%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU780^1 : 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 : n024.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 169.05s 25.17s
% Output : Refutation 169.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 5108 (1335 equ; 0 cnn)
% Maximal formula atoms : 304 ( 113 avg)
% Number of connectives : 3029 ( 64 ~; 44 |; 970 &; 730 @)
% ( 2 <=>;1212 =>; 0 <=; 0 <~>)
% Maximal formula depth : 315 ( 52 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 586 ( 582 usr; 309 con; 0-4 aty)
% ( 0 !!; 7 ??; 0 @@+; 0 @@-)
% Number of variables : 204 ( 69 ^; 87 !; 48 ?; 204 :)
% 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_364,type,
sP3: $i > ( $i > $i > $o ) > $o ).
thf(func_def_376,type,
sP15: $i > $i > $i > $i > $o ).
thf(func_def_384,type,
sP23: $i > $o > $i > $i > $o ).
thf(func_def_390,type,
sP29: $i > $i > $i > $o ).
thf(func_def_391,type,
sP30: $i > $i > $o ).
thf(func_def_392,type,
sP31: ( $i > $o ) > $i > $o ).
thf(func_def_396,type,
sP35: $i > $i > $i > $i > $o ).
thf(func_def_397,type,
sP36: $i > $i > $i > $o ).
thf(func_def_402,type,
sP41: $i > $i > ( $i > $i > $o ) > $o ).
thf(func_def_407,type,
sP46: ( $i > $o ) > $i > $o ).
thf(func_def_410,type,
sP49: $i > $i > $i > $o ).
thf(func_def_411,type,
sP50: $i > $i > $i > $o ).
thf(func_def_412,type,
sP51: $i > $i > $o ).
thf(func_def_413,type,
sP52: $i > $i > $i > $o ).
thf(func_def_414,type,
sP53: $i > $i > $o ).
thf(func_def_415,type,
sP54: $i > $o ).
thf(func_def_416,type,
sP55: $i > $i > $o ).
thf(func_def_417,type,
sP56: $i > $i > $o ).
thf(func_def_418,type,
sP57: $i > $i > $o ).
thf(func_def_432,type,
sK71: $i > $o ).
thf(func_def_434,type,
sK73: $i > ( $i > $o ) > $i ).
thf(func_def_438,type,
sK77: $i > $i > $i > $i ).
thf(func_def_439,type,
sK78: $i > $i > $i > $i ).
thf(func_def_442,type,
sK81: $i > $i ).
thf(func_def_443,type,
sK82: $i > $i ).
thf(func_def_453,type,
sK92: $i > $o ).
thf(func_def_482,type,
sK121: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_483,type,
sK122: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_484,type,
sK123: $i > ( $i > $i > $o ) > $i ).
thf(func_def_485,type,
sK124: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_486,type,
sK125: $i > $i > $o ).
thf(func_def_488,type,
sK127: $i > ( $i > $i > $o ) > $i ).
thf(func_def_493,type,
sK132: $i > $o ).
thf(func_def_494,type,
sK133: ( $i > $o ) > $i > $i > $i ).
thf(func_def_495,type,
sK134: $i > $o ).
thf(func_def_497,type,
sK136: $i > ( $i > $o ) > $i ).
thf(func_def_517,type,
sK156: $i > $i > $i ).
thf(func_def_519,type,
sK158: $i > $o ).
thf(func_def_521,type,
sK160: ( $i > $o ) > $i > $i ).
thf(func_def_534,type,
sK173: $i > $i > $o ).
thf(func_def_542,type,
sK181: $i > $o ).
thf(func_def_544,type,
sK183: ( $i > $o ) > $i > $i ).
thf(func_def_569,type,
sK208: $i > $i > $i > $i ).
thf(func_def_596,type,
sK235: $i > $i > $o ).
thf(func_def_603,type,
sK242: $i > $o ).
thf(func_def_604,type,
sK243: $i > $o ).
thf(func_def_605,type,
sK244: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_606,type,
sK245: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_625,type,
sK264: $i > $i > $o ).
thf(func_def_630,type,
sK269: $i > $o ).
thf(func_def_644,type,
sK283: $i > $i > $i > $i > $i ).
thf(func_def_664,type,
sK303: $i > $o ).
thf(func_def_666,type,
sK305: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_667,type,
sK306: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_671,type,
sK310: $i > $i ).
thf(func_def_675,type,
sK314: $i > $i > ( $i > $i ) > $i ).
thf(func_def_679,type,
sK318: $i > $i > $i ).
thf(func_def_712,type,
sK351: $i > $i > $i > $i > $i ).
thf(func_def_713,type,
sK352: $i > $i > $i > $i > $i ).
thf(func_def_714,type,
sK353: $i > $i > $i > $i > $i ).
thf(func_def_716,type,
sK355: $i > $o ).
thf(func_def_745,type,
sK384: $i > $o ).
thf(func_def_746,type,
sK385: $i > $i ).
thf(func_def_747,type,
sK386: ( $i > $o ) > $i ).
thf(func_def_788,type,
sK427: $i > $i > $i ).
thf(func_def_805,type,
sK444: $i > $i > $i > $i ).
thf(func_def_806,type,
sK445: $i > $i > $i > $i ).
thf(func_def_816,type,
sK455: $i > $i ).
thf(func_def_820,type,
sK459: $i > $o ).
thf(func_def_821,type,
sK460: ( $i > $i ) > $i > $i > $i ).
thf(func_def_824,type,
sK463: $i > $i ).
thf(func_def_826,type,
sK465: $i > $o ).
thf(func_def_828,type,
sK467: ( $i > $o ) > $i > $i ).
thf(func_def_831,type,
sK470: $i > $o ).
thf(func_def_832,type,
sK471: ( $i > $o ) > $i ).
thf(func_def_836,type,
sK475: $i > $o ).
thf(func_def_838,type,
sK477: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_839,type,
sK478: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_842,type,
sK481: $i > $o ).
thf(func_def_844,type,
sK483: ( $i > $o ) > $i > $i > $i ).
thf(func_def_845,type,
sK484: ( $i > $o ) > $i > $i > $i ).
thf(func_def_880,type,
sK519: $i > $i > $i ).
thf(func_def_886,type,
sK525: $i > $i > $i ).
thf(func_def_904,type,
sK543: $i > $o ).
thf(func_def_939,type,
sK578: $i > $i > $i ).
thf(func_def_940,type,
sK579: $i > $i > $i ).
thf(func_def_947,type,
sK586: $i > $o ).
thf(func_def_952,type,
sK591: $i > $i > $i ).
thf(func_def_962,type,
sK601: $i > $o ).
thf(func_def_967,type,
sK606: $i > $i ).
thf(func_def_969,type,
sK608: $i > $o ).
thf(func_def_971,type,
sK610: ( $i > $o ) > $i > $i ).
thf(func_def_972,type,
sK611: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_973,type,
sK612: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_974,type,
sK613: $i > $o ).
thf(func_def_975,type,
sK614: $i > $o ).
thf(func_def_989,type,
sK628: $i > $i ).
thf(func_def_998,type,
sK637: $i > $o ).
thf(func_def_1001,type,
sK640: $i > ( $i > $o ) > $i ).
thf(func_def_1009,type,
sK648: $i > $i > $i ).
thf(func_def_1010,type,
sK649: $i > $i > $i > $i ).
thf(func_def_1011,type,
sK650: $i > $i > $i > $i ).
thf(func_def_1012,type,
sK651: $i > $i > $i > $i ).
thf(func_def_1013,type,
sK652: $i > $i > $i > $i ).
thf(func_def_1017,type,
sK656: $i > $o ).
thf(func_def_1018,type,
sK657: ( $i > $o ) > $i > $i ).
thf(func_def_1024,type,
sK663: $i > $i ).
thf(func_def_1051,type,
sK690: $i > $i > $o ).
thf(func_def_1053,type,
sK692: ( $i > $o ) > $i > $i ).
thf(func_def_1054,type,
sK693: ( $i > $o ) > $i > $i ).
thf(func_def_1055,type,
sK694: $i > $o ).
thf(func_def_1059,type,
sK698: $i > $o ).
thf(func_def_1076,type,
sK715: $i > $o ).
thf(func_def_1077,type,
sK716: $i > $o ).
thf(func_def_1078,type,
sK717: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1079,type,
sK718: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1084,type,
sK723: $i > $o ).
thf(func_def_1085,type,
sK724: $i > $o ).
thf(func_def_1093,type,
sK732: $i > $i > $o ).
thf(func_def_1094,type,
sK733: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1095,type,
sK734: $i > $i ).
thf(func_def_1098,type,
sK737: $i > $i ).
thf(func_def_1111,type,
sK750: $i > $o ).
thf(func_def_1112,type,
sK751: $i > $i ).
thf(func_def_1113,type,
sK752: ( $i > $o ) > $i ).
thf(func_def_1114,type,
sK753: $i > $o ).
thf(func_def_1117,type,
sK756: $i > ( $i > $o ) > $i ).
thf(func_def_1120,type,
sK759: $i > $i > $i > $i ).
thf(func_def_1121,type,
sK760: $i > $i > $i > $i > $i ).
thf(func_def_1122,type,
sK761: $i > $i > $i > $i > $i ).
thf(func_def_1123,type,
sK762: $i > $i > $i > $i > $i ).
thf(func_def_1124,type,
sK763: $i > $i > $i > $i > $i ).
thf(func_def_1161,type,
sK800: $i > $i > $i ).
thf(func_def_1162,type,
sK801: $i > $i > $i ).
thf(func_def_1163,type,
sK802: $i > $o ).
thf(func_def_1165,type,
sK804: ( $i > $o ) > $i ).
thf(func_def_1166,type,
sK805: ( $i > $o ) > $i ).
thf(func_def_1171,type,
sK810: $i > $i > $i > $i > $i ).
thf(func_def_1172,type,
sK811: $i > $i > $i > $i > $i ).
thf(func_def_1178,type,
sK817: $i > $o ).
thf(func_def_1180,type,
sK819: ( $i > $o ) > $i > $i > $i ).
thf(func_def_1181,type,
sK820: ( $i > $o ) > $i > $i > $i ).
thf(func_def_1182,type,
sK821: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1183,type,
sK822: $i > $i ).
thf(func_def_1190,type,
sK829: $i > $i > $o ).
thf(func_def_1192,type,
sK831: $i > $i ).
thf(func_def_1193,type,
sK832: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_1194,type,
sK833: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_1195,type,
sK834: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_1219,type,
sK858: $i > $i > $o ).
thf(func_def_1225,type,
sK864: $i > $i ).
thf(func_def_1227,type,
sK866: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1229,type,
sK868: $i > $i > $o ).
thf(func_def_1242,type,
sK881: $i > $i ).
thf(func_def_1244,type,
sK883: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1252,type,
sK891: $i > $i > $i > $i ).
thf(func_def_1256,type,
sK895: ( $i > $o ) > $i > $i ).
thf(func_def_1257,type,
sK896: ( $i > $o ) > $i > $i ).
thf(func_def_1258,type,
sK897: $i > $o ).
thf(func_def_1286,type,
sK925: $i > $o ).
thf(func_def_1297,type,
sK936: $i > $i > $i > $i > $i ).
thf(func_def_1327,type,
sK966: $i > $i > $o ).
thf(func_def_1331,type,
sK970: $i > $o ).
thf(func_def_1332,type,
sK971: $i > $o ).
thf(func_def_1340,type,
sK979: $o > $i > $i > $i ).
thf(func_def_1356,type,
sK995: $i > $i > $i > $i ).
thf(func_def_1357,type,
sK996: $i > $i > $i > $o ).
thf(func_def_1361,type,
sK1000: $i > $i > $i ).
thf(func_def_1362,type,
sK1001: $i > $i > $i > $i ).
thf(func_def_1363,type,
sK1002: $i > $i > $i > $i ).
thf(func_def_1368,type,
sK1007: $i > $i > $i ).
thf(func_def_1369,type,
sK1008: $i > $i > $i ).
thf(func_def_1370,type,
sK1009: $i > $i > $i ).
thf(func_def_1371,type,
sK1010: $i > $i > $i ).
thf(func_def_1372,type,
sK1011: $i > $i > $i ).
thf(func_def_1373,type,
sK1012: $i > $i > $i ).
thf(func_def_1374,type,
sK1013: $i > $i > $i ).
thf(func_def_1375,type,
sK1014: $i > $i > $i > $i ).
thf(func_def_1376,type,
sK1015: $i > $i ).
thf(func_def_1377,type,
sK1016: $i > $i ).
thf(func_def_1378,type,
sK1017: $i > $i ).
thf(func_def_1379,type,
sK1018: $i > $i ).
thf(func_def_1380,type,
sK1019: $i > $i > $i ).
thf(func_def_1381,type,
sK1020: $i > $i > $i ).
thf(func_def_1382,type,
sK1021: $i > $i > $i ).
thf(func_def_1383,type,
sK1022: $i > $i > $i > $i ).
thf(func_def_1384,type,
sK1023: $i > $i > $i > $i ).
thf(func_def_1386,type,
sK1025: $i > $i ).
thf(func_def_1388,type,
sK1027: ( $i > $o ) > $i ).
thf(func_def_1389,type,
sK1028: ( $i > $o ) > $i > $i ).
thf(func_def_1391,type,
sK1030: ( $i > $o ) > $i ).
thf(func_def_1392,type,
sK1031: ( $i > $o ) > $i > $i ).
thf(func_def_1393,type,
sK1032: ( $i > $o ) > $i ).
thf(func_def_1394,type,
sK1033: ( $i > $o ) > $i ).
thf(func_def_1395,type,
sK1034: ( $i > $o ) > $i > $i ).
thf(func_def_1396,type,
sK1035: ( $i > $o ) > $i > $i ).
thf(func_def_1397,type,
sK1036: ( $i > $o ) > $i ).
thf(func_def_1398,type,
sK1037: ( $i > $o ) > $i > $i ).
thf(func_def_1399,type,
sK1038: ( $i > $o ) > $i > $i ).
thf(func_def_1400,type,
sK1039: ( $i > $o ) > $i ).
thf(func_def_1401,type,
sK1040: ( $i > $o ) > $i > $i ).
thf(func_def_1402,type,
sK1041: ( $i > $o ) > $i ).
thf(func_def_1404,type,
sK1043: ( $i > $o ) > $i > $i ).
thf(func_def_1405,type,
sK1044: $i > $i ).
thf(func_def_1407,type,
sK1046: ( $i > $o ) > $i > $i ).
thf(func_def_1408,type,
sK1047: $i > ( $i > $o ) > $i ).
thf(func_def_1409,type,
sK1048: $i > ( $i > $o ) > $i ).
thf(func_def_1410,type,
sK1049: $i > ( $i > $o ) > $i ).
thf(func_def_1411,type,
sK1050: $i > ( $i > $o ) > $i ).
thf(func_def_1412,type,
sK1051: $i > ( $i > $o ) > $i ).
thf(func_def_1413,type,
sK1052: ( $i > $o ) > $i > $i ).
thf(func_def_1414,type,
sK1053: ( $i > $o ) > $i > $i ).
thf(func_def_1416,type,
sK1055: ( $i > $o ) > $i ).
thf(func_def_1417,type,
sK1056: ( $i > $o ) > $i > $i ).
thf(func_def_1418,type,
sK1057: $i > ( $i > $o ) > $i ).
thf(func_def_1419,type,
sK1058: ( $i > $o ) > $i > $i ).
thf(func_def_1420,type,
sK1059: ( $i > $o ) > $i > $i ).
thf(func_def_1421,type,
sK1060: ( $i > $o ) > $i ).
thf(func_def_1422,type,
sK1061: $i > $i ).
thf(func_def_1423,type,
sK1062: $i > ( $i > $o ) > $i ).
thf(func_def_1424,type,
sK1063: ( $i > $o ) > $i ).
thf(func_def_1425,type,
sK1064: $i > $i ).
thf(func_def_1426,type,
sK1065: ( $i > $o ) > $i ).
thf(func_def_1427,type,
sK1066: ( $i > $o ) > $i > $i ).
thf(func_def_1428,type,
sK1067: ( $i > $o ) > $i > $i ).
thf(func_def_1429,type,
sK1068: ( $i > $o ) > $i > $i ).
thf(func_def_1430,type,
sK1069: ( $i > $o ) > $i ).
thf(func_def_1431,type,
sK1070: ( $i > $o ) > $i ).
thf(func_def_1432,type,
sK1071: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_1433,type,
ph1072:
!>[X0: $tType] : X0 ).
thf(f17672,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f17671,f15292]) ).
thf(f15292,plain,
( $true
= ( in @ sK1073 @ sK338 ) ),
inference(binary_proxy_clausification,[status(thm)],[f15290]) ).
thf(f15290,plain,
( ( ( in @ sK1073 @ sK338 )
& ( in @ ( kpair @ sK340 @ sK1073 ) @ sK337 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f15288]) ).
thf(f15288,plain,
( ( ( in @ sK1073 @ sK338 )
& ( in @ ( kpair @ sK340 @ sK1073 ) @ sK337 )
& ( in @ ( kpair @ sK1073 @ sK341 ) @ sK339 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f15287]) ).
thf(f15287,plain,
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK338 )
& ( in @ ( kpair @ sK340 @ Y0 ) @ sK337 )
& ( in @ ( kpair @ Y0 @ sK341 ) @ sK339 ) )
@ sK1073 )
= $true ),
inference(sigma_clausification,[status(thm)],[f15286]) ).
thf(f15286,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK338 )
& ( in @ ( kpair @ sK340 @ Y0 ) @ sK337 )
& ( in @ ( kpair @ Y0 @ sK341 ) @ sK339 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f15285]) ).
thf(f15285,plain,
( ( ^ [Y0: $i,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK338 )
& ( in @ ( kpair @ Y0 @ Y2 ) @ sK337 )
& ( in @ ( kpair @ Y2 @ Y1 ) @ sK339 ) ) )
@ sK340
@ sK341 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f15213]) ).
thf(f15213,plain,
( ( ( ^ [Y0: $i,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK338 )
& ( in @ ( kpair @ Y0 @ Y2 ) @ sK337 )
& ( in @ ( kpair @ Y2 @ Y1 ) @ sK339 ) ) )
@ sK340
@ sK341 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f6172,f6416]) ).
thf(f6416,plain,
( ( in @ ( kpair @ sK340 @ sK341 )
@ ( dpsetconstr @ sK338 @ sK338
@ ^ [Y0: $i,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK338 )
& ( in @ ( kpair @ Y0 @ Y2 ) @ sK337 )
& ( in @ ( kpair @ Y2 @ Y1 ) @ sK339 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f5012]) ).
thf(f5012,plain,
( ( in @ ( kpair @ sK340 @ sK341 )
@ ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y3: $i,Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y0 )
& ( in @ ( kpair @ Y3 @ Y5 ) @ Y1 )
& ( in @ ( kpair @ Y5 @ Y4 ) @ Y2 ) ) ) )
@ sK338
@ sK337
@ sK339 ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f3456,f2992]) ).
thf(f2992,plain,
( breln1compset
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y3: $i,Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y0 )
& ( in @ ( kpair @ Y3 @ Y5 ) @ Y1 )
& ( in @ ( kpair @ Y5 @ Y4 ) @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f818]) ).
thf(f818,plain,
( breln1compset
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y3: $i,Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y0 )
& ( in @ ( kpair @ Y3 @ Y5 ) @ Y1 )
& ( in @ ( kpair @ Y5 @ Y4 ) @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f817]) ).
thf(f817,plain,
( ( ^ [X0: $i,X1: $i,X2: $i] :
( dpsetconstr @ X0 @ X0
@ ^ [X3: $i,X4: $i] :
? [X5: $i] :
( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
& ( in @ ( kpair @ X3 @ X5 ) @ X1 )
& ( in @ X5 @ X0 ) ) ) )
= breln1compset ),
inference(rectify,[status(thm)],[f299]) ).
thf(f299,axiom,
( ( ^ [X3: $i,X13: $i,X15: $i] :
( dpsetconstr @ X3 @ X3
@ ^ [X1: $i,X2: $i] :
? [X8: $i] :
( ( in @ ( kpair @ X8 @ X2 ) @ X15 )
& ( in @ ( kpair @ X1 @ X8 ) @ X13 )
& ( in @ X8 @ X3 ) ) ) )
= breln1compset ),
file('/export/starexec/sandbox/tmp/tmp.uVZj498QyD/DTF2THF_20195.p',breln1compset) ).
thf(f3456,plain,
( ( in @ ( kpair @ sK340 @ sK341 ) @ ( breln1compset @ sK338 @ sK337 @ sK339 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f1868]) ).
thf(f1868,plain,
( ( exuI3 = $true )
& ( setukpairIL = $true )
& ( prop2setE = $true )
& ( setadjoinSub2 = $true )
& ( funcGraphProp2 = $true )
& ( woz1_3 = $true )
& ( ex1I = $true )
& ( setminusLsub = $true )
& ( cartprodmempaircEq = $true )
& ( omega__Cong = $true )
& ( binintersectSubset3 = $true )
& ( breln1invprop = $true )
& ( setadjoinIL = $true )
& ( exuE3e = $true )
& ( setunionsingleton = $true )
& ( ubforcartprodlem1 = $true )
& ( nonemptyE1 = $true )
& ( complementTE1 = $true )
& ( notinsingleton = $true )
& ( binintersectSubset5 = $true )
& ( setukpairinjR12 = $true )
& ( ap2p = $true )
& ( lamp = $true )
& ( theprop = $true )
& ( binunionTIRcontra = $true )
& ( dpsetconstrER = $true )
& ( emptysetimpfalse = $true )
& ( notinemptyset = $true )
& ( dsetconstr__Cong = $true )
& ( symdiffI1 = $true )
& ( setunionE = $true )
& ( replAx = $true )
& ( infuncsetfunc = $true )
& ( iffalse = $true )
& ( eqimpsubset2 = $true )
& ( emptysetE = $true )
& ( cartprodsndpairEq = $true )
& ( funcGraphProp3 = $true )
& ( emptyI = $true )
& ( setbeta = $true )
& ( subPowSU = $true )
& ( demorgan2b2 = $true )
& ( demorgan1a = $true )
& ( demorgan2 = $true )
& ( setext = $true )
& ( funcGraphProp4 = $true )
& ( secondinupair = $true )
& ( funcGraphProp1 = $true )
& ( binintersectTERcontra = $true )
& ( binintersectLsub = $true )
& ( setunionAx = $true )
& ( powersetsubset = $true )
& ( descr__Cong = $true )
& ( exu__Cong = $true )
& ( upairset2IR = $true )
& ( symdiffI2 = $true )
& ( emptyinPowerset = $true )
& ( demorgan2a1 = $true )
& ( upairset2E = $true )
& ( complementTI1 = $true )
& ( woz13rule4 = $true )
& ( setOfPairsIsBReln = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( binintersectI = $true )
& ( sepInPowerset = $true )
& ( eta1 = $true )
& ( subsetRefl = $true )
& ( ap2apEq1 = $true )
& ( binintersectER = $true )
& ( powersetTI1 = $true )
& ( setunion__Cong = $true )
& ( doubleComplementEq = $true )
& ( powerset__Cong = $true )
& ( symdiffIneg1 = $true )
& ( contrasubsetT = $true )
& ( setadjoinSub = $true )
& ( exuEu = $true )
& ( ex1E2 = $true )
& ( setukpairinjR = $true )
& ( emptyinunitempty = $true )
& ( powersetE1 = $true )
& ( beta1 = $true )
& ( woz13rule1 = $true )
& ( setukpairinjR1 = $true )
& ( setukpairIR = $true )
& ( nonemptyI1 = $true )
& ( cartprodmempair = $true )
& ( dsetconstrI = $true )
& ( powersetAx = $true )
& ( setadjoinIR = $true )
& ( notequalI2 = $true )
& ( ksndpairEq = $true )
& ( exuE2 = $true )
& ( cartprodfstin = $true )
& ( brelnall1 = $true )
& ( cartprodpairmemER = $true )
& ( powersetI1 = $true )
& ( iffalseProp1 = $true )
& ( setminusIRneg = $true )
& ( funcextLem = $true )
& ( setOfPairsIsBReln1 = $true )
& ( lam2lamEq = $true )
& ( upairsetIL = $true )
& ( funcinfuncset = $true )
& ( in__Cong = $true )
& ( demorgan1b = $true )
& ( woz1_2 = $true )
& ( setukpairinjL1 = $true )
& ( breln1invI = $true )
& ( nonemptyI = $true )
& ( binunionLsub = $true )
& ( quantDeMorgan1 = $true )
& ( kpairp = $true )
& ( subsetTrans = $true )
& ( singletonsswitch = $true )
& ( setukpairinjR2 = $true )
& ( upairsubunion = $true )
& ( notdexE = $true )
& ( breln1SetBreln1 = $true )
& ( eqimpsubset1 = $true )
& ( eqbreln = $true )
& ( woz13rule3 = $true )
& ( breln1compI = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem3 = $true )
& ( notdallE = $true )
& ( inPowerset = $true )
& ( iftrueProp1 = $true )
& ( binunionEcases = $true )
& ( setunionE2 = $true )
& ( ifp = $true )
& ( woz13rule0 = $true )
& ( quantDeMorgan2 = $true )
& ( upairequniteq = $true )
& ( ifSingleton = $true )
& ( breln1invE = $true )
& ( app = $true )
& ( iftrue = $true )
& ( demorgan2b = $true )
& ( setukpairinjL = $true )
& ( exuE1 = $true )
& ( doubleComplementI1 = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( contrasubsetT2 = $true )
& ( iftrueorfalse = $true )
& ( setadjoin__Cong = $true )
& ( singletoninpowunion = $true )
& ( subset2powerset = $true )
& ( powersetTE1 = $true )
& ( setukpairinjR11 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( exuE3u = $true )
& ( cartprodpairin = $true )
& ( theeq = $true )
& ( doubleComplementSub1 = $true )
& ( notsubsetI = $true )
& ( descrp = $true )
& ( sepSubset = $true )
& ( ex1I2 = $true )
& ( disjointsetsI1 = $true )
& ( ap2apEq2 = $true )
& ( binintersectEL = $true )
& ( setextT = $true )
& ( iffalseProp2 = $true )
& ( setminusI = $true )
& ( subsetI2 = $true )
& ( emptysetAx = $true )
& ( powersetE = $true )
& ( complementTcontraSubset = $true )
& ( breln1compprop = $true )
& ( binunionT_lem = $true )
& ( setunionsingleton2 = $true )
& ( quantDeMorgan4 = $true )
& ( uniqinunit = $true )
& ( setextAx = $true )
& ( woz13rule2 = $true )
& ( singletonsuniq = $true )
& ( doubleComplementE1 = $true )
& ( demorgan1 = $true )
& ( setadjoinOr = $true )
& ( binintersectT_lem = $true )
& ( dpsetconstrSub = $true )
& ( cartprodmempair1 = $true )
& ( demorgan2a2 = $true )
& ( quantDeMorgan3 = $true )
& ( setminusELneg = $true )
& ( binunionE = $true )
& ( kpairiskpair = $true )
& ( powersetI = $true )
& ( setminusT_lem = $true )
& ( setminusILneg = $true )
& ( binunionIL = $true )
& ( dpsetconstrI = $true )
& ( setminusSubset1 = $true )
& ( exuI2 = $true )
& ( setoftrueEq = $true )
& ( inIntersectImpInUnion = $true )
& ( setminusSubset2 = $true )
& ( cartprodpairmemEL = $true )
& ( ex1E1 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( setminusER = $true )
& ( eta2 = $true )
& ( cartprodfstpairEq = $true )
& ( dsetconstrEL = $true )
& ( subsetemptysetimpeq = $true )
& ( kfstsingleton = $true )
& ( setadjoinE = $true )
& ( nonemptyImpWitness = $true )
& ( binintersectRsub = $true )
& ( breln1all2 = $true )
& ( cartprodpairsurjEq = $true )
& ( prop2setI = $true )
& ( apProp = $true )
& ( setukpairinjL2 = $true )
& ( beta2 = $true )
& ( emptyE1 = $true )
& ( complementTnotintersectT = $true )
& ( binunionTEcontra = $true )
& ( inCongP = $true )
& ( funcext = $true )
& ( doubleComplementSub2 = $true )
& ( setunionI = $true )
& ( cartprodsndin = $true )
& ( contrasubsetT1 = $true )
& ( exuI1 = $true )
& ( ( breln1 @ sK338 @ sK339 )
= $true )
& ( ( in @ sK340 @ sK338 )
= $true )
& ( ( in @ sK341 @ sK338 )
= $true )
& ! [X5: $i] :
( ( ( in @ X5 @ sK338 )
!= $true )
| ( ( in @ ( kpair @ sK340 @ X5 ) @ sK337 )
!= $true )
| ( ( in @ ( kpair @ X5 @ sK341 ) @ sK339 )
!= $true ) )
& ( ( in @ ( kpair @ sK340 @ sK341 ) @ ( breln1compset @ sK338 @ sK337 @ sK339 ) )
= $true )
& ( ( breln1 @ sK338 @ sK337 )
= $true )
& ( lam2p = $true )
& ( binintersectSubset4 = $true )
& ( omega0Ax = $true )
& ( eqinunit = $true )
& ( kpairsurjEq = $true )
& ( breln1all1 = $true )
& ( binintersectSubset1 = $true )
& ( omegaSAx = $true )
& ( dpsetconstrEL2 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( lamProp = $true )
& ( woz1_1 = $true )
& ( emptyset__Cong = $true )
& ( binunionIR = $true )
& ( funcImageSingleton = $true )
& ( singletoninpowerset = $true )
& ( woz1_4 = $true )
& ( singletonsubset = $true )
& ( vacuousDall = $true )
& ( subsetE2 = $true )
& ( ksndsingleton = $true )
& ( brelnall2 = $true )
& ( complementSubsetComplementIntersect = $true )
& ( binunionTE = $true )
& ( dpsetconstrERa = $true )
& ( binintersectTELcontra = $true )
& ( setminusEL = $true )
& ( prop2set2propI = $true )
& ( emptysetsubset = $true )
& ( eqbreln1 = $true )
& ( upairsetIR = $true )
& ( upairsetE = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( bs114d = $true )
& ( emptyInPowerset = $true )
& ( binintersectSubset2 = $true )
& ( choice2fnsingleton = $true )
& ( binunionTILcontra = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( symdiffIneg2 = $true )
& ( omegaIndAx = $true )
& ( dsetconstrER = $true )
& ( setminusERneg = $true )
& ( symdiffE = $true )
& ( setunionsingleton1 = $true )
& ( subsetTI = $true )
& ( subsetI1 = $true )
& ( complementT_lem = $true )
& ( binunionRsub = $true )
& ( contraSubsetComplement = $true )
& ( woz1_5 = $true )
& ( contrasubsetT3 = $true )
& ( iftrueProp2 = $true )
& ( wellorderingAx = $true )
& ( setadjoinAx = $true )
& ( foundationAx = $true )
& ( singletonprop = $true )
& ( subbreln = $true )
& ( noeltsimpempty = $true )
& ( upairinpowunion = $true )
& ( setextsub = $true )
& ( powersetT_lem = $true )
& ( kfstpairEq = $true )
& ( notequalI1 = $true )
& ( subsetE = $true )
& ( subbreln1 = $true )
& ( complementImpComplementIntersect = $true )
& ( funcext2 = $true )
& ( demorgan2a = $true )
& ( dpsetconstrEL1 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK337,sK338,sK339,sK340,sK341])],[f1134,f1867,f1866,f1865,f1864]) ).
thf(f1864,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( breln1 @ X1 @ X2 ) )
& ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
& ! [X5: $i] :
( ( ( in @ X5 @ X1 )
!= $true )
| ( $true
!= ( in @ ( kpair @ X3 @ X5 ) @ X0 ) )
| ( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
!= $true ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) )
= $true ) ) ) )
& ( ( breln1 @ X1 @ X0 )
= $true ) )
=> ( ? [X2: $i] :
( ( ( breln1 @ sK338 @ X2 )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ sK338 )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ sK338 )
= $true )
& ! [X5: $i] :
( ( ( in @ X5 @ sK338 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X5 ) @ sK337 )
!= $true )
| ( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
!= $true ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK338 @ sK337 @ X2 ) )
= $true ) ) ) )
& ( ( breln1 @ sK338 @ sK337 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1865,plain,
( ? [X2: $i] :
( ( ( breln1 @ sK338 @ X2 )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ sK338 )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ sK338 )
= $true )
& ! [X5: $i] :
( ( ( in @ X5 @ sK338 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X5 ) @ sK337 )
!= $true )
| ( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
!= $true ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK338 @ sK337 @ X2 ) )
= $true ) ) ) )
=> ( ( ( breln1 @ sK338 @ sK339 )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ sK338 )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ sK338 )
= $true )
& ! [X5: $i] :
( ( ( in @ X5 @ sK338 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X5 ) @ sK337 )
!= $true )
| ( ( in @ ( kpair @ X5 @ X4 ) @ sK339 )
!= $true ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK338 @ sK337 @ sK339 ) )
= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1866,plain,
( ? [X3: $i] :
( ( ( in @ X3 @ sK338 )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ sK338 )
= $true )
& ! [X5: $i] :
( ( ( in @ X5 @ sK338 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X5 ) @ sK337 )
!= $true )
| ( ( in @ ( kpair @ X5 @ X4 ) @ sK339 )
!= $true ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK338 @ sK337 @ sK339 ) )
= $true ) ) )
=> ( ( ( in @ sK340 @ sK338 )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ sK338 )
= $true )
& ! [X5: $i] :
( ( ( in @ X5 @ sK338 )
!= $true )
| ( ( in @ ( kpair @ sK340 @ X5 ) @ sK337 )
!= $true )
| ( ( in @ ( kpair @ X5 @ X4 ) @ sK339 )
!= $true ) )
& ( ( in @ ( kpair @ sK340 @ X4 ) @ ( breln1compset @ sK338 @ sK337 @ sK339 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1867,plain,
( ? [X4: $i] :
( ( ( in @ X4 @ sK338 )
= $true )
& ! [X5: $i] :
( ( ( in @ X5 @ sK338 )
!= $true )
| ( ( in @ ( kpair @ sK340 @ X5 ) @ sK337 )
!= $true )
| ( ( in @ ( kpair @ X5 @ X4 ) @ sK339 )
!= $true ) )
& ( ( in @ ( kpair @ sK340 @ X4 ) @ ( breln1compset @ sK338 @ sK337 @ sK339 ) )
= $true ) )
=> ( ( ( in @ sK341 @ sK338 )
= $true )
& ! [X5: $i] :
( ( ( in @ X5 @ sK338 )
!= $true )
| ( ( in @ ( kpair @ sK340 @ X5 ) @ sK337 )
!= $true )
| ( ( in @ ( kpair @ X5 @ sK341 ) @ sK339 )
!= $true ) )
& ( ( in @ ( kpair @ sK340 @ sK341 ) @ ( breln1compset @ sK338 @ sK337 @ sK339 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1134,plain,
( ( exuI3 = $true )
& ( setukpairIL = $true )
& ( prop2setE = $true )
& ( setadjoinSub2 = $true )
& ( funcGraphProp2 = $true )
& ( woz1_3 = $true )
& ( ex1I = $true )
& ( setminusLsub = $true )
& ( cartprodmempaircEq = $true )
& ( omega__Cong = $true )
& ( binintersectSubset3 = $true )
& ( breln1invprop = $true )
& ( setadjoinIL = $true )
& ( exuE3e = $true )
& ( setunionsingleton = $true )
& ( ubforcartprodlem1 = $true )
& ( nonemptyE1 = $true )
& ( complementTE1 = $true )
& ( notinsingleton = $true )
& ( binintersectSubset5 = $true )
& ( setukpairinjR12 = $true )
& ( ap2p = $true )
& ( lamp = $true )
& ( theprop = $true )
& ( binunionTIRcontra = $true )
& ( dpsetconstrER = $true )
& ( emptysetimpfalse = $true )
& ( notinemptyset = $true )
& ( dsetconstr__Cong = $true )
& ( symdiffI1 = $true )
& ( setunionE = $true )
& ( replAx = $true )
& ( infuncsetfunc = $true )
& ( iffalse = $true )
& ( eqimpsubset2 = $true )
& ( emptysetE = $true )
& ( cartprodsndpairEq = $true )
& ( funcGraphProp3 = $true )
& ( emptyI = $true )
& ( setbeta = $true )
& ( subPowSU = $true )
& ( demorgan2b2 = $true )
& ( demorgan1a = $true )
& ( demorgan2 = $true )
& ( setext = $true )
& ( funcGraphProp4 = $true )
& ( secondinupair = $true )
& ( funcGraphProp1 = $true )
& ( binintersectTERcontra = $true )
& ( binintersectLsub = $true )
& ( setunionAx = $true )
& ( powersetsubset = $true )
& ( descr__Cong = $true )
& ( exu__Cong = $true )
& ( upairset2IR = $true )
& ( symdiffI2 = $true )
& ( emptyinPowerset = $true )
& ( demorgan2a1 = $true )
& ( upairset2E = $true )
& ( complementTI1 = $true )
& ( woz13rule4 = $true )
& ( setOfPairsIsBReln = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( binintersectI = $true )
& ( sepInPowerset = $true )
& ( eta1 = $true )
& ( subsetRefl = $true )
& ( ap2apEq1 = $true )
& ( binintersectER = $true )
& ( powersetTI1 = $true )
& ( setunion__Cong = $true )
& ( doubleComplementEq = $true )
& ( powerset__Cong = $true )
& ( symdiffIneg1 = $true )
& ( contrasubsetT = $true )
& ( setadjoinSub = $true )
& ( exuEu = $true )
& ( ex1E2 = $true )
& ( setukpairinjR = $true )
& ( emptyinunitempty = $true )
& ( powersetE1 = $true )
& ( beta1 = $true )
& ( woz13rule1 = $true )
& ( setukpairinjR1 = $true )
& ( setukpairIR = $true )
& ( nonemptyI1 = $true )
& ( cartprodmempair = $true )
& ( dsetconstrI = $true )
& ( powersetAx = $true )
& ( setadjoinIR = $true )
& ( notequalI2 = $true )
& ( ksndpairEq = $true )
& ( exuE2 = $true )
& ( cartprodfstin = $true )
& ( brelnall1 = $true )
& ( cartprodpairmemER = $true )
& ( powersetI1 = $true )
& ( iffalseProp1 = $true )
& ( setminusIRneg = $true )
& ( funcextLem = $true )
& ( setOfPairsIsBReln1 = $true )
& ( lam2lamEq = $true )
& ( upairsetIL = $true )
& ( funcinfuncset = $true )
& ( in__Cong = $true )
& ( demorgan1b = $true )
& ( woz1_2 = $true )
& ( setukpairinjL1 = $true )
& ( breln1invI = $true )
& ( nonemptyI = $true )
& ( binunionLsub = $true )
& ( quantDeMorgan1 = $true )
& ( kpairp = $true )
& ( subsetTrans = $true )
& ( singletonsswitch = $true )
& ( setukpairinjR2 = $true )
& ( upairsubunion = $true )
& ( notdexE = $true )
& ( breln1SetBreln1 = $true )
& ( eqimpsubset1 = $true )
& ( eqbreln = $true )
& ( woz13rule3 = $true )
& ( breln1compI = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem3 = $true )
& ( notdallE = $true )
& ( inPowerset = $true )
& ( iftrueProp1 = $true )
& ( binunionEcases = $true )
& ( setunionE2 = $true )
& ( ifp = $true )
& ( woz13rule0 = $true )
& ( quantDeMorgan2 = $true )
& ( upairequniteq = $true )
& ( ifSingleton = $true )
& ( breln1invE = $true )
& ( app = $true )
& ( iftrue = $true )
& ( demorgan2b = $true )
& ( setukpairinjL = $true )
& ( exuE1 = $true )
& ( doubleComplementI1 = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( contrasubsetT2 = $true )
& ( iftrueorfalse = $true )
& ( setadjoin__Cong = $true )
& ( singletoninpowunion = $true )
& ( subset2powerset = $true )
& ( powersetTE1 = $true )
& ( setukpairinjR11 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( exuE3u = $true )
& ( cartprodpairin = $true )
& ( theeq = $true )
& ( doubleComplementSub1 = $true )
& ( notsubsetI = $true )
& ( descrp = $true )
& ( sepSubset = $true )
& ( ex1I2 = $true )
& ( disjointsetsI1 = $true )
& ( ap2apEq2 = $true )
& ( binintersectEL = $true )
& ( setextT = $true )
& ( iffalseProp2 = $true )
& ( setminusI = $true )
& ( subsetI2 = $true )
& ( emptysetAx = $true )
& ( powersetE = $true )
& ( complementTcontraSubset = $true )
& ( breln1compprop = $true )
& ( binunionT_lem = $true )
& ( setunionsingleton2 = $true )
& ( quantDeMorgan4 = $true )
& ( uniqinunit = $true )
& ( setextAx = $true )
& ( woz13rule2 = $true )
& ( singletonsuniq = $true )
& ( doubleComplementE1 = $true )
& ( demorgan1 = $true )
& ( setadjoinOr = $true )
& ( binintersectT_lem = $true )
& ( dpsetconstrSub = $true )
& ( cartprodmempair1 = $true )
& ( demorgan2a2 = $true )
& ( quantDeMorgan3 = $true )
& ( setminusELneg = $true )
& ( binunionE = $true )
& ( kpairiskpair = $true )
& ( powersetI = $true )
& ( setminusT_lem = $true )
& ( setminusILneg = $true )
& ( binunionIL = $true )
& ( dpsetconstrI = $true )
& ( setminusSubset1 = $true )
& ( exuI2 = $true )
& ( setoftrueEq = $true )
& ( inIntersectImpInUnion = $true )
& ( setminusSubset2 = $true )
& ( cartprodpairmemEL = $true )
& ( ex1E1 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( setminusER = $true )
& ( eta2 = $true )
& ( cartprodfstpairEq = $true )
& ( dsetconstrEL = $true )
& ( subsetemptysetimpeq = $true )
& ( kfstsingleton = $true )
& ( setadjoinE = $true )
& ( nonemptyImpWitness = $true )
& ( binintersectRsub = $true )
& ( breln1all2 = $true )
& ( cartprodpairsurjEq = $true )
& ( prop2setI = $true )
& ( apProp = $true )
& ( setukpairinjL2 = $true )
& ( beta2 = $true )
& ( emptyE1 = $true )
& ( complementTnotintersectT = $true )
& ( binunionTEcontra = $true )
& ( inCongP = $true )
& ( funcext = $true )
& ( doubleComplementSub2 = $true )
& ( setunionI = $true )
& ( cartprodsndin = $true )
& ( contrasubsetT1 = $true )
& ( exuI1 = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( breln1 @ X1 @ X2 ) )
& ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
& ! [X5: $i] :
( ( ( in @ X5 @ X1 )
!= $true )
| ( $true
!= ( in @ ( kpair @ X3 @ X5 ) @ X0 ) )
| ( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
!= $true ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) )
= $true ) ) ) )
& ( ( breln1 @ X1 @ X0 )
= $true ) )
& ( lam2p = $true )
& ( binintersectSubset4 = $true )
& ( omega0Ax = $true )
& ( eqinunit = $true )
& ( kpairsurjEq = $true )
& ( breln1all1 = $true )
& ( binintersectSubset1 = $true )
& ( omegaSAx = $true )
& ( dpsetconstrEL2 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( lamProp = $true )
& ( woz1_1 = $true )
& ( emptyset__Cong = $true )
& ( binunionIR = $true )
& ( funcImageSingleton = $true )
& ( singletoninpowerset = $true )
& ( woz1_4 = $true )
& ( singletonsubset = $true )
& ( vacuousDall = $true )
& ( subsetE2 = $true )
& ( ksndsingleton = $true )
& ( brelnall2 = $true )
& ( complementSubsetComplementIntersect = $true )
& ( binunionTE = $true )
& ( dpsetconstrERa = $true )
& ( binintersectTELcontra = $true )
& ( setminusEL = $true )
& ( prop2set2propI = $true )
& ( emptysetsubset = $true )
& ( eqbreln1 = $true )
& ( upairsetIR = $true )
& ( upairsetE = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( bs114d = $true )
& ( emptyInPowerset = $true )
& ( binintersectSubset2 = $true )
& ( choice2fnsingleton = $true )
& ( binunionTILcontra = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( symdiffIneg2 = $true )
& ( omegaIndAx = $true )
& ( dsetconstrER = $true )
& ( setminusERneg = $true )
& ( symdiffE = $true )
& ( setunionsingleton1 = $true )
& ( subsetTI = $true )
& ( subsetI1 = $true )
& ( complementT_lem = $true )
& ( binunionRsub = $true )
& ( contraSubsetComplement = $true )
& ( woz1_5 = $true )
& ( contrasubsetT3 = $true )
& ( iftrueProp2 = $true )
& ( wellorderingAx = $true )
& ( setadjoinAx = $true )
& ( foundationAx = $true )
& ( singletonprop = $true )
& ( subbreln = $true )
& ( noeltsimpempty = $true )
& ( upairinpowunion = $true )
& ( setextsub = $true )
& ( powersetT_lem = $true )
& ( kfstpairEq = $true )
& ( notequalI1 = $true )
& ( subsetE = $true )
& ( subbreln1 = $true )
& ( complementImpComplementIntersect = $true )
& ( funcext2 = $true )
& ( demorgan2a = $true )
& ( dpsetconstrEL1 = $true ) ),
inference(flattening,[status(thm)],[f1133]) ).
thf(f1133,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ! [X5: $i] :
( ( ( in @ X5 @ X1 )
!= $true )
| ( $true
!= ( in @ ( kpair @ X3 @ X5 ) @ X0 ) )
| ( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
!= $true ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) )
= $true )
& ( ( in @ X4 @ X1 )
= $true ) )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( $true
= ( breln1 @ X1 @ X2 ) ) )
& ( ( breln1 @ X1 @ X0 )
= $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)],[f872]) ).
thf(f872,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 )
=> ! [X0: $i,X1: $i] :
( ( ( breln1 @ X1 @ X0 )
= $true )
=> ! [X2: $i] :
( ( $true
= ( breln1 @ X1 @ X2 ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) )
= $true )
=> ? [X5: $i] :
( ( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
= $true )
& ( $true
= ( in @ ( kpair @ X3 @ X5 ) @ X0 ) )
& ( ( in @ X5 @ X1 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f871]) ).
thf(f871,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
=> ! [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: $i] :
( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
& ( in @ ( kpair @ X3 @ X5 ) @ X0 )
& ( in @ X5 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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
=> ! [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 ) )
=> ? [X8: $i] :
( ( in @ ( kpair @ X8 @ X2 ) @ X15 )
& ( in @ ( kpair @ X1 @ X8 ) @ X13 )
& ( in @ X8 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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
=> ! [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 ) )
=> ? [X8: $i] :
( ( in @ ( kpair @ X8 @ X2 ) @ X15 )
& ( in @ ( kpair @ X1 @ X8 ) @ X13 )
& ( in @ X8 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uVZj498QyD/DTF2THF_20195.p',breln1compE) ).
thf(f6172,plain,
! [X8: $i > $i > $o,X6: $i,X9: $i,X7: $i,X5: $i] :
( ( ( in @ ( kpair @ X7 @ X5 ) @ ( dpsetconstr @ X9 @ X6 @ X8 ) )
!= $true )
| ( ( X8 @ X7 @ X5 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f6171]) ).
thf(f6171,plain,
! [X8: $i > $i > $o,X6: $i,X9: $i,X7: $i,X5: $i] :
( ( ( in @ ( kpair @ X7 @ X5 )
@ ( dpsetconstr @ X9 @ X6
@ ^ [Y0: $i,Y1: $i] : ( X8 @ Y0 @ Y1 ) ) )
!= $true )
| ( ( X8 @ X7 @ X5 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f5428]) ).
thf(f5428,plain,
! [X8: $i > $i > $o,X6: $i,X9: $i,X7: $i,X5: $i] :
( ( $true != $true )
| ( ( X8 @ X7 @ X5 )
= $true )
| ( ( in @ ( kpair @ X7 @ X5 )
@ ( dpsetconstr @ X9 @ X6
@ ^ [Y0: $i,Y1: $i] : ( X8 @ Y0 @ Y1 ) ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f4176,f3661]) ).
thf(f3661,plain,
dpsetconstrER = $true,
inference(cnf_transformation,[status(thm)],[f1868]) ).
thf(f4176,plain,
! [X8: $i > $i > $o,X6: $i,X9: $i,X7: $i,X5: $i] :
( ( ( X8 @ X7 @ X5 )
= $true )
| ( ( in @ ( kpair @ X7 @ X5 )
@ ( dpsetconstr @ X9 @ X6
@ ^ [Y0: $i,Y1: $i] : ( X8 @ Y0 @ Y1 ) ) )
!= $true )
| ( dpsetconstrER != $true ) ),
inference(cnf_transformation,[status(thm)],[f2426]) ).
thf(f2426,plain,
( ( ( dpsetconstrER = $true )
| ( ( ( sK690 @ sK689 @ sK687 )
!= $true )
& ( $true
= ( in @ ( kpair @ sK689 @ sK687 )
@ ( dpsetconstr @ sK691 @ sK688
@ ^ [Y0: $i,Y1: $i] : ( sK690 @ Y0 @ Y1 ) ) ) ) ) )
& ( ! [X5: $i,X6: $i,X7: $i,X8: $i > $i > $o,X9: $i] :
( ( ( X8 @ X7 @ X5 )
= $true )
| ( ( in @ ( kpair @ X7 @ X5 )
@ ( dpsetconstr @ X9 @ X6
@ ^ [Y0: $i,Y1: $i] : ( X8 @ Y0 @ Y1 ) ) )
!= $true ) )
| ( dpsetconstrER != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK687,sK688,sK689,sK690,sK691])],[f2424,f2425]) ).
thf(f2425,plain,
( ? [X0: $i,X1: $i,X2: $i,X3: $i > $i > $o,X4: $i] :
( ( ( X3 @ X2 @ X0 )
!= $true )
& ( ( in @ ( kpair @ X2 @ X0 )
@ ( dpsetconstr @ X4 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X3 @ Y0 @ Y1 ) ) )
= $true ) )
=> ( ( ( sK690 @ sK689 @ sK687 )
!= $true )
& ( $true
= ( in @ ( kpair @ sK689 @ sK687 )
@ ( dpsetconstr @ sK691 @ sK688
@ ^ [Y0: $i,Y1: $i] : ( sK690 @ Y0 @ Y1 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2424,plain,
( ( ( dpsetconstrER = $true )
| ? [X0: $i,X1: $i,X2: $i,X3: $i > $i > $o,X4: $i] :
( ( ( X3 @ X2 @ X0 )
!= $true )
& ( ( in @ ( kpair @ X2 @ X0 )
@ ( dpsetconstr @ X4 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X3 @ Y0 @ Y1 ) ) )
= $true ) ) )
& ( ! [X5: $i,X6: $i,X7: $i,X8: $i > $i > $o,X9: $i] :
( ( ( X8 @ X7 @ X5 )
= $true )
| ( ( in @ ( kpair @ X7 @ X5 )
@ ( dpsetconstr @ X9 @ X6
@ ^ [Y0: $i,Y1: $i] : ( X8 @ Y0 @ Y1 ) ) )
!= $true ) )
| ( dpsetconstrER != $true ) ) ),
inference(rectify,[status(thm)],[f2423]) ).
thf(f2423,plain,
( ( ( dpsetconstrER = $true )
| ? [X0: $i,X1: $i,X2: $i,X3: $i > $i > $o,X4: $i] :
( ( ( X3 @ X2 @ X0 )
!= $true )
& ( ( in @ ( kpair @ X2 @ X0 )
@ ( dpsetconstr @ X4 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X3 @ Y0 @ Y1 ) ) )
= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i,X3: $i > $i > $o,X4: $i] :
( ( ( X3 @ X2 @ X0 )
= $true )
| ( ( in @ ( kpair @ X2 @ X0 )
@ ( dpsetconstr @ X4 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X3 @ Y0 @ Y1 ) ) )
!= $true ) )
| ( dpsetconstrER != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f1132]) ).
thf(f1132,plain,
( ( dpsetconstrER = $true )
<=> ! [X0: $i,X1: $i,X2: $i,X3: $i > $i > $o,X4: $i] :
( ( ( X3 @ X2 @ X0 )
= $true )
| ( ( in @ ( kpair @ X2 @ X0 )
@ ( dpsetconstr @ X4 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X3 @ Y0 @ Y1 ) ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f674]) ).
thf(f674,plain,
( ! [X0: $i,X1: $i,X2: $i,X3: $i > $i > $o,X4: $i] :
( ( ( in @ ( kpair @ X2 @ X0 )
@ ( dpsetconstr @ X4 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X3 @ Y0 @ Y1 ) ) )
= $true )
=> ( ( X3 @ X2 @ X0 )
= $true ) )
<=> ( dpsetconstrER = $true ) ),
inference(fool_elimination,[status(thm)],[f673]) ).
thf(f673,plain,
( dpsetconstrER
= ( ! [X0: $i,X1: $i,X2: $i,X3: $i > $i > $o,X4: $i] :
( ( in @ ( kpair @ X2 @ X0 )
@ ( dpsetconstr @ X4 @ X1
@ ^ [X5: $i,X6: $i] : ( X3 @ X5 @ X6 ) ) )
=> ( X3 @ X2 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f191]) ).
thf(f191,axiom,
( dpsetconstrER
= ( ! [X2: $i,X4: $i,X1: $i,X0: $i > $i > $o,X3: $i] :
( ( in @ ( kpair @ X1 @ X2 )
@ ( dpsetconstr @ X3 @ X4
@ ^ [X8: $i,X10: $i] : ( X0 @ X8 @ X10 ) ) )
=> ( X0 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uVZj498QyD/DTF2THF_20195.p',dpsetconstrER) ).
thf(f17671,plain,
( $true
!= ( in @ sK1073 @ sK338 ) ),
inference(subsumption_resolution,[status(thm)],[f17649,f15289]) ).
thf(f15289,plain,
( ( in @ ( kpair @ sK1073 @ sK341 ) @ sK339 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f15288]) ).
thf(f17649,plain,
( ( ( in @ ( kpair @ sK1073 @ sK341 ) @ sK339 )
!= $true )
| ( $true
!= ( in @ sK1073 @ sK338 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f17588]) ).
thf(f17588,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK1073 @ sK338 ) )
| ( ( in @ ( kpair @ sK1073 @ sK341 ) @ sK339 )
!= $true ) ),
inference(superposition,[status(thm)],[f3457,f15291]) ).
thf(f15291,plain,
( $true
= ( in @ ( kpair @ sK340 @ sK1073 ) @ sK337 ) ),
inference(binary_proxy_clausification,[status(thm)],[f15290]) ).
thf(f3457,plain,
! [X5: $i] :
( ( ( in @ ( kpair @ sK340 @ X5 ) @ sK337 )
!= $true )
| ( ( in @ ( kpair @ X5 @ sK341 ) @ sK339 )
!= $true )
| ( ( in @ X5 @ sK338 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1868]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU780^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.06/0.25 % Computer : n024.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Tue Feb 24 07:36:25 EST 2026
% 0.06/0.25 % CPUTime :
% 0.06/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.06/0.31 ---- Original DTF file ---
% 0.06/0.31 thf(spec,logic,$$dhol).
% 0.06/0.31 %------------------------------------------------------------------------------
% 0.06/0.31 % File : SEU780^1 : TPTP v9.2.1. Released v3.7.0.
% 0.06/0.31 % Domain : Set Theory
% 0.06/0.31 % Problem : Binary Relations on a Set
% 0.06/0.31 % Version : Especial.
% 0.06/0.31 % English : (! A:i.! R:i.breln1 A R -> (! S:i.breln1 A S -> (! x:i.in x A ->
% 0.06/0.31 % (! y:i.in y A -> in (kpair x y) (breln1compset A R S) ->
% 0.06/0.31 % (? z:i.in z A & (in (kpair x z) R & in (kpair z y) S))))))
% 0.06/0.31
% 0.06/0.31 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.06/0.31 % Source : [Bro08]
% 0.06/0.31 % Names : ZFC282g [Bro08]
% 0.06/0.31
% 0.06/0.31 % Status : Theorem
% 0.06/0.31 % Rating : 0.56 v9.1.0, 0.62 v9.0.0, 0.70 v8.2.0, 0.77 v8.1.0, 0.82 v7.5.0, 0.71 v7.4.0, 0.78 v7.2.0, 0.75 v7.0.0, 0.71 v6.4.0, 0.67 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
% 0.06/0.31 % Syntax : Number of formulae : 646 ( 301 unt; 344 typ; 301 def)
% 0.06/0.31 % Number of atoms : 1831 ( 431 equ; 0 cnn)
% 0.06/0.31 % Maximal formula atoms : 304 ( 6 avg)
% 0.06/0.31 % Number of connectives : 3978 ( 73 ~; 12 |; 50 &;2888 @)
% 0.06/0.31 % ( 14 <=>; 941 =>; 0 <=; 0 <~>)
% 0.06/0.31 % Maximal formula depth : 314 ( 2 avg)
% 0.06/0.31 % Number of types : 2 ( 0 usr)
% 0.06/0.31 % Number of type conns : 157 ( 157 >; 0 *; 0 +; 0 <<)
% 0.06/0.31 % Number of symbols : 347 ( 344 usr; 300 con; 0-4 aty)
% 0.06/0.31 % Number of variables : 1052 ( 81 ^; 933 !; 38 ?;1052 :)
% 0.06/0.31 % SPC : TH0_THM_EQU_NAR
% 0.06/0.31
% 0.06/0.31 % Comments : http://mathgate.info/detsetitem.php?id=346
% 0.06/0.31 %------------------------------------------------------------------------------
% 0.06/0.31 thf(in_type,type,
% 0.06/0.31 in: $i > $i > $o ).
% 0.06/0.31
% 0.06/0.31 thf(exu_type,type,
% 0.06/0.31 exu: ( $i > $o ) > $o ).
% 0.06/0.31
% 0.06/0.31 thf(exu,definition,
% 0.06/0.31 ( exu
% 0.06/0.31 = ( ^ [Xphi: $i > $o] :
% 0.06/0.31 ? [Xx: $i] :
% 0.06/0.31 ( ( Xphi @ Xx )
% 0.06/0.31 & ! [Xy: $i] :
% 0.06/0.31 ( ( Xphi @ Xy )
% 0.06/0.31 => ( Xx = Xy ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(setextAx_type,type,
% 0.06/0.31 setextAx: $o ).
% 0.06/0.31
% 0.06/0.31 thf(setextAx,definition,
% 0.06/0.31 ( setextAx
% 0.06/0.31 = ( ! [A: $i,B: $i] :
% 0.06/0.31 ( ! [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 <=> ( in @ Xx @ B ) )
% 0.06/0.31 => ( A = B ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(emptyset_type,type,
% 0.06/0.31 emptyset: $i ).
% 0.06/0.31
% 0.06/0.31 thf(emptysetAx_type,type,
% 0.06/0.31 emptysetAx: $o ).
% 0.06/0.31
% 0.06/0.31 thf(emptysetAx,definition,
% 0.06/0.31 ( emptysetAx
% 0.06/0.31 = ( ! [Xx: $i] :
% 0.06/0.31 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(setadjoin_type,type,
% 0.06/0.31 setadjoin: $i > $i > $i ).
% 0.06/0.31
% 0.06/0.31 thf(setadjoinAx_type,type,
% 0.06/0.31 setadjoinAx: $o ).
% 0.06/0.31
% 0.06/0.31 thf(setadjoinAx,definition,
% 0.06/0.31 ( setadjoinAx
% 0.06/0.31 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.06/0.31 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.06/0.31 <=> ( ( Xy = Xx )
% 0.06/0.31 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(powerset_type,type,
% 0.06/0.31 powerset: $i > $i ).
% 0.06/0.31
% 0.06/0.31 thf(powersetAx_type,type,
% 0.06/0.31 powersetAx: $o ).
% 0.06/0.31
% 0.06/0.31 thf(powersetAx,definition,
% 0.06/0.31 ( powersetAx
% 0.06/0.31 = ( ! [A: $i,B: $i] :
% 0.06/0.31 ( ( in @ B @ ( powerset @ A ) )
% 0.06/0.31 <=> ! [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ B )
% 0.06/0.31 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(setunion_type,type,
% 0.06/0.31 setunion: $i > $i ).
% 0.06/0.31
% 0.06/0.31 thf(setunionAx_type,type,
% 0.06/0.31 setunionAx: $o ).
% 0.06/0.31
% 0.06/0.31 thf(setunionAx,definition,
% 0.06/0.31 ( setunionAx
% 0.06/0.31 = ( ! [A: $i,Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ ( setunion @ A ) )
% 0.06/0.31 <=> ? [B: $i] :
% 0.06/0.31 ( ( in @ Xx @ B )
% 0.06/0.31 & ( in @ B @ A ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(omega_type,type,
% 0.06/0.31 omega: $i ).
% 0.06/0.31
% 0.06/0.31 thf(omega0Ax_type,type,
% 0.06/0.31 omega0Ax: $o ).
% 0.06/0.31
% 0.06/0.31 thf(omega0Ax,definition,
% 0.06/0.31 ( omega0Ax
% 0.06/0.31 = ( in @ emptyset @ omega ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(omegaSAx_type,type,
% 0.06/0.31 omegaSAx: $o ).
% 0.06/0.31
% 0.06/0.31 thf(omegaSAx,definition,
% 0.06/0.31 ( omegaSAx
% 0.06/0.31 = ( ! [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ omega )
% 0.06/0.31 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(omegaIndAx_type,type,
% 0.06/0.31 omegaIndAx: $o ).
