% 31.93/5.98 % (4351)------------------------------
% 31.93/5.98 % (4351)------------------------------
% 31.93/5.99 % (4405)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_3905 for (2956ds/1174Mi)
% 31.93/6.01 % (4402)Instruction limit reached!
% 31.93/6.01 % (4402)------------------------------
% 31.93/6.01 % (4402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.93/6.01 % (4402)Termination reason: Unknown
% 31.93/6.01 % (4402)Termination phase: Saturation
% 31.93/6.01
% 31.93/6.01 % (4402)Memory used [KB]: 11129
% 31.93/6.01 % (4402)Time elapsed: 0.145 s
% 31.93/6.01 % (4402)Instructions burned: 580 (million)
% 31.93/6.01 % (4402)------------------------------
% 31.93/6.01 % (4402)------------------------------
% 31.93/6.02 % (4406)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_3905 for (2956ds/644Mi)
% 33.68/6.08 % (4403)Instruction limit reached!
% 33.68/6.08 % (4403)------------------------------
% 33.68/6.08 % (4403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.68/6.08 % (4403)Termination reason: Unknown
% 33.68/6.08 % (4403)Termination phase: Saturation
% 33.68/6.08
% 33.68/6.08 % (4403)Memory used [KB]: 7675
% 33.68/6.08 % (4403)Time elapsed: 0.164 s
% 33.68/6.08 % (4403)Instructions burned: 646 (million)
% 33.68/6.08 % (4403)------------------------------
% 33.68/6.08 % (4403)------------------------------
% 33.68/6.09 % (4407)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_3905 for (2955ds/1201Mi)
% 34.26/6.13 % (4399)Instruction limit reached!
% 34.26/6.13 % (4399)------------------------------
% 34.26/6.13 % (4399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.26/6.13 % (4399)Termination reason: Unknown
% 34.26/6.13 % (4399)Termination phase: Saturation
% 34.26/6.13
% 34.26/6.13 % (4399)Memory used [KB]: 11641
% 34.26/6.13 % (4399)Time elapsed: 0.303 s
% 34.26/6.13 % (4399)Instructions burned: 1002 (million)
% 34.26/6.13 % (4399)------------------------------
% 34.26/6.13 % (4399)------------------------------
% 34.26/6.14 % (4408)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_3905 for (2954ds/1046Mi)
% 34.26/6.15 % (4401)Instruction limit reached!
% 34.26/6.15 % (4401)------------------------------
% 34.26/6.15 % (4401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.26/6.15 % (4401)Termination reason: Unknown
% 34.26/6.15 % (4401)Termination phase: Saturation
% 34.26/6.15
% 34.26/6.15 % (4401)Memory used [KB]: 10490
% 34.26/6.15 % (4401)Time elapsed: 0.283 s
% 34.26/6.15 % (4401)Instructions burned: 953 (million)
% 34.26/6.15 % (4401)------------------------------
% 34.26/6.15 % (4401)------------------------------
% 34.26/6.16 % (4409)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_3905 for (2954ds/222Mi)
% 34.26/6.17 % (4404)Instruction limit reached!
% 34.26/6.17 % (4404)------------------------------
% 34.26/6.17 % (4404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.26/6.17 % (4404)Termination reason: Unknown
% 34.26/6.17 % (4404)Termination phase: Saturation
% 34.26/6.17
% 34.26/6.17 % (4404)Memory used [KB]: 7931
% 34.26/6.17 % (4404)Time elapsed: 0.239 s
% 34.26/6.17 % (4404)Instructions burned: 868 (million)
% 34.26/6.17 % (4404)------------------------------
% 34.26/6.17 % (4404)------------------------------
% 34.26/6.18 % (4410)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_3905 for (2954ds/68Mi)
% 34.53/6.20 % (4410)Instruction limit reached!
% 34.53/6.20 % (4410)------------------------------
% 34.53/6.20 % (4410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.53/6.20 % (4410)Termination reason: Unknown
% 34.53/6.20 % (4410)Termination phase: Property scanning
% 34.53/6.20
% 34.53/6.20 % (4410)Memory used [KB]: 2558
% 34.53/6.20 % (4410)Time elapsed: 0.020 s
% 34.53/6.20 % (4410)Instructions burned: 71 (million)
% 34.53/6.20 % (4410)------------------------------
% 34.53/6.20 % (4410)------------------------------
% 34.53/6.21 % (4406)Instruction limit reached!
% 34.53/6.21 % (4406)------------------------------
% 34.53/6.21 % (4406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.53/6.21 % (4406)Termination reason: Unknown
% 34.53/6.21 % (4406)Termination phase: Saturation
% 34.53/6.21
% 34.53/6.21 % (4406)Memory used [KB]: 8443
% 34.53/6.21 % (4406)Time elapsed: 0.186 s
% 34.53/6.21 % (4406)Instructions burned: 644 (million)
% 34.53/6.21 % (4406)------------------------------
% 34.53/6.21 % (4406)------------------------------
% 34.53/6.21 % (4411)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_3905 for (2954ds/454Mi)
% 34.53/6.22 % (4409)Instruction limit reached!
% 34.53/6.22 % (4409)------------------------------
% 34.53/6.22 % (4409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.53/6.22 % (4409)Termination reason: Unknown
% 34.53/6.22 % (4409)Termination phase: Saturation
% 34.53/6.22
% 34.53/6.22 % (4409)Memory used [KB]: 7547
% 34.53/6.22 % (4409)Time elapsed: 0.057 s
% 34.53/6.22 % (4409)Instructions burned: 223 (million)
% 34.53/6.22 % (4409)------------------------------
% 34.53/6.22 % (4409)------------------------------
% 34.53/6.22 % (4412)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_3905 for (2954ds/360Mi)
% 34.53/6.23 % (4413)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_3905 for (2954ds/157Mi)
% 34.53/6.26 % (4413)Instruction limit reached!
% 34.53/6.26 % (4413)------------------------------
% 34.53/6.26 % (4413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.53/6.26 % (4413)Termination reason: Unknown
% 34.53/6.26 % (4413)Termination phase: Function definition elimination
% 34.53/6.26
% 34.53/6.26 % (4413)Memory used [KB]: 2814
% 34.53/6.26 % (4413)Time elapsed: 0.040 s
% 34.53/6.26 % (4413)Instructions burned: 160 (million)
% 34.53/6.26 % (4413)------------------------------
% 34.53/6.26 % (4413)------------------------------
% 34.53/6.27 % (4414)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_3905 for (2953ds/5061Mi)
% 35.07/6.31 % (4412)Instruction limit reached!
% 35.07/6.31 % (4412)------------------------------
% 35.07/6.31 % (4412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.07/6.31 % (4412)Termination reason: Unknown
% 35.07/6.31 % (4412)Termination phase: Saturation
% 35.07/6.31
% 35.07/6.31 % (4412)Memory used [KB]: 7547
% 35.07/6.31 % (4412)Time elapsed: 0.090 s
% 35.07/6.31 % (4412)Instructions burned: 360 (million)
% 35.07/6.31 % (4412)------------------------------
% 35.07/6.31 % (4412)------------------------------
% 35.07/6.32 % (4415)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_3905 for (2953ds/2401Mi)
% 35.07/6.32 % (4411)Instruction limit reached!
% 35.07/6.32 % (4411)------------------------------
% 35.07/6.32 % (4411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.07/6.32 % (4411)Termination reason: Unknown
% 35.07/6.32 % (4411)Termination phase: Saturation
% 35.07/6.32
% 35.07/6.32 % (4411)Memory used [KB]: 12153
% 35.07/6.32 % (4411)Time elapsed: 0.114 s
% 35.07/6.32 % (4411)Instructions burned: 455 (million)
% 35.07/6.32 % (4411)------------------------------
% 35.07/6.32 % (4411)------------------------------
% 35.07/6.33 % (4416)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_3905 for (2953ds/5798Mi)
% 35.07/6.34 % (4405)Instruction limit reached!
% 35.07/6.34 % (4405)------------------------------
% 35.07/6.34 % (4405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.07/6.34 % (4405)Termination reason: Unknown
% 35.07/6.34 % (4405)Termination phase: Saturation
% 35.07/6.34
% 35.07/6.34 % (4405)Memory used [KB]: 10618
% 35.07/6.34 % (4405)Time elapsed: 0.352 s
% 35.07/6.34 % (4405)Instructions burned: 1174 (million)
% 35.07/6.34 % (4405)------------------------------
% 35.07/6.34 % (4405)------------------------------
% 35.07/6.35 % (4417)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_3905 for (2952ds/346Mi)
% 35.07/6.40 % (4407)Instruction limit reached!
% 35.07/6.40 % (4407)------------------------------
% 35.07/6.40 % (4407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.07/6.40 % (4407)Termination reason: Unknown
% 35.07/6.40 % (4407)Termination phase: Saturation
% 35.07/6.40
% 35.07/6.40 % (4407)Memory used [KB]: 11129
% 35.07/6.40 % (4407)Time elapsed: 0.308 s
% 35.07/6.40 % (4407)Instructions burned: 1203 (million)
% 35.07/6.40 % (4407)------------------------------
% 35.07/6.40 % (4407)------------------------------
% 35.44/6.40 % (4408)Instruction limit reached!
% 35.44/6.40 % (4408)------------------------------
% 35.44/6.40 % (4408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.44/6.40 % (4408)Termination reason: Unknown
% 35.44/6.40 % (4408)Termination phase: Saturation
% 35.44/6.40
% 35.44/6.40 % (4408)Memory used [KB]: 7803
% 35.44/6.40 % (4408)Time elapsed: 0.261 s
% 35.44/6.40 % (4408)Instructions burned: 1046 (million)
% 35.44/6.40 % (4408)------------------------------
% 35.44/6.40 % (4408)------------------------------
% 35.44/6.41 % (4418)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_3905 for (2952ds/1321Mi)
% 35.44/6.41 % (4419)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_3905 for (2952ds/1312Mi)
% 35.44/6.44 % (4417)Instruction limit reached!
% 35.44/6.44 % (4417)------------------------------
% 35.44/6.44 % (4417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.44/6.44 % (4417)Termination reason: Unknown
% 35.44/6.44 % (4417)Termination phase: Saturation
% 35.44/6.44
% 35.44/6.44 % (4417)Memory used [KB]: 7547
% 35.44/6.44 % (4417)Time elapsed: 0.086 s
% 35.44/6.44 % (4417)Instructions burned: 348 (million)
% 35.44/6.44 % (4417)------------------------------
% 35.44/6.44 % (4417)------------------------------
% 35.44/6.45 % (4420)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_3905 for (2951ds/672Mi)
% 36.32/6.66 % (4420)Instruction limit reached!
% 36.32/6.66 % (4420)------------------------------
% 36.32/6.66 % (4420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.32/6.66 % (4420)Termination reason: Unknown
% 36.32/6.66 % (4420)Termination phase: Saturation
% 36.32/6.66
% 36.32/6.66 % (4420)Memory used [KB]: 11385
% 36.32/6.66 % (4420)Time elapsed: 0.209 s
% 36.32/6.66 % (4420)Instructions burned: 672 (million)
% 36.32/6.66 % (4420)------------------------------
% 36.32/6.66 % (4420)------------------------------
% 36.32/6.67 % (4421)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_3905 for (2949ds/1897Mi)
% 36.65/6.74 % (4419)Instruction limit reached!
% 36.65/6.74 % (4419)------------------------------
% 36.65/6.74 % (4419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.65/6.74 % (4419)Termination reason: Unknown
% 36.65/6.74 % (4419)Termination phase: Saturation
% 36.65/6.74
% 36.65/6.74 % (4419)Memory used [KB]: 17398
% 36.65/6.74 % (4419)Time elapsed: 0.338 s
% 36.65/6.74 % (4419)Instructions burned: 1315 (million)
% 36.65/6.74 % (4419)------------------------------
% 36.65/6.74 % (4419)------------------------------
% 36.65/6.75 % (4422)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_3905 for (2948ds/1202Mi)
% 37.09/6.80 % (4418)Instruction limit reached!
% 37.09/6.80 % (4418)------------------------------
% 37.09/6.80 % (4418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.09/6.80 % (4418)Termination reason: Unknown
% 37.09/6.80 % (4418)Termination phase: Saturation
% 37.09/6.80
% 37.09/6.80 % (4418)Memory used [KB]: 8827
% 37.09/6.80 % (4418)Time elapsed: 0.396 s
% 37.09/6.80 % (4418)Instructions burned: 1323 (million)
% 37.09/6.80 % (4418)------------------------------
% 37.09/6.80 % (4418)------------------------------
% 37.09/6.81 % (4423)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_3905 for (2948ds/1493Mi)
% 40.69/7.04 % (4415)Instruction limit reached!
% 40.69/7.04 % (4415)------------------------------
% 40.69/7.04 % (4415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.69/7.04 % (4415)Termination reason: Unknown
% 40.69/7.04 % (4415)Termination phase: Saturation
% 40.69/7.04
% 40.69/7.04 % (4415)Memory used [KB]: 9210
% 40.69/7.04 % (4415)Time elapsed: 0.721 s
% 40.69/7.04 % (4415)Instructions burned: 2403 (million)
% 40.69/7.04 % (4415)------------------------------
% 40.69/7.04 % (4415)------------------------------
% 40.69/7.05 % (4424)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_3905 for (2945ds/7679Mi)
% 40.69/7.09 % (4422)Instruction limit reached!
% 40.69/7.09 % (4422)------------------------------
% 40.69/7.09 % (4422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.69/7.09 % (4422)Termination reason: Unknown
% 40.69/7.09 % (4422)Termination phase: Saturation
% 40.69/7.09
% 40.69/7.09 % (4422)Memory used [KB]: 9722
% 40.69/7.09 % (4422)Time elapsed: 0.335 s
% 40.69/7.09 % (4422)Instructions burned: 1204 (million)
% 40.69/7.09 % (4422)------------------------------
% 40.69/7.09 % (4422)------------------------------
% 40.69/7.10 % (4425)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_3905 for (2945ds/340Mi)
% 41.31/7.18 % (4423)Instruction limit reached!
% 41.31/7.18 % (4423)------------------------------
% 41.31/7.18 % (4423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.31/7.18 % (4423)Termination reason: Unknown
% 41.31/7.18 % (4423)Termination phase: Saturation
% 41.31/7.18
% 41.31/7.18 % (4423)Memory used [KB]: 8187
% 41.31/7.18 % (4423)Time elapsed: 0.369 s
% 41.31/7.18 % (4423)Instructions burned: 1495 (million)
% 41.31/7.18 % (4423)------------------------------
% 41.31/7.18 % (4423)------------------------------
% 41.31/7.19 % (4426)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_3905 for (2944ds/3672Mi)
% 41.31/7.20 % (4425)Instruction limit reached!
% 41.31/7.20 % (4425)------------------------------
% 41.31/7.20 % (4425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.31/7.20 % (4425)Termination reason: Unknown
% 41.31/7.20 % (4425)Termination phase: Saturation
% 41.31/7.20
% 41.31/7.20 % (4425)Memory used [KB]: 11129
% 41.31/7.20 % (4425)Time elapsed: 0.099 s
% 41.31/7.20 % (4425)Instructions burned: 341 (million)
% 41.31/7.20 % (4425)------------------------------
% 41.31/7.20 % (4425)------------------------------
% 41.69/7.21 % (4427)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_3905 for (2944ds/1535Mi)
% 41.69/7.26 % (4421)Instruction limit reached!
% 41.69/7.26 % (4421)------------------------------
% 41.69/7.26 % (4421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.69/7.26 % (4421)Termination reason: Unknown
% 41.69/7.26 % (4421)Termination phase: Saturation
% 41.69/7.26
% 41.69/7.26 % (4421)Memory used [KB]: 14200
% 41.69/7.26 % (4421)Time elapsed: 0.596 s
% 41.69/7.26 % (4421)Instructions burned: 1898 (million)
% 41.69/7.26 % (4421)------------------------------
% 41.69/7.26 % (4421)------------------------------
% 41.69/7.27 % (4428)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_3905 for (2943ds/4637Mi)
% 42.78/7.53 % (4414)Instruction limit reached!
% 42.78/7.53 % (4414)------------------------------
% 42.78/7.53 % (4414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.78/7.53 % (4414)Termination reason: Unknown
% 42.78/7.53 % (4414)Termination phase: Saturation
% 42.78/7.53
% 42.78/7.53 % (4414)Memory used [KB]: 8059
% 42.78/7.53 % (4414)Time elapsed: 1.255 s
% 42.78/7.53 % (4414)Instructions burned: 5062 (million)
% 42.78/7.53 % (4414)------------------------------
% 42.78/7.53 % (4414)------------------------------
% 42.78/7.54 % (4429)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_3905 for (2941ds/3174Mi)
% 42.78/7.55 % (4395)Instruction limit reached!
% 42.78/7.55 % (4395)------------------------------
% 42.78/7.55 % (4395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.78/7.55 % (4395)Termination reason: Unknown
% 42.78/7.55 % (4395)Termination phase: Saturation
% 42.78/7.55
% 42.78/7.55 % (4395)Memory used [KB]: 14200
% 42.78/7.55 % (4395)Time elapsed: 2.008 s
% 42.78/7.55 % (4395)Instructions burned: 6455 (million)
% 42.78/7.55 % (4395)------------------------------
% 42.78/7.55 % (4395)------------------------------
% 42.78/7.56 % (4430)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_3905 for (2940ds/307Mi)
% 42.78/7.58 % (4427)Instruction limit reached!
% 42.78/7.58 % (4427)------------------------------
% 42.78/7.58 % (4427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.78/7.58 % (4427)Termination reason: Unknown
% 42.78/7.58 % (4427)Termination phase: Saturation
% 42.78/7.58
% 42.78/7.58 % (4427)Memory used [KB]: 15607
% 42.78/7.58 % (4427)Time elapsed: 0.371 s
% 42.78/7.58 % (4427)Instructions burned: 1535 (million)
% 42.78/7.58 % (4427)------------------------------
% 42.78/7.58 % (4427)------------------------------
% 42.78/7.59 % (4431)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_3905 for (2940ds/3619Mi)
% 43.36/7.63 % (4430)Instruction limit reached!
% 43.36/7.63 % (4430)------------------------------
% 43.36/7.63 % (4430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.36/7.63 % (4430)Termination reason: Unknown
% 43.36/7.63 % (4430)Termination phase: Saturation
% 43.36/7.63
% 43.36/7.63 % (4430)Memory used [KB]: 7547
% 43.36/7.63 % (4430)Time elapsed: 0.077 s
% 43.36/7.63 % (4430)Instructions burned: 308 (million)
% 43.36/7.63 % (4430)------------------------------
% 43.36/7.63 % (4430)------------------------------
% 43.36/7.64 % (4432)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_3905 for (2940ds/2325Mi)
% 47.72/8.08 % (4429)Refutation not found, non-redundant clauses discarded% (4429)------------------------------
% 47.72/8.08 % (4429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.72/8.08 % (4429)Termination reason: Refutation not found, non-redundant clauses discarded
% 47.72/8.08
% 47.72/8.08 % (4429)Memory used [KB]: 17398
% 47.72/8.08 % (4429)Time elapsed: 0.542 s
% 47.72/8.08 % (4429)Instructions burned: 1843 (million)
% 47.72/8.08 % (4429)------------------------------
% 47.72/8.08 % (4429)------------------------------
% 47.72/8.09 % (4433)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_3905 for (2935ds/2341Mi)
% 48.41/8.14 % (4416)Instruction limit reached!
% 48.41/8.14 % (4416)------------------------------
% 48.41/8.14 % (4416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.41/8.14 % (4416)Termination reason: Unknown
% 48.41/8.14 % (4416)Termination phase: Saturation
% 48.41/8.14
% 48.41/8.14 % (4416)Memory used [KB]: 13176
% 48.41/8.14 % (4416)Time elapsed: 1.811 s
% 48.41/8.14 % (4416)Instructions burned: 5798 (million)
% 48.41/8.14 % (4416)------------------------------
% 48.41/8.14 % (4416)------------------------------
% 48.41/8.16 % (4434)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_3905 for (2934ds/7257Mi)
% 48.41/8.20 % (4432)Refutation not found, non-redundant clauses discarded% (4432)------------------------------
% 48.41/8.20 % (4432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.41/8.20 % (4432)Termination reason: Refutation not found, non-redundant clauses discarded
% 48.41/8.20
% 48.41/8.20 % (4432)Memory used [KB]: 17398
% 48.41/8.20 % (4432)Time elapsed: 0.553 s
% 48.41/8.20 % (4432)Instructions burned: 1869 (million)
% 48.41/8.20 % (4432)------------------------------
% 48.41/8.20 % (4432)------------------------------
% 48.27/8.21 % (4435)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_3905 for (2934ds/3710Mi)
% 49.23/8.32 % (4426)Instruction limit reached!
% 49.23/8.32 % (4426)------------------------------
% 49.23/8.32 % (4426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.23/8.32 % (4426)Termination reason: Unknown
% 49.23/8.32 % (4426)Termination phase: Saturation
% 49.23/8.32
% 49.23/8.32 % (4426)Memory used [KB]: 13048
% 49.23/8.32 % (4426)Time elapsed: 1.129 s
% 49.23/8.32 % (4426)Instructions burned: 3673 (million)
% 49.23/8.32 % (4426)------------------------------
% 49.23/8.32 % (4426)------------------------------
% 49.23/8.33 % (4436)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_3905 for (2933ds/326Mi)
% 49.56/8.41 % (4436)Instruction limit reached!
% 49.56/8.41 % (4436)------------------------------
% 49.56/8.41 % (4436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.56/8.41 % (4436)Termination reason: Unknown
% 49.56/8.41 % (4436)Termination phase: Saturation
% 49.56/8.41
% 49.56/8.41 % (4436)Memory used [KB]: 8571
% 49.56/8.41 % (4436)Time elapsed: 0.086 s
% 49.56/8.41 % (4436)Instructions burned: 326 (million)
% 49.56/8.41 % (4436)------------------------------
% 49.56/8.41 % (4436)------------------------------
% 49.56/8.42 % (4437)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_3905 for (2932ds/1100Mi)
% 50.25/8.66 % (4431)Instruction limit reached!
% 50.25/8.66 % (4431)------------------------------
% 50.25/8.66 % (4431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.25/8.66 % (4431)Termination reason: Unknown
% 50.25/8.66 % (4431)Termination phase: Saturation
% 50.25/8.66
% 50.25/8.66 % (4431)Memory used [KB]: 17782
% 50.25/8.66 % (4431)Time elapsed: 1.072 s
% 50.25/8.66 % (4431)Instructions burned: 3621 (million)
% 50.25/8.66 % (4431)------------------------------
% 50.25/8.66 % (4431)------------------------------
% 50.25/8.67 % (4438)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_3905 for (2929ds/406Mi)
% 50.52/8.70 % (4428)Instruction limit reached!
% 50.52/8.70 % (4428)------------------------------
% 50.52/8.70 % (4428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.52/8.70 % (4428)Termination reason: Unknown
% 50.52/8.70 % (4428)Termination phase: Saturation
% 50.52/8.70
% 50.52/8.70 % (4428)Memory used [KB]: 12025
% 50.52/8.70 % (4428)Time elapsed: 1.431 s
% 50.52/8.70 % (4428)Instructions burned: 4638 (million)
% 50.52/8.70 % (4428)------------------------------
% 50.52/8.70 % (4428)------------------------------
% 50.52/8.71 % (4439)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_3905 for (2929ds/1871Mi)
% 50.52/8.77 % (4437)Instruction limit reached!
% 50.52/8.77 % (4437)------------------------------
% 50.52/8.77 % (4437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.52/8.77 % (4437)Termination reason: Unknown
% 50.52/8.77 % (4437)Termination phase: Saturation
% 50.52/8.77
% 50.52/8.77 % (4437)Memory used [KB]: 15991
% 50.52/8.77 % (4437)Time elapsed: 0.346 s
% 50.52/8.77 % (4437)Instructions burned: 1102 (million)
% 50.52/8.77 % (4437)------------------------------
% 50.52/8.77 % (4437)------------------------------
% 50.52/8.78 % (4438)Instruction limit reached!
% 50.52/8.78 % (4438)------------------------------
% 50.52/8.78 % (4438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.52/8.78 % (4438)Termination reason: Unknown
% 50.52/8.78 % (4438)Termination phase: Saturation
% 50.52/8.78
% 50.52/8.78 % (4438)Memory used [KB]: 7931
% 50.52/8.78 % (4438)Time elapsed: 0.110 s
% 50.52/8.78 % (4438)Instructions burned: 408 (million)
% 50.52/8.78 % (4438)------------------------------
% 50.52/8.78 % (4438)------------------------------
% 50.52/8.78 % (4440)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_3905 for (2928ds/1194Mi)
% 50.52/8.79 % (4441)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_3905 for (2928ds/474Mi)
% 51.14/8.81 % (4433)Instruction limit reached!
% 51.14/8.81 % (4433)------------------------------
% 51.14/8.81 % (4433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.14/8.81 % (4433)Termination reason: Unknown
% 51.14/8.81 % (4433)Termination phase: Saturation
% 51.14/8.81
% 51.14/8.81 % (4433)Memory used [KB]: 11257
% 51.14/8.81 % (4433)Time elapsed: 0.718 s
% 51.14/8.81 % (4433)Instructions burned: 2343 (million)
% 51.14/8.81 % (4433)------------------------------
% 51.14/8.81 % (4433)------------------------------
% 51.14/8.82 % (4442)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_3905 for (2928ds/3115Mi)
% 51.96/8.91 % (4441)Instruction limit reached!
% 51.96/8.91 % (4441)------------------------------
% 51.96/8.91 % (4441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.96/8.91 % (4441)Termination reason: Unknown
% 51.96/8.91 % (4441)Termination phase: Saturation
% 51.96/8.91
% 51.96/8.91 % (4441)Memory used [KB]: 7675
% 51.96/8.91 % (4441)Time elapsed: 0.120 s
% 51.96/8.91 % (4441)Instructions burned: 475 (million)
% 51.96/8.91 % (4441)------------------------------
% 51.96/8.91 % (4441)------------------------------
% 51.96/8.92 % (4443)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_3905 for (2927ds/831Mi)
% 55.48/9.15 % (4440)Instruction limit reached!
% 55.48/9.15 % (4440)------------------------------
% 55.48/9.15 % (4440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.48/9.15 % (4440)Termination reason: Unknown
% 55.48/9.15 % (4440)Termination phase: Saturation
% 55.48/9.15
% 55.48/9.15 % (4440)Memory used [KB]: 13176
% 55.48/9.15 % (4440)Time elapsed: 0.379 s
% 55.48/9.15 % (4440)Instructions burned: 1197 (million)
% 55.48/9.15 % (4440)------------------------------
% 55.48/9.15 % (4440)------------------------------
% 55.48/9.16 % (4435)Instruction limit reached!