% 0.06/0.31
% 0.06/0.31 thf(omegaIndAx,definition,
% 0.06/0.31 ( omegaIndAx
% 0.06/0.31 = ( ! [A: $i] :
% 0.06/0.31 ( ( ( in @ emptyset @ A )
% 0.06/0.31 & ! [Xx: $i] :
% 0.06/0.31 ( ( ( in @ Xx @ omega )
% 0.06/0.31 & ( in @ Xx @ A ) )
% 0.06/0.31 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.06/0.31 => ! [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ omega )
% 0.06/0.31 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(replAx_type,type,
% 0.06/0.31 replAx: $o ).
% 0.06/0.31
% 0.06/0.31 thf(replAx,definition,
% 0.06/0.31 ( replAx
% 0.06/0.31 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.06/0.31 ( ! [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 => ( exu
% 0.06/0.31 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.06/0.31 => ? [B: $i] :
% 0.06/0.31 ! [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ B )
% 0.06/0.31 <=> ? [Xy: $i] :
% 0.06/0.31 ( ( in @ Xy @ A )
% 0.06/0.31 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(foundationAx_type,type,
% 0.06/0.31 foundationAx: $o ).
% 0.06/0.31
% 0.06/0.31 thf(foundationAx,definition,
% 0.06/0.31 ( foundationAx
% 0.06/0.31 = ( ! [A: $i] :
% 0.06/0.31 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.06/0.31 => ? [B: $i] :
% 0.06/0.31 ( ( in @ B @ A )
% 0.06/0.31 & ~ ? [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ B )
% 0.06/0.31 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(wellorderingAx_type,type,
% 0.06/0.31 wellorderingAx: $o ).
% 0.06/0.31
% 0.06/0.31 thf(wellorderingAx,definition,
% 0.06/0.31 ( wellorderingAx
% 0.06/0.31 = ( ! [A: $i] :
% 0.06/0.31 ? [B: $i] :
% 0.06/0.31 ( ! [C: $i] :
% 0.06/0.31 ( ( in @ C @ B )
% 0.06/0.31 => ! [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ C )
% 0.06/0.31 => ( in @ Xx @ A ) ) )
% 0.06/0.31 & ! [Xx: $i,Xy: $i] :
% 0.06/0.31 ( ( ( in @ Xx @ A )
% 0.06/0.31 & ( in @ Xy @ A ) )
% 0.06/0.31 => ( ! [C: $i] :
% 0.06/0.31 ( ( in @ C @ B )
% 0.06/0.31 => ( ( in @ Xx @ C )
% 0.06/0.31 <=> ( in @ Xy @ C ) ) )
% 0.06/0.31 => ( Xx = Xy ) ) )
% 0.06/0.31 & ! [C: $i,D: $i] :
% 0.06/0.31 ( ( ( in @ C @ B )
% 0.06/0.31 & ( in @ D @ B ) )
% 0.06/0.31 => ( ! [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ C )
% 0.06/0.31 => ( in @ Xx @ D ) )
% 0.06/0.31 | ! [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ D )
% 0.06/0.31 => ( in @ Xx @ C ) ) ) )
% 0.06/0.31 & ! [C: $i] :
% 0.06/0.31 ( ( ! [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ C )
% 0.06/0.31 => ( in @ Xx @ A ) )
% 0.06/0.31 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.06/0.31 => ? [D: $i,Xx: $i] :
% 0.06/0.31 ( ( in @ D @ B )
% 0.06/0.31 & ( in @ Xx @ C )
% 0.06/0.31 & ~ ? [Xy: $i] :
% 0.06/0.31 ( ( in @ Xy @ D )
% 0.06/0.31 & ( in @ Xy @ C ) )
% 0.06/0.31 & ! [E: $i] :
% 0.06/0.31 ( ( in @ E @ B )
% 0.06/0.31 => ( ! [Xy: $i] :
% 0.06/0.31 ( ( in @ Xy @ E )
% 0.06/0.31 => ( in @ Xy @ D ) )
% 0.06/0.31 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(descr_type,type,
% 0.06/0.31 descr: ( $i > $o ) > $i ).
% 0.06/0.31
% 0.06/0.31 thf(descrp_type,type,
% 0.06/0.31 descrp: $o ).
% 0.06/0.31
% 0.06/0.31 thf(descrp,definition,
% 0.06/0.31 ( descrp
% 0.06/0.31 = ( ! [Xphi: $i > $o] :
% 0.06/0.31 ( ( exu
% 0.06/0.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.06/0.31 => ( Xphi
% 0.06/0.31 @ ( descr
% 0.06/0.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(dsetconstr_type,type,
% 0.06/0.31 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.06/0.31
% 0.06/0.31 thf(dsetconstrI_type,type,
% 0.06/0.31 dsetconstrI: $o ).
% 0.06/0.31
% 0.06/0.31 thf(dsetconstrI,definition,
% 0.06/0.31 ( dsetconstrI
% 0.06/0.31 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 => ( ( Xphi @ Xx )
% 0.06/0.31 => ( in @ Xx
% 0.06/0.31 @ ( dsetconstr @ A
% 0.06/0.31 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(dsetconstrEL_type,type,
% 0.06/0.31 dsetconstrEL: $o ).
% 0.06/0.31
% 0.06/0.31 thf(dsetconstrEL,definition,
% 0.06/0.31 ( dsetconstrEL
% 0.06/0.31 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.06/0.31 ( ( in @ Xx
% 0.06/0.31 @ ( dsetconstr @ A
% 0.06/0.31 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.06/0.31 => ( in @ Xx @ A ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(dsetconstrER_type,type,
% 0.06/0.31 dsetconstrER: $o ).
% 0.06/0.31
% 0.06/0.31 thf(dsetconstrER,definition,
% 0.06/0.31 ( dsetconstrER
% 0.06/0.31 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.06/0.31 ( ( in @ Xx
% 0.06/0.31 @ ( dsetconstr @ A
% 0.06/0.31 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.06/0.31 => ( Xphi @ Xx ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(exuE1_type,type,
% 0.06/0.31 exuE1: $o ).
% 0.06/0.31
% 0.06/0.31 thf(exuE1,definition,
% 0.06/0.31 ( exuE1
% 0.06/0.31 = ( ! [Xphi: $i > $o] :
% 0.06/0.31 ( ( exu
% 0.06/0.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.06/0.31 => ? [Xx: $i] :
% 0.06/0.31 ( ( Xphi @ Xx )
% 0.06/0.31 & ! [Xy: $i] :
% 0.06/0.31 ( ( Xphi @ Xy )
% 0.06/0.31 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(prop2set_type,type,
% 0.06/0.31 prop2set: $o > $i ).
% 0.06/0.31
% 0.06/0.31 thf(prop2setE_type,type,
% 0.06/0.31 prop2setE: $o ).
% 0.06/0.31
% 0.06/0.31 thf(prop2setE,definition,
% 0.06/0.31 ( prop2setE
% 0.06/0.31 = ( ! [Xphi: $o,Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.06/0.31 => Xphi ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(emptysetE_type,type,
% 0.06/0.31 emptysetE: $o ).
% 0.06/0.31
% 0.06/0.31 thf(emptysetE,definition,
% 0.06/0.31 ( emptysetE
% 0.06/0.31 = ( ! [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ emptyset )
% 0.06/0.31 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(emptysetimpfalse_type,type,
% 0.06/0.31 emptysetimpfalse: $o ).
% 0.06/0.31
% 0.06/0.31 thf(emptysetimpfalse,definition,
% 0.06/0.31 ( emptysetimpfalse
% 0.06/0.31 = ( ! [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ emptyset )
% 0.06/0.31 => $false ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(notinemptyset_type,type,
% 0.06/0.31 notinemptyset: $o ).
% 0.06/0.31
% 0.06/0.31 thf(notinemptyset,definition,
% 0.06/0.31 ( notinemptyset
% 0.06/0.31 = ( ! [Xx: $i] :
% 0.06/0.31 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(exuE3e_type,type,
% 0.06/0.31 exuE3e: $o ).
% 0.06/0.31
% 0.06/0.31 thf(exuE3e,definition,
% 0.06/0.31 ( exuE3e
% 0.06/0.31 = ( ! [Xphi: $i > $o] :
% 0.06/0.31 ( ( exu
% 0.06/0.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.06/0.31 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(setext_type,type,
% 0.06/0.31 setext: $o ).
% 0.06/0.31
% 0.06/0.31 thf(setext,definition,
% 0.06/0.31 ( setext
% 0.06/0.31 = ( ! [A: $i,B: $i] :
% 0.06/0.31 ( ! [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 => ( in @ Xx @ B ) )
% 0.06/0.31 => ( ! [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ B )
% 0.06/0.31 => ( in @ Xx @ A ) )
% 0.06/0.31 => ( A = B ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(emptyI_type,type,
% 0.06/0.31 emptyI: $o ).
% 0.06/0.31
% 0.06/0.31 thf(emptyI,definition,
% 0.06/0.31 ( emptyI
% 0.06/0.31 = ( ! [A: $i] :
% 0.06/0.31 ( ! [Xx: $i] :
% 0.06/0.31 ~ ( in @ Xx @ A )
% 0.06/0.31 => ( A = emptyset ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(noeltsimpempty_type,type,
% 0.06/0.31 noeltsimpempty: $o ).
% 0.06/0.31
% 0.06/0.31 thf(noeltsimpempty,definition,
% 0.06/0.31 ( noeltsimpempty
% 0.06/0.31 = ( ! [A: $i] :
% 0.06/0.31 ( ! [Xx: $i] :
% 0.06/0.31 ~ ( in @ Xx @ A )
% 0.06/0.31 => ( A = emptyset ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(setbeta_type,type,
% 0.06/0.31 setbeta: $o ).
% 0.06/0.31
% 0.06/0.31 thf(setbeta,definition,
% 0.06/0.31 ( setbeta
% 0.06/0.31 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 => ( ( in @ Xx
% 0.06/0.31 @ ( dsetconstr @ A
% 0.06/0.31 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.06/0.31 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(nonempty_type,type,
% 0.06/0.31 nonempty: $i > $o ).
% 0.06/0.31
% 0.06/0.31 thf(nonempty,definition,
% 0.06/0.31 ( nonempty
% 0.06/0.31 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(nonemptyE1_type,type,
% 0.06/0.31 nonemptyE1: $o ).
% 0.06/0.31
% 0.06/0.31 thf(nonemptyE1,definition,
% 0.06/0.31 ( nonemptyE1
% 0.06/0.31 = ( ! [A: $i] :
% 0.06/0.31 ( ( nonempty @ A )
% 0.06/0.31 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(nonemptyI_type,type,
% 0.06/0.31 nonemptyI: $o ).
% 0.06/0.31
% 0.06/0.31 thf(nonemptyI,definition,
% 0.06/0.31 ( nonemptyI
% 0.06/0.31 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 => ( ( Xphi @ Xx )
% 0.06/0.31 => ( nonempty
% 0.06/0.31 @ ( dsetconstr @ A
% 0.06/0.31 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(nonemptyI1_type,type,
% 0.06/0.31 nonemptyI1: $o ).
% 0.06/0.31
% 0.06/0.31 thf(nonemptyI1,definition,
% 0.06/0.31 ( nonemptyI1
% 0.06/0.31 = ( ! [A: $i] :
% 0.06/0.31 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.06/0.31 => ( nonempty @ A ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(setadjoinIL_type,type,
% 0.06/0.31 setadjoinIL: $o ).
% 0.06/0.31
% 0.06/0.31 thf(setadjoinIL,definition,
% 0.06/0.31 ( setadjoinIL
% 0.06/0.31 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(emptyinunitempty_type,type,
% 0.06/0.31 emptyinunitempty: $o ).
% 0.06/0.31
% 0.06/0.31 thf(emptyinunitempty,definition,
% 0.06/0.31 ( emptyinunitempty
% 0.06/0.31 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(setadjoinIR_type,type,
% 0.06/0.31 setadjoinIR: $o ).
% 0.06/0.31
% 0.06/0.31 thf(setadjoinIR,definition,
% 0.06/0.31 ( setadjoinIR
% 0.06/0.31 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.06/0.31 ( ( in @ Xy @ A )
% 0.06/0.31 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(setadjoinE_type,type,
% 0.06/0.31 setadjoinE: $o ).
% 0.06/0.31
% 0.06/0.31 thf(setadjoinE,definition,
% 0.06/0.31 ( setadjoinE
% 0.06/0.31 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.06/0.31 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.06/0.31 => ! [Xphi: $o] :
% 0.06/0.31 ( ( ( Xy = Xx )
% 0.06/0.31 => Xphi )
% 0.06/0.31 => ( ( ( in @ Xy @ A )
% 0.06/0.31 => Xphi )
% 0.06/0.31 => Xphi ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(setadjoinOr_type,type,
% 0.06/0.31 setadjoinOr: $o ).
% 0.06/0.31
% 0.06/0.31 thf(setadjoinOr,definition,
% 0.06/0.31 ( setadjoinOr
% 0.06/0.31 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.06/0.31 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.06/0.31 => ( ( Xy = Xx )
% 0.06/0.31 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(setoftrueEq_type,type,
% 0.06/0.31 setoftrueEq: $o ).
% 0.06/0.31
% 0.06/0.31 thf(setoftrueEq,definition,
% 0.06/0.31 ( setoftrueEq
% 0.06/0.31 = ( ! [A: $i] :
% 0.06/0.31 ( ( dsetconstr @ A
% 0.06/0.31 @ ^ [Xx: $i] : $true )
% 0.06/0.31 = A ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(powersetI_type,type,
% 0.06/0.31 powersetI: $o ).
% 0.06/0.31
% 0.06/0.31 thf(powersetI,definition,
% 0.06/0.31 ( powersetI
% 0.06/0.31 = ( ! [A: $i,B: $i] :
% 0.06/0.31 ( ! [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ B )
% 0.06/0.31 => ( in @ Xx @ A ) )
% 0.06/0.31 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(emptyinPowerset_type,type,
% 0.06/0.31 emptyinPowerset: $o ).
% 0.06/0.31
% 0.06/0.31 thf(emptyinPowerset,definition,
% 0.06/0.31 ( emptyinPowerset
% 0.06/0.31 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(emptyInPowerset_type,type,
% 0.06/0.31 emptyInPowerset: $o ).
% 0.06/0.31
% 0.06/0.31 thf(emptyInPowerset,definition,
% 0.06/0.31 ( emptyInPowerset
% 0.06/0.31 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(powersetE_type,type,
% 0.06/0.31 powersetE: $o ).
% 0.06/0.31
% 0.06/0.31 thf(powersetE,definition,
% 0.06/0.31 ( powersetE
% 0.06/0.31 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.31 ( ( in @ B @ ( powerset @ A ) )
% 0.06/0.31 => ( ( in @ Xx @ B )
% 0.06/0.31 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(setunionI_type,type,
% 0.06/0.31 setunionI: $o ).
% 0.06/0.31
% 0.06/0.31 thf(setunionI,definition,
% 0.06/0.31 ( setunionI
% 0.06/0.31 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.06/0.31 ( ( in @ Xx @ B )
% 0.06/0.31 => ( ( in @ B @ A )
% 0.06/0.31 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(setunionE_type,type,
% 0.06/0.31 setunionE: $o ).
% 0.06/0.31
% 0.06/0.31 thf(setunionE,definition,
% 0.06/0.31 ( setunionE
% 0.06/0.31 = ( ! [A: $i,Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ ( setunion @ A ) )
% 0.06/0.31 => ! [Xphi: $o] :
% 0.06/0.31 ( ! [B: $i] :
% 0.06/0.31 ( ( in @ Xx @ B )
% 0.06/0.31 => ( ( in @ B @ A )
% 0.06/0.31 => Xphi ) )
% 0.06/0.31 => Xphi ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(subPowSU_type,type,
% 0.06/0.31 subPowSU: $o ).
% 0.06/0.31
% 0.06/0.31 thf(subPowSU,definition,
% 0.06/0.31 ( subPowSU
% 0.06/0.31 = ( ! [A: $i,Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(exuE2_type,type,
% 0.06/0.31 exuE2: $o ).
% 0.06/0.31
% 0.06/0.31 thf(exuE2,definition,
% 0.06/0.31 ( exuE2
% 0.06/0.31 = ( ! [Xphi: $i > $o] :
% 0.06/0.31 ( ( exu
% 0.06/0.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.06/0.31 => ? [Xx: $i] :
% 0.06/0.31 ! [Xy: $i] :
% 0.06/0.31 ( ( Xphi @ Xy )
% 0.06/0.31 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(nonemptyImpWitness_type,type,
% 0.06/0.31 nonemptyImpWitness: $o ).
% 0.06/0.31
% 0.06/0.31 thf(nonemptyImpWitness,definition,
% 0.06/0.31 ( nonemptyImpWitness
% 0.06/0.31 = ( ! [A: $i] :
% 0.06/0.31 ( ( nonempty @ A )
% 0.06/0.31 => ? [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 & $true ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(uniqinunit_type,type,
% 0.06/0.31 uniqinunit: $o ).
% 0.06/0.31
% 0.06/0.31 thf(uniqinunit,definition,
% 0.06/0.31 ( uniqinunit
% 0.06/0.31 = ( ! [Xx: $i,Xy: $i] :
% 0.06/0.31 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.06/0.31 => ( Xx = Xy ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(notinsingleton_type,type,
% 0.06/0.31 notinsingleton: $o ).
% 0.06/0.31
% 0.06/0.31 thf(notinsingleton,definition,
% 0.06/0.31 ( notinsingleton
% 0.06/0.31 = ( ! [Xx: $i,Xy: $i] :
% 0.06/0.31 ( ( Xx != Xy )
% 0.06/0.31 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(eqinunit_type,type,
% 0.06/0.31 eqinunit: $o ).
% 0.06/0.31
% 0.06/0.31 thf(eqinunit,definition,
% 0.06/0.31 ( eqinunit
% 0.06/0.31 = ( ! [Xx: $i,Xy: $i] :
% 0.06/0.31 ( ( Xx = Xy )
% 0.06/0.31 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(singletonsswitch_type,type,
% 0.06/0.31 singletonsswitch: $o ).
% 0.06/0.31
% 0.06/0.31 thf(singletonsswitch,definition,
% 0.06/0.31 ( singletonsswitch
% 0.06/0.31 = ( ! [Xx: $i,Xy: $i] :
% 0.06/0.31 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.06/0.31 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(upairsetE_type,type,
% 0.06/0.31 upairsetE: $o ).
% 0.06/0.31
% 0.06/0.31 thf(upairsetE,definition,
% 0.06/0.31 ( upairsetE
% 0.06/0.31 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.06/0.31 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.06/0.31 => ( ( Xz = Xx )
% 0.06/0.31 | ( Xz = Xy ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(upairsetIL_type,type,
% 0.06/0.31 upairsetIL: $o ).
% 0.06/0.31
% 0.06/0.31 thf(upairsetIL,definition,
% 0.06/0.31 ( upairsetIL
% 0.06/0.31 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(upairsetIR_type,type,
% 0.06/0.31 upairsetIR: $o ).
% 0.06/0.31
% 0.06/0.31 thf(upairsetIR,definition,
% 0.06/0.31 ( upairsetIR
% 0.06/0.31 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(emptyE1_type,type,
% 0.06/0.31 emptyE1: $o ).
% 0.06/0.31
% 0.06/0.31 thf(emptyE1,definition,
% 0.06/0.31 ( emptyE1
% 0.06/0.31 = ( ! [A: $i,Xphi: $i > $o] :
% 0.06/0.31 ( ? [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 & ( Xphi @ Xx ) )
% 0.06/0.31 => ( ( ( dsetconstr @ A
% 0.06/0.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.06/0.31 = emptyset )
% 0.06/0.31 => $false ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(vacuousDall_type,type,
% 0.06/0.31 vacuousDall: $o ).
% 0.06/0.31
% 0.06/0.31 thf(vacuousDall,definition,
% 0.06/0.31 ( vacuousDall
% 0.06/0.31 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ emptyset )
% 0.06/0.31 => ( Xphi @ Xx ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(quantDeMorgan1_type,type,
% 0.06/0.31 quantDeMorgan1: $o ).
% 0.06/0.31
% 0.06/0.31 thf(quantDeMorgan1,definition,
% 0.06/0.31 ( quantDeMorgan1
% 0.06/0.31 = ( ! [A: $i,Xphi: $i > $o] :
% 0.06/0.31 ( ~ ! [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 => ( Xphi @ Xx ) )
% 0.06/0.31 => ? [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(quantDeMorgan2_type,type,
% 0.06/0.31 quantDeMorgan2: $o ).
% 0.06/0.31
% 0.06/0.31 thf(quantDeMorgan2,definition,
% 0.06/0.31 ( quantDeMorgan2
% 0.06/0.31 = ( ! [A: $i,Xphi: $i > $o] :
% 0.06/0.31 ( ! [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 => ~ ( Xphi @ Xx ) )
% 0.06/0.31 => ~ ? [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(quantDeMorgan3_type,type,
% 0.06/0.31 quantDeMorgan3: $o ).
% 0.06/0.31
% 0.06/0.31 thf(quantDeMorgan3,definition,
% 0.06/0.31 ( quantDeMorgan3
% 0.06/0.31 = ( ! [A: $i,Xphi: $i > $o] :
% 0.06/0.31 ( ~ ? [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 & ( Xphi @ Xx ) )
% 0.06/0.31 => ! [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(quantDeMorgan4_type,type,
% 0.06/0.31 quantDeMorgan4: $o ).
% 0.06/0.31
% 0.06/0.31 thf(quantDeMorgan4,definition,
% 0.06/0.31 ( quantDeMorgan4
% 0.06/0.31 = ( ! [A: $i,Xphi: $i > $o] :
% 0.06/0.31 ( ? [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 & ~ ( Xphi @ Xx ) )
% 0.06/0.31 => ~ ! [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(prop2setI_type,type,
% 0.06/0.31 prop2setI: $o ).
% 0.06/0.31
% 0.06/0.31 thf(prop2setI,definition,
% 0.06/0.31 ( prop2setI
% 0.06/0.31 = ( ! [Xphi: $o] :
% 0.06/0.31 ( Xphi
% 0.06/0.31 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(set2prop_type,type,
% 0.06/0.31 set2prop: $i > $o ).
% 0.06/0.31
% 0.06/0.31 thf(prop2set2propI_type,type,
% 0.06/0.31 prop2set2propI: $o ).
% 0.06/0.31
% 0.06/0.31 thf(prop2set2propI,definition,
% 0.06/0.31 ( prop2set2propI
% 0.06/0.31 = ( ! [Xphi: $o] :
% 0.06/0.31 ( Xphi
% 0.06/0.31 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(notdexE_type,type,
% 0.06/0.31 notdexE: $o ).
% 0.06/0.31
% 0.06/0.31 thf(notdexE,definition,
% 0.06/0.31 ( notdexE
% 0.06/0.31 = ( ! [A: $i,Xphi: $i > $o] :
% 0.06/0.31 ( ~ ? [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 & ( Xphi @ Xx ) )
% 0.06/0.31 => ! [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(notdallE_type,type,
% 0.06/0.31 notdallE: $o ).
% 0.06/0.31
% 0.06/0.31 thf(notdallE,definition,
% 0.06/0.31 ( notdallE
% 0.06/0.31 = ( ! [A: $i,Xphi: $i > $o] :
% 0.06/0.31 ( ~ ! [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 => ( Xphi @ Xx ) )
% 0.06/0.31 => ? [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(exuI1_type,type,
% 0.06/0.31 exuI1: $o ).
% 0.06/0.31
% 0.06/0.31 thf(exuI1,definition,
% 0.06/0.31 ( exuI1
% 0.06/0.31 = ( ! [Xphi: $i > $o] :
% 0.06/0.31 ( ? [Xx: $i] :
% 0.06/0.31 ( ( Xphi @ Xx )
% 0.06/0.31 & ! [Xy: $i] :
% 0.06/0.31 ( ( Xphi @ Xy )
% 0.06/0.31 => ( Xx = Xy ) ) )
% 0.06/0.31 => ( exu
% 0.06/0.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(exuI3_type,type,
% 0.06/0.31 exuI3: $o ).
% 0.06/0.31
% 0.06/0.31 thf(exuI3,definition,
% 0.06/0.31 ( exuI3
% 0.06/0.31 = ( ! [Xphi: $i > $o] :
% 0.06/0.31 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.06/0.31 => ( ! [Xx: $i,Xy: $i] :
% 0.06/0.31 ( ( Xphi @ Xx )
% 0.06/0.31 => ( ( Xphi @ Xy )
% 0.06/0.31 => ( Xx = Xy ) ) )
% 0.06/0.31 => ( exu
% 0.06/0.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(exuI2_type,type,
% 0.06/0.31 exuI2: $o ).
% 0.06/0.31
% 0.06/0.31 thf(exuI2,definition,
% 0.06/0.31 ( exuI2
% 0.06/0.31 = ( ! [Xphi: $i > $o] :
% 0.06/0.31 ( ? [Xx: $i] :
% 0.06/0.31 ! [Xy: $i] :
% 0.06/0.31 ( ( Xphi @ Xy )
% 0.06/0.31 <=> ( Xy = Xx ) )
% 0.06/0.31 => ( exu
% 0.06/0.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(inCongP_type,type,
% 0.06/0.31 inCongP: $o ).
% 0.06/0.31
% 0.06/0.31 thf(inCongP,definition,
% 0.06/0.31 ( inCongP
% 0.06/0.31 = ( ! [A: $i,B: $i] :
% 0.06/0.31 ( ( A = B )
% 0.06/0.31 => ! [Xx: $i,Xy: $i] :
% 0.06/0.31 ( ( Xx = Xy )
% 0.06/0.31 => ( ( in @ Xx @ A )
% 0.06/0.31 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(in__Cong_type,type,
% 0.06/0.31 in__Cong: $o ).
% 0.06/0.31
% 0.06/0.31 thf(in__Cong,definition,
% 0.06/0.31 ( in__Cong
% 0.06/0.31 = ( ! [A: $i,B: $i] :
% 0.06/0.31 ( ( A = B )
% 0.06/0.31 => ! [Xx: $i,Xy: $i] :
% 0.06/0.31 ( ( Xx = Xy )
% 0.06/0.31 => ( ( in @ Xx @ A )
% 0.06/0.31 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(exuE3u_type,type,
% 0.06/0.31 exuE3u: $o ).
% 0.06/0.31
% 0.06/0.31 thf(exuE3u,definition,
% 0.06/0.31 ( exuE3u
% 0.06/0.31 = ( ! [Xphi: $i > $o] :
% 0.06/0.31 ( ( exu
% 0.06/0.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.06/0.31 => ! [Xx: $i,Xy: $i] :
% 0.06/0.31 ( ( Xphi @ Xx )
% 0.06/0.31 => ( ( Xphi @ Xy )
% 0.06/0.31 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(exu__Cong_type,type,
% 0.06/0.31 exu__Cong: $o ).
% 0.06/0.31
% 0.06/0.31 thf(exu__Cong,definition,
% 0.06/0.31 ( exu__Cong
% 0.06/0.31 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.06/0.31 ( ! [Xx: $i,Xy: $i] :
% 0.06/0.31 ( ( Xx = Xy )
% 0.06/0.31 => ( ( Xphi @ Xx )
% 0.06/0.31 <=> ( Xpsi @ Xy ) ) )
% 0.06/0.31 => ( ( exu
% 0.06/0.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.06/0.31 <=> ( exu
% 0.06/0.31 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(emptyset__Cong_type,type,
% 0.06/0.31 emptyset__Cong: $o ).
% 0.06/0.31
% 0.06/0.31 thf(emptyset__Cong,definition,
% 0.06/0.31 ( emptyset__Cong
% 0.06/0.31 = ( emptyset = emptyset ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(setadjoin__Cong_type,type,
% 0.06/0.31 setadjoin__Cong: $o ).
% 0.06/0.31
% 0.06/0.31 thf(setadjoin__Cong,definition,
% 0.06/0.31 ( setadjoin__Cong
% 0.06/0.31 = ( ! [Xx: $i,Xy: $i] :
% 0.06/0.31 ( ( Xx = Xy )
% 0.06/0.31 => ! [Xz: $i,Xu: $i] :
% 0.06/0.31 ( ( Xz = Xu )
% 0.06/0.31 => ( ( setadjoin @ Xx @ Xz )
% 0.06/0.31 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(powerset__Cong_type,type,
% 0.06/0.31 powerset__Cong: $o ).
% 0.06/0.31
% 0.06/0.31 thf(powerset__Cong,definition,
% 0.06/0.31 ( powerset__Cong
% 0.06/0.31 = ( ! [A: $i,B: $i] :
% 0.06/0.31 ( ( A = B )
% 0.06/0.31 => ( ( powerset @ A )
% 0.06/0.31 = ( powerset @ B ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(setunion__Cong_type,type,
% 0.06/0.31 setunion__Cong: $o ).
% 0.06/0.31
% 0.06/0.31 thf(setunion__Cong,definition,
% 0.06/0.31 ( setunion__Cong
% 0.06/0.31 = ( ! [A: $i,B: $i] :
% 0.06/0.31 ( ( A = B )
% 0.06/0.31 => ( ( setunion @ A )
% 0.06/0.31 = ( setunion @ B ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(omega__Cong_type,type,
% 0.06/0.31 omega__Cong: $o ).
% 0.06/0.31
% 0.06/0.31 thf(omega__Cong,definition,
% 0.06/0.31 ( omega__Cong
% 0.06/0.31 = ( omega = omega ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(exuEu_type,type,
% 0.06/0.31 exuEu: $o ).
% 0.06/0.31
% 0.06/0.31 thf(exuEu,definition,
% 0.06/0.31 ( exuEu
% 0.06/0.31 = ( ! [Xphi: $i > $o] :
% 0.06/0.31 ( ( exu
% 0.06/0.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.06/0.31 => ! [Xx: $i,Xy: $i] :
% 0.06/0.31 ( ( Xphi @ Xx )
% 0.06/0.31 => ( ( Xphi @ Xy )
% 0.06/0.31 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(descr__Cong_type,type,
% 0.06/0.31 descr__Cong: $o ).
% 0.06/0.31
% 0.06/0.31 thf(descr__Cong,definition,
% 0.06/0.31 ( descr__Cong
% 0.06/0.31 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.06/0.31 ( ! [Xx: $i,Xy: $i] :
% 0.06/0.31 ( ( Xx = Xy )
% 0.06/0.31 => ( ( Xphi @ Xx )
% 0.06/0.31 <=> ( Xpsi @ Xy ) ) )
% 0.06/0.31 => ( ( exu
% 0.06/0.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.06/0.31 => ( ( exu
% 0.06/0.31 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.06/0.31 => ( ( descr
% 0.06/0.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.06/0.31 = ( descr
% 0.06/0.31 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(dsetconstr__Cong_type,type,
% 0.06/0.31 dsetconstr__Cong: $o ).
% 0.06/0.31
% 0.06/0.31 thf(dsetconstr__Cong,definition,
% 0.06/0.31 ( dsetconstr__Cong
% 0.06/0.31 = ( ! [A: $i,B: $i] :
% 0.06/0.31 ( ( A = B )
% 0.06/0.31 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.06/0.31 ( ! [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 => ! [Xy: $i] :
% 0.06/0.31 ( ( in @ Xy @ B )
% 0.06/0.31 => ( ( Xx = Xy )
% 0.06/0.31 => ( ( Xphi @ Xx )
% 0.06/0.31 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.06/0.31 => ( ( dsetconstr @ A
% 0.06/0.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.06/0.31 = ( dsetconstr @ B
% 0.06/0.31 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(subset_type,type,
% 0.06/0.31 subset: $i > $i > $o ).
% 0.06/0.31
% 0.06/0.31 thf(disjoint_type,type,
% 0.06/0.31 disjoint: $i > $i > $o ).
% 0.06/0.31
% 0.06/0.31 thf(setsmeet_type,type,
% 0.06/0.31 setsmeet: $i > $i > $o ).
% 0.06/0.31
% 0.06/0.31 thf(subsetI1_type,type,
% 0.06/0.31 subsetI1: $o ).
% 0.06/0.31
% 0.06/0.31 thf(subsetI1,definition,
% 0.06/0.31 ( subsetI1
% 0.06/0.31 = ( ! [A: $i,B: $i] :
% 0.06/0.31 ( ! [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 => ( in @ Xx @ B ) )
% 0.06/0.31 => ( subset @ A @ B ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(eqimpsubset2_type,type,
% 0.06/0.31 eqimpsubset2: $o ).
% 0.06/0.31
% 0.06/0.31 thf(eqimpsubset2,definition,
% 0.06/0.31 ( eqimpsubset2
% 0.06/0.31 = ( ! [A: $i,B: $i] :
% 0.06/0.31 ( ( A = B )
% 0.06/0.31 => ( subset @ B @ A ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(eqimpsubset1_type,type,
% 0.06/0.31 eqimpsubset1: $o ).
% 0.06/0.31
% 0.06/0.31 thf(eqimpsubset1,definition,
% 0.06/0.31 ( eqimpsubset1
% 0.06/0.31 = ( ! [A: $i,B: $i] :
% 0.06/0.31 ( ( A = B )
% 0.06/0.31 => ( subset @ A @ B ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(subsetI2_type,type,
% 0.06/0.31 subsetI2: $o ).
% 0.06/0.31
% 0.06/0.31 thf(subsetI2,definition,
% 0.06/0.31 ( subsetI2
% 0.06/0.31 = ( ! [A: $i,B: $i] :
% 0.06/0.31 ( ! [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 => ( in @ Xx @ B ) )
% 0.06/0.31 => ( subset @ A @ B ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(emptysetsubset_type,type,
% 0.06/0.31 emptysetsubset: $o ).
% 0.06/0.31
% 0.06/0.31 thf(emptysetsubset,definition,
% 0.06/0.31 ( emptysetsubset
% 0.06/0.31 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(subsetE_type,type,
% 0.06/0.31 subsetE: $o ).
% 0.06/0.31
% 0.06/0.31 thf(subsetE,definition,
% 0.06/0.31 ( subsetE
% 0.06/0.31 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.31 ( ( subset @ A @ B )
% 0.06/0.31 => ( ( in @ Xx @ A )
% 0.06/0.31 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(subsetE2_type,type,
% 0.06/0.31 subsetE2: $o ).
% 0.06/0.31
% 0.06/0.31 thf(subsetE2,definition,
% 0.06/0.31 ( subsetE2
% 0.06/0.31 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.31 ( ( subset @ A @ B )
% 0.06/0.31 => ( ~ ( in @ Xx @ B )
% 0.06/0.31 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(notsubsetI_type,type,
% 0.06/0.31 notsubsetI: $o ).
% 0.06/0.31
% 0.06/0.31 thf(notsubsetI,definition,
% 0.06/0.31 ( notsubsetI
% 0.06/0.31 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 => ( ~ ( in @ Xx @ B )
% 0.06/0.31 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(notequalI1_type,type,
% 0.06/0.31 notequalI1: $o ).
% 0.06/0.31
% 0.06/0.31 thf(notequalI1,definition,
% 0.06/0.31 ( notequalI1
% 0.06/0.31 = ( ! [A: $i,B: $i] :
% 0.06/0.31 ( ~ ( subset @ A @ B )
% 0.06/0.31 => ( A != B ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(notequalI2_type,type,
% 0.06/0.31 notequalI2: $o ).
% 0.06/0.31
% 0.06/0.31 thf(notequalI2,definition,
% 0.06/0.31 ( notequalI2
% 0.06/0.31 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 => ( ~ ( in @ Xx @ B )
% 0.06/0.31 => ( A != B ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(subsetRefl_type,type,
% 0.06/0.31 subsetRefl: $o ).
% 0.06/0.31
% 0.06/0.31 thf(subsetRefl,definition,
% 0.06/0.31 ( subsetRefl
% 0.06/0.31 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(subsetTrans_type,type,
% 0.06/0.31 subsetTrans: $o ).
% 0.06/0.31
% 0.06/0.31 thf(subsetTrans,definition,
% 0.06/0.31 ( subsetTrans
% 0.06/0.31 = ( ! [A: $i,B: $i,C: $i] :
% 0.06/0.31 ( ( subset @ A @ B )
% 0.06/0.31 => ( ( subset @ B @ C )
% 0.06/0.31 => ( subset @ A @ C ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(setadjoinSub_type,type,
% 0.06/0.31 setadjoinSub: $o ).
% 0.06/0.31
% 0.06/0.31 thf(setadjoinSub,definition,
% 0.06/0.31 ( setadjoinSub
% 0.06/0.31 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(setadjoinSub2_type,type,
% 0.06/0.31 setadjoinSub2: $o ).
% 0.06/0.31
% 0.06/0.31 thf(setadjoinSub2,definition,
% 0.06/0.31 ( setadjoinSub2
% 0.06/0.31 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.06/0.31 ( ( subset @ A @ B )
% 0.06/0.31 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(subset2powerset_type,type,
% 0.06/0.31 subset2powerset: $o ).
% 0.06/0.31
% 0.06/0.31 thf(subset2powerset,definition,
% 0.06/0.31 ( subset2powerset
% 0.06/0.31 = ( ! [A: $i,B: $i] :
% 0.06/0.31 ( ( subset @ A @ B )
% 0.06/0.31 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(setextsub_type,type,
% 0.06/0.31 setextsub: $o ).
% 0.06/0.31
% 0.06/0.31 thf(setextsub,definition,
% 0.06/0.31 ( setextsub
% 0.06/0.31 = ( ! [A: $i,B: $i] :
% 0.06/0.31 ( ( subset @ A @ B )
% 0.06/0.31 => ( ( subset @ B @ A )
% 0.06/0.31 => ( A = B ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(subsetemptysetimpeq_type,type,
% 0.06/0.31 subsetemptysetimpeq: $o ).
% 0.06/0.31
% 0.06/0.31 thf(subsetemptysetimpeq,definition,
% 0.06/0.31 ( subsetemptysetimpeq
% 0.06/0.31 = ( ! [A: $i] :
% 0.06/0.31 ( ( subset @ A @ emptyset )
% 0.06/0.31 => ( A = emptyset ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(powersetI1_type,type,
% 0.06/0.31 powersetI1: $o ).
% 0.06/0.31
% 0.06/0.31 thf(powersetI1,definition,
% 0.06/0.31 ( powersetI1
% 0.06/0.31 = ( ! [A: $i,B: $i] :
% 0.06/0.31 ( ( subset @ B @ A )
% 0.06/0.31 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(powersetE1_type,type,
% 0.06/0.31 powersetE1: $o ).
% 0.06/0.31
% 0.06/0.31 thf(powersetE1,definition,
% 0.06/0.31 ( powersetE1
% 0.06/0.31 = ( ! [A: $i,B: $i] :
% 0.06/0.31 ( ( in @ B @ ( powerset @ A ) )
% 0.06/0.31 => ( subset @ B @ A ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(inPowerset_type,type,
% 0.06/0.31 inPowerset: $o ).
% 0.06/0.31
% 0.06/0.31 thf(inPowerset,definition,
% 0.06/0.31 ( inPowerset
% 0.06/0.31 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(powersetsubset_type,type,
% 0.06/0.31 powersetsubset: $o ).
% 0.06/0.31
% 0.06/0.31 thf(powersetsubset,definition,
% 0.06/0.31 ( powersetsubset
% 0.06/0.31 = ( ! [A: $i,B: $i] :
% 0.06/0.31 ( ( subset @ A @ B )
% 0.06/0.31 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(sepInPowerset_type,type,
% 0.06/0.31 sepInPowerset: $o ).
% 0.06/0.31
% 0.06/0.31 thf(sepInPowerset,definition,
% 0.06/0.31 ( sepInPowerset
% 0.06/0.31 = ( ! [A: $i,Xphi: $i > $o] :
% 0.06/0.31 ( in
% 0.06/0.31 @ ( dsetconstr @ A
% 0.06/0.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.06/0.31 @ ( powerset @ A ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(sepSubset_type,type,
% 0.06/0.31 sepSubset: $o ).
% 0.06/0.31
% 0.06/0.31 thf(sepSubset,definition,
% 0.06/0.31 ( sepSubset
% 0.06/0.31 = ( ! [A: $i,Xphi: $i > $o] :
% 0.06/0.31 ( subset
% 0.06/0.31 @ ( dsetconstr @ A
% 0.06/0.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.06/0.31 @ A ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(binunion_type,type,
% 0.06/0.31 binunion: $i > $i > $i ).
% 0.06/0.31
% 0.06/0.31 thf(binunionIL_type,type,
% 0.06/0.31 binunionIL: $o ).
% 0.06/0.31
% 0.06/0.31 thf(binunionIL,definition,
% 0.06/0.31 ( binunionIL
% 0.06/0.31 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(upairset2IR_type,type,
% 0.06/0.31 upairset2IR: $o ).
% 0.06/0.31
% 0.06/0.31 thf(upairset2IR,definition,
% 0.06/0.31 ( upairset2IR
% 0.06/0.31 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(binunionIR_type,type,
% 0.06/0.31 binunionIR: $o ).
% 0.06/0.31
% 0.06/0.31 thf(binunionIR,definition,
% 0.06/0.31 ( binunionIR
% 0.06/0.31 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ B )
% 0.06/0.31 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(binunionEcases_type,type,
% 0.06/0.31 binunionEcases: $o ).
% 0.06/0.31
% 0.06/0.31 thf(binunionEcases,definition,
% 0.06/0.31 ( binunionEcases
% 0.06/0.31 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.06/0.31 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.06/0.31 => ( ( ( in @ Xx @ A )
% 0.06/0.31 => Xphi )
% 0.06/0.31 => ( ( ( in @ Xx @ B )
% 0.06/0.31 => Xphi )
% 0.06/0.31 => Xphi ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(binunionE_type,type,
% 0.06/0.31 binunionE: $o ).
% 0.06/0.31
% 0.06/0.31 thf(binunionE,definition,
% 0.06/0.31 ( binunionE
% 0.06/0.31 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.06/0.31 => ( ( in @ Xx @ A )
% 0.06/0.31 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(binunionLsub_type,type,
% 0.06/0.31 binunionLsub: $o ).
% 0.06/0.31
% 0.06/0.31 thf(binunionLsub,definition,
% 0.06/0.31 ( binunionLsub
% 0.06/0.31 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(binunionRsub_type,type,
% 0.06/0.31 binunionRsub: $o ).
% 0.06/0.31
% 0.06/0.31 thf(binunionRsub,definition,
% 0.06/0.31 ( binunionRsub
% 0.06/0.31 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(binintersect_type,type,
% 0.06/0.31 binintersect: $i > $i > $i ).
% 0.06/0.31
% 0.06/0.31 thf(binintersectI_type,type,
% 0.06/0.31 binintersectI: $o ).
% 0.06/0.31
% 0.06/0.31 thf(binintersectI,definition,
% 0.06/0.31 ( binintersectI
% 0.06/0.31 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 => ( ( in @ Xx @ B )
% 0.06/0.31 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(binintersectSubset5_type,type,
% 0.06/0.31 binintersectSubset5: $o ).
% 0.06/0.31
% 0.06/0.31 thf(binintersectSubset5,definition,
% 0.06/0.31 ( binintersectSubset5
% 0.06/0.31 = ( ! [A: $i,B: $i,C: $i] :
% 0.06/0.31 ( ( subset @ C @ A )
% 0.06/0.31 => ( ( subset @ C @ B )
% 0.06/0.31 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(binintersectEL_type,type,
% 0.06/0.31 binintersectEL: $o ).
% 0.06/0.31
% 0.06/0.31 thf(binintersectEL,definition,
% 0.06/0.31 ( binintersectEL
% 0.06/0.31 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.06/0.31 => ( in @ Xx @ A ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(binintersectLsub_type,type,
% 0.06/0.31 binintersectLsub: $o ).
% 0.06/0.31
% 0.06/0.31 thf(binintersectLsub,definition,
% 0.06/0.31 ( binintersectLsub
% 0.06/0.31 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(binintersectSubset2_type,type,
% 0.06/0.31 binintersectSubset2: $o ).
% 0.06/0.31
% 0.06/0.31 thf(binintersectSubset2,definition,
% 0.06/0.31 ( binintersectSubset2
% 0.06/0.31 = ( ! [A: $i,B: $i] :
% 0.06/0.31 ( ( subset @ A @ B )
% 0.06/0.31 => ( ( binintersect @ A @ B )
% 0.06/0.31 = A ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(binintersectSubset3_type,type,
% 0.06/0.31 binintersectSubset3: $o ).
% 0.06/0.31
% 0.06/0.31 thf(binintersectSubset3,definition,
% 0.06/0.31 ( binintersectSubset3
% 0.06/0.31 = ( ! [A: $i,B: $i] :
% 0.06/0.31 ( ( ( binintersect @ A @ B )
% 0.06/0.31 = B )
% 0.06/0.31 => ( subset @ B @ A ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(binintersectER_type,type,
% 0.06/0.31 binintersectER: $o ).
% 0.06/0.31
% 0.06/0.31 thf(binintersectER,definition,
% 0.06/0.31 ( binintersectER
% 0.06/0.31 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.06/0.31 => ( in @ Xx @ B ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(disjointsetsI1_type,type,
% 0.06/0.31 disjointsetsI1: $o ).
% 0.06/0.31
% 0.06/0.31 thf(disjointsetsI1,definition,
% 0.06/0.31 ( disjointsetsI1
% 0.06/0.31 = ( ! [A: $i,B: $i] :
% 0.06/0.31 ( ~ ? [Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 & ( in @ Xx @ B ) )
% 0.06/0.31 => ( ( binintersect @ A @ B )
% 0.06/0.31 = emptyset ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(binintersectRsub_type,type,
% 0.06/0.31 binintersectRsub: $o ).
% 0.06/0.31
% 0.06/0.31 thf(binintersectRsub,definition,
% 0.06/0.31 ( binintersectRsub
% 0.06/0.31 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(binintersectSubset4_type,type,
% 0.06/0.31 binintersectSubset4: $o ).
% 0.06/0.31
% 0.06/0.31 thf(binintersectSubset4,definition,
% 0.06/0.31 ( binintersectSubset4
% 0.06/0.31 = ( ! [A: $i,B: $i] :
% 0.06/0.31 ( ( subset @ B @ A )
% 0.06/0.31 => ( ( binintersect @ A @ B )
% 0.06/0.31 = B ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(binintersectSubset1_type,type,
% 0.06/0.31 binintersectSubset1: $o ).
% 0.06/0.31
% 0.06/0.31 thf(binintersectSubset1,definition,
% 0.06/0.31 ( binintersectSubset1
% 0.06/0.31 = ( ! [A: $i,B: $i] :
% 0.06/0.31 ( ( ( binintersect @ A @ B )
% 0.06/0.31 = A )
% 0.06/0.31 => ( subset @ A @ B ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(bs114d_type,type,
% 0.06/0.31 bs114d: $o ).
% 0.06/0.31
% 0.06/0.31 thf(bs114d,definition,
% 0.06/0.31 ( bs114d
% 0.06/0.31 = ( ! [A: $i,B: $i,C: $i] :
% 0.06/0.31 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.06/0.31 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.06/0.31
% 0.06/0.31 thf(regular_type,type,
% 0.06/0.31 regular: $i > $o ).
% 0.06/0.31
% 0.06/0.31 thf(setminus_type,type,
% 0.06/0.31 setminus: $i > $i > $i ).
% 0.06/0.31
% 0.06/0.31 thf(setminusI_type,type,
% 0.06/0.31 setminusI: $o ).
% 0.06/0.31
% 0.06/0.31 thf(setminusI,definition,
% 0.06/0.31 ( setminusI
% 0.06/0.31 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.31 ( ( in @ Xx @ A )
% 0.06/0.31 => ( ~ ( in @ Xx @ B )
% 0.06/0.31 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(setminusEL_type,type,
% 0.06/0.32 setminusEL: $o ).
% 0.06/0.32
% 0.06/0.32 thf(setminusEL,definition,
% 0.06/0.32 ( setminusEL
% 0.06/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.06/0.32 => ( in @ Xx @ A ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(setminusER_type,type,
% 0.06/0.32 setminusER: $o ).
% 0.06/0.32
% 0.06/0.32 thf(setminusER,definition,
% 0.06/0.32 ( setminusER
% 0.06/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.06/0.32 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(setminusSubset2_type,type,
% 0.06/0.32 setminusSubset2: $o ).
% 0.06/0.32
% 0.06/0.32 thf(setminusSubset2,definition,
% 0.06/0.32 ( setminusSubset2
% 0.06/0.32 = ( ! [A: $i,B: $i] :
% 0.06/0.32 ( ( subset @ A @ B )
% 0.06/0.32 => ( ( setminus @ A @ B )
% 0.06/0.32 = emptyset ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(setminusERneg_type,type,
% 0.06/0.32 setminusERneg: $o ).
% 0.06/0.32
% 0.06/0.32 thf(setminusERneg,definition,
% 0.06/0.32 ( setminusERneg
% 0.06/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.32 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.06/0.32 => ( ( in @ Xx @ A )
% 0.06/0.32 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(setminusELneg_type,type,
% 0.06/0.32 setminusELneg: $o ).
% 0.06/0.32
% 0.06/0.32 thf(setminusELneg,definition,
% 0.06/0.32 ( setminusELneg
% 0.06/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.32 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.06/0.32 => ( ~ ( in @ Xx @ B )
% 0.06/0.32 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(setminusILneg_type,type,
% 0.06/0.32 setminusILneg: $o ).
% 0.06/0.32
% 0.06/0.32 thf(setminusILneg,definition,
% 0.06/0.32 ( setminusILneg
% 0.06/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.32 ( ~ ( in @ Xx @ A )
% 0.06/0.32 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(setminusIRneg_type,type,
% 0.06/0.32 setminusIRneg: $o ).
% 0.06/0.32
% 0.06/0.32 thf(setminusIRneg,definition,
% 0.06/0.32 ( setminusIRneg
% 0.06/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ B )
% 0.06/0.32 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(setminusLsub_type,type,
% 0.06/0.32 setminusLsub: $o ).
% 0.06/0.32
% 0.06/0.32 thf(setminusLsub,definition,
% 0.06/0.32 ( setminusLsub
% 0.06/0.32 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(setminusSubset1_type,type,
% 0.06/0.32 setminusSubset1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(setminusSubset1,definition,
% 0.06/0.32 ( setminusSubset1
% 0.06/0.32 = ( ! [A: $i,B: $i] :
% 0.06/0.32 ( ( ( setminus @ A @ B )
% 0.06/0.32 = emptyset )
% 0.06/0.32 => ( subset @ A @ B ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(symdiff_type,type,
% 0.06/0.32 symdiff: $i > $i > $i ).
% 0.06/0.32
% 0.06/0.32 thf(symdiffE_type,type,
% 0.06/0.32 symdiffE: $o ).
% 0.06/0.32
% 0.06/0.32 thf(symdiffE,definition,
% 0.06/0.32 ( symdiffE
% 0.06/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.06/0.32 => ! [Xphi: $o] :
% 0.06/0.32 ( ( ( in @ Xx @ A )
% 0.06/0.32 => ( ~ ( in @ Xx @ B )
% 0.06/0.32 => Xphi ) )
% 0.06/0.32 => ( ( ~ ( in @ Xx @ A )
% 0.06/0.32 => ( ( in @ Xx @ B )
% 0.06/0.32 => Xphi ) )
% 0.06/0.32 => Xphi ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(symdiffI1_type,type,
% 0.06/0.32 symdiffI1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(symdiffI1,definition,
% 0.06/0.32 ( symdiffI1
% 0.06/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ~ ( in @ Xx @ B )
% 0.06/0.32 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(symdiffI2_type,type,
% 0.06/0.32 symdiffI2: $o ).
% 0.06/0.32
% 0.06/0.32 thf(symdiffI2,definition,
% 0.06/0.32 ( symdiffI2
% 0.06/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.32 ( ~ ( in @ Xx @ A )
% 0.06/0.32 => ( ( in @ Xx @ B )
% 0.06/0.32 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(symdiffIneg1_type,type,
% 0.06/0.32 symdiffIneg1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(symdiffIneg1,definition,
% 0.06/0.32 ( symdiffIneg1
% 0.06/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( in @ Xx @ B )
% 0.06/0.32 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(symdiffIneg2_type,type,
% 0.06/0.32 symdiffIneg2: $o ).
% 0.06/0.32
% 0.06/0.32 thf(symdiffIneg2,definition,
% 0.06/0.32 ( symdiffIneg2
% 0.06/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.32 ( ~ ( in @ Xx @ A )
% 0.06/0.32 => ( ~ ( in @ Xx @ B )
% 0.06/0.32 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(iskpair_type,type,
% 0.06/0.32 iskpair: $i > $o ).
% 0.06/0.32
% 0.06/0.32 thf(secondinupair_type,type,
% 0.06/0.32 secondinupair: $o ).
% 0.06/0.32
% 0.06/0.32 thf(secondinupair,definition,
% 0.06/0.32 ( secondinupair
% 0.06/0.32 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(setukpairIL_type,type,
% 0.06/0.32 setukpairIL: $o ).
% 0.06/0.32
% 0.06/0.32 thf(setukpairIL,definition,
% 0.06/0.32 ( setukpairIL
% 0.06/0.32 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(setukpairIR_type,type,
% 0.06/0.32 setukpairIR: $o ).
% 0.06/0.32
% 0.06/0.32 thf(setukpairIR,definition,
% 0.06/0.32 ( setukpairIR
% 0.06/0.32 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(kpairiskpair_type,type,
% 0.06/0.32 kpairiskpair: $o ).
% 0.06/0.32
% 0.06/0.32 thf(kpairiskpair,definition,
% 0.06/0.32 ( kpairiskpair
% 0.06/0.32 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(kpair_type,type,
% 0.06/0.32 kpair: $i > $i > $i ).
% 0.06/0.32
% 0.06/0.32 thf(kpairp_type,type,
% 0.06/0.32 kpairp: $o ).
% 0.06/0.32
% 0.06/0.32 thf(kpairp,definition,
% 0.06/0.32 ( kpairp
% 0.06/0.32 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(cartprod_type,type,
% 0.06/0.32 cartprod: $i > $i > $i ).
% 0.06/0.32
% 0.06/0.32 thf(singletonsubset_type,type,
% 0.06/0.32 singletonsubset: $o ).
% 0.06/0.32
% 0.06/0.32 thf(singletonsubset,definition,
% 0.06/0.32 ( singletonsubset
% 0.06/0.32 = ( ! [A: $i,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(singletoninpowerset_type,type,
% 0.06/0.32 singletoninpowerset: $o ).
% 0.06/0.32
% 0.06/0.32 thf(singletoninpowerset,definition,
% 0.06/0.32 ( singletoninpowerset
% 0.06/0.32 = ( ! [A: $i,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(singletoninpowunion_type,type,
% 0.06/0.32 singletoninpowunion: $o ).
% 0.06/0.32
% 0.06/0.32 thf(singletoninpowunion,definition,
% 0.06/0.32 ( singletoninpowunion
% 0.06/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(upairset2E_type,type,
% 0.06/0.32 upairset2E: $o ).
% 0.06/0.32
% 0.06/0.32 thf(upairset2E,definition,
% 0.06/0.32 ( upairset2E
% 0.06/0.32 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.06/0.32 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.06/0.32 => ( ( Xz = Xx )
% 0.06/0.32 | ( Xz = Xy ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(upairsubunion_type,type,
% 0.06/0.32 upairsubunion: $o ).
% 0.06/0.32
% 0.06/0.32 thf(upairsubunion,definition,
% 0.06/0.32 ( upairsubunion
% 0.06/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ B )
% 0.06/0.32 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(upairinpowunion_type,type,
% 0.06/0.32 upairinpowunion: $o ).
% 0.06/0.32
% 0.06/0.32 thf(upairinpowunion,definition,
% 0.06/0.32 ( upairinpowunion
% 0.06/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ B )
% 0.06/0.32 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(ubforcartprodlem1_type,type,
% 0.06/0.32 ubforcartprodlem1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(ubforcartprodlem1,definition,
% 0.06/0.32 ( ubforcartprodlem1
% 0.06/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ B )
% 0.06/0.32 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(ubforcartprodlem2_type,type,
% 0.06/0.32 ubforcartprodlem2: $o ).
% 0.06/0.32
% 0.06/0.32 thf(ubforcartprodlem2,definition,
% 0.06/0.32 ( ubforcartprodlem2
% 0.06/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ B )
% 0.06/0.32 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(ubforcartprodlem3_type,type,
% 0.06/0.32 ubforcartprodlem3: $o ).
% 0.06/0.32
% 0.06/0.32 thf(ubforcartprodlem3,definition,
% 0.06/0.32 ( ubforcartprodlem3
% 0.06/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ B )
% 0.06/0.32 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(cartprodpairin_type,type,
% 0.06/0.32 cartprodpairin: $o ).
% 0.06/0.32
% 0.06/0.32 thf(cartprodpairin,definition,
% 0.06/0.32 ( cartprodpairin
% 0.06/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ B )
% 0.06/0.32 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(cartprodmempair1_type,type,
% 0.06/0.32 cartprodmempair1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(cartprodmempair1,definition,
% 0.06/0.32 ( cartprodmempair1
% 0.06/0.32 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.06/0.32 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.06/0.32 => ? [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 & ? [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ B )
% 0.06/0.32 & ( Xu
% 0.06/0.32 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(cartprodmempair_type,type,
% 0.06/0.32 cartprodmempair: $o ).
% 0.06/0.32
% 0.06/0.32 thf(cartprodmempair,definition,
% 0.06/0.32 ( cartprodmempair
% 0.06/0.32 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.06/0.32 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.06/0.32 => ( iskpair @ Xu ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(setunionE2_type,type,
% 0.06/0.32 setunionE2: $o ).
% 0.06/0.32
% 0.06/0.32 thf(setunionE2,definition,
% 0.06/0.32 ( setunionE2
% 0.06/0.32 = ( ! [A: $i,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ ( setunion @ A ) )
% 0.06/0.32 => ? [X: $i] :
% 0.06/0.32 ( ( in @ X @ A )
% 0.06/0.32 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(setunionsingleton1_type,type,
% 0.06/0.32 setunionsingleton1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(setunionsingleton1,definition,
% 0.06/0.32 ( setunionsingleton1
% 0.06/0.32 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(setunionsingleton2_type,type,
% 0.06/0.32 setunionsingleton2: $o ).
% 0.06/0.32
% 0.06/0.32 thf(setunionsingleton2,definition,
% 0.06/0.32 ( setunionsingleton2
% 0.06/0.32 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(setunionsingleton_type,type,
% 0.06/0.32 setunionsingleton: $o ).
% 0.06/0.32
% 0.06/0.32 thf(setunionsingleton,definition,
% 0.06/0.32 ( setunionsingleton
% 0.06/0.32 = ( ! [Xx: $i] :
% 0.06/0.32 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.06/0.32 = Xx ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(singleton_type,type,
% 0.06/0.32 singleton: $i > $o ).
% 0.06/0.32
% 0.06/0.32 thf(singletonprop_type,type,
% 0.06/0.32 singletonprop: $o ).
% 0.06/0.32
% 0.06/0.32 thf(singletonprop,definition,
% 0.06/0.32 ( singletonprop
% 0.06/0.32 = ( ! [A: $i,Xphi: $i > $o] :
% 0.06/0.32 ( ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ A )
% 0.06/0.32 => ( ( Xphi @ Xx )
% 0.06/0.32 => ( ( Xphi @ Xy )
% 0.06/0.32 => ( Xx = Xy ) ) ) ) )
% 0.06/0.32 => ( ? [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 & ( Xphi @ Xx ) )
% 0.06/0.32 => ( singleton
% 0.06/0.32 @ ( dsetconstr @ A
% 0.06/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(ex1_type,type,
% 0.06/0.32 ex1: $i > ( $i > $o ) > $o ).
% 0.06/0.32
% 0.06/0.32 thf(ex1E1_type,type,
% 0.06/0.32 ex1E1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(ex1E1,definition,
% 0.06/0.32 ( ex1E1
% 0.06/0.32 = ( ! [A: $i,Xphi: $i > $o] :
% 0.06/0.32 ( ( ex1 @ A
% 0.06/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.06/0.32 => ? [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(ex1I_type,type,
% 0.06/0.32 ex1I: $o ).
% 0.06/0.32
% 0.06/0.32 thf(ex1I,definition,
% 0.06/0.32 ( ex1I
% 0.06/0.32 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( Xphi @ Xx )
% 0.06/0.32 => ( ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ A )
% 0.06/0.32 => ( ( Xphi @ Xy )
% 0.06/0.32 => ( Xy = Xx ) ) )
% 0.06/0.32 => ( ex1 @ A
% 0.06/0.32 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(ex1I2_type,type,
% 0.06/0.32 ex1I2: $o ).
% 0.06/0.32
% 0.06/0.32 thf(ex1I2,definition,
% 0.06/0.32 ( ex1I2
% 0.06/0.32 = ( ! [A: $i,Xphi: $i > $o] :
% 0.06/0.32 ( ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ A )
% 0.06/0.32 => ( ( Xphi @ Xx )
% 0.06/0.32 => ( ( Xphi @ Xy )
% 0.06/0.32 => ( Xx = Xy ) ) ) ) )
% 0.06/0.32 => ( ? [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 & ( Xphi @ Xx ) )
% 0.06/0.32 => ( ex1 @ A
% 0.06/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(singletonsuniq_type,type,
% 0.06/0.32 singletonsuniq: $o ).
% 0.06/0.32
% 0.06/0.32 thf(singletonsuniq,definition,
% 0.06/0.32 ( singletonsuniq
% 0.06/0.32 = ( ! [Xx: $i,Xy: $i] :
% 0.06/0.32 ( ( ( setadjoin @ Xx @ emptyset )
% 0.06/0.32 = ( setadjoin @ Xy @ emptyset ) )
% 0.06/0.32 => ( Xx = Xy ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(atmost1p_type,type,
% 0.06/0.32 atmost1p: $i > $o ).
% 0.06/0.32
% 0.06/0.32 thf(atleast2p_type,type,
% 0.06/0.32 atleast2p: $i > $o ).
% 0.06/0.32
% 0.06/0.32 thf(atmost2p_type,type,
% 0.06/0.32 atmost2p: $i > $o ).
% 0.06/0.32
% 0.06/0.32 thf(upairsetp_type,type,
% 0.06/0.32 upairsetp: $i > $o ).
% 0.06/0.32
% 0.06/0.32 thf(setukpairinjL1_type,type,
% 0.06/0.32 setukpairinjL1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(setukpairinjL1,definition,
% 0.06/0.32 ( setukpairinjL1
% 0.06/0.32 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.06/0.32 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.06/0.32 => ( Xx = Xz ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(kfstsingleton_type,type,
% 0.06/0.32 kfstsingleton: $o ).
% 0.06/0.32
% 0.06/0.32 thf(kfstsingleton,definition,
% 0.06/0.32 ( kfstsingleton
% 0.06/0.32 = ( ! [Xu: $i] :
% 0.06/0.32 ( ( iskpair @ Xu )
% 0.06/0.32 => ( singleton
% 0.06/0.32 @ ( dsetconstr @ ( setunion @ Xu )
% 0.06/0.32 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(theprop_type,type,
% 0.06/0.32 theprop: $o ).
% 0.06/0.32
% 0.06/0.32 thf(theprop,definition,
% 0.06/0.32 ( theprop
% 0.06/0.32 = ( ! [X: $i] :
% 0.06/0.32 ( ( singleton @ X )
% 0.06/0.32 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(kfst_type,type,
% 0.06/0.32 kfst: $i > $i ).
% 0.06/0.32
% 0.06/0.32 thf(kfstpairEq_type,type,
% 0.06/0.32 kfstpairEq: $o ).
% 0.06/0.32
% 0.06/0.32 thf(kfstpairEq,definition,
% 0.06/0.32 ( kfstpairEq
% 0.06/0.32 = ( ! [Xx: $i,Xy: $i] :
% 0.06/0.32 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.06/0.32 = Xx ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(cartprodfstin_type,type,
% 0.06/0.32 cartprodfstin: $o ).
% 0.06/0.32
% 0.06/0.32 thf(cartprodfstin,definition,
% 0.06/0.32 ( cartprodfstin
% 0.06/0.32 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.06/0.32 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.06/0.32 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(setukpairinjL2_type,type,
% 0.06/0.32 setukpairinjL2: $o ).
% 0.06/0.32
% 0.06/0.32 thf(setukpairinjL2,definition,
% 0.06/0.32 ( setukpairinjL2
% 0.06/0.32 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.06/0.32 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.06/0.32 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.06/0.32 => ( Xx = Xz ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(setukpairinjL_type,type,
% 0.06/0.32 setukpairinjL: $o ).
% 0.06/0.32
% 0.06/0.32 thf(setukpairinjL,definition,
% 0.06/0.32 ( setukpairinjL
% 0.06/0.32 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.06/0.32 ( ( ( kpair @ Xx @ Xy )
% 0.06/0.32 = ( kpair @ Xz @ Xu ) )
% 0.06/0.32 => ( Xx = Xz ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(setukpairinjR11_type,type,
% 0.06/0.32 setukpairinjR11: $o ).
% 0.06/0.32
% 0.06/0.32 thf(setukpairinjR11,definition,
% 0.06/0.32 ( setukpairinjR11
% 0.06/0.32 = ( ! [Xx: $i,Xy: $i] :
% 0.06/0.32 ( ( Xx = Xy )
% 0.06/0.32 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.06/0.32 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(setukpairinjR12_type,type,
% 0.06/0.32 setukpairinjR12: $o ).
% 0.06/0.32
% 0.06/0.32 thf(setukpairinjR12,definition,
% 0.06/0.32 ( setukpairinjR12
% 0.06/0.32 = ( ! [Xx: $i,Xy: $i] :
% 0.06/0.32 ( ( Xx = Xy )
% 0.06/0.32 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.06/0.32 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(setukpairinjR1_type,type,
% 0.06/0.32 setukpairinjR1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(setukpairinjR1,definition,
% 0.06/0.32 ( setukpairinjR1
% 0.06/0.32 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.06/0.32 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.06/0.32 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.06/0.32 => ( ( Xz = Xu )
% 0.06/0.32 => ( Xy = Xu ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(upairequniteq_type,type,
% 0.06/0.32 upairequniteq: $o ).
% 0.06/0.32
% 0.06/0.32 thf(upairequniteq,definition,
% 0.06/0.32 ( upairequniteq
% 0.06/0.32 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.06/0.32 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.06/0.32 = ( setadjoin @ Xz @ emptyset ) )
% 0.06/0.32 => ( Xx = Xy ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(setukpairinjR2_type,type,
% 0.06/0.32 setukpairinjR2: $o ).
% 0.06/0.32
% 0.06/0.32 thf(setukpairinjR2,definition,
% 0.06/0.32 ( setukpairinjR2
% 0.06/0.32 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.06/0.32 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.06/0.32 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.06/0.32 => ( Xy = Xu ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(setukpairinjR_type,type,
% 0.06/0.32 setukpairinjR: $o ).
% 0.06/0.32
% 0.06/0.32 thf(setukpairinjR,definition,
% 0.06/0.32 ( setukpairinjR
% 0.06/0.32 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.06/0.32 ( ( ( kpair @ Xx @ Xy )
% 0.06/0.32 = ( kpair @ Xz @ Xu ) )
% 0.06/0.32 => ( Xy = Xu ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(ksndsingleton_type,type,
% 0.06/0.32 ksndsingleton: $o ).
% 0.06/0.32
% 0.06/0.32 thf(ksndsingleton,definition,
% 0.06/0.32 ( ksndsingleton
% 0.06/0.32 = ( ! [Xu: $i] :
% 0.06/0.32 ( ( iskpair @ Xu )
% 0.06/0.32 => ( singleton
% 0.06/0.32 @ ( dsetconstr @ ( setunion @ Xu )
% 0.06/0.32 @ ^ [Xx: $i] :
% 0.06/0.32 ( Xu
% 0.06/0.32 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(ksnd_type,type,
% 0.06/0.32 ksnd: $i > $i ).
% 0.06/0.32
% 0.06/0.32 thf(ksndpairEq_type,type,
% 0.06/0.32 ksndpairEq: $o ).
% 0.06/0.32
% 0.06/0.32 thf(ksndpairEq,definition,
% 0.06/0.32 ( ksndpairEq
% 0.06/0.32 = ( ! [Xx: $i,Xy: $i] :
% 0.06/0.32 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.06/0.32 = Xy ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(kpairsurjEq_type,type,
% 0.06/0.32 kpairsurjEq: $o ).
% 0.06/0.32
% 0.06/0.32 thf(kpairsurjEq,definition,
% 0.06/0.32 ( kpairsurjEq
% 0.06/0.32 = ( ! [Xu: $i] :
% 0.06/0.32 ( ( iskpair @ Xu )
% 0.06/0.32 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.06/0.32 = Xu ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(cartprodsndin_type,type,
% 0.06/0.32 cartprodsndin: $o ).
% 0.06/0.32
% 0.06/0.32 thf(cartprodsndin,definition,
% 0.06/0.32 ( cartprodsndin
% 0.06/0.32 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.06/0.32 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.06/0.32 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(cartprodpairmemEL_type,type,
% 0.06/0.32 cartprodpairmemEL: $o ).
% 0.06/0.32
% 0.06/0.32 thf(cartprodpairmemEL,definition,
% 0.06/0.32 ( cartprodpairmemEL
% 0.06/0.32 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.06/0.32 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.06/0.32 => ( in @ Xx @ A ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(cartprodpairmemER_type,type,
% 0.06/0.32 cartprodpairmemER: $o ).
% 0.06/0.32
% 0.06/0.32 thf(cartprodpairmemER,definition,
% 0.06/0.32 ( cartprodpairmemER
% 0.06/0.32 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.06/0.32 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.06/0.32 => ( in @ Xy @ B ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(cartprodmempaircEq_type,type,
% 0.06/0.32 cartprodmempaircEq: $o ).
% 0.06/0.32
% 0.06/0.32 thf(cartprodmempaircEq,definition,
% 0.06/0.32 ( cartprodmempaircEq
% 0.06/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ B )
% 0.06/0.32 => ( ( kpair @ Xx @ Xy )
% 0.06/0.32 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(cartprodfstpairEq_type,type,
% 0.06/0.32 cartprodfstpairEq: $o ).
% 0.06/0.32
% 0.06/0.32 thf(cartprodfstpairEq,definition,
% 0.06/0.32 ( cartprodfstpairEq
% 0.06/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ B )
% 0.06/0.32 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.06/0.32 = Xx ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(cartprodsndpairEq_type,type,
% 0.06/0.32 cartprodsndpairEq: $o ).
% 0.06/0.32
% 0.06/0.32 thf(cartprodsndpairEq,definition,
% 0.06/0.32 ( cartprodsndpairEq
% 0.06/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ B )
% 0.06/0.32 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.06/0.32 = Xy ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(cartprodpairsurjEq_type,type,
% 0.06/0.32 cartprodpairsurjEq: $o ).
% 0.06/0.32
% 0.06/0.32 thf(cartprodpairsurjEq,definition,
% 0.06/0.32 ( cartprodpairsurjEq
% 0.06/0.32 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.06/0.32 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.06/0.32 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.06/0.32 = Xu ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(breln_type,type,
% 0.06/0.32 breln: $i > $i > $i > $o ).
% 0.06/0.32
% 0.06/0.32 thf(breln,definition,
% 0.06/0.32 ( breln
% 0.06/0.32 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(dpsetconstr_type,type,
% 0.06/0.32 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.06/0.32
% 0.06/0.32 thf(dpsetconstrI_type,type,
% 0.06/0.32 dpsetconstrI: $o ).
% 0.06/0.32
% 0.06/0.32 thf(dpsetconstrI,definition,
% 0.06/0.32 ( dpsetconstrI
% 0.06/0.32 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ B )
% 0.06/0.32 => ( ( Xphi @ Xx @ Xy )
% 0.06/0.32 => ( in @ ( kpair @ Xx @ Xy )
% 0.06/0.32 @ ( dpsetconstr @ A @ B
% 0.06/0.32 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(dpsetconstrSub_type,type,
% 0.06/0.32 dpsetconstrSub: $o ).
% 0.06/0.32
% 0.06/0.32 thf(dpsetconstrSub,definition,
% 0.06/0.32 ( dpsetconstrSub
% 0.06/0.32 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.06/0.32 ( subset
% 0.06/0.32 @ ( dpsetconstr @ A @ B
% 0.06/0.32 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.06/0.32 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(setOfPairsIsBReln_type,type,
% 0.06/0.32 setOfPairsIsBReln: $o ).
% 0.06/0.32
% 0.06/0.32 thf(setOfPairsIsBReln,definition,
% 0.06/0.32 ( setOfPairsIsBReln
% 0.06/0.32 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.06/0.32 ( breln @ A @ B
% 0.06/0.32 @ ( dpsetconstr @ A @ B
% 0.06/0.32 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(dpsetconstrERa_type,type,
% 0.06/0.32 dpsetconstrERa: $o ).
% 0.06/0.32
% 0.06/0.32 thf(dpsetconstrERa,definition,
% 0.06/0.32 ( dpsetconstrERa
% 0.06/0.32 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ B )
% 0.06/0.32 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.06/0.32 @ ( dpsetconstr @ A @ B
% 0.06/0.32 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.06/0.32 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(dpsetconstrEL1_type,type,
% 0.06/0.32 dpsetconstrEL1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(dpsetconstrEL1,definition,
% 0.06/0.32 ( dpsetconstrEL1
% 0.06/0.32 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.06/0.32 ( ( in @ ( kpair @ Xx @ Xy )
% 0.06/0.32 @ ( dpsetconstr @ A @ B
% 0.06/0.32 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.06/0.32 => ( in @ Xx @ A ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(dpsetconstrEL2_type,type,
% 0.06/0.32 dpsetconstrEL2: $o ).
% 0.06/0.32
% 0.06/0.32 thf(dpsetconstrEL2,definition,
% 0.06/0.32 ( dpsetconstrEL2
% 0.06/0.32 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.06/0.32 ( ( in @ ( kpair @ Xx @ Xy )
% 0.06/0.32 @ ( dpsetconstr @ A @ B
% 0.06/0.32 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.06/0.32 => ( in @ Xy @ B ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(dpsetconstrER_type,type,
% 0.06/0.32 dpsetconstrER: $o ).
% 0.06/0.32
% 0.06/0.32 thf(dpsetconstrER,definition,
% 0.06/0.32 ( dpsetconstrER
% 0.06/0.32 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.06/0.32 ( ( in @ ( kpair @ Xx @ Xy )
% 0.06/0.32 @ ( dpsetconstr @ A @ B
% 0.06/0.32 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.06/0.32 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(func_type,type,
% 0.06/0.32 func: $i > $i > $i > $o ).
% 0.06/0.32
% 0.06/0.32 thf(funcSet_type,type,
% 0.06/0.32 funcSet: $i > $i > $i ).
% 0.06/0.32
% 0.06/0.32 thf(funcImageSingleton_type,type,
% 0.06/0.32 funcImageSingleton: $o ).
% 0.06/0.32
% 0.06/0.32 thf(funcImageSingleton,definition,
% 0.06/0.32 ( funcImageSingleton
% 0.06/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.06/0.32 ( ( func @ A @ B @ Xf )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( singleton
% 0.06/0.32 @ ( dsetconstr @ B
% 0.06/0.32 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(apProp_type,type,
% 0.06/0.32 apProp: $o ).
% 0.06/0.32
% 0.06/0.32 thf(apProp,definition,
% 0.06/0.32 ( apProp
% 0.06/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.06/0.32 ( ( func @ A @ B @ Xf )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( in
% 0.06/0.32 @ ( setunion
% 0.06/0.32 @ ( dsetconstr @ B
% 0.06/0.32 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.06/0.32 @ B ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(ap_type,type,
% 0.06/0.32 ap: $i > $i > $i > $i > $i ).
% 0.06/0.32
% 0.06/0.32 thf(app_type,type,
% 0.06/0.32 app: $o ).
% 0.06/0.32
% 0.06/0.32 thf(app,definition,
% 0.06/0.32 ( app
% 0.06/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.06/0.32 ( ( func @ A @ B @ Xf )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(infuncsetfunc_type,type,
% 0.06/0.32 infuncsetfunc: $o ).
% 0.06/0.32
% 0.06/0.32 thf(infuncsetfunc,definition,
% 0.06/0.32 ( infuncsetfunc
% 0.06/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.06/0.32 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.06/0.32 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(ap2p_type,type,
% 0.06/0.32 ap2p: $o ).
% 0.06/0.32
% 0.06/0.32 thf(ap2p,definition,
% 0.06/0.32 ( ap2p
% 0.06/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.06/0.32 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(funcinfuncset_type,type,
% 0.06/0.32 funcinfuncset: $o ).
% 0.06/0.32
% 0.06/0.32 thf(funcinfuncset,definition,
% 0.06/0.32 ( funcinfuncset
% 0.06/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.06/0.32 ( ( func @ A @ B @ Xf )
% 0.06/0.32 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(lamProp_type,type,
% 0.06/0.32 lamProp: $o ).
% 0.06/0.32
% 0.06/0.32 thf(lamProp,definition,
% 0.06/0.32 ( lamProp
% 0.06/0.32 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.06/0.32 ( ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.06/0.32 => ( func @ A @ B
% 0.06/0.32 @ ( dpsetconstr @ A @ B
% 0.06/0.32 @ ^ [Xx: $i,Xy: $i] :
% 0.06/0.32 ( ( Xf @ Xx )
% 0.06/0.32 = Xy ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(lam_type,type,
% 0.06/0.32 lam: $i > $i > ( $i > $i ) > $i ).
% 0.06/0.32
% 0.06/0.32 thf(lamp_type,type,
% 0.06/0.32 lamp: $o ).
% 0.06/0.32
% 0.06/0.32 thf(lamp,definition,
% 0.06/0.32 ( lamp
% 0.06/0.32 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.06/0.32 ( ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.06/0.32 => ( func @ A @ B
% 0.06/0.32 @ ( lam @ A @ B
% 0.06/0.32 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(lam2p_type,type,
% 0.06/0.32 lam2p: $o ).
% 0.06/0.32
% 0.06/0.32 thf(lam2p,definition,
% 0.06/0.32 ( lam2p
% 0.06/0.32 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.06/0.32 ( ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.06/0.32 => ( in
% 0.06/0.32 @ ( lam @ A @ B
% 0.06/0.32 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.06/0.32 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(brelnall1_type,type,
% 0.06/0.32 brelnall1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(brelnall1,definition,
% 0.06/0.32 ( brelnall1
% 0.06/0.32 = ( ! [A: $i,B: $i,R: $i] :
% 0.06/0.32 ( ( breln @ A @ B @ R )
% 0.06/0.32 => ! [Xphi: $i > $o] :
% 0.06/0.32 ( ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ B )
% 0.06/0.32 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.06/0.32 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ R )
% 0.06/0.32 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(brelnall2_type,type,
% 0.06/0.32 brelnall2: $o ).
% 0.06/0.32
% 0.06/0.32 thf(brelnall2,definition,
% 0.06/0.32 ( brelnall2
% 0.06/0.32 = ( ! [A: $i,B: $i,R: $i] :
% 0.06/0.32 ( ( breln @ A @ B @ R )
% 0.06/0.32 => ! [Xphi: $i > $o] :
% 0.06/0.32 ( ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ B )
% 0.06/0.32 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.06/0.32 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ R )
% 0.06/0.32 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(ex1E2_type,type,
% 0.06/0.32 ex1E2: $o ).
% 0.06/0.32
% 0.06/0.32 thf(ex1E2,definition,
% 0.06/0.32 ( ex1E2
% 0.06/0.32 = ( ! [A: $i,Xphi: $i > $o] :
% 0.06/0.32 ( ( ex1 @ A
% 0.06/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ A )
% 0.06/0.32 => ( ( Xphi @ Xx )
% 0.06/0.32 => ( ( Xphi @ Xy )
% 0.06/0.32 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(funcGraphProp1_type,type,
% 0.06/0.32 funcGraphProp1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(funcGraphProp1,definition,
% 0.06/0.32 ( funcGraphProp1
% 0.06/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.06/0.32 ( ( func @ A @ B @ Xf )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(funcGraphProp3_type,type,
% 0.06/0.32 funcGraphProp3: $o ).
% 0.06/0.32
% 0.06/0.32 thf(funcGraphProp3,definition,
% 0.06/0.32 ( funcGraphProp3
% 0.06/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.06/0.32 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(funcGraphProp2_type,type,
% 0.06/0.32 funcGraphProp2: $o ).
% 0.06/0.32
% 0.06/0.32 thf(funcGraphProp2,definition,
% 0.06/0.32 ( funcGraphProp2
% 0.06/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.06/0.32 ( ( func @ A @ B @ Xf )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ B )
% 0.06/0.32 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.06/0.32 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.06/0.32 = Xy ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(funcextLem_type,type,
% 0.06/0.32 funcextLem: $o ).
% 0.06/0.32
% 0.06/0.32 thf(funcextLem,definition,
% 0.06/0.32 ( funcextLem
% 0.06/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.06/0.32 ( ( func @ A @ B @ Xf )
% 0.06/0.32 => ! [Xg: $i] :
% 0.06/0.32 ( ( func @ A @ B @ Xg )
% 0.06/0.32 => ( ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.06/0.32 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ B )
% 0.06/0.32 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 0.06/0.32 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(funcGraphProp4_type,type,
% 0.06/0.32 funcGraphProp4: $o ).
% 0.06/0.32
% 0.06/0.32 thf(funcGraphProp4,definition,
% 0.06/0.32 ( funcGraphProp4
% 0.06/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.06/0.32 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ B )
% 0.06/0.32 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.06/0.32 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.06/0.32 = Xy ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(subbreln_type,type,
% 0.06/0.32 subbreln: $o ).
% 0.06/0.32
% 0.06/0.32 thf(subbreln,definition,
% 0.06/0.32 ( subbreln
% 0.06/0.32 = ( ! [A: $i,B: $i,R: $i] :
% 0.06/0.32 ( ( breln @ A @ B @ R )
% 0.06/0.32 => ! [S: $i] :
% 0.06/0.32 ( ( breln @ A @ B @ S )
% 0.06/0.32 => ( ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ B )
% 0.06/0.32 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.06/0.32 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.06/0.32 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(eqbreln_type,type,
% 0.06/0.32 eqbreln: $o ).
% 0.06/0.32
% 0.06/0.32 thf(eqbreln,definition,
% 0.06/0.32 ( eqbreln
% 0.06/0.32 = ( ! [A: $i,B: $i,R: $i] :
% 0.06/0.32 ( ( breln @ A @ B @ R )
% 0.06/0.32 => ! [S: $i] :
% 0.06/0.32 ( ( breln @ A @ B @ S )
% 0.06/0.32 => ( ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ B )
% 0.06/0.32 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.06/0.32 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.06/0.32 => ( ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ B )
% 0.06/0.32 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.06/0.32 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.06/0.32 => ( R = S ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(funcext_type,type,
% 0.06/0.32 funcext: $o ).
% 0.06/0.32
% 0.06/0.32 thf(funcext,definition,
% 0.06/0.32 ( funcext
% 0.06/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.06/0.32 ( ( func @ A @ B @ Xf )
% 0.06/0.32 => ! [Xg: $i] :
% 0.06/0.32 ( ( func @ A @ B @ Xg )
% 0.06/0.32 => ( ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.06/0.32 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.06/0.32 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(funcext2_type,type,
% 0.06/0.32 funcext2: $o ).
% 0.06/0.32
% 0.06/0.32 thf(funcext2,definition,
% 0.06/0.32 ( funcext2
% 0.06/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.06/0.32 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.06/0.32 => ! [Xg: $i] :
% 0.06/0.32 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 0.06/0.32 => ( ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.06/0.32 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.06/0.32 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(ap2apEq1_type,type,
% 0.06/0.32 ap2apEq1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(ap2apEq1,definition,
% 0.06/0.32 ( ap2apEq1
% 0.06/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.06/0.32 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.06/0.32 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(ap2apEq2_type,type,
% 0.06/0.32 ap2apEq2: $o ).
% 0.06/0.32
% 0.06/0.32 thf(ap2apEq2,definition,
% 0.06/0.32 ( ap2apEq2
% 0.06/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.06/0.32 ( ( func @ A @ B @ Xf )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.06/0.32 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(beta1_type,type,
% 0.06/0.32 beta1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(beta1,definition,
% 0.06/0.32 ( beta1
% 0.06/0.32 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.06/0.32 ( ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( ap @ A @ B
% 0.06/0.32 @ ( lam @ A @ B
% 0.06/0.32 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.06/0.32 @ Xx )
% 0.06/0.32 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(eta1_type,type,
% 0.06/0.32 eta1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(eta1,definition,
% 0.06/0.32 ( eta1
% 0.06/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.06/0.32 ( ( func @ A @ B @ Xf )
% 0.06/0.32 => ( ( lam @ A @ B
% 0.06/0.32 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.06/0.32 = Xf ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(lam2lamEq_type,type,
% 0.06/0.32 lam2lamEq: $o ).
% 0.06/0.32
% 0.06/0.32 thf(lam2lamEq,definition,
% 0.06/0.32 ( lam2lamEq
% 0.06/0.32 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.06/0.32 ( ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.06/0.32 => ( ( lam @ A @ B
% 0.06/0.32 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.06/0.32 = ( lam @ A @ B
% 0.06/0.32 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(beta2_type,type,
% 0.06/0.32 beta2: $o ).
% 0.06/0.32
% 0.06/0.32 thf(beta2,definition,
% 0.06/0.32 ( beta2
% 0.06/0.32 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.06/0.32 ( ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( ap @ A @ B
% 0.06/0.32 @ ( lam @ A @ B
% 0.06/0.32 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.06/0.32 @ Xx )
% 0.06/0.32 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(eta2_type,type,
% 0.06/0.32 eta2: $o ).
% 0.06/0.32
% 0.06/0.32 thf(eta2,definition,
% 0.06/0.32 ( eta2
% 0.06/0.32 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.06/0.32 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.06/0.32 => ( ( lam @ A @ B
% 0.06/0.32 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.06/0.32 = Xf ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(iffalseProp1_type,type,
% 0.06/0.32 iffalseProp1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(iffalseProp1,definition,
% 0.06/0.32 ( iffalseProp1
% 0.06/0.32 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ A )
% 0.06/0.32 => ( ~ Xphi
% 0.06/0.32 => ( in @ Xy
% 0.06/0.32 @ ( dsetconstr @ A
% 0.06/0.32 @ ^ [Xz: $i] :
% 0.06/0.32 ( ( Xphi
% 0.06/0.32 & ( Xz = Xx ) )
% 0.06/0.32 | ( ~ Xphi
% 0.06/0.32 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(iffalseProp2_type,type,
% 0.06/0.32 iffalseProp2: $o ).
% 0.06/0.32
% 0.06/0.32 thf(iffalseProp2,definition,
% 0.06/0.32 ( iffalseProp2
% 0.06/0.32 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ A )
% 0.06/0.32 => ( ~ Xphi
% 0.06/0.32 => ( ( dsetconstr @ A
% 0.06/0.32 @ ^ [Xz: $i] :
% 0.06/0.32 ( ( Xphi
% 0.06/0.32 & ( Xz = Xx ) )
% 0.06/0.32 | ( ~ Xphi
% 0.06/0.32 & ( Xz = Xy ) ) ) )
% 0.06/0.32 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(iftrueProp1_type,type,
% 0.06/0.32 iftrueProp1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(iftrueProp1,definition,
% 0.06/0.32 ( iftrueProp1
% 0.06/0.32 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ A )
% 0.06/0.32 => ( Xphi
% 0.06/0.32 => ( in @ Xx
% 0.06/0.32 @ ( dsetconstr @ A
% 0.06/0.32 @ ^ [Xz: $i] :
% 0.06/0.32 ( ( Xphi
% 0.06/0.32 & ( Xz = Xx ) )
% 0.06/0.32 | ( ~ Xphi
% 0.06/0.32 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(iftrueProp2_type,type,
% 0.06/0.32 iftrueProp2: $o ).
% 0.06/0.32
% 0.06/0.32 thf(iftrueProp2,definition,
% 0.06/0.32 ( iftrueProp2
% 0.06/0.32 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ A )
% 0.06/0.32 => ( Xphi
% 0.06/0.32 => ( ( dsetconstr @ A
% 0.06/0.32 @ ^ [Xz: $i] :
% 0.06/0.32 ( ( Xphi
% 0.06/0.32 & ( Xz = Xx ) )
% 0.06/0.32 | ( ~ Xphi
% 0.06/0.32 & ( Xz = Xy ) ) ) )
% 0.06/0.32 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(ifSingleton_type,type,
% 0.06/0.32 ifSingleton: $o ).
% 0.06/0.32
% 0.06/0.32 thf(ifSingleton,definition,
% 0.06/0.32 ( ifSingleton
% 0.06/0.32 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ A )
% 0.06/0.32 => ( singleton
% 0.06/0.32 @ ( dsetconstr @ A
% 0.06/0.32 @ ^ [Xz: $i] :
% 0.06/0.32 ( ( Xphi
% 0.06/0.32 & ( Xz = Xx ) )
% 0.06/0.32 | ( ~ Xphi
% 0.06/0.32 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(if_type,type,
% 0.06/0.32 if: $i > $o > $i > $i > $i ).
% 0.06/0.32
% 0.06/0.32 thf(ifp_type,type,
% 0.06/0.32 ifp: $o ).
% 0.06/0.32
% 0.06/0.32 thf(ifp,definition,
% 0.06/0.32 ( ifp
% 0.06/0.32 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ A )
% 0.06/0.32 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(theeq_type,type,
% 0.06/0.32 theeq: $o ).
% 0.06/0.32
% 0.06/0.32 thf(theeq,definition,
% 0.06/0.32 ( theeq
% 0.06/0.32 = ( ! [X: $i] :
% 0.06/0.32 ( ( singleton @ X )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ X )
% 0.06/0.32 => ( ( setunion @ X )
% 0.06/0.32 = Xx ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(iftrue_type,type,
% 0.06/0.32 iftrue: $o ).
% 0.06/0.32
% 0.06/0.32 thf(iftrue,definition,
% 0.06/0.32 ( iftrue
% 0.06/0.32 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ A )
% 0.06/0.32 => ( Xphi
% 0.06/0.32 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.06/0.32 = Xx ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(iffalse_type,type,
% 0.06/0.32 iffalse: $o ).
% 0.06/0.32
% 0.06/0.32 thf(iffalse,definition,
% 0.06/0.32 ( iffalse
% 0.06/0.32 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ A )
% 0.06/0.32 => ( ~ Xphi
% 0.06/0.32 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.06/0.32 = Xy ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(iftrueorfalse_type,type,
% 0.06/0.32 iftrueorfalse: $o ).
% 0.06/0.32
% 0.06/0.32 thf(iftrueorfalse,definition,
% 0.06/0.32 ( iftrueorfalse
% 0.06/0.32 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ A )
% 0.06/0.32 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(binintersectT_lem_type,type,
% 0.06/0.32 binintersectT_lem: $o ).
% 0.06/0.32
% 0.06/0.32 thf(binintersectT_lem,definition,
% 0.06/0.32 ( binintersectT_lem
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(binunionT_lem_type,type,
% 0.06/0.32 binunionT_lem: $o ).
% 0.06/0.32
% 0.06/0.32 thf(binunionT_lem,definition,
% 0.06/0.32 ( binunionT_lem
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(powersetT_lem_type,type,
% 0.06/0.32 powersetT_lem: $o ).
% 0.06/0.32
% 0.06/0.32 thf(powersetT_lem,definition,
% 0.06/0.32 ( powersetT_lem
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(setminusT_lem_type,type,
% 0.06/0.32 setminusT_lem: $o ).
% 0.06/0.32
% 0.06/0.32 thf(setminusT_lem,definition,
% 0.06/0.32 ( setminusT_lem
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(complementT_lem_type,type,
% 0.06/0.32 complementT_lem: $o ).
% 0.06/0.32
% 0.06/0.32 thf(complementT_lem,definition,
% 0.06/0.32 ( complementT_lem
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(setextT_type,type,
% 0.06/0.32 setextT: $o ).
% 0.06/0.32
% 0.06/0.32 thf(setextT,definition,
% 0.06/0.32 ( setextT
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ( ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( in @ Xx @ X )
% 0.06/0.32 => ( in @ Xx @ Y ) ) )
% 0.06/0.32 => ( ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( in @ Xx @ Y )
% 0.06/0.32 => ( in @ Xx @ X ) ) )
% 0.06/0.32 => ( X = Y ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(subsetTI_type,type,
% 0.06/0.32 subsetTI: $o ).
% 0.06/0.32
% 0.06/0.32 thf(subsetTI,definition,
% 0.06/0.32 ( subsetTI
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ( ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( in @ Xx @ X )
% 0.06/0.32 => ( in @ Xx @ Y ) ) )
% 0.06/0.32 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(powersetTI1_type,type,
% 0.06/0.32 powersetTI1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(powersetTI1,definition,
% 0.06/0.32 ( powersetTI1
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ( ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( in @ Xx @ X )
% 0.06/0.32 => ( in @ Xx @ Y ) ) )
% 0.06/0.32 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(powersetTE1_type,type,
% 0.06/0.32 powersetTE1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(powersetTE1,definition,
% 0.06/0.32 ( powersetTE1
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( in @ X @ ( powerset @ Y ) )
% 0.06/0.32 => ( ( in @ Xx @ X )
% 0.06/0.32 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(complementTI1_type,type,
% 0.06/0.32 complementTI1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(complementTI1,definition,
% 0.06/0.32 ( complementTI1
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( in @ Xx @ X )
% 0.06/0.32 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(complementTE1_type,type,
% 0.06/0.32 complementTE1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(complementTE1,definition,
% 0.06/0.32 ( complementTE1
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 0.06/0.32 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(binintersectTELcontra_type,type,
% 0.06/0.32 binintersectTELcontra: $o ).
% 0.06/0.32
% 0.06/0.32 thf(binintersectTELcontra,definition,
% 0.06/0.32 ( binintersectTELcontra
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ~ ( in @ Xx @ X )
% 0.06/0.32 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(binintersectTERcontra_type,type,
% 0.06/0.32 binintersectTERcontra: $o ).
% 0.06/0.32
% 0.06/0.32 thf(binintersectTERcontra,definition,
% 0.06/0.32 ( binintersectTERcontra
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ~ ( in @ Xx @ Y )
% 0.06/0.32 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(contrasubsetT_type,type,
% 0.06/0.32 contrasubsetT: $o ).
% 0.06/0.32
% 0.06/0.32 thf(contrasubsetT,definition,
% 0.06/0.32 ( contrasubsetT
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.06/0.32 => ( ( in @ Xx @ Y )
% 0.06/0.32 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(contrasubsetT1_type,type,
% 0.06/0.32 contrasubsetT1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(contrasubsetT1,definition,
% 0.06/0.32 ( contrasubsetT1
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( subset @ X @ Y )
% 0.06/0.32 => ( ~ ( in @ Xx @ Y )
% 0.06/0.32 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(contrasubsetT2_type,type,
% 0.06/0.32 contrasubsetT2: $o ).
% 0.06/0.32
% 0.06/0.32 thf(contrasubsetT2,definition,
% 0.06/0.32 ( contrasubsetT2
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ( ( subset @ X @ Y )
% 0.06/0.32 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(contrasubsetT3_type,type,
% 0.06/0.32 contrasubsetT3: $o ).
% 0.06/0.32
% 0.06/0.32 thf(contrasubsetT3,definition,
% 0.06/0.32 ( contrasubsetT3
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 0.06/0.32 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(doubleComplementI1_type,type,
% 0.06/0.32 doubleComplementI1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(doubleComplementI1,definition,
% 0.06/0.32 ( doubleComplementI1
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( in @ Xx @ X )
% 0.06/0.32 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(doubleComplementE1_type,type,
% 0.06/0.32 doubleComplementE1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(doubleComplementE1,definition,
% 0.06/0.32 ( doubleComplementE1
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 0.06/0.32 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(doubleComplementSub1_type,type,
% 0.06/0.32 doubleComplementSub1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(doubleComplementSub1,definition,
% 0.06/0.32 ( doubleComplementSub1
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(doubleComplementSub2_type,type,
% 0.06/0.32 doubleComplementSub2: $o ).
% 0.06/0.32
% 0.06/0.32 thf(doubleComplementSub2,definition,
% 0.06/0.32 ( doubleComplementSub2
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(doubleComplementEq_type,type,
% 0.06/0.32 doubleComplementEq: $o ).
% 0.06/0.32
% 0.06/0.32 thf(doubleComplementEq,definition,
% 0.06/0.32 ( doubleComplementEq
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ( X
% 0.06/0.32 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(complementTnotintersectT_type,type,
% 0.06/0.32 complementTnotintersectT: $o ).
% 0.06/0.32
% 0.06/0.32 thf(complementTnotintersectT,definition,
% 0.06/0.32 ( complementTnotintersectT
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.06/0.32 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(complementImpComplementIntersect_type,type,
% 0.06/0.32 complementImpComplementIntersect: $o ).
% 0.06/0.32
% 0.06/0.32 thf(complementImpComplementIntersect,definition,
% 0.06/0.32 ( complementImpComplementIntersect
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.06/0.32 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(complementSubsetComplementIntersect_type,type,
% 0.06/0.32 complementSubsetComplementIntersect: $o ).
% 0.06/0.32
% 0.06/0.32 thf(complementSubsetComplementIntersect,definition,
% 0.06/0.32 ( complementSubsetComplementIntersect
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(complementInPowersetComplementIntersect_type,type,
% 0.06/0.32 complementInPowersetComplementIntersect: $o ).
% 0.06/0.32
% 0.06/0.32 thf(complementInPowersetComplementIntersect,definition,
% 0.06/0.32 ( complementInPowersetComplementIntersect
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(contraSubsetComplement_type,type,
% 0.06/0.32 contraSubsetComplement: $o ).
% 0.06/0.32
% 0.06/0.32 thf(contraSubsetComplement,definition,
% 0.06/0.32 ( contraSubsetComplement
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( in @ Xx @ Y )
% 0.06/0.32 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(complementTcontraSubset_type,type,
% 0.06/0.32 complementTcontraSubset: $o ).
% 0.06/0.32
% 0.06/0.32 thf(complementTcontraSubset,definition,
% 0.06/0.32 ( complementTcontraSubset
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.06/0.32 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(binunionTILcontra_type,type,
% 0.06/0.32 binunionTILcontra: $o ).
% 0.06/0.32
% 0.06/0.32 thf(binunionTILcontra,definition,
% 0.06/0.32 ( binunionTILcontra
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.06/0.32 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(binunionTIRcontra_type,type,
% 0.06/0.32 binunionTIRcontra: $o ).
% 0.06/0.32
% 0.06/0.32 thf(binunionTIRcontra,definition,
% 0.06/0.32 ( binunionTIRcontra
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.06/0.32 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(inIntersectImpInUnion_type,type,
% 0.06/0.32 inIntersectImpInUnion: $o ).
% 0.06/0.32
% 0.06/0.32 thf(inIntersectImpInUnion,definition,
% 0.06/0.32 ( inIntersectImpInUnion
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Z: $i] :
% 0.06/0.32 ( ( in @ Z @ ( powerset @ A ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.06/0.32 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(inIntersectImpInUnion2_type,type,
% 0.06/0.32 inIntersectImpInUnion2: $o ).
% 0.06/0.32
% 0.06/0.32 thf(inIntersectImpInUnion2,definition,
% 0.06/0.32 ( inIntersectImpInUnion2
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Z: $i] :
% 0.06/0.32 ( ( in @ Z @ ( powerset @ A ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.06/0.32 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(inIntersectImpInIntersectUnions_type,type,
% 0.06/0.32 inIntersectImpInIntersectUnions: $o ).
% 0.06/0.32
% 0.06/0.32 thf(inIntersectImpInIntersectUnions,definition,
% 0.06/0.32 ( inIntersectImpInIntersectUnions
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Z: $i] :
% 0.06/0.32 ( ( in @ Z @ ( powerset @ A ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.06/0.32 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(intersectInPowersetIntersectUnions_type,type,
% 0.06/0.32 intersectInPowersetIntersectUnions: $o ).
% 0.06/0.32
% 0.06/0.32 thf(intersectInPowersetIntersectUnions,definition,
% 0.06/0.32 ( intersectInPowersetIntersectUnions
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Z: $i] :
% 0.06/0.32 ( ( in @ Z @ ( powerset @ A ) )
% 0.06/0.32 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(inComplementUnionImpNotIn1_type,type,
% 0.06/0.32 inComplementUnionImpNotIn1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(inComplementUnionImpNotIn1,definition,
% 0.06/0.32 ( inComplementUnionImpNotIn1
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.06/0.32 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(inComplementUnionImpInComplement1_type,type,
% 0.06/0.32 inComplementUnionImpInComplement1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(inComplementUnionImpInComplement1,definition,
% 0.06/0.32 ( inComplementUnionImpInComplement1
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.06/0.32 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(binunionTE_type,type,
% 0.06/0.32 binunionTE: $o ).
% 0.06/0.32
% 0.06/0.32 thf(binunionTE,definition,
% 0.06/0.32 ( binunionTE
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Xphi: $o,Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.06/0.32 => ( ( ( in @ Xx @ X )
% 0.06/0.32 => Xphi )
% 0.06/0.32 => ( ( ( in @ Xx @ Y )
% 0.06/0.32 => Xphi )
% 0.06/0.32 => Xphi ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(binunionTEcontra_type,type,
% 0.06/0.32 binunionTEcontra: $o ).
% 0.06/0.32
% 0.06/0.32 thf(binunionTEcontra,definition,
% 0.06/0.32 ( binunionTEcontra
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ~ ( in @ Xx @ X )
% 0.06/0.32 => ( ~ ( in @ Xx @ Y )
% 0.06/0.32 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(demorgan2a1_type,type,
% 0.06/0.32 demorgan2a1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(demorgan2a1,definition,
% 0.06/0.32 ( demorgan2a1
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.06/0.32 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(complementUnionInPowersetComplement_type,type,
% 0.06/0.32 complementUnionInPowersetComplement: $o ).
% 0.06/0.32
% 0.06/0.32 thf(complementUnionInPowersetComplement,definition,
% 0.06/0.32 ( complementUnionInPowersetComplement
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(demorgan2a2_type,type,
% 0.06/0.32 demorgan2a2: $o ).
% 0.06/0.32
% 0.06/0.32 thf(demorgan2a2,definition,
% 0.06/0.32 ( demorgan2a2
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.06/0.32 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(demorgan1a_type,type,
% 0.06/0.32 demorgan1a: $o ).
% 0.06/0.32
% 0.06/0.32 thf(demorgan1a,definition,
% 0.06/0.32 ( demorgan1a
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 0.06/0.32 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(demorgan1b_type,type,
% 0.06/0.32 demorgan1b: $o ).
% 0.06/0.32
% 0.06/0.32 thf(demorgan1b,definition,
% 0.06/0.32 ( demorgan1b
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.06/0.32 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(demorgan1_type,type,
% 0.06/0.32 demorgan1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(demorgan1,definition,
% 0.06/0.32 ( demorgan1
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 0.06/0.32 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(demorgan2a_type,type,
% 0.06/0.32 demorgan2a: $o ).
% 0.06/0.32
% 0.06/0.32 thf(demorgan2a,definition,
% 0.06/0.32 ( demorgan2a
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.06/0.32 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(demorgan2b2_type,type,
% 0.06/0.32 demorgan2b2: $o ).
% 0.06/0.32
% 0.06/0.32 thf(demorgan2b2,definition,
% 0.06/0.32 ( demorgan2b2
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.06/0.32 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 0.06/0.32 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(demorgan2b_type,type,
% 0.06/0.32 demorgan2b: $o ).
% 0.06/0.32
% 0.06/0.32 thf(demorgan2b,definition,
% 0.06/0.32 ( demorgan2b
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.06/0.32 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(demorgan2_type,type,
% 0.06/0.32 demorgan2: $o ).
% 0.06/0.32
% 0.06/0.32 thf(demorgan2,definition,
% 0.06/0.32 ( demorgan2
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 0.06/0.32 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(woz13rule0_type,type,
% 0.06/0.32 woz13rule0: $o ).
% 0.06/0.32
% 0.06/0.32 thf(woz13rule0,definition,
% 0.06/0.32 ( woz13rule0
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.06/0.32 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(woz13rule1_type,type,
% 0.06/0.32 woz13rule1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(woz13rule1,definition,
% 0.06/0.32 ( woz13rule1
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Z: $i] :
% 0.06/0.32 ( ( in @ Z @ ( powerset @ A ) )
% 0.06/0.32 => ( ( subset @ X @ Z )
% 0.06/0.32 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(woz13rule2_type,type,
% 0.06/0.32 woz13rule2: $o ).
% 0.06/0.32
% 0.06/0.32 thf(woz13rule2,definition,
% 0.06/0.32 ( woz13rule2
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Z: $i] :
% 0.06/0.32 ( ( in @ Z @ ( powerset @ A ) )
% 0.06/0.32 => ( ( subset @ Y @ Z )
% 0.06/0.32 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(woz13rule3_type,type,
% 0.06/0.32 woz13rule3: $o ).
% 0.06/0.32
% 0.06/0.32 thf(woz13rule3,definition,
% 0.06/0.32 ( woz13rule3
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Z: $i] :
% 0.06/0.32 ( ( in @ Z @ ( powerset @ A ) )
% 0.06/0.32 => ( ( subset @ X @ Y )
% 0.06/0.32 => ( ( subset @ X @ Z )
% 0.06/0.32 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(woz13rule4_type,type,
% 0.06/0.32 woz13rule4: $o ).
% 0.06/0.32
% 0.06/0.32 thf(woz13rule4,definition,
% 0.06/0.32 ( woz13rule4
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Z: $i] :
% 0.06/0.32 ( ( in @ Z @ ( powerset @ A ) )
% 0.06/0.32 => ! [W: $i] :
% 0.06/0.32 ( ( in @ W @ ( powerset @ A ) )
% 0.06/0.32 => ( ( subset @ X @ Z )
% 0.06/0.32 => ( ( subset @ Y @ W )
% 0.06/0.32 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(woz1_1_type,type,
% 0.06/0.32 woz1_1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(woz1_1,definition,
% 0.06/0.32 ( woz1_1
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(woz1_2_type,type,
% 0.06/0.32 woz1_2: $o ).
% 0.06/0.32
% 0.06/0.32 thf(woz1_2,definition,
% 0.06/0.32 ( woz1_2
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Z: $i] :
% 0.06/0.32 ( ( in @ Z @ ( powerset @ A ) )
% 0.06/0.32 => ! [W: $i] :
% 0.06/0.32 ( ( in @ W @ ( powerset @ A ) )
% 0.06/0.32 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 0.06/0.32 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(woz1_3_type,type,
% 0.06/0.32 woz1_3: $o ).
% 0.06/0.32
% 0.06/0.32 thf(woz1_3,definition,
% 0.06/0.32 ( woz1_3
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ! [Z: $i] :
% 0.06/0.32 ( ( in @ Z @ ( powerset @ A ) )
% 0.06/0.32 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(woz1_4_type,type,
% 0.06/0.32 woz1_4: $o ).
% 0.06/0.32
% 0.06/0.32 thf(woz1_4,definition,
% 0.06/0.32 ( woz1_4
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.06/0.32 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(woz1_5_type,type,
% 0.06/0.32 woz1_5: $o ).
% 0.06/0.32
% 0.06/0.32 thf(woz1_5,definition,
% 0.06/0.32 ( woz1_5
% 0.06/0.32 = ( ! [A: $i,X: $i] :
% 0.06/0.32 ( ( in @ X @ ( powerset @ A ) )
% 0.06/0.32 => ! [Y: $i] :
% 0.06/0.32 ( ( in @ Y @ ( powerset @ A ) )
% 0.06/0.32 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(breln1_type,type,
% 0.06/0.32 breln1: $i > $i > $o ).
% 0.06/0.32
% 0.06/0.32 thf(breln1,definition,
% 0.06/0.32 ( breln1
% 0.06/0.32 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(breln1all2_type,type,
% 0.06/0.32 breln1all2: $o ).
% 0.06/0.32
% 0.06/0.32 thf(breln1all2,definition,
% 0.06/0.32 ( breln1all2
% 0.06/0.32 = ( ! [A: $i,R: $i] :
% 0.06/0.32 ( ( breln1 @ A @ R )
% 0.06/0.32 => ! [Xphi: $i > $o] :
% 0.06/0.32 ( ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ A )
% 0.06/0.32 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.06/0.32 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ R )
% 0.06/0.32 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(breln1Set_type,type,
% 0.06/0.32 breln1Set: $i > $i ).
% 0.06/0.32
% 0.06/0.32 thf(breln1SetBreln1_type,type,
% 0.06/0.32 breln1SetBreln1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(breln1SetBreln1,definition,
% 0.06/0.32 ( breln1SetBreln1
% 0.06/0.32 = ( ! [A: $i,R: $i] :
% 0.06/0.32 ( ( in @ R @ ( breln1Set @ A ) )
% 0.06/0.32 => ( breln1 @ A @ R ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(transitive_type,type,
% 0.06/0.32 transitive: $i > $i > $o ).
% 0.06/0.32
% 0.06/0.32 thf(antisymmetric_type,type,
% 0.06/0.32 antisymmetric: $i > $i > $o ).
% 0.06/0.32
% 0.06/0.32 thf(reflexive_type,type,
% 0.06/0.32 reflexive: $i > $i > $o ).
% 0.06/0.32
% 0.06/0.32 thf(refltransitive_type,type,
% 0.06/0.32 refltransitive: $i > $i > $o ).
% 0.06/0.32
% 0.06/0.32 thf(refllinearorder_type,type,
% 0.06/0.32 refllinearorder: $i > $i > $o ).
% 0.06/0.32
% 0.06/0.32 thf(reflwellordering_type,type,
% 0.06/0.32 reflwellordering: $i > $i > $o ).
% 0.06/0.32
% 0.06/0.32 thf(choice2fnsingleton_type,type,
% 0.06/0.32 choice2fnsingleton: $o ).
% 0.06/0.32
% 0.06/0.32 thf(choice2fnsingleton,definition,
% 0.06/0.32 ( choice2fnsingleton
% 0.06/0.32 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.06/0.32 ( ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ? [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ B )
% 0.06/0.32 & ( Xphi @ Xx @ Xy ) ) )
% 0.06/0.32 => ! [R: $i] :
% 0.06/0.32 ( ( in @ R @ ( breln1Set @ B ) )
% 0.06/0.32 => ( ( reflwellordering @ B @ R )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ( singleton
% 0.06/0.32 @ ( dsetconstr @ B
% 0.06/0.32 @ ^ [Xy: $i] :
% 0.06/0.32 ( ( Xphi @ Xx @ Xy )
% 0.06/0.32 & ! [Xz: $i] :
% 0.06/0.32 ( ( in @ Xz @ B )
% 0.06/0.32 => ( ( Xphi @ Xx @ Xz )
% 0.06/0.32 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(setOfPairsIsBReln1_type,type,
% 0.06/0.32 setOfPairsIsBReln1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(setOfPairsIsBReln1,definition,
% 0.06/0.32 ( setOfPairsIsBReln1
% 0.06/0.32 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 0.06/0.32 ( breln1 @ A
% 0.06/0.32 @ ( dpsetconstr @ A @ A
% 0.06/0.32 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(breln1all1_type,type,
% 0.06/0.32 breln1all1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(breln1all1,definition,
% 0.06/0.32 ( breln1all1
% 0.06/0.32 = ( ! [A: $i,R: $i] :
% 0.06/0.32 ( ( breln1 @ A @ R )
% 0.06/0.32 => ! [Xphi: $i > $o] :
% 0.06/0.32 ( ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ A )
% 0.06/0.32 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.06/0.32 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ R )
% 0.06/0.32 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(subbreln1_type,type,
% 0.06/0.32 subbreln1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(subbreln1,definition,
% 0.06/0.32 ( subbreln1
% 0.06/0.32 = ( ! [A: $i,R: $i] :
% 0.06/0.32 ( ( breln1 @ A @ R )
% 0.06/0.32 => ! [S: $i] :
% 0.06/0.32 ( ( breln1 @ A @ S )
% 0.06/0.32 => ( ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ A )
% 0.06/0.32 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.06/0.32 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.06/0.32 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(eqbreln1_type,type,
% 0.06/0.32 eqbreln1: $o ).
% 0.06/0.32
% 0.06/0.32 thf(eqbreln1,definition,
% 0.06/0.32 ( eqbreln1
% 0.06/0.32 = ( ! [A: $i,R: $i] :
% 0.06/0.32 ( ( breln1 @ A @ R )
% 0.06/0.32 => ! [S: $i] :
% 0.06/0.32 ( ( breln1 @ A @ S )
% 0.06/0.32 => ( ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ A )
% 0.06/0.32 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.06/0.32 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.06/0.32 => ( ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ A )
% 0.06/0.32 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.06/0.32 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.06/0.32 => ( R = S ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(breln1invset_type,type,
% 0.06/0.32 breln1invset: $i > $i > $i ).
% 0.06/0.32
% 0.06/0.32 thf(breln1invprop_type,type,
% 0.06/0.32 breln1invprop: $o ).
% 0.06/0.32
% 0.06/0.32 thf(breln1invprop,definition,
% 0.06/0.32 ( breln1invprop
% 0.06/0.32 = ( ! [A: $i,R: $i] :
% 0.06/0.32 ( ( breln1 @ A @ R )
% 0.06/0.32 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(breln1invI_type,type,
% 0.06/0.32 breln1invI: $o ).
% 0.06/0.32
% 0.06/0.32 thf(breln1invI,definition,
% 0.06/0.32 ( breln1invI
% 0.06/0.32 = ( ! [A: $i,R: $i] :
% 0.06/0.32 ( ( breln1 @ A @ R )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ A )
% 0.06/0.32 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.06/0.32 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(breln1invE_type,type,
% 0.06/0.32 breln1invE: $o ).
% 0.06/0.32
% 0.06/0.32 thf(breln1invE,definition,
% 0.06/0.32 ( breln1invE
% 0.06/0.32 = ( ! [A: $i,R: $i] :
% 0.06/0.32 ( ( breln1 @ A @ R )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ A )
% 0.06/0.32 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 0.06/0.32 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(breln1compset_type,type,
% 0.06/0.32 breln1compset: $i > $i > $i > $i ).
% 0.06/0.32
% 0.06/0.32 thf(breln1compset,definition,
% 0.06/0.32 ( breln1compset
% 0.06/0.32 = ( ^ [A: $i,R: $i,S: $i] :
% 0.06/0.32 ( dpsetconstr @ A @ A
% 0.06/0.32 @ ^ [Xx: $i,Xy: $i] :
% 0.06/0.32 ? [Xz: $i] :
% 0.06/0.32 ( ( in @ Xz @ A )
% 0.06/0.32 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.06/0.32 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(breln1compprop_type,type,
% 0.06/0.32 breln1compprop: $o ).
% 0.06/0.32
% 0.06/0.32 thf(breln1compprop,definition,
% 0.06/0.32 ( breln1compprop
% 0.06/0.32 = ( ! [A: $i,R: $i] :
% 0.06/0.32 ( ( breln1 @ A @ R )
% 0.06/0.32 => ! [S: $i] :
% 0.06/0.32 ( ( breln1 @ A @ S )
% 0.06/0.32 => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(breln1compI_type,type,
% 0.06/0.32 breln1compI: $o ).