% 55.48/9.16 % (4435)------------------------------
% 55.48/9.16 % (4435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.48/9.16 % (4435)Termination reason: Unknown
% 55.48/9.16 % (4435)Termination phase: Saturation
% 55.48/9.16
% 55.48/9.16 % (4435)Memory used [KB]: 19445
% 55.48/9.16 % (4435)Time elapsed: 0.956 s
% 55.48/9.16 % (4435)Instructions burned: 3712 (million)
% 55.48/9.16 % (4435)------------------------------
% 55.48/9.16 % (4435)------------------------------
% 55.48/9.17 % (4444)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_3905 for (2924ds/1188Mi)
% 55.48/9.17 % (4443)Instruction limit reached!
% 55.48/9.17 % (4443)------------------------------
% 55.48/9.17 % (4443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.48/9.17 % (4443)Termination reason: Unknown
% 55.48/9.17 % (4443)Termination phase: Saturation
% 55.48/9.17
% 55.48/9.17 % (4443)Memory used [KB]: 10234
% 55.48/9.17 % (4443)Time elapsed: 0.256 s
% 55.48/9.17 % (4443)Instructions burned: 833 (million)
% 55.48/9.17 % (4443)------------------------------
% 55.48/9.17 % (4443)------------------------------
% 55.48/9.17 % (4445)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_3905 for (2924ds/2868Mi)
% 55.48/9.18 % (4446)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_3905 for (2924ds/1516Mi)
% 55.91/9.29 % (4439)Instruction limit reached!
% 55.91/9.29 % (4439)------------------------------
% 55.91/9.29 % (4439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.91/9.29 % (4439)Termination reason: Unknown
% 55.91/9.29 % (4439)Termination phase: Saturation
% 55.91/9.29
% 55.91/9.29 % (4439)Memory used [KB]: 20340
% 55.91/9.29 % (4439)Time elapsed: 0.582 s
% 55.91/9.29 % (4439)Instructions burned: 1871 (million)
% 55.91/9.29 % (4439)------------------------------
% 55.91/9.29 % (4439)------------------------------
% 56.34/9.30 % (4447)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_3905 for (2923ds/2321Mi)
% 56.34/9.36 % (4424)Instruction limit reached!
% 56.34/9.36 % (4424)------------------------------
% 56.34/9.36 % (4424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.34/9.36 % (4424)Termination reason: Unknown
% 56.34/9.36 % (4424)Termination phase: Saturation
% 56.34/9.36
% 56.34/9.36 % (4424)Memory used [KB]: 19189
% 56.34/9.36 % (4424)Time elapsed: 2.310 s
% 56.34/9.36 % (4424)Instructions burned: 7681 (million)
% 56.34/9.36 % (4424)------------------------------
% 56.34/9.36 % (4424)------------------------------
% 56.34/9.37 % (4448)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_3905 for (2922ds/2812Mi)
% 56.60/9.47 % (4444)Instruction limit reached!
% 56.60/9.47 % (4444)------------------------------
% 56.60/9.47 % (4444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.60/9.47 % (4444)Termination reason: Unknown
% 56.60/9.47 % (4444)Termination phase: Saturation
% 56.60/9.47
% 56.60/9.47 % (4444)Memory used [KB]: 17270
% 56.60/9.47 % (4444)Time elapsed: 0.301 s
% 56.60/9.47 % (4444)Instructions burned: 1191 (million)
% 56.60/9.47 % (4444)------------------------------
% 56.60/9.47 % (4444)------------------------------
% 56.60/9.48 % (4449)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_3905 for (2921ds/4604Mi)
% 57.31/9.60 % (4442)Instruction limit reached!
% 57.31/9.60 % (4442)------------------------------
% 57.31/9.60 % (4442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.31/9.60 % (4442)Termination reason: Unknown
% 57.31/9.60 % (4442)Termination phase: Saturation
% 57.31/9.60
% 57.31/9.60 % (4442)Memory used [KB]: 17782
% 57.31/9.60 % (4442)Time elapsed: 0.787 s
% 57.31/9.60 % (4442)Instructions burned: 3117 (million)
% 57.31/9.60 % (4442)------------------------------
% 57.31/9.60 % (4442)------------------------------
% 57.31/9.61 % (4450)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_3905 for (2920ds/2678Mi)
% 57.31/9.65 % (4446)Instruction limit reached!
% 57.31/9.65 % (4446)------------------------------
% 57.31/9.65 % (4446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.31/9.65 % (4446)Termination reason: Unknown
% 57.31/9.65 % (4446)Termination phase: Saturation
% 57.31/9.65
% 57.31/9.65 % (4446)Memory used [KB]: 12665
% 57.31/9.65 % (4446)Time elapsed: 0.468 s
% 57.31/9.65 % (4446)Instructions burned: 1516 (million)
% 57.31/9.65 % (4446)------------------------------
% 57.31/9.65 % (4446)------------------------------
% 57.31/9.66 % (4451)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_3905 for (2919ds/643Mi)
% 58.02/9.82 % (4451)Instruction limit reached!
% 58.02/9.82 % (4451)------------------------------
% 58.02/9.82 % (4451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.02/9.82 % (4451)Termination reason: Unknown
% 58.02/9.82 % (4451)Termination phase: Saturation
% 58.02/9.82
% 58.02/9.82 % (4451)Memory used [KB]: 7803
% 58.02/9.82 % (4451)Time elapsed: 0.166 s
% 58.02/9.82 % (4451)Instructions burned: 645 (million)
% 58.02/9.82 % (4451)------------------------------
% 58.02/9.82 % (4451)------------------------------
% 58.02/9.83 % (4452)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_3905 for (2918ds/458Mi)
% 58.02/9.89 % (4447)Instruction limit reached!
% 58.02/9.89 % (4447)------------------------------
% 58.02/9.89 % (4447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.02/9.89 % (4447)Termination reason: Unknown
% 58.02/9.89 % (4447)Termination phase: Saturation
% 58.02/9.89
% 58.02/9.89 % (4447)Memory used [KB]: 17142
% 58.02/9.89 % (4447)Time elapsed: 0.591 s
% 58.02/9.89 % (4447)Instructions burned: 2321 (million)
% 58.02/9.89 % (4447)------------------------------
% 58.02/9.89 % (4447)------------------------------
% 58.02/9.90 % (4445)Instruction limit reached!
% 58.02/9.90 % (4445)------------------------------
% 58.02/9.90 % (4445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.02/9.90 % (4445)Termination reason: Unknown
% 58.02/9.90 % (4445)Termination phase: Saturation
% 58.02/9.90
% 58.02/9.90 % (4445)Memory used [KB]: 7675
% 58.02/9.90 % (4445)Time elapsed: 0.725 s
% 58.02/9.90 % (4445)Instructions burned: 2870 (million)
% 58.02/9.90 % (4445)------------------------------
% 58.02/9.90 % (4445)------------------------------
% 58.89/9.90 % (4453)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_3905 for (2917ds/2546Mi)
% 58.89/9.91 % (4454)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_3905 for (2917ds/1432Mi)
% 58.89/9.95 % (4452)Instruction limit reached!
% 58.89/9.95 % (4452)------------------------------
% 58.89/9.95 % (4452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.89/9.95 % (4452)Termination reason: Unknown
% 58.89/9.95 % (4452)Termination phase: Saturation
% 58.89/9.95
% 58.89/9.95 % (4452)Memory used [KB]: 7675
% 58.89/9.95 % (4452)Time elapsed: 0.114 s
% 58.89/9.95 % (4452)Instructions burned: 461 (million)
% 58.89/9.95 % (4452)------------------------------
% 58.89/9.95 % (4452)------------------------------
% 58.89/9.96 % (4455)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_3905 for (2916ds/386Mi)
% 61.74/10.05 % (4455)Instruction limit reached!
% 61.74/10.05 % (4455)------------------------------
% 61.74/10.05 % (4455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 61.74/10.05 % (4455)Termination reason: Unknown
% 61.74/10.05 % (4455)Termination phase: Saturation
% 61.74/10.05
% 61.74/10.05 % (4455)Memory used [KB]: 7675
% 61.74/10.05 % (4455)Time elapsed: 0.096 s
% 61.74/10.05 % (4455)Instructions burned: 389 (million)
% 61.74/10.05 % (4455)------------------------------
% 61.74/10.05 % (4455)------------------------------
% 61.74/10.06 % (4456)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_3905 for (2915ds/360Mi)
% 62.44/10.15 % (4456)Instruction limit reached!
% 62.44/10.15 % (4456)------------------------------
% 62.44/10.15 % (4456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.44/10.15 % (4456)Termination reason: Unknown
% 62.44/10.15 % (4456)Termination phase: Saturation
% 62.44/10.15
% 62.44/10.15 % (4456)Memory used [KB]: 7547
% 62.44/10.15 % (4456)Time elapsed: 0.093 s
% 62.44/10.15 % (4456)Instructions burned: 361 (million)
% 62.44/10.15 % (4456)------------------------------
% 62.44/10.15 % (4456)------------------------------
% 62.44/10.16 % (4457)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_3905 for (2914ds/5446Mi)
% 62.97/10.24 % (4448)Instruction limit reached!
% 62.97/10.24 % (4448)------------------------------
% 62.97/10.24 % (4448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.97/10.24 % (4448)Termination reason: Unknown
% 62.97/10.24 % (4448)Termination phase: Saturation
% 62.97/10.24
% 62.97/10.24 % (4448)Memory used [KB]: 13432
% 62.97/10.24 % (4448)Time elapsed: 0.871 s
% 62.97/10.24 % (4448)Instructions burned: 2812 (million)
% 62.97/10.24 % (4448)------------------------------
% 62.97/10.24 % (4448)------------------------------
% 62.97/10.25 % (4458)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_3905 for (2913ds/2573Mi)
% 62.97/10.25 % (4454)Instruction limit reached!
% 62.97/10.25 % (4454)------------------------------
% 62.97/10.25 % (4454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.97/10.25 % (4454)Termination reason: Unknown
% 62.97/10.25 % (4454)Termination phase: Saturation
% 62.97/10.25
% 62.97/10.25 % (4454)Memory used [KB]: 18805
% 62.97/10.25 % (4454)Time elapsed: 0.347 s
% 62.97/10.25 % (4454)Instructions burned: 1434 (million)
% 62.97/10.25 % (4454)------------------------------
% 62.97/10.25 % (4454)------------------------------
% 62.97/10.26 % (4459)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_3905 for (2913ds/2655Mi)
% 62.97/10.27 % (4450)Instruction limit reached!
% 62.97/10.27 % (4450)------------------------------
% 62.97/10.27 % (4450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.97/10.27 % (4450)Termination reason: Unknown
% 62.97/10.27 % (4450)Termination phase: Saturation
% 62.97/10.27
% 62.97/10.27 % (4450)Memory used [KB]: 26865
% 62.97/10.27 % (4450)Time elapsed: 0.659 s
% 62.97/10.27 % (4450)Instructions burned: 2679 (million)
% 62.97/10.27 % (4450)------------------------------
% 62.97/10.27 % (4450)------------------------------
% 62.97/10.28 % (4460)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_3905 for (2913ds/2781Mi)
% 63.47/10.39 % (4434)Instruction limit reached!
% 63.47/10.39 % (4434)------------------------------
% 63.47/10.39 % (4434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.47/10.39 % (4434)Termination reason: Unknown
% 63.47/10.39 % (4434)Termination phase: Saturation
% 63.47/10.39
% 63.47/10.39 % (4434)Memory used [KB]: 10746
% 63.47/10.39 % (4434)Time elapsed: 2.232 s
% 63.47/10.39 % (4434)Instructions burned: 7257 (million)
% 63.47/10.39 % (4434)------------------------------
% 63.47/10.39 % (4434)------------------------------
% 63.47/10.40 % (4461)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_3905 for (2912ds/307Mi)
% 63.77/10.47 % (4461)Instruction limit reached!
% 63.77/10.47 % (4461)------------------------------
% 63.77/10.47 % (4461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.77/10.47 % (4461)Termination reason: Unknown
% 63.77/10.47 % (4461)Termination phase: Saturation
% 63.77/10.47
% 63.77/10.47 % (4461)Memory used [KB]: 7547
% 63.77/10.47 % (4461)Time elapsed: 0.080 s
% 63.77/10.47 % (4461)Instructions burned: 307 (million)
% 63.77/10.47 % (4461)------------------------------
% 63.77/10.47 % (4461)------------------------------
% 63.77/10.48 % (4462)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_3905 for (2911ds/1548Mi)
% 64.27/10.64 % (4453)Instruction limit reached!
% 64.27/10.64 % (4453)------------------------------
% 64.27/10.64 % (4453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.27/10.64 % (4453)Termination reason: Unknown
% 64.27/10.64 % (4453)Termination phase: Saturation
% 64.27/10.64
% 64.27/10.64 % (4453)Memory used [KB]: 10874
% 64.27/10.64 % (4453)Time elapsed: 0.741 s
% 64.27/10.64 % (4453)Instructions burned: 2546 (million)
% 64.27/10.64 % (4453)------------------------------
% 64.27/10.64 % (4453)------------------------------
% 64.27/10.65 % (4463)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_3905 for (2909ds/5214Mi)
% 64.55/10.88 % (4449)Instruction limit reached!
% 64.55/10.88 % (4449)------------------------------
% 64.55/10.88 % (4449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.55/10.88 % (4449)Termination reason: Unknown
% 64.55/10.88 % (4449)Termination phase: Saturation
% 64.55/10.88
% 64.55/10.88 % (4449)Memory used [KB]: 14583
% 64.55/10.88 % (4449)Time elapsed: 1.405 s
% 64.55/10.88 % (4449)Instructions burned: 4604 (million)
% 64.55/10.88 % (4449)------------------------------
% 64.55/10.88 % (4449)------------------------------
% 64.55/10.89 % (4464)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_3905 for (2907ds/3201Mi)
% 64.64/10.90 % (4458)Instruction limit reached!
% 64.64/10.90 % (4458)------------------------------
% 64.64/10.90 % (4458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.64/10.90 % (4458)Termination reason: Unknown
% 64.64/10.90 % (4458)Termination phase: Saturation
% 64.64/10.90
% 64.64/10.90 % (4458)Memory used [KB]: 19445
% 64.64/10.90 % (4458)Time elapsed: 0.654 s
% 64.64/10.90 % (4458)Instructions burned: 2575 (million)
% 64.64/10.90 % (4458)------------------------------
% 64.64/10.90 % (4458)------------------------------
% 64.64/10.91 % (4465)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_3905 for (2907ds/454Mi)
% 64.64/10.93 % (4459)Instruction limit reached!
% 64.64/10.93 % (4459)------------------------------
% 64.64/10.93 % (4459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.64/10.93 % (4459)Termination reason: Unknown
% 64.64/10.93 % (4459)Termination phase: Saturation
% 64.64/10.93
% 64.64/10.93 % (4459)Memory used [KB]: 5245
% 64.64/10.93 % (4459)Time elapsed: 0.672 s
% 64.64/10.93 % (4459)Instructions burned: 2655 (million)
% 64.64/10.93 % (4459)------------------------------
% 64.64/10.93 % (4459)------------------------------
% 64.64/10.94 % (4462)Instruction limit reached!
% 64.64/10.94 % (4462)------------------------------
% 64.64/10.94 % (4462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.64/10.94 % (4462)Termination reason: Unknown
% 64.64/10.94 % (4462)Termination phase: Saturation
% 64.64/10.94
% 64.64/10.94 % (4462)Memory used [KB]: 11129
% 64.64/10.94 % (4462)Time elapsed: 0.459 s
% 64.64/10.94 % (4462)Instructions burned: 1550 (million)
% 64.64/10.94 % (4462)------------------------------
% 64.64/10.94 % (4462)------------------------------
% 64.64/10.94 % (4466)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_3905 for (2907ds/3049Mi)
% 64.64/10.95 % (4467)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_3905 for (2906ds/7311Mi)
% 64.64/11.02 % (4465)Instruction limit reached!
% 64.64/11.02 % (4465)------------------------------
% 64.64/11.02 % (4465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.64/11.02 % (4465)Termination reason: Unknown
% 64.64/11.02 % (4465)Termination phase: Saturation
% 64.64/11.02
% 64.64/11.02 % (4465)Memory used [KB]: 12153
% 64.64/11.02 % (4465)Time elapsed: 0.113 s
% 64.64/11.02 % (4465)Instructions burned: 457 (million)
% 64.64/11.02 % (4465)------------------------------
% 64.64/11.02 % (4465)------------------------------
% 68.80/11.03 % (4468)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_3905 for (2906ds/6804Mi)
% 68.80/11.12 % (4460)Instruction limit reached!
% 68.80/11.12 % (4460)------------------------------
% 68.80/11.12 % (4460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 68.80/11.12 % (4460)Termination reason: Unknown
% 68.80/11.12 % (4460)Termination phase: Saturation
% 68.80/11.12
% 68.80/11.12 % (4460)Memory used [KB]: 9594
% 68.80/11.12 % (4460)Time elapsed: 0.841 s
% 68.80/11.12 % (4460)Instructions burned: 2783 (million)
% 68.80/11.12 % (4460)------------------------------
% 68.80/11.12 % (4460)------------------------------
% 69.44/11.13 % (4469)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_3905 for (2905ds/1683Mi)
% 71.81/11.61 % (4469)Instruction limit reached!
% 71.81/11.61 % (4469)------------------------------
% 71.81/11.61 % (4469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.81/11.61 % (4469)Termination reason: Unknown
% 71.81/11.61 % (4469)Termination phase: Saturation
% 71.81/11.61
% 71.81/11.61 % (4469)Memory used [KB]: 21236
% 71.81/11.61 % (4469)Time elapsed: 0.475 s
% 71.81/11.61 % (4469)Instructions burned: 1684 (million)
% 71.81/11.61 % (4469)------------------------------
% 71.81/11.61 % (4469)------------------------------
% 71.81/11.62 % (4470)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_3905 for (2900ds/4688Mi)
% 73.30/11.87 % (4466)Instruction limit reached!
% 73.30/11.87 % (4466)------------------------------
% 73.30/11.87 % (4466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.30/11.87 % (4466)Termination reason: Unknown
% 73.30/11.87 % (4466)Termination phase: Saturation
% 73.30/11.87
% 73.30/11.87 % (4466)Memory used [KB]: 11257
% 73.30/11.87 % (4466)Time elapsed: 0.924 s
% 73.30/11.87 % (4466)Instructions burned: 3050 (million)
% 73.30/11.87 % (4466)------------------------------
% 73.30/11.87 % (4466)------------------------------
% 73.30/11.88 % (4471)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_3905 for (2897ds/2207Mi)
% 73.30/11.88 % (4464)Instruction limit reached!
% 73.30/11.88 % (4464)------------------------------
% 73.30/11.88 % (4464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.30/11.88 % (4464)Termination reason: Unknown
% 73.30/11.88 % (4464)Termination phase: Saturation
% 73.30/11.88
% 73.30/11.88 % (4464)Memory used [KB]: 13816
% 73.30/11.88 % (4464)Time elapsed: 0.989 s
% 73.30/11.88 % (4464)Instructions burned: 3203 (million)
% 73.30/11.88 % (4464)------------------------------
% 73.30/11.88 % (4464)------------------------------
% 73.30/11.89 % (4472)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_3905 for (2897ds/8216Mi)
% 73.30/11.89 % (4457)Instruction limit reached!
% 73.30/11.89 % (4457)------------------------------
% 73.30/11.89 % (4457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.30/11.89 % (4457)Termination reason: Unknown
% 73.30/11.89 % (4457)Termination phase: Saturation
% 73.30/11.89
% 73.30/11.89 % (4457)Memory used [KB]: 16502
% 73.30/11.89 % (4457)Time elapsed: 1.731 s
% 73.30/11.89 % (4457)Instructions burned: 5448 (million)
% 73.30/11.89 % (4457)------------------------------
% 73.30/11.89 % (4457)------------------------------
% 73.78/11.90 % (4473)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_3905 for (2897ds/430Mi)
% 73.78/12.01 % (4473)Instruction limit reached!
% 73.78/12.01 % (4473)------------------------------
% 73.78/12.01 % (4473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.78/12.01 % (4473)Termination reason: Unknown
% 73.78/12.01 % (4473)Termination phase: Saturation
% 73.78/12.01
% 73.78/12.01 % (4473)Memory used [KB]: 7675
% 73.78/12.01 % (4473)Time elapsed: 0.107 s
% 73.78/12.01 % (4473)Instructions burned: 430 (million)
% 73.78/12.01 % (4473)------------------------------
% 73.78/12.01 % (4473)------------------------------
% 73.78/12.02 % (4474)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_3905 for (2896ds/2012Mi)
% 76.88/12.23 % (4463)Instruction limit reached!
% 76.88/12.23 % (4463)------------------------------
% 76.88/12.23 % (4463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.88/12.23 % (4463)Termination reason: Unknown
% 76.88/12.23 % (4463)Termination phase: Saturation
% 76.88/12.23
% 76.88/12.23 % (4463)Memory used [KB]: 11641
% 76.88/12.23 % (4463)Time elapsed: 1.581 s
% 76.88/12.23 % (4463)Instructions burned: 5214 (million)
% 76.88/12.23 % (4463)------------------------------
% 76.88/12.23 % (4463)------------------------------
% 76.88/12.24 % (4475)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_3905 for (2894ds/631Mi)
% 77.93/12.42 % (4475)Instruction limit reached!
% 77.93/12.42 % (4475)------------------------------
% 77.93/12.42 % (4475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.93/12.42 % (4475)Termination reason: Unknown
% 77.93/12.42 % (4475)Termination phase: Saturation
% 77.93/12.42
% 77.93/12.42 % (4475)Memory used [KB]: 8443
% 77.93/12.42 % (4475)Time elapsed: 0.181 s
% 77.93/12.42 % (4475)Instructions burned: 632 (million)
% 77.93/12.42 % (4475)------------------------------
% 77.93/12.42 % (4475)------------------------------
% 77.93/12.43 % (4476)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_3905 for (2892ds/8785Mi)
% 78.63/12.53 % (4474)Instruction limit reached!
% 78.63/12.53 % (4474)------------------------------
% 78.63/12.53 % (4474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.63/12.53 % (4474)Termination reason: Unknown
% 78.63/12.53 % (4474)Termination phase: Saturation
% 78.63/12.53
% 78.63/12.53 % (4474)Memory used [KB]: 12153
% 78.63/12.53 % (4474)Time elapsed: 0.509 s
% 78.63/12.53 % (4474)Instructions burned: 2014 (million)
% 78.63/12.53 % (4474)------------------------------
% 78.63/12.53 % (4474)------------------------------
% 78.63/12.54 % (4477)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_3905 for (2891ds/739Mi)
% 78.63/12.55 % (4471)Instruction limit reached!
% 78.63/12.55 % (4471)------------------------------
% 78.63/12.55 % (4471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.63/12.55 % (4471)Termination reason: Unknown
% 78.63/12.55 % (4471)Termination phase: Saturation
% 78.63/12.55
% 78.63/12.55 % (4471)Memory used [KB]: 11513
% 78.63/12.55 % (4471)Time elapsed: 0.672 s
% 78.63/12.55 % (4471)Instructions burned: 2207 (million)
% 78.63/12.55 % (4471)------------------------------
% 78.63/12.55 % (4471)------------------------------
% 78.63/12.56 % (4478)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_3905 for (2890ds/5473Mi)
% 79.99/12.76 % (4477)Instruction limit reached!
% 79.99/12.76 % (4477)------------------------------
% 79.99/12.76 % (4477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.99/12.76 % (4477)Termination reason: Unknown
% 79.99/12.76 % (4477)Termination phase: Saturation
% 79.99/12.76
% 79.99/12.76 % (4477)Memory used [KB]: 14072
% 79.99/12.76 % (4477)Time elapsed: 0.228 s
% 79.99/12.76 % (4477)Instructions burned: 739 (million)
% 79.99/12.76 % (4477)------------------------------
% 79.99/12.76 % (4477)------------------------------
% 79.99/12.77 % (4479)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_3905 for (2888ds/43570Mi)
% 82.83/13.04 % (4470)Instruction limit reached!
% 82.83/13.04 % (4470)------------------------------
% 82.83/13.04 % (4470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 82.83/13.04 % (4470)Termination reason: Unknown
% 82.83/13.04 % (4470)Termination phase: Saturation
% 82.83/13.04
% 82.83/13.04 % (4470)Memory used [KB]: 15607
% 82.83/13.04 % (4470)Time elapsed: 1.421 s
% 82.83/13.04 % (4470)Instructions burned: 4688 (million)
% 82.83/13.04 % (4470)------------------------------
% 82.83/13.04 % (4470)------------------------------
% 82.83/13.05 % (4480)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_3905 for (2885ds/8382Mi)
% 82.83/13.07 % (4468)Instruction limit reached!
% 82.83/13.07 % (4468)------------------------------
% 82.83/13.07 % (4468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 82.83/13.07 % (4468)Termination reason: Unknown
% 82.83/13.07 % (4468)Termination phase: Saturation
% 82.83/13.07
% 82.83/13.07 % (4468)Memory used [KB]: 17654
% 82.83/13.07 % (4468)Time elapsed: 2.041 s
% 82.83/13.07 % (4468)Instructions burned: 6805 (million)
% 82.83/13.07 % (4468)------------------------------
% 82.83/13.07 % (4468)------------------------------
% 82.83/13.08 % (4481)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_3905 for (2885ds/407Mi)
% 83.46/13.19 % (4481)Instruction limit reached!
% 83.46/13.19 % (4481)------------------------------
% 83.46/13.19 % (4481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.46/13.19 % (4481)Termination reason: Unknown
% 83.46/13.19 % (4481)Termination phase: Saturation
% 83.46/13.19
% 83.46/13.19 % (4481)Memory used [KB]: 9594
% 83.46/13.19 % (4481)Time elapsed: 0.108 s
% 83.46/13.19 % (4481)Instructions burned: 408 (million)
% 83.46/13.19 % (4481)------------------------------
% 83.46/13.19 % (4481)------------------------------
% 83.93/13.20 % (4482)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_3905 for (2884ds/2971Mi)
% 83.93/13.28 % (4467)Instruction limit reached!
% 83.93/13.28 % (4467)------------------------------
% 83.93/13.28 % (4467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.93/13.28 % (4467)Termination reason: Unknown
% 83.93/13.28 % (4467)Termination phase: Saturation
% 83.93/13.28
% 83.93/13.28 % (4467)Memory used [KB]: 22131
% 83.93/13.28 % (4467)Time elapsed: 2.331 s
% 83.93/13.28 % (4467)Instructions burned: 7311 (million)
% 83.93/13.28 % (4467)------------------------------
% 83.93/13.28 % (4467)------------------------------
% 83.93/13.29 % (4483)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_3905 for (2883ds/9822Mi)
% 86.44/13.89 % (4472)Instruction limit reached!
% 86.44/13.89 % (4472)------------------------------
% 86.44/13.89 % (4472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 86.44/13.89 % (4472)Termination reason: Unknown
% 86.44/13.89 % (4472)Termination phase: Saturation
% 86.44/13.89
% 86.44/13.89 % (4472)Memory used [KB]: 8059
% 86.44/13.89 % (4472)Time elapsed: 1.999 s
% 86.44/13.89 % (4472)Instructions burned: 8219 (million)
% 86.44/13.89 % (4472)------------------------------
% 86.44/13.89 % (4472)------------------------------
% 86.44/13.90 % (4484)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_3905 for (2877ds/8425Mi)
% 86.85/13.93 % (4482)Instruction limit reached!
% 86.85/13.93 % (4482)------------------------------
% 86.85/13.93 % (4482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 86.85/13.93 % (4482)Termination reason: Unknown
% 86.85/13.93 % (4482)Termination phase: Saturation
% 86.85/13.93
% 86.85/13.93 % (4482)Memory used [KB]: 7803
% 86.85/13.93 % (4482)Time elapsed: 0.732 s
% 86.85/13.93 % (4482)Instructions burned: 2972 (million)
% 86.85/13.93 % (4482)------------------------------
% 86.85/13.93 % (4482)------------------------------
% 86.85/13.94 % (4485)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_3905 for (2877ds/3107Mi)
% 91.11/14.25 % (4478)Instruction limit reached!
% 91.11/14.25 % (4478)------------------------------
% 91.11/14.25 % (4478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.11/14.25 % (4478)Termination reason: Unknown
% 91.11/14.25 % (4478)Termination phase: Saturation
% 91.11/14.25
% 91.11/14.25 % (4478)Memory used [KB]: 13688
% 91.11/14.25 % (4478)Time elapsed: 1.713 s
% 91.11/14.25 % (4478)Instructions burned: 5476 (million)
% 91.11/14.25 % (4478)------------------------------
% 91.11/14.25 % (4478)------------------------------
% 91.11/14.26 % (4487)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_3905 for (2873ds/7967Mi)
% 94.77/14.87 % (4485)Instruction limit reached!
% 94.77/14.87 % (4485)------------------------------
% 94.77/14.87 % (4485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 94.77/14.87 % (4485)Termination reason: Unknown
% 94.77/14.87 % (4485)Termination phase: Saturation
% 94.77/14.87
% 94.77/14.87 % (4485)Memory used [KB]: 17654
% 94.77/14.87 % (4485)Time elapsed: 0.927 s
% 94.77/14.87 % (4485)Instructions burned: 3107 (million)
% 94.77/14.87 % (4485)------------------------------
% 94.77/14.87 % (4485)------------------------------
% 94.77/14.88 % (4706)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_3905 for (2867ds/3629Mi)
% 97.67/15.18 % (4476)Instruction limit reached!
% 97.67/15.18 % (4476)------------------------------
% 97.67/15.18 % (4476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 97.67/15.18 % (4476)Termination reason: Unknown
% 97.67/15.18 % (4476)Termination phase: Saturation
% 97.67/15.18
% 97.67/15.18 % (4476)Memory used [KB]: 19957
% 97.67/15.18 % (4476)Time elapsed: 2.769 s
% 97.67/15.18 % (4476)Instructions burned: 8786 (million)
% 97.67/15.18 % (4476)------------------------------
% 97.67/15.18 % (4476)------------------------------
% 97.67/15.19 % (4855)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_3905 for (2864ds/939Mi)
% 98.71/15.33 % (4480)Instruction limit reached!
% 98.71/15.33 % (4480)------------------------------
% 98.71/15.33 % (4480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.71/15.33 % (4480)Termination reason: Unknown
% 98.71/15.33 % (4480)Termination phase: Saturation
% 98.71/15.33
% 98.71/15.33 % (4480)Memory used [KB]: 14839
% 98.71/15.33 % (4480)Time elapsed: 2.281 s
% 98.71/15.33 % (4480)Instructions burned: 8382 (million)
% 98.71/15.33 % (4480)------------------------------
% 98.71/15.33 % (4480)------------------------------
% 98.71/15.34 % (4860)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_3905 for (2863ds/1188Mi)
% 99.26/15.47 % (4855)Instruction limit reached!
% 99.26/15.47 % (4855)------------------------------
% 99.26/15.47 % (4855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 99.26/15.47 % (4855)Termination reason: Unknown
% 99.26/15.47 % (4855)Termination phase: Saturation
% 99.26/15.47
% 99.26/15.47 % (4855)Memory used [KB]: 10490
% 99.26/15.47 % (4855)Time elapsed: 0.308 s
% 99.26/15.47 % (4855)Instructions burned: 940 (million)
% 99.26/15.47 % (4855)------------------------------
% 99.26/15.47 % (4855)------------------------------
% 99.26/15.48 % (4938)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_3905 for (2861ds/3205Mi)
% 100.55/15.64 % (4860)Instruction limit reached!
% 100.55/15.64 % (4860)------------------------------
% 100.55/15.64 % (4860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 100.55/15.64 % (4860)Termination reason: Unknown
% 100.55/15.64 % (4860)Termination phase: Saturation
% 100.55/15.64
% 100.55/15.64 % (4860)Memory used [KB]: 17526
% 100.55/15.64 % (4860)Time elapsed: 0.298 s
% 100.55/15.64 % (4860)Instructions burned: 1189 (million)
% 100.55/15.64 % (4860)------------------------------
% 100.55/15.64 % (4860)------------------------------
% 100.55/15.65 % (4954)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_3905 for (2859ds/865Mi)
% 101.36/15.78 % (4706)Instruction limit reached!
% 101.36/15.78 % (4706)------------------------------
% 101.36/15.78 % (4706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 101.36/15.78 % (4706)Termination reason: Unknown
% 101.36/15.78 % (4706)Termination phase: Saturation
% 101.36/15.78
% 101.36/15.78 % (4706)Memory used [KB]: 7931
% 101.36/15.78 % (4706)Time elapsed: 0.904 s
% 101.36/15.78 % (4706)Instructions burned: 3632 (million)
% 101.36/15.78 % (4706)------------------------------
% 101.36/15.78 % (4706)------------------------------
% 101.36/15.79 % (4955)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_3905 for (2858ds/7469Mi)
% 101.87/15.88 % (4954)Instruction limit reached!
% 101.87/15.88 % (4954)------------------------------
% 101.87/15.88 % (4954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 101.87/15.88 % (4954)Termination reason: Unknown
% 101.87/15.88 % (4954)Termination phase: Saturation
% 101.87/15.88
% 101.87/15.88 % (4954)Memory used [KB]: 8059
% 101.87/15.88 % (4954)Time elapsed: 0.232 s
% 101.87/15.88 % (4954)Instructions burned: 866 (million)
% 101.87/15.88 % (4954)------------------------------
% 101.87/15.88 % (4954)------------------------------
% 101.87/15.89 % (4956)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_3905 for (2857ds/4165Mi)
% 105.15/16.22 % (4483)Refutation not found, non-redundant clauses discarded% (4483)------------------------------
% 105.15/16.22 % (4483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 105.15/16.22 % (4483)Termination reason: Refutation not found, non-redundant clauses discarded
% 105.15/16.22
% 105.15/16.22 % (4483)Memory used [KB]: 22131
% 105.15/16.22 % (4483)Time elapsed: 2.925 s
% 105.15/16.22 % (4483)Instructions burned: 9156 (million)
% 105.15/16.22 % (4483)------------------------------
% 105.15/16.22 % (4483)------------------------------
% 105.15/16.23 % (4959)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_3905 for (2854ds/13468Mi)
% 105.78/16.30 % (4487)Instruction limit reached!
% 105.78/16.30 % (4487)------------------------------
% 105.78/16.30 % (4487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 105.78/16.30 % (4487)Termination reason: Unknown
% 105.78/16.30 % (4487)Termination phase: Saturation
% 105.78/16.30
% 105.78/16.30 % (4487)Memory used [KB]: 17270
% 105.78/16.30 % (4487)Time elapsed: 2.047 s
% 105.78/16.30 % (4487)Instructions burned: 7969 (million)
% 105.78/16.30 % (4487)------------------------------
% 105.78/16.30 % (4487)------------------------------
% 105.78/16.31 % (4960)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_3905 for (2853ds/2635Mi)
% 106.78/16.55 % (4484)Instruction limit reached!
% 106.78/16.55 % (4484)------------------------------
% 106.78/16.55 % (4484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 106.78/16.55 % (4484)Termination reason: Unknown
% 106.78/16.55 % (4484)Termination phase: Saturation
% 106.78/16.55
% 106.78/16.55 % (4484)Memory used [KB]: 12665
% 106.78/16.55 % (4484)Time elapsed: 2.657 s
% 106.78/16.55 % (4484)Instructions burned: 8425 (million)
% 106.78/16.55 % (4484)------------------------------
% 106.78/16.55 % (4484)------------------------------
% 106.78/16.56 % (4966)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_3905 for (2850ds/631Mi)
% 106.78/16.57 % (4938)Instruction limit reached!
% 106.78/16.57 % (4938)------------------------------
% 106.78/16.57 % (4938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 106.78/16.57 % (4938)Termination reason: Unknown
% 106.78/16.57 % (4938)Termination phase: Saturation
% 106.78/16.57
% 106.78/16.57 % (4938)Memory used [KB]: 16247
% 106.78/16.57 % (4938)Time elapsed: 1.089 s
% 106.78/16.57 % (4938)Instructions burned: 3205 (million)
% 106.78/16.57 % (4938)------------------------------
% 106.78/16.57 % (4938)------------------------------
% 106.78/16.58 % (4968)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_3905 for (2850ds/15557Mi)
% 107.55/16.79 % (4966)Instruction limit reached!
% 107.55/16.79 % (4966)------------------------------
% 107.55/16.79 % (4966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 107.55/16.79 % (4966)Termination reason: Unknown
% 107.55/16.79 % (4966)Termination phase: Saturation
% 107.55/16.79
% 107.55/16.79 % (4966)Memory used [KB]: 7675
% 107.55/16.79 % (4966)Time elapsed: 0.225 s
% 107.55/16.79 % (4966)Instructions burned: 631 (million)
% 107.55/16.79 % (4966)------------------------------
% 107.55/16.79 % (4966)------------------------------
% 108.08/16.81 % (5003)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_3905 for (2848ds/2142Mi)
% 112.12/17.30 % (4960)Instruction limit reached!
% 112.12/17.30 % (4960)------------------------------
% 112.12/17.30 % (4960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 112.12/17.30 % (4960)Termination reason: Unknown
% 112.12/17.30 % (4960)Termination phase: Saturation
% 112.12/17.30
% 112.12/17.30 % (4960)Memory used [KB]: 12665
% 112.12/17.30 % (4960)Time elapsed: 0.970 s
% 112.12/17.30 % (4960)Instructions burned: 2636 (million)
% 112.12/17.30 % (4960)------------------------------
% 112.12/17.30 % (4960)------------------------------
% 112.85/17.31 % (5154)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_3905 for (2843ds/5624Mi)
% 112.85/17.38 % (4956)Instruction limit reached!
% 112.85/17.38 % (4956)------------------------------
% 112.85/17.38 % (4956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 112.85/17.38 % (4956)Termination reason: Unknown
% 112.85/17.38 % (4956)Termination phase: Saturation
% 112.85/17.38
% 112.85/17.38 % (4956)Memory used [KB]: 25713
% 112.85/17.38 % (4956)Time elapsed: 1.497 s
% 112.85/17.38 % (4956)Instructions burned: 4168 (million)
% 112.85/17.38 % (4956)------------------------------
% 112.85/17.38 % (4956)------------------------------
% 112.85/17.39 % (5179)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_3905 for (2842ds/1665Mi)
% 113.44/17.48 % (5003)Instruction limit reached!
% 113.44/17.48 % (5003)------------------------------
% 113.44/17.48 % (5003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 113.44/17.48 % (5003)Termination reason: Unknown
% 113.44/17.48 % (5003)Termination phase: Saturation
% 113.44/17.48
% 113.44/17.48 % (5003)Memory used [KB]: 11257
% 113.44/17.48 % (5003)Time elapsed: 0.677 s
% 113.44/17.48 % (5003)Instructions burned: 2142 (million)
% 113.44/17.48 % (5003)------------------------------
% 113.44/17.48 % (5003)------------------------------
% 113.44/17.49 % (5220)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_3905 for (2841ds/64912Mi)
% 115.14/17.82 % (5179)Instruction limit reached!
% 115.14/17.82 % (5179)------------------------------
% 115.14/17.82 % (5179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 115.14/17.82 % (5179)Termination reason: Unknown
% 115.14/17.82 % (5179)Termination phase: Saturation
% 115.14/17.82
% 115.14/17.82 % (5179)Memory used [KB]: 17014
% 115.14/17.82 % (5179)Time elapsed: 0.428 s
% 115.14/17.82 % (5179)Instructions burned: 1666 (million)
% 115.14/17.82 % (5179)------------------------------
% 115.14/17.82 % (5179)------------------------------
% 115.14/17.83 % (5237)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_3905 for (2838ds/7801Mi)
% 115.98/18.01 % (4955)Instruction limit reached!
% 115.98/18.01 % (4955)------------------------------
% 115.98/18.01 % (4955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 115.98/18.01 % (4955)Termination reason: Unknown
% 115.98/18.01 % (4955)Termination phase: Saturation
% 115.98/18.01
% 115.98/18.01 % (4955)Memory used [KB]: 12792
% 115.98/18.01 % (4955)Time elapsed: 2.225 s
% 115.98/18.01 % (4955)Instructions burned: 7470 (million)
% 115.98/18.01 % (4955)------------------------------
% 115.98/18.01 % (4955)------------------------------
% 117.89/18.03 % (5238)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_3905 for (2836ds/15194Mi)
% 123.19/19.02 % (5154)Instruction limit reached!
% 123.19/19.02 % (5154)------------------------------
% 123.19/19.02 % (5154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 123.19/19.02 % (5154)Termination reason: Unknown
% 123.19/19.02 % (5154)Termination phase: Saturation
% 123.19/19.02
% 123.19/19.02 % (5154)Memory used [KB]: 14839
% 123.19/19.02 % (5154)Time elapsed: 1.718 s
% 123.19/19.02 % (5154)Instructions burned: 5625 (million)
% 123.19/19.02 % (5154)------------------------------
% 123.19/19.02 % (5154)------------------------------
% 124.90/19.03 % (5239)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_3905 for (2826ds/6753Mi)
% 127.80/19.59 % (4959)Instruction limit reached!
% 127.80/19.59 % (4959)------------------------------
% 127.80/19.59 % (4959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 127.80/19.59 % (4959)Termination reason: Unknown
% 127.80/19.59 % (4959)Termination phase: Saturation
% 127.80/19.59
% 127.80/19.59 % (4959)Memory used [KB]: 8187
% 127.80/19.59 % (4959)Time elapsed: 3.367 s
% 127.80/19.59 % (4959)Instructions burned: 13470 (million)
% 127.80/19.59 % (4959)------------------------------
% 127.80/19.59 % (4959)------------------------------
% 128.42/19.60 % (5240)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_3905 for (2820ds/1003Mi)
% 129.44/19.85 % (5240)Instruction limit reached!
% 129.44/19.85 % (5240)------------------------------
% 129.44/19.85 % (5240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 129.44/19.85 % (5240)Termination reason: Unknown
% 129.44/19.85 % (5240)Termination phase: Saturation
% 129.44/19.85
% 129.44/19.85 % (5240)Memory used [KB]: 7803
% 129.44/19.85 % (5240)Time elapsed: 0.248 s
% 129.44/19.85 % (5240)Instructions burned: 1006 (million)
% 129.44/19.85 % (5240)------------------------------
% 129.44/19.85 % (5240)------------------------------
% 129.44/19.86 % (5241)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_3905 for (2817ds/13018Mi)
% 131.93/20.09 % (5237)Instruction limit reached!
% 131.93/20.09 % (5237)------------------------------
% 131.93/20.09 % (5237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 131.93/20.09 % (5237)Termination reason: Unknown
% 131.93/20.09 % (5237)Termination phase: Saturation
% 131.93/20.09
% 131.93/20.09 % (5237)Memory used [KB]: 13560
% 131.93/20.09 % (5237)Time elapsed: 2.261 s
% 131.93/20.09 % (5237)Instructions burned: 7803 (million)
% 131.93/20.09 % (5237)------------------------------
% 131.93/20.09 % (5237)------------------------------
% 131.93/20.10 % (5242)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_3905 for (2815ds/1267Mi)
% 134.30/20.48 % (4968)Instruction limit reached!
% 134.30/20.48 % (4968)------------------------------
% 134.30/20.48 % (4968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 134.30/20.48 % (4968)Termination reason: Unknown
% 134.30/20.48 % (4968)Termination phase: Saturation
% 134.30/20.48
% 134.30/20.48 % (4968)Memory used [KB]: 18166
% 134.30/20.48 % (4968)Time elapsed: 3.900 s
% 134.30/20.48 % (4968)Instructions burned: 15560 (million)
% 134.30/20.48 % (4968)------------------------------
% 134.30/20.48 % (4968)------------------------------
% 134.30/20.49 % (5243)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_3905 for (2811ds/2570Mi)
% 134.30/20.49 % (5242)Instruction limit reached!
% 134.30/20.49 % (5242)------------------------------
% 134.30/20.49 % (5242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 134.30/20.49 % (5242)Termination reason: Unknown
% 134.30/20.49 % (5242)Termination phase: Saturation
% 134.30/20.49
% 134.30/20.49 % (5242)Memory used [KB]: 12409
% 134.30/20.49 % (5242)Time elapsed: 0.390 s
% 134.30/20.49 % (5242)Instructions burned: 1267 (million)
% 134.30/20.49 % (5242)------------------------------
% 134.30/20.49 % (5242)------------------------------
% 135.29/20.50 % (5244)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=13163:si=on:rtra=on_0 on DTF2THF_3905 for (2811ds/13163Mi)
% 136.29/20.73 % (5239)Instruction limit reached!
% 136.29/20.73 % (5239)------------------------------
% 136.29/20.73 % (5239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 136.29/20.73 % (5239)Termination reason: Unknown
% 136.29/20.73 % (5239)Termination phase: Saturation
% 136.29/20.73
% 136.29/20.73 % (5239)Memory used [KB]: 16375
% 136.29/20.73 % (5239)Time elapsed: 1.694 s
% 136.29/20.73 % (5239)Instructions burned: 6756 (million)
% 136.29/20.73 % (5239)------------------------------
% 136.29/20.73 % (5239)------------------------------
% 136.29/20.74 % (5245)lrs+1666_1:1_au=on:s2a=on:sd=2:ss=axioms:st=5.0:i=5087:si=on:rtra=on_0 on DTF2THF_3905 for (2809ds/5087Mi)
% 138.96/21.11 % (5243)Instruction limit reached!
% 138.96/21.11 % (5243)------------------------------
% 138.96/21.11 % (5243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 138.96/21.11 % (5243)Termination reason: Unknown
% 138.96/21.11 % (5243)Termination phase: Saturation
% 138.96/21.11
% 138.96/21.11 % (5243)Memory used [KB]: 26737
% 138.96/21.11 % (5243)Time elapsed: 0.621 s
% 138.96/21.11 % (5243)Instructions burned: 2571 (million)
% 138.96/21.11 % (5243)------------------------------
% 138.96/21.11 % (5243)------------------------------
% 138.96/21.12 % (5246)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_3905 for (2805ds/10380Mi)
% 147.21/22.29 % (5245)Instruction limit reached!
% 147.21/22.29 % (5245)------------------------------
% 147.21/22.29 % (5245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 147.21/22.29 % (5245)Termination reason: Unknown
% 147.21/22.29 % (5245)Termination phase: Saturation
% 147.21/22.29
% 147.21/22.29 % (5245)Memory used [KB]: 14200
% 147.21/22.29 % (5245)Time elapsed: 1.559 s
% 147.21/22.29 % (5245)Instructions burned: 5088 (million)
% 147.21/22.29 % (5245)------------------------------
% 147.21/22.29 % (5245)------------------------------
% 147.94/22.31 % (5247)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_3905 for (2793ds/4218Mi)
% 149.13/22.55 % (5238)Instruction limit reached!
% 149.13/22.55 % (5238)------------------------------
% 149.13/22.55 % (5238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 149.13/22.55 % (5238)Termination reason: Unknown
% 149.13/22.55 % (5238)Termination phase: Saturation
% 149.13/22.55
% 149.13/22.55 % (5238)Memory used [KB]: 23027
% 149.13/22.55 % (5238)Time elapsed: 4.548 s
% 149.13/22.55 % (5238)Instructions burned: 15195 (million)
% 149.13/22.55 % (5238)------------------------------
% 149.13/22.55 % (5238)------------------------------
% 149.13/22.56 % (5248)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_3905 for (2790ds/3971Mi)
% 157.06/23.61 % (5247)Instruction limit reached!
% 157.06/23.61 % (5247)------------------------------
% 157.06/23.61 % (5247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 157.06/23.61 % (5247)Termination reason: Unknown
% 157.06/23.61 % (5247)Termination phase: Saturation
% 157.06/23.61
% 157.06/23.61 % (5247)Memory used [KB]: 13816
% 157.06/23.61 % (5247)Time elapsed: 1.307 s
% 157.06/23.61 % (5247)Instructions burned: 4218 (million)
% 157.06/23.61 % (5247)------------------------------
% 157.06/23.61 % (5247)------------------------------
% 157.06/23.62 % (5249)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_3905 for (2780ds/14014Mi)
% 157.06/23.68 % (5246)Instruction limit reached!
% 157.06/23.68 % (5246)------------------------------
% 157.06/23.68 % (5246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 157.06/23.68 % (5246)Termination reason: Unknown
% 157.06/23.68 % (5246)Termination phase: Saturation
% 157.06/23.68
% 157.06/23.68 % (5246)Memory used [KB]: 7803
% 157.06/23.68 % (5246)Time elapsed: 2.559 s
% 157.06/23.68 % (5246)Instructions burned: 10380 (million)
% 157.06/23.68 % (5246)------------------------------
% 157.06/23.68 % (5246)------------------------------
% 157.06/23.69 % (5250)lrs+10_1:1_ins=1:sgt=8:ss=axioms:i=8517:si=on:rtra=on_0 on DTF2THF_3905 for (2779ds/8517Mi)
% 157.68/23.76 % (5248)Instruction limit reached!
% 157.68/23.76 % (5248)------------------------------
% 157.68/23.76 % (5248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 157.68/23.76 % (5248)Termination reason: Unknown
% 157.68/23.76 % (5248)Termination phase: Saturation
% 157.68/23.76
% 157.68/23.76 % (5248)Memory used [KB]: 16630
% 157.68/23.76 % (5248)Time elapsed: 1.198 s
% 157.68/23.76 % (5248)Instructions burned: 3972 (million)
% 157.68/23.76 % (5248)------------------------------
% 157.68/23.76 % (5248)------------------------------
% 157.68/23.77 % (5251)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=10148:si=on:rtra=on_0 on DTF2THF_3905 for (2778ds/10148Mi)
% 158.54/23.98 % (5241)Instruction limit reached!
% 158.54/23.98 % (5241)------------------------------
% 158.54/23.98 % (5241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 158.54/23.98 % (5241)Termination reason: Unknown
% 158.54/23.98 % (5241)Termination phase: Saturation
% 158.54/23.98
% 158.54/23.98 % (5241)Memory used [KB]: 37739
% 158.54/23.98 % (5241)Time elapsed: 4.116 s
% 158.54/23.98 % (5241)Instructions burned: 13019 (million)
% 158.54/23.98 % (5241)------------------------------
% 158.54/23.98 % (5241)------------------------------
% 158.54/23.99 % (5252)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_3905 for (2776ds/9078Mi)
% 163.38/24.51 % (5244)Instruction limit reached!
% 163.38/24.51 % (5244)------------------------------
% 163.38/24.51 % (5244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 163.38/24.51 % (5244)Termination reason: Unknown
% 163.38/24.51 % (5244)Termination phase: Saturation
% 163.38/24.51
% 163.38/24.51 % (5244)Memory used [KB]: 26353
% 163.38/24.51 % (5244)Time elapsed: 4.015 s
% 163.38/24.51 % (5244)Instructions burned: 13165 (million)
% 163.38/24.51 % (5244)------------------------------
% 163.38/24.51 % (5244)------------------------------
% 163.38/24.53 % (5253)lrs+2_1:1_bet=on:bsr=on:cnfonf=lazy_pi_sigma_gen:er=filter:kws=inv_frequency:ntd=on:sd=3:ss=axioms:i=16164:si=on:rtra=on_0 on DTF2THF_3905 for (2771ds/16164Mi)
% 176.00/26.30 % (5250)Instruction limit reached!
% 176.00/26.30 % (5250)------------------------------
% 176.00/26.30 % (5250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 176.00/26.30 % (5250)Termination reason: Unknown
% 176.00/26.30 % (5250)Termination phase: Saturation
% 176.00/26.30
% 176.00/26.30 % (5250)Memory used [KB]: 15479
% 176.00/26.30 % (5250)Time elapsed: 2.613 s
% 176.00/26.30 % (5250)Instructions burned: 8520 (million)
% 176.00/26.30 % (5250)------------------------------
% 176.00/26.30 % (5250)------------------------------
% 176.00/26.31 % (5254)lrs+32_1:1_au=on:bet=on:cbe=off:cs=on:ins=3:i=6102:si=on:rtra=on_0 on DTF2THF_3905 for (2753ds/6102Mi)
% 176.00/26.32 % (4479)Instruction limit reached!