% 0.06/0.32
% 0.06/0.32 thf(breln1compI,definition,
% 0.06/0.32 ( breln1compI
% 0.06/0.32 = ( ! [A: $i,R: $i] :
% 0.06/0.32 ( ( breln1 @ A @ R )
% 0.06/0.32 => ! [S: $i] :
% 0.06/0.32 ( ( breln1 @ A @ S )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ A )
% 0.06/0.32 => ! [Xz: $i] :
% 0.06/0.32 ( ( in @ Xz @ A )
% 0.06/0.32 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.06/0.32 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 0.06/0.32 => ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 thf(breln1compE,conjecture,
% 0.06/0.32 ( setextAx
% 0.06/0.32 => ( emptysetAx
% 0.06/0.32 => ( setadjoinAx
% 0.06/0.32 => ( powersetAx
% 0.06/0.32 => ( setunionAx
% 0.06/0.32 => ( omega0Ax
% 0.06/0.32 => ( omegaSAx
% 0.06/0.32 => ( omegaIndAx
% 0.06/0.32 => ( replAx
% 0.06/0.32 => ( foundationAx
% 0.06/0.32 => ( wellorderingAx
% 0.06/0.32 => ( descrp
% 0.06/0.32 => ( dsetconstrI
% 0.06/0.32 => ( dsetconstrEL
% 0.06/0.32 => ( dsetconstrER
% 0.06/0.32 => ( exuE1
% 0.06/0.32 => ( prop2setE
% 0.06/0.32 => ( emptysetE
% 0.06/0.32 => ( emptysetimpfalse
% 0.06/0.32 => ( notinemptyset
% 0.06/0.32 => ( exuE3e
% 0.06/0.32 => ( setext
% 0.06/0.32 => ( emptyI
% 0.06/0.32 => ( noeltsimpempty
% 0.06/0.32 => ( setbeta
% 0.06/0.32 => ( nonemptyE1
% 0.06/0.32 => ( nonemptyI
% 0.06/0.32 => ( nonemptyI1
% 0.06/0.32 => ( setadjoinIL
% 0.06/0.32 => ( emptyinunitempty
% 0.06/0.32 => ( setadjoinIR
% 0.06/0.32 => ( setadjoinE
% 0.06/0.32 => ( setadjoinOr
% 0.06/0.32 => ( setoftrueEq
% 0.06/0.32 => ( powersetI
% 0.06/0.32 => ( emptyinPowerset
% 0.06/0.32 => ( emptyInPowerset
% 0.06/0.32 => ( powersetE
% 0.06/0.32 => ( setunionI
% 0.06/0.32 => ( setunionE
% 0.06/0.32 => ( subPowSU
% 0.06/0.32 => ( exuE2
% 0.06/0.32 => ( nonemptyImpWitness
% 0.06/0.32 => ( uniqinunit
% 0.06/0.32 => ( notinsingleton
% 0.06/0.32 => ( eqinunit
% 0.06/0.32 => ( singletonsswitch
% 0.06/0.32 => ( upairsetE
% 0.06/0.32 => ( upairsetIL
% 0.06/0.32 => ( upairsetIR
% 0.06/0.32 => ( emptyE1
% 0.06/0.32 => ( vacuousDall
% 0.06/0.32 => ( quantDeMorgan1
% 0.06/0.32 => ( quantDeMorgan2
% 0.06/0.32 => ( quantDeMorgan3
% 0.06/0.32 => ( quantDeMorgan4
% 0.06/0.32 => ( prop2setI
% 0.06/0.32 => ( prop2set2propI
% 0.06/0.32 => ( notdexE
% 0.06/0.32 => ( notdallE
% 0.06/0.32 => ( exuI1
% 0.06/0.32 => ( exuI3
% 0.06/0.32 => ( exuI2
% 0.06/0.32 => ( inCongP
% 0.06/0.32 => ( in__Cong
% 0.06/0.32 => ( exuE3u
% 0.06/0.32 => ( exu__Cong
% 0.06/0.32 => ( emptyset__Cong
% 0.06/0.32 => ( setadjoin__Cong
% 0.06/0.32 => ( powerset__Cong
% 0.06/0.32 => ( setunion__Cong
% 0.06/0.32 => ( omega__Cong
% 0.06/0.32 => ( exuEu
% 0.06/0.32 => ( descr__Cong
% 0.06/0.32 => ( dsetconstr__Cong
% 0.06/0.32 => ( subsetI1
% 0.06/0.32 => ( eqimpsubset2
% 0.06/0.32 => ( eqimpsubset1
% 0.06/0.32 => ( subsetI2
% 0.06/0.32 => ( emptysetsubset
% 0.06/0.32 => ( subsetE
% 0.06/0.32 => ( subsetE2
% 0.06/0.32 => ( notsubsetI
% 0.06/0.32 => ( notequalI1
% 0.06/0.32 => ( notequalI2
% 0.06/0.32 => ( subsetRefl
% 0.06/0.32 => ( subsetTrans
% 0.06/0.32 => ( setadjoinSub
% 0.06/0.32 => ( setadjoinSub2
% 0.06/0.32 => ( subset2powerset
% 0.06/0.32 => ( setextsub
% 0.06/0.32 => ( subsetemptysetimpeq
% 0.06/0.32 => ( powersetI1
% 0.06/0.32 => ( powersetE1
% 0.06/0.32 => ( inPowerset
% 0.06/0.32 => ( powersetsubset
% 0.06/0.32 => ( sepInPowerset
% 0.06/0.32 => ( sepSubset
% 0.06/0.32 => ( binunionIL
% 0.06/0.32 => ( upairset2IR
% 0.06/0.32 => ( binunionIR
% 0.06/0.32 => ( binunionEcases
% 0.06/0.32 => ( binunionE
% 0.06/0.32 => ( binunionLsub
% 0.06/0.32 => ( binunionRsub
% 0.06/0.32 => ( binintersectI
% 0.06/0.32 => ( binintersectSubset5
% 0.06/0.32 => ( binintersectEL
% 0.06/0.32 => ( binintersectLsub
% 0.06/0.32 => ( binintersectSubset2
% 0.06/0.32 => ( binintersectSubset3
% 0.06/0.32 => ( binintersectER
% 0.06/0.32 => ( disjointsetsI1
% 0.06/0.32 => ( binintersectRsub
% 0.06/0.32 => ( binintersectSubset4
% 0.06/0.32 => ( binintersectSubset1
% 0.06/0.32 => ( bs114d
% 0.06/0.32 => ( setminusI
% 0.06/0.32 => ( setminusEL
% 0.06/0.32 => ( setminusER
% 0.06/0.32 => ( setminusSubset2
% 0.06/0.32 => ( setminusERneg
% 0.06/0.32 => ( setminusELneg
% 0.06/0.32 => ( setminusILneg
% 0.06/0.32 => ( setminusIRneg
% 0.06/0.32 => ( setminusLsub
% 0.06/0.32 => ( setminusSubset1
% 0.06/0.32 => ( symdiffE
% 0.06/0.32 => ( symdiffI1
% 0.06/0.32 => ( symdiffI2
% 0.06/0.32 => ( symdiffIneg1
% 0.06/0.32 => ( symdiffIneg2
% 0.06/0.32 => ( secondinupair
% 0.06/0.32 => ( setukpairIL
% 0.06/0.32 => ( setukpairIR
% 0.06/0.32 => ( kpairiskpair
% 0.06/0.32 => ( kpairp
% 0.06/0.32 => ( singletonsubset
% 0.06/0.32 => ( singletoninpowerset
% 0.06/0.32 => ( singletoninpowunion
% 0.06/0.32 => ( upairset2E
% 0.06/0.32 => ( upairsubunion
% 0.06/0.32 => ( upairinpowunion
% 0.06/0.32 => ( ubforcartprodlem1
% 0.06/0.32 => ( ubforcartprodlem2
% 0.06/0.32 => ( ubforcartprodlem3
% 0.06/0.32 => ( cartprodpairin
% 0.06/0.32 => ( cartprodmempair1
% 0.06/0.32 => ( cartprodmempair
% 0.06/0.32 => ( setunionE2
% 0.06/0.32 => ( setunionsingleton1
% 0.06/0.32 => ( setunionsingleton2
% 0.06/0.32 => ( setunionsingleton
% 0.06/0.32 => ( singletonprop
% 0.06/0.32 => ( ex1E1
% 0.06/0.32 => ( ex1I
% 0.06/0.32 => ( ex1I2
% 0.06/0.32 => ( singletonsuniq
% 0.06/0.32 => ( setukpairinjL1
% 0.06/0.32 => ( kfstsingleton
% 0.06/0.32 => ( theprop
% 0.06/0.32 => ( kfstpairEq
% 0.06/0.32 => ( cartprodfstin
% 0.06/0.32 => ( setukpairinjL2
% 0.06/0.32 => ( setukpairinjL
% 0.06/0.32 => ( setukpairinjR11
% 0.06/0.32 => ( setukpairinjR12
% 0.06/0.32 => ( setukpairinjR1
% 0.06/0.32 => ( upairequniteq
% 0.06/0.32 => ( setukpairinjR2
% 0.06/0.32 => ( setukpairinjR
% 0.06/0.32 => ( ksndsingleton
% 0.06/0.32 => ( ksndpairEq
% 0.06/0.32 => ( kpairsurjEq
% 0.06/0.32 => ( cartprodsndin
% 0.06/0.32 => ( cartprodpairmemEL
% 0.06/0.32 => ( cartprodpairmemER
% 0.06/0.32 => ( cartprodmempaircEq
% 0.06/0.32 => ( cartprodfstpairEq
% 0.06/0.32 => ( cartprodsndpairEq
% 0.06/0.32 => ( cartprodpairsurjEq
% 0.06/0.32 => ( dpsetconstrI
% 0.06/0.32 => ( dpsetconstrSub
% 0.06/0.32 => ( setOfPairsIsBReln
% 0.06/0.32 => ( dpsetconstrERa
% 0.06/0.32 => ( dpsetconstrEL1
% 0.06/0.32 => ( dpsetconstrEL2
% 0.06/0.32 => ( dpsetconstrER
% 0.06/0.32 => ( funcImageSingleton
% 0.06/0.32 => ( apProp
% 0.06/0.32 => ( app
% 0.06/0.32 => ( infuncsetfunc
% 0.06/0.32 => ( ap2p
% 0.06/0.32 => ( funcinfuncset
% 0.06/0.32 => ( lamProp
% 0.06/0.32 => ( lamp
% 0.06/0.32 => ( lam2p
% 0.06/0.32 => ( brelnall1
% 0.06/0.32 => ( brelnall2
% 0.06/0.32 => ( ex1E2
% 0.06/0.32 => ( funcGraphProp1
% 0.06/0.32 => ( funcGraphProp3
% 0.06/0.32 => ( funcGraphProp2
% 0.06/0.32 => ( funcextLem
% 0.06/0.32 => ( funcGraphProp4
% 0.06/0.32 => ( subbreln
% 0.06/0.32 => ( eqbreln
% 0.06/0.32 => ( funcext
% 0.06/0.32 => ( funcext2
% 0.06/0.32 => ( ap2apEq1
% 0.06/0.32 => ( ap2apEq2
% 0.06/0.32 => ( beta1
% 0.06/0.32 => ( eta1
% 0.06/0.32 => ( lam2lamEq
% 0.06/0.32 => ( beta2
% 0.06/0.32 => ( eta2
% 0.06/0.32 => ( iffalseProp1
% 0.06/0.32 => ( iffalseProp2
% 0.06/0.32 => ( iftrueProp1
% 0.06/0.32 => ( iftrueProp2
% 0.06/0.32 => ( ifSingleton
% 0.06/0.32 => ( ifp
% 0.06/0.32 => ( theeq
% 0.06/0.32 => ( iftrue
% 0.06/0.32 => ( iffalse
% 0.06/0.32 => ( iftrueorfalse
% 0.06/0.32 => ( binintersectT_lem
% 0.06/0.32 => ( binunionT_lem
% 0.06/0.32 => ( powersetT_lem
% 0.06/0.32 => ( setminusT_lem
% 0.06/0.32 => ( complementT_lem
% 0.06/0.32 => ( setextT
% 0.06/0.32 => ( subsetTI
% 0.06/0.32 => ( powersetTI1
% 0.06/0.32 => ( powersetTE1
% 0.06/0.32 => ( complementTI1
% 0.06/0.32 => ( complementTE1
% 0.06/0.32 => ( binintersectTELcontra
% 0.06/0.32 => ( binintersectTERcontra
% 0.06/0.32 => ( contrasubsetT
% 0.06/0.32 => ( contrasubsetT1
% 0.06/0.32 => ( contrasubsetT2
% 0.06/0.32 => ( contrasubsetT3
% 0.06/0.32 => ( doubleComplementI1
% 0.06/0.32 => ( doubleComplementE1
% 0.06/0.32 => ( doubleComplementSub1
% 0.06/0.32 => ( doubleComplementSub2
% 0.06/0.32 => ( doubleComplementEq
% 0.06/0.32 => ( complementTnotintersectT
% 0.06/0.32 => ( complementImpComplementIntersect
% 0.06/0.32 => ( complementSubsetComplementIntersect
% 0.06/0.32 => ( complementInPowersetComplementIntersect
% 0.06/0.32 => ( contraSubsetComplement
% 0.06/0.32 => ( complementTcontraSubset
% 0.06/0.32 => ( binunionTILcontra
% 0.06/0.32 => ( binunionTIRcontra
% 0.06/0.32 => ( inIntersectImpInUnion
% 0.06/0.32 => ( inIntersectImpInUnion2
% 0.06/0.32 => ( inIntersectImpInIntersectUnions
% 0.06/0.32 => ( intersectInPowersetIntersectUnions
% 0.06/0.32 => ( inComplementUnionImpNotIn1
% 0.06/0.32 => ( inComplementUnionImpInComplement1
% 0.06/0.32 => ( binunionTE
% 0.06/0.32 => ( binunionTEcontra
% 0.06/0.32 => ( demorgan2a1
% 0.06/0.32 => ( complementUnionInPowersetComplement
% 0.06/0.32 => ( demorgan2a2
% 0.06/0.32 => ( demorgan1a
% 0.06/0.32 => ( demorgan1b
% 0.06/0.32 => ( demorgan1
% 0.06/0.32 => ( demorgan2a
% 0.06/0.32 => ( demorgan2b2
% 0.06/0.32 => ( demorgan2b
% 0.06/0.32 => ( demorgan2
% 0.06/0.32 => ( woz13rule0
% 0.06/0.32 => ( woz13rule1
% 0.06/0.32 => ( woz13rule2
% 0.06/0.32 => ( woz13rule3
% 0.06/0.32 => ( woz13rule4
% 0.06/0.32 => ( woz1_1
% 0.06/0.32 => ( woz1_2
% 0.06/0.32 => ( woz1_3
% 0.06/0.32 => ( woz1_4
% 0.06/0.32 => ( woz1_5
% 0.06/0.32 => ( breln1all2
% 0.06/0.32 => ( breln1SetBreln1
% 0.06/0.32 => ( choice2fnsingleton
% 0.06/0.32 => ( setOfPairsIsBReln1
% 0.06/0.32 => ( breln1all1
% 0.06/0.32 => ( subbreln1
% 0.06/0.32 => ( eqbreln1
% 0.06/0.32 => ( breln1invprop
% 0.06/0.32 => ( breln1invI
% 0.06/0.32 => ( breln1invE
% 0.06/0.32 => ( breln1compprop
% 0.06/0.32 => ( breln1compI
% 0.06/0.32 => ! [A: $i,R: $i] :
% 0.06/0.32 ( ( breln1 @ A @ R )
% 0.06/0.32 => ! [S: $i] :
% 0.06/0.32 ( ( breln1 @ A @ S )
% 0.06/0.32 => ! [Xx: $i] :
% 0.06/0.32 ( ( in @ Xx @ A )
% 0.06/0.32 => ! [Xy: $i] :
% 0.06/0.32 ( ( in @ Xy @ A )
% 0.06/0.32 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 0.06/0.32 => ? [Xz: $i] :
% 0.06/0.32 ( ( in @ Xz @ A )
% 0.06/0.32 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.06/0.32 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.06/0.32
% 0.06/0.32 %------------------------------------------------------------------------------
% 0.06/0.32 ------------------------
% 2.46/1.21 ---- Embedded in THF ---
% 2.46/1.21 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.46/1.21 %%% Generated on Tue Feb 24 07:36:26 EST 2026
% 2.46/1.21 %%% using '$$dhol' embedding, version 1.3.0.
% 2.46/1.21 %%% Logic specification used:
% 2.46/1.21 %%% thf(spec, logic, $$dhol).
% 2.46/1.21
% 2.46/1.21 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.uVZj498QyD/DTF2DTF20195.p
% See solution above
% 2.46/1.22 ------------------------
% 2.46/1.25 ---- Cleaned THF ---
% 2.46/1.26 thf(in_type,type,
% 2.46/1.26 in: $i > $i > $o ).
% 2.46/1.26
% 2.46/1.26 thf(exu_type,type,
% 2.46/1.26 exu: ( $i > $o ) > $o ).
% 2.46/1.26
% 2.46/1.26 thf(exu,definition,
% 2.46/1.26 ( exu
% 2.46/1.26 = ( ^ [Xphi: $i > $o] :
% 2.46/1.26 ? [Xx: $i] :
% 2.46/1.26 ( ( Xphi @ Xx )
% 2.46/1.26 & ! [Xy: $i] :
% 2.46/1.26 ( ( Xphi @ Xy )
% 2.46/1.26 => ( Xx = Xy ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setextAx_type,type,
% 2.46/1.26 setextAx: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setextAx,definition,
% 2.46/1.26 ( setextAx
% 2.46/1.26 = ( ! [A: $i,B: $i] :
% 2.46/1.26 ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 <=> ( in @ Xx @ B ) )
% 2.46/1.26 => ( A = B ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(emptyset_type,type,
% 2.46/1.26 emptyset: $i ).
% 2.46/1.26
% 2.46/1.26 thf(emptysetAx_type,type,
% 2.46/1.26 emptysetAx: $o ).
% 2.46/1.26
% 2.46/1.26 thf(emptysetAx,definition,
% 2.46/1.26 ( emptysetAx
% 2.46/1.26 = ( ! [Xx: $i] :
% 2.46/1.26 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setadjoin_type,type,
% 2.46/1.26 setadjoin: $i > $i > $i ).
% 2.46/1.26
% 2.46/1.26 thf(setadjoinAx_type,type,
% 2.46/1.26 setadjoinAx: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setadjoinAx,definition,
% 2.46/1.26 ( setadjoinAx
% 2.46/1.26 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.46/1.26 <=> ( ( Xy = Xx )
% 2.46/1.26 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(powerset_type,type,
% 2.46/1.26 powerset: $i > $i ).
% 2.46/1.26
% 2.46/1.26 thf(powersetAx_type,type,
% 2.46/1.26 powersetAx: $o ).
% 2.46/1.26
% 2.46/1.26 thf(powersetAx,definition,
% 2.46/1.26 ( powersetAx
% 2.46/1.26 = ( ! [A: $i,B: $i] :
% 2.46/1.26 ( ( in @ B @ ( powerset @ A ) )
% 2.46/1.26 <=> ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ B )
% 2.46/1.26 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setunion_type,type,
% 2.46/1.26 setunion: $i > $i ).
% 2.46/1.26
% 2.46/1.26 thf(setunionAx_type,type,
% 2.46/1.26 setunionAx: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setunionAx,definition,
% 2.46/1.26 ( setunionAx
% 2.46/1.26 = ( ! [A: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ ( setunion @ A ) )
% 2.46/1.26 <=> ? [B: $i] :
% 2.46/1.26 ( ( in @ Xx @ B )
% 2.46/1.26 & ( in @ B @ A ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(omega_type,type,
% 2.46/1.26 omega: $i ).
% 2.46/1.26
% 2.46/1.26 thf(omega0Ax_type,type,
% 2.46/1.26 omega0Ax: $o ).
% 2.46/1.26
% 2.46/1.26 thf(omega0Ax,definition,
% 2.46/1.26 ( omega0Ax
% 2.46/1.26 = ( in @ emptyset @ omega ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(omegaSAx_type,type,
% 2.46/1.26 omegaSAx: $o ).
% 2.46/1.26
% 2.46/1.26 thf(omegaSAx,definition,
% 2.46/1.26 ( omegaSAx
% 2.46/1.26 = ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ omega )
% 2.46/1.26 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(omegaIndAx_type,type,
% 2.46/1.26 omegaIndAx: $o ).
% 2.46/1.26
% 2.46/1.26 thf(omegaIndAx,definition,
% 2.46/1.26 ( omegaIndAx
% 2.46/1.26 = ( ! [A: $i] :
% 2.46/1.26 ( ( ( in @ emptyset @ A )
% 2.46/1.26 & ! [Xx: $i] :
% 2.46/1.26 ( ( ( in @ Xx @ omega )
% 2.46/1.26 & ( in @ Xx @ A ) )
% 2.46/1.26 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ omega )
% 2.46/1.26 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(replAx_type,type,
% 2.46/1.26 replAx: $o ).
% 2.46/1.26
% 2.46/1.26 thf(replAx,definition,
% 2.46/1.26 ( replAx
% 2.46/1.26 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.46/1.26 ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( exu
% 2.46/1.26 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.46/1.26 => ? [B: $i] :
% 2.46/1.26 ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ B )
% 2.46/1.26 <=> ? [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ A )
% 2.46/1.26 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(foundationAx_type,type,
% 2.46/1.26 foundationAx: $o ).
% 2.46/1.26
% 2.46/1.26 thf(foundationAx,definition,
% 2.46/1.26 ( foundationAx
% 2.46/1.26 = ( ! [A: $i] :
% 2.46/1.26 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.46/1.26 => ? [B: $i] :
% 2.46/1.26 ( ( in @ B @ A )
% 2.46/1.26 & ~ ? [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ B )
% 2.46/1.26 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(wellorderingAx_type,type,
% 2.46/1.26 wellorderingAx: $o ).
% 2.46/1.26
% 2.46/1.26 thf(wellorderingAx,definition,
% 2.46/1.26 ( wellorderingAx
% 2.46/1.26 = ( ! [A: $i] :
% 2.46/1.26 ? [B: $i] :
% 2.46/1.26 ( ! [C: $i] :
% 2.46/1.26 ( ( in @ C @ B )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ C )
% 2.46/1.26 => ( in @ Xx @ A ) ) )
% 2.46/1.26 & ! [Xx: $i,Xy: $i] :
% 2.46/1.26 ( ( ( in @ Xx @ A )
% 2.46/1.26 & ( in @ Xy @ A ) )
% 2.46/1.26 => ( ! [C: $i] :
% 2.46/1.26 ( ( in @ C @ B )
% 2.46/1.26 => ( ( in @ Xx @ C )
% 2.46/1.26 <=> ( in @ Xy @ C ) ) )
% 2.46/1.26 => ( Xx = Xy ) ) )
% 2.46/1.26 & ! [C: $i,D: $i] :
% 2.46/1.26 ( ( ( in @ C @ B )
% 2.46/1.26 & ( in @ D @ B ) )
% 2.46/1.26 => ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ C )
% 2.46/1.26 => ( in @ Xx @ D ) )
% 2.46/1.26 | ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ D )
% 2.46/1.26 => ( in @ Xx @ C ) ) ) )
% 2.46/1.26 & ! [C: $i] :
% 2.46/1.26 ( ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ C )
% 2.46/1.26 => ( in @ Xx @ A ) )
% 2.46/1.26 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.46/1.26 => ? [D: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ D @ B )
% 2.46/1.26 & ( in @ Xx @ C )
% 2.46/1.26 & ~ ? [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ D )
% 2.46/1.26 & ( in @ Xy @ C ) )
% 2.46/1.26 & ! [E: $i] :
% 2.46/1.26 ( ( in @ E @ B )
% 2.46/1.26 => ( ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ E )
% 2.46/1.26 => ( in @ Xy @ D ) )
% 2.46/1.26 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(descr_type,type,
% 2.46/1.26 descr: ( $i > $o ) > $i ).
% 2.46/1.26
% 2.46/1.26 thf(descrp_type,type,
% 2.46/1.26 descrp: $o ).
% 2.46/1.26
% 2.46/1.26 thf(descrp,definition,
% 2.46/1.26 ( descrp
% 2.46/1.26 = ( ! [Xphi: $i > $o] :
% 2.46/1.26 ( ( exu
% 2.46/1.26 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.46/1.26 => ( Xphi
% 2.46/1.26 @ ( descr
% 2.46/1.26 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(dsetconstr_type,type,
% 2.46/1.26 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.46/1.26
% 2.46/1.26 thf(dsetconstrI_type,type,
% 2.46/1.26 dsetconstrI: $o ).
% 2.46/1.26
% 2.46/1.26 thf(dsetconstrI,definition,
% 2.46/1.26 ( dsetconstrI
% 2.46/1.26 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( Xphi @ Xx )
% 2.46/1.26 => ( in @ Xx
% 2.46/1.26 @ ( dsetconstr @ A
% 2.46/1.26 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(dsetconstrEL_type,type,
% 2.46/1.26 dsetconstrEL: $o ).
% 2.46/1.26
% 2.46/1.26 thf(dsetconstrEL,definition,
% 2.46/1.26 ( dsetconstrEL
% 2.46/1.26 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx
% 2.46/1.26 @ ( dsetconstr @ A
% 2.46/1.26 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.46/1.26 => ( in @ Xx @ A ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(dsetconstrER_type,type,
% 2.46/1.26 dsetconstrER: $o ).
% 2.46/1.26
% 2.46/1.26 thf(dsetconstrER,definition,
% 2.46/1.26 ( dsetconstrER
% 2.46/1.26 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx
% 2.46/1.26 @ ( dsetconstr @ A
% 2.46/1.26 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.46/1.26 => ( Xphi @ Xx ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(exuE1_type,type,
% 2.46/1.26 exuE1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(exuE1,definition,
% 2.46/1.26 ( exuE1
% 2.46/1.26 = ( ! [Xphi: $i > $o] :
% 2.46/1.26 ( ( exu
% 2.46/1.26 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.46/1.26 => ? [Xx: $i] :
% 2.46/1.26 ( ( Xphi @ Xx )
% 2.46/1.26 & ! [Xy: $i] :
% 2.46/1.26 ( ( Xphi @ Xy )
% 2.46/1.26 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(prop2set_type,type,
% 2.46/1.26 prop2set: $o > $i ).
% 2.46/1.26
% 2.46/1.26 thf(prop2setE_type,type,
% 2.46/1.26 prop2setE: $o ).
% 2.46/1.26
% 2.46/1.26 thf(prop2setE,definition,
% 2.46/1.26 ( prop2setE
% 2.46/1.26 = ( ! [Xphi: $o,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.46/1.26 => Xphi ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(emptysetE_type,type,
% 2.46/1.26 emptysetE: $o ).
% 2.46/1.26
% 2.46/1.26 thf(emptysetE,definition,
% 2.46/1.26 ( emptysetE
% 2.46/1.26 = ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ emptyset )
% 2.46/1.26 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(emptysetimpfalse_type,type,
% 2.46/1.26 emptysetimpfalse: $o ).
% 2.46/1.26
% 2.46/1.26 thf(emptysetimpfalse,definition,
% 2.46/1.26 ( emptysetimpfalse
% 2.46/1.26 = ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ emptyset )
% 2.46/1.26 => $false ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(notinemptyset_type,type,
% 2.46/1.26 notinemptyset: $o ).
% 2.46/1.26
% 2.46/1.26 thf(notinemptyset,definition,
% 2.46/1.26 ( notinemptyset
% 2.46/1.26 = ( ! [Xx: $i] :
% 2.46/1.26 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(exuE3e_type,type,
% 2.46/1.26 exuE3e: $o ).
% 2.46/1.26
% 2.46/1.26 thf(exuE3e,definition,
% 2.46/1.26 ( exuE3e
% 2.46/1.26 = ( ! [Xphi: $i > $o] :
% 2.46/1.26 ( ( exu
% 2.46/1.26 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.46/1.26 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setext_type,type,
% 2.46/1.26 setext: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setext,definition,
% 2.46/1.26 ( setext
% 2.46/1.26 = ( ! [A: $i,B: $i] :
% 2.46/1.26 ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( in @ Xx @ B ) )
% 2.46/1.26 => ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ B )
% 2.46/1.26 => ( in @ Xx @ A ) )
% 2.46/1.26 => ( A = B ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(emptyI_type,type,
% 2.46/1.26 emptyI: $o ).
% 2.46/1.26
% 2.46/1.26 thf(emptyI,definition,
% 2.46/1.26 ( emptyI
% 2.46/1.26 = ( ! [A: $i] :
% 2.46/1.26 ( ! [Xx: $i] :
% 2.46/1.26 ~ ( in @ Xx @ A )
% 2.46/1.26 => ( A = emptyset ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(noeltsimpempty_type,type,
% 2.46/1.26 noeltsimpempty: $o ).
% 2.46/1.26
% 2.46/1.26 thf(noeltsimpempty,definition,
% 2.46/1.26 ( noeltsimpempty
% 2.46/1.26 = ( ! [A: $i] :
% 2.46/1.26 ( ! [Xx: $i] :
% 2.46/1.26 ~ ( in @ Xx @ A )
% 2.46/1.26 => ( A = emptyset ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setbeta_type,type,
% 2.46/1.26 setbeta: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setbeta,definition,
% 2.46/1.26 ( setbeta
% 2.46/1.26 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( in @ Xx
% 2.46/1.26 @ ( dsetconstr @ A
% 2.46/1.26 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.46/1.26 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(nonempty_type,type,
% 2.46/1.26 nonempty: $i > $o ).
% 2.46/1.26
% 2.46/1.26 thf(nonempty,definition,
% 2.46/1.26 ( nonempty
% 2.46/1.26 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(nonemptyE1_type,type,
% 2.46/1.26 nonemptyE1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(nonemptyE1,definition,
% 2.46/1.26 ( nonemptyE1
% 2.46/1.26 = ( ! [A: $i] :
% 2.46/1.26 ( ( nonempty @ A )
% 2.46/1.26 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(nonemptyI_type,type,
% 2.46/1.26 nonemptyI: $o ).
% 2.46/1.26
% 2.46/1.26 thf(nonemptyI,definition,
% 2.46/1.26 ( nonemptyI
% 2.46/1.26 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( Xphi @ Xx )
% 2.46/1.26 => ( nonempty
% 2.46/1.26 @ ( dsetconstr @ A
% 2.46/1.26 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(nonemptyI1_type,type,
% 2.46/1.26 nonemptyI1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(nonemptyI1,definition,
% 2.46/1.26 ( nonemptyI1
% 2.46/1.26 = ( ! [A: $i] :
% 2.46/1.26 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.46/1.26 => ( nonempty @ A ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setadjoinIL_type,type,
% 2.46/1.26 setadjoinIL: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setadjoinIL,definition,
% 2.46/1.26 ( setadjoinIL
% 2.46/1.26 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(emptyinunitempty_type,type,
% 2.46/1.26 emptyinunitempty: $o ).
% 2.46/1.26
% 2.46/1.26 thf(emptyinunitempty,definition,
% 2.46/1.26 ( emptyinunitempty
% 2.46/1.26 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setadjoinIR_type,type,
% 2.46/1.26 setadjoinIR: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setadjoinIR,definition,
% 2.46/1.26 ( setadjoinIR
% 2.46/1.26 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ A )
% 2.46/1.26 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setadjoinE_type,type,
% 2.46/1.26 setadjoinE: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setadjoinE,definition,
% 2.46/1.26 ( setadjoinE
% 2.46/1.26 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.46/1.26 => ! [Xphi: $o] :
% 2.46/1.26 ( ( ( Xy = Xx )
% 2.46/1.26 => Xphi )
% 2.46/1.26 => ( ( ( in @ Xy @ A )
% 2.46/1.26 => Xphi )
% 2.46/1.26 => Xphi ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setadjoinOr_type,type,
% 2.46/1.26 setadjoinOr: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setadjoinOr,definition,
% 2.46/1.26 ( setadjoinOr
% 2.46/1.26 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.46/1.26 => ( ( Xy = Xx )
% 2.46/1.26 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setoftrueEq_type,type,
% 2.46/1.26 setoftrueEq: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setoftrueEq,definition,
% 2.46/1.26 ( setoftrueEq
% 2.46/1.26 = ( ! [A: $i] :
% 2.46/1.26 ( ( dsetconstr @ A
% 2.46/1.26 @ ^ [Xx: $i] : $true )
% 2.46/1.26 = A ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(powersetI_type,type,
% 2.46/1.26 powersetI: $o ).
% 2.46/1.26
% 2.46/1.26 thf(powersetI,definition,
% 2.46/1.26 ( powersetI
% 2.46/1.26 = ( ! [A: $i,B: $i] :
% 2.46/1.26 ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ B )
% 2.46/1.26 => ( in @ Xx @ A ) )
% 2.46/1.26 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(emptyinPowerset_type,type,
% 2.46/1.26 emptyinPowerset: $o ).
% 2.46/1.26
% 2.46/1.26 thf(emptyinPowerset,definition,
% 2.46/1.26 ( emptyinPowerset
% 2.46/1.26 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(emptyInPowerset_type,type,
% 2.46/1.26 emptyInPowerset: $o ).
% 2.46/1.26
% 2.46/1.26 thf(emptyInPowerset,definition,
% 2.46/1.26 ( emptyInPowerset
% 2.46/1.26 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(powersetE_type,type,
% 2.46/1.26 powersetE: $o ).
% 2.46/1.26
% 2.46/1.26 thf(powersetE,definition,
% 2.46/1.26 ( powersetE
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ B @ ( powerset @ A ) )
% 2.46/1.26 => ( ( in @ Xx @ B )
% 2.46/1.26 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setunionI_type,type,
% 2.46/1.26 setunionI: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setunionI,definition,
% 2.46/1.26 ( setunionI
% 2.46/1.26 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.46/1.26 ( ( in @ Xx @ B )
% 2.46/1.26 => ( ( in @ B @ A )
% 2.46/1.26 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setunionE_type,type,
% 2.46/1.26 setunionE: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setunionE,definition,
% 2.46/1.26 ( setunionE
% 2.46/1.26 = ( ! [A: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ ( setunion @ A ) )
% 2.46/1.26 => ! [Xphi: $o] :
% 2.46/1.26 ( ! [B: $i] :
% 2.46/1.26 ( ( in @ Xx @ B )
% 2.46/1.26 => ( ( in @ B @ A )
% 2.46/1.26 => Xphi ) )
% 2.46/1.26 => Xphi ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(subPowSU_type,type,
% 2.46/1.26 subPowSU: $o ).
% 2.46/1.26
% 2.46/1.26 thf(subPowSU,definition,
% 2.46/1.26 ( subPowSU
% 2.46/1.26 = ( ! [A: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(exuE2_type,type,
% 2.46/1.26 exuE2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(exuE2,definition,
% 2.46/1.26 ( exuE2
% 2.46/1.26 = ( ! [Xphi: $i > $o] :
% 2.46/1.26 ( ( exu
% 2.46/1.26 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.46/1.26 => ? [Xx: $i] :
% 2.46/1.26 ! [Xy: $i] :
% 2.46/1.26 ( ( Xphi @ Xy )
% 2.46/1.26 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(nonemptyImpWitness_type,type,
% 2.46/1.26 nonemptyImpWitness: $o ).
% 2.46/1.26
% 2.46/1.26 thf(nonemptyImpWitness,definition,
% 2.46/1.26 ( nonemptyImpWitness
% 2.46/1.26 = ( ! [A: $i] :
% 2.46/1.26 ( ( nonempty @ A )
% 2.46/1.26 => ? [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 & $true ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(uniqinunit_type,type,
% 2.46/1.26 uniqinunit: $o ).
% 2.46/1.26
% 2.46/1.26 thf(uniqinunit,definition,
% 2.46/1.26 ( uniqinunit
% 2.46/1.26 = ( ! [Xx: $i,Xy: $i] :
% 2.46/1.26 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.46/1.26 => ( Xx = Xy ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(notinsingleton_type,type,
% 2.46/1.26 notinsingleton: $o ).
% 2.46/1.26
% 2.46/1.26 thf(notinsingleton,definition,
% 2.46/1.26 ( notinsingleton
% 2.46/1.26 = ( ! [Xx: $i,Xy: $i] :
% 2.46/1.26 ( ( Xx != Xy )
% 2.46/1.26 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(eqinunit_type,type,
% 2.46/1.26 eqinunit: $o ).
% 2.46/1.26
% 2.46/1.26 thf(eqinunit,definition,
% 2.46/1.26 ( eqinunit
% 2.46/1.26 = ( ! [Xx: $i,Xy: $i] :
% 2.46/1.26 ( ( Xx = Xy )
% 2.46/1.26 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(singletonsswitch_type,type,
% 2.46/1.26 singletonsswitch: $o ).
% 2.46/1.26
% 2.46/1.26 thf(singletonsswitch,definition,
% 2.46/1.26 ( singletonsswitch
% 2.46/1.26 = ( ! [Xx: $i,Xy: $i] :
% 2.46/1.26 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.46/1.26 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(upairsetE_type,type,
% 2.46/1.26 upairsetE: $o ).
% 2.46/1.26
% 2.46/1.26 thf(upairsetE,definition,
% 2.46/1.26 ( upairsetE
% 2.46/1.26 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.46/1.26 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.46/1.26 => ( ( Xz = Xx )
% 2.46/1.26 | ( Xz = Xy ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(upairsetIL_type,type,
% 2.46/1.26 upairsetIL: $o ).
% 2.46/1.26
% 2.46/1.26 thf(upairsetIL,definition,
% 2.46/1.26 ( upairsetIL
% 2.46/1.26 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(upairsetIR_type,type,
% 2.46/1.26 upairsetIR: $o ).
% 2.46/1.26
% 2.46/1.26 thf(upairsetIR,definition,
% 2.46/1.26 ( upairsetIR
% 2.46/1.26 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(emptyE1_type,type,
% 2.46/1.26 emptyE1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(emptyE1,definition,
% 2.46/1.26 ( emptyE1
% 2.46/1.26 = ( ! [A: $i,Xphi: $i > $o] :
% 2.46/1.26 ( ? [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 & ( Xphi @ Xx ) )
% 2.46/1.26 => ( ( ( dsetconstr @ A
% 2.46/1.26 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.46/1.26 = emptyset )
% 2.46/1.26 => $false ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(vacuousDall_type,type,
% 2.46/1.26 vacuousDall: $o ).
% 2.46/1.26
% 2.46/1.26 thf(vacuousDall,definition,
% 2.46/1.26 ( vacuousDall
% 2.46/1.26 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ emptyset )
% 2.46/1.26 => ( Xphi @ Xx ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(quantDeMorgan1_type,type,
% 2.46/1.26 quantDeMorgan1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(quantDeMorgan1,definition,
% 2.46/1.26 ( quantDeMorgan1
% 2.46/1.26 = ( ! [A: $i,Xphi: $i > $o] :
% 2.46/1.26 ( ~ ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( Xphi @ Xx ) )
% 2.46/1.26 => ? [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(quantDeMorgan2_type,type,
% 2.46/1.26 quantDeMorgan2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(quantDeMorgan2,definition,
% 2.46/1.26 ( quantDeMorgan2
% 2.46/1.26 = ( ! [A: $i,Xphi: $i > $o] :
% 2.46/1.26 ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ~ ( Xphi @ Xx ) )
% 2.46/1.26 => ~ ? [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(quantDeMorgan3_type,type,
% 2.46/1.26 quantDeMorgan3: $o ).
% 2.46/1.26
% 2.46/1.26 thf(quantDeMorgan3,definition,
% 2.46/1.26 ( quantDeMorgan3
% 2.46/1.26 = ( ! [A: $i,Xphi: $i > $o] :
% 2.46/1.26 ( ~ ? [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 & ( Xphi @ Xx ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(quantDeMorgan4_type,type,
% 2.46/1.26 quantDeMorgan4: $o ).
% 2.46/1.26
% 2.46/1.26 thf(quantDeMorgan4,definition,
% 2.46/1.26 ( quantDeMorgan4
% 2.46/1.26 = ( ! [A: $i,Xphi: $i > $o] :
% 2.46/1.26 ( ? [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 & ~ ( Xphi @ Xx ) )
% 2.46/1.26 => ~ ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(prop2setI_type,type,
% 2.46/1.26 prop2setI: $o ).
% 2.46/1.26
% 2.46/1.26 thf(prop2setI,definition,
% 2.46/1.26 ( prop2setI
% 2.46/1.26 = ( ! [Xphi: $o] :
% 2.46/1.26 ( Xphi
% 2.46/1.26 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(set2prop_type,type,
% 2.46/1.26 set2prop: $i > $o ).
% 2.46/1.26
% 2.46/1.26 thf(prop2set2propI_type,type,
% 2.46/1.26 prop2set2propI: $o ).
% 2.46/1.26
% 2.46/1.26 thf(prop2set2propI,definition,
% 2.46/1.26 ( prop2set2propI
% 2.46/1.26 = ( ! [Xphi: $o] :
% 2.46/1.26 ( Xphi
% 2.46/1.26 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(notdexE_type,type,
% 2.46/1.26 notdexE: $o ).
% 2.46/1.26
% 2.46/1.26 thf(notdexE,definition,
% 2.46/1.26 ( notdexE
% 2.46/1.26 = ( ! [A: $i,Xphi: $i > $o] :
% 2.46/1.26 ( ~ ? [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 & ( Xphi @ Xx ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(notdallE_type,type,
% 2.46/1.26 notdallE: $o ).
% 2.46/1.26
% 2.46/1.26 thf(notdallE,definition,
% 2.46/1.26 ( notdallE
% 2.46/1.26 = ( ! [A: $i,Xphi: $i > $o] :
% 2.46/1.26 ( ~ ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( Xphi @ Xx ) )
% 2.46/1.26 => ? [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(exuI1_type,type,
% 2.46/1.26 exuI1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(exuI1,definition,
% 2.46/1.26 ( exuI1
% 2.46/1.26 = ( ! [Xphi: $i > $o] :
% 2.46/1.26 ( ? [Xx: $i] :
% 2.46/1.26 ( ( Xphi @ Xx )
% 2.46/1.26 & ! [Xy: $i] :
% 2.46/1.26 ( ( Xphi @ Xy )
% 2.46/1.26 => ( Xx = Xy ) ) )
% 2.46/1.26 => ( exu
% 2.46/1.26 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(exuI3_type,type,
% 2.46/1.26 exuI3: $o ).
% 2.46/1.26
% 2.46/1.26 thf(exuI3,definition,
% 2.46/1.26 ( exuI3
% 2.46/1.26 = ( ! [Xphi: $i > $o] :
% 2.46/1.26 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.46/1.26 => ( ! [Xx: $i,Xy: $i] :
% 2.46/1.26 ( ( Xphi @ Xx )
% 2.46/1.26 => ( ( Xphi @ Xy )
% 2.46/1.26 => ( Xx = Xy ) ) )
% 2.46/1.26 => ( exu
% 2.46/1.26 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(exuI2_type,type,
% 2.46/1.26 exuI2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(exuI2,definition,
% 2.46/1.26 ( exuI2
% 2.46/1.26 = ( ! [Xphi: $i > $o] :
% 2.46/1.26 ( ? [Xx: $i] :
% 2.46/1.26 ! [Xy: $i] :
% 2.46/1.26 ( ( Xphi @ Xy )
% 2.46/1.26 <=> ( Xy = Xx ) )
% 2.46/1.26 => ( exu
% 2.46/1.26 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(inCongP_type,type,
% 2.46/1.26 inCongP: $o ).
% 2.46/1.26
% 2.46/1.26 thf(inCongP,definition,
% 2.46/1.26 ( inCongP
% 2.46/1.26 = ( ! [A: $i,B: $i] :
% 2.46/1.26 ( ( A = B )
% 2.46/1.26 => ! [Xx: $i,Xy: $i] :
% 2.46/1.26 ( ( Xx = Xy )
% 2.46/1.26 => ( ( in @ Xx @ A )
% 2.46/1.26 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(in__Cong_type,type,
% 2.46/1.26 in__Cong: $o ).
% 2.46/1.26
% 2.46/1.26 thf(in__Cong,definition,
% 2.46/1.26 ( in__Cong
% 2.46/1.26 = ( ! [A: $i,B: $i] :
% 2.46/1.26 ( ( A = B )
% 2.46/1.26 => ! [Xx: $i,Xy: $i] :
% 2.46/1.26 ( ( Xx = Xy )
% 2.46/1.26 => ( ( in @ Xx @ A )
% 2.46/1.26 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(exuE3u_type,type,
% 2.46/1.26 exuE3u: $o ).
% 2.46/1.26
% 2.46/1.26 thf(exuE3u,definition,
% 2.46/1.26 ( exuE3u
% 2.46/1.26 = ( ! [Xphi: $i > $o] :
% 2.46/1.26 ( ( exu
% 2.46/1.26 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.46/1.26 => ! [Xx: $i,Xy: $i] :
% 2.46/1.26 ( ( Xphi @ Xx )
% 2.46/1.26 => ( ( Xphi @ Xy )
% 2.46/1.26 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(exu__Cong_type,type,
% 2.46/1.26 exu__Cong: $o ).
% 2.46/1.26
% 2.46/1.26 thf(exu__Cong,definition,
% 2.46/1.26 ( exu__Cong
% 2.46/1.26 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.46/1.26 ( ! [Xx: $i,Xy: $i] :
% 2.46/1.26 ( ( Xx = Xy )
% 2.46/1.26 => ( ( Xphi @ Xx )
% 2.46/1.26 <=> ( Xpsi @ Xy ) ) )
% 2.46/1.26 => ( ( exu
% 2.46/1.26 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.46/1.26 <=> ( exu
% 2.46/1.26 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(emptyset__Cong_type,type,
% 2.46/1.26 emptyset__Cong: $o ).
% 2.46/1.26
% 2.46/1.26 thf(emptyset__Cong,definition,
% 2.46/1.26 ( emptyset__Cong
% 2.46/1.26 = ( emptyset = emptyset ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setadjoin__Cong_type,type,
% 2.46/1.26 setadjoin__Cong: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setadjoin__Cong,definition,
% 2.46/1.26 ( setadjoin__Cong
% 2.46/1.26 = ( ! [Xx: $i,Xy: $i] :
% 2.46/1.26 ( ( Xx = Xy )
% 2.46/1.26 => ! [Xz: $i,Xu: $i] :
% 2.46/1.26 ( ( Xz = Xu )
% 2.46/1.26 => ( ( setadjoin @ Xx @ Xz )
% 2.46/1.26 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(powerset__Cong_type,type,
% 2.46/1.26 powerset__Cong: $o ).
% 2.46/1.26
% 2.46/1.26 thf(powerset__Cong,definition,
% 2.46/1.26 ( powerset__Cong
% 2.46/1.26 = ( ! [A: $i,B: $i] :
% 2.46/1.26 ( ( A = B )
% 2.46/1.26 => ( ( powerset @ A )
% 2.46/1.26 = ( powerset @ B ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setunion__Cong_type,type,
% 2.46/1.26 setunion__Cong: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setunion__Cong,definition,
% 2.46/1.26 ( setunion__Cong
% 2.46/1.26 = ( ! [A: $i,B: $i] :
% 2.46/1.26 ( ( A = B )
% 2.46/1.26 => ( ( setunion @ A )
% 2.46/1.26 = ( setunion @ B ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(omega__Cong_type,type,
% 2.46/1.26 omega__Cong: $o ).
% 2.46/1.26
% 2.46/1.26 thf(omega__Cong,definition,
% 2.46/1.26 ( omega__Cong
% 2.46/1.26 = ( omega = omega ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(exuEu_type,type,
% 2.46/1.26 exuEu: $o ).
% 2.46/1.26
% 2.46/1.26 thf(exuEu,definition,
% 2.46/1.26 ( exuEu
% 2.46/1.26 = ( ! [Xphi: $i > $o] :
% 2.46/1.26 ( ( exu
% 2.46/1.26 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.46/1.26 => ! [Xx: $i,Xy: $i] :
% 2.46/1.26 ( ( Xphi @ Xx )
% 2.46/1.26 => ( ( Xphi @ Xy )
% 2.46/1.26 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(descr__Cong_type,type,
% 2.46/1.26 descr__Cong: $o ).
% 2.46/1.26
% 2.46/1.26 thf(descr__Cong,definition,
% 2.46/1.26 ( descr__Cong
% 2.46/1.26 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.46/1.26 ( ! [Xx: $i,Xy: $i] :
% 2.46/1.26 ( ( Xx = Xy )
% 2.46/1.26 => ( ( Xphi @ Xx )
% 2.46/1.26 <=> ( Xpsi @ Xy ) ) )
% 2.46/1.26 => ( ( exu
% 2.46/1.26 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.46/1.26 => ( ( exu
% 2.46/1.26 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.46/1.26 => ( ( descr
% 2.46/1.26 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.46/1.26 = ( descr
% 2.46/1.26 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(dsetconstr__Cong_type,type,
% 2.46/1.26 dsetconstr__Cong: $o ).
% 2.46/1.26
% 2.46/1.26 thf(dsetconstr__Cong,definition,
% 2.46/1.26 ( dsetconstr__Cong
% 2.46/1.26 = ( ! [A: $i,B: $i] :
% 2.46/1.26 ( ( A = B )
% 2.46/1.26 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.46/1.26 ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ B )
% 2.46/1.26 => ( ( Xx = Xy )
% 2.46/1.26 => ( ( Xphi @ Xx )
% 2.46/1.26 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.46/1.26 => ( ( dsetconstr @ A
% 2.46/1.26 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.46/1.26 = ( dsetconstr @ B
% 2.46/1.26 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(subset_type,type,
% 2.46/1.26 subset: $i > $i > $o ).
% 2.46/1.26
% 2.46/1.26 thf(disjoint_type,type,
% 2.46/1.26 disjoint: $i > $i > $o ).
% 2.46/1.26
% 2.46/1.26 thf(setsmeet_type,type,
% 2.46/1.26 setsmeet: $i > $i > $o ).
% 2.46/1.26
% 2.46/1.26 thf(subsetI1_type,type,
% 2.46/1.26 subsetI1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(subsetI1,definition,
% 2.46/1.26 ( subsetI1
% 2.46/1.26 = ( ! [A: $i,B: $i] :
% 2.46/1.26 ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( in @ Xx @ B ) )
% 2.46/1.26 => ( subset @ A @ B ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(eqimpsubset2_type,type,
% 2.46/1.26 eqimpsubset2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(eqimpsubset2,definition,
% 2.46/1.26 ( eqimpsubset2
% 2.46/1.26 = ( ! [A: $i,B: $i] :
% 2.46/1.26 ( ( A = B )
% 2.46/1.26 => ( subset @ B @ A ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(eqimpsubset1_type,type,
% 2.46/1.26 eqimpsubset1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(eqimpsubset1,definition,
% 2.46/1.26 ( eqimpsubset1
% 2.46/1.26 = ( ! [A: $i,B: $i] :
% 2.46/1.26 ( ( A = B )
% 2.46/1.26 => ( subset @ A @ B ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(subsetI2_type,type,
% 2.46/1.26 subsetI2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(subsetI2,definition,
% 2.46/1.26 ( subsetI2
% 2.46/1.26 = ( ! [A: $i,B: $i] :
% 2.46/1.26 ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( in @ Xx @ B ) )
% 2.46/1.26 => ( subset @ A @ B ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(emptysetsubset_type,type,
% 2.46/1.26 emptysetsubset: $o ).
% 2.46/1.26
% 2.46/1.26 thf(emptysetsubset,definition,
% 2.46/1.26 ( emptysetsubset
% 2.46/1.26 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(subsetE_type,type,
% 2.46/1.26 subsetE: $o ).
% 2.46/1.26
% 2.46/1.26 thf(subsetE,definition,
% 2.46/1.26 ( subsetE
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ( subset @ A @ B )
% 2.46/1.26 => ( ( in @ Xx @ A )
% 2.46/1.26 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(subsetE2_type,type,
% 2.46/1.26 subsetE2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(subsetE2,definition,
% 2.46/1.26 ( subsetE2
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ( subset @ A @ B )
% 2.46/1.26 => ( ~ ( in @ Xx @ B )
% 2.46/1.26 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(notsubsetI_type,type,
% 2.46/1.26 notsubsetI: $o ).
% 2.46/1.26
% 2.46/1.26 thf(notsubsetI,definition,
% 2.46/1.26 ( notsubsetI
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ~ ( in @ Xx @ B )
% 2.46/1.26 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(notequalI1_type,type,
% 2.46/1.26 notequalI1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(notequalI1,definition,
% 2.46/1.26 ( notequalI1
% 2.46/1.26 = ( ! [A: $i,B: $i] :
% 2.46/1.26 ( ~ ( subset @ A @ B )
% 2.46/1.26 => ( A != B ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(notequalI2_type,type,
% 2.46/1.26 notequalI2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(notequalI2,definition,
% 2.46/1.26 ( notequalI2
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ~ ( in @ Xx @ B )
% 2.46/1.26 => ( A != B ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(subsetRefl_type,type,
% 2.46/1.26 subsetRefl: $o ).
% 2.46/1.26
% 2.46/1.26 thf(subsetRefl,definition,
% 2.46/1.26 ( subsetRefl
% 2.46/1.26 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(subsetTrans_type,type,
% 2.46/1.26 subsetTrans: $o ).
% 2.46/1.26
% 2.46/1.26 thf(subsetTrans,definition,
% 2.46/1.26 ( subsetTrans
% 2.46/1.26 = ( ! [A: $i,B: $i,C: $i] :
% 2.46/1.26 ( ( subset @ A @ B )
% 2.46/1.26 => ( ( subset @ B @ C )
% 2.46/1.26 => ( subset @ A @ C ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setadjoinSub_type,type,
% 2.46/1.26 setadjoinSub: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setadjoinSub,definition,
% 2.46/1.26 ( setadjoinSub
% 2.46/1.26 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setadjoinSub2_type,type,
% 2.46/1.26 setadjoinSub2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setadjoinSub2,definition,
% 2.46/1.26 ( setadjoinSub2
% 2.46/1.26 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.46/1.26 ( ( subset @ A @ B )
% 2.46/1.26 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(subset2powerset_type,type,
% 2.46/1.26 subset2powerset: $o ).
% 2.46/1.26
% 2.46/1.26 thf(subset2powerset,definition,
% 2.46/1.26 ( subset2powerset
% 2.46/1.26 = ( ! [A: $i,B: $i] :
% 2.46/1.26 ( ( subset @ A @ B )
% 2.46/1.26 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setextsub_type,type,
% 2.46/1.26 setextsub: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setextsub,definition,
% 2.46/1.26 ( setextsub
% 2.46/1.26 = ( ! [A: $i,B: $i] :
% 2.46/1.26 ( ( subset @ A @ B )
% 2.46/1.26 => ( ( subset @ B @ A )
% 2.46/1.26 => ( A = B ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(subsetemptysetimpeq_type,type,
% 2.46/1.26 subsetemptysetimpeq: $o ).
% 2.46/1.26
% 2.46/1.26 thf(subsetemptysetimpeq,definition,
% 2.46/1.26 ( subsetemptysetimpeq
% 2.46/1.26 = ( ! [A: $i] :
% 2.46/1.26 ( ( subset @ A @ emptyset )
% 2.46/1.26 => ( A = emptyset ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(powersetI1_type,type,
% 2.46/1.26 powersetI1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(powersetI1,definition,
% 2.46/1.26 ( powersetI1
% 2.46/1.26 = ( ! [A: $i,B: $i] :
% 2.46/1.26 ( ( subset @ B @ A )
% 2.46/1.26 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(powersetE1_type,type,
% 2.46/1.26 powersetE1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(powersetE1,definition,
% 2.46/1.26 ( powersetE1
% 2.46/1.26 = ( ! [A: $i,B: $i] :
% 2.46/1.26 ( ( in @ B @ ( powerset @ A ) )
% 2.46/1.26 => ( subset @ B @ A ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(inPowerset_type,type,
% 2.46/1.26 inPowerset: $o ).
% 2.46/1.26
% 2.46/1.26 thf(inPowerset,definition,
% 2.46/1.26 ( inPowerset
% 2.46/1.26 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(powersetsubset_type,type,
% 2.46/1.26 powersetsubset: $o ).
% 2.46/1.26
% 2.46/1.26 thf(powersetsubset,definition,
% 2.46/1.26 ( powersetsubset
% 2.46/1.26 = ( ! [A: $i,B: $i] :
% 2.46/1.26 ( ( subset @ A @ B )
% 2.46/1.26 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(sepInPowerset_type,type,
% 2.46/1.26 sepInPowerset: $o ).
% 2.46/1.26
% 2.46/1.26 thf(sepInPowerset,definition,
% 2.46/1.26 ( sepInPowerset
% 2.46/1.26 = ( ! [A: $i,Xphi: $i > $o] :
% 2.46/1.26 ( in
% 2.46/1.26 @ ( dsetconstr @ A
% 2.46/1.26 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.46/1.26 @ ( powerset @ A ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(sepSubset_type,type,
% 2.46/1.26 sepSubset: $o ).
% 2.46/1.26
% 2.46/1.26 thf(sepSubset,definition,
% 2.46/1.26 ( sepSubset
% 2.46/1.26 = ( ! [A: $i,Xphi: $i > $o] :
% 2.46/1.26 ( subset
% 2.46/1.26 @ ( dsetconstr @ A
% 2.46/1.26 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.46/1.26 @ A ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(binunion_type,type,
% 2.46/1.26 binunion: $i > $i > $i ).
% 2.46/1.26
% 2.46/1.26 thf(binunionIL_type,type,
% 2.46/1.26 binunionIL: $o ).
% 2.46/1.26
% 2.46/1.26 thf(binunionIL,definition,
% 2.46/1.26 ( binunionIL
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(upairset2IR_type,type,
% 2.46/1.26 upairset2IR: $o ).
% 2.46/1.26
% 2.46/1.26 thf(upairset2IR,definition,
% 2.46/1.26 ( upairset2IR
% 2.46/1.26 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(binunionIR_type,type,
% 2.46/1.26 binunionIR: $o ).
% 2.46/1.26
% 2.46/1.26 thf(binunionIR,definition,
% 2.46/1.26 ( binunionIR
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ B )
% 2.46/1.26 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(binunionEcases_type,type,
% 2.46/1.26 binunionEcases: $o ).
% 2.46/1.26
% 2.46/1.26 thf(binunionEcases,definition,
% 2.46/1.26 ( binunionEcases
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.46/1.26 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.46/1.26 => ( ( ( in @ Xx @ A )
% 2.46/1.26 => Xphi )
% 2.46/1.26 => ( ( ( in @ Xx @ B )
% 2.46/1.26 => Xphi )
% 2.46/1.26 => Xphi ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(binunionE_type,type,
% 2.46/1.26 binunionE: $o ).
% 2.46/1.26
% 2.46/1.26 thf(binunionE,definition,
% 2.46/1.26 ( binunionE
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.46/1.26 => ( ( in @ Xx @ A )
% 2.46/1.26 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(binunionLsub_type,type,
% 2.46/1.26 binunionLsub: $o ).
% 2.46/1.26
% 2.46/1.26 thf(binunionLsub,definition,
% 2.46/1.26 ( binunionLsub
% 2.46/1.26 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(binunionRsub_type,type,
% 2.46/1.26 binunionRsub: $o ).
% 2.46/1.26
% 2.46/1.26 thf(binunionRsub,definition,
% 2.46/1.26 ( binunionRsub
% 2.46/1.26 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(binintersect_type,type,
% 2.46/1.26 binintersect: $i > $i > $i ).
% 2.46/1.26
% 2.46/1.26 thf(binintersectI_type,type,
% 2.46/1.26 binintersectI: $o ).
% 2.46/1.26
% 2.46/1.26 thf(binintersectI,definition,
% 2.46/1.26 ( binintersectI
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( in @ Xx @ B )
% 2.46/1.26 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(binintersectSubset5_type,type,
% 2.46/1.26 binintersectSubset5: $o ).
% 2.46/1.26
% 2.46/1.26 thf(binintersectSubset5,definition,
% 2.46/1.26 ( binintersectSubset5
% 2.46/1.26 = ( ! [A: $i,B: $i,C: $i] :
% 2.46/1.26 ( ( subset @ C @ A )
% 2.46/1.26 => ( ( subset @ C @ B )
% 2.46/1.26 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(binintersectEL_type,type,
% 2.46/1.26 binintersectEL: $o ).
% 2.46/1.26
% 2.46/1.26 thf(binintersectEL,definition,
% 2.46/1.26 ( binintersectEL
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.46/1.26 => ( in @ Xx @ A ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(binintersectLsub_type,type,
% 2.46/1.26 binintersectLsub: $o ).
% 2.46/1.26
% 2.46/1.26 thf(binintersectLsub,definition,
% 2.46/1.26 ( binintersectLsub
% 2.46/1.26 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(binintersectSubset2_type,type,
% 2.46/1.26 binintersectSubset2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(binintersectSubset2,definition,
% 2.46/1.26 ( binintersectSubset2
% 2.46/1.26 = ( ! [A: $i,B: $i] :
% 2.46/1.26 ( ( subset @ A @ B )
% 2.46/1.26 => ( ( binintersect @ A @ B )
% 2.46/1.26 = A ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(binintersectSubset3_type,type,
% 2.46/1.26 binintersectSubset3: $o ).
% 2.46/1.26
% 2.46/1.26 thf(binintersectSubset3,definition,
% 2.46/1.26 ( binintersectSubset3
% 2.46/1.26 = ( ! [A: $i,B: $i] :
% 2.46/1.26 ( ( ( binintersect @ A @ B )
% 2.46/1.26 = B )
% 2.46/1.26 => ( subset @ B @ A ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(binintersectER_type,type,
% 2.46/1.26 binintersectER: $o ).
% 2.46/1.26
% 2.46/1.26 thf(binintersectER,definition,
% 2.46/1.26 ( binintersectER
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.46/1.26 => ( in @ Xx @ B ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(disjointsetsI1_type,type,
% 2.46/1.26 disjointsetsI1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(disjointsetsI1,definition,
% 2.46/1.26 ( disjointsetsI1
% 2.46/1.26 = ( ! [A: $i,B: $i] :
% 2.46/1.26 ( ~ ? [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 & ( in @ Xx @ B ) )
% 2.46/1.26 => ( ( binintersect @ A @ B )
% 2.46/1.26 = emptyset ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(binintersectRsub_type,type,
% 2.46/1.26 binintersectRsub: $o ).
% 2.46/1.26
% 2.46/1.26 thf(binintersectRsub,definition,
% 2.46/1.26 ( binintersectRsub
% 2.46/1.26 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(binintersectSubset4_type,type,
% 2.46/1.26 binintersectSubset4: $o ).
% 2.46/1.26
% 2.46/1.26 thf(binintersectSubset4,definition,
% 2.46/1.26 ( binintersectSubset4
% 2.46/1.26 = ( ! [A: $i,B: $i] :
% 2.46/1.26 ( ( subset @ B @ A )
% 2.46/1.26 => ( ( binintersect @ A @ B )
% 2.46/1.26 = B ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(binintersectSubset1_type,type,
% 2.46/1.26 binintersectSubset1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(binintersectSubset1,definition,
% 2.46/1.26 ( binintersectSubset1
% 2.46/1.26 = ( ! [A: $i,B: $i] :
% 2.46/1.26 ( ( ( binintersect @ A @ B )
% 2.46/1.26 = A )
% 2.46/1.26 => ( subset @ A @ B ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(bs114d_type,type,
% 2.46/1.26 bs114d: $o ).
% 2.46/1.26
% 2.46/1.26 thf(bs114d,definition,
% 2.46/1.26 ( bs114d
% 2.46/1.26 = ( ! [A: $i,B: $i,C: $i] :
% 2.46/1.26 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.46/1.26 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(regular_type,type,
% 2.46/1.26 regular: $i > $o ).
% 2.46/1.26
% 2.46/1.26 thf(setminus_type,type,
% 2.46/1.26 setminus: $i > $i > $i ).
% 2.46/1.26
% 2.46/1.26 thf(setminusI_type,type,
% 2.46/1.26 setminusI: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setminusI,definition,
% 2.46/1.26 ( setminusI
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ~ ( in @ Xx @ B )
% 2.46/1.26 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setminusEL_type,type,
% 2.46/1.26 setminusEL: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setminusEL,definition,
% 2.46/1.26 ( setminusEL
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.46/1.26 => ( in @ Xx @ A ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setminusER_type,type,
% 2.46/1.26 setminusER: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setminusER,definition,
% 2.46/1.26 ( setminusER
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.46/1.26 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setminusSubset2_type,type,
% 2.46/1.26 setminusSubset2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setminusSubset2,definition,
% 2.46/1.26 ( setminusSubset2
% 2.46/1.26 = ( ! [A: $i,B: $i] :
% 2.46/1.26 ( ( subset @ A @ B )
% 2.46/1.26 => ( ( setminus @ A @ B )
% 2.46/1.26 = emptyset ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setminusERneg_type,type,
% 2.46/1.26 setminusERneg: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setminusERneg,definition,
% 2.46/1.26 ( setminusERneg
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.46/1.26 => ( ( in @ Xx @ A )
% 2.46/1.26 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setminusELneg_type,type,
% 2.46/1.26 setminusELneg: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setminusELneg,definition,
% 2.46/1.26 ( setminusELneg
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.46/1.26 => ( ~ ( in @ Xx @ B )
% 2.46/1.26 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setminusILneg_type,type,
% 2.46/1.26 setminusILneg: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setminusILneg,definition,
% 2.46/1.26 ( setminusILneg
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ~ ( in @ Xx @ A )
% 2.46/1.26 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setminusIRneg_type,type,
% 2.46/1.26 setminusIRneg: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setminusIRneg,definition,
% 2.46/1.26 ( setminusIRneg
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ B )
% 2.46/1.26 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setminusLsub_type,type,
% 2.46/1.26 setminusLsub: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setminusLsub,definition,
% 2.46/1.26 ( setminusLsub
% 2.46/1.26 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setminusSubset1_type,type,
% 2.46/1.26 setminusSubset1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setminusSubset1,definition,
% 2.46/1.26 ( setminusSubset1
% 2.46/1.26 = ( ! [A: $i,B: $i] :
% 2.46/1.26 ( ( ( setminus @ A @ B )
% 2.46/1.26 = emptyset )
% 2.46/1.26 => ( subset @ A @ B ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(symdiff_type,type,
% 2.46/1.26 symdiff: $i > $i > $i ).
% 2.46/1.26
% 2.46/1.26 thf(symdiffE_type,type,
% 2.46/1.26 symdiffE: $o ).
% 2.46/1.26
% 2.46/1.26 thf(symdiffE,definition,
% 2.46/1.26 ( symdiffE
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.46/1.26 => ! [Xphi: $o] :
% 2.46/1.26 ( ( ( in @ Xx @ A )
% 2.46/1.26 => ( ~ ( in @ Xx @ B )
% 2.46/1.26 => Xphi ) )
% 2.46/1.26 => ( ( ~ ( in @ Xx @ A )
% 2.46/1.26 => ( ( in @ Xx @ B )
% 2.46/1.26 => Xphi ) )
% 2.46/1.26 => Xphi ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(symdiffI1_type,type,
% 2.46/1.26 symdiffI1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(symdiffI1,definition,
% 2.46/1.26 ( symdiffI1
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ~ ( in @ Xx @ B )
% 2.46/1.26 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(symdiffI2_type,type,
% 2.46/1.26 symdiffI2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(symdiffI2,definition,
% 2.46/1.26 ( symdiffI2
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ~ ( in @ Xx @ A )
% 2.46/1.26 => ( ( in @ Xx @ B )
% 2.46/1.26 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(symdiffIneg1_type,type,
% 2.46/1.26 symdiffIneg1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(symdiffIneg1,definition,
% 2.46/1.26 ( symdiffIneg1
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( in @ Xx @ B )
% 2.46/1.26 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(symdiffIneg2_type,type,
% 2.46/1.26 symdiffIneg2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(symdiffIneg2,definition,
% 2.46/1.26 ( symdiffIneg2
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ~ ( in @ Xx @ A )
% 2.46/1.26 => ( ~ ( in @ Xx @ B )
% 2.46/1.26 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(iskpair_type,type,
% 2.46/1.26 iskpair: $i > $o ).
% 2.46/1.26
% 2.46/1.26 thf(secondinupair_type,type,
% 2.46/1.26 secondinupair: $o ).
% 2.46/1.26
% 2.46/1.26 thf(secondinupair,definition,
% 2.46/1.26 ( secondinupair
% 2.46/1.26 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setukpairIL_type,type,
% 2.46/1.26 setukpairIL: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setukpairIL,definition,
% 2.46/1.26 ( setukpairIL
% 2.46/1.26 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setukpairIR_type,type,
% 2.46/1.26 setukpairIR: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setukpairIR,definition,
% 2.46/1.26 ( setukpairIR
% 2.46/1.26 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(kpairiskpair_type,type,
% 2.46/1.26 kpairiskpair: $o ).