% 176.00/26.32 % (4479)------------------------------
% 176.00/26.32 % (4479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 176.00/26.32 % (4479)Termination reason: Unknown
% 176.00/26.32 % (4479)Termination phase: Saturation
% 176.00/26.32
% 176.00/26.32 % (4479)Memory used [KB]: 43112
% 176.00/26.32 % (4479)Time elapsed: 13.542 s
% 176.00/26.32 % (4479)Instructions burned: 43572 (million)
% 176.00/26.32 % (4479)------------------------------
% 176.00/26.32 % (4479)------------------------------
% 176.00/26.33 % (5255)lrs+1010_1:1_au=on:bd=off:e2e=on:fde=unused:nm=4:s2a=on:sos=all:sp=const_frequency:i=10308:si=on:rtra=on_0 on DTF2THF_3905 for (2753ds/10308Mi)
% 178.07/26.71 % (5252)Instruction limit reached!
% 178.07/26.71 % (5252)------------------------------
% 178.07/26.71 % (5252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 178.07/26.71 % (5252)Termination reason: Unknown
% 178.07/26.71 % (5252)Termination phase: Saturation
% 178.07/26.71
% 178.07/26.71 % (5252)Memory used [KB]: 13560
% 178.07/26.71 % (5252)Time elapsed: 2.725 s
% 178.07/26.71 % (5252)Instructions burned: 9079 (million)
% 178.07/26.71 % (5252)------------------------------
% 178.07/26.71 % (5252)------------------------------
% 178.07/26.72 % (5256)dis+1010_1:1_au=on:avsq=on:bd=off:cbe=off:cnfonf=off:cs=on:hud=5:nm=0:plsq=on:plsqc=1:plsqr=7,1:ss=axioms:tgt=full:i=4041:si=on:rtra=on_0 on DTF2THF_3905 for (2749ds/4041Mi)
% 178.88/26.91 % (5251)Instruction limit reached!
% 178.88/26.91 % (5251)------------------------------
% 178.88/26.91 % (5251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 178.88/26.91 % (5251)Termination reason: Unknown
% 178.88/26.91 % (5251)Termination phase: Saturation
% 178.88/26.91
% 178.88/26.91 % (5251)Memory used [KB]: 20468
% 178.88/26.91 % (5251)Time elapsed: 3.140 s
% 178.88/26.91 % (5251)Instructions burned: 10150 (million)
% 178.88/26.91 % (5251)------------------------------
% 178.88/26.91 % (5251)------------------------------
% 178.88/26.92 % (5257)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=6901:si=on:rtra=on_0 on DTF2THF_3905 for (2747ds/6901Mi)
% 186.56/27.89 % (5256)Instruction limit reached!
% 186.56/27.89 % (5256)------------------------------
% 186.56/27.89 % (5256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 186.56/27.89 % (5256)Termination reason: Unknown
% 186.56/27.89 % (5256)Termination phase: Saturation
% 186.56/27.89
% 186.56/27.89 % (5256)Memory used [KB]: 11385
% 186.56/27.89 % (5256)Time elapsed: 1.167 s
% 186.56/27.89 % (5256)Instructions burned: 4043 (million)
% 186.56/27.89 % (5256)------------------------------
% 186.56/27.89 % (5256)------------------------------
% 187.25/27.90 % (5258)lrs-1_1:1_au=on:cbe=off:ntd=on:i=5576:si=on:rtra=on_0 on DTF2THF_3905 for (2737ds/5576Mi)
% 187.25/28.02 % (5249)Instruction limit reached!
% 187.25/28.02 % (5249)------------------------------
% 187.25/28.02 % (5249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 187.25/28.02 % (5249)Termination reason: Unknown
% 187.25/28.02 % (5249)Termination phase: Saturation
% 187.25/28.02
% 187.25/28.02 % (5249)Memory used [KB]: 25713
% 187.25/28.02 % (5249)Time elapsed: 4.422 s
% 187.25/28.02 % (5249)Instructions burned: 14016 (million)
% 187.25/28.02 % (5249)------------------------------
% 187.25/28.02 % (5249)------------------------------
% 188.10/28.03 % (5259)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=2014:si=on:rtra=on_0 on DTF2THF_3905 for (2736ds/2014Mi)
% 188.10/28.08 % (5254)Instruction limit reached!
% 188.10/28.08 % (5254)------------------------------
% 188.10/28.08 % (5254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 188.10/28.08 % (5254)Termination reason: Unknown
% 188.10/28.08 % (5254)Termination phase: Saturation
% 188.10/28.08
% 188.10/28.08 % (5254)Memory used [KB]: 31854
% 188.10/28.08 % (5254)Time elapsed: 1.768 s
% 188.10/28.08 % (5254)Instructions burned: 6105 (million)
% 188.10/28.08 % (5254)------------------------------
% 188.10/28.08 % (5254)------------------------------
% 188.10/28.09 % (5260)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=5115:si=on:rtra=on_0 on DTF2THF_3905 for (2735ds/5115Mi)
% 190.07/28.42 % (5253)Refutation not found, non-redundant clauses discarded% (5253)------------------------------
% 190.07/28.42 % (5253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 190.07/28.42 % (5253)Termination reason: Refutation not found, non-redundant clauses discarded
% 190.07/28.42
% 190.07/28.42 % (5253)Memory used [KB]: 8699
% 190.07/28.42 % (5253)Time elapsed: 3.891 s
% 190.07/28.42 % (5253)Instructions burned: 16002 (million)
% 190.07/28.42 % (5253)------------------------------
% 190.07/28.42 % (5253)------------------------------
% 190.07/28.43 % (5261)lrs+2_1:1_au=on:cnfonf=lazy_pi_sigma_gen:sos=on:ss=axioms:i=13001:si=on:rtra=on_0 on DTF2THF_3905 for (2732ds/13001Mi)
% 190.92/28.63 % (5259)Instruction limit reached!
% 190.92/28.63 % (5259)------------------------------
% 190.92/28.63 % (5259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 190.92/28.63 % (5259)Termination reason: Unknown
% 190.92/28.63 % (5259)Termination phase: Saturation
% 190.92/28.63
% 190.92/28.63 % (5259)Memory used [KB]: 13560
% 190.92/28.63 % (5259)Time elapsed: 0.604 s
% 190.92/28.63 % (5259)Instructions burned: 2015 (million)
% 190.92/28.63 % (5259)------------------------------
% 190.92/28.63 % (5259)------------------------------
% 190.92/28.64 % (5262)dis+10_1:2_aac=none:acc=on:atotf=0.1:au=on:fde=none:ins=1:ixr=off:nwc=5.0:i=11105:si=on:rtra=on_0 on DTF2THF_3905 for (2730ds/11105Mi)
% 195.12/29.04 % (5257)Instruction limit reached!
% 195.12/29.04 % (5257)------------------------------
% 195.12/29.04 % (5257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 195.12/29.04 % (5257)Termination reason: Unknown
% 195.12/29.04 % (5257)Termination phase: Saturation
% 195.12/29.04
% 195.12/29.04 % (5257)Memory used [KB]: 16119
% 195.12/29.04 % (5257)Time elapsed: 2.123 s
% 195.12/29.04 % (5257)Instructions burned: 6902 (million)
% 195.12/29.04 % (5257)------------------------------
% 195.12/29.04 % (5257)------------------------------
% 195.12/29.05 % (5263)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=13832:si=on:rtra=on_0 on DTF2THF_3905 for (2725ds/13832Mi)
% 197.41/29.41 % (5260)Instruction limit reached!
% 197.41/29.41 % (5260)------------------------------
% 197.41/29.41 % (5260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 197.41/29.41 % (5260)Termination reason: Unknown
% 197.41/29.41 % (5260)Termination phase: Saturation
% 197.41/29.41
% 197.41/29.41 % (5260)Memory used [KB]: 19573
% 197.41/29.41 % (5260)Time elapsed: 1.317 s
% 197.41/29.41 % (5260)Instructions burned: 5115 (million)
% 197.41/29.41 % (5260)------------------------------
% 197.41/29.41 % (5260)------------------------------
% 197.41/29.42 % (5322)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=32887:si=on:rtra=on_0 on DTF2THF_3905 for (2722ds/32887Mi)
% 197.94/29.56 % (5255)Instruction limit reached!
% 197.94/29.56 % (5255)------------------------------
% 197.94/29.56 % (5255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 197.94/29.56 % (5255)Termination reason: Unknown
% 197.94/29.56 % (5255)Termination phase: Saturation
% 197.94/29.56
% 197.94/29.56 % (5255)Memory used [KB]: 20724
% 197.94/29.56 % (5255)Time elapsed: 3.229 s
% 197.94/29.56 % (5255)Instructions burned: 10311 (million)
% 197.94/29.56 % (5255)------------------------------
% 197.94/29.56 % (5255)------------------------------
% 197.94/29.57 % (5383)dis+1010_2:1_avsq=on:fde=unused:prag=on:i=3362:si=on:rtra=on_0 on DTF2THF_3905 for (2720ds/3362Mi)
% 198.43/29.63 % (5258)Instruction limit reached!
% 198.43/29.63 % (5258)------------------------------
% 198.43/29.63 % (5258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 198.43/29.63 % (5258)Termination reason: Unknown
% 198.43/29.63 % (5258)Termination phase: Saturation
% 198.43/29.63
% 198.43/29.63 % (5258)Memory used [KB]: 14072
% 198.43/29.63 % (5258)Time elapsed: 1.736 s
% 198.43/29.63 % (5258)Instructions burned: 5576 (million)
% 198.43/29.63 % (5258)------------------------------
% 198.43/29.63 % (5258)------------------------------
% 198.43/29.64 % (5407)ott+1002_1:1_au=on:cnfonf=lazy_simp:nwc=5.0:sgt=5:ss=axioms:st=1.5:i=24965:si=on:rtra=on_0 on DTF2THF_3905 for (2719ds/24965Mi)
% 205.51/30.55 % (5383)Instruction limit reached!
% 205.51/30.55 % (5383)------------------------------
% 205.51/30.55 % (5383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 205.51/30.55 % (5383)Termination reason: Unknown
% 205.51/30.55 % (5383)Termination phase: Saturation
% 205.51/30.55
% 205.51/30.55 % (5383)Memory used [KB]: 23922
% 205.51/30.55 % (5383)Time elapsed: 0.982 s
% 205.51/30.55 % (5383)Instructions burned: 3362 (million)
% 205.51/30.55 % (5383)------------------------------
% 205.51/30.55 % (5383)------------------------------
% 205.51/30.56 % (5729)lrs+1010_2:1_amm=off:avsq=on:c=on:cbe=off:e2e=on:fsr=off:ins=3:s2a=on:s2at=-1.0:i=15705:si=on:rtra=on_0 on DTF2THF_3905 for (2710ds/15705Mi)
% 213.93/31.75 % (5261)Instruction limit reached!
% 213.93/31.75 % (5261)------------------------------
% 213.93/31.75 % (5261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 213.93/31.75 % (5261)Termination reason: Unknown
% 213.93/31.75 % (5261)Termination phase: Saturation
% 213.93/31.75
% 213.93/31.75 % (5261)Memory used [KB]: 7931
% 213.93/31.75 % (5261)Time elapsed: 3.328 s
% 213.93/31.75 % (5261)Instructions burned: 13003 (million)
% 213.93/31.75 % (5261)------------------------------
% 213.93/31.75 % (5261)------------------------------
% 213.93/31.78 % (5788)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1536:si=on:rtra=on_0 on DTF2THF_3905 for (2698ds/1536Mi)
% 218.79/32.41 % (5788)Instruction limit reached!
% 218.79/32.41 % (5788)------------------------------
% 218.79/32.41 % (5788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 218.79/32.41 % (5788)Termination reason: Unknown
% 218.79/32.41 % (5788)Termination phase: Saturation
% 218.79/32.41
% 218.79/32.41 % (5788)Memory used [KB]: 10618
% 218.79/32.41 % (5788)Time elapsed: 0.628 s
% 218.79/32.41 % (5788)Instructions burned: 1537 (million)
% 218.79/32.41 % (5788)------------------------------
% 218.79/32.41 % (5788)------------------------------
% 218.79/32.42 % (5833)dis+10_1:1_fde=none:kws=precedence:piset=not:prag=on:slsq=on:slsqc=1:sp=unary_frequency:i=23684:si=on:rtra=on_0 on DTF2THF_3905 for (2692ds/23684Mi)
% 218.79/32.50 % (5262)Instruction limit reached!
% 218.79/32.50 % (5262)------------------------------
% 218.79/32.50 % (5262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 218.79/32.50 % (5262)Termination reason: Unknown
% 218.79/32.50 % (5262)Termination phase: Saturation
% 218.79/32.50
% 218.79/32.50 % (5262)Memory used [KB]: 31086
% 218.79/32.50 % (5262)Time elapsed: 3.878 s
% 218.79/32.50 % (5262)Instructions burned: 11106 (million)
% 218.79/32.50 % (5262)------------------------------
% 218.79/32.50 % (5262)------------------------------
% 215.55/32.52 % (5838)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=4925:si=on:rtra=on_0 on DTF2THF_3905 for (2691ds/4925Mi)
% 224.36/33.21 % (5263)Instruction limit reached!
% 224.36/33.21 % (5263)------------------------------
% 224.36/33.21 % (5263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 224.36/33.21 % (5263)Termination reason: Unknown
% 224.36/33.21 % (5263)Termination phase: Saturation
% 224.36/33.21
% 224.36/33.21 % (5263)Memory used [KB]: 19573
% 224.36/33.21 % (5263)Time elapsed: 4.160 s
% 224.36/33.21 % (5263)Instructions burned: 13832 (million)
% 224.36/33.21 % (5263)------------------------------
% 224.36/33.21 % (5263)------------------------------
% 224.36/33.23 % (5858)lrs-1010_1:50_au=on:awrs=converge:awrsf=430:bet=on:cbe=off:cha=on:nm=20:sac=on:i=14666:si=on:rtra=on_0 on DTF2THF_3905 for (2684ds/14666Mi)
% 225.00/33.30 % (5729)First to succeed.
% 225.00/33.32 % (5729)Refutation found. Thanks to Tanya!
% 225.00/33.32 % SZS status Theorem for DTF2THF_3905
% 225.00/33.32 % SZS output start Proof for DTF2THF_3905
% 225.00/33.32 thf(func_def_0, type, in: $i > $i > $o).
% 225.00/33.32 thf(func_def_1, type, exu: ($i > $o) > $o).
% 225.00/33.32 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 225.00/33.32 thf(func_def_8, type, powerset: $i > $i).
% 225.00/33.32 thf(func_def_10, type, setunion: $i > $i).
% 225.00/33.32 thf(func_def_19, type, descr: ($i > $o) > $i).
% 225.00/33.32 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 225.00/33.32 thf(func_def_26, type, prop2set: $o > $i).
% 225.00/33.32 thf(func_def_36, type, nonempty: $i > $o).
% 225.00/33.32 thf(func_def_69, type, set2prop: $i > $o).
% 225.00/33.32 thf(func_def_88, type, subset: $i > $i > $o).
% 225.00/33.32 thf(func_def_89, type, disjoint: $i > $i > $o).
% 225.00/33.32 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 225.00/33.32 thf(func_def_114, type, binunion: $i > $i > $i).
% 225.00/33.32 thf(func_def_122, type, binintersect: $i > $i > $i).
% 225.00/33.32 thf(func_def_135, type, regular: $i > $o).
% 225.00/33.32 thf(func_def_136, type, setminus: $i > $i > $i).
% 225.00/33.32 thf(func_def_147, type, symdiff: $i > $i > $i).
% 225.00/33.32 thf(func_def_153, type, iskpair: $i > $o).
% 225.00/33.32 thf(func_def_158, type, kpair: $i > $i > $i).
% 225.00/33.32 thf(func_def_160, type, cartprod: $i > $i > $i).
% 225.00/33.32 thf(func_def_177, type, singleton: $i > $o).
% 225.00/33.32 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 225.00/33.32 thf(func_def_184, type, atmost1p: $i > $o).
% 225.00/33.32 thf(func_def_185, type, atleast2p: $i > $o).
% 225.00/33.32 thf(func_def_186, type, atmost2p: $i > $o).
% 225.00/33.32 thf(func_def_187, type, upairsetp: $i > $o).
% 225.00/33.32 thf(func_def_191, type, kfst: $i > $i).
% 225.00/33.32 thf(func_def_203, type, ksnd: $i > $i).
% 225.00/33.32 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 225.00/33.32 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 225.00/33.32 thf(func_def_222, type, func: $i > $i > $i > $o).
% 225.00/33.32 thf(func_def_223, type, funcSet: $i > $i > $i).
% 225.00/33.32 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 225.00/33.32 thf(func_def_259, type, if: $i > $o > $i > $i > $i).
% 225.00/33.32 thf(func_def_323, type, breln1: $i > $i > $o).
% 225.00/33.32 thf(func_def_325, type, breln1Set: $i > $i).
% 225.00/33.32 thf(func_def_327, type, transitive: $i > $i > $o).
% 225.00/33.32 thf(func_def_328, type, antisymmetric: $i > $i > $o).
% 225.00/33.32 thf(func_def_329, type, reflexive: $i > $i > $o).
% 225.00/33.32 thf(func_def_330, type, refltransitive: $i > $i > $o).
% 225.00/33.32 thf(func_def_331, type, refllinearorder: $i > $i > $o).
% 225.00/33.32 thf(func_def_332, type, reflwellordering: $i > $i > $o).
% 225.00/33.32 thf(func_def_338, type, breln1invset: $i > $i > $i).
% 225.00/33.32 thf(func_def_342, type, breln1compset: $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_360, type, sP1: $i > $i > $i > $i > $o).
% 225.00/33.32 thf(func_def_364, type, sP5: $i > $i > $i > $o).
% 225.00/33.32 thf(func_def_365, type, sP6: $i > $i > $i > $o > $o).
% 225.00/33.32 thf(func_def_368, type, sP9: $i > $i > $o).
% 225.00/33.32 thf(func_def_369, type, sP10: $i > $o).
% 225.00/33.32 thf(func_def_370, type, sP11: $i > $i > $o).
% 225.00/33.32 thf(func_def_371, type, sP12: $i > $i > $o).
% 225.00/33.32 thf(func_def_373, type, sP14: $i > $i > $i > $o).
% 225.00/33.32 thf(func_def_380, type, sK21: $i > $o).
% 225.00/33.32 thf(func_def_383, type, sK24: $i > $i).
% 225.00/33.32 thf(func_def_386, type, sK27: $i > $i > ($i > $i) > $i).
% 225.00/33.32 thf(func_def_398, type, sK39: $i > $o).
% 225.00/33.32 thf(func_def_420, type, sK61: $i > $i > $o).
% 225.00/33.32 thf(func_def_438, type, sK79: $i > $i > $o).
% 225.00/33.32 thf(func_def_440, type, sK81: $i > $i).
% 225.00/33.32 thf(func_def_443, type, sK84: $i > ($i > $i > $o) > $i > $i).
% 225.00/33.32 thf(func_def_444, type, sK85: $i > ($i > $o) > $i).
% 225.00/33.32 thf(func_def_445, type, sK86: $i > $o).
% 225.00/33.32 thf(func_def_451, type, sK92: $i > $i > $o).
% 225.00/33.32 thf(func_def_457, type, sK98: $i > $o).
% 225.00/33.32 thf(func_def_459, type, sK100: ($i > $o) > $i > $i).
% 225.00/33.32 thf(func_def_468, type, sK109: $i > $o).
% 225.00/33.32 thf(func_def_469, type, sK110: $i > $o).
% 225.00/33.32 thf(func_def_472, type, sK113: $i > ($i > $o) > $i).
% 225.00/33.32 thf(func_def_481, type, sK122: $i > $i > $o).
% 225.00/33.32 thf(func_def_482, type, sK123: $i > $o).
% 225.00/33.32 thf(func_def_485, type, sK126: $i > ($i > $o) > $i).
% 225.00/33.32 thf(func_def_486, type, sK127: $i > ($i > $o) > $i).
% 225.00/33.32 thf(func_def_491, type, sK132: $i > $i > $o).
% 225.00/33.32 thf(func_def_505, type, sK146: ($i > $o) > $i > $i).
% 225.00/33.32 thf(func_def_507, type, sK148: $i > $o).
% 225.00/33.32 thf(func_def_525, type, sK166: $i > $i > $o).
% 225.00/33.32 thf(func_def_533, type, sK174: $i > $o).
% 225.00/33.32 thf(func_def_540, type, sK181: $i > $o).
% 225.00/33.32 thf(func_def_542, type, sK183: $i > $o).
% 225.00/33.32 thf(func_def_544, type, sK185: $i > ($i > $o) > $i > $i).
% 225.00/33.32 thf(func_def_545, type, sK186: $i > $o).
% 225.00/33.32 thf(func_def_552, type, sK193: $i > $i).
% 225.00/33.32 thf(func_def_554, type, sK195: $i > $i).
% 225.00/33.32 thf(func_def_560, type, sK201: $i > $i > $i).
% 225.00/33.32 thf(func_def_577, type, sK218: $i > $i).
% 225.00/33.32 thf(func_def_580, type, sK221: $i > $i > ($i > $i) > $i).
% 225.00/33.32 thf(func_def_587, type, sK228: $i > ($i > $o) > $i).
% 225.00/33.32 thf(func_def_588, type, sK229: $i > $o).
% 225.00/33.32 thf(func_def_595, type, sK236: $i > $o).
% 225.00/33.32 thf(func_def_631, type, sK272: $i > $i > $i).
% 225.00/33.32 thf(func_def_639, type, sK280: $i > $o).
% 225.00/33.32 thf(func_def_644, type, sK285: $i > $o).
% 225.00/33.32 thf(func_def_646, type, sK287: $i > ($i > $o) > $i).
% 225.00/33.32 thf(func_def_649, type, sK290: ($i > $o) > $i).
% 225.00/33.32 thf(func_def_650, type, sK291: ($i > $o) > $i).
% 225.00/33.32 thf(func_def_651, type, sK292: $i > $o).
% 225.00/33.32 thf(func_def_663, type, sK304: $i > $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_664, type, sK305: $i > $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_665, type, sK306: $i > $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_666, type, sK307: $i > $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_676, type, sK317: $i > $i > $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_702, type, sK343: $i > $i > $i).
% 225.00/33.32 thf(func_def_709, type, sK350: $i > $i > $i).
% 225.00/33.32 thf(func_def_713, type, sK354: ($i > $o) > $i > $i > $i).
% 225.00/33.32 thf(func_def_714, type, sK355: ($i > $o) > $i > $i > $i).
% 225.00/33.32 thf(func_def_717, type, sK358: $i > $o).
% 225.00/33.32 thf(func_def_719, type, sK360: $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_755, type, sK396: $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_759, type, sK400: $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_765, type, sK406: ($i > $o) > $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_766, type, sK407: ($i > $o) > $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_770, type, sK411: $i > $o).
% 225.00/33.32 thf(func_def_777, type, sK418: $i > $i).
% 225.00/33.32 thf(func_def_780, type, sK421: $i > $i > $i).
% 225.00/33.32 thf(func_def_783, type, sK424: $i > $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_795, type, sK436: ($i > $o) > $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_796, type, sK437: ($i > $o) > $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_800, type, sK441: $i > $o).
% 225.00/33.32 thf(func_def_802, type, sK443: ($i > $o) > $i > $i > $i).
% 225.00/33.32 thf(func_def_803, type, sK444: ($i > $o) > $i > $i > $i).
% 225.00/33.32 thf(func_def_806, type, sK447: $i > $o).
% 225.00/33.32 thf(func_def_810, type, sK451: $i > $i > $i).
% 225.00/33.32 thf(func_def_811, type, sK452: $i > $i > $i).
% 225.00/33.32 thf(func_def_816, type, sK457: $i > ($i > $o) > $i).
% 225.00/33.32 thf(func_def_817, type, sK458: $i > $o).
% 225.00/33.32 thf(func_def_844, type, sK485: $i > $o).
% 225.00/33.32 thf(func_def_860, type, sK501: $i > ($i > $i) > $i > $i).
% 225.00/33.32 thf(func_def_862, type, sK503: $i > $i).
% 225.00/33.32 thf(func_def_890, type, sK531: ($i > $o) > ($i > $o) > $i > $i > $i).
% 225.00/33.32 thf(func_def_891, type, sK532: ($i > $o) > ($i > $o) > $i > $i > $i).
% 225.00/33.32 thf(func_def_894, type, sK535: $i > $o).
% 225.00/33.32 thf(func_def_895, type, sK536: $i > $o).
% 225.00/33.32 thf(func_def_907, type, sK548: $i > $o).
% 225.00/33.32 thf(func_def_908, type, sK549: $i > $i).
% 225.00/33.32 thf(func_def_909, type, sK550: ($i > $o) > $i).
% 225.00/33.32 thf(func_def_914, type, sK555: $i > $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_915, type, sK556: $i > $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_927, type, sK568: $i > $o).
% 225.00/33.32 thf(func_def_938, type, sK579: $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_939, type, sK580: $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_945, type, sK586: $i > $i).
% 225.00/33.32 thf(func_def_952, type, sK593: $i > $i > $i).
% 225.00/33.32 thf(func_def_957, type, sK598: $i > $o).
% 225.00/33.32 thf(func_def_975, type, sK616: $i > $i).
% 225.00/33.32 thf(func_def_977, type, sK618: ($i > $i) > $i > $i > $i).
% 225.00/33.32 thf(func_def_992, type, sK633: $i > $o).
% 225.00/33.32 thf(func_def_993, type, sK634: $i > $o).
% 225.00/33.32 thf(func_def_994, type, sK635: ($i > $o) > ($i > $o) > $i).
% 225.00/33.32 thf(func_def_995, type, sK636: ($i > $o) > ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1005, type, sK646: $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_1006, type, sK647: $i > $i > $i).
% 225.00/33.32 thf(func_def_1014, type, sK655: $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_1015, type, sK656: $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_1023, type, sK664: $i > $i).
% 225.00/33.32 thf(func_def_1029, type, sK670: $i > $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_1036, type, sK677: $i > $i > $o).
% 225.00/33.32 thf(func_def_1045, type, sK686: ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1046, type, sK687: $i > $o).
% 225.00/33.32 thf(func_def_1047, type, sK688: $i > $i).
% 225.00/33.32 thf(func_def_1053, type, sK694: $i > $i).
% 225.00/33.32 thf(func_def_1054, type, sK695: ($i > $i) > $i > $i > $i).
% 225.00/33.32 thf(func_def_1055, type, sK696: ($i > $o) > $i > $i).
% 225.00/33.32 thf(func_def_1057, type, sK698: $i > $o).
% 225.00/33.32 thf(func_def_1059, type, sK700: $i > $o).
% 225.00/33.32 thf(func_def_1062, type, sK703: $i > ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1063, type, sK704: $i > ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1076, type, sK717: $i > $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_1084, type, sK725: $o > $i > $i > $i).
% 225.00/33.32 thf(func_def_1088, type, sK729: $i > $i > $i).
% 225.00/33.32 thf(func_def_1089, type, sK730: $i > $i > $i).
% 225.00/33.32 thf(func_def_1090, type, sK731: $i > $i > $i).
% 225.00/33.32 thf(func_def_1091, type, sK732: $i > $i > $i).
% 225.00/33.32 thf(func_def_1092, type, sK733: $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_1093, type, sK734: $i > $i).
% 225.00/33.32 thf(func_def_1094, type, sK735: $i > $i).
% 225.00/33.32 thf(func_def_1095, type, sK736: $i > $i).
% 225.00/33.32 thf(func_def_1096, type, sK737: $i > $i).
% 225.00/33.32 thf(func_def_1097, type, sK738: $i > $i > $i).
% 225.00/33.32 thf(func_def_1098, type, sK739: $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_1099, type, sK740: $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_1100, type, sK741: $i > $i > $i).
% 225.00/33.32 thf(func_def_1101, type, sK742: $i > $i > $i).
% 225.00/33.32 thf(func_def_1103, type, sK744: $i > $i).
% 225.00/33.32 thf(func_def_1104, type, sK745: $i > $i).
% 225.00/33.32 thf(func_def_1105, type, sK746: $i > $i).
% 225.00/33.32 thf(func_def_1106, type, sK747: $i > $i > $i).
% 225.00/33.32 thf(func_def_1121, type, sK762: ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1122, type, sK763: $i > $o).
% 225.00/33.32 thf(func_def_1159, type, sK800: $i > $i > $i).
% 225.00/33.32 thf(func_def_1174, type, sK815: $i > $i > $o).
% 225.00/33.32 thf(func_def_1176, type, sK817: $i > $i).
% 225.00/33.32 thf(func_def_1177, type, sK818: $i > $i).
% 225.00/33.32 thf(func_def_1178, type, sK819: $i > ($i > $i > $o) > $i).
% 225.00/33.32 thf(func_def_1179, type, sK820: $i > $i > ($i > $i > $o) > $i).
% 225.00/33.32 thf(func_def_1180, type, sK821: $i > ($i > $i > $o) > $i).
% 225.00/33.32 thf(func_def_1204, type, sK845: $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_1205, type, sK846: $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_1206, type, sK847: $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_1207, type, sK848: $i > $i > $i > $i).
% 225.00/33.32 thf(func_def_1236, type, sK877: $i > $o).
% 225.00/33.32 thf(func_def_1237, type, sK878: $i > $o).
% 225.00/33.32 thf(func_def_1238, type, sK879: ($i > $o) > ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1239, type, sK880: ($i > $o) > ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1258, type, sK899: $i > $i > ($i > $i) > $i).
% 225.00/33.32 thf(func_def_1259, type, sK900: $i > $i).
% 225.00/33.32 thf(func_def_1266, type, sK907: ($i > $o) > $i > $i).
% 225.00/33.32 thf(func_def_1268, type, sK909: $i > $o).
% 225.00/33.32 thf(func_def_1301, type, sK942: $i > $i).
% 225.00/33.32 thf(func_def_1305, type, sK946: $i > $i > $o).
% 225.00/33.32 thf(func_def_1311, type, sK952: $i > $o).
% 225.00/33.32 thf(func_def_1316, type, sK957: $i > $i > $o).
% 225.00/33.32 thf(func_def_1321, type, sK962: $i > $o).
% 225.00/33.32 thf(func_def_1335, type, sK976: $i > $i).
% 225.00/33.32 thf(func_def_1351, type, sP992: $o > $o).
% 225.00/33.32 thf(func_def_1352, type, sP993: $o > $o).
% 225.00/33.32 thf(func_def_1353, type, sP994: $o > $o).
% 225.00/33.32 thf(func_def_1354, type, sP995: $o > $o).
% 225.00/33.32 thf(func_def_1355, type, sP996: $o > $o).
% 225.00/33.32 thf(func_def_1356, type, sP997: $o > $o).
% 225.00/33.32 thf(func_def_1357, type, sP998: $o > $o).
% 225.00/33.32 thf(func_def_1358, type, sP999: $o > $o).
% 225.00/33.32 thf(func_def_1359, type, sP1000: $o > $o).
% 225.00/33.32 thf(func_def_1360, type, sP1001: $i > $o).
% 225.00/33.32 thf(func_def_1361, type, sP1002: $o > $o).
% 225.00/33.32 thf(func_def_1362, type, sP1003: $o > $o).
% 225.00/33.32 thf(func_def_1363, type, sP1004: $o > $o).
% 225.00/33.32 thf(func_def_1364, type, sP1005: $i > $o).
% 225.00/33.32 thf(func_def_1365, type, sP1006: $o > $o).
% 225.00/33.32 thf(func_def_1366, type, sP1007: $o > $o).
% 225.00/33.32 thf(func_def_1367, type, sP1008: $o > $o).
% 225.00/33.32 thf(func_def_1368, type, sP1009: $o > $o).
% 225.00/33.32 thf(func_def_1369, type, sP1010: $o > $o).
% 225.00/33.32 thf(func_def_1370, type, sP1011: $o > $o).
% 225.00/33.32 thf(func_def_1371, type, sP1012: $o > $o).
% 225.00/33.32 thf(func_def_1372, type, sP1013: $o > $o).
% 225.00/33.32 thf(func_def_1373, type, sP1014: $o > $o).
% 225.00/33.32 thf(func_def_1374, type, sP1015: $o > $o).
% 225.00/33.32 thf(func_def_1375, type, sP1016: $o > $o).
% 225.00/33.32 thf(func_def_1376, type, sP1017: $o > $o).
% 225.00/33.32 thf(func_def_1377, type, sP1018: $o > $o).
% 225.00/33.32 thf(func_def_1378, type, sP1019: $o > $o).
% 225.00/33.32 thf(func_def_1379, type, sP1020: $o > $o).
% 225.00/33.32 thf(func_def_1380, type, sP1021: $o > $o).
% 225.00/33.32 thf(func_def_1381, type, sP1022: $o > $o).
% 225.00/33.32 thf(func_def_1382, type, sP1023: $i > $o).
% 225.00/33.32 thf(func_def_1383, type, sP1024: $o > $o).
% 225.00/33.32 thf(func_def_1384, type, sP1025: $o > $o).
% 225.00/33.32 thf(func_def_1385, type, sP1026: $o > $o).
% 225.00/33.32 thf(func_def_1386, type, sP1027: $o > $o).
% 225.00/33.32 thf(func_def_1387, type, sP1028: $o > $o).
% 225.00/33.32 thf(func_def_1388, type, sP1029: $o > $o).
% 225.00/33.32 thf(func_def_1389, type, sP1030: $o > $o).
% 225.00/33.32 thf(func_def_1390, type, sP1031: $o > $o).
% 225.00/33.32 thf(func_def_1391, type, sP1032: $o > $o).
% 225.00/33.32 thf(func_def_1392, type, sP1033: $o > $o).
% 225.00/33.32 thf(func_def_1393, type, sP1034: $o > $o).
% 225.00/33.32 thf(func_def_1394, type, sP1035: $o > $o).
% 225.00/33.32 thf(func_def_1395, type, sP1036: $o > $o).
% 225.00/33.32 thf(func_def_1396, type, sP1037: $o > $o).
% 225.00/33.32 thf(func_def_1397, type, sP1038: $o > $o).
% 225.00/33.32 thf(func_def_1398, type, sP1039: $o > $o).
% 225.00/33.32 thf(func_def_1399, type, sP1040: $o > $o).
% 225.00/33.32 thf(func_def_1400, type, sP1041: $o > $o).
% 225.00/33.32 thf(func_def_1401, type, sP1042: $o > $o).
% 225.00/33.32 thf(func_def_1402, type, sP1043: $i > $o).
% 225.00/33.32 thf(func_def_1403, type, sP1044: $o > $o).
% 225.00/33.32 thf(func_def_1404, type, sP1045: $o > $o).
% 225.00/33.32 thf(func_def_1405, type, sP1046: $o > $o).
% 225.00/33.32 thf(func_def_1406, type, sP1047: $o > $o).
% 225.00/33.32 thf(func_def_1407, type, sP1048: $o > $o).
% 225.00/33.32 thf(func_def_1408, type, sP1049: $o > $o).
% 225.00/33.32 thf(func_def_1409, type, sP1050: $o > $o).
% 225.00/33.32 thf(func_def_1410, type, sP1051: $o > $o).
% 225.00/33.32 thf(func_def_1411, type, sP1052: $i > $o).
% 225.00/33.32 thf(func_def_1412, type, sP1053: $o > $o).
% 225.00/33.32 thf(func_def_1413, type, sP1054: $o > $o).
% 225.00/33.32 thf(func_def_1414, type, sP1055: $o > $o).
% 225.00/33.32 thf(func_def_1415, type, sP1056: $o > $o).
% 225.00/33.32 thf(func_def_1416, type, sP1057: $o > $o).
% 225.00/33.32 thf(func_def_1417, type, sP1058: $o > $o).
% 225.00/33.32 thf(func_def_1418, type, sP1059: $o > $o).
% 225.00/33.32 thf(func_def_1419, type, sP1060: $o > $o).
% 225.00/33.32 thf(func_def_1420, type, sP1061: $o > $o).
% 225.00/33.32 thf(func_def_1421, type, sP1062: $o > $o).
% 225.00/33.32 thf(func_def_1422, type, sP1063: $o > $o).
% 225.00/33.32 thf(func_def_1423, type, sP1064: $o > $o).
% 225.00/33.32 thf(func_def_1424, type, sP1065: $o > $o).
% 225.00/33.32 thf(func_def_1425, type, sP1066: $o > $o).
% 225.00/33.32 thf(func_def_1426, type, sP1067: $o > $o).
% 225.00/33.32 thf(func_def_1427, type, sP1068: $o > $o).
% 225.00/33.32 thf(func_def_1428, type, sP1069: $o > $o).
% 225.00/33.32 thf(func_def_1429, type, sP1070: $o > $o).
% 225.00/33.32 thf(func_def_1430, type, sP1071: $o > $o).
% 225.00/33.32 thf(func_def_1431, type, sP1072: $o > $o).
% 225.00/33.32 thf(func_def_1432, type, sP1073: $o > $o).
% 225.00/33.32 thf(func_def_1433, type, sP1074: $o > $o).
% 225.00/33.32 thf(func_def_1434, type, sP1075: $o > $o).
% 225.00/33.32 thf(func_def_1435, type, sP1076: $o > $o).
% 225.00/33.32 thf(func_def_1436, type, sP1077: $o > $o).
% 225.00/33.32 thf(func_def_1437, type, sP1078: $i > $o).
% 225.00/33.32 thf(func_def_1438, type, sP1079: $o > $o).
% 225.00/33.32 thf(func_def_1439, type, sP1080: $o > $o).
% 225.00/33.32 thf(func_def_1440, type, sP1081: $o > $o).
% 225.00/33.32 thf(func_def_1441, type, sP1082: $i > $o).
% 225.00/33.32 thf(func_def_1442, type, sP1083: $o > $o).
% 225.00/33.32 thf(func_def_1443, type, sP1084: $o > $o).
% 225.00/33.32 thf(func_def_1444, type, sP1085: $o > $o).
% 225.00/33.32 thf(func_def_1445, type, sP1086: $o > $o).
% 225.00/33.32 thf(func_def_1446, type, sP1087: $o > $o).
% 225.00/33.32 thf(func_def_1447, type, sP1088: $o > $o).
% 225.00/33.32 thf(func_def_1448, type, sP1089: $o > $o).
% 225.00/33.32 thf(func_def_1449, type, sP1090: $i > $o).
% 225.00/33.32 thf(func_def_1450, type, sP1091: $o > $o).
% 225.00/33.32 thf(func_def_1451, type, sP1092: $i > $o).
% 225.00/33.32 thf(func_def_1452, type, sP1093: $i > $o).
% 225.00/33.32 thf(func_def_1453, type, sP1094: $o > $o).
% 225.00/33.32 thf(func_def_1454, type, sP1095: $o > $o).
% 225.00/33.32 thf(func_def_1455, type, sP1096: $o > $o).
% 225.00/33.32 thf(func_def_1456, type, sP1097: $o > $o).
% 225.00/33.32 thf(func_def_1457, type, sP1098: $o > $o).
% 225.00/33.32 thf(func_def_1458, type, sP1099: $o > $o).
% 225.00/33.32 thf(func_def_1459, type, sP1100: $o > $o).
% 225.00/33.32 thf(func_def_1460, type, sP1101: $o > $o).
% 225.00/33.32 thf(func_def_1461, type, sP1102: $o > $o).
% 225.00/33.32 thf(func_def_1462, type, sP1103: $o > $o).
% 225.00/33.32 thf(func_def_1463, type, sP1104: $o > $o).
% 225.00/33.32 thf(func_def_1464, type, sP1105: $o > $o).
% 225.00/33.32 thf(func_def_1465, type, sP1106: $o > $o).
% 225.00/33.32 thf(func_def_1466, type, sP1107: $o > $o).
% 225.00/33.32 thf(func_def_1467, type, sP1108: $o > $o).
% 225.00/33.32 thf(func_def_1468, type, sP1109: $o > $o).
% 225.00/33.32 thf(func_def_1469, type, sP1110: $o > $o).
% 225.00/33.32 thf(func_def_1470, type, sP1111: $o > $o).
% 225.00/33.32 thf(func_def_1471, type, sP1112: $o > $o).
% 225.00/33.32 thf(func_def_1472, type, sP1113: $o > $o).
% 225.00/33.32 thf(func_def_1473, type, sP1114: $o > $o).
% 225.00/33.32 thf(func_def_1474, type, sP1115: $i > $o).
% 225.00/33.32 thf(func_def_1475, type, sP1116: $o > $o).
% 225.00/33.32 thf(func_def_1476, type, sP1117: $o > $o).
% 225.00/33.32 thf(func_def_1477, type, sP1118: $o > $o).
% 225.00/33.32 thf(func_def_1478, type, sP1119: $i > $o).
% 225.00/33.32 thf(func_def_1479, type, sP1120: $o > $o).
% 225.00/33.32 thf(func_def_1480, type, sP1121: $o > $o).
% 225.00/33.32 thf(func_def_1481, type, sP1122: $o > $o).
% 225.00/33.32 thf(func_def_1482, type, sP1123: $o > $o).
% 225.00/33.32 thf(func_def_1483, type, sP1124: $o > $o).
% 225.00/33.32 thf(func_def_1484, type, sP1125: $o > $o).
% 225.00/33.32 thf(func_def_1485, type, sP1126: $o > $o).
% 225.00/33.32 thf(func_def_1486, type, sP1127: $o > $o).
% 225.00/33.32 thf(func_def_1487, type, sP1128: $o > $o).
% 225.00/33.32 thf(func_def_1488, type, sP1129: $o > $o).
% 225.00/33.32 thf(func_def_1489, type, sP1130: $i > $o).
% 225.00/33.32 thf(func_def_1490, type, sP1131: $o > $o).
% 225.00/33.32 thf(func_def_1491, type, sP1132: $o > $o).
% 225.00/33.32 thf(func_def_1492, type, sP1133: $i > $o).
% 225.00/33.32 thf(func_def_1493, type, sP1134: $o > $o).
% 225.00/33.32 thf(func_def_1494, type, sP1135: $o > $o).
% 225.00/33.32 thf(func_def_1495, type, sP1136: $i > $o).
% 225.00/33.32 thf(func_def_1496, type, sP1137: $o > $o).
% 225.00/33.32 thf(func_def_1497, type, sP1138: $o > $o).
% 225.00/33.32 thf(func_def_1498, type, sP1139: $o > $o).
% 225.00/33.32 thf(func_def_1499, type, sP1140: $o > $o).
% 225.00/33.32 thf(func_def_1500, type, sP1141: $o > $o).
% 225.00/33.32 thf(func_def_1501, type, sP1142: $o > $o).
% 225.00/33.32 thf(func_def_1502, type, sP1143: $i > $o).
% 225.00/33.32 thf(func_def_1503, type, sP1144: $o > $o).
% 225.00/33.32 thf(func_def_1504, type, sP1145: $i > $o).
% 225.00/33.32 thf(func_def_1505, type, sP1146: $i > $o).
% 225.00/33.32 thf(func_def_1506, type, sP1147: $o > $o).
% 225.00/33.32 thf(func_def_1507, type, sP1148: $o > $o).
% 225.00/33.32 thf(func_def_1508, type, sP1149: $o > $o).
% 225.00/33.32 thf(func_def_1509, type, sP1150: $o > $o).
% 225.00/33.32 thf(func_def_1510, type, sP1151: $i > $o).
% 225.00/33.32 thf(func_def_1511, type, sP1152: $o > $o).
% 225.00/33.32 thf(func_def_1512, type, sP1153: $i > $o).
% 225.00/33.32 thf(func_def_1513, type, sP1154: $o > $o).
% 225.00/33.32 thf(func_def_1514, type, sP1155: $i > $o).
% 225.00/33.32 thf(func_def_1515, type, sP1156: $i > $o).
% 225.00/33.32 thf(func_def_1516, type, sP1157: $o > $o).
% 225.00/33.32 thf(func_def_1517, type, sP1158: $o > $o).
% 225.00/33.32 thf(func_def_1518, type, sP1159: $o > $o).
% 225.00/33.32 thf(func_def_1519, type, sP1160: $o > $o).
% 225.00/33.32 thf(func_def_1520, type, sP1161: $o > $o).
% 225.00/33.32 thf(func_def_1521, type, sP1162: $o > $o).
% 225.00/33.32 thf(func_def_1522, type, sP1163: $o > $o).
% 225.00/33.32 thf(func_def_1523, type, sP1164: $o > $o).
% 225.00/33.32 thf(func_def_1524, type, sP1165: $i > $o).
% 225.00/33.32 thf(func_def_1525, type, sP1166: $o > $o).
% 225.00/33.32 thf(func_def_1526, type, sP1167: $o > $o).
% 225.00/33.32 thf(func_def_1527, type, sP1168: $o > $o).
% 225.00/33.32 thf(func_def_1528, type, sP1169: $o > $o).
% 225.00/33.32 thf(func_def_1529, type, sP1170: $o > $o).
% 225.00/33.32 thf(func_def_1530, type, sP1171: $o > $o).
% 225.00/33.32 thf(func_def_1531, type, sP1172: $o > $o).
% 225.00/33.32 thf(func_def_1532, type, sP1173: $i > $o).
% 225.00/33.32 thf(func_def_1533, type, sP1174: $i > $o).
% 225.00/33.32 thf(func_def_1534, type, sP1175: $o > $o).
% 225.00/33.32 thf(func_def_1535, type, sP1176: $o > $o).
% 225.00/33.32 thf(func_def_1536, type, sP1177: $o > $o).
% 225.00/33.32 thf(func_def_1537, type, sP1178: $o > $o).
% 225.00/33.32 thf(func_def_1538, type, sP1179: $o > $o).
% 225.00/33.32 thf(func_def_1539, type, sP1180: $o > $o).
% 225.00/33.32 thf(func_def_1540, type, sP1181: $o > $o).
% 225.00/33.32 thf(func_def_1541, type, sP1182: $o > $o).
% 225.00/33.32 thf(func_def_1542, type, sP1183: $i > $o).
% 225.00/33.32 thf(func_def_1543, type, sP1184: $o > $o).
% 225.00/33.32 thf(func_def_1544, type, sP1185: $i > $o).
% 225.00/33.32 thf(func_def_1545, type, sP1186: $o > $o).
% 225.00/33.32 thf(func_def_1546, type, sP1187: $o > $o).
% 225.00/33.32 thf(func_def_1547, type, sP1188: $o > $o).
% 225.00/33.32 thf(func_def_1548, type, sP1189: $i > $o).
% 225.00/33.32 thf(func_def_1549, type, sP1190: $o > $o).
% 225.00/33.32 thf(func_def_1550, type, sP1191: $o > $o).
% 225.00/33.32 thf(func_def_1551, type, sP1192: $i > $o).
% 225.00/33.32 thf(func_def_1552, type, sP1193: $o > $o).
% 225.00/33.32 thf(func_def_1553, type, sP1194: $i > $o).
% 225.00/33.32 thf(func_def_1554, type, sP1195: $o > $o).
% 225.00/33.32 thf(func_def_1555, type, sP1196: $o > $o).
% 225.00/33.32 thf(func_def_1556, type, sP1197: $i > $o).
% 225.00/33.32 thf(func_def_1557, type, sP1198: $o > $o).
% 225.00/33.32 thf(func_def_1558, type, sP1199: $o > $o).
% 225.00/33.32 thf(func_def_1559, type, sP1200: $o > $o).
% 225.00/33.32 thf(func_def_1560, type, sP1201: $o > $o).
% 225.00/33.32 thf(func_def_1561, type, sP1202: $o > $o).
% 225.00/33.32 thf(func_def_1562, type, sP1203: $o > $o).
% 225.00/33.32 thf(func_def_1563, type, sP1204: $o > $o).
% 225.00/33.32 thf(func_def_1564, type, sP1205: $o > $o).
% 225.00/33.32 thf(func_def_1565, type, sP1206: $o > $o).
% 225.00/33.32 thf(func_def_1566, type, sP1207: $i > $o).
% 225.00/33.32 thf(func_def_1567, type, sP1208: $i > $o).
% 225.00/33.32 thf(func_def_1568, type, sP1209: $o > $o).
% 225.00/33.32 thf(func_def_1569, type, sP1210: $o > $o).
% 225.00/33.32 thf(func_def_1570, type, sP1211: $o > $o).
% 225.00/33.32 thf(func_def_1571, type, sP1212: $i > $o).
% 225.00/33.32 thf(func_def_1572, type, sP1213: $o > $o).
% 225.00/33.32 thf(func_def_1573, type, sP1214: $o > $o).
% 225.00/33.32 thf(func_def_1574, type, sP1215: $i > $o).
% 225.00/33.32 thf(func_def_1575, type, sP1216: $o > $o).
% 225.00/33.32 thf(func_def_1576, type, sP1217: $i > $o).
% 225.00/33.32 thf(func_def_1577, type, sP1218: $o > $o).
% 225.00/33.32 thf(func_def_1578, type, sP1219: $o > $o).
% 225.00/33.32 thf(func_def_1579, type, sP1220: $i > $o).
% 225.00/33.32 thf(func_def_1580, type, sP1221: $o > $o).
% 225.00/33.32 thf(func_def_1581, type, sP1222: $o > $o).
% 225.00/33.32 thf(func_def_1582, type, sP1223: $o > $o).
% 225.00/33.32 thf(func_def_1583, type, sP1224: $o > $o).
% 225.00/33.32 thf(func_def_1584, type, sP1225: $o > $o).
% 225.00/33.32 thf(func_def_1585, type, sP1226: $i > $o).
% 225.00/33.32 thf(func_def_1586, type, sP1227: $o > $o).
% 225.00/33.32 thf(func_def_1587, type, sP1228: $o > $o).
% 225.00/33.32 thf(func_def_1588, type, sP1229: $o > $o).
% 225.00/33.32 thf(func_def_1589, type, sP1230: $o > $o).
% 225.00/33.32 thf(func_def_1590, type, sP1231: $o > $o).
% 225.00/33.32 thf(func_def_1591, type, sP1232: $o > $o).
% 225.00/33.32 thf(func_def_1592, type, sP1233: $o > $o).
% 225.00/33.32 thf(func_def_1593, type, sP1234: $o > $o).
% 225.00/33.32 thf(func_def_1594, type, sP1235: $i > $o).
% 225.00/33.32 thf(func_def_1595, type, sP1236: $o > $o).
% 225.00/33.32 thf(func_def_1596, type, sP1237: $o > $o).
% 225.00/33.32 thf(func_def_1597, type, sP1238: $o > $o).
% 225.00/33.32 thf(func_def_1598, type, sP1239: $o > $o).
% 225.00/33.32 thf(func_def_1599, type, sP1240: $o > $o).
% 225.00/33.32 thf(func_def_1600, type, sP1241: $o > $o).
% 225.00/33.32 thf(func_def_1601, type, sP1242: $o > $o).
% 225.00/33.32 thf(func_def_1602, type, sP1243: $o > $o).
% 225.00/33.32 thf(func_def_1603, type, sP1244: $o > $o).
% 225.00/33.32 thf(func_def_1604, type, sP1245: $o > $o).
% 225.00/33.32 thf(func_def_1605, type, sP1246: $o > $o).
% 225.00/33.32 thf(func_def_1606, type, sP1247: $o > $o).
% 225.00/33.32 thf(func_def_1607, type, sP1248: $o > $o).
% 225.00/33.32 thf(func_def_1609, type, sK1250: ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1610, type, sK1251: $i > ($i > $i > $o) > $i > $i).
% 225.00/33.32 thf(func_def_1611, type, sK1252: ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1612, type, sK1253: $i > ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1613, type, sK1254: $i > ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1614, type, sK1255: ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1615, type, sK1256: ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1616, type, sK1257: ($i > $o) > $i > $i).
% 225.00/33.32 thf(func_def_1617, type, sK1258: ($i > $o) > $i > $i).
% 225.00/33.32 thf(func_def_1618, type, sK1259: ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1619, type, sK1260: ($i > $o) > $i > $i).
% 225.00/33.32 thf(func_def_1620, type, sK1261: ($i > $o) > $i > $i).
% 225.00/33.32 thf(func_def_1621, type, sK1262: ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1622, type, sK1263: ($i > $o) > $i > $i).
% 225.00/33.32 thf(func_def_1623, type, sK1264: $i > ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1624, type, sK1265: ($i > $o) > $i > $i).
% 225.00/33.32 thf(func_def_1625, type, sK1266: ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1626, type, sK1267: ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1627, type, sK1268: ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1628, type, sK1269: ($i > $o) > $i > $i).
% 225.00/33.32 thf(func_def_1629, type, sK1270: ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1630, type, sK1271: ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1631, type, sK1272: ($i > $o) > $i > $i).
% 225.00/33.32 thf(func_def_1632, type, sK1273: ($i > $o) > $i > $i).
% 225.00/33.32 thf(func_def_1633, type, sK1274: $i > $i).
% 225.00/33.32 thf(func_def_1634, type, sK1275: ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1635, type, sK1276: $i > ($i > $i > $o) > $i > $i).
% 225.00/33.32 thf(func_def_1636, type, sK1277: $i > ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1637, type, sK1278: $i > ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1638, type, sK1279: ($i > $o) > $i > $i).
% 225.00/33.32 thf(func_def_1639, type, sK1280: ($i > $o) > $i > $i).