% 2.46/1.26
% 2.46/1.26 thf(kpairiskpair,definition,
% 2.46/1.26 ( kpairiskpair
% 2.46/1.26 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(kpair_type,type,
% 2.46/1.26 kpair: $i > $i > $i ).
% 2.46/1.26
% 2.46/1.26 thf(kpairp_type,type,
% 2.46/1.26 kpairp: $o ).
% 2.46/1.26
% 2.46/1.26 thf(kpairp,definition,
% 2.46/1.26 ( kpairp
% 2.46/1.26 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(cartprod_type,type,
% 2.46/1.26 cartprod: $i > $i > $i ).
% 2.46/1.26
% 2.46/1.26 thf(singletonsubset_type,type,
% 2.46/1.26 singletonsubset: $o ).
% 2.46/1.26
% 2.46/1.26 thf(singletonsubset,definition,
% 2.46/1.26 ( singletonsubset
% 2.46/1.26 = ( ! [A: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(singletoninpowerset_type,type,
% 2.46/1.26 singletoninpowerset: $o ).
% 2.46/1.26
% 2.46/1.26 thf(singletoninpowerset,definition,
% 2.46/1.26 ( singletoninpowerset
% 2.46/1.26 = ( ! [A: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(singletoninpowunion_type,type,
% 2.46/1.26 singletoninpowunion: $o ).
% 2.46/1.26
% 2.46/1.26 thf(singletoninpowunion,definition,
% 2.46/1.26 ( singletoninpowunion
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(upairset2E_type,type,
% 2.46/1.26 upairset2E: $o ).
% 2.46/1.26
% 2.46/1.26 thf(upairset2E,definition,
% 2.46/1.26 ( upairset2E
% 2.46/1.26 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.46/1.26 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.46/1.26 => ( ( Xz = Xx )
% 2.46/1.26 | ( Xz = Xy ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(upairsubunion_type,type,
% 2.46/1.26 upairsubunion: $o ).
% 2.46/1.26
% 2.46/1.26 thf(upairsubunion,definition,
% 2.46/1.26 ( upairsubunion
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ B )
% 2.46/1.26 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(upairinpowunion_type,type,
% 2.46/1.26 upairinpowunion: $o ).
% 2.46/1.26
% 2.46/1.26 thf(upairinpowunion,definition,
% 2.46/1.26 ( upairinpowunion
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ B )
% 2.46/1.26 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(ubforcartprodlem1_type,type,
% 2.46/1.26 ubforcartprodlem1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(ubforcartprodlem1,definition,
% 2.46/1.26 ( ubforcartprodlem1
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ B )
% 2.46/1.26 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(ubforcartprodlem2_type,type,
% 2.46/1.26 ubforcartprodlem2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(ubforcartprodlem2,definition,
% 2.46/1.26 ( ubforcartprodlem2
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ B )
% 2.46/1.26 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(ubforcartprodlem3_type,type,
% 2.46/1.26 ubforcartprodlem3: $o ).
% 2.46/1.26
% 2.46/1.26 thf(ubforcartprodlem3,definition,
% 2.46/1.26 ( ubforcartprodlem3
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ B )
% 2.46/1.26 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(cartprodpairin_type,type,
% 2.46/1.26 cartprodpairin: $o ).
% 2.46/1.26
% 2.46/1.26 thf(cartprodpairin,definition,
% 2.46/1.26 ( cartprodpairin
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ B )
% 2.46/1.26 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(cartprodmempair1_type,type,
% 2.46/1.26 cartprodmempair1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(cartprodmempair1,definition,
% 2.46/1.26 ( cartprodmempair1
% 2.46/1.26 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.46/1.26 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.46/1.26 => ? [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 & ? [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ B )
% 2.46/1.26 & ( Xu
% 2.46/1.26 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(cartprodmempair_type,type,
% 2.46/1.26 cartprodmempair: $o ).
% 2.46/1.26
% 2.46/1.26 thf(cartprodmempair,definition,
% 2.46/1.26 ( cartprodmempair
% 2.46/1.26 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.46/1.26 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.46/1.26 => ( iskpair @ Xu ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setunionE2_type,type,
% 2.46/1.26 setunionE2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setunionE2,definition,
% 2.46/1.26 ( setunionE2
% 2.46/1.26 = ( ! [A: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ ( setunion @ A ) )
% 2.46/1.26 => ? [X: $i] :
% 2.46/1.26 ( ( in @ X @ A )
% 2.46/1.26 & ( in @ Xx @ X ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setunionsingleton1_type,type,
% 2.46/1.26 setunionsingleton1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setunionsingleton1,definition,
% 2.46/1.26 ( setunionsingleton1
% 2.46/1.26 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setunionsingleton2_type,type,
% 2.46/1.26 setunionsingleton2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setunionsingleton2,definition,
% 2.46/1.26 ( setunionsingleton2
% 2.46/1.26 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setunionsingleton_type,type,
% 2.46/1.26 setunionsingleton: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setunionsingleton,definition,
% 2.46/1.26 ( setunionsingleton
% 2.46/1.26 = ( ! [Xx: $i] :
% 2.46/1.26 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 2.46/1.26 = Xx ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(singleton_type,type,
% 2.46/1.26 singleton: $i > $o ).
% 2.46/1.26
% 2.46/1.26 thf(singletonprop_type,type,
% 2.46/1.26 singletonprop: $o ).
% 2.46/1.26
% 2.46/1.26 thf(singletonprop,definition,
% 2.46/1.26 ( singletonprop
% 2.46/1.26 = ( ! [A: $i,Xphi: $i > $o] :
% 2.46/1.26 ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ A )
% 2.46/1.26 => ( ( Xphi @ Xx )
% 2.46/1.26 => ( ( Xphi @ Xy )
% 2.46/1.26 => ( Xx = Xy ) ) ) ) )
% 2.46/1.26 => ( ? [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 & ( Xphi @ Xx ) )
% 2.46/1.26 => ( singleton
% 2.46/1.26 @ ( dsetconstr @ A
% 2.46/1.26 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(ex1_type,type,
% 2.46/1.26 ex1: $i > ( $i > $o ) > $o ).
% 2.46/1.26
% 2.46/1.26 thf(ex1E1_type,type,
% 2.46/1.26 ex1E1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(ex1E1,definition,
% 2.46/1.26 ( ex1E1
% 2.46/1.26 = ( ! [A: $i,Xphi: $i > $o] :
% 2.46/1.26 ( ( ex1 @ A
% 2.46/1.26 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.46/1.26 => ? [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(ex1I_type,type,
% 2.46/1.26 ex1I: $o ).
% 2.46/1.26
% 2.46/1.26 thf(ex1I,definition,
% 2.46/1.26 ( ex1I
% 2.46/1.26 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( Xphi @ Xx )
% 2.46/1.26 => ( ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ A )
% 2.46/1.26 => ( ( Xphi @ Xy )
% 2.46/1.26 => ( Xy = Xx ) ) )
% 2.46/1.26 => ( ex1 @ A
% 2.46/1.26 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(ex1I2_type,type,
% 2.46/1.26 ex1I2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(ex1I2,definition,
% 2.46/1.26 ( ex1I2
% 2.46/1.26 = ( ! [A: $i,Xphi: $i > $o] :
% 2.46/1.26 ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ A )
% 2.46/1.26 => ( ( Xphi @ Xx )
% 2.46/1.26 => ( ( Xphi @ Xy )
% 2.46/1.26 => ( Xx = Xy ) ) ) ) )
% 2.46/1.26 => ( ? [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 & ( Xphi @ Xx ) )
% 2.46/1.26 => ( ex1 @ A
% 2.46/1.26 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(singletonsuniq_type,type,
% 2.46/1.26 singletonsuniq: $o ).
% 2.46/1.26
% 2.46/1.26 thf(singletonsuniq,definition,
% 2.46/1.26 ( singletonsuniq
% 2.46/1.26 = ( ! [Xx: $i,Xy: $i] :
% 2.46/1.26 ( ( ( setadjoin @ Xx @ emptyset )
% 2.46/1.26 = ( setadjoin @ Xy @ emptyset ) )
% 2.46/1.26 => ( Xx = Xy ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(atmost1p_type,type,
% 2.46/1.26 atmost1p: $i > $o ).
% 2.46/1.26
% 2.46/1.26 thf(atleast2p_type,type,
% 2.46/1.26 atleast2p: $i > $o ).
% 2.46/1.26
% 2.46/1.26 thf(atmost2p_type,type,
% 2.46/1.26 atmost2p: $i > $o ).
% 2.46/1.26
% 2.46/1.26 thf(upairsetp_type,type,
% 2.46/1.26 upairsetp: $i > $o ).
% 2.46/1.26
% 2.46/1.26 thf(setukpairinjL1_type,type,
% 2.46/1.26 setukpairinjL1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setukpairinjL1,definition,
% 2.46/1.26 ( setukpairinjL1
% 2.46/1.26 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.46/1.26 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 2.46/1.26 => ( Xx = Xz ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(kfstsingleton_type,type,
% 2.46/1.26 kfstsingleton: $o ).
% 2.46/1.26
% 2.46/1.26 thf(kfstsingleton,definition,
% 2.46/1.26 ( kfstsingleton
% 2.46/1.26 = ( ! [Xu: $i] :
% 2.46/1.26 ( ( iskpair @ Xu )
% 2.46/1.26 => ( singleton
% 2.46/1.26 @ ( dsetconstr @ ( setunion @ Xu )
% 2.46/1.26 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(theprop_type,type,
% 2.46/1.26 theprop: $o ).
% 2.46/1.26
% 2.46/1.26 thf(theprop,definition,
% 2.46/1.26 ( theprop
% 2.46/1.26 = ( ! [X: $i] :
% 2.46/1.26 ( ( singleton @ X )
% 2.46/1.26 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(kfst_type,type,
% 2.46/1.26 kfst: $i > $i ).
% 2.46/1.26
% 2.46/1.26 thf(kfstpairEq_type,type,
% 2.46/1.26 kfstpairEq: $o ).
% 2.46/1.26
% 2.46/1.26 thf(kfstpairEq,definition,
% 2.46/1.26 ( kfstpairEq
% 2.46/1.26 = ( ! [Xx: $i,Xy: $i] :
% 2.46/1.26 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.46/1.26 = Xx ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(cartprodfstin_type,type,
% 2.46/1.26 cartprodfstin: $o ).
% 2.46/1.26
% 2.46/1.26 thf(cartprodfstin,definition,
% 2.46/1.26 ( cartprodfstin
% 2.46/1.26 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.46/1.26 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.46/1.26 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setukpairinjL2_type,type,
% 2.46/1.26 setukpairinjL2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setukpairinjL2,definition,
% 2.46/1.26 ( setukpairinjL2
% 2.46/1.26 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.46/1.26 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.46/1.26 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.46/1.26 => ( Xx = Xz ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setukpairinjL_type,type,
% 2.46/1.26 setukpairinjL: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setukpairinjL,definition,
% 2.46/1.26 ( setukpairinjL
% 2.46/1.26 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.46/1.26 ( ( ( kpair @ Xx @ Xy )
% 2.46/1.26 = ( kpair @ Xz @ Xu ) )
% 2.46/1.26 => ( Xx = Xz ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setukpairinjR11_type,type,
% 2.46/1.26 setukpairinjR11: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setukpairinjR11,definition,
% 2.46/1.26 ( setukpairinjR11
% 2.46/1.26 = ( ! [Xx: $i,Xy: $i] :
% 2.46/1.26 ( ( Xx = Xy )
% 2.46/1.26 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.46/1.26 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setukpairinjR12_type,type,
% 2.46/1.26 setukpairinjR12: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setukpairinjR12,definition,
% 2.46/1.26 ( setukpairinjR12
% 2.46/1.26 = ( ! [Xx: $i,Xy: $i] :
% 2.46/1.26 ( ( Xx = Xy )
% 2.46/1.26 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.46/1.26 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setukpairinjR1_type,type,
% 2.46/1.26 setukpairinjR1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setukpairinjR1,definition,
% 2.46/1.26 ( setukpairinjR1
% 2.46/1.26 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.46/1.26 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.46/1.26 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.46/1.26 => ( ( Xz = Xu )
% 2.46/1.26 => ( Xy = Xu ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(upairequniteq_type,type,
% 2.46/1.26 upairequniteq: $o ).
% 2.46/1.26
% 2.46/1.26 thf(upairequniteq,definition,
% 2.46/1.26 ( upairequniteq
% 2.46/1.26 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.46/1.26 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.46/1.26 = ( setadjoin @ Xz @ emptyset ) )
% 2.46/1.26 => ( Xx = Xy ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setukpairinjR2_type,type,
% 2.46/1.26 setukpairinjR2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setukpairinjR2,definition,
% 2.46/1.26 ( setukpairinjR2
% 2.46/1.26 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.46/1.26 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.46/1.26 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.46/1.26 => ( Xy = Xu ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setukpairinjR_type,type,
% 2.46/1.26 setukpairinjR: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setukpairinjR,definition,
% 2.46/1.26 ( setukpairinjR
% 2.46/1.26 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.46/1.26 ( ( ( kpair @ Xx @ Xy )
% 2.46/1.26 = ( kpair @ Xz @ Xu ) )
% 2.46/1.26 => ( Xy = Xu ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(ksndsingleton_type,type,
% 2.46/1.26 ksndsingleton: $o ).
% 2.46/1.26
% 2.46/1.26 thf(ksndsingleton,definition,
% 2.46/1.26 ( ksndsingleton
% 2.46/1.26 = ( ! [Xu: $i] :
% 2.46/1.26 ( ( iskpair @ Xu )
% 2.46/1.26 => ( singleton
% 2.46/1.26 @ ( dsetconstr @ ( setunion @ Xu )
% 2.46/1.26 @ ^ [Xx: $i] :
% 2.46/1.26 ( Xu
% 2.46/1.26 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(ksnd_type,type,
% 2.46/1.26 ksnd: $i > $i ).
% 2.46/1.26
% 2.46/1.26 thf(ksndpairEq_type,type,
% 2.46/1.26 ksndpairEq: $o ).
% 2.46/1.26
% 2.46/1.26 thf(ksndpairEq,definition,
% 2.46/1.26 ( ksndpairEq
% 2.46/1.26 = ( ! [Xx: $i,Xy: $i] :
% 2.46/1.26 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.46/1.26 = Xy ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(kpairsurjEq_type,type,
% 2.46/1.26 kpairsurjEq: $o ).
% 2.46/1.26
% 2.46/1.26 thf(kpairsurjEq,definition,
% 2.46/1.26 ( kpairsurjEq
% 2.46/1.26 = ( ! [Xu: $i] :
% 2.46/1.26 ( ( iskpair @ Xu )
% 2.46/1.26 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.46/1.26 = Xu ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(cartprodsndin_type,type,
% 2.46/1.26 cartprodsndin: $o ).
% 2.46/1.26
% 2.46/1.26 thf(cartprodsndin,definition,
% 2.46/1.26 ( cartprodsndin
% 2.46/1.26 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.46/1.26 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.46/1.26 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(cartprodpairmemEL_type,type,
% 2.46/1.26 cartprodpairmemEL: $o ).
% 2.46/1.26
% 2.46/1.26 thf(cartprodpairmemEL,definition,
% 2.46/1.26 ( cartprodpairmemEL
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.46/1.26 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.46/1.26 => ( in @ Xx @ A ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(cartprodpairmemER_type,type,
% 2.46/1.26 cartprodpairmemER: $o ).
% 2.46/1.26
% 2.46/1.26 thf(cartprodpairmemER,definition,
% 2.46/1.26 ( cartprodpairmemER
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.46/1.26 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.46/1.26 => ( in @ Xy @ B ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(cartprodmempaircEq_type,type,
% 2.46/1.26 cartprodmempaircEq: $o ).
% 2.46/1.26
% 2.46/1.26 thf(cartprodmempaircEq,definition,
% 2.46/1.26 ( cartprodmempaircEq
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ B )
% 2.46/1.26 => ( ( kpair @ Xx @ Xy )
% 2.46/1.26 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(cartprodfstpairEq_type,type,
% 2.46/1.26 cartprodfstpairEq: $o ).
% 2.46/1.26
% 2.46/1.26 thf(cartprodfstpairEq,definition,
% 2.46/1.26 ( cartprodfstpairEq
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ B )
% 2.46/1.26 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.46/1.26 = Xx ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(cartprodsndpairEq_type,type,
% 2.46/1.26 cartprodsndpairEq: $o ).
% 2.46/1.26
% 2.46/1.26 thf(cartprodsndpairEq,definition,
% 2.46/1.26 ( cartprodsndpairEq
% 2.46/1.26 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ B )
% 2.46/1.26 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.46/1.26 = Xy ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(cartprodpairsurjEq_type,type,
% 2.46/1.26 cartprodpairsurjEq: $o ).
% 2.46/1.26
% 2.46/1.26 thf(cartprodpairsurjEq,definition,
% 2.46/1.26 ( cartprodpairsurjEq
% 2.46/1.26 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.46/1.26 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.46/1.26 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.46/1.26 = Xu ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(breln_type,type,
% 2.46/1.26 breln: $i > $i > $i > $o ).
% 2.46/1.26
% 2.46/1.26 thf(breln,definition,
% 2.46/1.26 ( breln
% 2.46/1.26 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(dpsetconstr_type,type,
% 2.46/1.26 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 2.46/1.26
% 2.46/1.26 thf(dpsetconstrI_type,type,
% 2.46/1.26 dpsetconstrI: $o ).
% 2.46/1.26
% 2.46/1.26 thf(dpsetconstrI,definition,
% 2.46/1.26 ( dpsetconstrI
% 2.46/1.26 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ B )
% 2.46/1.26 => ( ( Xphi @ Xx @ Xy )
% 2.46/1.26 => ( in @ ( kpair @ Xx @ Xy )
% 2.46/1.26 @ ( dpsetconstr @ A @ B
% 2.46/1.26 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(dpsetconstrSub_type,type,
% 2.46/1.26 dpsetconstrSub: $o ).
% 2.46/1.26
% 2.46/1.26 thf(dpsetconstrSub,definition,
% 2.46/1.26 ( dpsetconstrSub
% 2.46/1.26 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.46/1.26 ( subset
% 2.46/1.26 @ ( dpsetconstr @ A @ B
% 2.46/1.26 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 2.46/1.26 @ ( cartprod @ A @ B ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setOfPairsIsBReln_type,type,
% 2.46/1.26 setOfPairsIsBReln: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setOfPairsIsBReln,definition,
% 2.46/1.26 ( setOfPairsIsBReln
% 2.46/1.26 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.46/1.26 ( breln @ A @ B
% 2.46/1.26 @ ( dpsetconstr @ A @ B
% 2.46/1.26 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(dpsetconstrERa_type,type,
% 2.46/1.26 dpsetconstrERa: $o ).
% 2.46/1.26
% 2.46/1.26 thf(dpsetconstrERa,definition,
% 2.46/1.26 ( dpsetconstrERa
% 2.46/1.26 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ B )
% 2.46/1.26 => ( ( in @ ( kpair @ Xx @ Xy )
% 2.46/1.26 @ ( dpsetconstr @ A @ B
% 2.46/1.26 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.46/1.26 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(dpsetconstrEL1_type,type,
% 2.46/1.26 dpsetconstrEL1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(dpsetconstrEL1,definition,
% 2.46/1.26 ( dpsetconstrEL1
% 2.46/1.26 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.46/1.26 ( ( in @ ( kpair @ Xx @ Xy )
% 2.46/1.26 @ ( dpsetconstr @ A @ B
% 2.46/1.26 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.46/1.26 => ( in @ Xx @ A ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(dpsetconstrEL2_type,type,
% 2.46/1.26 dpsetconstrEL2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(dpsetconstrEL2,definition,
% 2.46/1.26 ( dpsetconstrEL2
% 2.46/1.26 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.46/1.26 ( ( in @ ( kpair @ Xx @ Xy )
% 2.46/1.26 @ ( dpsetconstr @ A @ B
% 2.46/1.26 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.46/1.26 => ( in @ Xy @ B ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(dpsetconstrER_type,type,
% 2.46/1.26 dpsetconstrER: $o ).
% 2.46/1.26
% 2.46/1.26 thf(dpsetconstrER,definition,
% 2.46/1.26 ( dpsetconstrER
% 2.46/1.26 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.46/1.26 ( ( in @ ( kpair @ Xx @ Xy )
% 2.46/1.26 @ ( dpsetconstr @ A @ B
% 2.46/1.26 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.46/1.26 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(func_type,type,
% 2.46/1.26 func: $i > $i > $i > $o ).
% 2.46/1.26
% 2.46/1.26 thf(funcSet_type,type,
% 2.46/1.26 funcSet: $i > $i > $i ).
% 2.46/1.26
% 2.46/1.26 thf(funcImageSingleton_type,type,
% 2.46/1.26 funcImageSingleton: $o ).
% 2.46/1.26
% 2.46/1.26 thf(funcImageSingleton,definition,
% 2.46/1.26 ( funcImageSingleton
% 2.46/1.26 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.46/1.26 ( ( func @ A @ B @ Xf )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( singleton
% 2.46/1.26 @ ( dsetconstr @ B
% 2.46/1.26 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(apProp_type,type,
% 2.46/1.26 apProp: $o ).
% 2.46/1.26
% 2.46/1.26 thf(apProp,definition,
% 2.46/1.26 ( apProp
% 2.46/1.26 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.46/1.26 ( ( func @ A @ B @ Xf )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( in
% 2.46/1.26 @ ( setunion
% 2.46/1.26 @ ( dsetconstr @ B
% 2.46/1.26 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 2.46/1.26 @ B ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(ap_type,type,
% 2.46/1.26 ap: $i > $i > $i > $i > $i ).
% 2.46/1.26
% 2.46/1.26 thf(app_type,type,
% 2.46/1.26 app: $o ).
% 2.46/1.26
% 2.46/1.26 thf(app,definition,
% 2.46/1.26 ( app
% 2.46/1.26 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.46/1.26 ( ( func @ A @ B @ Xf )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(infuncsetfunc_type,type,
% 2.46/1.26 infuncsetfunc: $o ).
% 2.46/1.26
% 2.46/1.26 thf(infuncsetfunc,definition,
% 2.46/1.26 ( infuncsetfunc
% 2.46/1.26 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.46/1.26 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.46/1.26 => ( func @ A @ B @ Xf ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(ap2p_type,type,
% 2.46/1.26 ap2p: $o ).
% 2.46/1.26
% 2.46/1.26 thf(ap2p,definition,
% 2.46/1.26 ( ap2p
% 2.46/1.26 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.46/1.26 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(funcinfuncset_type,type,
% 2.46/1.26 funcinfuncset: $o ).
% 2.46/1.26
% 2.46/1.26 thf(funcinfuncset,definition,
% 2.46/1.26 ( funcinfuncset
% 2.46/1.26 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.46/1.26 ( ( func @ A @ B @ Xf )
% 2.46/1.26 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(lamProp_type,type,
% 2.46/1.26 lamProp: $o ).
% 2.46/1.26
% 2.46/1.26 thf(lamProp,definition,
% 2.46/1.26 ( lamProp
% 2.46/1.26 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.46/1.26 ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.46/1.26 => ( func @ A @ B
% 2.46/1.26 @ ( dpsetconstr @ A @ B
% 2.46/1.26 @ ^ [Xx: $i,Xy: $i] :
% 2.46/1.26 ( ( Xf @ Xx )
% 2.46/1.26 = Xy ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(lam_type,type,
% 2.46/1.26 lam: $i > $i > ( $i > $i ) > $i ).
% 2.46/1.26
% 2.46/1.26 thf(lamp_type,type,
% 2.46/1.26 lamp: $o ).
% 2.46/1.26
% 2.46/1.26 thf(lamp,definition,
% 2.46/1.26 ( lamp
% 2.46/1.26 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.46/1.26 ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.46/1.26 => ( func @ A @ B
% 2.46/1.26 @ ( lam @ A @ B
% 2.46/1.26 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(lam2p_type,type,
% 2.46/1.26 lam2p: $o ).
% 2.46/1.26
% 2.46/1.26 thf(lam2p,definition,
% 2.46/1.26 ( lam2p
% 2.46/1.26 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.46/1.26 ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.46/1.26 => ( in
% 2.46/1.26 @ ( lam @ A @ B
% 2.46/1.26 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 2.46/1.26 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(brelnall1_type,type,
% 2.46/1.26 brelnall1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(brelnall1,definition,
% 2.46/1.26 ( brelnall1
% 2.46/1.26 = ( ! [A: $i,B: $i,R: $i] :
% 2.46/1.26 ( ( breln @ A @ B @ R )
% 2.46/1.26 => ! [Xphi: $i > $o] :
% 2.46/1.26 ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ B )
% 2.46/1.26 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.46/1.26 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ R )
% 2.46/1.26 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(brelnall2_type,type,
% 2.46/1.26 brelnall2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(brelnall2,definition,
% 2.46/1.26 ( brelnall2
% 2.46/1.26 = ( ! [A: $i,B: $i,R: $i] :
% 2.46/1.26 ( ( breln @ A @ B @ R )
% 2.46/1.26 => ! [Xphi: $i > $o] :
% 2.46/1.26 ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ B )
% 2.46/1.26 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.46/1.26 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ R )
% 2.46/1.26 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(ex1E2_type,type,
% 2.46/1.26 ex1E2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(ex1E2,definition,
% 2.46/1.26 ( ex1E2
% 2.46/1.26 = ( ! [A: $i,Xphi: $i > $o] :
% 2.46/1.26 ( ( ex1 @ A
% 2.46/1.26 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ A )
% 2.46/1.26 => ( ( Xphi @ Xx )
% 2.46/1.26 => ( ( Xphi @ Xy )
% 2.46/1.26 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(funcGraphProp1_type,type,
% 2.46/1.26 funcGraphProp1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(funcGraphProp1,definition,
% 2.46/1.26 ( funcGraphProp1
% 2.46/1.26 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.46/1.26 ( ( func @ A @ B @ Xf )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(funcGraphProp3_type,type,
% 2.46/1.26 funcGraphProp3: $o ).
% 2.46/1.26
% 2.46/1.26 thf(funcGraphProp3,definition,
% 2.46/1.26 ( funcGraphProp3
% 2.46/1.26 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.46/1.26 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(funcGraphProp2_type,type,
% 2.46/1.26 funcGraphProp2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(funcGraphProp2,definition,
% 2.46/1.26 ( funcGraphProp2
% 2.46/1.26 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.46/1.26 ( ( func @ A @ B @ Xf )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ B )
% 2.46/1.26 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 2.46/1.26 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.46/1.26 = Xy ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(funcextLem_type,type,
% 2.46/1.26 funcextLem: $o ).
% 2.46/1.26
% 2.46/1.26 thf(funcextLem,definition,
% 2.46/1.26 ( funcextLem
% 2.46/1.26 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.46/1.26 ( ( func @ A @ B @ Xf )
% 2.46/1.26 => ! [Xg: $i] :
% 2.46/1.26 ( ( func @ A @ B @ Xg )
% 2.46/1.26 => ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.46/1.26 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ B )
% 2.46/1.26 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 2.46/1.26 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(funcGraphProp4_type,type,
% 2.46/1.26 funcGraphProp4: $o ).
% 2.46/1.26
% 2.46/1.26 thf(funcGraphProp4,definition,
% 2.46/1.26 ( funcGraphProp4
% 2.46/1.26 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.46/1.26 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ B )
% 2.46/1.26 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 2.46/1.26 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.46/1.26 = Xy ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(subbreln_type,type,
% 2.46/1.26 subbreln: $o ).
% 2.46/1.26
% 2.46/1.26 thf(subbreln,definition,
% 2.46/1.26 ( subbreln
% 2.46/1.26 = ( ! [A: $i,B: $i,R: $i] :
% 2.46/1.26 ( ( breln @ A @ B @ R )
% 2.46/1.26 => ! [S: $i] :
% 2.46/1.26 ( ( breln @ A @ B @ S )
% 2.46/1.26 => ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ B )
% 2.46/1.26 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.46/1.26 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.46/1.26 => ( subset @ R @ S ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(eqbreln_type,type,
% 2.46/1.26 eqbreln: $o ).
% 2.46/1.26
% 2.46/1.26 thf(eqbreln,definition,
% 2.46/1.26 ( eqbreln
% 2.46/1.26 = ( ! [A: $i,B: $i,R: $i] :
% 2.46/1.26 ( ( breln @ A @ B @ R )
% 2.46/1.26 => ! [S: $i] :
% 2.46/1.26 ( ( breln @ A @ B @ S )
% 2.46/1.26 => ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ B )
% 2.46/1.26 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.46/1.26 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.46/1.26 => ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ B )
% 2.46/1.26 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 2.46/1.26 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 2.46/1.26 => ( R = S ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(funcext_type,type,
% 2.46/1.26 funcext: $o ).
% 2.46/1.26
% 2.46/1.26 thf(funcext,definition,
% 2.46/1.26 ( funcext
% 2.46/1.26 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.46/1.26 ( ( func @ A @ B @ Xf )
% 2.46/1.26 => ! [Xg: $i] :
% 2.46/1.26 ( ( func @ A @ B @ Xg )
% 2.46/1.26 => ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.46/1.26 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.46/1.26 => ( Xf = Xg ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(funcext2_type,type,
% 2.46/1.26 funcext2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(funcext2,definition,
% 2.46/1.26 ( funcext2
% 2.46/1.26 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.46/1.26 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.46/1.26 => ! [Xg: $i] :
% 2.46/1.26 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 2.46/1.26 => ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.46/1.26 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.46/1.26 => ( Xf = Xg ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(ap2apEq1_type,type,
% 2.46/1.26 ap2apEq1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(ap2apEq1,definition,
% 2.46/1.26 ( ap2apEq1
% 2.46/1.26 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.46/1.26 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.46/1.26 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(ap2apEq2_type,type,
% 2.46/1.26 ap2apEq2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(ap2apEq2,definition,
% 2.46/1.26 ( ap2apEq2
% 2.46/1.26 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.46/1.26 ( ( func @ A @ B @ Xf )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.46/1.26 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(beta1_type,type,
% 2.46/1.26 beta1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(beta1,definition,
% 2.46/1.26 ( beta1
% 2.46/1.26 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.46/1.26 ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( ap @ A @ B
% 2.46/1.26 @ ( lam @ A @ B
% 2.46/1.26 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 2.46/1.26 @ Xx )
% 2.46/1.26 = ( Xf @ Xx ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(eta1_type,type,
% 2.46/1.26 eta1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(eta1,definition,
% 2.46/1.26 ( eta1
% 2.46/1.26 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.46/1.26 ( ( func @ A @ B @ Xf )
% 2.46/1.26 => ( ( lam @ A @ B
% 2.46/1.26 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 2.46/1.26 = Xf ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(lam2lamEq_type,type,
% 2.46/1.26 lam2lamEq: $o ).
% 2.46/1.26
% 2.46/1.26 thf(lam2lamEq,definition,
% 2.46/1.26 ( lam2lamEq
% 2.46/1.26 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.46/1.26 ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.46/1.26 => ( ( lam @ A @ B
% 2.46/1.26 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 2.46/1.26 = ( lam @ A @ B
% 2.46/1.26 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(beta2_type,type,
% 2.46/1.26 beta2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(beta2,definition,
% 2.46/1.26 ( beta2
% 2.46/1.26 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.46/1.26 ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( ap @ A @ B
% 2.46/1.26 @ ( lam @ A @ B
% 2.46/1.26 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 2.46/1.26 @ Xx )
% 2.46/1.26 = ( Xf @ Xx ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(eta2_type,type,
% 2.46/1.26 eta2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(eta2,definition,
% 2.46/1.26 ( eta2
% 2.46/1.26 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.46/1.26 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.46/1.26 => ( ( lam @ A @ B
% 2.46/1.26 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 2.46/1.26 = Xf ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(iffalseProp1_type,type,
% 2.46/1.26 iffalseProp1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(iffalseProp1,definition,
% 2.46/1.26 ( iffalseProp1
% 2.46/1.26 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ A )
% 2.46/1.26 => ( ~ Xphi
% 2.46/1.26 => ( in @ Xy
% 2.46/1.26 @ ( dsetconstr @ A
% 2.46/1.26 @ ^ [Xz: $i] :
% 2.46/1.26 ( ( Xphi
% 2.46/1.26 & ( Xz = Xx ) )
% 2.46/1.26 | ( ~ Xphi
% 2.46/1.26 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(iffalseProp2_type,type,
% 2.46/1.26 iffalseProp2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(iffalseProp2,definition,
% 2.46/1.26 ( iffalseProp2
% 2.46/1.26 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ A )
% 2.46/1.26 => ( ~ Xphi
% 2.46/1.26 => ( ( dsetconstr @ A
% 2.46/1.26 @ ^ [Xz: $i] :
% 2.46/1.26 ( ( Xphi
% 2.46/1.26 & ( Xz = Xx ) )
% 2.46/1.26 | ( ~ Xphi
% 2.46/1.26 & ( Xz = Xy ) ) ) )
% 2.46/1.26 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(iftrueProp1_type,type,
% 2.46/1.26 iftrueProp1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(iftrueProp1,definition,
% 2.46/1.26 ( iftrueProp1
% 2.46/1.26 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ A )
% 2.46/1.26 => ( Xphi
% 2.46/1.26 => ( in @ Xx
% 2.46/1.26 @ ( dsetconstr @ A
% 2.46/1.26 @ ^ [Xz: $i] :
% 2.46/1.26 ( ( Xphi
% 2.46/1.26 & ( Xz = Xx ) )
% 2.46/1.26 | ( ~ Xphi
% 2.46/1.26 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(iftrueProp2_type,type,
% 2.46/1.26 iftrueProp2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(iftrueProp2,definition,
% 2.46/1.26 ( iftrueProp2
% 2.46/1.26 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ A )
% 2.46/1.26 => ( Xphi
% 2.46/1.26 => ( ( dsetconstr @ A
% 2.46/1.26 @ ^ [Xz: $i] :
% 2.46/1.26 ( ( Xphi
% 2.46/1.26 & ( Xz = Xx ) )
% 2.46/1.26 | ( ~ Xphi
% 2.46/1.26 & ( Xz = Xy ) ) ) )
% 2.46/1.26 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(ifSingleton_type,type,
% 2.46/1.26 ifSingleton: $o ).
% 2.46/1.26
% 2.46/1.26 thf(ifSingleton,definition,
% 2.46/1.26 ( ifSingleton
% 2.46/1.26 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ A )
% 2.46/1.26 => ( singleton
% 2.46/1.26 @ ( dsetconstr @ A
% 2.46/1.26 @ ^ [Xz: $i] :
% 2.46/1.26 ( ( Xphi
% 2.46/1.26 & ( Xz = Xx ) )
% 2.46/1.26 | ( ~ Xphi
% 2.46/1.26 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(if_type,type,
% 2.46/1.26 if: $i > $o > $i > $i > $i ).
% 2.46/1.26
% 2.46/1.26 thf(ifp_type,type,
% 2.46/1.26 ifp: $o ).
% 2.46/1.26
% 2.46/1.26 thf(ifp,definition,
% 2.46/1.26 ( ifp
% 2.46/1.26 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ A )
% 2.46/1.26 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(theeq_type,type,
% 2.46/1.26 theeq: $o ).
% 2.46/1.26
% 2.46/1.26 thf(theeq,definition,
% 2.46/1.26 ( theeq
% 2.46/1.26 = ( ! [X: $i] :
% 2.46/1.26 ( ( singleton @ X )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ X )
% 2.46/1.26 => ( ( setunion @ X )
% 2.46/1.26 = Xx ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(iftrue_type,type,
% 2.46/1.26 iftrue: $o ).
% 2.46/1.26
% 2.46/1.26 thf(iftrue,definition,
% 2.46/1.26 ( iftrue
% 2.46/1.26 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ A )
% 2.46/1.26 => ( Xphi
% 2.46/1.26 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 2.46/1.26 = Xx ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(iffalse_type,type,
% 2.46/1.26 iffalse: $o ).
% 2.46/1.26
% 2.46/1.26 thf(iffalse,definition,
% 2.46/1.26 ( iffalse
% 2.46/1.26 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ A )
% 2.46/1.26 => ( ~ Xphi
% 2.46/1.26 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 2.46/1.26 = Xy ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(iftrueorfalse_type,type,
% 2.46/1.26 iftrueorfalse: $o ).
% 2.46/1.26
% 2.46/1.26 thf(iftrueorfalse,definition,
% 2.46/1.26 ( iftrueorfalse
% 2.46/1.26 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ A )
% 2.46/1.26 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(binintersectT_lem_type,type,
% 2.46/1.26 binintersectT_lem: $o ).
% 2.46/1.26
% 2.46/1.26 thf(binintersectT_lem,definition,
% 2.46/1.26 ( binintersectT_lem
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(binunionT_lem_type,type,
% 2.46/1.26 binunionT_lem: $o ).
% 2.46/1.26
% 2.46/1.26 thf(binunionT_lem,definition,
% 2.46/1.26 ( binunionT_lem
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(powersetT_lem_type,type,
% 2.46/1.26 powersetT_lem: $o ).
% 2.46/1.26
% 2.46/1.26 thf(powersetT_lem,definition,
% 2.46/1.26 ( powersetT_lem
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setminusT_lem_type,type,
% 2.46/1.26 setminusT_lem: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setminusT_lem,definition,
% 2.46/1.26 ( setminusT_lem
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(complementT_lem_type,type,
% 2.46/1.26 complementT_lem: $o ).
% 2.46/1.26
% 2.46/1.26 thf(complementT_lem,definition,
% 2.46/1.26 ( complementT_lem
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setextT_type,type,
% 2.46/1.26 setextT: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setextT,definition,
% 2.46/1.26 ( setextT
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( in @ Xx @ X )
% 2.46/1.26 => ( in @ Xx @ Y ) ) )
% 2.46/1.26 => ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( in @ Xx @ Y )
% 2.46/1.26 => ( in @ Xx @ X ) ) )
% 2.46/1.26 => ( X = Y ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(subsetTI_type,type,
% 2.46/1.26 subsetTI: $o ).
% 2.46/1.26
% 2.46/1.26 thf(subsetTI,definition,
% 2.46/1.26 ( subsetTI
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( in @ Xx @ X )
% 2.46/1.26 => ( in @ Xx @ Y ) ) )
% 2.46/1.26 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(powersetTI1_type,type,
% 2.46/1.26 powersetTI1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(powersetTI1,definition,
% 2.46/1.26 ( powersetTI1
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( in @ Xx @ X )
% 2.46/1.26 => ( in @ Xx @ Y ) ) )
% 2.46/1.26 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(powersetTE1_type,type,
% 2.46/1.26 powersetTE1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(powersetTE1,definition,
% 2.46/1.26 ( powersetTE1
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( in @ X @ ( powerset @ Y ) )
% 2.46/1.26 => ( ( in @ Xx @ X )
% 2.46/1.26 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(complementTI1_type,type,
% 2.46/1.26 complementTI1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(complementTI1,definition,
% 2.46/1.26 ( complementTI1
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( in @ Xx @ X )
% 2.46/1.26 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(complementTE1_type,type,
% 2.46/1.26 complementTE1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(complementTE1,definition,
% 2.46/1.26 ( complementTE1
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 2.46/1.26 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(binintersectTELcontra_type,type,
% 2.46/1.26 binintersectTELcontra: $o ).
% 2.46/1.26
% 2.46/1.26 thf(binintersectTELcontra,definition,
% 2.46/1.26 ( binintersectTELcontra
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ~ ( in @ Xx @ X )
% 2.46/1.26 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(binintersectTERcontra_type,type,
% 2.46/1.26 binintersectTERcontra: $o ).
% 2.46/1.26
% 2.46/1.26 thf(binintersectTERcontra,definition,
% 2.46/1.26 ( binintersectTERcontra
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ~ ( in @ Xx @ Y )
% 2.46/1.26 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(contrasubsetT_type,type,
% 2.46/1.26 contrasubsetT: $o ).
% 2.46/1.26
% 2.46/1.26 thf(contrasubsetT,definition,
% 2.46/1.26 ( contrasubsetT
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.46/1.26 => ( ( in @ Xx @ Y )
% 2.46/1.26 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(contrasubsetT1_type,type,
% 2.46/1.26 contrasubsetT1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(contrasubsetT1,definition,
% 2.46/1.26 ( contrasubsetT1
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( subset @ X @ Y )
% 2.46/1.26 => ( ~ ( in @ Xx @ Y )
% 2.46/1.26 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(contrasubsetT2_type,type,
% 2.46/1.26 contrasubsetT2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(contrasubsetT2,definition,
% 2.46/1.26 ( contrasubsetT2
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ( ( subset @ X @ Y )
% 2.46/1.26 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(contrasubsetT3_type,type,
% 2.46/1.26 contrasubsetT3: $o ).
% 2.46/1.26
% 2.46/1.26 thf(contrasubsetT3,definition,
% 2.46/1.26 ( contrasubsetT3
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 2.46/1.26 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(doubleComplementI1_type,type,
% 2.46/1.26 doubleComplementI1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(doubleComplementI1,definition,
% 2.46/1.26 ( doubleComplementI1
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( in @ Xx @ X )
% 2.46/1.26 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(doubleComplementE1_type,type,
% 2.46/1.26 doubleComplementE1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(doubleComplementE1,definition,
% 2.46/1.26 ( doubleComplementE1
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 2.46/1.26 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(doubleComplementSub1_type,type,
% 2.46/1.26 doubleComplementSub1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(doubleComplementSub1,definition,
% 2.46/1.26 ( doubleComplementSub1
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(doubleComplementSub2_type,type,
% 2.46/1.26 doubleComplementSub2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(doubleComplementSub2,definition,
% 2.46/1.26 ( doubleComplementSub2
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(doubleComplementEq_type,type,
% 2.46/1.26 doubleComplementEq: $o ).
% 2.46/1.26
% 2.46/1.26 thf(doubleComplementEq,definition,
% 2.46/1.26 ( doubleComplementEq
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ( X
% 2.46/1.26 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(complementTnotintersectT_type,type,
% 2.46/1.26 complementTnotintersectT: $o ).
% 2.46/1.26
% 2.46/1.26 thf(complementTnotintersectT,definition,
% 2.46/1.26 ( complementTnotintersectT
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 2.46/1.26 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(complementImpComplementIntersect_type,type,
% 2.46/1.26 complementImpComplementIntersect: $o ).
% 2.46/1.26
% 2.46/1.26 thf(complementImpComplementIntersect,definition,
% 2.46/1.26 ( complementImpComplementIntersect
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 2.46/1.26 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(complementSubsetComplementIntersect_type,type,
% 2.46/1.26 complementSubsetComplementIntersect: $o ).
% 2.46/1.26
% 2.46/1.26 thf(complementSubsetComplementIntersect,definition,
% 2.46/1.26 ( complementSubsetComplementIntersect
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(complementInPowersetComplementIntersect_type,type,
% 2.46/1.26 complementInPowersetComplementIntersect: $o ).
% 2.46/1.26
% 2.46/1.26 thf(complementInPowersetComplementIntersect,definition,
% 2.46/1.26 ( complementInPowersetComplementIntersect
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(contraSubsetComplement_type,type,
% 2.46/1.26 contraSubsetComplement: $o ).
% 2.46/1.26
% 2.46/1.26 thf(contraSubsetComplement,definition,
% 2.46/1.26 ( contraSubsetComplement
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( in @ Xx @ Y )
% 2.46/1.26 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(complementTcontraSubset_type,type,
% 2.46/1.26 complementTcontraSubset: $o ).
% 2.46/1.26
% 2.46/1.26 thf(complementTcontraSubset,definition,
% 2.46/1.26 ( complementTcontraSubset
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.46/1.26 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(binunionTILcontra_type,type,
% 2.46/1.26 binunionTILcontra: $o ).
% 2.46/1.26
% 2.46/1.26 thf(binunionTILcontra,definition,
% 2.46/1.26 ( binunionTILcontra
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 2.46/1.26 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(binunionTIRcontra_type,type,
% 2.46/1.26 binunionTIRcontra: $o ).
% 2.46/1.26
% 2.46/1.26 thf(binunionTIRcontra,definition,
% 2.46/1.26 ( binunionTIRcontra
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 2.46/1.26 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(inIntersectImpInUnion_type,type,
% 2.46/1.26 inIntersectImpInUnion: $o ).
% 2.46/1.26
% 2.46/1.26 thf(inIntersectImpInUnion,definition,
% 2.46/1.26 ( inIntersectImpInUnion
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Z: $i] :
% 2.46/1.26 ( ( in @ Z @ ( powerset @ A ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 2.46/1.26 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(inIntersectImpInUnion2_type,type,
% 2.46/1.26 inIntersectImpInUnion2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(inIntersectImpInUnion2,definition,
% 2.46/1.26 ( inIntersectImpInUnion2
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Z: $i] :
% 2.46/1.26 ( ( in @ Z @ ( powerset @ A ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 2.46/1.26 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(inIntersectImpInIntersectUnions_type,type,
% 2.46/1.26 inIntersectImpInIntersectUnions: $o ).
% 2.46/1.26
% 2.46/1.26 thf(inIntersectImpInIntersectUnions,definition,
% 2.46/1.26 ( inIntersectImpInIntersectUnions
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Z: $i] :
% 2.46/1.26 ( ( in @ Z @ ( powerset @ A ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 2.46/1.26 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(intersectInPowersetIntersectUnions_type,type,
% 2.46/1.26 intersectInPowersetIntersectUnions: $o ).
% 2.46/1.26
% 2.46/1.26 thf(intersectInPowersetIntersectUnions,definition,
% 2.46/1.26 ( intersectInPowersetIntersectUnions
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Z: $i] :
% 2.46/1.26 ( ( in @ Z @ ( powerset @ A ) )
% 2.46/1.26 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(inComplementUnionImpNotIn1_type,type,
% 2.46/1.26 inComplementUnionImpNotIn1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(inComplementUnionImpNotIn1,definition,
% 2.46/1.26 ( inComplementUnionImpNotIn1
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.46/1.26 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(inComplementUnionImpInComplement1_type,type,
% 2.46/1.26 inComplementUnionImpInComplement1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(inComplementUnionImpInComplement1,definition,
% 2.46/1.26 ( inComplementUnionImpInComplement1
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.46/1.26 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(binunionTE_type,type,
% 2.46/1.26 binunionTE: $o ).
% 2.46/1.26
% 2.46/1.26 thf(binunionTE,definition,
% 2.46/1.26 ( binunionTE
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Xphi: $o,Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 2.46/1.26 => ( ( ( in @ Xx @ X )
% 2.46/1.26 => Xphi )
% 2.46/1.26 => ( ( ( in @ Xx @ Y )
% 2.46/1.26 => Xphi )
% 2.46/1.26 => Xphi ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(binunionTEcontra_type,type,
% 2.46/1.26 binunionTEcontra: $o ).
% 2.46/1.26
% 2.46/1.26 thf(binunionTEcontra,definition,
% 2.46/1.26 ( binunionTEcontra
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ~ ( in @ Xx @ X )
% 2.46/1.26 => ( ~ ( in @ Xx @ Y )
% 2.46/1.26 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(demorgan2a1_type,type,
% 2.46/1.26 demorgan2a1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(demorgan2a1,definition,
% 2.46/1.26 ( demorgan2a1
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.46/1.26 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(complementUnionInPowersetComplement_type,type,
% 2.46/1.26 complementUnionInPowersetComplement: $o ).
% 2.46/1.26
% 2.46/1.26 thf(complementUnionInPowersetComplement,definition,
% 2.46/1.26 ( complementUnionInPowersetComplement
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(demorgan2a2_type,type,
% 2.46/1.26 demorgan2a2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(demorgan2a2,definition,
% 2.46/1.26 ( demorgan2a2
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.46/1.26 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(demorgan1a_type,type,
% 2.46/1.26 demorgan1a: $o ).
% 2.46/1.26
% 2.46/1.26 thf(demorgan1a,definition,
% 2.46/1.26 ( demorgan1a
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 2.46/1.26 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(demorgan1b_type,type,
% 2.46/1.26 demorgan1b: $o ).
% 2.46/1.26
% 2.46/1.26 thf(demorgan1b,definition,
% 2.46/1.26 ( demorgan1b
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 2.46/1.26 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(demorgan1_type,type,
% 2.46/1.26 demorgan1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(demorgan1,definition,
% 2.46/1.26 ( demorgan1
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 2.46/1.26 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(demorgan2a_type,type,
% 2.46/1.26 demorgan2a: $o ).
% 2.46/1.26
% 2.46/1.26 thf(demorgan2a,definition,
% 2.46/1.26 ( demorgan2a
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.46/1.26 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(demorgan2b2_type,type,
% 2.46/1.26 demorgan2b2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(demorgan2b2,definition,
% 2.46/1.26 ( demorgan2b2
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 2.46/1.26 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 2.46/1.26 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(demorgan2b_type,type,
% 2.46/1.26 demorgan2b: $o ).
% 2.46/1.26
% 2.46/1.26 thf(demorgan2b,definition,
% 2.46/1.26 ( demorgan2b
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 2.46/1.26 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(demorgan2_type,type,
% 2.46/1.26 demorgan2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(demorgan2,definition,
% 2.46/1.26 ( demorgan2
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 2.46/1.26 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(woz13rule0_type,type,
% 2.46/1.26 woz13rule0: $o ).
% 2.46/1.26
% 2.46/1.26 thf(woz13rule0,definition,
% 2.46/1.26 ( woz13rule0
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 2.46/1.26 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(woz13rule1_type,type,
% 2.46/1.26 woz13rule1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(woz13rule1,definition,
% 2.46/1.26 ( woz13rule1
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Z: $i] :
% 2.46/1.26 ( ( in @ Z @ ( powerset @ A ) )
% 2.46/1.26 => ( ( subset @ X @ Z )
% 2.46/1.26 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(woz13rule2_type,type,
% 2.46/1.26 woz13rule2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(woz13rule2,definition,
% 2.46/1.26 ( woz13rule2
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Z: $i] :
% 2.46/1.26 ( ( in @ Z @ ( powerset @ A ) )
% 2.46/1.26 => ( ( subset @ Y @ Z )
% 2.46/1.26 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(woz13rule3_type,type,
% 2.46/1.26 woz13rule3: $o ).
% 2.46/1.26
% 2.46/1.26 thf(woz13rule3,definition,
% 2.46/1.26 ( woz13rule3
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Z: $i] :
% 2.46/1.26 ( ( in @ Z @ ( powerset @ A ) )
% 2.46/1.26 => ( ( subset @ X @ Y )
% 2.46/1.26 => ( ( subset @ X @ Z )
% 2.46/1.26 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(woz13rule4_type,type,
% 2.46/1.26 woz13rule4: $o ).
% 2.46/1.26
% 2.46/1.26 thf(woz13rule4,definition,
% 2.46/1.26 ( woz13rule4
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Z: $i] :
% 2.46/1.26 ( ( in @ Z @ ( powerset @ A ) )
% 2.46/1.26 => ! [W: $i] :
% 2.46/1.26 ( ( in @ W @ ( powerset @ A ) )
% 2.46/1.26 => ( ( subset @ X @ Z )
% 2.46/1.26 => ( ( subset @ Y @ W )
% 2.46/1.26 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(woz1_1_type,type,
% 2.46/1.26 woz1_1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(woz1_1,definition,
% 2.46/1.26 ( woz1_1
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(woz1_2_type,type,
% 2.46/1.26 woz1_2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(woz1_2,definition,
% 2.46/1.26 ( woz1_2
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Z: $i] :
% 2.46/1.26 ( ( in @ Z @ ( powerset @ A ) )
% 2.46/1.26 => ! [W: $i] :
% 2.46/1.26 ( ( in @ W @ ( powerset @ A ) )
% 2.46/1.26 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 2.46/1.26 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(woz1_3_type,type,
% 2.46/1.26 woz1_3: $o ).
% 2.46/1.26
% 2.46/1.26 thf(woz1_3,definition,
% 2.46/1.26 ( woz1_3
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ! [Z: $i] :
% 2.46/1.26 ( ( in @ Z @ ( powerset @ A ) )
% 2.46/1.26 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(woz1_4_type,type,
% 2.46/1.26 woz1_4: $o ).
% 2.46/1.26
% 2.46/1.26 thf(woz1_4,definition,
% 2.46/1.26 ( woz1_4
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.46/1.26 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(woz1_5_type,type,
% 2.46/1.26 woz1_5: $o ).
% 2.46/1.26
% 2.46/1.26 thf(woz1_5,definition,
% 2.46/1.26 ( woz1_5
% 2.46/1.26 = ( ! [A: $i,X: $i] :
% 2.46/1.26 ( ( in @ X @ ( powerset @ A ) )
% 2.46/1.26 => ! [Y: $i] :
% 2.46/1.26 ( ( in @ Y @ ( powerset @ A ) )
% 2.46/1.26 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(breln1_type,type,
% 2.46/1.26 breln1: $i > $i > $o ).
% 2.46/1.26
% 2.46/1.26 thf(breln1,definition,
% 2.46/1.26 ( breln1
% 2.46/1.26 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(breln1all2_type,type,
% 2.46/1.26 breln1all2: $o ).
% 2.46/1.26
% 2.46/1.26 thf(breln1all2,definition,
% 2.46/1.26 ( breln1all2
% 2.46/1.26 = ( ! [A: $i,R: $i] :
% 2.46/1.26 ( ( breln1 @ A @ R )
% 2.46/1.26 => ! [Xphi: $i > $o] :
% 2.46/1.26 ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ A )
% 2.46/1.26 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.46/1.26 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ R )
% 2.46/1.26 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(breln1Set_type,type,
% 2.46/1.26 breln1Set: $i > $i ).
% 2.46/1.26
% 2.46/1.26 thf(breln1SetBreln1_type,type,
% 2.46/1.26 breln1SetBreln1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(breln1SetBreln1,definition,
% 2.46/1.26 ( breln1SetBreln1
% 2.46/1.26 = ( ! [A: $i,R: $i] :
% 2.46/1.26 ( ( in @ R @ ( breln1Set @ A ) )
% 2.46/1.26 => ( breln1 @ A @ R ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(transitive_type,type,
% 2.46/1.26 transitive: $i > $i > $o ).
% 2.46/1.26
% 2.46/1.26 thf(antisymmetric_type,type,
% 2.46/1.26 antisymmetric: $i > $i > $o ).
% 2.46/1.26
% 2.46/1.26 thf(reflexive_type,type,
% 2.46/1.26 reflexive: $i > $i > $o ).
% 2.46/1.26
% 2.46/1.26 thf(refltransitive_type,type,
% 2.46/1.26 refltransitive: $i > $i > $o ).
% 2.46/1.26
% 2.46/1.26 thf(refllinearorder_type,type,
% 2.46/1.26 refllinearorder: $i > $i > $o ).
% 2.46/1.26
% 2.46/1.26 thf(reflwellordering_type,type,
% 2.46/1.26 reflwellordering: $i > $i > $o ).
% 2.46/1.26
% 2.46/1.26 thf(choice2fnsingleton_type,type,
% 2.46/1.26 choice2fnsingleton: $o ).
% 2.46/1.26
% 2.46/1.26 thf(choice2fnsingleton,definition,
% 2.46/1.26 ( choice2fnsingleton
% 2.46/1.26 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.46/1.26 ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ? [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ B )
% 2.46/1.26 & ( Xphi @ Xx @ Xy ) ) )
% 2.46/1.26 => ! [R: $i] :
% 2.46/1.26 ( ( in @ R @ ( breln1Set @ B ) )
% 2.46/1.26 => ( ( reflwellordering @ B @ R )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ( singleton
% 2.46/1.26 @ ( dsetconstr @ B
% 2.46/1.26 @ ^ [Xy: $i] :
% 2.46/1.26 ( ( Xphi @ Xx @ Xy )
% 2.46/1.26 & ! [Xz: $i] :
% 2.46/1.26 ( ( in @ Xz @ B )
% 2.46/1.26 => ( ( Xphi @ Xx @ Xz )
% 2.46/1.26 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(setOfPairsIsBReln1_type,type,
% 2.46/1.26 setOfPairsIsBReln1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(setOfPairsIsBReln1,definition,
% 2.46/1.26 ( setOfPairsIsBReln1
% 2.46/1.26 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 2.46/1.26 ( breln1 @ A
% 2.46/1.26 @ ( dpsetconstr @ A @ A
% 2.46/1.26 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(breln1all1_type,type,
% 2.46/1.26 breln1all1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(breln1all1,definition,
% 2.46/1.26 ( breln1all1
% 2.46/1.26 = ( ! [A: $i,R: $i] :
% 2.46/1.26 ( ( breln1 @ A @ R )
% 2.46/1.26 => ! [Xphi: $i > $o] :
% 2.46/1.26 ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ A )
% 2.46/1.26 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.46/1.26 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ R )
% 2.46/1.26 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(subbreln1_type,type,
% 2.46/1.26 subbreln1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(subbreln1,definition,
% 2.46/1.26 ( subbreln1
% 2.46/1.26 = ( ! [A: $i,R: $i] :
% 2.46/1.26 ( ( breln1 @ A @ R )
% 2.46/1.26 => ! [S: $i] :
% 2.46/1.26 ( ( breln1 @ A @ S )
% 2.46/1.26 => ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ A )
% 2.46/1.26 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.46/1.26 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.46/1.26 => ( subset @ R @ S ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(eqbreln1_type,type,
% 2.46/1.26 eqbreln1: $o ).
% 2.46/1.26
% 2.46/1.26 thf(eqbreln1,definition,
% 2.46/1.26 ( eqbreln1
% 2.46/1.26 = ( ! [A: $i,R: $i] :
% 2.46/1.26 ( ( breln1 @ A @ R )
% 2.46/1.26 => ! [S: $i] :
% 2.46/1.26 ( ( breln1 @ A @ S )
% 2.46/1.26 => ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ A )
% 2.46/1.26 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.46/1.26 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.46/1.26 => ( ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ A )
% 2.46/1.26 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 2.46/1.26 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 2.46/1.26 => ( R = S ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(breln1invset_type,type,
% 2.46/1.26 breln1invset: $i > $i > $i ).
% 2.46/1.26
% 2.46/1.26 thf(breln1invprop_type,type,
% 2.46/1.26 breln1invprop: $o ).
% 2.46/1.26
% 2.46/1.26 thf(breln1invprop,definition,
% 2.46/1.26 ( breln1invprop
% 2.46/1.26 = ( ! [A: $i,R: $i] :
% 2.46/1.26 ( ( breln1 @ A @ R )
% 2.46/1.26 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(breln1invI_type,type,
% 2.46/1.26 breln1invI: $o ).
% 2.46/1.26
% 2.46/1.26 thf(breln1invI,definition,
% 2.46/1.26 ( breln1invI
% 2.46/1.26 = ( ! [A: $i,R: $i] :
% 2.46/1.26 ( ( breln1 @ A @ R )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ A )
% 2.46/1.26 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.46/1.26 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(breln1invE_type,type,
% 2.46/1.26 breln1invE: $o ).
% 2.46/1.26
% 2.46/1.26 thf(breln1invE,definition,
% 2.46/1.26 ( breln1invE
% 2.46/1.26 = ( ! [A: $i,R: $i] :
% 2.46/1.26 ( ( breln1 @ A @ R )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ A )
% 2.46/1.26 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 2.46/1.26 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(breln1compset_type,type,
% 2.46/1.26 breln1compset: $i > $i > $i > $i ).
% 2.46/1.26
% 2.46/1.26 thf(breln1compset,definition,
% 2.46/1.26 ( breln1compset
% 2.46/1.26 = ( ^ [A: $i,R: $i,S: $i] :
% 2.46/1.26 ( dpsetconstr @ A @ A
% 2.46/1.26 @ ^ [Xx: $i,Xy: $i] :
% 2.46/1.26 ? [Xz: $i] :
% 2.46/1.26 ( ( in @ Xz @ A )
% 2.46/1.26 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 2.46/1.26 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(breln1compprop_type,type,
% 2.46/1.26 breln1compprop: $o ).
% 2.46/1.26
% 2.46/1.26 thf(breln1compprop,definition,
% 2.46/1.26 ( breln1compprop
% 2.46/1.26 = ( ! [A: $i,R: $i] :
% 2.46/1.26 ( ( breln1 @ A @ R )
% 2.46/1.26 => ! [S: $i] :
% 2.46/1.26 ( ( breln1 @ A @ S )
% 2.46/1.26 => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(breln1compI_type,type,
% 2.46/1.26 breln1compI: $o ).
% 2.46/1.26
% 2.46/1.26 thf(breln1compI,definition,
% 2.46/1.26 ( breln1compI
% 2.46/1.26 = ( ! [A: $i,R: $i] :
% 2.46/1.26 ( ( breln1 @ A @ R )
% 2.46/1.26 => ! [S: $i] :
% 2.46/1.26 ( ( breln1 @ A @ S )
% 2.46/1.26 => ! [Xx: $i] :
% 2.46/1.26 ( ( in @ Xx @ A )
% 2.46/1.26 => ! [Xy: $i] :
% 2.46/1.26 ( ( in @ Xy @ A )
% 2.46/1.26 => ! [Xz: $i] :
% 2.46/1.26 ( ( in @ Xz @ A )
% 2.46/1.26 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 2.46/1.26 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 2.46/1.26 => ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ) ).