% 225.00/33.32 thf(func_def_1640, type, sK1281: $i > ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1641, type, sK1282: $i > ($i > $i > $o) > $i > $i).
% 225.00/33.32 thf(func_def_1642, type, sK1283: ($i > $o) > $i > $i).
% 225.00/33.32 thf(func_def_1643, type, sK1284: ($i > $o) > $i > $i).
% 225.00/33.32 thf(func_def_1644, type, sK1285: ($i > $o) > $i > $i).
% 225.00/33.32 thf(func_def_1645, type, sK1286: $i > ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1646, type, sK1287: $i > ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1647, type, sK1288: ($i > $o) > $i > $i).
% 225.00/33.32 thf(func_def_1648, type, sK1289: ($i > $o) > $i > $i).
% 225.00/33.32 thf(func_def_1649, type, sK1290: $i > ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1650, type, sK1291: ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1651, type, sK1292: ($i > $o) > $i).
% 225.00/33.32 thf(func_def_1652, type, ph1293: !>[X0: $tType]:(X0)).
% 225.00/33.32 thf(f22114,plain,(
% 225.00/33.32 $false),
% 225.00/33.32 inference(avatar_sat_refutation,[status(thm)],[f7219,f7285,f7388,f7443,f7517,f8392,f22113])).
% 225.00/33.32 thf(f22113,plain,(
% 225.00/33.32 ~spl1249_11 | ~spl1249_26 | ~spl1249_47 | ~spl1249_56),
% 225.00/33.32 inference(avatar_contradiction_clause,[status(thm)],[f22112])).
% 225.00/33.32 thf(f22112,plain,(
% 225.00/33.32 $false | (~spl1249_11 | ~spl1249_26 | ~spl1249_47 | ~spl1249_56)),
% 225.00/33.32 inference(trivial_inequality_removal,[status(thm)],[f22111])).
% 225.00/33.32 thf(f22111,plain,(
% 225.00/33.32 ($true = $false) | (~spl1249_11 | ~spl1249_26 | ~spl1249_47 | ~spl1249_56)),
% 225.00/33.32 inference(backward_demodulation,[status(thm)],[f16335,f22110])).
% 225.00/33.32 thf(f22110,plain,(
% 225.00/33.32 ((in @ (kpair @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638) @ sK641) @ sK639) = $false) | (~spl1249_26 | ~spl1249_47 | ~spl1249_56)),
% 225.00/33.32 inference(trivial_inequality_removal,[status(thm)],[f22109])).
% 225.00/33.32 thf(f22109,plain,(
% 225.00/33.32 ((in @ (kpair @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638) @ sK641) @ sK639) = $false) | ($true = $false) | (~spl1249_26 | ~spl1249_47 | ~spl1249_56)),
% 225.00/33.32 inference(forward_demodulation,[status(thm)],[f22092,f16318])).
% 225.00/33.32 thf(f16318,plain,(
% 225.00/33.32 ($true = (in @ (kpair @ sK640 @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638)) @ sK637)) | ~spl1249_47),
% 225.00/33.32 inference(trivial_inequality_removal,[status(thm)],[f16317])).
% 225.00/33.32 thf(f16317,plain,(
% 225.00/33.32 ($true = (in @ (kpair @ sK640 @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638)) @ sK637)) | ($true != $true) | ~spl1249_47),
% 225.00/33.32 inference(forward_demodulation,[status(thm)],[f16316,f3896])).
% 225.00/33.32 thf(f3896,plain,(
% 225.00/33.32 ($true = (in @ sK641 @ sK638))),
% 225.00/33.32 inference(cnf_transformation,[status(thm)],[f2293])).
% 225.00/33.32 thf(f2293,plain,(
% 225.00/33.32 (binintersectT_lem = $true) & (foundationAx = $true) & (powersetTE1 = $true) & (notinsingleton = $true) & (setminusLsub = $true) & (setunionE = $true) & (complementTnotintersectT = $true) & (exuEu = $true) & (powersetTI1 = $true) & (setextT = $true) & (ap2apEq1 = $true) & (setoftrueEq = $true) & (apProp = $true) & (cartprodpairin = $true) & (subsetE2 = $true) & (exuE1 = $true) & (replAx = $true) & (singletonprop = $true) & (emptysetsubset = $true) & (binintersectLsub = $true) & (funcinfuncset = $true) & (demorgan2a2 = $true) & (ap2apEq2 = $true) & (app = $true) & (binunionEcases = $true) & (inComplementUnionImpNotIn1 = $true) & (binunionE = $true) & (singletoninpowerset = $true) & (contrasubsetT3 = $true) & (ex1E2 = $true) & (lamp = $true) & (cartprodfstpairEq = $true) & (binunionRsub = $true) & (ubforcartprodlem3 = $true) & (upairset2IR = $true) & (binintersectER = $true) & (uniqinunit = $true) & (setadjoinE = $true) & (ubforcartprodlem1 = $true) & (upairsubunion = $true) & (breln1invI = $true) & (ksndsingleton = $true) & (sepSubset = $true) & (binintersectTELcontra = $true) & (beta2 = $true) & (setunionsingleton = $true) & (dpsetconstrERa = $true) & (woz1_2 = $true) & (nonemptyI = $true) & (doubleComplementEq = $true) & (demorgan2 = $true) & (singletonsubset = $true) & (binintersectSubset2 = $true) & (inIntersectImpInIntersectUnions = $true) & (omegaSAx = $true) & (setminusI = $true) & (nonemptyE1 = $true) & (binintersectSubset1 = $true) & (subPowSU = $true) & (wellorderingAx = $true) & (kpairp = $true) & (beta1 = $true) & (emptyinunitempty = $true) & (woz13rule3 = $true) & (setukpairinjR = $true) & (symdiffE = $true) & (funcImageSingleton = $true) & (symdiffI2 = $true) & (doubleComplementE1 = $true) & (funcext = $true) & (emptysetE = $true) & (notequalI2 = $true) & (exuE3e = $true) & (upairsetE = $true) & (binintersectSubset5 = $true) & (lam2lamEq = $true) & (eta2 = $true) & (cartprodmempair = $true) & (iftrueProp1 = $true) & (symdiffIneg1 = $true) & (ifSingleton = $true) & (cartprodsndpairEq = $true) & (inIntersectImpInUnion = $true) & (woz1_5 = $true) & (setOfPairsIsBReln1 = $true) & (ap2p = $true) & (dpsetconstrI = $true) & (exuI3 = $true) & (exuI1 = $true) & ((($true = (breln1 @ sK638 @ sK639)) & ((((sK642 != $true) & ! [X6 : $i] : ((sK642 = $true) | ($true != (in @ (kpair @ sK640 @ X6) @ sK637)) | ($true != (in @ X6 @ sK638)) | ($true != (in @ (kpair @ X6 @ sK641) @ sK639)))) & ($true = (in @ sK641 @ sK638)) & ($true = (in @ (kpair @ sK640 @ sK641) @ (breln1compset @ sK638 @ sK637 @ sK639)))) & ($true = (in @ sK640 @ sK638)))) & ($true = (breln1 @ sK638 @ sK637))) & (binintersectSubset3 = $true) & (subbreln = $true) & (iftrueProp2 = $true) & (funcGraphProp2 = $true) & (subsetI1 = $true) & (funcextLem = $true) & (emptyE1 = $true) & (setukpairinjL2 = $true) & (quantDeMorgan4 = $true) & (binunionTE = $true) & (complementT_lem = $true) & (notinemptyset = $true) & (singletoninpowunion = $true) & (setext = $true) & (setadjoinOr = $true) & (omega0Ax = $true) & (setunionI = $true) & (ex1I2 = $true) & (cartprodmempaircEq = $true) & (demorgan2b = $true) & (inCongP = $true) & (woz13rule4 = $true) & (contrasubsetT1 = $true) & (subsetTI = $true) & (setadjoin__Cong = $true) & (breln1invprop = $true) & (dpsetconstrER = $true) & (setukpairinjR1 = $true) & (binintersectEL = $true) & (in__Cong = $true) & (theprop = $true) & (exu__Cong = $true) & (exuE2 = $true) & (cartprodfstin = $true) & (brelnall1 = $true) & (subsetemptysetimpeq = $true) & (complementSubsetComplementIntersect = $true) & (inPowerset = $true) & (dsetconstrEL = $true) & (lam2p = $true) & (vacuousDall = $true) & (funcext2 = $true) & (inIntersectImpInUnion2 = $true) & (demorgan2a = $true) & (binunionT_lem = $true) & (funcGraphProp1 = $true) & (emptyInPowerset = $true) & (iffalseProp2 = $true) & (complementImpComplementIntersect = $true) & (setminusSubset1 = $true) & (nonemptyI1 = $true) & (complementTE1 = $true) & (powersetsubset = $true) & (iftrueorfalse = $true) & (setOfPairsIsBReln = $true) & (woz1_1 = $true) & (prop2setI = $true) & (upairequniteq = $true) & (descrp = $true) & (setadjoinSub2 = $true) & (setextAx = $true) & (sepInPowerset = $true) & (exuI2 = $true) & (doubleComplementSub1 = $true) & (breln1SetBreln1 = $true) & (complementTcontraSubset = $true) & (woz13rule1 = $true) & (emptysetimpfalse = $true) & (subbreln1 = $true) & (dpsetconstrEL2 = $true) & (notsubsetI = $true) & (setunionE2 = $true) & (contraSubsetComplement = $true) & (disjointsetsI1 = $true) & (bs114d = $true) & (binunionLsub = $true) & (setminusIRneg = $true) & (symdiffI1 = $true) & (complementInPowersetComplementIntersect = $true) & (dsetconstrER = $true) & (upairinpowunion = $true) & (eqimpsubset1 = $true) & (setminusERneg = $true) & (setukpairinjR2 = $true) & (cartprodpairmemEL = $true) & (demorgan1 = $true) & (setunion__Cong = $true) & (setminusELneg = $true) & (setadjoinAx = $true) & (powersetE1 = $true) & (cartprodpairsurjEq = $true) & (eqinunit = $true) & (doubleComplementSub2 = $true) & (dsetconstr__Cong = $true) & (breln1compprop = $true) & (woz1_3 = $true) & (iffalseProp1 = $true) & (ifp = $true) & (setminusER = $true) & (upairsetIL = $true) & (setunionsingleton2 = $true) & (setadjoinSub = $true) & (ksndpairEq = $true) & (kpairsurjEq = $true) & (cartprodmempair1 = $true) & (inComplementUnionImpInComplement1 = $true) & (kpairiskpair = $true) & (demorgan2b2 = $true) & (upairsetIR = $true) & (omega__Cong = $true) & (subsetI2 = $true) & (kfstsingleton = $true) & (kfstpairEq = $true) & (notequalI1 = $true) & (contrasubsetT = $true) & (breln1all1 = $true) & (choice2fnsingleton = $true) & (symdiffIneg2 = $true) & (theeq = $true) & (demorgan1a = $true) & (funcGraphProp3 = $true) & (secondinupair = $true) & (setminusILneg = $true) & (lamProp = $true) & (contrasubsetT2 = $true) & (powersetI = $true) & (breln1compE = $true) & (powerset__Cong = $true) & (setukpairIL = $true) & (setextsub = $true) & (binunionIL = $true) & (descr__Cong = $true) & (setminusEL = $true) & (eqbreln = $true) & (subsetTrans = $true) & (setbeta = $true) & (complementUnionInPowersetComplement = $true) & (powersetAx = $true) & (powersetT_lem = $true) & (cartprodsndin = $true) & (notdexE = $true) & (setukpairinjL1 = $true) & (woz13rule0 = $true) & (setadjoinIL = $true) & (emptyinPowerset = $true) & (demorgan2a1 = $true) & (iffalse = $true) & (ex1I = $true) & (quantDeMorgan2 = $true) & (powersetI1 = $true) & (omegaIndAx = $true) & (upairset2E = $true) & (setukpairinjR11 = $true) & (setukpairinjR12 = $true) & (ex1E1 = $true) & (emptyset__Cong = $true) & (doubleComplementI1 = $true) & (breln1compI = $true) & (prop2setE = $true) & (setunionsingleton1 = $true) & (woz1_4 = $true) & (infuncsetfunc = $true) & (setminusT_lem = $true) & (setukpairIR = $true) & (brelnall2 = $true) & (dpsetconstrSub = $true) & (woz13rule2 = $true) & (ubforcartprodlem2 = $true) & (setukpairinjL = $true) & (binintersectSubset4 = $true) & (singletonsswitch = $true) & (setminusSubset2 = $true) & (setunionAx = $true) & (binintersectI = $true) & (powersetE = $true) & (breln1invE = $true) & (quantDeMorgan1 = $true) & (dsetconstrI = $true) & (breln1all2 = $true) & (intersectInPowersetIntersectUnions = $true) & (subset2powerset = $true) & (nonemptyImpWitness = $true) & (eqbreln1 = $true) & (complementTI1 = $true) & (cartprodpairmemER = $true) & (emptyI = $true) & (setadjoinIR = $true) & (eta1 = $true) & (quantDeMorgan3 = $true) & (binintersectRsub = $true) & (emptysetAx = $true) & (eqimpsubset2 = $true) & (binintersectTERcontra = $true) & (binunionTILcontra = $true) & (iftrue = $true) & (noeltsimpempty = $true) & (demorgan1b = $true) & (subsetE = $true) & (prop2set2propI = $true) & (binunionIR = $true) & (singletonsuniq = $true) & (dpsetconstrEL1 = $true) & (subsetRefl = $true) & (funcGraphProp4 = $true) & (binunionTEcontra = $true) & (binunionTIRcontra = $true) & (exuE3u = $true) & (notdallE = $true)),
% 225.00/33.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK637,sK638,sK639,sK640,sK641,sK642])],[f1015,f2292,f2291,f2290,f2289,f2288])).
% 225.00/33.32 thf(f2288,plain,(
% 225.00/33.32 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (breln1 @ X1 @ X2)) & ? [X3 : $i] : (? [X4 : $i] : (? [X5 : $o] : (($true != X5) & ! [X6 : $i] : (($true = X5) | ($true != (in @ (kpair @ X3 @ X6) @ X0)) | ($true != (in @ X6 @ X1)) | ($true != (in @ (kpair @ X6 @ X4) @ X2)))) & ($true = (in @ X4 @ X1)) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)))) & ($true = (in @ X3 @ X1)))) & ($true = (breln1 @ X1 @ X0))) => (? [X2 : $i] : (($true = (breln1 @ sK638 @ X2)) & ? [X3 : $i] : (? [X4 : $i] : (? [X5 : $o] : (($true != X5) & ! [X6 : $i] : (($true = X5) | ((in @ (kpair @ X3 @ X6) @ sK637) != $true) | ($true != (in @ X6 @ sK638)) | ($true != (in @ (kpair @ X6 @ X4) @ X2)))) & ($true = (in @ X4 @ sK638)) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK638 @ sK637 @ X2)))) & ((in @ X3 @ sK638) = $true))) & ($true = (breln1 @ sK638 @ sK637)))),
% 225.00/33.32 introduced(definition,[],[choice_axiom])).
% 225.00/33.32 thf(f2289,plain,(
% 225.00/33.32 ? [X2 : $i] : (($true = (breln1 @ sK638 @ X2)) & ? [X3 : $i] : (? [X4 : $i] : (? [X5 : $o] : (($true != X5) & ! [X6 : $i] : (($true = X5) | ((in @ (kpair @ X3 @ X6) @ sK637) != $true) | ($true != (in @ X6 @ sK638)) | ($true != (in @ (kpair @ X6 @ X4) @ X2)))) & ($true = (in @ X4 @ sK638)) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK638 @ sK637 @ X2)))) & ((in @ X3 @ sK638) = $true))) => (($true = (breln1 @ sK638 @ sK639)) & ? [X3 : $i] : (? [X4 : $i] : (? [X5 : $o] : (($true != X5) & ! [X6 : $i] : (($true = X5) | ((in @ (kpair @ X3 @ X6) @ sK637) != $true) | ($true != (in @ X6 @ sK638)) | ($true != (in @ (kpair @ X6 @ X4) @ sK639)))) & ($true = (in @ X4 @ sK638)) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK638 @ sK637 @ sK639)))) & ((in @ X3 @ sK638) = $true)))),
% 225.00/33.32 introduced(definition,[],[choice_axiom])).
% 225.00/33.32 thf(f2290,plain,(
% 225.00/33.32 ? [X3 : $i] : (? [X4 : $i] : (? [X5 : $o] : (($true != X5) & ! [X6 : $i] : (($true = X5) | ((in @ (kpair @ X3 @ X6) @ sK637) != $true) | ($true != (in @ X6 @ sK638)) | ($true != (in @ (kpair @ X6 @ X4) @ sK639)))) & ($true = (in @ X4 @ sK638)) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK638 @ sK637 @ sK639)))) & ((in @ X3 @ sK638) = $true)) => (? [X4 : $i] : (? [X5 : $o] : (($true != X5) & ! [X6 : $i] : (($true = X5) | ($true != (in @ (kpair @ sK640 @ X6) @ sK637)) | ($true != (in @ X6 @ sK638)) | ($true != (in @ (kpair @ X6 @ X4) @ sK639)))) & ($true = (in @ X4 @ sK638)) & ($true = (in @ (kpair @ sK640 @ X4) @ (breln1compset @ sK638 @ sK637 @ sK639)))) & ($true = (in @ sK640 @ sK638)))),
% 225.00/33.32 introduced(definition,[],[choice_axiom])).
% 225.00/33.32 thf(f2291,plain,(
% 225.00/33.32 ? [X4 : $i] : (? [X5 : $o] : (($true != X5) & ! [X6 : $i] : (($true = X5) | ($true != (in @ (kpair @ sK640 @ X6) @ sK637)) | ($true != (in @ X6 @ sK638)) | ($true != (in @ (kpair @ X6 @ X4) @ sK639)))) & ($true = (in @ X4 @ sK638)) & ($true = (in @ (kpair @ sK640 @ X4) @ (breln1compset @ sK638 @ sK637 @ sK639)))) => (? [X5 : $o] : (($true != X5) & ! [X6 : $i] : (($true = X5) | ($true != (in @ (kpair @ sK640 @ X6) @ sK637)) | ($true != (in @ X6 @ sK638)) | ($true != (in @ (kpair @ X6 @ sK641) @ sK639)))) & ($true = (in @ sK641 @ sK638)) & ($true = (in @ (kpair @ sK640 @ sK641) @ (breln1compset @ sK638 @ sK637 @ sK639))))),
% 225.00/33.32 introduced(definition,[],[choice_axiom])).
% 225.00/33.32 thf(f2292,plain,(
% 225.00/33.32 ? [X5 : $o] : (($true != X5) & ! [X6 : $i] : (($true = X5) | ($true != (in @ (kpair @ sK640 @ X6) @ sK637)) | ($true != (in @ X6 @ sK638)) | ($true != (in @ (kpair @ X6 @ sK641) @ sK639)))) => ((sK642 != $true) & ! [X6 : $i] : ((sK642 = $true) | ($true != (in @ (kpair @ sK640 @ X6) @ sK637)) | ($true != (in @ X6 @ sK638)) | ($true != (in @ (kpair @ X6 @ sK641) @ sK639))))),
% 225.00/33.32 introduced(definition,[],[choice_axiom])).
% 225.00/33.32 thf(f1015,plain,(
% 225.00/33.32 (binintersectT_lem = $true) & (foundationAx = $true) & (powersetTE1 = $true) & (notinsingleton = $true) & (setminusLsub = $true) & (setunionE = $true) & (complementTnotintersectT = $true) & (exuEu = $true) & (powersetTI1 = $true) & (setextT = $true) & (ap2apEq1 = $true) & (setoftrueEq = $true) & (apProp = $true) & (cartprodpairin = $true) & (subsetE2 = $true) & (exuE1 = $true) & (replAx = $true) & (singletonprop = $true) & (emptysetsubset = $true) & (binintersectLsub = $true) & (funcinfuncset = $true) & (demorgan2a2 = $true) & (ap2apEq2 = $true) & (app = $true) & (binunionEcases = $true) & (inComplementUnionImpNotIn1 = $true) & (binunionE = $true) & (singletoninpowerset = $true) & (contrasubsetT3 = $true) & (ex1E2 = $true) & (lamp = $true) & (cartprodfstpairEq = $true) & (binunionRsub = $true) & (ubforcartprodlem3 = $true) & (upairset2IR = $true) & (binintersectER = $true) & (uniqinunit = $true) & (setadjoinE = $true) & (ubforcartprodlem1 = $true) & (upairsubunion = $true) & (breln1invI = $true) & (ksndsingleton = $true) & (sepSubset = $true) & (binintersectTELcontra = $true) & (beta2 = $true) & (setunionsingleton = $true) & (dpsetconstrERa = $true) & (woz1_2 = $true) & (nonemptyI = $true) & (doubleComplementEq = $true) & (demorgan2 = $true) & (singletonsubset = $true) & (binintersectSubset2 = $true) & (inIntersectImpInIntersectUnions = $true) & (omegaSAx = $true) & (setminusI = $true) & (nonemptyE1 = $true) & (binintersectSubset1 = $true) & (subPowSU = $true) & (wellorderingAx = $true) & (kpairp = $true) & (beta1 = $true) & (emptyinunitempty = $true) & (woz13rule3 = $true) & (setukpairinjR = $true) & (symdiffE = $true) & (funcImageSingleton = $true) & (symdiffI2 = $true) & (doubleComplementE1 = $true) & (funcext = $true) & (emptysetE = $true) & (notequalI2 = $true) & (exuE3e = $true) & (upairsetE = $true) & (binintersectSubset5 = $true) & (lam2lamEq = $true) & (eta2 = $true) & (cartprodmempair = $true) & (iftrueProp1 = $true) & (symdiffIneg1 = $true) & (ifSingleton = $true) & (cartprodsndpairEq = $true) & (inIntersectImpInUnion = $true) & (woz1_5 = $true) & (setOfPairsIsBReln1 = $true) & (ap2p = $true) & (dpsetconstrI = $true) & (exuI3 = $true) & (exuI1 = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (breln1 @ X1 @ X2)) & ? [X3 : $i] : (? [X4 : $i] : (? [X5 : $o] : (($true != X5) & ! [X6 : $i] : (($true = X5) | ($true != (in @ (kpair @ X3 @ X6) @ X0)) | ($true != (in @ X6 @ X1)) | ($true != (in @ (kpair @ X6 @ X4) @ X2)))) & ($true = (in @ X4 @ X1)) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)))) & ($true = (in @ X3 @ X1)))) & ($true = (breln1 @ X1 @ X0))) & (binintersectSubset3 = $true) & (subbreln = $true) & (iftrueProp2 = $true) & (funcGraphProp2 = $true) & (subsetI1 = $true) & (funcextLem = $true) & (emptyE1 = $true) & (setukpairinjL2 = $true) & (quantDeMorgan4 = $true) & (binunionTE = $true) & (complementT_lem = $true) & (notinemptyset = $true) & (singletoninpowunion = $true) & (setext = $true) & (setadjoinOr = $true) & (omega0Ax = $true) & (setunionI = $true) & (ex1I2 = $true) & (cartprodmempaircEq = $true) & (demorgan2b = $true) & (inCongP = $true) & (woz13rule4 = $true) & (contrasubsetT1 = $true) & (subsetTI = $true) & (setadjoin__Cong = $true) & (breln1invprop = $true) & (dpsetconstrER = $true) & (setukpairinjR1 = $true) & (binintersectEL = $true) & (in__Cong = $true) & (theprop = $true) & (exu__Cong = $true) & (exuE2 = $true) & (cartprodfstin = $true) & (brelnall1 = $true) & (subsetemptysetimpeq = $true) & (complementSubsetComplementIntersect = $true) & (inPowerset = $true) & (dsetconstrEL = $true) & (lam2p = $true) & (vacuousDall = $true) & (funcext2 = $true) & (inIntersectImpInUnion2 = $true) & (demorgan2a = $true) & (binunionT_lem = $true) & (funcGraphProp1 = $true) & (emptyInPowerset = $true) & (iffalseProp2 = $true) & (complementImpComplementIntersect = $true) & (setminusSubset1 = $true) & (nonemptyI1 = $true) & (complementTE1 = $true) & (powersetsubset = $true) & (iftrueorfalse = $true) & (setOfPairsIsBReln = $true) & (woz1_1 = $true) & (prop2setI = $true) & (upairequniteq = $true) & (descrp = $true) & (setadjoinSub2 = $true) & (setextAx = $true) & (sepInPowerset = $true) & (exuI2 = $true) & (doubleComplementSub1 = $true) & (breln1SetBreln1 = $true) & (complementTcontraSubset = $true) & (woz13rule1 = $true) & (emptysetimpfalse = $true) & (subbreln1 = $true) & (dpsetconstrEL2 = $true) & (notsubsetI = $true) & (setunionE2 = $true) & (contraSubsetComplement = $true) & (disjointsetsI1 = $true) & (bs114d = $true) & (binunionLsub = $true) & (setminusIRneg = $true) & (symdiffI1 = $true) & (complementInPowersetComplementIntersect = $true) & (dsetconstrER = $true) & (upairinpowunion = $true) & (eqimpsubset1 = $true) & (setminusERneg = $true) & (setukpairinjR2 = $true) & (cartprodpairmemEL = $true) & (demorgan1 = $true) & (setunion__Cong = $true) & (setminusELneg = $true) & (setadjoinAx = $true) & (powersetE1 = $true) & (cartprodpairsurjEq = $true) & (eqinunit = $true) & (doubleComplementSub2 = $true) & (dsetconstr__Cong = $true) & (breln1compprop = $true) & (woz1_3 = $true) & (iffalseProp1 = $true) & (ifp = $true) & (setminusER = $true) & (upairsetIL = $true) & (setunionsingleton2 = $true) & (setadjoinSub = $true) & (ksndpairEq = $true) & (kpairsurjEq = $true) & (cartprodmempair1 = $true) & (inComplementUnionImpInComplement1 = $true) & (kpairiskpair = $true) & (demorgan2b2 = $true) & (upairsetIR = $true) & (omega__Cong = $true) & (subsetI2 = $true) & (kfstsingleton = $true) & (kfstpairEq = $true) & (notequalI1 = $true) & (contrasubsetT = $true) & (breln1all1 = $true) & (choice2fnsingleton = $true) & (symdiffIneg2 = $true) & (theeq = $true) & (demorgan1a = $true) & (funcGraphProp3 = $true) & (secondinupair = $true) & (setminusILneg = $true) & (lamProp = $true) & (contrasubsetT2 = $true) & (powersetI = $true) & (breln1compE = $true) & (powerset__Cong = $true) & (setukpairIL = $true) & (setextsub = $true) & (binunionIL = $true) & (descr__Cong = $true) & (setminusEL = $true) & (eqbreln = $true) & (subsetTrans = $true) & (setbeta = $true) & (complementUnionInPowersetComplement = $true) & (powersetAx = $true) & (powersetT_lem = $true) & (cartprodsndin = $true) & (notdexE = $true) & (setukpairinjL1 = $true) & (woz13rule0 = $true) & (setadjoinIL = $true) & (emptyinPowerset = $true) & (demorgan2a1 = $true) & (iffalse = $true) & (ex1I = $true) & (quantDeMorgan2 = $true) & (powersetI1 = $true) & (omegaIndAx = $true) & (upairset2E = $true) & (setukpairinjR11 = $true) & (setukpairinjR12 = $true) & (ex1E1 = $true) & (emptyset__Cong = $true) & (doubleComplementI1 = $true) & (breln1compI = $true) & (prop2setE = $true) & (setunionsingleton1 = $true) & (woz1_4 = $true) & (infuncsetfunc = $true) & (setminusT_lem = $true) & (setukpairIR = $true) & (brelnall2 = $true) & (dpsetconstrSub = $true) & (woz13rule2 = $true) & (ubforcartprodlem2 = $true) & (setukpairinjL = $true) & (binintersectSubset4 = $true) & (singletonsswitch = $true) & (setminusSubset2 = $true) & (setunionAx = $true) & (binintersectI = $true) & (powersetE = $true) & (breln1invE = $true) & (quantDeMorgan1 = $true) & (dsetconstrI = $true) & (breln1all2 = $true) & (intersectInPowersetIntersectUnions = $true) & (subset2powerset = $true) & (nonemptyImpWitness = $true) & (eqbreln1 = $true) & (complementTI1 = $true) & (cartprodpairmemER = $true) & (emptyI = $true) & (setadjoinIR = $true) & (eta1 = $true) & (quantDeMorgan3 = $true) & (binintersectRsub = $true) & (emptysetAx = $true) & (eqimpsubset2 = $true) & (binintersectTERcontra = $true) & (binunionTILcontra = $true) & (iftrue = $true) & (noeltsimpempty = $true) & (demorgan1b = $true) & (subsetE = $true) & (prop2set2propI = $true) & (binunionIR = $true) & (singletonsuniq = $true) & (dpsetconstrEL1 = $true) & (subsetRefl = $true) & (funcGraphProp4 = $true) & (binunionTEcontra = $true) & (binunionTIRcontra = $true) & (exuE3u = $true) & (notdallE = $true)),
% 225.00/33.32 inference(flattening,[status(thm)],[f1014])).
% 225.00/33.32 thf(f1014,plain,(
% 225.00/33.32 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : ((? [X5 : $o] : (($true != X5) & ! [X6 : $i] : (((($true = X5) | ($true != (in @ (kpair @ X6 @ X4) @ X2))) | ($true != (in @ (kpair @ X3 @ X6) @ X0))) | ($true != (in @ X6 @ X1)))) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)))) & ($true = (in @ X4 @ X1))) & ($true = (in @ X3 @ X1))) & ($true = (breln1 @ X1 @ X2))) & ($true = (breln1 @ X1 @ X0))) & (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)),
% 225.00/33.32 inference(ennf_transformation,[status(thm)],[f782])).
% 225.00/33.32 thf(f782,plain,(
% 225.00/33.32 ~((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) => ! [X0 : $i,X1 : $i] : (($true = (breln1 @ X1 @ X0)) => ! [X2 : $i] : (($true = (breln1 @ X1 @ X2)) => ! [X3 : $i] : (($true = (in @ X3 @ X1)) => ! [X4 : $i] : (($true = (in @ X4 @ X1)) => (($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2))) => ! [X5 : $o] : (! [X6 : $i] : (($true = (in @ X6 @ X1)) => (($true = (in @ (kpair @ X3 @ X6) @ X0)) => (($true = (in @ (kpair @ X6 @ X4) @ X2)) => ($true = X5)))) => ($true = X5))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 225.00/33.32 inference(fool_elimination,[status(thm)],[f781])).
% 225.00/33.32 thf(f781,plain,(
% 225.00/33.32 ~(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 => ! [X0 : $i,X1 : $i] : ((breln1 @ X1 @ X0) => ! [X2 : $i] : ((breln1 @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X1) => ! [X4 : $i] : ((in @ X4 @ X1) => ((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) => ! [X5 : $o] : (! [X6 : $i] : ((in @ X6 @ X1) => ((in @ (kpair @ X3 @ X6) @ X0) => ((in @ (kpair @ X6 @ X4) @ X2) => X5))) => X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 225.00/33.32 inference(rectify,[status(thm)],[f303])).
% 225.00/33.32 thf(f303,negated_conjecture,(
% 225.00/33.32 ~(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 => ! [X13 : $i,X3 : $i] : ((breln1 @ X3 @ X13) => ! [X15 : $i] : ((breln1 @ X3 @ X15) => ! [X1 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X3) => ((in @ (kpair @ X1 @ X2) @ (breln1compset @ X3 @ X13 @ X15)) => ! [X0 : $o] : (! [X8 : $i] : ((in @ X8 @ X3) => ((in @ (kpair @ X1 @ X8) @ X13) => ((in @ (kpair @ X8 @ X2) @ X15) => X0))) => X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 225.00/33.32 inference(negated_conjecture,[status(cth)],[f302])).
% 225.00/33.32 thf(f302,conjecture,(
% 225.00/33.32 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 => ! [X13 : $i,X3 : $i] : ((breln1 @ X3 @ X13) => ! [X15 : $i] : ((breln1 @ X3 @ X15) => ! [X1 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X3) => ((in @ (kpair @ X1 @ X2) @ (breln1compset @ X3 @ X13 @ X15)) => ! [X0 : $o] : (! [X8 : $i] : ((in @ X8 @ X3) => ((in @ (kpair @ X1 @ X8) @ X13) => ((in @ (kpair @ X8 @ X2) @ X15) => X0))) => X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 225.00/33.32 file('/export/starexec/sandbox/tmp/tmp.LcmRL7iW1w/DTF2THF_3905.p',breln1compEex)).
% 225.00/33.32 thf(f16316,plain,(
% 225.00/33.32 ($true != (in @ sK641 @ sK638)) | ($true = (in @ (kpair @ sK640 @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638)) @ sK637)) | ~spl1249_47),
% 225.00/33.32 inference(trivial_inequality_removal,[status(thm)],[f16315])).
% 225.00/33.32 thf(f16315,plain,(
% 225.00/33.32 ($true = (in @ (kpair @ sK640 @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638)) @ sK637)) | ($true != $true) | ($true != (in @ sK641 @ sK638)) | ~spl1249_47),
% 225.00/33.32 inference(forward_demodulation,[status(thm)],[f16314,f6836])).
% 225.00/33.32 thf(f6836,plain,(
% 225.00/33.32 ((subset @ sK637 @ (cartprod @ sK638 @ sK638)) = $true)),
% 225.00/33.32 inference(beta_eta_normalization,[status(thm)],[f5284])).
% 225.00/33.32 thf(f5284,plain,(
% 225.00/33.32 ($true = ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))) @ sK638 @ sK637))),
% 225.00/33.32 inference(definition_unfolding,[status(thm)],[f3893,f4484])).
% 225.00/33.32 thf(f4484,plain,(
% 225.00/33.32 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))))),
% 225.00/33.32 inference(definition_unfolding,[status(thm)],[f4444,f2971])).
% 225.00/33.32 thf(f2971,plain,(
% 225.00/33.32 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 225.00/33.32 inference(cnf_transformation,[status(thm)],[f730])).
% 225.00/33.32 thf(f730,plain,(
% 225.00/33.32 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 225.00/33.32 inference(fool_elimination,[status(thm)],[f729])).
% 225.00/33.32 thf(f729,plain,(
% 225.00/33.32 (breln = (^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))))),
% 225.00/33.32 inference(rectify,[status(thm)],[f184])).
% 225.00/33.32 thf(f184,axiom,(
% 225.00/33.32 (breln = (^[X3 : $i, X4 : $i, X5 : $i] : (subset @ X5 @ (cartprod @ X3 @ X4))))),
% 225.00/33.32 file('/export/starexec/sandbox/tmp/tmp.LcmRL7iW1w/DTF2THF_3905.p',breln)).
% 225.00/33.32 thf(f4444,plain,(
% 225.00/33.32 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 225.00/33.32 inference(cnf_transformation,[status(thm)],[f726])).
% 225.00/33.32 thf(f726,plain,(
% 225.00/33.32 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 225.00/33.32 inference(fool_elimination,[status(thm)],[f725])).
% 225.00/33.32 thf(f725,plain,(
% 225.00/33.32 ((^[X0 : $i, X1 : $i] : (breln @ X0 @ X0 @ X1)) = breln1)),
% 225.00/33.32 inference(rectify,[status(thm)],[f288])).
% 225.00/33.32 thf(f288,axiom,(
% 225.00/33.32 ((^[X3 : $i, X13 : $i] : (breln @ X3 @ X3 @ X13)) = breln1)),
% 225.00/33.32 file('/export/starexec/sandbox/tmp/tmp.LcmRL7iW1w/DTF2THF_3905.p',breln1)).
% 225.00/33.32 thf(f3893,plain,(
% 225.00/33.32 ($true = (breln1 @ sK638 @ sK637))),
% 225.00/33.32 inference(cnf_transformation,[status(thm)],[f2293])).
% 225.00/33.32 thf(f16314,plain,(
% 225.00/33.32 ((subset @ sK637 @ (cartprod @ sK638 @ sK638)) != $true) | ($true = (in @ (kpair @ sK640 @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638)) @ sK637)) | ($true != (in @ sK641 @ sK638)) | ~spl1249_47),
% 225.00/33.32 inference(trivial_inequality_removal,[status(thm)],[f16313])).
% 225.00/33.32 thf(f16313,plain,(
% 225.00/33.32 ($true = (in @ (kpair @ sK640 @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638)) @ sK637)) | ($true != (in @ sK641 @ sK638)) | ((subset @ sK637 @ (cartprod @ sK638 @ sK638)) != $true) | ($true != $true) | ~spl1249_47),
% 225.00/33.32 inference(forward_demodulation,[status(thm)],[f16312,f3894])).
% 225.00/33.32 thf(f3894,plain,(
% 225.00/33.32 ($true = (in @ sK640 @ sK638))),
% 225.00/33.32 inference(cnf_transformation,[status(thm)],[f2293])).
% 225.00/33.32 thf(f16312,plain,(
% 225.00/33.32 ($true != (in @ sK640 @ sK638)) | ((subset @ sK637 @ (cartprod @ sK638 @ sK638)) != $true) | ($true = (in @ (kpair @ sK640 @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638)) @ sK637)) | ($true != (in @ sK641 @ sK638)) | ~spl1249_47),
% 225.00/33.32 inference(trivial_inequality_removal,[status(thm)],[f16311])).
% 225.00/33.32 thf(f16311,plain,(
% 225.00/33.32 ($true = (in @ (kpair @ sK640 @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638)) @ sK637)) | ($true != $true) | ((subset @ sK637 @ (cartprod @ sK638 @ sK638)) != $true) | ($true != (in @ sK641 @ sK638)) | ($true != (in @ sK640 @ sK638)) | ~spl1249_47),
% 225.00/33.32 inference(forward_demodulation,[status(thm)],[f16307,f6327])).
% 225.00/33.32 thf(f6327,plain,(
% 225.00/33.32 ($true = (subset @ sK639 @ (cartprod @ sK638 @ sK638)))),
% 225.00/33.32 inference(beta_eta_normalization,[status(thm)],[f5283])).
% 225.00/33.32 thf(f5283,plain,(
% 225.00/33.32 ($true = ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))) @ sK638 @ sK639))),
% 225.00/33.32 inference(definition_unfolding,[status(thm)],[f3899,f4484])).
% 225.00/33.32 thf(f3899,plain,(
% 225.00/33.32 ($true = (breln1 @ sK638 @ sK639))),
% 225.00/33.32 inference(cnf_transformation,[status(thm)],[f2293])).
% 225.00/33.32 thf(f16307,plain,(
% 225.00/33.32 ($true = (in @ (kpair @ sK640 @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638)) @ sK637)) | ($true != (subset @ sK639 @ (cartprod @ sK638 @ sK638))) | ($true != (in @ sK641 @ sK638)) | ((subset @ sK637 @ (cartprod @ sK638 @ sK638)) != $true) | ($true != (in @ sK640 @ sK638)) | ~spl1249_47),
% 225.00/33.32 inference(trivial_inequality_removal,[status(thm)],[f16253])).
% 225.00/33.32 thf(f16253,plain,(
% 225.00/33.32 ($true != $true) | ($true != (subset @ sK639 @ (cartprod @ sK638 @ sK638))) | ($true != (in @ sK641 @ sK638)) | ($true != (in @ sK640 @ sK638)) | ($true = (in @ (kpair @ sK640 @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638)) @ sK637)) | ((subset @ sK637 @ (cartprod @ sK638 @ sK638)) != $true) | ~spl1249_47),
% 225.00/33.32 inference(superposition,[status(thm)],[f7387,f3895])).
% 225.00/33.32 thf(f3895,plain,(
% 225.00/33.32 ($true = (in @ (kpair @ sK640 @ sK641) @ (breln1compset @ sK638 @ sK637 @ sK639)))),
% 225.00/33.32 inference(cnf_transformation,[status(thm)],[f2293])).
% 225.00/33.32 thf(f7387,plain,(
% 225.00/33.32 ( ! [X10 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true != (in @ (kpair @ X9 @ X10) @ (breln1compset @ X6 @ X7 @ X8))) | ($true != (in @ X10 @ X6)) | ($true != (subset @ X7 @ (cartprod @ X6 @ X6))) | ($true != (subset @ X8 @ (cartprod @ X6 @ X6))) | ($true = (in @ (kpair @ X9 @ (sK317 @ X10 @ X9 @ X8 @ X7 @ X6)) @ X7)) | ($true != (in @ X9 @ X6))) ) | ~spl1249_47),
% 225.00/33.32 inference(avatar_component_clause,[status(thm)],[f7386])).
% 225.00/33.32 thf(f7386,definition,(
% 225.00/33.32 spl1249_47 <=> ! [X10 : $i,X9 : $i,X7 : $i,X6 : $i,X8 : $i] : (($true != (in @ X9 @ X6)) | ($true = (in @ (kpair @ X9 @ (sK317 @ X10 @ X9 @ X8 @ X7 @ X6)) @ X7)) | ($true != (subset @ X7 @ (cartprod @ X6 @ X6))) | ($true != (subset @ X8 @ (cartprod @ X6 @ X6))) | ($true != (in @ (kpair @ X9 @ X10) @ (breln1compset @ X6 @ X7 @ X8))) | ($true != (in @ X10 @ X6)))),
% 225.00/33.32 introduced(definition,[new_symbols(naming,[spl1249_47])],[avatar_definition])).
% 225.00/33.32 thf(f22092,plain,(
% 225.00/33.32 ((in @ (kpair @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638) @ sK641) @ sK639) = $false) | ($false = (in @ (kpair @ sK640 @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638)) @ sK637)) | (~spl1249_26 | ~spl1249_56)),
% 225.00/33.32 inference(trivial_inequality_removal,[status(thm)],[f22067])).
% 225.00/33.32 thf(f22067,plain,(
% 225.00/33.32 ($false = (in @ (kpair @ sK640 @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638)) @ sK637)) | ((in @ (kpair @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638) @ sK641) @ sK639) = $false) | ($true != $true) | (~spl1249_26 | ~spl1249_56)),
% 225.00/33.32 inference(superposition,[status(thm)],[f8493,f16343])).
% 225.00/33.32 thf(f16343,plain,(
% 225.00/33.32 ($true = (in @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638) @ sK638)) | ~spl1249_26),
% 225.00/33.32 inference(trivial_inequality_removal,[status(thm)],[f16342])).
% 225.00/33.32 thf(f16342,plain,(
% 225.00/33.32 ($true = (in @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638) @ sK638)) | ($true != $true) | ~spl1249_26),
% 225.00/33.32 inference(forward_demodulation,[status(thm)],[f16341,f3894])).
% 225.00/33.32 thf(f16341,plain,(
% 225.00/33.32 ($true != (in @ sK640 @ sK638)) | ($true = (in @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638) @ sK638)) | ~spl1249_26),
% 225.00/33.32 inference(trivial_inequality_removal,[status(thm)],[f16340])).
% 225.00/33.32 thf(f16340,plain,(
% 225.00/33.32 ($true != (in @ sK640 @ sK638)) | ($true = (in @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638) @ sK638)) | ($true != $true) | ~spl1249_26),
% 225.00/33.32 inference(forward_demodulation,[status(thm)],[f16339,f6836])).
% 225.00/33.32 thf(f16339,plain,(
% 225.00/33.32 ((subset @ sK637 @ (cartprod @ sK638 @ sK638)) != $true) | ($true != (in @ sK640 @ sK638)) | ($true = (in @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638) @ sK638)) | ~spl1249_26),
% 225.00/33.32 inference(trivial_inequality_removal,[status(thm)],[f16338])).
% 225.00/33.32 thf(f16338,plain,(
% 225.00/33.32 ($true != $true) | ($true = (in @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638) @ sK638)) | ((subset @ sK637 @ (cartprod @ sK638 @ sK638)) != $true) | ($true != (in @ sK640 @ sK638)) | ~spl1249_26),
% 225.00/33.32 inference(forward_demodulation,[status(thm)],[f16337,f6327])).
% 225.00/33.32 thf(f16337,plain,(
% 225.00/33.32 ($true != (subset @ sK639 @ (cartprod @ sK638 @ sK638))) | ((subset @ sK637 @ (cartprod @ sK638 @ sK638)) != $true) | ($true != (in @ sK640 @ sK638)) | ($true = (in @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638) @ sK638)) | ~spl1249_26),
% 225.00/33.32 inference(trivial_inequality_removal,[status(thm)],[f16336])).
% 225.00/33.32 thf(f16336,plain,(
% 225.00/33.32 ($true != $true) | ($true != (subset @ sK639 @ (cartprod @ sK638 @ sK638))) | ($true = (in @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638) @ sK638)) | ($true != (in @ sK640 @ sK638)) | ((subset @ sK637 @ (cartprod @ sK638 @ sK638)) != $true) | ~spl1249_26),
% 225.00/33.32 inference(forward_demodulation,[status(thm)],[f16277,f3896])).
% 225.00/33.32 thf(f16277,plain,(
% 225.00/33.32 ($true = (in @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638) @ sK638)) | ($true != (in @ sK641 @ sK638)) | ($true != (in @ sK640 @ sK638)) | ($true != (subset @ sK639 @ (cartprod @ sK638 @ sK638))) | ((subset @ sK637 @ (cartprod @ sK638 @ sK638)) != $true) | ~spl1249_26),
% 225.00/33.32 inference(trivial_inequality_removal,[status(thm)],[f16255])).
% 225.00/33.32 thf(f16255,plain,(
% 225.00/33.32 ((subset @ sK637 @ (cartprod @ sK638 @ sK638)) != $true) | ($true != (in @ sK640 @ sK638)) | ($true != $true) | ($true = (in @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638) @ sK638)) | ($true != (in @ sK641 @ sK638)) | ($true != (subset @ sK639 @ (cartprod @ sK638 @ sK638))) | ~spl1249_26),
% 225.00/33.32 inference(superposition,[status(thm)],[f7284,f3895])).
% 225.00/33.32 thf(f7284,plain,(
% 225.00/33.32 ( ! [X10 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true != (in @ (kpair @ X9 @ X10) @ (breln1compset @ X6 @ X7 @ X8))) | ($true != (in @ X9 @ X6)) | ($true = (in @ (sK317 @ X10 @ X9 @ X8 @ X7 @ X6) @ X6)) | ($true != (subset @ X8 @ (cartprod @ X6 @ X6))) | ($true != (subset @ X7 @ (cartprod @ X6 @ X6))) | ($true != (in @ X10 @ X6))) ) | ~spl1249_26),
% 225.00/33.32 inference(avatar_component_clause,[status(thm)],[f7283])).
% 225.00/33.32 thf(f7283,definition,(
% 225.00/33.32 spl1249_26 <=> ! [X10 : $i,X9 : $i,X7 : $i,X6 : $i,X8 : $i] : (($true != (in @ X9 @ X6)) | ($true != (subset @ X8 @ (cartprod @ X6 @ X6))) | ($true != (subset @ X7 @ (cartprod @ X6 @ X6))) | ($true = (in @ (sK317 @ X10 @ X9 @ X8 @ X7 @ X6) @ X6)) | ($true != (in @ X10 @ X6)) | ($true != (in @ (kpair @ X9 @ X10) @ (breln1compset @ X6 @ X7 @ X8))))),
% 225.00/33.32 introduced(definition,[new_symbols(naming,[spl1249_26])],[avatar_definition])).
% 225.00/33.32 thf(f8493,plain,(
% 225.00/33.32 ( ! [X6 : $i] : (($true != (in @ X6 @ sK638)) | ($false = (in @ (kpair @ sK640 @ X6) @ sK637)) | ($false = (in @ (kpair @ X6 @ sK641) @ sK639))) ) | ~spl1249_56),
% 225.00/33.32 inference(trivial_inequality_removal,[status(thm)],[f8492])).
% 225.00/33.32 thf(f8492,plain,(
% 225.00/33.32 ( ! [X6 : $i] : (($true != $true) | ($false = (in @ (kpair @ X6 @ sK641) @ sK639)) | ($true != (in @ X6 @ sK638)) | ($false = (in @ (kpair @ sK640 @ X6) @ sK637))) ) | ~spl1249_56),
% 225.00/33.32 inference(fool_paramodulation,[status(thm)],[f8484])).
% 225.00/33.32 thf(f8484,plain,(
% 225.00/33.32 ( ! [X6 : $i] : (($true != (in @ (kpair @ X6 @ sK641) @ sK639)) | ($false = (in @ (kpair @ sK640 @ X6) @ sK637)) | ($true != (in @ X6 @ sK638))) ) | ~spl1249_56),
% 225.00/33.32 inference(trivial_inequality_removal,[status(thm)],[f8483])).
% 225.00/33.32 thf(f8483,plain,(
% 225.00/33.32 ( ! [X6 : $i] : (($true != (in @ (kpair @ X6 @ sK641) @ sK639)) | ($true != (in @ X6 @ sK638)) | ($false = (in @ (kpair @ sK640 @ X6) @ sK637)) | ($true != $true)) ) | ~spl1249_56),
% 225.00/33.32 inference(fool_paramodulation,[status(thm)],[f7438])).
% 225.00/33.32 thf(f7438,plain,(
% 225.00/33.32 ( ! [X6 : $i] : (($true != (in @ (kpair @ sK640 @ X6) @ sK637)) | ($true != (in @ (kpair @ X6 @ sK641) @ sK639)) | ($true != (in @ X6 @ sK638))) ) | ~spl1249_56),
% 225.00/33.32 inference(avatar_component_clause,[status(thm)],[f7437])).
% 225.00/33.32 thf(f7437,definition,(
% 225.00/33.32 spl1249_56 <=> ! [X6 : $i] : (($true != (in @ (kpair @ sK640 @ X6) @ sK637)) | ($true != (in @ (kpair @ X6 @ sK641) @ sK639)) | ($true != (in @ X6 @ sK638)))),
% 225.00/33.32 introduced(definition,[new_symbols(naming,[spl1249_56])],[avatar_definition])).
% 225.00/33.32 thf(f16335,plain,(
% 225.00/33.32 ((in @ (kpair @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638) @ sK641) @ sK639) = $true) | ~spl1249_11),
% 225.00/33.32 inference(trivial_inequality_removal,[status(thm)],[f16334])).
% 225.00/33.32 thf(f16334,plain,(
% 225.00/33.32 ($true != $true) | ((in @ (kpair @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638) @ sK641) @ sK639) = $true) | ~spl1249_11),
% 225.00/33.32 inference(forward_demodulation,[status(thm)],[f16333,f6327])).
% 225.00/33.32 thf(f16333,plain,(
% 225.00/33.32 ((in @ (kpair @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638) @ sK641) @ sK639) = $true) | ($true != (subset @ sK639 @ (cartprod @ sK638 @ sK638))) | ~spl1249_11),
% 225.00/33.32 inference(trivial_inequality_removal,[status(thm)],[f16332])).
% 225.00/33.32 thf(f16332,plain,(
% 225.00/33.32 ($true != (subset @ sK639 @ (cartprod @ sK638 @ sK638))) | ((in @ (kpair @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638) @ sK641) @ sK639) = $true) | ($true != $true) | ~spl1249_11),
% 225.00/33.32 inference(forward_demodulation,[status(thm)],[f16331,f3894])).
% 225.00/33.32 thf(f16331,plain,(
% 225.00/33.32 ((in @ (kpair @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638) @ sK641) @ sK639) = $true) | ($true != (in @ sK640 @ sK638)) | ($true != (subset @ sK639 @ (cartprod @ sK638 @ sK638))) | ~spl1249_11),
% 225.00/33.32 inference(trivial_inequality_removal,[status(thm)],[f16330])).
% 225.00/33.32 thf(f16330,plain,(
% 225.00/33.32 ($true != $true) | ((in @ (kpair @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638) @ sK641) @ sK639) = $true) | ($true != (subset @ sK639 @ (cartprod @ sK638 @ sK638))) | ($true != (in @ sK640 @ sK638)) | ~spl1249_11),
% 225.00/33.32 inference(forward_demodulation,[status(thm)],[f16329,f6836])).
% 225.00/33.32 thf(f16329,plain,(
% 225.00/33.32 ((subset @ sK637 @ (cartprod @ sK638 @ sK638)) != $true) | ($true != (in @ sK640 @ sK638)) | ($true != (subset @ sK639 @ (cartprod @ sK638 @ sK638))) | ((in @ (kpair @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638) @ sK641) @ sK639) = $true) | ~spl1249_11),
% 225.00/33.32 inference(trivial_inequality_removal,[status(thm)],[f16328])).
% 225.00/33.32 thf(f16328,plain,(
% 225.00/33.32 ($true != (in @ sK640 @ sK638)) | ($true != $true) | ((in @ (kpair @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638) @ sK641) @ sK639) = $true) | ($true != (subset @ sK639 @ (cartprod @ sK638 @ sK638))) | ((subset @ sK637 @ (cartprod @ sK638 @ sK638)) != $true) | ~spl1249_11),
% 225.00/33.32 inference(forward_demodulation,[status(thm)],[f16287,f3896])).