% 2.46/1.26
% 2.46/1.26 thf(breln1compE,conjecture,
% 2.46/1.26 ( setextAx
% 2.46/1.26 => ( emptysetAx
% 2.46/1.26 => ( setadjoinAx
% 2.46/1.26 => ( powersetAx
% 2.46/1.26 => ( setunionAx
% 2.46/1.26 => ( omega0Ax
% 2.46/1.26 => ( omegaSAx
% 2.46/1.26 => ( omegaIndAx
% 2.46/1.26 => ( replAx
% 2.46/1.26 => ( foundationAx
% 2.46/1.26 => ( wellorderingAx
% 2.46/1.26 => ( descrp
% 2.46/1.26 => ( dsetconstrI
% 2.46/1.26 => ( dsetconstrEL
% 2.46/1.26 => ( dsetconstrER
% 2.46/1.26 => ( exuE1
% 2.46/1.26 => ( prop2setE
% 2.46/1.26 => ( emptysetE
% 2.46/1.26 => ( emptysetimpfalse
% 2.46/1.26 => ( notinemptyset
% 2.46/1.26 => ( exuE3e
% 2.46/1.26 => ( setext
% 2.46/1.26 => ( emptyI
% 2.46/1.26 => ( noeltsimpempty
% 2.46/1.26 => ( setbeta
% 2.46/1.26 => ( nonemptyE1
% 2.46/1.26 => ( nonemptyI
% 2.46/1.26 => ( nonemptyI1
% 2.46/1.26 => ( setadjoinIL
% 2.46/1.26 => ( emptyinunitempty
% 2.46/1.26 => ( setadjoinIR
% 2.46/1.26 => ( setadjoinE
% 2.46/1.26 => ( setadjoinOr
% 2.46/1.26 => ( setoftrueEq
% 2.46/1.26 => ( powersetI
% 2.46/1.26 => ( emptyinPowerset
% 2.46/1.26 => ( emptyInPowerset
% 2.46/1.26 => ( powersetE
% 2.46/1.26 => ( setunionI
% 2.46/1.26 => ( setunionE
% 2.46/1.26 => ( subPowSU
% 2.46/1.26 => ( exuE2
% 2.46/1.26 => ( nonemptyImpWitness
% 2.46/1.26 => ( uniqinunit
% 2.46/1.26 => ( notinsingleton
% 2.46/1.26 => ( eqinunit
% 2.46/1.26 => ( singletonsswitch
% 2.46/1.26 => ( upairsetE
% 2.46/1.26 => ( upairsetIL
% 2.46/1.26 => ( upairsetIR
% 2.46/1.26 => ( emptyE1
% 2.46/1.26 => ( vacuousDall
% 2.46/1.26 => ( quantDeMorgan1
% 2.46/1.26 => ( quantDeMorgan2
% 2.46/1.26 => ( quantDeMorgan3
% 2.46/1.26 => ( quantDeMorgan4
% 2.46/1.26 => ( prop2setI
% 2.46/1.26 => ( prop2set2propI
% 2.46/1.26 => ( notdexE
% 2.46/1.26 => ( notdallE
% 2.46/1.26 => ( exuI1
% 2.46/1.26 => ( exuI3
% 2.46/1.26 => ( exuI2
% 2.46/1.26 => ( inCongP
% 2.46/1.26 => ( in__Cong
% 2.46/1.26 => ( exuE3u
% 2.46/1.26 => ( exu__Cong
% 2.46/1.26 => ( emptyset__Cong
% 2.46/1.26 => ( setadjoin__Cong
% 2.46/1.26 => ( powerset__Cong
% 2.46/1.26 => ( setunion__Cong
% 2.46/1.26 => ( omega__Cong
% 2.46/1.26 => ( exuEu
% 2.46/1.26 => ( descr__Cong
% 2.46/1.26 => ( dsetconstr__Cong
% 2.46/1.26 => ( subsetI1
% 2.46/1.26 => ( eqimpsubset2
% 2.46/1.26 => ( eqimpsubset1
% 2.46/1.26 => ( subsetI2
% 2.46/1.26 => ( emptysetsubset
% 2.46/1.26 => ( subsetE
% 2.46/1.26 => ( subsetE2
% 2.46/1.26 => ( notsubsetI
% 2.46/1.26 => ( notequalI1
% 2.46/1.26 => ( notequalI2
% 2.46/1.26 => ( subsetRefl
% 2.46/1.26 => ( subsetTrans
% 2.46/1.26 => ( setadjoinSub
% 2.46/1.26 => ( setadjoinSub2
% 2.46/1.26 => ( subset2powerset
% 2.46/1.26 => ( setextsub
% 2.46/1.27 => ( subsetemptysetimpeq
% 2.46/1.27 => ( powersetI1
% 2.46/1.27 => ( powersetE1
% 2.46/1.27 => ( inPowerset
% 2.46/1.27 => ( powersetsubset
% 2.46/1.27 => ( sepInPowerset
% 2.46/1.27 => ( sepSubset
% 2.46/1.27 => ( binunionIL
% 2.46/1.27 => ( upairset2IR
% 2.46/1.27 => ( binunionIR
% 2.46/1.27 => ( binunionEcases
% 2.46/1.27 => ( binunionE
% 2.46/1.27 => ( binunionLsub
% 2.46/1.27 => ( binunionRsub
% 2.46/1.27 => ( binintersectI
% 2.46/1.27 => ( binintersectSubset5
% 2.46/1.27 => ( binintersectEL
% 2.46/1.27 => ( binintersectLsub
% 2.46/1.27 => ( binintersectSubset2
% 2.46/1.27 => ( binintersectSubset3
% 2.46/1.27 => ( binintersectER
% 2.46/1.27 => ( disjointsetsI1
% 2.46/1.27 => ( binintersectRsub
% 2.46/1.27 => ( binintersectSubset4
% 2.46/1.27 => ( binintersectSubset1
% 2.46/1.27 => ( bs114d
% 2.46/1.27 => ( setminusI
% 2.46/1.27 => ( setminusEL
% 2.46/1.27 => ( setminusER
% 2.46/1.27 => ( setminusSubset2
% 2.46/1.27 => ( setminusERneg
% 2.46/1.27 => ( setminusELneg
% 2.46/1.27 => ( setminusILneg
% 2.46/1.27 => ( setminusIRneg
% 2.46/1.27 => ( setminusLsub
% 2.46/1.27 => ( setminusSubset1
% 2.46/1.27 => ( symdiffE
% 2.46/1.27 => ( symdiffI1
% 2.46/1.27 => ( symdiffI2
% 2.46/1.27 => ( symdiffIneg1
% 2.46/1.27 => ( symdiffIneg2
% 2.46/1.27 => ( secondinupair
% 2.46/1.27 => ( setukpairIL
% 2.46/1.27 => ( setukpairIR
% 2.46/1.27 => ( kpairiskpair
% 2.46/1.27 => ( kpairp
% 2.46/1.27 => ( singletonsubset
% 2.46/1.27 => ( singletoninpowerset
% 2.46/1.27 => ( singletoninpowunion
% 2.46/1.27 => ( upairset2E
% 2.46/1.27 => ( upairsubunion
% 2.46/1.27 => ( upairinpowunion
% 2.46/1.27 => ( ubforcartprodlem1
% 2.46/1.27 => ( ubforcartprodlem2
% 2.46/1.27 => ( ubforcartprodlem3
% 2.46/1.27 => ( cartprodpairin
% 2.46/1.27 => ( cartprodmempair1
% 2.46/1.27 => ( cartprodmempair
% 2.46/1.27 => ( setunionE2
% 2.46/1.27 => ( setunionsingleton1
% 2.46/1.27 => ( setunionsingleton2
% 2.46/1.27 => ( setunionsingleton
% 2.46/1.27 => ( singletonprop
% 2.46/1.27 => ( ex1E1
% 2.46/1.27 => ( ex1I
% 2.46/1.27 => ( ex1I2
% 2.46/1.27 => ( singletonsuniq
% 2.46/1.27 => ( setukpairinjL1
% 2.46/1.27 => ( kfstsingleton
% 2.46/1.27 => ( theprop
% 2.46/1.27 => ( kfstpairEq
% 2.46/1.27 => ( cartprodfstin
% 2.46/1.27 => ( setukpairinjL2
% 2.46/1.27 => ( setukpairinjL
% 2.46/1.27 => ( setukpairinjR11
% 2.46/1.27 => ( setukpairinjR12
% 2.46/1.27 => ( setukpairinjR1
% 2.46/1.27 => ( upairequniteq
% 2.46/1.27 => ( setukpairinjR2
% 2.46/1.27 => ( setukpairinjR
% 2.46/1.27 => ( ksndsingleton
% 2.46/1.27 => ( ksndpairEq
% 2.46/1.27 => ( kpairsurjEq
% 2.46/1.27 => ( cartprodsndin
% 2.46/1.27 => ( cartprodpairmemEL
% 2.46/1.27 => ( cartprodpairmemER
% 2.46/1.27 => ( cartprodmempaircEq
% 2.46/1.27 => ( cartprodfstpairEq
% 2.46/1.27 => ( cartprodsndpairEq
% 2.46/1.27 => ( cartprodpairsurjEq
% 2.46/1.27 => ( dpsetconstrI
% 2.46/1.27 => ( dpsetconstrSub
% 2.46/1.27 => ( setOfPairsIsBReln
% 2.46/1.27 => ( dpsetconstrERa
% 2.46/1.27 => ( dpsetconstrEL1
% 2.46/1.27 => ( dpsetconstrEL2
% 2.46/1.27 => ( dpsetconstrER
% 2.46/1.27 => ( funcImageSingleton
% 2.46/1.27 => ( apProp
% 2.46/1.27 => ( app
% 2.46/1.27 => ( infuncsetfunc
% 2.46/1.27 => ( ap2p
% 2.46/1.27 => ( funcinfuncset
% 2.46/1.27 => ( lamProp
% 2.46/1.27 => ( lamp
% 2.46/1.27 => ( lam2p
% 2.46/1.27 => ( brelnall1
% 2.46/1.27 => ( brelnall2
% 2.46/1.27 => ( ex1E2
% 2.46/1.27 => ( funcGraphProp1
% 2.46/1.27 => ( funcGraphProp3
% 2.46/1.27 => ( funcGraphProp2
% 2.46/1.27 => ( funcextLem
% 2.46/1.27 => ( funcGraphProp4
% 2.46/1.27 => ( subbreln
% 2.46/1.27 => ( eqbreln
% 2.46/1.27 => ( funcext
% 2.46/1.27 => ( funcext2
% 2.46/1.27 => ( ap2apEq1
% 2.46/1.27 => ( ap2apEq2
% 2.46/1.27 => ( beta1
% 2.46/1.27 => ( eta1
% 2.46/1.27 => ( lam2lamEq
% 2.46/1.27 => ( beta2
% 2.46/1.27 => ( eta2
% 2.46/1.27 => ( iffalseProp1
% 2.46/1.27 => ( iffalseProp2
% 2.46/1.27 => ( iftrueProp1
% 2.46/1.27 => ( iftrueProp2
% 2.46/1.27 => ( ifSingleton
% 2.46/1.27 => ( ifp
% 2.46/1.27 => ( theeq
% 2.46/1.27 => ( iftrue
% 2.46/1.27 => ( iffalse
% 2.46/1.27 => ( iftrueorfalse
% 2.46/1.27 => ( binintersectT_lem
% 2.46/1.27 => ( binunionT_lem
% 2.46/1.27 => ( powersetT_lem
% 2.46/1.27 => ( setminusT_lem
% 2.46/1.27 => ( complementT_lem
% 2.46/1.27 => ( setextT
% 2.46/1.27 => ( subsetTI
% 2.46/1.27 => ( powersetTI1
% 2.46/1.27 => ( powersetTE1
% 2.46/1.27 => ( complementTI1
% 2.46/1.27 => ( complementTE1
% 2.46/1.27 => ( binintersectTELcontra
% 2.46/1.27 => ( binintersectTERcontra
% 2.46/1.27 => ( contrasubsetT
% 2.46/1.27 => ( contrasubsetT1
% 2.46/1.27 => ( contrasubsetT2
% 2.46/1.27 => ( contrasubsetT3
% 2.46/1.27 => ( doubleComplementI1
% 2.46/1.27 => ( doubleComplementE1
% 2.46/1.27 => ( doubleComplementSub1
% 2.46/1.27 => ( doubleComplementSub2
% 2.46/1.27 => ( doubleComplementEq
% 2.46/1.27 => ( complementTnotintersectT
% 2.46/1.27 => ( complementImpComplementIntersect
% 2.46/1.27 => ( complementSubsetComplementIntersect
% 2.46/1.27 => ( complementInPowersetComplementIntersect
% 2.46/1.27 => ( contraSubsetComplement
% 2.46/1.27 => ( complementTcontraSubset
% 2.46/1.27 => ( binunionTILcontra
% 2.46/1.27 => ( binunionTIRcontra
% 2.46/1.27 => ( inIntersectImpInUnion
% 2.46/1.27 => ( inIntersectImpInUnion2
% 2.46/1.27 => ( inIntersectImpInIntersectUnions
% 2.46/1.27 => ( intersectInPowersetIntersectUnions
% 2.46/1.27 => ( inComplementUnionImpNotIn1
% 2.46/1.27 => ( inComplementUnionImpInComplement1
% 2.46/1.27 => ( binunionTE
% 2.46/1.27 => ( binunionTEcontra
% 2.46/1.27 => ( demorgan2a1
% 2.46/1.27 => ( complementUnionInPowersetComplement
% 2.46/1.27 => ( demorgan2a2
% 2.46/1.27 => ( demorgan1a
% 2.46/1.27 => ( demorgan1b
% 2.46/1.27 => ( demorgan1
% 2.46/1.27 => ( demorgan2a
% 2.46/1.27 => ( demorgan2b2
% 2.46/1.27 => ( demorgan2b
% 2.46/1.27 => ( demorgan2
% 2.46/1.27 => ( woz13rule0
% 2.46/1.27 => ( woz13rule1
% 2.46/1.27 => ( woz13rule2
% 2.46/1.27 => ( woz13rule3
% 2.46/1.27 => ( woz13rule4
% 2.46/1.27 => ( woz1_1
% 2.46/1.27 => ( woz1_2
% 2.46/1.27 => ( woz1_3
% 2.46/1.27 => ( woz1_4
% 2.46/1.27 => ( woz1_5
% 2.46/1.27 => ( breln1all2
% 2.46/1.27 => ( breln1SetBreln1
% 2.46/1.27 => ( choice2fnsingleton
% 2.46/1.27 => ( setOfPairsIsBReln1
% 2.46/1.27 => ( breln1all1
% 2.46/1.27 => ( subbreln1
% 2.46/1.27 => ( eqbreln1
% 2.46/1.27 => ( breln1invprop
% 2.46/1.27 => ( breln1invI
% 2.46/1.27 => ( breln1invE
% 2.46/1.27 => ( breln1compprop
% 2.46/1.27 => ( breln1compI
% 2.46/1.27 => ! [A: $i,R: $i] :
% 2.46/1.27 ( ( breln1 @ A @ R )
% 2.46/1.27 => ! [S: $i] :
% 2.46/1.27 ( ( breln1 @ A @ S )
% 2.46/1.27 => ! [Xx: $i] :
% 2.46/1.27 ( ( in @ Xx @ A )
% 2.46/1.27 => ! [Xy: $i] :
% 2.46/1.27 ( ( in @ Xy @ A )
% 2.46/1.27 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 2.46/1.27 => ? [Xz: $i] :
% 2.46/1.27 ( ( in @ Xz @ A )
% 2.46/1.27 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 2.46/1.27 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.46/1.27 ------------------------
% 2.46/1.29 % (20436)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20195 for (2999ds/183Mi)
% 2.53/1.30 % (20441)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_20195 for (2999ds/275Mi)
% 2.53/1.30 % (20437)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_20195 for (2999ds/4Mi)
% 2.53/1.30 % (20438)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_20195 for (2999ds/27Mi)
% 2.53/1.30 % (20439)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20195 for (2999ds/2Mi)
% 2.53/1.30 % (20442)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20195 for (2999ds/18Mi)
% 2.53/1.30 % (20440)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_20195 for (2999ds/2Mi)
% 2.53/1.30 % (20439)Instruction limit reached!
% 2.53/1.30 % (20439)------------------------------
% 2.53/1.30 % (20439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.30 % (20439)Termination reason: Unknown
% 2.53/1.30 % (20440)Instruction limit reached!
% 2.53/1.30 % (20440)------------------------------
% 2.53/1.30 % (20440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.30 % (20440)Termination reason: Unknown
% 2.53/1.30 % (20440)Termination phase: shuffling
% 2.53/1.30
% 2.53/1.30 % (20440)Memory used [KB]: 1535
% 2.53/1.30 % (20440)Time elapsed: 0.003 s
% 2.53/1.30 % (20440)Instructions burned: 2 (million)
% 2.53/1.30 % (20440)------------------------------
% 2.53/1.30 % (20440)------------------------------
% 2.53/1.30 % (20439)Termination phase: shuffling
% 2.53/1.30
% 2.53/1.30 % (20439)Memory used [KB]: 1535
% 2.53/1.30 % (20439)Time elapsed: 0.003 s
% 2.53/1.30 % (20439)Instructions burned: 3 (million)
% 2.53/1.30 % (20439)------------------------------
% 2.53/1.30 % (20439)------------------------------
% 2.53/1.30 % (20437)Instruction limit reached!
% 2.53/1.30 % (20437)------------------------------
% 2.53/1.30 % (20437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.30 % (20437)Termination reason: Unknown
% 2.53/1.30 % (20437)Termination phase: shuffling
% 2.53/1.30
% 2.53/1.30 % (20437)Memory used [KB]: 1535
% 2.53/1.30 % (20437)Time elapsed: 0.004 s
% 2.53/1.30 % (20437)Instructions burned: 5 (million)
% 2.53/1.30 % (20437)------------------------------
% 2.53/1.30 % (20437)------------------------------
% 2.53/1.31 % (20442)Instruction limit reached!
% 2.53/1.31 % (20442)------------------------------
% 2.53/1.31 % (20442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.31 % (20442)Termination reason: Unknown
% 2.53/1.31 % (20442)Termination phase: shuffling
% 2.53/1.31
% 2.53/1.31 % (20442)Memory used [KB]: 1918
% 2.53/1.31 % (20442)Time elapsed: 0.011 s
% 2.53/1.31 % (20442)Instructions burned: 19 (million)
% 2.53/1.31 % (20442)------------------------------
% 2.53/1.31 % (20442)------------------------------
% 2.53/1.31 % (20438)Instruction limit reached!
% 2.53/1.31 % (20438)------------------------------
% 2.53/1.31 % (20438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.31 % (20438)Termination reason: Unknown
% 2.53/1.31 % (20438)Termination phase: shuffling
% 2.53/1.31
% 2.53/1.31 % (20438)Memory used [KB]: 2046
% 2.53/1.31 % (20438)Time elapsed: 0.014 s
% 2.53/1.31 % (20438)Instructions burned: 27 (million)
% 2.53/1.31 % (20438)------------------------------
% 2.53/1.31 % (20438)------------------------------
% 2.53/1.32 % (20443)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20195 for (2999ds/3Mi)
% 2.53/1.32 % (20444)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_20195 for (2999ds/37Mi)
% 2.53/1.32 % (20443)Instruction limit reached!
% 2.53/1.32 % (20443)------------------------------
% 2.53/1.32 % (20443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.32 % (20443)Termination reason: Unknown
% 2.53/1.32 % (20443)Termination phase: shuffling
% 2.53/1.32
% 2.53/1.32 % (20443)Memory used [KB]: 1535
% 2.53/1.32 % (20443)Time elapsed: 0.003 s
% 2.53/1.32 % (20443)Instructions burned: 4 (million)
% 2.53/1.32 % (20443)------------------------------
% 2.53/1.32 % (20443)------------------------------
% 2.53/1.32 % (20445)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_20195 for (2999ds/15Mi)
% 2.53/1.32 % (20447)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_20195 for (2999ds/3Mi)
% 2.53/1.32 % (20445)Instruction limit reached!
% 2.53/1.32 % (20445)------------------------------
% 2.53/1.32 % (20445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.32 % (20445)Termination reason: Unknown
% 2.53/1.32 % (20445)Termination phase: shuffling
% 2.53/1.32
% 2.53/1.32 % (20445)Memory used [KB]: 1791
% 2.53/1.32 % (20445)Time elapsed: 0.009 s
% 2.53/1.32 % (20445)Instructions burned: 15 (million)
% 2.53/1.32 % (20445)------------------------------
% 2.53/1.32 % (20445)------------------------------
% 2.53/1.33 % (20447)Instruction limit reached!
% 2.53/1.33 % (20447)------------------------------
% 2.53/1.33 % (20447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.33 % (20447)Termination reason: Unknown
% 2.53/1.33 % (20447)Termination phase: shuffling
% 2.53/1.33
% 2.53/1.33 % (20447)Memory used [KB]: 1535
% 2.53/1.33 % (20447)Time elapsed: 0.003 s
% 2.53/1.33 % (20447)Instructions burned: 3 (million)
% 2.53/1.33 % (20447)------------------------------
% 2.53/1.33 % (20447)------------------------------
% 2.53/1.33 % (20448)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_20195 for (2999ds/1041Mi)
% 2.53/1.33 % (20444)Instruction limit reached!
% 2.53/1.33 % (20444)------------------------------
% 2.53/1.33 % (20444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.33 % (20444)Termination reason: Unknown
% 2.53/1.33 % (20444)Termination phase: shuffling
% 2.53/1.33
% 2.53/1.33 % (20444)Memory used [KB]: 2302
% 2.53/1.33 % (20444)Time elapsed: 0.018 s
% 2.53/1.33 % (20444)Instructions burned: 38 (million)
% 2.53/1.33 % (20444)------------------------------
% 2.53/1.33 % (20444)------------------------------
% 2.53/1.33 % (20449)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_20195 for (2999ds/7Mi)
% 2.53/1.34 % (20449)Instruction limit reached!
% 2.53/1.34 % (20449)------------------------------
% 2.53/1.34 % (20449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.34 % (20449)Termination reason: Unknown
% 2.53/1.34 % (20449)Termination phase: shuffling
% 2.53/1.34
% 2.53/1.34 % (20449)Memory used [KB]: 1663
% 2.53/1.34 % (20449)Time elapsed: 0.005 s
% 2.53/1.34 % (20449)Instructions burned: 8 (million)
% 2.53/1.34 % (20449)------------------------------
% 2.53/1.34 % (20449)------------------------------
% 2.53/1.34 % (20436)Instruction limit reached!
% 2.53/1.34 % (20436)------------------------------
% 2.53/1.34 % (20436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.34 % (20436)Termination reason: Unknown
% 2.53/1.34 % (20436)Termination phase: Saturation
% 2.53/1.34
% 2.53/1.34 % (20436)Memory used [KB]: 7419
% 2.53/1.34 % (20436)Time elapsed: 0.048 s
% 2.53/1.34 % (20436)Instructions burned: 185 (million)
% 2.53/1.34 % (20436)------------------------------
% 2.53/1.34 % (20436)------------------------------
% 2.53/1.34 % (20451)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_20195 for (2999ds/16Mi)
% 2.53/1.34 % (20452)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_20195 for (2999ds/3Mi)
% 2.53/1.34 % (20452)Instruction limit reached!
% 2.53/1.34 % (20452)------------------------------
% 2.53/1.34 % (20452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.34 % (20452)Termination reason: Unknown
% 2.53/1.34 % (20452)Termination phase: shuffling
% 2.53/1.34
% 2.53/1.34 % (20452)Memory used [KB]: 1535
% 2.53/1.34 % (20452)Time elapsed: 0.003 s
% 2.53/1.34 % (20452)Instructions burned: 3 (million)
% 2.53/1.34 % (20452)------------------------------
% 2.53/1.34 % (20452)------------------------------
% 2.53/1.35 % (20451)Instruction limit reached!
% 2.53/1.35 % (20451)------------------------------
% 2.53/1.35 % (20451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.35 % (20451)Termination reason: Unknown
% 2.53/1.35 % (20451)Termination phase: shuffling
% 2.53/1.35
% 2.53/1.35 % (20451)Memory used [KB]: 1791
% 2.53/1.35 % (20451)Time elapsed: 0.009 s
% 2.53/1.35 % (20451)Instructions burned: 16 (million)
% 2.53/1.35 % (20451)------------------------------
% 2.53/1.35 % (20451)------------------------------
% 2.53/1.35 % (20454)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_20195 for (2999ds/3Mi)
% 2.53/1.35 % (20456)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_20195 for (2999ds/3Mi)
% 2.53/1.35 % (20454)Instruction limit reached!
% 2.53/1.35 % (20454)------------------------------
% 2.53/1.35 % (20454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.35 % (20454)Termination reason: Unknown
% 2.53/1.35 % (20454)Termination phase: shuffling
% 2.53/1.35
% 2.53/1.35 % (20454)Memory used [KB]: 1535
% 2.53/1.35 % (20454)Time elapsed: 0.003 s
% 2.53/1.35 % (20454)Instructions burned: 3 (million)
% 2.53/1.35 % (20454)------------------------------
% 2.53/1.35 % (20454)------------------------------
% 2.53/1.35 % (20456)Instruction limit reached!
% 2.53/1.35 % (20456)------------------------------
% 2.53/1.35 % (20456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.35 % (20456)Termination reason: Unknown
% 2.53/1.35 % (20456)Termination phase: shuffling
% 2.53/1.35
% 2.53/1.35 % (20456)Memory used [KB]: 1535
% 2.53/1.35 % (20456)Time elapsed: 0.003 s
% 2.53/1.35 % (20456)Instructions burned: 6 (million)
% 2.53/1.35 % (20456)------------------------------
% 2.53/1.35 % (20456)------------------------------
% 2.53/1.35 % (20455)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_20195 for (2999ds/7Mi)
% 2.53/1.36 % (20455)Instruction limit reached!
% 2.53/1.36 % (20455)------------------------------
% 2.53/1.36 % (20455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.36 % (20455)Termination reason: Unknown
% 2.53/1.36 % (20455)Termination phase: shuffling
% 2.53/1.36
% 2.53/1.36 % (20455)Memory used [KB]: 1663
% 2.53/1.36 % (20455)Time elapsed: 0.005 s
% 2.53/1.36 % (20455)Instructions burned: 7 (million)
% 2.53/1.36 % (20455)------------------------------
% 2.53/1.36 % (20455)------------------------------
% 2.53/1.36 % (20459)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_20195 for (2999ds/4Mi)
% 2.53/1.36 % (20462)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_20195 for (2999ds/6Mi)
% 2.53/1.36 % (20459)Instruction limit reached!
% 2.53/1.36 % (20459)------------------------------
% 2.53/1.36 % (20459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.36 % (20459)Termination reason: Unknown
% 2.53/1.36 % (20459)Termination phase: shuffling
% 2.53/1.36
% 2.53/1.36 % (20459)Memory used [KB]: 1663
% 2.53/1.36 % (20459)Time elapsed: 0.004 s
% 2.53/1.36 % (20459)Instructions burned: 5 (million)
% 2.53/1.36 % (20459)------------------------------
% 2.53/1.36 % (20459)------------------------------
% 2.53/1.36 % (20462)Instruction limit reached!
% 2.53/1.36 % (20462)------------------------------
% 2.53/1.36 % (20462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.36 % (20462)Termination reason: Unknown
% 2.53/1.36 % (20462)Termination phase: shuffling
% 2.53/1.36
% 2.53/1.36 % (20462)Memory used [KB]: 1535
% 2.53/1.36 % (20462)Time elapsed: 0.003 s
% 2.53/1.36 % (20462)Instructions burned: 6 (million)
% 2.53/1.36 % (20462)------------------------------
% 2.53/1.36 % (20462)------------------------------
% 2.53/1.36 % (20461)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_20195 for (2999ds/710Mi)
% 2.53/1.36 % (20460)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_20195 for (2999ds/18Mi)
% 2.53/1.37 % (20460)Instruction limit reached!
% 2.53/1.37 % (20460)------------------------------
% 2.53/1.37 % (20460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.37 % (20460)Termination reason: Unknown
% 2.53/1.37 % (20460)Termination phase: shuffling
% 2.53/1.37
% 2.53/1.37 % (20460)Memory used [KB]: 1791
% 2.53/1.37 % (20460)Time elapsed: 0.010 s
% 2.53/1.37 % (20460)Instructions burned: 18 (million)
% 2.53/1.37 % (20460)------------------------------
% 2.53/1.37 % (20460)------------------------------
% 2.53/1.37 % (20463)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_20195 for (2999ds/902Mi)
% 2.53/1.38 % (20465)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_20195 for (2999ds/21Mi)
% 2.53/1.38 % (20466)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_20195 for (2999ds/5Mi)
% 2.53/1.38 % (20466)Instruction limit reached!
% 2.53/1.38 % (20466)------------------------------
% 2.53/1.38 % (20466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.38 % (20466)Termination reason: Unknown
% 2.53/1.38 % (20466)Termination phase: shuffling
% 2.53/1.38
% 2.53/1.38 % (20466)Memory used [KB]: 1535
% 2.53/1.38 % (20466)Time elapsed: 0.004 s
% 2.53/1.38 % (20466)Instructions burned: 5 (million)
% 2.53/1.38 % (20466)------------------------------
% 2.53/1.38 % (20466)------------------------------
% 2.53/1.39 % (20465)Instruction limit reached!
% 2.53/1.39 % (20465)------------------------------
% 2.53/1.39 % (20465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.39 % (20465)Termination reason: Unknown
% 2.53/1.39 % (20465)Termination phase: shuffling
% 2.53/1.39
% 2.53/1.39 % (20465)Memory used [KB]: 1918
% 2.53/1.39 % (20465)Time elapsed: 0.011 s
% 2.53/1.39 % (20465)Instructions burned: 21 (million)
% 2.53/1.39 % (20465)------------------------------
% 2.53/1.39 % (20465)------------------------------
% 2.53/1.40 % (20468)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_20195 for (2998ds/377Mi)
% 2.53/1.40 % (20467)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_20195 for (2999ds/6Mi)
% 2.53/1.41 % (20471)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_20195 for (2998ds/779Mi)
% 2.53/1.41 % (20467)Instruction limit reached!
% 2.53/1.41 % (20467)------------------------------
% 2.53/1.41 % (20467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.41 % (20467)Termination reason: Unknown
% 2.53/1.41 % (20467)Termination phase: shuffling
% 2.53/1.41
% 2.53/1.41 % (20467)Memory used [KB]: 1663
% 2.53/1.41 % (20467)Time elapsed: 0.005 s
% 2.53/1.41 % (20467)Instructions burned: 7 (million)
% 2.53/1.41 % (20467)------------------------------
% 2.53/1.41 % (20467)------------------------------
% 2.53/1.42 % (20441)Instruction limit reached!
% 2.53/1.42 % (20441)------------------------------
% 2.53/1.42 % (20441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.42 % (20441)Termination reason: Unknown
% 2.53/1.42 % (20441)Termination phase: Saturation
% 2.53/1.42
% 2.53/1.42 % (20441)Memory used [KB]: 10362
% 2.53/1.42 % (20441)Time elapsed: 0.124 s
% 2.53/1.42 % (20441)Instructions burned: 275 (million)
% 2.53/1.42 % (20441)------------------------------
% 2.53/1.42 % (20441)------------------------------
% 2.53/1.42 % (20474)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_20195 for (2998ds/19Mi)
% 2.53/1.43 % (20474)Instruction limit reached!
% 2.53/1.43 % (20474)------------------------------
% 2.53/1.43 % (20474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.43 % (20474)Termination reason: Unknown
% 2.53/1.43 % (20474)Termination phase: shuffling
% 2.53/1.43
% 2.53/1.43 % (20474)Memory used [KB]: 1918
% 2.53/1.43 % (20474)Time elapsed: 0.011 s
% 2.53/1.43 % (20474)Instructions burned: 21 (million)
% 2.53/1.43 % (20474)------------------------------
% 2.53/1.43 % (20474)------------------------------
% 2.53/1.44 % (20475)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_20195 for (2998ds/879Mi)
% 2.53/1.45 % (20478)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_20195 for (2998ds/17Mi)
% 2.53/1.46 % (20478)Instruction limit reached!
% 2.53/1.46 % (20478)------------------------------
% 2.53/1.46 % (20478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.46 % (20478)Termination reason: Unknown
% 2.53/1.46 % (20478)Termination phase: shuffling
% 2.53/1.46
% 2.53/1.46 % (20478)Memory used [KB]: 1791
% 2.53/1.46 % (20478)Time elapsed: 0.010 s
% 2.53/1.46 % (20478)Instructions burned: 18 (million)
% 2.53/1.46 % (20478)------------------------------
% 2.53/1.46 % (20478)------------------------------
% 2.53/1.47 % (20480)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_20195 for (2998ds/3Mi)
% 2.53/1.48 % (20480)Instruction limit reached!
% 2.53/1.48 % (20480)------------------------------
% 2.53/1.48 % (20480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.48 % (20480)Termination reason: Unknown
% 2.53/1.48 % (20480)Termination phase: shuffling
% 2.53/1.48
% 2.53/1.48 % (20480)Memory used [KB]: 1535
% 2.53/1.48 % (20480)Time elapsed: 0.003 s
% 2.53/1.48 % (20480)Instructions burned: 3 (million)
% 2.53/1.48 % (20480)------------------------------
% 2.53/1.48 % (20480)------------------------------
% 2.53/1.49 % (20483)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_20195 for (2998ds/30Mi)
% 2.53/1.50 % (20483)Instruction limit reached!
% 2.53/1.50 % (20483)------------------------------
% 2.53/1.50 % (20483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.50 % (20483)Termination reason: Unknown
% 2.53/1.50 % (20483)Termination phase: shuffling
% 2.53/1.50
% 2.53/1.50 % (20483)Memory used [KB]: 2046
% 2.53/1.50 % (20483)Time elapsed: 0.013 s
% 2.53/1.50 % (20483)Instructions burned: 31 (million)
% 2.53/1.50 % (20483)------------------------------
% 2.53/1.50 % (20483)------------------------------
% 2.53/1.51 % (20487)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_20195 for (2997ds/127Mi)
% 2.53/1.55 % (20468)Instruction limit reached!
% 2.53/1.55 % (20468)------------------------------
% 2.53/1.55 % (20468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.55 % (20468)Termination reason: Unknown
% 2.53/1.55 % (20468)Termination phase: Saturation
% 2.53/1.55
% 2.53/1.55 % (20468)Memory used [KB]: 9338
% 2.53/1.55 % (20468)Time elapsed: 0.156 s
% 2.53/1.55 % (20468)Instructions burned: 377 (million)
% 2.53/1.55 % (20468)------------------------------
% 2.53/1.55 % (20468)------------------------------
% 2.53/1.56 % (20487)Instruction limit reached!
% 2.53/1.56 % (20487)------------------------------
% 2.53/1.56 % (20487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.56 % (20487)Termination reason: Unknown
% 2.53/1.56 % (20487)Termination phase: Property scanning
% 2.53/1.56
% 2.53/1.56 % (20487)Memory used [KB]: 2814
% 2.53/1.56 % (20487)Time elapsed: 0.050 s
% 2.53/1.56 % (20487)Instructions burned: 128 (million)
% 2.53/1.56 % (20487)------------------------------
% 2.53/1.56 % (20487)------------------------------
% 2.53/1.57 % (20491)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_20195 for (2997ds/100Mi)
% 2.53/1.58 % (20493)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_20195 for (2997ds/3Mi)
% 2.53/1.58 % (20493)Instruction limit reached!
% 2.53/1.58 % (20493)------------------------------
% 2.53/1.58 % (20493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.58 % (20493)Termination reason: Unknown
% 2.53/1.58 % (20493)Termination phase: shuffling
% 2.53/1.58
% 2.53/1.58 % (20493)Memory used [KB]: 1535
% 2.53/1.58 % (20493)Time elapsed: 0.004 s
% 2.53/1.58 % (20493)Instructions burned: 4 (million)
% 2.53/1.58 % (20493)------------------------------
% 2.53/1.58 % (20493)------------------------------
% 2.53/1.60 % (20495)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_20195 for (2996ds/20Mi)
% 2.53/1.60 % (20491)Instruction limit reached!
% 2.53/1.60 % (20491)------------------------------
% 2.53/1.60 % (20491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.60 % (20491)Termination reason: Unknown
% 2.53/1.60 % (20491)Termination phase: Property scanning
% 2.53/1.60
% 2.53/1.60 % (20491)Memory used [KB]: 2814
% 2.53/1.60 % (20491)Time elapsed: 0.033 s
% 2.53/1.60 % (20491)Instructions burned: 101 (million)
% 2.53/1.60 % (20491)------------------------------
% 2.53/1.60 % (20491)------------------------------
% 2.53/1.61 % (20495)Instruction limit reached!
% 2.53/1.61 % (20495)------------------------------
% 2.53/1.61 % (20495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.61 % (20495)Termination reason: Unknown
% 2.53/1.61 % (20495)Termination phase: shuffling
% 2.53/1.61
% 2.53/1.61 % (20495)Memory used [KB]: 1918
% 2.53/1.61 % (20495)Time elapsed: 0.012 s
% 2.53/1.61 % (20495)Instructions burned: 21 (million)
% 2.53/1.61 % (20495)------------------------------
% 2.53/1.61 % (20495)------------------------------
% 2.53/1.61 % (20497)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_20195 for (2996ds/86Mi)
% 2.53/1.62 % (20498)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_20195 for (2996ds/107Mi)
% 2.53/1.63 % (20497)Instruction limit reached!
% 2.53/1.63 % (20497)------------------------------
% 2.53/1.63 % (20497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.63 % (20497)Termination reason: Unknown
% 2.53/1.63 % (20497)Termination phase: Property scanning
% 2.53/1.63
% 2.53/1.63 % (20497)Memory used [KB]: 2558
% 2.53/1.63 % (20497)Time elapsed: 0.024 s
% 2.53/1.63 % (20497)Instructions burned: 89 (million)
% 2.53/1.63 % (20497)------------------------------
% 2.53/1.63 % (20497)------------------------------
% 2.53/1.64 % (20499)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_20195 for (2996ds/39Mi)
% 2.53/1.66 % (20499)Instruction limit reached!
% 2.53/1.66 % (20499)------------------------------
% 2.53/1.66 % (20499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.66 % (20499)Termination reason: Unknown
% 2.53/1.66 % (20499)Termination phase: shuffling
% 2.53/1.66
% 2.53/1.66 % (20499)Memory used [KB]: 2302
% 2.53/1.66 % (20499)Time elapsed: 0.015 s
% 2.53/1.66 % (20499)Instructions burned: 41 (million)
% 2.53/1.66 % (20499)------------------------------
% 2.53/1.66 % (20499)------------------------------
% 2.53/1.67 % (20498)Instruction limit reached!
% 2.53/1.67 % (20498)------------------------------
% 2.53/1.67 % (20498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.67 % (20498)Termination reason: Unknown
% 2.53/1.67 % (20498)Termination phase: SInE selection
% 2.53/1.67
% 2.53/1.67 % (20498)Memory used [KB]: 2686
% 2.53/1.67 % (20498)Time elapsed: 0.048 s
% 2.53/1.67 % (20498)Instructions burned: 108 (million)
% 2.53/1.67 % (20498)------------------------------
% 2.53/1.67 % (20498)------------------------------
% 2.53/1.67 % (20461)Instruction limit reached!
% 2.53/1.67 % (20461)------------------------------
% 2.53/1.67 % (20461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.67 % (20461)Termination reason: Unknown
% 2.53/1.67 % (20461)Termination phase: Saturation
% 2.53/1.67
% 2.53/1.67 % (20461)Memory used [KB]: 12153
% 2.53/1.67 % (20461)Time elapsed: 0.309 s
% 2.53/1.67 % (20461)Instructions burned: 711 (million)
% 2.53/1.67 % (20461)------------------------------
% 2.53/1.67 % (20461)------------------------------
% 2.53/1.67 % (20502)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_20195 for (2996ds/448Mi)
% 2.53/1.69 % (20505)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_20195 for (2995ds/98Mi)
% 2.53/1.69 % (20471)Instruction limit reached!
% 2.53/1.69 % (20471)------------------------------
% 2.53/1.69 % (20471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.69 % (20471)Termination reason: Unknown
% 2.53/1.69 % (20471)Termination phase: Saturation
% 2.53/1.69
% 2.53/1.69 % (20471)Memory used [KB]: 7803
% 2.53/1.69 % (20471)Time elapsed: 0.287 s
% 2.53/1.69 % (20471)Instructions burned: 782 (million)
% 2.53/1.69 % (20471)------------------------------
% 2.53/1.69 % (20471)------------------------------
% 2.53/1.69 % (20504)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_20195 for (2995ds/46Mi)
% 2.53/1.70 % (20504)Instruction limit reached!
% 2.53/1.70 % (20504)------------------------------
% 2.53/1.70 % (20504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.70 % (20504)Termination reason: Unknown
% 2.53/1.70 % (20504)Termination phase: shuffling
% 2.53/1.70
% 2.53/1.70 % (20504)Memory used [KB]: 2430
% 2.53/1.70 % (20504)Time elapsed: 0.014 s
% 2.53/1.70 % (20504)Instructions burned: 48 (million)
% 2.53/1.70 % (20504)------------------------------
% 2.53/1.70 % (20504)------------------------------
% 2.53/1.71 % (20507)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_20195 for (2995ds/507Mi)
% 2.53/1.71 % (20508)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_20195 for (2995ds/149Mi)
% 2.53/1.73 % (20448)Instruction limit reached!
% 2.53/1.73 % (20448)------------------------------
% 2.53/1.73 % (20448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.73 % (20448)Termination reason: Unknown
% 2.53/1.73 % (20448)Termination phase: Saturation
% 2.53/1.73
% 2.53/1.73 % (20448)Memory used [KB]: 16502
% 2.53/1.73 % (20448)Time elapsed: 0.394 s
% 2.53/1.73 % (20448)Instructions burned: 1041 (million)
% 2.53/1.73 % (20448)------------------------------
% 2.53/1.73 % (20448)------------------------------
% 2.53/1.73 % (20505)Instruction limit reached!
% 2.53/1.73 % (20505)------------------------------
% 2.53/1.73 % (20505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.73 % (20505)Termination reason: Unknown
% 2.53/1.73 % (20505)Termination phase: Property scanning
% 2.53/1.73
% 2.53/1.73 % (20505)Memory used [KB]: 2686
% 2.53/1.73 % (20505)Time elapsed: 0.044 s
% 2.53/1.73 % (20505)Instructions burned: 98 (million)
% 2.53/1.73 % (20505)------------------------------
% 2.53/1.73 % (20505)------------------------------
% 2.53/1.74 % (20510)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_20195 for (2995ds/39Mi)
% 2.53/1.75 % (20511)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_20195 for (2995ds/6Mi)
% 2.53/1.75 % (20511)Instruction limit reached!
% 2.53/1.75 % (20511)------------------------------
% 2.53/1.75 % (20511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.75 % (20511)Termination reason: Unknown
% 2.53/1.75 % (20511)Termination phase: shuffling
% 2.53/1.75
% 2.53/1.75 % (20511)Memory used [KB]: 1535
% 2.53/1.75 % (20511)Time elapsed: 0.003 s
% 2.53/1.75 % (20511)Instructions burned: 6 (million)
% 2.53/1.75 % (20511)------------------------------
% 2.53/1.75 % (20511)------------------------------
% 2.53/1.76 % (20463)Instruction limit reached!
% 2.53/1.76 % (20463)------------------------------
% 2.53/1.76 % (20463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.76 % (20463)Termination reason: Unknown
% 2.53/1.76 % (20463)Termination phase: Saturation
% 2.53/1.76
% 2.53/1.76 % (20463)Memory used [KB]: 11897
% 2.53/1.76 % (20463)Time elapsed: 0.384 s
% 2.53/1.76 % (20463)Instructions burned: 903 (million)
% 2.53/1.76 % (20463)------------------------------
% 2.53/1.76 % (20463)------------------------------
% 2.53/1.76 % (20510)Instruction limit reached!
% 2.53/1.76 % (20510)------------------------------
% 2.53/1.76 % (20510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.76 % (20510)Termination reason: Unknown
% 2.53/1.76 % (20510)Termination phase: shuffling
% 2.53/1.76
% 2.53/1.76 % (20510)Memory used [KB]: 2302
% 2.53/1.76 % (20510)Time elapsed: 0.014 s
% 2.53/1.76 % (20510)Instructions burned: 42 (million)
% 2.53/1.76 % (20510)------------------------------
% 2.53/1.76 % (20510)------------------------------
% 2.53/1.77 % (20508)Instruction limit reached!
% 2.53/1.77 % (20508)------------------------------
% 2.53/1.77 % (20508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.77 % (20508)Termination reason: Unknown
% 2.53/1.77 % (20508)Termination phase: Twee Goal Transformation
% 2.53/1.77
% 2.53/1.77 % (20508)Memory used [KB]: 2942
% 2.53/1.77 % (20508)Time elapsed: 0.055 s
% 2.53/1.77 % (20508)Instructions burned: 150 (million)
% 2.53/1.77 % (20508)------------------------------
% 2.53/1.77 % (20508)------------------------------
% 2.53/1.77 % (20515)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_20195 for (2995ds/47Mi)
% 2.53/1.77 % (20514)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_20195 for (2995ds/1087Mi)
% 2.53/1.78 % (20516)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_20195 for (2995ds/44Mi)
% 2.53/1.79 % (20516)Instruction limit reached!
% 2.53/1.79 % (20516)------------------------------
% 2.53/1.79 % (20516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.79 % (20515)Instruction limit reached!
% 2.53/1.79 % (20515)------------------------------
% 2.53/1.79 % (20515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.79 % (20516)Termination reason: Unknown
% 2.53/1.79 % (20516)Termination phase: shuffling
% 2.53/1.79
% 2.53/1.79 % (20516)Memory used [KB]: 2430
% 2.53/1.79 % (20516)Time elapsed: 0.016 s
% 2.53/1.79 % (20516)Instructions burned: 45 (million)
% 2.53/1.79 % (20516)------------------------------
% 2.53/1.79 % (20516)------------------------------
% 2.53/1.79 % (20515)Termination reason: Unknown
% 2.53/1.79 % (20515)Termination phase: shuffling
% 2.53/1.79
% 2.53/1.79 % (20515)Memory used [KB]: 2430
% 2.53/1.79 % (20515)Time elapsed: 0.023 s
% 2.53/1.79 % (20515)Instructions burned: 47 (million)
% 2.53/1.79 % (20515)------------------------------
% 2.53/1.79 % (20515)------------------------------
% 2.53/1.80 % (20517)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_20195 for (2995ds/432Mi)
% 2.53/1.80 % (20519)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_20195 for (2994ds/62Mi)
% 2.53/1.81 % (20520)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_20195 for (2994ds/31Mi)
% 2.53/1.81 % (20475)Instruction limit reached!
% 2.53/1.81 % (20475)------------------------------
% 2.53/1.81 % (20475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.81 % (20475)Termination reason: Unknown
% 2.53/1.81 % (20475)Termination phase: Saturation
% 2.53/1.81
% 2.53/1.81 % (20475)Memory used [KB]: 10362
% 2.53/1.81 % (20475)Time elapsed: 0.374 s
% 2.53/1.81 % (20475)Instructions burned: 880 (million)
% 2.53/1.81 % (20475)------------------------------
% 2.53/1.81 % (20475)------------------------------
% 2.53/1.82 % (20519)Instruction limit reached!
% 2.53/1.82 % (20519)------------------------------
% 2.53/1.82 % (20519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.82 % (20519)Termination reason: Unknown
% 2.53/1.82 % (20519)Termination phase: Property scanning
% 2.53/1.82
% 2.53/1.82 % (20519)Memory used [KB]: 2558
% 2.53/1.82 % (20519)Time elapsed: 0.018 s
% 2.53/1.82 % (20519)Instructions burned: 66 (million)
% 2.53/1.82 % (20519)------------------------------
% 2.53/1.82 % (20519)------------------------------
% 2.53/1.82 % (20520)Instruction limit reached!
% 2.53/1.82 % (20520)------------------------------
% 2.53/1.82 % (20520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.82 % (20520)Termination reason: Unknown
% 2.53/1.82 % (20520)Termination phase: shuffling
% 2.53/1.82
% 2.53/1.82 % (20520)Memory used [KB]: 2174
% 2.53/1.82 % (20520)Time elapsed: 0.016 s
% 2.53/1.82 % (20520)Instructions burned: 32 (million)
% 2.53/1.82 % (20520)------------------------------
% 2.53/1.82 % (20520)------------------------------
% 2.53/1.83 % (20522)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_20195 for (2994ds/96Mi)
% 2.53/1.84 % (20502)Instruction limit reached!
% 2.53/1.84 % (20502)------------------------------
% 2.53/1.84 % (20502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.84 % (20502)Termination reason: Unknown
% 2.53/1.84 % (20502)Termination phase: Saturation
% 2.53/1.84
% 2.53/1.84 % (20502)Memory used [KB]: 7675
% 2.53/1.84 % (20502)Time elapsed: 0.168 s
% 2.53/1.84 % (20502)Instructions burned: 448 (million)
% 2.53/1.84 % (20502)------------------------------
% 2.53/1.84 % (20502)------------------------------
% 2.53/1.84 % (20527)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_20195 for (2994ds/71Mi)
% 2.53/1.85 % (20526)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_20195 for (2994ds/453Mi)
% 2.53/1.86 % (20529)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_20195 for (2994ds/83Mi)
% 2.53/1.87 % (20522)Instruction limit reached!
% 2.53/1.87 % (20522)------------------------------
% 2.53/1.87 % (20522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.87 % (20522)Termination reason: Unknown
% 2.53/1.87 % (20522)Termination phase: Property scanning
% 2.53/1.87
% 2.53/1.87 % (20522)Memory used [KB]: 2814
% 2.53/1.87 % (20522)Time elapsed: 0.043 s
% 2.53/1.87 % (20522)Instructions burned: 96 (million)
% 2.53/1.87 % (20522)------------------------------
% 2.53/1.87 % (20522)------------------------------
% 2.53/1.87 % (20527)Instruction limit reached!
% 2.53/1.87 % (20527)------------------------------
% 2.53/1.87 % (20527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.87 % (20527)Termination reason: Unknown
% 2.53/1.87 % (20527)Termination phase: Property scanning
% 2.53/1.87
% 2.53/1.87 % (20527)Memory used [KB]: 2558
% 2.53/1.87 % (20527)Time elapsed: 0.034 s
% 2.53/1.87 % (20527)Instructions burned: 72 (million)
% 2.53/1.87 % (20527)------------------------------
% 2.53/1.87 % (20527)------------------------------
% 2.53/1.89 % (20529)Instruction limit reached!
% 2.53/1.89 % (20529)------------------------------
% 2.53/1.89 % (20529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.89 % (20529)Termination reason: Unknown
% 2.53/1.89 % (20529)Termination phase: Property scanning
% 2.53/1.89
% 2.53/1.89 % (20529)Memory used [KB]: 2558
% 2.53/1.89 % (20529)Time elapsed: 0.032 s
% 2.53/1.89 % (20529)Instructions burned: 85 (million)
% 2.53/1.89 % (20529)------------------------------
% 2.53/1.89 % (20529)------------------------------
% 2.53/1.89 % (20532)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_20195 for (2994ds/11Mi)
% 2.53/1.89 % (20533)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_20195 for (2994ds/41Mi)
% 2.53/1.89 % (20532)Instruction limit reached!
% 2.53/1.89 % (20532)------------------------------
% 2.53/1.89 % (20532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.89 % (20532)Termination reason: Unknown
% 2.53/1.89 % (20532)Termination phase: shuffling
% 2.53/1.89
% 2.53/1.89 % (20532)Memory used [KB]: 1791
% 2.53/1.89 % (20532)Time elapsed: 0.007 s
% 2.53/1.89 % (20532)Instructions burned: 12 (million)
% 2.53/1.89 % (20532)------------------------------
% 2.53/1.89 % (20532)------------------------------
% 2.53/1.89 % (20507)Instruction limit reached!
% 2.53/1.89 % (20507)------------------------------
% 2.53/1.89 % (20507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.89 % (20507)Termination reason: Unknown
% 2.53/1.89 % (20507)Termination phase: Saturation
% 2.53/1.89
% 2.53/1.89 % (20507)Memory used [KB]: 8187
% 2.53/1.89 % (20507)Time elapsed: 0.188 s
% 2.53/1.89 % (20507)Instructions burned: 508 (million)
% 2.53/1.89 % (20507)------------------------------
% 2.53/1.89 % (20507)------------------------------
% 2.53/1.90 % (20536)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_20195 for (2993ds/343Mi)
% 2.53/1.91 % (20533)Instruction limit reached!
% 2.53/1.91 % (20533)------------------------------
% 2.53/1.91 % (20533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.91 % (20533)Termination reason: Unknown
% 2.53/1.91 % (20533)Termination phase: shuffling
% 2.53/1.91
% 2.53/1.91 % (20533)Memory used [KB]: 2302
% 2.53/1.91 % (20533)Time elapsed: 0.020 s
% 2.53/1.91 % (20533)Instructions burned: 41 (million)
% 2.53/1.91 % (20533)------------------------------
% 2.53/1.91 % (20533)------------------------------
% 2.53/1.91 % (20535)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_20195 for (2993ds/150Mi)
% 2.53/1.92 % (20534)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_20195 for (2993ds/6Mi)
% 2.53/1.92 % (20534)Instruction limit reached!
% 2.53/1.92 % (20534)------------------------------
% 2.53/1.92 % (20534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.92 % (20534)Termination reason: Unknown
% 2.53/1.92 % (20534)Termination phase: shuffling
% 2.53/1.92
% 2.53/1.92 % (20534)Memory used [KB]: 1663
% 2.53/1.92 % (20534)Time elapsed: 0.003 s
% 2.53/1.92 % (20534)Instructions burned: 6 (million)
% 2.53/1.92 % (20534)------------------------------
% 2.53/1.92 % (20534)------------------------------
% 2.53/1.92 % (20537)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_20195 for (2993ds/109Mi)
% 2.53/1.94 % (20538)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_20195 for (2993ds/253Mi)
% 2.53/1.95 % (20517)Instruction limit reached!
% 2.53/1.95 % (20517)------------------------------
% 2.53/1.95 % (20517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.95 % (20517)Termination reason: Unknown
% 2.53/1.95 % (20517)Termination phase: Saturation
% 2.53/1.95
% 2.53/1.95 % (20517)Memory used [KB]: 3198
% 2.53/1.95 % (20517)Time elapsed: 0.135 s
% 2.53/1.95 % (20517)Instructions burned: 434 (million)
% 2.53/1.95 % (20517)------------------------------
% 2.53/1.95 % (20517)------------------------------
% 2.53/1.96 % (20543)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_20195 for (2993ds/140Mi)
% 2.53/1.97 % (20537)Instruction limit reached!
% 2.53/1.97 % (20537)------------------------------
% 2.53/1.97 % (20537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.97 % (20537)Termination reason: Unknown
% 2.53/1.97 % (20537)Termination phase: SInE selection
% 2.53/1.97
% 2.53/1.97 % (20537)Memory used [KB]: 2558
% 2.53/1.97 % (20537)Time elapsed: 0.049 s
% 2.53/1.97 % (20537)Instructions burned: 109 (million)
% 2.53/1.97 % (20537)------------------------------
% 2.53/1.97 % (20537)------------------------------
% 2.53/1.98 % (20535)Instruction limit reached!
% 2.53/1.98 % (20535)------------------------------
% 2.53/1.98 % (20535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.98 % (20535)Termination reason: Unknown
% 2.53/1.98 % (20535)Termination phase: Property scanning
% 2.53/1.98
% 2.53/1.98 % (20535)Memory used [KB]: 5245
% 2.53/1.98 % (20535)Time elapsed: 0.072 s
% 2.53/1.98 % (20535)Instructions burned: 150 (million)
% 2.53/1.98 % (20535)------------------------------
% 2.53/1.98 % (20535)------------------------------
% 2.53/1.99 % (20545)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_20195 for (2993ds/614Mi)
% 2.53/2.00 % (20546)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_20195 for (2993ds/202Mi)
% 7.42/2.03 % (20543)Instruction limit reached!
% 7.42/2.03 % (20543)------------------------------
% 7.42/2.03 % (20543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.42/2.03 % (20543)Termination reason: Unknown
% 7.42/2.03 % (20543)Termination phase: Property scanning
% 7.42/2.03
% 7.42/2.03 % (20543)Memory used [KB]: 2814
% 7.42/2.03 % (20543)Time elapsed: 0.063 s
% 7.42/2.03 % (20543)Instructions burned: 141 (million)
% 7.42/2.03 % (20543)------------------------------
% 7.42/2.03 % (20543)------------------------------
% 7.42/2.03 % (20538)Instruction limit reached!
% 7.42/2.03 % (20538)------------------------------
% 7.42/2.03 % (20538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.42/2.03 % (20538)Termination reason: Unknown
% 7.42/2.03 % (20538)Termination phase: Saturation
% 7.42/2.03
% 7.42/2.03 % (20538)Memory used [KB]: 5628
% 7.42/2.03 % (20538)Time elapsed: 0.072 s
% 7.42/2.03 % (20538)Instructions burned: 253 (million)
% 7.42/2.03 % (20538)------------------------------
% 7.42/2.03 % (20538)------------------------------
% 7.42/2.03 % (20536)Instruction limit reached!
% 7.42/2.03 % (20536)------------------------------
% 7.42/2.03 % (20536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.42/2.03 % (20536)Termination reason: Unknown
% 7.42/2.03 % (20536)Termination phase: Saturation
% 7.42/2.03
% 7.42/2.03 % (20536)Memory used [KB]: 8315
% 7.42/2.03 % (20536)Time elapsed: 0.117 s
% 7.42/2.03 % (20536)Instructions burned: 343 (million)
% 7.42/2.03 % (20536)------------------------------
% 7.42/2.03 % (20536)------------------------------
% 7.42/2.03 % (20526)Instruction limit reached!
% 7.42/2.03 % (20526)------------------------------
% 7.42/2.03 % (20526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.42/2.03 % (20526)Termination reason: Unknown
% 7.42/2.03 % (20526)Termination phase: Saturation
% 7.42/2.03
% 7.42/2.03 % (20526)Memory used [KB]: 7675
% 7.42/2.03 % (20526)Time elapsed: 0.186 s
% 7.42/2.03 % (20526)Instructions burned: 454 (million)
% 7.42/2.03 % (20526)------------------------------
% 7.42/2.03 % (20526)------------------------------
% 7.42/2.04 % (20551)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_20195 for (2992ds/283Mi)
% 7.42/2.04 % (20549)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_20195 for (2992ds/339Mi)
% 7.42/2.05 % (20552)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_20195 for (2992ds/134Mi)
% 7.42/2.05 % (20553)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_20195 for (2992ds/298Mi)
% 7.42/2.09 % (20546)Instruction limit reached!
% 7.42/2.09 % (20546)------------------------------
% 7.42/2.09 % (20546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.42/2.09 % (20546)Termination reason: Unknown
% 7.42/2.09 % (20546)Termination phase: Property scanning
% 7.42/2.09
% 7.42/2.09 % (20546)Memory used [KB]: 5373
% 7.42/2.09 % (20546)Time elapsed: 0.095 s
% 7.42/2.09 % (20546)Instructions burned: 203 (million)
% 7.42/2.09 % (20546)------------------------------
% 7.42/2.09 % (20546)------------------------------
% 7.42/2.09 % (20552)Instruction limit reached!
% 7.42/2.09 % (20552)------------------------------
% 7.42/2.09 % (20552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.42/2.09 % (20552)Termination reason: Unknown
% 7.42/2.09 % (20552)Termination phase: Function definition elimination
% 7.42/2.09
% 7.42/2.09 % (20552)Memory used [KB]: 2814
% 7.42/2.09 % (20552)Time elapsed: 0.046 s
% 7.42/2.09 % (20552)Instructions burned: 134 (million)
% 7.42/2.09 % (20552)------------------------------
% 7.42/2.09 % (20552)------------------------------
% 7.42/2.11 % (20558)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_20195 for (2991ds/192Mi)
% 7.42/2.11 % (20559)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_20195 for (2991ds/258Mi)
% 7.85/2.12 % (20551)Instruction limit reached!
% 7.85/2.12 % (20551)------------------------------
% 7.85/2.12 % (20551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.85/2.12 % (20551)Termination reason: Unknown
% 7.85/2.12 % (20551)Termination phase: Saturation
% 7.85/2.12
% 7.85/2.12 % (20551)Memory used [KB]: 7547
% 7.85/2.12 % (20551)Time elapsed: 0.083 s
% 7.85/2.12 % (20551)Instructions burned: 284 (million)
% 7.85/2.12 % (20551)------------------------------
% 7.85/2.12 % (20551)------------------------------
% 7.85/2.13 % (20561)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_20195 for (2991ds/90Mi)
% 7.85/2.16 % (20561)Instruction limit reached!
% 7.85/2.16 % (20561)------------------------------
% 7.85/2.16 % (20561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.85/2.16 % (20561)Termination reason: Unknown
% 7.85/2.16 % (20561)Termination phase: Property scanning
% 7.85/2.16
% 7.85/2.16 % (20561)Memory used [KB]: 2558
% 7.85/2.16 % (20561)Time elapsed: 0.025 s
% 7.85/2.16 % (20561)Instructions burned: 93 (million)
% 7.85/2.16 % (20561)------------------------------
% 7.85/2.16 % (20561)------------------------------
% 7.85/2.16 % (20563)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_20195 for (2991ds/231Mi)
% 7.85/2.17 % (20553)Instruction limit reached!
% 7.85/2.17 % (20553)------------------------------
% 7.85/2.17 % (20553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.85/2.17 % (20553)Termination reason: Unknown
% 7.85/2.17 % (20553)Termination phase: Saturation
% 7.85/2.17
% 7.85/2.17 % (20553)Memory used [KB]: 7547
% 7.85/2.17 % (20553)Time elapsed: 0.126 s
% 7.85/2.17 % (20553)Instructions burned: 300 (million)
% 7.85/2.17 % (20553)------------------------------
% 7.85/2.17 % (20553)------------------------------
% 7.85/2.19 % (20564)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_20195 for (2991ds/458Mi)
% 7.85/2.19 % (20558)Instruction limit reached!
% 7.85/2.19 % (20558)------------------------------
% 7.85/2.19 % (20558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.85/2.19 % (20558)Termination reason: Unknown
% 7.85/2.19 % (20558)Termination phase: Saturation
% 7.85/2.19
% 7.85/2.19 % (20558)Memory used [KB]: 7547
% 7.85/2.19 % (20558)Time elapsed: 0.086 s
% 7.85/2.19 % (20558)Instructions burned: 194 (million)
% 7.85/2.19 % (20558)------------------------------
% 7.85/2.19 % (20558)------------------------------
% 7.85/2.19 % (20549)Instruction limit reached!
% 7.85/2.19 % (20549)------------------------------
% 7.85/2.19 % (20549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.85/2.19 % (20549)Termination reason: Unknown
% 7.85/2.19 % (20549)Termination phase: Saturation
% 7.85/2.19
% 7.85/2.19 % (20549)Memory used [KB]: 8059
% 7.85/2.19 % (20549)Time elapsed: 0.152 s
% 7.85/2.19 % (20549)Instructions burned: 341 (million)
% 7.85/2.19 % (20549)------------------------------
% 7.85/2.19 % (20549)------------------------------
% 8.52/2.21 % (20566)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_20195 for (2990ds/31Mi)
% 8.52/2.21 % (20567)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_20195 for (2990ds/297Mi)
% 8.52/2.22 % (20559)Instruction limit reached!
% 8.52/2.22 % (20559)------------------------------
% 8.52/2.22 % (20559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.52/2.22 % (20559)Termination reason: Unknown
% 8.52/2.22 % (20559)Termination phase: Saturation
% 8.52/2.22
% 8.52/2.22 % (20559)Memory used [KB]: 7803
% 8.52/2.22 % (20559)Time elapsed: 0.113 s
% 8.52/2.22 % (20559)Instructions burned: 259 (million)
% 8.52/2.22 % (20559)------------------------------
% 8.52/2.22 % (20559)------------------------------
% 8.52/2.22 % (20566)Instruction limit reached!
% 8.52/2.22 % (20566)------------------------------
% 8.52/2.22 % (20566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.52/2.22 % (20566)Termination reason: Unknown
% 8.52/2.22 % (20566)Termination phase: shuffling
% 8.52/2.22
% 8.52/2.22 % (20566)Memory used [KB]: 2174
% 8.52/2.22 % (20566)Time elapsed: 0.016 s
% 8.52/2.22 % (20566)Instructions burned: 32 (million)
% 8.52/2.22 % (20566)------------------------------
% 8.52/2.22 % (20566)------------------------------
% 8.52/2.24 % (20563)Instruction limit reached!
% 8.52/2.24 % (20563)------------------------------
% 8.52/2.24 % (20563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.52/2.24 % (20563)Termination reason: Unknown
% 8.52/2.24 % (20563)Termination phase: Saturation
% 8.52/2.24
% 8.52/2.24 % (20563)Memory used [KB]: 3965
% 8.52/2.24 % (20563)Time elapsed: 0.073 s
% 8.52/2.24 % (20563)Instructions burned: 232 (million)
% 8.52/2.24 % (20563)------------------------------
% 8.52/2.24 % (20563)------------------------------
% 8.52/2.24 % (20570)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_20195 for (2990ds/182Mi)
% 8.52/2.24 % (20569)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_20195 for (2990ds/987Mi)
% 8.52/2.26 % (20571)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_20195 for (2990ds/182Mi)
% 8.52/2.27 % (20545)Instruction limit reached!
% 8.52/2.27 % (20545)------------------------------
% 8.52/2.27 % (20545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.52/2.27 % (20545)Termination reason: Unknown
% 8.52/2.27 % (20545)Termination phase: Saturation
% 8.52/2.27
% 8.52/2.27 % (20545)Memory used [KB]: 10362
% 8.52/2.27 % (20545)Time elapsed: 0.286 s
% 8.52/2.27 % (20545)Instructions burned: 615 (million)
% 8.52/2.27 % (20545)------------------------------
% 8.52/2.27 % (20545)------------------------------
% 8.52/2.28 % (20514)Instruction limit reached!
% 8.52/2.28 % (20514)------------------------------
% 8.52/2.28 % (20514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.52/2.28 % (20514)Termination reason: Unknown
% 8.52/2.28 % (20514)Termination phase: Saturation
% 8.52/2.28
% 8.52/2.28 % (20514)Memory used [KB]: 12665
% 8.52/2.28 % (20514)Time elapsed: 0.523 s
% 8.52/2.28 % (20514)Instructions burned: 1088 (million)
% 8.52/2.28 % (20514)------------------------------
% 8.52/2.28 % (20514)------------------------------
% 8.52/2.29 % (20572)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_20195 for (2989ds/154Mi)
% 8.52/2.29 % (20573)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_20195 for (2989ds/79Mi)
% 8.95/2.31 % (20573)Instruction limit reached!
% 8.95/2.31 % (20573)------------------------------
% 8.95/2.31 % (20573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.95/2.31 % (20573)Termination reason: Unknown
% 8.95/2.31 % (20573)Termination phase: Property scanning
% 8.95/2.31
% 8.95/2.31 % (20573)Memory used [KB]: 2558
% 8.95/2.31 % (20573)Time elapsed: 0.022 s
% 8.95/2.31 % (20573)Instructions burned: 81 (million)
% 8.95/2.31 % (20573)------------------------------
% 8.95/2.31 % (20573)------------------------------
% 8.95/2.32 % (20570)Instruction limit reached!
% 8.95/2.32 % (20570)------------------------------
% 8.95/2.32 % (20570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.95/2.32 % (20570)Termination reason: Unknown
% 8.95/2.32 % (20570)Termination phase: Saturation
% 8.95/2.32
% 8.95/2.32 % (20570)Memory used [KB]: 7419
% 8.95/2.32 % (20570)Time elapsed: 0.081 s
% 8.95/2.32 % (20570)Instructions burned: 183 (million)
% 8.95/2.32 % (20570)------------------------------
% 8.95/2.32 % (20570)------------------------------
% 8.95/2.32 % (20576)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_20195 for (2989ds/216Mi)
% 8.95/2.33 % (20567)Instruction limit reached!
% 8.95/2.33 % (20567)------------------------------
% 8.95/2.33 % (20567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.95/2.33 % (20567)Termination reason: Unknown
% 8.95/2.33 % (20567)Termination phase: Saturation
% 8.95/2.33
% 8.95/2.33 % (20567)Memory used [KB]: 7547
% 8.95/2.33 % (20567)Time elapsed: 0.124 s
% 8.95/2.33 % (20567)Instructions burned: 297 (million)
% 8.95/2.33 % (20567)------------------------------
% 8.95/2.33 % (20567)------------------------------
% 8.95/2.33 % (20577)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_20195 for (2989ds/114Mi)
% 8.95/2.35 % (20578)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_20195 for (2989ds/922Mi)
% 8.95/2.35 % (20571)Instruction limit reached!
% 8.95/2.35 % (20571)------------------------------
% 8.95/2.35 % (20571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.95/2.35 % (20571)Termination reason: Unknown
% 8.95/2.35 % (20571)Termination phase: Property scanning
% 8.95/2.35
% 8.95/2.35 % (20571)Memory used [KB]: 5245
% 8.95/2.35 % (20571)Time elapsed: 0.085 s
% 8.95/2.35 % (20571)Instructions burned: 183 (million)
% 8.95/2.35 % (20571)------------------------------
% 8.95/2.35 % (20571)------------------------------
% 8.95/2.35 % (20572)Instruction limit reached!
% 8.95/2.35 % (20572)------------------------------
% 8.95/2.35 % (20572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.95/2.35 % (20572)Termination reason: Unknown
% 8.95/2.35 % (20572)Termination phase: Property scanning
% 8.95/2.35
% 8.95/2.35 % (20572)Memory used [KB]: 3070
% 8.95/2.35 % (20572)Time elapsed: 0.067 s
% 8.95/2.35 % (20572)Instructions burned: 155 (million)
% 8.95/2.35 % (20572)------------------------------
% 8.95/2.35 % (20572)------------------------------
% 8.95/2.36 % (20579)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_20195 for (2989ds/182Mi)
% 8.95/2.38 % (20580)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_20195 for (2989ds/164Mi)
% 8.95/2.38 % (20577)Instruction limit reached!
% 8.95/2.38 % (20577)------------------------------
% 8.95/2.38 % (20577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.95/2.38 % (20577)Termination reason: Unknown
% 8.95/2.38 % (20577)Termination phase: Property scanning
% 8.95/2.38
% 8.95/2.38 % (20577)Memory used [KB]: 2814
% 8.95/2.38 % (20577)Time elapsed: 0.052 s
% 8.95/2.38 % (20577)Instructions burned: 116 (million)
% 8.95/2.38 % (20577)------------------------------
% 8.95/2.38 % (20577)------------------------------
% 8.95/2.39 % (20564)Instruction limit reached!
% 8.95/2.39 % (20564)------------------------------
% 8.95/2.39 % (20564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.95/2.39 % (20564)Termination reason: Unknown
% 8.95/2.39 % (20564)Termination phase: Saturation
% 8.95/2.39
% 8.95/2.39 % (20564)Memory used [KB]: 9722
% 8.95/2.39 % (20564)Time elapsed: 0.200 s
% 8.95/2.39 % (20564)Instructions burned: 458 (million)
% 8.95/2.39 % (20564)------------------------------
% 8.95/2.39 % (20564)------------------------------
% 8.95/2.39 % (20576)Instruction limit reached!
% 8.95/2.39 % (20576)------------------------------
% 8.95/2.39 % (20576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.95/2.39 % (20576)Termination reason: Unknown
% 8.95/2.39 % (20576)Termination phase: Property scanning
% 8.95/2.39
% 8.95/2.39 % (20576)Memory used [KB]: 3070
% 8.95/2.39 % (20576)Time elapsed: 0.069 s
% 8.95/2.39 % (20576)Instructions burned: 217 (million)
% 8.95/2.39 % (20576)------------------------------
% 8.95/2.39 % (20576)------------------------------
% 9.75/2.40 % (20584)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_20195 for (2988ds/50Mi)
% 9.75/2.40 % (20585)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_20195 for (2988ds/368Mi)
% 9.75/2.40 % (20586)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_20195 for (2988ds/1021Mi)
% 9.75/2.41 % (20579)Instruction limit reached!
% 9.75/2.41 % (20579)------------------------------
% 9.75/2.41 % (20579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.75/2.41 % (20579)Termination reason: Unknown
% 9.75/2.41 % (20579)Termination phase: Property scanning
% 9.75/2.41
% 9.75/2.41 % (20579)Memory used [KB]: 3070
% 9.75/2.41 % (20579)Time elapsed: 0.047 s
% 9.75/2.41 % (20579)Instructions burned: 186 (million)
% 9.75/2.41 % (20579)------------------------------
% 9.75/2.41 % (20579)------------------------------
% 9.75/2.42 % (20587)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_20195 for (2988ds/267Mi)
% 9.75/2.42 % (20584)Instruction limit reached!
% 9.75/2.42 % (20584)------------------------------
% 9.75/2.42 % (20584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.75/2.42 % (20584)Termination reason: Unknown
% 9.75/2.42 % (20584)Termination phase: shuffling
% 9.75/2.42
% 9.75/2.42 % (20584)Memory used [KB]: 2430
% 9.75/2.42 % (20584)Time elapsed: 0.020 s
% 9.75/2.42 % (20584)Instructions burned: 51 (million)
% 9.75/2.42 % (20584)------------------------------
% 9.75/2.42 % (20584)------------------------------
% 9.75/2.43 % (20589)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_20195 for (2988ds/204Mi)
% 9.75/2.45 % (20580)Instruction limit reached!
% 9.75/2.45 % (20580)------------------------------
% 9.75/2.45 % (20580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.75/2.45 % (20580)Termination reason: Unknown
% 9.75/2.45 % (20580)Termination phase: Function definition elimination
% 9.75/2.45
% 9.75/2.45 % (20580)Memory used [KB]: 2814
% 9.75/2.45 % (20580)Time elapsed: 0.071 s
% 9.75/2.45 % (20580)Instructions burned: 166 (million)
% 9.75/2.45 % (20580)------------------------------
% 9.75/2.45 % (20580)------------------------------
% 9.75/2.47 % (20590)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_20195 for (2988ds/26Mi)
% 9.75/2.49 % (20590)Instruction limit reached!
% 9.75/2.49 % (20590)------------------------------
% 9.75/2.49 % (20590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.75/2.49 % (20590)Termination reason: Unknown
% 9.75/2.49 % (20590)Termination phase: shuffling
% 9.75/2.49
% 9.75/2.49 % (20590)Memory used [KB]: 2174
% 9.75/2.49 % (20590)Time elapsed: 0.010 s
% 9.75/2.49 % (20590)Instructions burned: 29 (million)
% 9.75/2.49 % (20590)------------------------------
% 9.75/2.49 % (20590)------------------------------
% 9.94/2.50 % (20589)Instruction limit reached!
% 9.94/2.50 % (20589)------------------------------
% 9.94/2.50 % (20589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.94/2.50 % (20589)Termination reason: Unknown
% 9.94/2.50 % (20589)Termination phase: Property scanning
% 9.94/2.50
% 9.94/2.50 % (20589)Memory used [KB]: 2942
% 9.94/2.50 % (20589)Time elapsed: 0.054 s
% 9.94/2.50 % (20589)Instructions burned: 207 (million)
% 9.94/2.50 % (20589)------------------------------
% 9.94/2.50 % (20589)------------------------------
% 9.94/2.51 % (20591)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_20195 for (2987ds/53Mi)
% 9.94/2.51 % (20592)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_20195 for (2987ds/4436Mi)
% 9.94/2.53 % (20587)Instruction limit reached!
% 9.94/2.53 % (20587)------------------------------
% 9.94/2.53 % (20587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.94/2.53 % (20587)Termination reason: Unknown
% 9.94/2.53 % (20587)Termination phase: Saturation
% 9.94/2.53
% 9.94/2.53 % (20587)Memory used [KB]: 7547
% 9.94/2.53 % (20587)Time elapsed: 0.112 s
% 9.94/2.53 % (20587)Instructions burned: 267 (million)
% 9.94/2.53 % (20587)------------------------------
% 9.94/2.53 % (20587)------------------------------
% 9.94/2.53 % (20591)Instruction limit reached!
% 9.94/2.53 % (20591)------------------------------
% 9.94/2.53 % (20591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.94/2.53 % (20591)Termination reason: Unknown
% 9.94/2.53 % (20591)Termination phase: shuffling
% 9.94/2.53
% 9.94/2.53 % (20591)Memory used [KB]: 2558
% 9.94/2.53 % (20591)Time elapsed: 0.025 s
% 9.94/2.53 % (20591)Instructions burned: 53 (million)
% 9.94/2.53 % (20591)------------------------------
% 9.94/2.53 % (20591)------------------------------
% 9.94/2.54 % (20595)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_20195 for (2987ds/1539Mi)
% 9.94/2.55 % (20597)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_20195 for (2987ds/408Mi)
% 9.94/2.56 % (20585)Instruction limit reached!
% 9.94/2.56 % (20585)------------------------------
% 9.94/2.56 % (20585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.94/2.56 % (20585)Termination reason: Unknown
% 9.94/2.56 % (20585)Termination phase: Saturation
% 9.94/2.56
% 9.94/2.56 % (20585)Memory used [KB]: 9338
% 9.94/2.56 % (20585)Time elapsed: 0.158 s
% 9.94/2.56 % (20585)Instructions burned: 369 (million)
% 9.94/2.56 % (20585)------------------------------
% 9.94/2.56 % (20585)------------------------------
% 9.94/2.57 % (20600)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_20195 for (2987ds/5205Mi)
% 10.33/2.62 % (20569)Instruction limit reached!
% 10.33/2.62 % (20569)------------------------------
% 10.33/2.62 % (20569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.33/2.62 % (20569)Termination reason: Unknown
% 10.33/2.62 % (20569)Termination phase: Saturation
% 10.33/2.62
% 10.33/2.62 % (20569)Memory used [KB]: 16886
% 10.33/2.62 % (20569)Time elapsed: 0.381 s
% 10.33/2.62 % (20569)Instructions burned: 988 (million)
% 10.33/2.62 % (20569)------------------------------
% 10.33/2.62 % (20569)------------------------------
% 10.33/2.64 % (20602)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_20195 for (2986ds/1913Mi)
% 10.73/2.74 % (20597)Instruction limit reached!
% 10.73/2.74 % (20597)------------------------------
% 10.73/2.74 % (20597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.73/2.74 % (20597)Termination reason: Unknown
% 10.73/2.74 % (20597)Termination phase: Saturation
% 10.73/2.74
% 10.73/2.74 % (20597)Memory used [KB]: 11513
% 10.73/2.74 % (20597)Time elapsed: 0.196 s
% 10.73/2.74 % (20597)Instructions burned: 408 (million)
% 10.73/2.74 % (20597)------------------------------
% 10.73/2.74 % (20597)------------------------------
% 10.73/2.76 % (20606)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_20195 for (2985ds/4350Mi)
% 10.73/2.77 % (20578)Instruction limit reached!
% 10.73/2.77 % (20578)------------------------------
% 10.73/2.77 % (20578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.73/2.77 % (20578)Termination reason: Unknown
% 10.73/2.77 % (20578)Termination phase: Saturation
% 10.73/2.77
% 10.73/2.77 % (20578)Memory used [KB]: 12537
% 10.73/2.77 % (20578)Time elapsed: 0.423 s
% 10.73/2.77 % (20578)Instructions burned: 923 (million)
% 10.73/2.77 % (20578)------------------------------
% 10.73/2.77 % (20578)------------------------------
% 10.73/2.80 % (20607)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_20195 for (2985ds/68Mi)
% 11.38/2.82 % (20607)Instruction limit reached!
% 11.38/2.82 % (20607)------------------------------
% 11.38/2.82 % (20607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.38/2.82 % (20607)Termination reason: Unknown
% 11.38/2.82 % (20607)Termination phase: Property scanning
% 11.38/2.82
% 11.38/2.82 % (20607)Memory used [KB]: 2558
% 11.38/2.82 % (20607)Time elapsed: 0.023 s
% 11.38/2.82 % (20607)Instructions burned: 71 (million)
% 11.38/2.82 % (20607)------------------------------
% 11.38/2.82 % (20607)------------------------------
% 11.38/2.83 % (20610)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_20195 for (2984ds/358Mi)
% 11.38/2.87 % (20586)Instruction limit reached!
% 11.38/2.87 % (20586)------------------------------
% 11.38/2.87 % (20586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.38/2.87 % (20586)Termination reason: Unknown
% 11.38/2.87 % (20586)Termination phase: Saturation
% 11.38/2.87
% 11.38/2.87 % (20586)Memory used [KB]: 12792
% 11.38/2.87 % (20586)Time elapsed: 0.470 s
% 11.38/2.87 % (20586)Instructions burned: 1022 (million)
% 11.38/2.87 % (20586)------------------------------
% 11.38/2.87 % (20586)------------------------------
% 11.38/2.88 % (20611)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_20195 for (2984ds/31Mi)
% 11.38/2.89 % (20611)Instruction limit reached!
% 11.38/2.89 % (20611)------------------------------
% 11.38/2.89 % (20611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.38/2.89 % (20611)Termination reason: Unknown
% 11.38/2.89 % (20611)Termination phase: shuffling
% 11.38/2.89
% 11.38/2.89 % (20611)Memory used [KB]: 2046
% 11.38/2.89 % (20611)Time elapsed: 0.010 s
% 11.38/2.89 % (20611)Instructions burned: 31 (million)
% 11.38/2.89 % (20611)------------------------------
% 11.38/2.89 % (20611)------------------------------
% 11.92/2.90 % (20617)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_20195 for (2983ds/279Mi)
% 11.92/2.93 % (20610)Instruction limit reached!
% 11.92/2.93 % (20610)------------------------------
% 11.92/2.93 % (20610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.92/2.93 % (20610)Termination reason: Unknown
% 11.92/2.93 % (20610)Termination phase: Saturation
% 11.92/2.93
% 11.92/2.93 % (20610)Memory used [KB]: 8443
% 11.92/2.93 % (20610)Time elapsed: 0.093 s
% 11.92/2.93 % (20610)Instructions burned: 359 (million)
% 11.92/2.93 % (20610)------------------------------
% 11.92/2.93 % (20610)------------------------------
% 11.92/2.94 % (20641)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_20195 for (2983ds/258Mi)
% 11.92/2.97 % (20617)Instruction limit reached!
% 11.92/2.97 % (20617)------------------------------
% 11.92/2.97 % (20617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.92/2.97 % (20617)Termination reason: Unknown
% 11.92/2.97 % (20617)Termination phase: Saturation
% 11.92/2.97
% 11.92/2.97 % (20617)Memory used [KB]: 7547
% 11.92/2.97 % (20617)Time elapsed: 0.070 s
% 11.92/2.97 % (20617)Instructions burned: 282 (million)
% 11.92/2.97 % (20617)------------------------------
% 11.92/2.97 % (20617)------------------------------
% 11.92/2.98 % (20671)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_20195 for (2983ds/26Mi)
% 11.92/2.99 % (20671)Instruction limit reached!
% 11.92/2.99 % (20671)------------------------------
% 11.92/2.99 % (20671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.92/2.99 % (20671)Termination reason: Unknown
% 11.92/2.99 % (20671)Termination phase: shuffling
% 11.92/2.99
% 11.92/2.99 % (20671)Memory used [KB]: 2174
% 11.92/2.99 % (20671)Time elapsed: 0.009 s
% 11.92/2.99 % (20671)Instructions burned: 28 (million)
% 11.92/2.99 % (20671)------------------------------
% 11.92/2.99 % (20671)------------------------------
% 11.92/3.00 % (20681)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_20195 for (2982ds/995Mi)
% 11.92/3.00 % (20641)Instruction limit reached!
% 11.92/3.00 % (20641)------------------------------
% 11.92/3.00 % (20641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.92/3.00 % (20641)Termination reason: Unknown
% 11.92/3.00 % (20641)Termination phase: Saturation
% 11.92/3.00
% 11.92/3.00 % (20641)Memory used [KB]: 8187
% 11.92/3.00 % (20641)Time elapsed: 0.069 s
% 11.92/3.00 % (20641)Instructions burned: 260 (million)
% 11.92/3.00 % (20641)------------------------------
% 11.92/3.00 % (20641)------------------------------
% 14.14/3.01 % (20702)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_20195 for (2982ds/373Mi)
% 14.14/3.11 % (20702)Instruction limit reached!
% 14.14/3.11 % (20702)------------------------------
% 14.14/3.11 % (20702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.14/3.11 % (20702)Termination reason: Unknown
% 14.14/3.11 % (20702)Termination phase: Saturation
% 14.14/3.11
% 14.14/3.11 % (20702)Memory used [KB]: 9466
% 14.14/3.11 % (20702)Time elapsed: 0.099 s
% 14.14/3.11 % (20702)Instructions burned: 374 (million)
% 14.14/3.11 % (20702)------------------------------
% 14.14/3.11 % (20702)------------------------------
% 14.86/3.12 % (20595)Instruction limit reached!
% 14.86/3.12 % (20595)------------------------------
% 14.86/3.12 % (20595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.86/3.12 % (20595)Termination reason: Unknown
% 14.86/3.12 % (20595)Termination phase: Saturation
% 14.86/3.12
% 14.86/3.12 % (20595)Memory used [KB]: 10874
% 14.86/3.12 % (20595)Time elapsed: 0.575 s
% 14.86/3.12 % (20595)Instructions burned: 1541 (million)
% 14.86/3.12 % (20595)------------------------------
% 14.86/3.12 % (20595)------------------------------
% 14.86/3.12 % (20781)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_20195 for (2981ds/253Mi)
% 14.86/3.13 % (20785)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_20195 for (2981ds/832Mi)
% 14.86/3.18 % (20781)Instruction limit reached!
% 14.86/3.18 % (20781)------------------------------
% 14.86/3.18 % (20781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.86/3.18 % (20781)Termination reason: Unknown
% 14.86/3.18 % (20781)Termination phase: Saturation
% 14.86/3.18
% 14.86/3.18 % (20781)Memory used [KB]: 7547
% 14.86/3.18 % (20781)Time elapsed: 0.064 s
% 14.86/3.18 % (20781)Instructions burned: 254 (million)
% 14.86/3.18 % (20781)------------------------------
% 14.86/3.18 % (20781)------------------------------
% 14.86/3.19 % (20819)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_20195 for (2980ds/668Mi)
% 15.37/3.25 % (20681)Instruction limit reached!
% 15.37/3.25 % (20681)------------------------------
% 15.37/3.25 % (20681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.37/3.25 % (20681)Termination reason: Unknown
% 15.37/3.25 % (20681)Termination phase: Saturation
% 15.37/3.25
% 15.37/3.25 % (20681)Memory used [KB]: 16886
% 15.37/3.25 % (20681)Time elapsed: 0.249 s
% 15.37/3.25 % (20681)Instructions burned: 995 (million)
% 15.37/3.25 % (20681)------------------------------
% 15.37/3.25 % (20681)------------------------------
% 15.37/3.26 % (20851)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_20195 for (2980ds/40Mi)
% 15.37/3.27 % (20851)Instruction limit reached!
% 15.37/3.27 % (20851)------------------------------
% 15.37/3.27 % (20851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.37/3.27 % (20851)Termination reason: Unknown
% 15.37/3.27 % (20851)Termination phase: shuffling
% 15.37/3.27
% 15.37/3.27 % (20851)Memory used [KB]: 2302
% 15.37/3.27 % (20851)Time elapsed: 0.012 s
% 15.37/3.27 % (20851)Instructions burned: 40 (million)
% 15.37/3.27 % (20851)------------------------------
% 15.37/3.27 % (20851)------------------------------
% 15.37/3.28 % (20852)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_20195 for (2979ds/294Mi)
% 15.86/3.30 % (20602)Instruction limit reached!
% 15.86/3.30 % (20602)------------------------------
% 15.86/3.30 % (20602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.86/3.30 % (20602)Termination reason: Unknown
% 15.86/3.30 % (20602)Termination phase: Saturation
% 15.86/3.30
% 15.86/3.30 % (20602)Memory used [KB]: 6396
% 15.86/3.30 % (20602)Time elapsed: 0.687 s
% 15.86/3.30 % (20602)Instructions burned: 1915 (million)
% 15.86/3.30 % (20602)------------------------------
% 15.86/3.30 % (20602)------------------------------
% 15.86/3.31 % (20853)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_20195 for (2979ds/187Mi)
% 15.86/3.35 % (20852)Instruction limit reached!
% 15.86/3.35 % (20852)------------------------------
% 15.86/3.35 % (20852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.86/3.35 % (20852)Termination reason: Unknown
% 15.86/3.35 % (20852)Termination phase: Saturation
% 15.86/3.35
% 15.86/3.35 % (20852)Memory used [KB]: 7547
% 15.86/3.35 % (20852)Time elapsed: 0.072 s
% 15.86/3.35 % (20852)Instructions burned: 295 (million)
% 15.86/3.35 % (20852)------------------------------
% 15.86/3.35 % (20852)------------------------------
% 15.86/3.36 % (20854)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_20195 for (2979ds/371Mi)
% 15.86/3.36 % (20819)Instruction limit reached!
% 15.86/3.36 % (20819)------------------------------
% 15.86/3.36 % (20819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.86/3.36 % (20819)Termination reason: Unknown
% 15.86/3.36 % (20819)Termination phase: Saturation
% 15.86/3.36
% 15.86/3.36 % (20819)Memory used [KB]: 14456
% 15.86/3.36 % (20819)Time elapsed: 0.166 s
% 15.86/3.36 % (20819)Instructions burned: 668 (million)
% 15.86/3.36 % (20819)------------------------------
% 15.86/3.36 % (20819)------------------------------
% 15.86/3.36 % (20853)Instruction limit reached!
% 15.86/3.36 % (20853)------------------------------
% 15.86/3.36 % (20853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.86/3.36 % (20853)Termination reason: Unknown
% 15.86/3.36 % (20853)Termination phase: Saturation
% 15.86/3.36
% 15.86/3.36 % (20853)Memory used [KB]: 7547
% 15.86/3.36 % (20853)Time elapsed: 0.048 s
% 15.86/3.36 % (20853)Instructions burned: 188 (million)
% 15.86/3.36 % (20853)------------------------------
% 15.86/3.36 % (20853)------------------------------
% 15.86/3.37 % (20855)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_20195 for (2979ds/1827Mi)
% 15.86/3.37 % (20856)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_20195 for (2979ds/70Mi)
% 15.86/3.37 % (20785)Instruction limit reached!
% 15.86/3.37 % (20785)------------------------------
% 15.86/3.37 % (20785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.86/3.37 % (20785)Termination reason: Unknown
% 15.86/3.37 % (20785)Termination phase: Saturation
% 15.86/3.37
% 15.86/3.37 % (20785)Memory used [KB]: 11641
% 15.86/3.37 % (20785)Time elapsed: 0.245 s
% 15.86/3.37 % (20785)Instructions burned: 832 (million)
% 15.86/3.37 % (20785)------------------------------
% 15.86/3.37 % (20785)------------------------------
% 15.86/3.38 % (20857)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_20195 for (2978ds/316Mi)
% 15.86/3.39 % (20856)Instruction limit reached!
% 15.86/3.39 % (20856)------------------------------
% 15.86/3.39 % (20856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.86/3.39 % (20856)Termination reason: Unknown
% 15.86/3.39 % (20856)Termination phase: Property scanning
% 15.86/3.39
% 15.86/3.39 % (20856)Memory used [KB]: 2558
% 15.86/3.39 % (20856)Time elapsed: 0.019 s
% 15.86/3.39 % (20856)Instructions burned: 71 (million)
% 15.86/3.39 % (20856)------------------------------
% 15.86/3.39 % (20856)------------------------------
% 16.76/3.40 % (20858)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_20195 for (2978ds/932Mi)
% 16.76/3.45 % (20854)Instruction limit reached!
% 16.76/3.45 % (20854)------------------------------
% 16.76/3.45 % (20854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.76/3.45 % (20854)Termination reason: Unknown
% 16.76/3.45 % (20854)Termination phase: Saturation
% 16.76/3.45
% 16.76/3.45 % (20854)Memory used [KB]: 9210
% 16.76/3.45 % (20854)Time elapsed: 0.096 s
% 16.76/3.45 % (20854)Instructions burned: 372 (million)
% 16.76/3.45 % (20854)------------------------------
% 16.76/3.45 % (20854)------------------------------
% 16.76/3.46 % (20857)Instruction limit reached!
% 16.76/3.46 % (20857)------------------------------
% 16.76/3.46 % (20857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.76/3.46 % (20857)Termination reason: Unknown
% 16.76/3.46 % (20857)Termination phase: Saturation
% 16.76/3.46
% 16.76/3.46 % (20857)Memory used [KB]: 7547
% 16.76/3.46 % (20857)Time elapsed: 0.079 s
% 16.76/3.46 % (20857)Instructions burned: 317 (million)
% 16.76/3.46 % (20857)------------------------------
% 16.76/3.46 % (20857)------------------------------
% 16.76/3.46 % (20859)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_20195 for (2978ds/4714Mi)
% 16.76/3.47 % (20860)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_20195 for (2978ds/8250Mi)
% 17.56/3.63 % (20858)Instruction limit reached!
% 17.56/3.63 % (20858)------------------------------
% 17.56/3.63 % (20858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.56/3.63 % (20858)Termination reason: Unknown
% 17.56/3.63 % (20858)Termination phase: Saturation
% 17.56/3.63
% 17.56/3.63 % (20858)Memory used [KB]: 16758
% 17.56/3.63 % (20858)Time elapsed: 0.232 s
% 17.56/3.63 % (20858)Instructions burned: 932 (million)
% 17.56/3.63 % (20858)------------------------------
% 17.56/3.63 % (20858)------------------------------
% 17.56/3.64 % (20861)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_20195 for (2976ds/770Mi)
% 18.40/3.85 % (20861)Instruction limit reached!
% 18.40/3.85 % (20861)------------------------------
% 18.40/3.85 % (20861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.40/3.85 % (20861)Termination reason: Unknown
% 18.40/3.85 % (20861)Termination phase: Saturation
% 18.40/3.85
% 18.40/3.85 % (20861)Memory used [KB]: 7803
% 18.40/3.85 % (20861)Time elapsed: 0.207 s
% 18.40/3.85 % (20861)Instructions burned: 770 (million)
% 18.40/3.85 % (20861)------------------------------
% 18.40/3.85 % (20861)------------------------------
% 18.40/3.86 % (20862)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_20195 for (2974ds/794Mi)
% 18.40/3.87 % (20855)Instruction limit reached!
% 18.40/3.87 % (20855)------------------------------
% 18.40/3.87 % (20855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.40/3.87 % (20855)Termination reason: Unknown
% 18.40/3.87 % (20855)Termination phase: Saturation
% 18.40/3.87
% 18.40/3.87 % (20855)Memory used [KB]: 21236
% 18.40/3.87 % (20855)Time elapsed: 0.506 s
% 18.40/3.87 % (20855)Instructions burned: 1827 (million)
% 18.40/3.87 % (20855)------------------------------
% 18.40/3.87 % (20855)------------------------------
% 18.40/3.88 % (20863)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_20195 for (2973ds/464Mi)
% 18.40/3.89 % (20600)Instruction limit reached!
% 18.40/3.89 % (20600)------------------------------
% 18.40/3.89 % (20600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.40/3.89 % (20600)Termination reason: Unknown
% 18.40/3.89 % (20600)Termination phase: Saturation
% 18.40/3.89
% 18.40/3.89 % (20600)Memory used [KB]: 17654
% 18.40/3.89 % (20600)Time elapsed: 1.334 s
% 18.40/3.89 % (20600)Instructions burned: 5206 (million)
% 18.40/3.89 % (20600)------------------------------
% 18.40/3.89 % (20600)------------------------------
% 19.44/3.90 % (20864)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_20195 for (2973ds/1376Mi)
% 19.44/4.00 % (20592)Instruction limit reached!
% 19.44/4.00 % (20592)------------------------------
% 19.44/4.00 % (20592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.44/4.00 % (20592)Termination reason: Unknown
% 19.44/4.00 % (20592)Termination phase: Saturation
% 19.44/4.00
% 19.44/4.00 % (20592)Memory used [KB]: 15351
% 19.44/4.00 % (20592)Time elapsed: 1.497 s
% 19.44/4.00 % (20592)Instructions burned: 4436 (million)
% 19.44/4.00 % (20592)------------------------------
% 19.44/4.00 % (20592)------------------------------
% 19.44/4.01 % (20863)Instruction limit reached!
% 19.44/4.01 % (20863)------------------------------
% 19.44/4.01 % (20863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.44/4.01 % (20863)Termination reason: Unknown
% 19.44/4.01 % (20863)Termination phase: Saturation
% 19.44/4.01
% 19.44/4.01 % (20863)Memory used [KB]: 9594
% 19.44/4.01 % (20863)Time elapsed: 0.125 s
% 19.44/4.01 % (20863)Instructions burned: 466 (million)
% 19.44/4.01 % (20863)------------------------------
% 19.44/4.01 % (20863)------------------------------
% 19.44/4.01 % (20865)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_20195 for (2972ds/906Mi)
% 21.15/4.02 % (20866)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_20195 for (2972ds/434Mi)
% 21.15/4.09 % (20862)Instruction limit reached!
% 21.15/4.09 % (20862)------------------------------
% 21.15/4.09 % (20862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.15/4.09 % (20862)Termination reason: Unknown
% 21.15/4.09 % (20862)Termination phase: Saturation
% 21.15/4.09
% 21.15/4.09 % (20862)Memory used [KB]: 6140
% 21.15/4.09 % (20862)Time elapsed: 0.231 s
% 21.15/4.09 % (20862)Instructions burned: 794 (million)
% 21.15/4.09 % (20862)------------------------------
% 21.15/4.09 % (20862)------------------------------
% 21.15/4.10 % (20867)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_20195 for (2971ds/865Mi)
% 21.15/4.11 % (20606)Instruction limit reached!
% 21.15/4.11 % (20606)------------------------------
% 21.15/4.11 % (20606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.15/4.11 % (20606)Termination reason: Unknown
% 21.15/4.11 % (20606)Termination phase: Saturation
% 21.15/4.11
% 21.15/4.11 % (20606)Memory used [KB]: 13816
% 21.15/4.11 % (20606)Time elapsed: 1.348 s
% 21.15/4.11 % (20606)Instructions burned: 4350 (million)
% 21.15/4.11 % (20606)------------------------------
% 21.15/4.11 % (20606)------------------------------
% 21.65/4.12 % (20868)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_20195 for (2971ds/593Mi)
% 21.65/4.14 % (20866)Instruction limit reached!
% 21.65/4.14 % (20866)------------------------------
% 21.65/4.14 % (20866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.65/4.14 % (20866)Termination reason: Unknown
% 21.65/4.14 % (20866)Termination phase: Saturation
% 21.65/4.14
% 21.65/4.14 % (20866)Memory used [KB]: 11513
% 21.65/4.14 % (20866)Time elapsed: 0.126 s
% 21.65/4.14 % (20866)Instructions burned: 436 (million)
% 21.65/4.14 % (20866)------------------------------
% 21.65/4.14 % (20866)------------------------------
% 21.65/4.15 % (20869)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_20195 for (2971ds/443Mi)
% 22.05/4.25 % (20864)Instruction limit reached!
% 22.05/4.25 % (20864)------------------------------
% 22.05/4.25 % (20864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.05/4.25 % (20864)Termination reason: Unknown
% 22.05/4.25 % (20864)Termination phase: Saturation
% 22.05/4.25
% 22.05/4.25 % (20864)Memory used [KB]: 9850
% 22.05/4.25 % (20864)Time elapsed: 0.345 s
% 22.05/4.25 % (20864)Instructions burned: 1378 (million)
% 22.05/4.25 % (20864)------------------------------
% 22.05/4.25 % (20864)------------------------------
% 22.05/4.26 % (20870)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_20195 for (2970ds/594Mi)
% 22.05/4.26 % (20868)Instruction limit reached!
% 22.05/4.26 % (20868)------------------------------
% 22.05/4.26 % (20868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.05/4.26 % (20868)Termination reason: Unknown
% 22.05/4.26 % (20868)Termination phase: Saturation
% 22.05/4.26
% 22.05/4.26 % (20868)Memory used [KB]: 7675
% 22.05/4.26 % (20868)Time elapsed: 0.147 s
% 22.05/4.26 % (20868)Instructions burned: 595 (million)
% 22.05/4.26 % (20868)------------------------------
% 22.05/4.26 % (20868)------------------------------
% 22.05/4.27 % (20869)Instruction limit reached!
% 22.05/4.27 % (20869)------------------------------
% 22.05/4.27 % (20869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.05/4.27 % (20869)Termination reason: Unknown
% 22.05/4.27 % (20869)Termination phase: Saturation
% 22.05/4.27
% 22.05/4.27 % (20869)Memory used [KB]: 9594
% 22.05/4.27 % (20869)Time elapsed: 0.116 s
% 22.05/4.27 % (20869)Instructions burned: 446 (million)
% 22.05/4.27 % (20869)------------------------------
% 22.05/4.27 % (20869)------------------------------
% 22.05/4.27 % (20871)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_20195 for (2970ds/327Mi)
% 22.05/4.28 % (20872)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_20195 for (2970ds/5411Mi)
% 22.05/4.28 % (20865)Instruction limit reached!
% 22.05/4.28 % (20865)------------------------------
% 22.05/4.28 % (20865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.05/4.28 % (20865)Termination reason: Unknown
% 22.05/4.28 % (20865)Termination phase: Saturation
% 22.05/4.28
% 22.05/4.28 % (20865)Memory used [KB]: 11513
% 22.05/4.28 % (20865)Time elapsed: 0.270 s
% 22.05/4.28 % (20865)Instructions burned: 908 (million)
% 22.05/4.28 % (20865)------------------------------
% 22.05/4.28 % (20865)------------------------------
% 22.05/4.29 % (20873)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_20195 for (2970ds/1762Mi)
% 22.88/4.35 % (20867)Instruction limit reached!
% 22.88/4.35 % (20867)------------------------------
% 22.88/4.35 % (20867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.88/4.35 % (20867)Termination reason: Unknown
% 22.88/4.35 % (20867)Termination phase: Saturation
% 22.88/4.35
% 22.88/4.35 % (20867)Memory used [KB]: 10746
% 22.88/4.35 % (20867)Time elapsed: 0.252 s
% 22.88/4.35 % (20867)Instructions burned: 867 (million)
% 22.88/4.35 % (20867)------------------------------
% 22.88/4.35 % (20867)------------------------------
% 22.88/4.36 % (20874)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_20195 for (2969ds/96Mi)
% 22.88/4.37 % (20871)Instruction limit reached!
% 22.88/4.37 % (20871)------------------------------
% 22.88/4.37 % (20871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.88/4.37 % (20871)Termination reason: Unknown
% 22.88/4.37 % (20871)Termination phase: Saturation
% 22.88/4.37
% 22.88/4.37 % (20871)Memory used [KB]: 11385
% 22.88/4.37 % (20871)Time elapsed: 0.094 s
% 22.88/4.37 % (20871)Instructions burned: 328 (million)
% 22.88/4.37 % (20871)------------------------------
% 22.88/4.37 % (20871)------------------------------
% 22.88/4.38 % (20875)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_20195 for (2969ds/503Mi)
% 22.88/4.38 % (20874)Instruction limit reached!
% 22.88/4.38 % (20874)------------------------------
% 22.88/4.38 % (20874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.88/4.38 % (20874)Termination reason: Unknown
% 22.88/4.38 % (20874)Termination phase: Property scanning
% 22.88/4.38
% 22.88/4.38 % (20874)Memory used [KB]: 2686
% 22.88/4.38 % (20874)Time elapsed: 0.026 s
% 22.88/4.38 % (20874)Instructions burned: 99 (million)
% 22.88/4.38 % (20874)------------------------------
% 22.88/4.38 % (20874)------------------------------
% 22.88/4.39 % (20876)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_20195 for (2969ds/90Mi)
% 23.47/4.41 % (20876)Instruction limit reached!
% 23.47/4.41 % (20876)------------------------------
% 23.47/4.41 % (20876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.47/4.41 % (20876)Termination reason: Unknown
% 23.47/4.41 % (20876)Termination phase: Property scanning
% 23.47/4.41
% 23.47/4.41 % (20876)Memory used [KB]: 2558
% 23.47/4.41 % (20876)Time elapsed: 0.024 s
% 23.47/4.41 % (20876)Instructions burned: 91 (million)
% 23.47/4.41 % (20876)------------------------------
% 23.47/4.41 % (20876)------------------------------
% 23.47/4.42 % (20870)Instruction limit reached!
% 23.47/4.42 % (20870)------------------------------
% 23.47/4.42 % (20870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.47/4.42 % (20870)Termination reason: Unknown
% 23.47/4.42 % (20870)Termination phase: Saturation
% 23.47/4.42
% 23.47/4.42 % (20870)Memory used [KB]: 9850
% 23.47/4.42 % (20870)Time elapsed: 0.164 s
% 23.47/4.42 % (20870)Instructions burned: 594 (million)
% 23.47/4.42 % (20870)------------------------------
% 23.47/4.42 % (20870)------------------------------
% 23.47/4.42 % (20877)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_20195 for (2968ds/593Mi)
% 23.47/4.43 % (20878)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_20195 for (2968ds/1512Mi)
% 23.88/4.51 % (20875)Instruction limit reached!
% 23.88/4.51 % (20875)------------------------------
% 23.88/4.51 % (20875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.88/4.51 % (20875)Termination reason: Unknown
% 23.88/4.51 % (20875)Termination phase: Saturation
% 23.88/4.51
% 23.88/4.51 % (20875)Memory used [KB]: 9978
% 23.88/4.51 % (20875)Time elapsed: 0.136 s
% 23.88/4.51 % (20875)Instructions burned: 505 (million)
% 23.88/4.51 % (20875)------------------------------
% 23.88/4.51 % (20875)------------------------------
% 23.88/4.52 % (20879)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_20195 for (2967ds/569Mi)
% 23.88/4.59 % (20877)Instruction limit reached!
% 23.88/4.59 % (20877)------------------------------
% 23.88/4.59 % (20877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.88/4.59 % (20877)Termination reason: Unknown
% 23.88/4.59 % (20877)Termination phase: Saturation
% 23.88/4.59
% 23.88/4.59 % (20877)Memory used [KB]: 10234
% 23.88/4.59 % (20877)Time elapsed: 0.164 s
% 23.88/4.59 % (20877)Instructions burned: 593 (million)
% 23.88/4.59 % (20877)------------------------------
% 23.88/4.59 % (20877)------------------------------
% 23.88/4.60 % (20880)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_20195 for (2966ds/501Mi)
% 24.40/4.62 % (20859)Instruction limit reached!
% 24.40/4.62 % (20859)------------------------------
% 24.40/4.62 % (20859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.40/4.62 % (20859)Termination reason: Unknown
% 24.40/4.62 % (20859)Termination phase: Saturation
% 24.40/4.62
% 24.40/4.62 % (20859)Memory used [KB]: 7803
% 24.40/4.62 % (20859)Time elapsed: 1.159 s
% 24.40/4.62 % (20859)Instructions burned: 4719 (million)
% 24.40/4.62 % (20859)------------------------------
% 24.40/4.62 % (20859)------------------------------
% 24.40/4.63 % (20881)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_20195 for (2966ds/562Mi)
% 24.40/4.66 % (20879)Instruction limit reached!
% 24.40/4.66 % (20879)------------------------------
% 24.40/4.66 % (20879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.40/4.66 % (20879)Termination reason: Unknown
% 24.40/4.66 % (20879)Termination phase: Saturation
% 24.40/4.66
% 24.40/4.66 % (20879)Memory used [KB]: 7675
% 24.40/4.66 % (20879)Time elapsed: 0.142 s
% 24.40/4.66 % (20879)Instructions burned: 572 (million)
% 24.40/4.66 % (20879)------------------------------
% 24.40/4.66 % (20879)------------------------------
% 24.40/4.67 % (20882)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_20195 for (2966ds/406Mi)
% 24.67/4.71 % (20873)Instruction limit reached!
% 24.67/4.71 % (20873)------------------------------
% 24.67/4.71 % (20873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.67/4.71 % (20873)Termination reason: Unknown
% 24.67/4.71 % (20873)Termination phase: Saturation
% 24.67/4.71
% 24.67/4.71 % (20873)Memory used [KB]: 21108
% 24.67/4.71 % (20873)Time elapsed: 0.422 s
% 24.67/4.71 % (20873)Instructions burned: 1762 (million)
% 24.67/4.71 % (20873)------------------------------
% 24.67/4.71 % (20873)------------------------------
% 24.67/4.72 % (20883)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_20195 for (2965ds/582Mi)
% 24.67/4.74 % (20880)Instruction limit reached!
% 24.67/4.74 % (20880)------------------------------
% 24.67/4.74 % (20880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.67/4.74 % (20880)Termination reason: Unknown
% 24.67/4.74 % (20880)Termination phase: Saturation
% 24.67/4.74
% 24.67/4.74 % (20880)Memory used [KB]: 10874
% 24.67/4.74 % (20880)Time elapsed: 0.146 s
% 24.67/4.74 % (20880)Instructions burned: 503 (million)
% 24.67/4.74 % (20880)------------------------------
% 24.67/4.74 % (20880)------------------------------
% 24.67/4.75 % (20884)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_20195 for (2965ds/456Mi)
% 24.67/4.78 % (20882)Instruction limit reached!
% 24.67/4.78 % (20882)------------------------------
% 24.67/4.78 % (20882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.67/4.78 % (20882)Termination reason: Unknown
% 24.67/4.78 % (20882)Termination phase: Saturation
% 24.67/4.78
% 24.67/4.78 % (20882)Memory used [KB]: 7803
% 24.67/4.78 % (20882)Time elapsed: 0.108 s
% 24.67/4.78 % (20882)Instructions burned: 406 (million)
% 24.67/4.78 % (20882)------------------------------
% 24.67/4.78 % (20882)------------------------------
% 24.67/4.79 % (20881)Instruction limit reached!
% 24.67/4.79 % (20881)------------------------------
% 24.67/4.79 % (20881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.67/4.79 % (20881)Termination reason: Unknown
% 24.67/4.79 % (20881)Termination phase: Saturation
% 24.67/4.79
% 24.67/4.79 % (20881)Memory used [KB]: 9338
% 24.67/4.79 % (20881)Time elapsed: 0.159 s
% 24.67/4.79 % (20881)Instructions burned: 564 (million)
% 24.67/4.79 % (20881)------------------------------
% 24.67/4.79 % (20881)------------------------------
% 24.67/4.79 % (20885)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_20195 for (2965ds/393Mi)
% 25.64/4.80 % (20886)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_20195 for (2964ds/1335Mi)
% 25.64/4.87 % (20884)Instruction limit reached!
% 25.64/4.87 % (20884)------------------------------
% 25.64/4.87 % (20884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.64/4.87 % (20884)Termination reason: Unknown
% 25.64/4.87 % (20884)Termination phase: Saturation
% 25.64/4.87
% 25.64/4.87 % (20884)Memory used [KB]: 9722
% 25.64/4.87 % (20884)Time elapsed: 0.121 s
% 25.64/4.87 % (20884)Instructions burned: 457 (million)
% 25.64/4.87 % (20884)------------------------------
% 25.64/4.87 % (20884)------------------------------
% 25.64/4.87 % (20878)Instruction limit reached!
% 25.64/4.87 % (20878)------------------------------
% 25.64/4.87 % (20878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.64/4.87 % (20878)Termination reason: Unknown
% 25.64/4.87 % (20878)Termination phase: Saturation
% 25.64/4.87
% 25.64/4.87 % (20878)Memory used [KB]: 12409
% 25.64/4.87 % (20878)Time elapsed: 0.447 s
% 25.64/4.87 % (20878)Instructions burned: 1512 (million)
% 25.64/4.87 % (20878)------------------------------
% 25.64/4.87 % (20878)------------------------------
% 25.64/4.88 % (20887)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_20195 for (2964ds/3373Mi)
% 25.64/4.88 % (20888)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_20195 for (2963ds/474Mi)
% 25.64/4.89 % (20885)Instruction limit reached!
% 25.64/4.89 % (20885)------------------------------
% 25.64/4.89 % (20885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.64/4.89 % (20885)Termination reason: Unknown
% 25.64/4.89 % (20885)Termination phase: Saturation
% 25.64/4.89
% 25.64/4.89 % (20885)Memory used [KB]: 9850
% 25.64/4.89 % (20885)Time elapsed: 0.105 s
% 25.64/4.89 % (20885)Instructions burned: 394 (million)
% 25.64/4.89 % (20885)------------------------------
% 25.64/4.89 % (20885)------------------------------
% 25.64/4.89 % (20883)Instruction limit reached!
% 25.64/4.89 % (20883)------------------------------
% 25.64/4.89 % (20883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.64/4.89 % (20883)Termination reason: Unknown
% 25.64/4.89 % (20883)Termination phase: Saturation
% 25.64/4.89
% 25.64/4.89 % (20883)Memory used [KB]: 11001
% 25.64/4.89 % (20883)Time elapsed: 0.195 s
% 25.64/4.89 % (20883)Instructions burned: 584 (million)
% 25.64/4.89 % (20883)------------------------------
% 25.64/4.89 % (20883)------------------------------
% 26.64/4.90 % (20889)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_20195 for (2963ds/157Mi)
% 26.64/4.90 % (20890)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_20195 for (2963ds/590Mi)
% 26.64/4.94 % (20889)Instruction limit reached!
% 26.64/4.94 % (20889)------------------------------
% 26.64/4.94 % (20889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.64/4.94 % (20889)Termination reason: Unknown
% 26.64/4.94 % (20889)Termination phase: Function definition elimination
% 26.64/4.94
% 26.64/4.94 % (20889)Memory used [KB]: 2814
% 26.64/4.94 % (20889)Time elapsed: 0.040 s
% 26.64/4.94 % (20889)Instructions burned: 157 (million)
% 26.64/4.94 % (20889)------------------------------
% 26.64/4.94 % (20889)------------------------------
% 26.64/4.95 % (20891)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_20195 for (2963ds/104Mi)
% 26.64/4.98 % (20891)Instruction limit reached!
% 26.64/4.98 % (20891)------------------------------
% 26.64/4.98 % (20891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.64/4.98 % (20891)Termination reason: Unknown
% 26.64/4.98 % (20891)Termination phase: Property scanning
% 26.64/4.98
% 26.64/4.98 % (20891)Memory used [KB]: 2814
% 26.64/4.98 % (20891)Time elapsed: 0.028 s
% 26.64/4.98 % (20891)Instructions burned: 105 (million)
% 26.64/4.98 % (20891)------------------------------
% 26.64/4.98 % (20891)------------------------------
% 26.64/4.99 % (20892)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_20195 for (2962ds/414Mi)
% 26.64/5.00 % (20888)Instruction limit reached!
% 26.64/5.00 % (20888)------------------------------
% 26.64/5.00 % (20888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.64/5.00 % (20888)Termination reason: Unknown
% 26.64/5.00 % (20888)Termination phase: Saturation
% 26.64/5.00
% 26.64/5.00 % (20888)Memory used [KB]: 7675
% 26.64/5.00 % (20888)Time elapsed: 0.119 s
% 26.64/5.00 % (20888)Instructions burned: 477 (million)
% 26.64/5.00 % (20888)------------------------------
% 26.64/5.00 % (20888)------------------------------
% 28.17/5.01 % (20893)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_20195 for (2962ds/715Mi)
% 28.17/5.07 % (20890)Instruction limit reached!
% 28.17/5.07 % (20890)------------------------------
% 28.17/5.07 % (20890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.17/5.07 % (20890)Termination reason: Unknown
% 28.17/5.07 % (20890)Termination phase: Saturation
% 28.17/5.07
% 28.17/5.07 % (20890)Memory used [KB]: 8827
% 28.17/5.07 % (20890)Time elapsed: 0.167 s
% 28.17/5.07 % (20890)Instructions burned: 590 (million)
% 28.17/5.07 % (20890)------------------------------
% 28.17/5.07 % (20890)------------------------------
% 28.17/5.08 % (20894)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_20195 for (2961ds/961Mi)
% 28.17/5.09 % (20892)Instruction limit reached!
% 28.17/5.09 % (20892)------------------------------
% 28.17/5.09 % (20892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.17/5.09 % (20892)Termination reason: Unknown
% 28.17/5.09 % (20892)Termination phase: Saturation
% 28.17/5.09
% 28.17/5.09 % (20892)Memory used [KB]: 7675
% 28.17/5.09 % (20892)Time elapsed: 0.104 s
% 28.17/5.09 % (20892)Instructions burned: 415 (million)
% 28.17/5.09 % (20892)------------------------------
% 28.17/5.09 % (20892)------------------------------
% 28.17/5.10 % (20895)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_20195 for (2961ds/1213Mi)
% 28.72/5.17 % (20886)Instruction limit reached!
% 28.72/5.17 % (20886)------------------------------
% 28.72/5.17 % (20886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.72/5.17 % (20886)Termination reason: Unknown
% 28.72/5.17 % (20886)Termination phase: Saturation
% 28.72/5.17
% 28.72/5.17 % (20886)Memory used [KB]: 10106
% 28.72/5.17 % (20886)Time elapsed: 0.375 s
% 28.72/5.17 % (20886)Instructions burned: 1336 (million)
% 28.72/5.17 % (20886)------------------------------
% 28.72/5.17 % (20886)------------------------------
% 28.72/5.18 % (20896)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_20195 for (2960ds/1979Mi)
% 29.04/5.22 % (20893)Instruction limit reached!
% 29.04/5.22 % (20893)------------------------------
% 29.04/5.22 % (20893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.04/5.22 % (20893)Termination reason: Unknown
% 29.04/5.22 % (20893)Termination phase: Saturation
% 29.04/5.22
% 29.04/5.22 % (20893)Memory used [KB]: 5756
% 29.04/5.22 % (20893)Time elapsed: 0.207 s
% 29.04/5.22 % (20893)Instructions burned: 716 (million)
% 29.04/5.22 % (20893)------------------------------
% 29.04/5.22 % (20893)------------------------------
% 29.04/5.23 % (20897)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_20195 for (2960ds/481Mi)
% 29.55/5.34 % (20897)Instruction limit reached!
% 29.55/5.34 % (20897)------------------------------
% 29.55/5.34 % (20897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.55/5.34 % (20897)Termination reason: Unknown
% 29.55/5.34 % (20897)Termination phase: Saturation
% 29.55/5.34
% 29.55/5.34 % (20897)Memory used [KB]: 7675
% 29.55/5.34 % (20897)Time elapsed: 0.118 s
% 29.55/5.34 % (20897)Instructions burned: 481 (million)
% 29.55/5.34 % (20897)------------------------------
% 29.55/5.34 % (20897)------------------------------
% 29.55/5.35 % (20898)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_20195 for (2959ds/783Mi)
% 29.55/5.36 % (20894)Instruction limit reached!
% 29.55/5.36 % (20894)------------------------------
% 29.55/5.36 % (20894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.55/5.36 % (20894)Termination reason: Unknown
% 29.55/5.36 % (20894)Termination phase: Saturation
% 29.55/5.36
% 29.55/5.36 % (20894)Memory used [KB]: 10362
% 29.55/5.36 % (20894)Time elapsed: 0.280 s
% 29.55/5.36 % (20894)Instructions burned: 962 (million)
% 29.55/5.36 % (20894)------------------------------
% 29.55/5.36 % (20894)------------------------------
% 29.55/5.37 % (20899)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_20195 for (2959ds/432Mi)
% 30.26/5.47 % (20895)Instruction limit reached!
% 30.26/5.47 % (20895)------------------------------
% 30.26/5.47 % (20895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.26/5.47 % (20895)Termination reason: Unknown
% 30.26/5.47 % (20895)Termination phase: Saturation
% 30.26/5.47
% 30.26/5.47 % (20895)Memory used [KB]: 15223
% 30.26/5.47 % (20895)Time elapsed: 0.371 s
% 30.26/5.47 % (20895)Instructions burned: 1213 (million)
% 30.26/5.47 % (20895)------------------------------
% 30.26/5.47 % (20895)------------------------------
% 30.26/5.48 % (20900)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_20195 for (2958ds/1670Mi)
% 30.26/5.48 % (20899)Instruction limit reached!
% 30.26/5.48 % (20899)------------------------------
% 30.26/5.48 % (20899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.26/5.48 % (20899)Termination reason: Unknown
% 30.26/5.48 % (20899)Termination phase: Saturation
% 30.26/5.48
% 30.26/5.48 % (20899)Memory used [KB]: 9722
% 30.26/5.48 % (20899)Time elapsed: 0.117 s
% 30.26/5.48 % (20899)Instructions burned: 434 (million)
% 30.26/5.48 % (20899)------------------------------
% 30.26/5.48 % (20899)------------------------------
% 30.26/5.49 % (20901)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_20195 for (2957ds/90Mi)
% 31.06/5.52 % (20901)Instruction limit reached!
% 31.06/5.52 % (20901)------------------------------
% 31.06/5.52 % (20901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.06/5.52 % (20901)Termination reason: Unknown
% 31.06/5.52 % (20901)Termination phase: Preprocessing 2
% 31.06/5.52
% 31.06/5.52 % (20901)Memory used [KB]: 2686
% 31.06/5.52 % (20901)Time elapsed: 0.025 s
% 31.06/5.52 % (20901)Instructions burned: 93 (million)
% 31.06/5.52 % (20901)------------------------------
% 31.06/5.52 % (20901)------------------------------
% 31.06/5.53 % (20902)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_20195 for (2957ds/346Mi)
% 31.06/5.60 % (20898)Instruction limit reached!
% 31.06/5.60 % (20898)------------------------------
% 31.06/5.60 % (20898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.06/5.60 % (20898)Termination reason: Unknown
% 31.06/5.60 % (20898)Termination phase: Saturation
% 31.06/5.60
% 31.06/5.60 % (20898)Memory used [KB]: 12025
% 31.06/5.60 % (20898)Time elapsed: 0.242 s
% 31.06/5.60 % (20898)Instructions burned: 784 (million)
% 31.06/5.60 % (20898)------------------------------
% 31.06/5.60 % (20898)------------------------------
% 31.40/5.61 % (20903)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_20195 for (2956ds/401Mi)
% 31.40/5.62 % (20902)Instruction limit reached!