% 225.00/33.32 thf(f16287,plain,(
% 225.00/33.32 ((in @ (kpair @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638) @ sK641) @ sK639) = $true) | ($true != (in @ sK641 @ sK638)) | ((subset @ sK637 @ (cartprod @ sK638 @ sK638)) != $true) | ($true != (in @ sK640 @ sK638)) | ($true != (subset @ sK639 @ (cartprod @ sK638 @ sK638))) | ~spl1249_11),
% 225.00/33.32 inference(trivial_inequality_removal,[status(thm)],[f16254])).
% 225.00/33.32 thf(f16254,plain,(
% 225.00/33.32 ($true != (subset @ sK639 @ (cartprod @ sK638 @ sK638))) | ((in @ (kpair @ (sK317 @ sK641 @ sK640 @ sK639 @ sK637 @ sK638) @ sK641) @ sK639) = $true) | ((subset @ sK637 @ (cartprod @ sK638 @ sK638)) != $true) | ($true != (in @ sK640 @ sK638)) | ($true != $true) | ($true != (in @ sK641 @ sK638)) | ~spl1249_11),
% 225.00/33.32 inference(superposition,[status(thm)],[f7218,f3895])).
% 225.00/33.32 thf(f7218,plain,(
% 225.00/33.32 ( ! [X10 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true != (in @ (kpair @ X9 @ X10) @ (breln1compset @ X6 @ X7 @ X8))) | ($true != (subset @ X8 @ (cartprod @ X6 @ X6))) | ($true != (subset @ X7 @ (cartprod @ X6 @ X6))) | ($true = (in @ (kpair @ (sK317 @ X10 @ X9 @ X8 @ X7 @ X6) @ X10) @ X8)) | ($true != (in @ X10 @ X6)) | ($true != (in @ X9 @ X6))) ) | ~spl1249_11),
% 225.00/33.32 inference(avatar_component_clause,[status(thm)],[f7217])).
% 225.00/33.32 thf(f7217,definition,(
% 225.00/33.32 spl1249_11 <=> ! [X10 : $i,X9 : $i,X7 : $i,X6 : $i,X8 : $i] : (($true != (subset @ X7 @ (cartprod @ X6 @ X6))) | ($true != (in @ (kpair @ X9 @ X10) @ (breln1compset @ X6 @ X7 @ X8))) | ($true != (in @ X10 @ X6)) | ($true != (subset @ X8 @ (cartprod @ X6 @ X6))) | ($true = (in @ (kpair @ (sK317 @ X10 @ X9 @ X8 @ X7 @ X6) @ X10) @ X8)) | ($true != (in @ X9 @ X6)))),
% 225.00/33.32 introduced(definition,[new_symbols(naming,[spl1249_11])],[avatar_definition])).
% 225.00/33.32 thf(f8392,plain,(
% 225.00/33.32 ~spl1249_57),
% 225.00/33.32 inference(avatar_contradiction_clause,[status(thm)],[f8391])).
% 225.00/33.32 thf(f8391,plain,(
% 225.00/33.32 $false | ~spl1249_57),
% 225.00/33.32 inference(trivial_inequality_removal,[status(thm)],[f8390])).
% 225.00/33.32 thf(f8390,plain,(
% 225.00/33.32 ($true = $false) | ~spl1249_57),
% 225.00/33.32 inference(forward_demodulation,[status(thm)],[f7442,f7559])).
% 225.00/33.32 thf(f7559,plain,(
% 225.00/33.32 (sK642 = $false)),
% 225.00/33.32 inference(trivial_inequality_removal,[status(thm)],[f7558])).
% 225.00/33.32 thf(f7558,plain,(
% 225.00/33.32 (sK642 = $false) | ($true != $true)),
% 225.00/33.32 inference(fool_paramodulation,[status(thm)],[f3898])).
% 225.00/33.32 thf(f3898,plain,(
% 225.00/33.32 (sK642 != $true)),
% 225.00/33.32 inference(cnf_transformation,[status(thm)],[f2293])).
% 225.00/33.32 thf(f7442,plain,(
% 225.00/33.32 (sK642 = $true) | ~spl1249_57),
% 225.00/33.32 inference(avatar_component_clause,[status(thm)],[f7440])).
% 225.00/33.32 thf(f7440,definition,(
% 225.00/33.32 spl1249_57 <=> (sK642 = $true)),
% 225.00/33.32 introduced(definition,[new_symbols(naming,[spl1249_57])],[avatar_definition])).
% 225.00/33.32 thf(f7517,plain,(
% 225.00/33.32 spl1249_10),
% 225.00/33.32 inference(avatar_split_clause,[status(thm)],[f6333,f7213])).
% 225.00/33.32 thf(f7213,definition,(
% 225.00/33.32 spl1249_10 <=> ($true = sP3)),
% 225.00/33.32 introduced(definition,[new_symbols(naming,[spl1249_10])],[avatar_definition])).
% 225.00/33.32 thf(f6333,plain,(
% 225.00/33.32 ($true = sP3)),
% 225.00/33.32 inference(trivial_inequality_removal,[status(thm)],[f4860])).
% 225.00/33.32 thf(f4860,plain,(
% 225.00/33.32 ($true = sP3) | ($true != $true)),
% 225.00/33.32 inference(definition_unfolding,[status(thm)],[f3244,f3766])).
% 225.00/33.32 thf(f3766,plain,(
% 225.00/33.32 (breln1compE = $true)),
% 225.00/33.32 inference(cnf_transformation,[status(thm)],[f2293])).
% 225.00/33.32 thf(f3244,plain,(
% 225.00/33.32 ($true = sP3) | (breln1compE != $true)),
% 225.00/33.32 inference(cnf_transformation,[status(thm)],[f1813])).
% 225.00/33.32 thf(f1813,plain,(
% 225.00/33.32 (($true = sP3) | (breln1compE != $true)) & ((breln1compE = $true) | ($true != sP3))),
% 225.00/33.32 inference(nnf_transformation,[status(thm)],[f1326])).
% 225.00/33.32 thf(f1326,plain,(
% 225.00/33.32 ($true = sP3) <=> (breln1compE = $true)),
% 225.00/33.32 inference(definition_folding,[status(thm)],[f966,f1325])).
% 225.00/33.32 thf(f1325,plain,(
% 225.00/33.32 ($true = sP3) <=> ! [X0 : $i,X1 : $i] : (($true != (breln1 @ X0 @ X1)) | ! [X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : (? [X5 : $i] : (((in @ (kpair @ X3 @ X5) @ X1) = $true) & ($true = (in @ X5 @ X0)) & ($true = (in @ (kpair @ X5 @ X4) @ X2))) | ($true != (in @ X4 @ X0)) | ($true != (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2)))) | ($true != (in @ X3 @ X0))) | ($true != (breln1 @ X0 @ X2))))),
% 225.00/33.32 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 225.00/33.32 thf(f966,plain,(
% 225.00/33.32 ! [X0 : $i,X1 : $i] : (($true != (breln1 @ X0 @ X1)) | ! [X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : (? [X5 : $i] : (((in @ (kpair @ X3 @ X5) @ X1) = $true) & ($true = (in @ X5 @ X0)) & ($true = (in @ (kpair @ X5 @ X4) @ X2))) | ($true != (in @ X4 @ X0)) | ($true != (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2)))) | ($true != (in @ X3 @ X0))) | ($true != (breln1 @ X0 @ X2)))) <=> (breln1compE = $true)),
% 225.00/33.32 inference(flattening,[status(thm)],[f965])).
% 225.00/33.32 thf(f965,plain,(
% 225.00/33.32 (breln1compE = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : ((? [X5 : $i] : (((in @ (kpair @ X3 @ X5) @ X1) = $true) & ($true = (in @ X5 @ X0)) & ($true = (in @ (kpair @ X5 @ X4) @ X2))) | ($true != (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2)))) | ($true != (in @ X4 @ X0))) | ($true != (in @ X3 @ X0))) | ($true != (breln1 @ X0 @ X2))) | ($true != (breln1 @ X0 @ X1)))),
% 225.00/33.32 inference(ennf_transformation,[status(thm)],[f760])).
% 225.00/33.32 thf(f760,plain,(
% 225.00/33.32 (breln1compE = $true) <=> ! [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) => ! [X2 : $i] : (($true = (breln1 @ X0 @ X2)) => ! [X3 : $i] : (($true = (in @ X3 @ X0)) => ! [X4 : $i] : (($true = (in @ X4 @ X0)) => (($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2))) => ? [X5 : $i] : (((in @ (kpair @ X3 @ X5) @ X1) = $true) & ($true = (in @ X5 @ X0)) & ($true = (in @ (kpair @ X5 @ X4) @ X2))))))))),
% 225.00/33.32 inference(fool_elimination,[status(thm)],[f759])).
% 225.00/33.32 thf(f759,plain,(
% 225.00/33.32 (breln1compE = ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2)) => ? [X5 : $i] : ((in @ X5 @ X0) & (in @ (kpair @ X5 @ X4) @ X2) & (in @ (kpair @ X3 @ X5) @ X1))))))))),
% 225.00/33.32 inference(rectify,[status(thm)],[f301])).
% 225.00/33.32 thf(f301,axiom,(
% 225.00/33.32 (breln1compE = ! [X3 : $i,X13 : $i] : ((breln1 @ X3 @ X13) => ! [X15 : $i] : ((breln1 @ X3 @ X15) => ! [X1 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X3) => ((in @ (kpair @ X1 @ X2) @ (breln1compset @ X3 @ X13 @ X15)) => ? [X8 : $i] : ((in @ X8 @ X3) & (in @ (kpair @ X8 @ X2) @ X15) & (in @ (kpair @ X1 @ X8) @ X13))))))))),
% 225.00/33.32 file('/export/starexec/sandbox/tmp/tmp.LcmRL7iW1w/DTF2THF_3905.p',breln1compE)).
% 225.00/33.32 thf(f7443,plain,(
% 225.00/33.32 spl1249_56 | spl1249_57),
% 225.00/33.32 inference(avatar_split_clause,[status(thm)],[f3897,f7440,f7437])).
% 225.00/33.32 thf(f3897,plain,(
% 225.00/33.32 ( ! [X6 : $i] : (($true != (in @ (kpair @ sK640 @ X6) @ sK637)) | ($true != (in @ X6 @ sK638)) | ($true != (in @ (kpair @ X6 @ sK641) @ sK639)) | (sK642 = $true)) )),
% 225.00/33.32 inference(cnf_transformation,[status(thm)],[f2293])).
% 225.00/33.32 thf(f7388,plain,(
% 225.00/33.32 spl1249_47 | ~spl1249_10),
% 225.00/33.32 inference(avatar_split_clause,[status(thm)],[f6668,f7213,f7386])).
% 225.00/33.32 thf(f6668,plain,(
% 225.00/33.32 ( ! [X10 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true != (in @ X9 @ X6)) | ($true != (in @ X10 @ X6)) | ($true != sP3) | ($true != (in @ (kpair @ X9 @ X10) @ (breln1compset @ X6 @ X7 @ X8))) | ($true != (subset @ X8 @ (cartprod @ X6 @ X6))) | ($true != (subset @ X7 @ (cartprod @ X6 @ X6))) | ($true = (in @ (kpair @ X9 @ (sK317 @ X10 @ X9 @ X8 @ X7 @ X6)) @ X7))) )),
% 225.00/33.32 inference(beta_eta_normalization,[status(thm)],[f4857])).
% 225.00/33.32 thf(f4857,plain,(
% 225.00/33.32 ( ! [X10 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true = (in @ (kpair @ X9 @ (sK317 @ X10 @ X9 @ X8 @ X7 @ X6)) @ X7)) | ($true != (in @ X10 @ X6)) | ($true != (in @ (kpair @ X9 @ X10) @ (breln1compset @ X6 @ X7 @ X8))) | ($true != (in @ X9 @ X6)) | ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))) @ X6 @ X7)) | ($true != sP3) | ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))) @ X6 @ X8))) )),
% 225.00/33.32 inference(definition_unfolding,[status(thm)],[f3236,f4484,f4484])).
% 225.00/33.32 thf(f3236,plain,(
% 225.00/33.32 ( ! [X10 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true != (breln1 @ X6 @ X7)) | ($true = (in @ (kpair @ X9 @ (sK317 @ X10 @ X9 @ X8 @ X7 @ X6)) @ X7)) | ($true != (in @ X10 @ X6)) | ($true != (in @ (kpair @ X9 @ X10) @ (breln1compset @ X6 @ X7 @ X8))) | ($true != (in @ X9 @ X6)) | ((breln1 @ X6 @ X8) != $true) | ($true != sP3)) )),
% 225.00/33.32 inference(cnf_transformation,[status(thm)],[f1812])).
% 225.00/33.32 thf(f1812,plain,(
% 225.00/33.32 (($true = sP3) | (($true = (breln1 @ sK312 @ sK313)) & (((! [X5 : $i] : (($true != (in @ (kpair @ sK315 @ X5) @ sK313)) | ($true != (in @ X5 @ sK312)) | ($true != (in @ (kpair @ X5 @ sK316) @ sK314))) & ($true = (in @ sK316 @ sK312)) & ((in @ (kpair @ sK315 @ sK316) @ (breln1compset @ sK312 @ sK313 @ sK314)) = $true)) & ($true = (in @ sK315 @ sK312))) & ($true = (breln1 @ sK312 @ sK314))))) & (! [X6 : $i,X7 : $i] : (($true != (breln1 @ X6 @ X7)) | ! [X8 : $i] : (! [X9 : $i] : (! [X10 : $i] : ((($true = (in @ (kpair @ X9 @ (sK317 @ X10 @ X9 @ X8 @ X7 @ X6)) @ X7)) & ($true = (in @ (sK317 @ X10 @ X9 @ X8 @ X7 @ X6) @ X6)) & ($true = (in @ (kpair @ (sK317 @ X10 @ X9 @ X8 @ X7 @ X6) @ X10) @ X8))) | ($true != (in @ X10 @ X6)) | ($true != (in @ (kpair @ X9 @ X10) @ (breln1compset @ X6 @ X7 @ X8)))) | ($true != (in @ X9 @ X6))) | ((breln1 @ X6 @ X8) != $true))) | ($true != sP3))),
% 225.00/33.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK312,sK313,sK314,sK315,sK316,sK317])],[f1806,f1811,f1810,f1809,f1808,f1807])).
% 225.00/33.32 thf(f1807,plain,(
% 225.00/33.32 ? [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) & ? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (! [X5 : $i] : (((in @ (kpair @ X3 @ X5) @ X1) != $true) | ($true != (in @ X5 @ X0)) | ($true != (in @ (kpair @ X5 @ X4) @ X2))) & ($true = (in @ X4 @ X0)) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2)))) & ($true = (in @ X3 @ X0))) & ($true = (breln1 @ X0 @ X2)))) => (($true = (breln1 @ sK312 @ sK313)) & ? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (! [X5 : $i] : (((in @ (kpair @ X3 @ X5) @ sK313) != $true) | ($true != (in @ X5 @ sK312)) | ($true != (in @ (kpair @ X5 @ X4) @ X2))) & ($true = (in @ X4 @ sK312)) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK312 @ sK313 @ X2)))) & ($true = (in @ X3 @ sK312))) & ($true = (breln1 @ sK312 @ X2))))),
% 225.00/33.32 introduced(definition,[],[choice_axiom])).
% 225.00/33.32 thf(f1808,plain,(
% 225.00/33.32 ? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (! [X5 : $i] : (((in @ (kpair @ X3 @ X5) @ sK313) != $true) | ($true != (in @ X5 @ sK312)) | ($true != (in @ (kpair @ X5 @ X4) @ X2))) & ($true = (in @ X4 @ sK312)) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK312 @ sK313 @ X2)))) & ($true = (in @ X3 @ sK312))) & ($true = (breln1 @ sK312 @ X2))) => (? [X3 : $i] : (? [X4 : $i] : (! [X5 : $i] : (((in @ (kpair @ X3 @ X5) @ sK313) != $true) | ($true != (in @ X5 @ sK312)) | ($true != (in @ (kpair @ X5 @ X4) @ sK314))) & ($true = (in @ X4 @ sK312)) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK312 @ sK313 @ sK314)))) & ($true = (in @ X3 @ sK312))) & ($true = (breln1 @ sK312 @ sK314)))),
% 225.00/33.32 introduced(definition,[],[choice_axiom])).
% 225.00/33.32 thf(f1809,plain,(
% 225.00/33.32 ? [X3 : $i] : (? [X4 : $i] : (! [X5 : $i] : (((in @ (kpair @ X3 @ X5) @ sK313) != $true) | ($true != (in @ X5 @ sK312)) | ($true != (in @ (kpair @ X5 @ X4) @ sK314))) & ($true = (in @ X4 @ sK312)) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK312 @ sK313 @ sK314)))) & ($true = (in @ X3 @ sK312))) => (? [X4 : $i] : (! [X5 : $i] : (($true != (in @ (kpair @ sK315 @ X5) @ sK313)) | ($true != (in @ X5 @ sK312)) | ($true != (in @ (kpair @ X5 @ X4) @ sK314))) & ($true = (in @ X4 @ sK312)) & ($true = (in @ (kpair @ sK315 @ X4) @ (breln1compset @ sK312 @ sK313 @ sK314)))) & ($true = (in @ sK315 @ sK312)))),
% 225.00/33.32 introduced(definition,[],[choice_axiom])).
% 225.00/33.32 thf(f1810,plain,(
% 225.00/33.32 ? [X4 : $i] : (! [X5 : $i] : (($true != (in @ (kpair @ sK315 @ X5) @ sK313)) | ($true != (in @ X5 @ sK312)) | ($true != (in @ (kpair @ X5 @ X4) @ sK314))) & ($true = (in @ X4 @ sK312)) & ($true = (in @ (kpair @ sK315 @ X4) @ (breln1compset @ sK312 @ sK313 @ sK314)))) => (! [X5 : $i] : (($true != (in @ (kpair @ sK315 @ X5) @ sK313)) | ($true != (in @ X5 @ sK312)) | ($true != (in @ (kpair @ X5 @ sK316) @ sK314))) & ($true = (in @ sK316 @ sK312)) & ((in @ (kpair @ sK315 @ sK316) @ (breln1compset @ sK312 @ sK313 @ sK314)) = $true))),
% 225.00/33.32 introduced(definition,[],[choice_axiom])).
% 225.00/33.32 thf(f1811,plain,(
% 225.00/33.32 ! [X6 : $i,X7 : $i,X8 : $i,X9 : $i,X10 : $i] : (? [X11 : $i] : (($true = (in @ (kpair @ X9 @ X11) @ X7)) & ($true = (in @ X11 @ X6)) & ($true = (in @ (kpair @ X11 @ X10) @ X8))) => (($true = (in @ (kpair @ X9 @ (sK317 @ X10 @ X9 @ X8 @ X7 @ X6)) @ X7)) & ($true = (in @ (sK317 @ X10 @ X9 @ X8 @ X7 @ X6) @ X6)) & ($true = (in @ (kpair @ (sK317 @ X10 @ X9 @ X8 @ X7 @ X6) @ X10) @ X8))))),
% 225.00/33.32 introduced(definition,[],[choice_axiom])).
% 225.00/33.32 thf(f1806,plain,(
% 225.00/33.32 (($true = sP3) | ? [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) & ? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (! [X5 : $i] : (((in @ (kpair @ X3 @ X5) @ X1) != $true) | ($true != (in @ X5 @ X0)) | ($true != (in @ (kpair @ X5 @ X4) @ X2))) & ($true = (in @ X4 @ X0)) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2)))) & ($true = (in @ X3 @ X0))) & ($true = (breln1 @ X0 @ X2))))) & (! [X6 : $i,X7 : $i] : (($true != (breln1 @ X6 @ X7)) | ! [X8 : $i] : (! [X9 : $i] : (! [X10 : $i] : (? [X11 : $i] : (($true = (in @ (kpair @ X9 @ X11) @ X7)) & ($true = (in @ X11 @ X6)) & ($true = (in @ (kpair @ X11 @ X10) @ X8))) | ($true != (in @ X10 @ X6)) | ($true != (in @ (kpair @ X9 @ X10) @ (breln1compset @ X6 @ X7 @ X8)))) | ($true != (in @ X9 @ X6))) | ((breln1 @ X6 @ X8) != $true))) | ($true != sP3))),
% 225.00/33.32 inference(rectify,[status(thm)],[f1805])).
% 225.00/33.32 thf(f1805,plain,(
% 225.00/33.32 (($true = sP3) | ? [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) & ? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (! [X5 : $i] : (((in @ (kpair @ X3 @ X5) @ X1) != $true) | ($true != (in @ X5 @ X0)) | ($true != (in @ (kpair @ X5 @ X4) @ X2))) & ($true = (in @ X4 @ X0)) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2)))) & ($true = (in @ X3 @ X0))) & ($true = (breln1 @ X0 @ X2))))) & (! [X0 : $i,X1 : $i] : (($true != (breln1 @ X0 @ X1)) | ! [X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : (? [X5 : $i] : (((in @ (kpair @ X3 @ X5) @ X1) = $true) & ($true = (in @ X5 @ X0)) & ($true = (in @ (kpair @ X5 @ X4) @ X2))) | ($true != (in @ X4 @ X0)) | ($true != (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2)))) | ($true != (in @ X3 @ X0))) | ($true != (breln1 @ X0 @ X2)))) | ($true != sP3))),
% 225.00/33.32 inference(nnf_transformation,[status(thm)],[f1325])).
% 225.00/33.32 thf(f7285,plain,(
% 225.00/33.32 ~spl1249_10 | spl1249_26),
% 225.00/33.32 inference(avatar_split_clause,[status(thm)],[f6902,f7283,f7213])).
% 225.00/33.32 thf(f6902,plain,(
% 225.00/33.32 ( ! [X10 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true != (in @ X9 @ X6)) | ($true != (in @ (kpair @ X9 @ X10) @ (breln1compset @ X6 @ X7 @ X8))) | ($true != (in @ X10 @ X6)) | ($true = (in @ (sK317 @ X10 @ X9 @ X8 @ X7 @ X6) @ X6)) | ($true != (subset @ X7 @ (cartprod @ X6 @ X6))) | ($true != sP3) | ($true != (subset @ X8 @ (cartprod @ X6 @ X6)))) )),
% 225.00/33.32 inference(beta_eta_normalization,[status(thm)],[f4858])).
% 225.00/33.32 thf(f4858,plain,(
% 225.00/33.32 ( ! [X10 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true != (in @ X10 @ X6)) | ($true != (in @ (kpair @ X9 @ X10) @ (breln1compset @ X6 @ X7 @ X8))) | ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))) @ X6 @ X8)) | ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))) @ X6 @ X7)) | ($true = (in @ (sK317 @ X10 @ X9 @ X8 @ X7 @ X6) @ X6)) | ($true != (in @ X9 @ X6)) | ($true != sP3)) )),
% 225.00/33.32 inference(definition_unfolding,[status(thm)],[f3235,f4484,f4484])).
% 225.00/33.32 thf(f3235,plain,(
% 225.00/33.32 ( ! [X10 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true != (breln1 @ X6 @ X7)) | ($true = (in @ (sK317 @ X10 @ X9 @ X8 @ X7 @ X6) @ X6)) | ($true != (in @ X10 @ X6)) | ($true != (in @ (kpair @ X9 @ X10) @ (breln1compset @ X6 @ X7 @ X8))) | ($true != (in @ X9 @ X6)) | ((breln1 @ X6 @ X8) != $true) | ($true != sP3)) )),
% 225.00/33.32 inference(cnf_transformation,[status(thm)],[f1812])).
% 225.00/33.32 thf(f7219,plain,(
% 225.00/33.32 ~spl1249_10 | spl1249_11),
% 225.00/33.32 inference(avatar_split_clause,[status(thm)],[f7038,f7217,f7213])).
% 225.00/33.32 thf(f7038,plain,(
% 225.00/33.32 ( ! [X10 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true != (subset @ X7 @ (cartprod @ X6 @ X6))) | ($true != (in @ X9 @ X6)) | ($true != sP3) | ($true = (in @ (kpair @ (sK317 @ X10 @ X9 @ X8 @ X7 @ X6) @ X10) @ X8)) | ($true != (subset @ X8 @ (cartprod @ X6 @ X6))) | ($true != (in @ X10 @ X6)) | ($true != (in @ (kpair @ X9 @ X10) @ (breln1compset @ X6 @ X7 @ X8)))) )),
% 225.00/33.32 inference(beta_eta_normalization,[status(thm)],[f4859])).
% 225.00/33.32 thf(f4859,plain,(
% 225.00/33.32 ( ! [X10 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true != ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))) @ X6 @ X7)) | ($true != (in @ X9 @ X6)) | ($true != (in @ (kpair @ X9 @ X10) @ (breln1compset @ X6 @ X7 @ X8))) | ($true != (in @ X10 @ X6)) | ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))) @ X6 @ X8)) | ($true != sP3) | ($true = (in @ (kpair @ (sK317 @ X10 @ X9 @ X8 @ X7 @ X6) @ X10) @ X8))) )),
% 225.00/33.32 inference(definition_unfolding,[status(thm)],[f3234,f4484,f4484])).
% 225.00/33.32 thf(f3234,plain,(
% 225.00/33.32 ( ! [X10 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true != (breln1 @ X6 @ X7)) | ($true = (in @ (kpair @ (sK317 @ X10 @ X9 @ X8 @ X7 @ X6) @ X10) @ X8)) | ($true != (in @ X10 @ X6)) | ($true != (in @ (kpair @ X9 @ X10) @ (breln1compset @ X6 @ X7 @ X8))) | ($true != (in @ X9 @ X6)) | ((breln1 @ X6 @ X8) != $true) | ($true != sP3)) )),
% 225.00/33.32 inference(cnf_transformation,[status(thm)],[f1812])).
% 225.00/33.32 % SZS output end Proof for DTF2THF_3905
% 225.00/33.32 % (5729)------------------------------
% 225.00/33.32 % (5729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 225.00/33.32 % (5729)Termination reason: Refutation
% 225.00/33.32
% 225.00/33.32 % (5729)Memory used [KB]: 23666
% 225.00/33.32 % (5729)Time elapsed: 2.765 s
% 225.00/33.32 % (5729)Instructions burned: 6919 (million)
% 225.00/33.32 % (5729)------------------------------
% 225.00/33.32 % (5729)------------------------------
% 225.00/33.32 % (4228)Success in time 31.687 s
%------------------------------------------------------------------------------