% 31.40/5.62 % (20902)------------------------------
% 31.40/5.62 % (20902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.40/5.62 % (20902)Termination reason: Unknown
% 31.40/5.62 % (20902)Termination phase: Saturation
% 31.40/5.62
% 31.40/5.62 % (20902)Memory used [KB]: 7547
% 31.40/5.62 % (20902)Time elapsed: 0.090 s
% 31.40/5.62 % (20902)Instructions burned: 347 (million)
% 31.40/5.62 % (20902)------------------------------
% 31.40/5.62 % (20902)------------------------------
% 31.40/5.63 % (20904)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_20195 for (2956ds/6454Mi)
% 32.06/5.70 % (20903)Instruction limit reached!
% 32.06/5.70 % (20903)------------------------------
% 32.06/5.70 % (20903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.06/5.70 % (20903)Termination reason: Unknown
% 32.06/5.70 % (20903)Termination phase: Saturation
% 32.06/5.70
% 32.06/5.70 % (20903)Memory used [KB]: 7675
% 32.06/5.70 % (20903)Time elapsed: 0.100 s
% 32.06/5.70 % (20903)Instructions burned: 403 (million)
% 32.06/5.70 % (20903)------------------------------
% 32.06/5.70 % (20903)------------------------------
% 32.06/5.71 % (20905)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_20195 for (2955ds/283Mi)
% 32.06/5.77 % (20896)Instruction limit reached!
% 32.06/5.77 % (20896)------------------------------
% 32.06/5.77 % (20896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.06/5.77 % (20896)Termination reason: Unknown
% 32.06/5.77 % (20896)Termination phase: Saturation
% 32.06/5.77
% 32.06/5.77 % (20896)Memory used [KB]: 10746
% 32.06/5.77 % (20896)Time elapsed: 0.589 s
% 32.06/5.77 % (20896)Instructions burned: 1979 (million)
% 32.06/5.77 % (20896)------------------------------
% 32.06/5.77 % (20896)------------------------------
% 32.06/5.78 % (20906)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_20195 for (2955ds/865Mi)
% 32.06/5.79 % (20905)Instruction limit reached!
% 32.06/5.79 % (20905)------------------------------
% 32.06/5.79 % (20905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.06/5.79 % (20905)Termination reason: Unknown
% 32.06/5.79 % (20905)Termination phase: Saturation
% 32.06/5.79
% 32.06/5.79 % (20905)Memory used [KB]: 8187
% 32.06/5.79 % (20905)Time elapsed: 0.075 s
% 32.06/5.79 % (20905)Instructions burned: 286 (million)
% 32.06/5.79 % (20905)------------------------------
% 32.06/5.79 % (20905)------------------------------
% 33.15/5.80 % (20907)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_20195 for (2954ds/4528Mi)
% 33.45/5.90 % (20887)Instruction limit reached!
% 33.45/5.90 % (20887)------------------------------
% 33.45/5.90 % (20887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.45/5.90 % (20887)Termination reason: Unknown
% 33.45/5.90 % (20887)Termination phase: Saturation
% 33.45/5.90
% 33.45/5.90 % (20887)Memory used [KB]: 14200
% 33.45/5.90 % (20887)Time elapsed: 1.039 s
% 33.45/5.90 % (20887)Instructions burned: 3375 (million)
% 33.45/5.90 % (20887)------------------------------
% 33.45/5.90 % (20887)------------------------------
% 33.45/5.91 % (20900)Instruction limit reached!
% 33.45/5.91 % (20900)------------------------------
% 33.45/5.91 % (20900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.45/5.91 % (20900)Termination reason: Unknown
% 33.45/5.91 % (20900)Termination phase: Saturation
% 33.45/5.91
% 33.45/5.91 % (20900)Memory used [KB]: 18933
% 33.45/5.91 % (20900)Time elapsed: 0.426 s
% 33.45/5.91 % (20900)Instructions burned: 1673 (million)
% 33.45/5.91 % (20900)------------------------------
% 33.45/5.91 % (20900)------------------------------
% 33.45/5.91 % (20908)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_20195 for (2953ds/1001Mi)
% 33.45/5.92 % (20909)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_20195 for (2953ds/102Mi)
% 33.45/5.94 % (20909)Instruction limit reached!
% 33.45/5.94 % (20909)------------------------------
% 33.45/5.94 % (20909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.45/5.94 % (20909)Termination reason: Unknown
% 33.45/5.94 % (20909)Termination phase: Property scanning
% 33.45/5.94
% 33.45/5.94 % (20909)Memory used [KB]: 2814
% 33.45/5.94 % (20909)Time elapsed: 0.027 s
% 33.45/5.94 % (20909)Instructions burned: 102 (million)
% 33.45/5.94 % (20909)------------------------------
% 33.45/5.94 % (20909)------------------------------
% 33.45/5.95 % (20872)Instruction limit reached!
% 33.45/5.95 % (20872)------------------------------
% 33.45/5.95 % (20872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.45/5.95 % (20872)Termination reason: Unknown
% 33.45/5.95 % (20872)Termination phase: Saturation
% 33.45/5.95
% 33.45/5.95 % (20872)Memory used [KB]: 17014
% 33.45/5.95 % (20872)Time elapsed: 1.671 s
% 33.45/5.95 % (20872)Instructions burned: 5412 (million)
% 33.45/5.95 % (20872)------------------------------
% 33.45/5.95 % (20872)------------------------------
% 33.45/5.95 % (20910)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_20195 for (2953ds/952Mi)
% 33.45/5.96 % (20911)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_20195 for (2953ds/578Mi)
% 33.45/6.01 % (20907)Refutation not found, incomplete strategy
% 33.45/6.01 % (20907)------------------------------
% 33.45/6.01 % (20907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.45/6.01 % (20907)Termination reason: Refutation not found, incomplete strategy
% 33.45/6.01
% 33.45/6.01
% 33.45/6.01 % (20907)Memory used [KB]: 3198
% 33.45/6.01 % (20907)Time elapsed: 0.210 s
% 33.45/6.01 % (20907)Instructions burned: 814 (million)
% 33.45/6.01 % (20907)------------------------------
% 33.45/6.01 % (20907)------------------------------
% 33.45/6.01 % (20906)Instruction limit reached!
% 33.45/6.01 % (20906)------------------------------
% 33.45/6.01 % (20906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.45/6.01 % (20906)Termination reason: Unknown
% 33.45/6.01 % (20906)Termination phase: Saturation
% 33.45/6.01
% 33.45/6.01 % (20906)Memory used [KB]: 8315
% 33.45/6.01 % (20906)Time elapsed: 0.232 s
% 33.45/6.01 % (20906)Instructions burned: 867 (million)
% 33.45/6.01 % (20906)------------------------------
% 33.45/6.01 % (20906)------------------------------
% 35.19/6.02 % (20912)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_20195 for (2952ds/643Mi)
% 35.19/6.02 % (20913)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_20195 for (2952ds/865Mi)
% 35.19/6.04 % (20860)Instruction limit reached!
% 35.19/6.04 % (20860)------------------------------
% 35.19/6.04 % (20860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.19/6.04 % (20860)Termination reason: Unknown
% 35.19/6.04 % (20860)Termination phase: Saturation
% 35.19/6.04
% 35.19/6.04 % (20860)Memory used [KB]: 30575
% 35.19/6.04 % (20860)Time elapsed: 2.574 s
% 35.19/6.04 % (20860)Instructions burned: 8252 (million)
% 35.19/6.04 % (20860)------------------------------
% 35.19/6.04 % (20860)------------------------------
% 35.19/6.05 % (20914)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_20195 for (2952ds/1174Mi)
% 35.19/6.10 % (20911)Instruction limit reached!
% 35.19/6.10 % (20911)------------------------------
% 35.19/6.10 % (20911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.19/6.10 % (20911)Termination reason: Unknown
% 35.19/6.10 % (20911)Termination phase: Saturation
% 35.19/6.10
% 35.19/6.10 % (20911)Memory used [KB]: 11129
% 35.19/6.10 % (20911)Time elapsed: 0.142 s
% 35.19/6.10 % (20911)Instructions burned: 581 (million)
% 35.19/6.10 % (20911)------------------------------
% 35.19/6.10 % (20911)------------------------------
% 35.19/6.11 % (20915)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_20195 for (2951ds/644Mi)
% 35.63/6.18 % (20912)Instruction limit reached!
% 35.63/6.18 % (20912)------------------------------
% 35.63/6.18 % (20912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.63/6.18 % (20912)Termination reason: Unknown
% 35.63/6.18 % (20912)Termination phase: Saturation
% 35.63/6.18
% 35.63/6.18 % (20912)Memory used [KB]: 7675
% 35.63/6.18 % (20912)Time elapsed: 0.161 s
% 35.63/6.18 % (20912)Instructions burned: 643 (million)
% 35.63/6.18 % (20912)------------------------------
% 35.63/6.18 % (20912)------------------------------
% 35.63/6.19 % (20916)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_20195 for (2950ds/1201Mi)
% 36.06/6.21 % (20908)Instruction limit reached!
% 36.06/6.21 % (20908)------------------------------
% 36.06/6.21 % (20908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.06/6.21 % (20908)Termination reason: Unknown
% 36.06/6.21 % (20908)Termination phase: Saturation
% 36.06/6.21
% 36.06/6.21 % (20908)Memory used [KB]: 11513
% 36.06/6.21 % (20908)Time elapsed: 0.303 s
% 36.06/6.21 % (20908)Instructions burned: 1003 (million)
% 36.06/6.21 % (20908)------------------------------
% 36.06/6.21 % (20908)------------------------------
% 36.06/6.22 % (20917)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_20195 for (2950ds/1046Mi)
% 36.06/6.23 % (20910)Instruction limit reached!
% 36.06/6.23 % (20910)------------------------------
% 36.06/6.23 % (20910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.06/6.23 % (20910)Termination reason: Unknown
% 36.06/6.23 % (20910)Termination phase: Saturation
% 36.06/6.23
% 36.06/6.23 % (20910)Memory used [KB]: 10490
% 36.06/6.23 % (20910)Time elapsed: 0.278 s
% 36.06/6.23 % (20910)Instructions burned: 953 (million)
% 36.06/6.23 % (20910)------------------------------
% 36.06/6.23 % (20910)------------------------------
% 36.06/6.24 % (20918)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_20195 for (2950ds/222Mi)
% 36.06/6.25 % (20913)Instruction limit reached!
% 36.06/6.25 % (20913)------------------------------
% 36.06/6.25 % (20913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.06/6.25 % (20913)Termination reason: Unknown
% 36.06/6.25 % (20913)Termination phase: Saturation
% 36.06/6.25
% 36.06/6.25 % (20913)Memory used [KB]: 7931
% 36.06/6.25 % (20913)Time elapsed: 0.257 s
% 36.06/6.25 % (20913)Instructions burned: 865 (million)
% 36.06/6.25 % (20913)------------------------------
% 36.06/6.25 % (20913)------------------------------
% 36.06/6.26 % (20919)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_20195 for (2950ds/68Mi)
% 36.06/6.28 % (20919)Instruction limit reached!
% 36.06/6.28 % (20919)------------------------------
% 36.06/6.28 % (20919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.06/6.28 % (20919)Termination reason: Unknown
% 36.06/6.28 % (20919)Termination phase: Property scanning
% 36.06/6.28
% 36.06/6.28 % (20919)Memory used [KB]: 2558
% 36.06/6.28 % (20919)Time elapsed: 0.019 s
% 36.06/6.28 % (20919)Instructions burned: 68 (million)
% 36.06/6.28 % (20919)------------------------------
% 36.06/6.28 % (20919)------------------------------
% 36.06/6.29 % (20915)Instruction limit reached!
% 36.06/6.29 % (20915)------------------------------
% 36.06/6.29 % (20915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.06/6.29 % (20915)Termination reason: Unknown
% 36.06/6.29 % (20915)Termination phase: Saturation
% 36.06/6.29
% 36.06/6.29 % (20915)Memory used [KB]: 8443
% 36.06/6.29 % (20915)Time elapsed: 0.184 s
% 36.06/6.29 % (20915)Instructions burned: 644 (million)
% 36.06/6.29 % (20915)------------------------------
% 36.06/6.29 % (20915)------------------------------
% 36.06/6.29 % (20920)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_20195 for (2949ds/454Mi)
% 36.06/6.29 % (20918)Instruction limit reached!
% 36.06/6.29 % (20918)------------------------------
% 36.06/6.29 % (20918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.06/6.29 % (20918)Termination reason: Unknown
% 36.06/6.29 % (20918)Termination phase: Saturation
% 36.06/6.29
% 36.06/6.29 % (20918)Memory used [KB]: 7547
% 36.06/6.29 % (20918)Time elapsed: 0.055 s
% 36.06/6.29 % (20918)Instructions burned: 222 (million)
% 36.06/6.29 % (20918)------------------------------
% 36.06/6.29 % (20918)------------------------------
% 36.75/6.30 % (20921)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_20195 for (2949ds/360Mi)
% 36.75/6.30 % (20922)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_20195 for (2949ds/157Mi)
% 36.75/6.34 % (20922)Instruction limit reached!
% 36.75/6.34 % (20922)------------------------------
% 36.75/6.34 % (20922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.75/6.34 % (20922)Termination reason: Unknown
% 36.75/6.34 % (20922)Termination phase: Property scanning
% 36.75/6.34
% 36.75/6.34 % (20922)Memory used [KB]: 2814
% 36.75/6.34 % (20922)Time elapsed: 0.040 s
% 36.75/6.34 % (20922)Instructions burned: 160 (million)
% 36.75/6.34 % (20922)------------------------------
% 36.75/6.34 % (20922)------------------------------
% 36.75/6.35 % (20923)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_20195 for (2949ds/5061Mi)
% 36.75/6.39 % (20921)Instruction limit reached!
% 36.75/6.39 % (20921)------------------------------
% 36.75/6.39 % (20921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.75/6.39 % (20921)Termination reason: Unknown
% 36.75/6.39 % (20921)Termination phase: Saturation
% 36.75/6.39
% 36.75/6.39 % (20921)Memory used [KB]: 7547
% 36.75/6.39 % (20921)Time elapsed: 0.088 s
% 36.75/6.39 % (20921)Instructions burned: 360 (million)
% 36.75/6.39 % (20921)------------------------------
% 36.75/6.39 % (20921)------------------------------
% 37.00/6.40 % (20924)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_20195 for (2948ds/2401Mi)
% 37.00/6.40 % (20920)Instruction limit reached!
% 37.00/6.40 % (20920)------------------------------
% 37.00/6.40 % (20920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.00/6.40 % (20920)Termination reason: Unknown
% 37.00/6.40 % (20920)Termination phase: Saturation
% 37.00/6.40
% 37.00/6.40 % (20920)Memory used [KB]: 12153
% 37.00/6.40 % (20920)Time elapsed: 0.112 s
% 37.00/6.40 % (20920)Instructions burned: 457 (million)
% 37.00/6.40 % (20920)------------------------------
% 37.00/6.40 % (20920)------------------------------
% 37.00/6.40 % (20914)Instruction limit reached!
% 37.00/6.40 % (20914)------------------------------
% 37.00/6.40 % (20914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.00/6.40 % (20914)Termination reason: Unknown
% 37.00/6.40 % (20914)Termination phase: Saturation
% 37.00/6.40
% 37.00/6.40 % (20914)Memory used [KB]: 10746
% 37.00/6.40 % (20914)Time elapsed: 0.350 s
% 37.00/6.40 % (20914)Instructions burned: 1176 (million)
% 37.00/6.40 % (20914)------------------------------
% 37.00/6.40 % (20914)------------------------------
% 37.00/6.41 % (20925)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_20195 for (2948ds/5798Mi)
% 37.00/6.41 % (20926)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_20195 for (2948ds/346Mi)
% 37.00/6.47 % (20917)Instruction limit reached!
% 37.00/6.47 % (20917)------------------------------
% 37.00/6.47 % (20917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.00/6.47 % (20917)Termination reason: Unknown
% 37.00/6.47 % (20917)Termination phase: Saturation
% 37.00/6.47
% 37.00/6.47 % (20917)Memory used [KB]: 7675
% 37.00/6.47 % (20917)Time elapsed: 0.257 s
% 37.00/6.47 % (20917)Instructions burned: 1046 (million)
% 37.00/6.47 % (20917)------------------------------
% 37.00/6.47 % (20917)------------------------------
% 37.00/6.48 % (20927)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_20195 for (2947ds/1321Mi)
% 37.00/6.49 % (20916)Instruction limit reached!
% 37.00/6.49 % (20916)------------------------------
% 37.00/6.49 % (20916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.00/6.49 % (20916)Termination reason: Unknown
% 37.00/6.49 % (20916)Termination phase: Saturation
% 37.00/6.49
% 37.00/6.49 % (20916)Memory used [KB]: 11001
% 37.00/6.49 % (20916)Time elapsed: 0.306 s
% 37.00/6.49 % (20916)Instructions burned: 1201 (million)
% 37.00/6.49 % (20916)------------------------------
% 37.00/6.49 % (20916)------------------------------
% 38.16/6.50 % (20926)Instruction limit reached!
% 38.16/6.50 % (20926)------------------------------
% 38.16/6.50 % (20926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.16/6.50 % (20926)Termination reason: Unknown
% 38.16/6.50 % (20926)Termination phase: Saturation
% 38.16/6.50
% 38.16/6.50 % (20926)Memory used [KB]: 7675
% 38.16/6.50 % (20926)Time elapsed: 0.085 s
% 38.16/6.50 % (20926)Instructions burned: 348 (million)
% 38.16/6.50 % (20926)------------------------------
% 38.16/6.50 % (20926)------------------------------
% 38.16/6.50 % (20928)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_20195 for (2947ds/1312Mi)
% 38.16/6.51 % (20929)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_20195 for (2947ds/672Mi)
% 38.45/6.70 % (20929)Instruction limit reached!
% 38.45/6.70 % (20929)------------------------------
% 38.45/6.70 % (20929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.45/6.70 % (20929)Termination reason: Unknown
% 38.45/6.70 % (20929)Termination phase: Saturation
% 38.45/6.70
% 38.45/6.70 % (20929)Memory used [KB]: 11385
% 38.45/6.70 % (20929)Time elapsed: 0.200 s
% 38.45/6.70 % (20929)Instructions burned: 672 (million)
% 38.45/6.70 % (20929)------------------------------
% 38.45/6.70 % (20929)------------------------------
% 38.45/6.71 % (20930)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_20195 for (2945ds/1897Mi)
% 38.76/6.83 % (20928)Instruction limit reached!
% 38.76/6.83 % (20928)------------------------------
% 38.76/6.83 % (20928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.76/6.83 % (20928)Termination reason: Unknown
% 38.76/6.83 % (20928)Termination phase: Saturation
% 38.76/6.83
% 38.76/6.83 % (20928)Memory used [KB]: 17526
% 38.76/6.83 % (20928)Time elapsed: 0.327 s
% 38.76/6.83 % (20928)Instructions burned: 1314 (million)
% 38.76/6.83 % (20928)------------------------------
% 38.76/6.83 % (20928)------------------------------
% 38.76/6.84 % (20931)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_20195 for (2944ds/1202Mi)
% 38.76/6.86 % (20927)Instruction limit reached!
% 38.76/6.86 % (20927)------------------------------
% 38.76/6.86 % (20927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.76/6.86 % (20927)Termination reason: Unknown
% 38.76/6.86 % (20927)Termination phase: Saturation
% 38.76/6.86
% 38.76/6.86 % (20927)Memory used [KB]: 8059
% 38.76/6.86 % (20927)Time elapsed: 0.373 s
% 38.76/6.86 % (20927)Instructions burned: 1322 (million)
% 38.76/6.86 % (20927)------------------------------
% 38.76/6.86 % (20927)------------------------------
% 38.76/6.87 % (20932)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_20195 for (2944ds/1493Mi)
% 42.18/7.11 % (20924)Instruction limit reached!
% 42.18/7.11 % (20924)------------------------------
% 42.18/7.11 % (20924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.18/7.11 % (20924)Termination reason: Unknown
% 42.18/7.11 % (20924)Termination phase: Saturation
% 42.18/7.11
% 42.18/7.11 % (20924)Memory used [KB]: 9722
% 42.18/7.11 % (20924)Time elapsed: 0.711 s
% 42.18/7.11 % (20924)Instructions burned: 2402 (million)
% 42.18/7.11 % (20924)------------------------------
% 42.18/7.11 % (20924)------------------------------
% 42.90/7.12 % (20933)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_20195 for (2941ds/7679Mi)
% 42.90/7.17 % (20931)Instruction limit reached!
% 42.90/7.17 % (20931)------------------------------
% 42.90/7.17 % (20931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.90/7.17 % (20931)Termination reason: Unknown
% 42.90/7.17 % (20931)Termination phase: Saturation
% 42.90/7.17
% 42.90/7.17 % (20931)Memory used [KB]: 9722
% 42.90/7.17 % (20931)Time elapsed: 0.331 s
% 42.90/7.17 % (20931)Instructions burned: 1204 (million)
% 42.90/7.17 % (20931)------------------------------
% 42.90/7.17 % (20931)------------------------------
% 42.90/7.18 % (20934)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_20195 for (2941ds/340Mi)
% 43.37/7.23 % (20932)Instruction limit reached!
% 43.37/7.23 % (20932)------------------------------
% 43.37/7.23 % (20932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.37/7.23 % (20932)Termination reason: Unknown
% 43.37/7.23 % (20932)Termination phase: Saturation
% 43.37/7.23
% 43.37/7.23 % (20932)Memory used [KB]: 8187
% 43.37/7.23 % (20932)Time elapsed: 0.363 s
% 43.37/7.23 % (20932)Instructions burned: 1494 (million)
% 43.37/7.23 % (20932)------------------------------
% 43.37/7.23 % (20932)------------------------------
% 43.37/7.24 % (20935)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_20195 for (2940ds/3672Mi)
% 43.37/7.27 % (20934)Instruction limit reached!
% 43.37/7.27 % (20934)------------------------------
% 43.37/7.27 % (20934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.37/7.27 % (20934)Termination reason: Unknown
% 43.37/7.27 % (20934)Termination phase: Saturation
% 43.37/7.27
% 43.37/7.27 % (20934)Memory used [KB]: 11001
% 43.37/7.27 % (20934)Time elapsed: 0.093 s
% 43.37/7.27 % (20934)Instructions burned: 341 (million)
% 43.37/7.27 % (20934)------------------------------
% 43.37/7.27 % (20934)------------------------------
% 43.37/7.28 % (20936)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_20195 for (2940ds/1535Mi)
% 43.92/7.30 % (20930)Instruction limit reached!
% 43.92/7.30 % (20930)------------------------------
% 43.92/7.30 % (20930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.92/7.30 % (20930)Termination reason: Unknown
% 43.92/7.30 % (20930)Termination phase: Saturation
% 43.92/7.30
% 43.92/7.30 % (20930)Memory used [KB]: 14711
% 43.92/7.30 % (20930)Time elapsed: 0.586 s
% 43.92/7.30 % (20930)Instructions burned: 1899 (million)
% 43.92/7.30 % (20930)------------------------------
% 43.92/7.30 % (20930)------------------------------
% 43.92/7.31 % (20937)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_20195 for (2939ds/4637Mi)
% 44.54/7.60 % (20923)Instruction limit reached!
% 44.54/7.60 % (20923)------------------------------
% 44.54/7.60 % (20923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.54/7.60 % (20923)Termination reason: Unknown
% 44.54/7.60 % (20923)Termination phase: Saturation
% 44.54/7.60
% 44.54/7.60 % (20923)Memory used [KB]: 7931
% 44.54/7.60 % (20923)Time elapsed: 1.247 s
% 44.84/7.60 % (20923)Instructions burned: 5063 (million)
% 44.84/7.60 % (20923)------------------------------
% 44.84/7.60 % (20923)------------------------------
% 44.84/7.61 % (20938)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_20195 for (2936ds/3174Mi)
% 44.84/7.61 % (20904)Instruction limit reached!
% 44.84/7.61 % (20904)------------------------------
% 44.84/7.61 % (20904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.84/7.61 % (20904)Termination reason: Unknown
% 44.84/7.61 % (20904)Termination phase: Saturation
% 44.84/7.61
% 44.84/7.61 % (20904)Memory used [KB]: 14583
% 44.84/7.61 % (20904)Time elapsed: 1.988 s
% 44.84/7.61 % (20904)Instructions burned: 6455 (million)
% 44.84/7.61 % (20904)------------------------------
% 44.84/7.61 % (20904)------------------------------
% 44.84/7.62 % (20939)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_20195 for (2936ds/307Mi)
% 44.84/7.64 % (20936)Instruction limit reached!
% 44.84/7.64 % (20936)------------------------------
% 44.84/7.64 % (20936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.84/7.64 % (20936)Termination reason: Unknown
% 44.84/7.64 % (20936)Termination phase: Saturation
% 44.84/7.64
% 44.84/7.64 % (20936)Memory used [KB]: 15735
% 44.84/7.64 % (20936)Time elapsed: 0.365 s
% 44.84/7.64 % (20936)Instructions burned: 1536 (million)
% 44.84/7.64 % (20936)------------------------------
% 44.84/7.64 % (20936)------------------------------
% 44.84/7.65 % (20940)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_20195 for (2936ds/3619Mi)
% 45.35/7.70 % (20939)Instruction limit reached!
% 45.35/7.70 % (20939)------------------------------
% 45.35/7.70 % (20939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.35/7.70 % (20939)Termination reason: Unknown
% 45.35/7.70 % (20939)Termination phase: Saturation
% 45.35/7.70
% 45.35/7.70 % (20939)Memory used [KB]: 7547
% 45.35/7.70 % (20939)Time elapsed: 0.077 s
% 45.35/7.70 % (20939)Instructions burned: 309 (million)
% 45.35/7.70 % (20939)------------------------------
% 45.35/7.70 % (20939)------------------------------
% 45.35/7.71 % (20941)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_20195 for (2935ds/2325Mi)
% 49.88/8.17 % (20941)Refutation not found, non-redundant clauses discarded% (20941)------------------------------
% 49.88/8.17 % (20941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.88/8.17 % (20941)Termination reason: Refutation not found, non-redundant clauses discarded
% 49.88/8.17
% 49.88/8.17 % (20941)Memory used [KB]: 16758
% 49.88/8.17 % (20941)Time elapsed: 0.466 s
% 49.88/8.17 % (20941)Instructions burned: 1614 (million)
% 49.88/8.17 % (20941)------------------------------
% 49.88/8.17 % (20941)------------------------------
% 49.88/8.19 % (20958)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_20195 for (2931ds/2341Mi)
% 49.88/8.19 % (20925)Instruction limit reached!
% 49.88/8.19 % (20925)------------------------------
% 49.88/8.19 % (20925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.88/8.19 % (20925)Termination reason: Unknown
% 49.88/8.19 % (20925)Termination phase: Saturation
% 49.88/8.19
% 49.88/8.19 % (20925)Memory used [KB]: 13560
% 49.88/8.19 % (20925)Time elapsed: 1.778 s
% 49.88/8.19 % (20925)Instructions burned: 5800 (million)
% 49.88/8.19 % (20925)------------------------------
% 49.88/8.19 % (20925)------------------------------
% 50.48/8.20 % (20959)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_20195 for (2930ds/7257Mi)
% 50.97/8.31 % (20938)Refutation not found, non-redundant clauses discarded% (20938)------------------------------
% 50.97/8.31 % (20938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.97/8.31 % (20938)Termination reason: Refutation not found, non-redundant clauses discarded
% 50.97/8.31
% 50.97/8.31 % (20938)Memory used [KB]: 20084
% 50.97/8.31 % (20938)Time elapsed: 0.706 s
% 50.97/8.31 % (20938)Instructions burned: 2397 (million)
% 50.97/8.31 % (20938)------------------------------
% 50.97/8.31 % (20938)------------------------------
% 50.97/8.32 % (20960)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_20195 for (2929ds/3710Mi)
% 50.97/8.35 % (20935)Instruction limit reached!
% 50.97/8.35 % (20935)------------------------------
% 50.97/8.35 % (20935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.97/8.35 % (20935)Termination reason: Unknown
% 50.97/8.35 % (20935)Termination phase: Saturation
% 50.97/8.35
% 50.97/8.35 % (20935)Memory used [KB]: 12792
% 50.97/8.35 % (20935)Time elapsed: 1.115 s
% 50.97/8.35 % (20935)Instructions burned: 3674 (million)
% 50.97/8.35 % (20935)------------------------------
% 50.97/8.35 % (20935)------------------------------
% 50.97/8.36 % (20961)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_20195 for (2929ds/326Mi)
% 51.36/8.45 % (20961)Instruction limit reached!
% 51.36/8.45 % (20961)------------------------------
% 51.36/8.45 % (20961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.36/8.45 % (20961)Termination reason: Unknown
% 51.36/8.45 % (20961)Termination phase: Saturation
% 51.36/8.45
% 51.36/8.45 % (20961)Memory used [KB]: 8571
% 51.36/8.45 % (20961)Time elapsed: 0.085 s
% 51.36/8.45 % (20961)Instructions burned: 326 (million)
% 51.36/8.45 % (20961)------------------------------
% 51.36/8.45 % (20961)------------------------------
% 51.36/8.46 % (20962)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_20195 for (2928ds/1100Mi)
% 52.37/8.70 % (20940)Instruction limit reached!
% 52.37/8.70 % (20940)------------------------------
% 52.37/8.70 % (20940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.37/8.70 % (20940)Termination reason: Unknown
% 52.37/8.70 % (20940)Termination phase: Saturation
% 52.37/8.70
% 52.37/8.70 % (20940)Memory used [KB]: 16630
% 52.37/8.70 % (20940)Time elapsed: 1.048 s
% 52.37/8.70 % (20940)Instructions burned: 3621 (million)
% 52.37/8.70 % (20940)------------------------------
% 52.37/8.70 % (20940)------------------------------
% 52.37/8.71 % (20937)Instruction limit reached!
% 52.37/8.71 % (20937)------------------------------
% 52.37/8.71 % (20937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.37/8.71 % (20937)Termination reason: Unknown
% 52.37/8.71 % (20937)Termination phase: Saturation
% 52.37/8.71
% 52.37/8.71 % (20937)Memory used [KB]: 12025
% 52.37/8.71 % (20937)Time elapsed: 1.399 s
% 52.37/8.71 % (20937)Instructions burned: 4638 (million)
% 52.37/8.71 % (20937)------------------------------
% 52.37/8.71 % (20937)------------------------------
% 52.37/8.71 % (20963)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_20195 for (2925ds/406Mi)
% 52.37/8.72 % (20964)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_20195 for (2925ds/1871Mi)
% 52.37/8.79 % (20962)Instruction limit reached!
% 52.37/8.79 % (20962)------------------------------
% 52.37/8.79 % (20962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.37/8.79 % (20962)Termination reason: Unknown
% 52.37/8.79 % (20962)Termination phase: Saturation
% 52.37/8.79
% 52.37/8.79 % (20962)Memory used [KB]: 15863
% 52.37/8.79 % (20962)Time elapsed: 0.338 s
% 52.37/8.79 % (20962)Instructions burned: 1100 (million)
% 52.37/8.79 % (20962)------------------------------
% 52.37/8.79 % (20962)------------------------------
% 52.86/8.80 % (20965)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_20195 for (2924ds/1194Mi)
% 52.86/8.82 % (20963)Instruction limit reached!
% 52.86/8.82 % (20963)------------------------------
% 52.86/8.82 % (20963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.86/8.82 % (20963)Termination reason: Unknown
% 52.86/8.82 % (20963)Termination phase: Saturation
% 52.86/8.82
% 52.86/8.82 % (20963)Memory used [KB]: 7803
% 52.86/8.82 % (20963)Time elapsed: 0.106 s
% 52.86/8.82 % (20963)Instructions burned: 407 (million)
% 52.86/8.82 % (20963)------------------------------
% 52.86/8.82 % (20963)------------------------------
% 52.86/8.83 % (20966)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_20195 for (2924ds/474Mi)
% 52.86/8.89 % (20958)Instruction limit reached!
% 52.86/8.89 % (20958)------------------------------
% 52.86/8.89 % (20958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.86/8.89 % (20958)Termination reason: Unknown
% 52.86/8.89 % (20958)Termination phase: Saturation
% 52.86/8.89
% 52.86/8.89 % (20958)Memory used [KB]: 11385
% 52.86/8.89 % (20958)Time elapsed: 0.704 s
% 52.86/8.89 % (20958)Instructions burned: 2341 (million)
% 52.86/8.89 % (20958)------------------------------
% 52.86/8.89 % (20958)------------------------------
% 53.79/8.90 % (20967)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_20195 for (2923ds/3115Mi)
% 53.79/8.94 % (20966)Instruction limit reached!
% 53.79/8.94 % (20966)------------------------------
% 53.79/8.94 % (20966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.79/8.94 % (20966)Termination reason: Unknown
% 53.79/8.94 % (20966)Termination phase: Saturation
% 53.79/8.94
% 53.79/8.94 % (20966)Memory used [KB]: 7675
% 53.79/8.94 % (20966)Time elapsed: 0.120 s
% 53.79/8.94 % (20966)Instructions burned: 475 (million)
% 53.79/8.94 % (20966)------------------------------
% 53.79/8.94 % (20966)------------------------------
% 53.79/8.95 % (20968)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_20195 for (2923ds/831Mi)
% 56.91/9.17 % (20965)Instruction limit reached!
% 56.91/9.17 % (20965)------------------------------
% 56.91/9.17 % (20965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.91/9.17 % (20965)Termination reason: Unknown
% 56.91/9.17 % (20965)Termination phase: Saturation
% 56.91/9.17
% 56.91/9.17 % (20965)Memory used [KB]: 13176
% 56.91/9.17 % (20965)Time elapsed: 0.365 s
% 56.91/9.17 % (20965)Instructions burned: 1196 (million)
% 56.91/9.17 % (20965)------------------------------
% 56.91/9.17 % (20965)------------------------------
% 56.91/9.18 % (20969)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_20195 for (2920ds/1188Mi)
% 56.91/9.19 % (20968)Instruction limit reached!
% 56.91/9.19 % (20968)------------------------------
% 56.91/9.19 % (20968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.91/9.19 % (20968)Termination reason: Unknown
% 56.91/9.19 % (20968)Termination phase: Saturation
% 56.91/9.19
% 56.91/9.19 % (20968)Memory used [KB]: 10362
% 56.91/9.19 % (20968)Time elapsed: 0.242 s
% 56.91/9.19 % (20968)Instructions burned: 833 (million)
% 56.91/9.19 % (20968)------------------------------
% 56.91/9.19 % (20968)------------------------------
% 57.48/9.20 % (20970)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_20195 for (2920ds/2868Mi)
% 57.48/9.26 % (20960)Instruction limit reached!
% 57.48/9.26 % (20960)------------------------------
% 57.48/9.26 % (20960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.48/9.26 % (20960)Termination reason: Unknown
% 57.48/9.26 % (20960)Termination phase: Saturation
% 57.48/9.26
% 57.48/9.26 % (20960)Memory used [KB]: 18805
% 57.48/9.26 % (20960)Time elapsed: 0.938 s
% 57.48/9.26 % (20960)Instructions burned: 3711 (million)
% 57.48/9.26 % (20960)------------------------------
% 57.48/9.26 % (20960)------------------------------
% 57.48/9.27 % (20971)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_20195 for (2920ds/1516Mi)
% 57.48/9.28 % (20964)Instruction limit reached!
% 57.48/9.28 % (20964)------------------------------
% 57.48/9.28 % (20964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.48/9.28 % (20964)Termination reason: Unknown
% 57.48/9.28 % (20964)Termination phase: Saturation
% 57.48/9.28
% 57.48/9.28 % (20964)Memory used [KB]: 20212
% 57.48/9.28 % (20964)Time elapsed: 0.583 s
% 57.48/9.28 % (20964)Instructions burned: 1871 (million)
% 57.48/9.28 % (20964)------------------------------
% 57.48/9.28 % (20964)------------------------------
% 57.48/9.29 % (20972)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_20195 for (2919ds/2321Mi)
% 57.95/9.39 % (20933)Instruction limit reached!
% 57.95/9.39 % (20933)------------------------------
% 57.95/9.39 % (20933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.95/9.39 % (20933)Termination reason: Unknown
% 57.95/9.39 % (20933)Termination phase: Saturation
% 57.95/9.39
% 57.95/9.39 % (20933)Memory used [KB]: 18293
% 57.95/9.39 % (20933)Time elapsed: 2.270 s
% 57.95/9.39 % (20933)Instructions burned: 7680 (million)
% 57.95/9.39 % (20933)------------------------------
% 57.95/9.39 % (20933)------------------------------
% 58.25/9.40 % (20973)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_20195 for (2918ds/2812Mi)
% 58.25/9.47 % (20969)Instruction limit reached!
% 58.25/9.47 % (20969)------------------------------
% 58.25/9.47 % (20969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.25/9.47 % (20969)Termination reason: Unknown
% 58.25/9.47 % (20969)Termination phase: Saturation
% 58.25/9.47
% 58.25/9.47 % (20969)Memory used [KB]: 16758
% 58.25/9.47 % (20969)Time elapsed: 0.295 s
% 58.25/9.47 % (20969)Instructions burned: 1189 (million)
% 58.25/9.47 % (20969)------------------------------
% 58.25/9.47 % (20969)------------------------------
% 58.25/9.48 % (20974)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_20195 for (2917ds/4604Mi)
% 58.95/9.67 % (20967)Instruction limit reached!
% 58.95/9.67 % (20967)------------------------------
% 58.95/9.67 % (20967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.95/9.67 % (20967)Termination reason: Unknown
% 58.95/9.67 % (20967)Termination phase: Saturation
% 58.95/9.67
% 58.95/9.67 % (20967)Memory used [KB]: 17654
% 58.95/9.67 % (20967)Time elapsed: 0.772 s
% 58.95/9.67 % (20967)Instructions burned: 3118 (million)
% 58.95/9.67 % (20967)------------------------------
% 58.95/9.67 % (20967)------------------------------
% 58.95/9.68 % (20975)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_20195 for (2915ds/2678Mi)
% 59.14/9.73 % (20971)Instruction limit reached!
% 59.14/9.73 % (20971)------------------------------
% 59.14/9.73 % (20971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.14/9.73 % (20971)Termination reason: Unknown
% 59.14/9.73 % (20971)Termination phase: Saturation
% 59.14/9.73
% 59.14/9.73 % (20971)Memory used [KB]: 12537
% 59.14/9.73 % (20971)Time elapsed: 0.461 s
% 59.14/9.73 % (20971)Instructions burned: 1516 (million)
% 59.14/9.73 % (20971)------------------------------
% 59.14/9.73 % (20971)------------------------------
% 59.14/9.74 % (20976)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_20195 for (2915ds/643Mi)
% 59.71/9.86 % (20972)Instruction limit reached!
% 59.71/9.86 % (20972)------------------------------
% 59.71/9.86 % (20972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.71/9.86 % (20972)Termination reason: Unknown
% 59.71/9.86 % (20972)Termination phase: Saturation
% 59.71/9.86
% 59.71/9.86 % (20972)Memory used [KB]: 16758
% 59.71/9.86 % (20972)Time elapsed: 0.574 s
% 59.71/9.86 % (20972)Instructions burned: 2322 (million)
% 59.71/9.86 % (20972)------------------------------
% 59.71/9.86 % (20972)------------------------------
% 59.71/9.87 % (20977)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_20195 for (2914ds/458Mi)
% 60.39/9.90 % (20976)Instruction limit reached!
% 60.39/9.90 % (20976)------------------------------
% 60.39/9.90 % (20976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 60.39/9.90 % (20976)Termination reason: Unknown
% 60.39/9.90 % (20976)Termination phase: Saturation
% 60.39/9.90
% 60.39/9.90 % (20976)Memory used [KB]: 7803
% 60.39/9.90 % (20976)Time elapsed: 0.158 s
% 60.39/9.90 % (20976)Instructions burned: 646 (million)
% 60.39/9.90 % (20976)------------------------------
% 60.39/9.90 % (20976)------------------------------
% 60.39/9.91 % (20978)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_20195 for (2913ds/2546Mi)
% 60.39/9.91 % (20970)Instruction limit reached!
% 60.39/9.91 % (20970)------------------------------
% 60.39/9.91 % (20970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 60.39/9.91 % (20970)Termination reason: Unknown
% 60.39/9.91 % (20970)Termination phase: Saturation
% 60.39/9.91
% 60.39/9.91 % (20970)Memory used [KB]: 7803
% 60.39/9.91 % (20970)Time elapsed: 0.703 s
% 60.39/9.91 % (20970)Instructions burned: 2871 (million)
% 60.39/9.91 % (20970)------------------------------
% 60.39/9.91 % (20970)------------------------------
% 60.39/9.92 % (20979)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_20195 for (2913ds/1432Mi)
% 60.39/9.98 % (20977)Instruction limit reached!
% 60.39/9.98 % (20977)------------------------------
% 60.39/9.98 % (20977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 60.39/9.98 % (20977)Termination reason: Unknown
% 60.39/9.98 % (20977)Termination phase: Saturation
% 60.39/9.98
% 60.39/9.98 % (20977)Memory used [KB]: 7675
% 60.39/9.98 % (20977)Time elapsed: 0.112 s
% 60.39/9.98 % (20977)Instructions burned: 458 (million)
% 60.39/9.98 % (20977)------------------------------
% 60.39/9.98 % (20977)------------------------------
% 60.39/9.99 % (20980)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_20195 for (2912ds/386Mi)
% 63.20/10.09 % (20980)Instruction limit reached!
% 63.20/10.09 % (20980)------------------------------
% 63.20/10.09 % (20980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.20/10.09 % (20980)Termination reason: Unknown
% 63.20/10.09 % (20980)Termination phase: Saturation
% 63.20/10.09
% 63.20/10.09 % (20980)Memory used [KB]: 7675
% 63.20/10.09 % (20980)Time elapsed: 0.095 s
% 63.20/10.09 % (20980)Instructions burned: 386 (million)
% 63.20/10.09 % (20980)------------------------------
% 63.20/10.09 % (20980)------------------------------
% 63.20/10.10 % (20981)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_20195 for (2911ds/360Mi)
% 63.89/10.18 % (20981)Instruction limit reached!
% 63.89/10.18 % (20981)------------------------------
% 63.89/10.18 % (20981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.89/10.18 % (20981)Termination reason: Unknown
% 63.89/10.18 % (20981)Termination phase: Saturation
% 63.89/10.18
% 63.89/10.18 % (20981)Memory used [KB]: 7547
% 63.89/10.18 % (20981)Time elapsed: 0.090 s
% 63.89/10.18 % (20981)Instructions burned: 361 (million)
% 63.89/10.18 % (20981)------------------------------
% 63.89/10.18 % (20981)------------------------------
% 63.89/10.19 % (21012)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_20195 for (2910ds/5446Mi)
% 64.50/10.25 % (20973)Instruction limit reached!
% 64.50/10.25 % (20973)------------------------------
% 64.50/10.25 % (20973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.50/10.25 % (20973)Termination reason: Unknown
% 64.50/10.25 % (20973)Termination phase: Saturation
% 64.50/10.25
% 64.50/10.25 % (20973)Memory used [KB]: 13432
% 64.50/10.25 % (20973)Time elapsed: 0.849 s
% 64.50/10.25 % (20973)Instructions burned: 2815 (million)
% 64.50/10.25 % (20973)------------------------------
% 64.50/10.25 % (20973)------------------------------
% 64.50/10.26 % (21013)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_20195 for (2910ds/2573Mi)
% 64.50/10.26 % (20979)Instruction limit reached!
% 64.50/10.26 % (20979)------------------------------
% 64.50/10.26 % (20979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.50/10.26 % (20979)Termination reason: Unknown
% 64.50/10.26 % (20979)Termination phase: Saturation
% 64.50/10.26
% 64.50/10.26 % (20979)Memory used [KB]: 17142
% 64.50/10.26 % (20979)Time elapsed: 0.344 s
% 64.50/10.26 % (20979)Instructions burned: 1432 (million)
% 64.50/10.26 % (20979)------------------------------
% 64.50/10.26 % (20979)------------------------------
% 64.50/10.27 % (21014)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_20195 for (2910ds/2655Mi)
% 65.03/10.32 % (20975)Instruction limit reached!
% 65.03/10.32 % (20975)------------------------------
% 65.03/10.32 % (20975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.03/10.32 % (20975)Termination reason: Unknown
% 65.03/10.32 % (20975)Termination phase: Saturation
% 65.03/10.32
% 65.03/10.32 % (20975)Memory used [KB]: 26865
% 65.03/10.32 % (20975)Time elapsed: 0.645 s
% 65.03/10.32 % (20975)Instructions burned: 2680 (million)
% 65.03/10.32 % (20975)------------------------------
% 65.03/10.32 % (20975)------------------------------
% 65.03/10.33 % (21015)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_20195 for (2909ds/2781Mi)
% 65.03/10.39 % (20959)Instruction limit reached!
% 65.03/10.39 % (20959)------------------------------
% 65.03/10.39 % (20959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.03/10.39 % (20959)Termination reason: Unknown
% 65.03/10.39 % (20959)Termination phase: Saturation
% 65.03/10.39
% 65.03/10.39 % (20959)Memory used [KB]: 10362
% 65.03/10.39 % (20959)Time elapsed: 2.188 s
% 65.03/10.39 % (20959)Instructions burned: 7257 (million)
% 65.03/10.39 % (20959)------------------------------
% 65.03/10.39 % (20959)------------------------------
% 65.03/10.40 % (21016)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_20195 for (2908ds/307Mi)
% 65.36/10.47 % (21016)Instruction limit reached!
% 65.36/10.47 % (21016)------------------------------
% 65.36/10.47 % (21016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.36/10.47 % (21016)Termination reason: Unknown
% 65.36/10.47 % (21016)Termination phase: Saturation
% 65.36/10.47
% 65.36/10.47 % (21016)Memory used [KB]: 7547
% 65.36/10.47 % (21016)Time elapsed: 0.076 s
% 65.36/10.47 % (21016)Instructions burned: 309 (million)
% 65.36/10.47 % (21016)------------------------------
% 65.36/10.47 % (21016)------------------------------
% 65.36/10.48 % (21017)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_20195 for (2908ds/1548Mi)
% 65.85/10.64 % (20978)Instruction limit reached!
% 65.85/10.64 % (20978)------------------------------
% 65.85/10.64 % (20978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.85/10.64 % (20978)Termination reason: Unknown
% 65.85/10.64 % (20978)Termination phase: Saturation
% 65.85/10.64
% 65.85/10.64 % (20978)Memory used [KB]: 10746
% 65.85/10.64 % (20978)Time elapsed: 0.732 s
% 65.85/10.64 % (20978)Instructions burned: 2547 (million)
% 65.85/10.64 % (20978)------------------------------
% 65.85/10.64 % (20978)------------------------------
% 65.85/10.65 % (21018)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_20195 for (2906ds/5214Mi)
% 66.11/10.86 % (20974)Instruction limit reached!
% 66.11/10.86 % (20974)------------------------------
% 66.11/10.86 % (20974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.11/10.86 % (20974)Termination reason: Unknown
% 66.11/10.86 % (20974)Termination phase: Saturation
% 66.11/10.86
% 66.11/10.86 % (20974)Memory used [KB]: 14328
% 66.11/10.86 % (20974)Time elapsed: 1.381 s
% 66.11/10.86 % (20974)Instructions burned: 4606 (million)
% 66.11/10.86 % (20974)------------------------------
% 66.11/10.86 % (20974)------------------------------
% 66.11/10.87 % (21019)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_20195 for (2904ds/3201Mi)
% 66.19/10.90 % (21013)Instruction limit reached!
% 66.19/10.90 % (21013)------------------------------
% 66.19/10.90 % (21013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.19/10.90 % (21013)Termination reason: Unknown
% 66.19/10.90 % (21013)Termination phase: Saturation
% 66.19/10.90
% 66.19/10.90 % (21013)Memory used [KB]: 19189
% 66.19/10.90 % (21013)Time elapsed: 0.644 s
% 66.19/10.90 % (21013)Instructions burned: 2575 (million)
% 66.19/10.90 % (21013)------------------------------
% 66.19/10.90 % (21013)------------------------------
% 66.19/10.91 % (21020)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_20195 for (2903ds/454Mi)
% 66.19/10.93 % (21014)Instruction limit reached!
% 66.19/10.93 % (21014)------------------------------
% 66.19/10.93 % (21014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.19/10.93 % (21014)Termination reason: Unknown
% 66.19/10.93 % (21014)Termination phase: Saturation
% 66.19/10.93
% 66.19/10.93 % (21014)Memory used [KB]: 5756
% 66.19/10.93 % (21014)Time elapsed: 0.659 s
% 66.19/10.93 % (21014)Instructions burned: 2655 (million)
% 66.19/10.93 % (21014)------------------------------
% 66.19/10.93 % (21014)------------------------------
% 66.19/10.94 % (21021)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_20195 for (2903ds/3049Mi)
% 66.19/10.94 % (21017)Instruction limit reached!
% 66.19/10.94 % (21017)------------------------------
% 66.19/10.94 % (21017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.19/10.94 % (21017)Termination reason: Unknown
% 66.19/10.94 % (21017)Termination phase: Saturation
% 66.19/10.94
% 66.19/10.94 % (21017)Memory used [KB]: 10746
% 66.19/10.94 % (21017)Time elapsed: 0.463 s
% 66.19/10.94 % (21017)Instructions burned: 1550 (million)
% 66.19/10.94 % (21017)------------------------------
% 66.19/10.94 % (21017)------------------------------
% 66.19/10.95 % (21022)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_20195 for (2903ds/7311Mi)
% 70.23/11.02 % (21020)Instruction limit reached!
% 70.23/11.02 % (21020)------------------------------
% 70.23/11.02 % (21020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.23/11.02 % (21020)Termination reason: Unknown
% 70.23/11.02 % (21020)Termination phase: Saturation
% 70.23/11.02
% 70.23/11.02 % (21020)Memory used [KB]: 12153
% 70.23/11.02 % (21020)Time elapsed: 0.112 s
% 70.23/11.02 % (21020)Instructions burned: 456 (million)
% 70.23/11.02 % (21020)------------------------------
% 70.23/11.02 % (21020)------------------------------
% 70.23/11.03 % (21023)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_20195 for (2902ds/6804Mi)
% 70.85/11.17 % (21015)Instruction limit reached!
% 70.85/11.17 % (21015)------------------------------
% 70.85/11.17 % (21015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.85/11.17 % (21015)Termination reason: Unknown
% 70.85/11.17 % (21015)Termination phase: Saturation
% 70.85/11.17
% 70.85/11.17 % (21015)Memory used [KB]: 9338
% 70.85/11.17 % (21015)Time elapsed: 0.833 s
% 70.85/11.17 % (21015)Instructions burned: 2782 (million)
% 70.85/11.17 % (21015)------------------------------
% 70.85/11.17 % (21015)------------------------------
% 70.85/11.18 % (21024)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_20195 for (2901ds/1683Mi)
% 73.33/11.63 % (21024)Instruction limit reached!
% 73.33/11.63 % (21024)------------------------------
% 73.33/11.63 % (21024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.33/11.63 % (21024)Termination reason: Unknown
% 73.33/11.63 % (21024)Termination phase: Saturation
% 73.33/11.63
% 73.33/11.63 % (21024)Memory used [KB]: 21236
% 73.33/11.63 % (21024)Time elapsed: 0.453 s
% 73.33/11.63 % (21024)Instructions burned: 1684 (million)
% 73.33/11.63 % (21024)------------------------------
% 73.33/11.63 % (21024)------------------------------
% 73.33/11.64 % (21025)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_20195 for (2896ds/4688Mi)
% 74.80/11.83 % (21019)Instruction limit reached!
% 74.80/11.83 % (21019)------------------------------
% 74.80/11.83 % (21019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 74.80/11.83 % (21019)Termination reason: Unknown
% 74.80/11.83 % (21019)Termination phase: Saturation
% 74.80/11.83
% 74.80/11.83 % (21019)Memory used [KB]: 12665
% 74.80/11.83 % (21019)Time elapsed: 0.964 s
% 74.80/11.83 % (21019)Instructions burned: 3203 (million)
% 74.80/11.83 % (21019)------------------------------
% 74.80/11.83 % (21019)------------------------------
% 74.80/11.84 % (21026)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_20195 for (2894ds/2207Mi)
% 74.80/11.85 % (21021)Instruction limit reached!
% 74.80/11.85 % (21021)------------------------------
% 74.80/11.85 % (21021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 74.80/11.85 % (21021)Termination reason: Unknown
% 74.80/11.85 % (21021)Termination phase: Saturation
% 74.80/11.85
% 74.80/11.85 % (21021)Memory used [KB]: 11769
% 74.80/11.85 % (21021)Time elapsed: 0.911 s
% 74.80/11.85 % (21021)Instructions burned: 3049 (million)
% 74.80/11.85 % (21021)------------------------------
% 74.80/11.85 % (21021)------------------------------
% 74.80/11.86 % (21027)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_20195 for (2894ds/8216Mi)
% 74.80/11.88 % (21012)Instruction limit reached!
% 74.80/11.88 % (21012)------------------------------
% 74.80/11.88 % (21012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 74.80/11.88 % (21012)Termination reason: Unknown
% 74.80/11.88 % (21012)Termination phase: Saturation
% 74.80/11.88
% 74.80/11.88 % (21012)Memory used [KB]: 16758
% 74.80/11.88 % (21012)Time elapsed: 1.688 s
% 74.80/11.88 % (21012)Instructions burned: 5447 (million)
% 74.80/11.88 % (21012)------------------------------
% 74.80/11.88 % (21012)------------------------------
% 74.80/11.89 % (21028)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_20195 for (2894ds/430Mi)
% 75.20/12.00 % (21028)Instruction limit reached!
% 75.20/12.00 % (21028)------------------------------
% 75.20/12.00 % (21028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.20/12.00 % (21028)Termination reason: Unknown
% 75.20/12.00 % (21028)Termination phase: Saturation
% 75.20/12.00
% 75.20/12.00 % (21028)Memory used [KB]: 7675
% 75.20/12.00 % (21028)Time elapsed: 0.106 s
% 75.20/12.00 % (21028)Instructions burned: 432 (million)
% 75.20/12.00 % (21028)------------------------------
% 75.20/12.00 % (21028)------------------------------
% 75.20/12.01 % (21029)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_20195 for (2892ds/2012Mi)
% 77.82/12.19 % (21018)Instruction limit reached!
% 77.82/12.19 % (21018)------------------------------
% 77.82/12.19 % (21018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.82/12.19 % (21018)Termination reason: Unknown
% 77.82/12.19 % (21018)Termination phase: Saturation
% 77.82/12.19
% 77.82/12.19 % (21018)Memory used [KB]: 11641
% 77.82/12.19 % (21018)Time elapsed: 1.540 s
% 77.82/12.19 % (21018)Instructions burned: 5217 (million)
% 77.82/12.19 % (21018)------------------------------
% 77.82/12.19 % (21018)------------------------------
% 78.32/12.20 % (21030)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_20195 for (2890ds/631Mi)
% 78.83/12.37 % (21030)Instruction limit reached!
% 78.83/12.37 % (21030)------------------------------
% 78.83/12.37 % (21030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.83/12.37 % (21030)Termination reason: Unknown
% 78.83/12.37 % (21030)Termination phase: Saturation
% 78.83/12.37
% 78.83/12.37 % (21030)Memory used [KB]: 8443
% 78.83/12.37 % (21030)Time elapsed: 0.197 s
% 78.83/12.37 % (21030)Instructions burned: 633 (million)
% 78.83/12.37 % (21030)------------------------------
% 78.83/12.37 % (21030)------------------------------
% 78.83/12.38 % (21031)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_20195 for (2889ds/8785Mi)
% 80.00/12.50 % (21026)Instruction limit reached!
% 80.00/12.50 % (21026)------------------------------
% 80.00/12.50 % (21026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 80.00/12.50 % (21026)Termination reason: Unknown
% 80.00/12.50 % (21026)Termination phase: Saturation
% 80.00/12.50
% 80.00/12.50 % (21026)Memory used [KB]: 11513
% 80.00/12.50 % (21026)Time elapsed: 0.659 s
% 80.00/12.50 % (21026)Instructions burned: 2209 (million)
% 80.00/12.50 % (21026)------------------------------
% 80.00/12.50 % (21026)------------------------------
% 80.00/12.51 % (21029)Instruction limit reached!
% 80.00/12.51 % (21029)------------------------------
% 80.00/12.51 % (21029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 80.00/12.51 % (21029)Termination reason: Unknown
% 80.00/12.51 % (21029)Termination phase: Saturation
% 80.00/12.51
% 80.00/12.51 % (21029)Memory used [KB]: 12281
% 80.00/12.51 % (21029)Time elapsed: 0.506 s
% 80.00/12.51 % (21029)Instructions burned: 2015 (million)
% 80.00/12.51 % (21029)------------------------------
% 80.00/12.51 % (21029)------------------------------
% 80.00/12.51 % (21032)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_20195 for (2887ds/739Mi)
% 80.00/12.52 % (21033)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_20195 for (2887ds/5473Mi)
% 81.34/12.74 % (21032)Instruction limit reached!
% 81.34/12.74 % (21032)------------------------------
% 81.34/12.74 % (21032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 81.34/12.74 % (21032)Termination reason: Unknown
% 81.34/12.74 % (21032)Termination phase: Saturation
% 81.34/12.74
% 81.34/12.74 % (21032)Memory used [KB]: 13816
% 81.34/12.74 % (21032)Time elapsed: 0.225 s
% 81.34/12.74 % (21032)Instructions burned: 740 (million)
% 81.34/12.74 % (21032)------------------------------
% 81.34/12.74 % (21032)------------------------------
% 81.34/12.75 % (21034)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_20195 for (2885ds/43570Mi)
% 84.22/13.02 % (21023)Instruction limit reached!
% 84.22/13.02 % (21023)------------------------------
% 84.22/13.02 % (21023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 84.22/13.02 % (21023)Termination reason: Unknown
% 84.22/13.02 % (21023)Termination phase: Saturation
% 84.22/13.02
% 84.22/13.02 % (21023)Memory used [KB]: 17526
% 84.22/13.02 % (21023)Time elapsed: 1.996 s
% 84.22/13.02 % (21023)Instructions burned: 6805 (million)
% 84.22/13.02 % (21023)------------------------------
% 84.22/13.02 % (21023)------------------------------
% 84.22/13.03 % (21025)Instruction limit reached!
% 84.22/13.03 % (21025)------------------------------
% 84.22/13.03 % (21025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 84.22/13.03 % (21025)Termination reason: Unknown
% 84.22/13.03 % (21025)Termination phase: Saturation
% 84.22/13.03
% 84.22/13.03 % (21025)Memory used [KB]: 15479
% 84.22/13.03 % (21025)Time elapsed: 1.396 s
% 84.22/13.03 % (21025)Instructions burned: 4689 (million)
% 84.22/13.03 % (21025)------------------------------
% 84.22/13.03 % (21025)------------------------------
% 84.22/13.04 % (21035)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_20195 for (2882ds/8382Mi)
% 84.22/13.04 % (21036)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_20195 for (2882ds/407Mi)
% 84.78/13.15 % (21036)Instruction limit reached!
% 84.78/13.15 % (21036)------------------------------
% 84.78/13.15 % (21036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 84.78/13.15 % (21036)Termination reason: Unknown
% 84.78/13.15 % (21036)Termination phase: Saturation
% 84.78/13.15
% 84.78/13.15 % (21036)Memory used [KB]: 9594
% 84.78/13.15 % (21036)Time elapsed: 0.107 s
% 84.78/13.15 % (21036)Instructions burned: 409 (million)
% 84.78/13.15 % (21036)------------------------------
% 84.78/13.15 % (21036)------------------------------
% 84.78/13.16 % (21037)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_20195 for (2881ds/2971Mi)
% 85.32/13.22 % (21022)Refutation not found, non-redundant clauses discarded% (21022)------------------------------
% 85.32/13.22 % (21022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.32/13.22 % (21022)Termination reason: Refutation not found, non-redundant clauses discarded
% 85.32/13.22
% 85.32/13.22 % (21022)Memory used [KB]: 21364
% 85.32/13.22 % (21022)Time elapsed: 2.273 s
% 85.32/13.22 % (21022)Instructions burned: 7198 (million)
% 85.32/13.22 % (21022)------------------------------
% 85.32/13.22 % (21022)------------------------------
% 85.32/13.24 % (21038)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_20195 for (2880ds/9822Mi)
% 87.76/13.83 % (21027)Instruction limit reached!
% 87.76/13.83 % (21027)------------------------------
% 87.76/13.83 % (21027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 87.76/13.83 % (21027)Termination reason: Unknown
% 87.76/13.83 % (21027)Termination phase: Saturation
% 87.76/13.83
% 87.76/13.83 % (21027)Memory used [KB]: 7931
% 87.76/13.83 % (21027)Time elapsed: 1.973 s
% 87.76/13.83 % (21027)Instructions burned: 8217 (million)
% 87.76/13.83 % (21027)------------------------------
% 87.76/13.83 % (21027)------------------------------
% 87.76/13.84 % (21039)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_20195 for (2874ds/8425Mi)
% 87.76/13.89 % (21037)Instruction limit reached!
% 87.76/13.89 % (21037)------------------------------
% 87.76/13.89 % (21037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 87.76/13.89 % (21037)Termination reason: Unknown
% 87.76/13.89 % (21037)Termination phase: Saturation
% 87.76/13.89
% 87.76/13.89 % (21037)Memory used [KB]: 7803
% 87.76/13.89 % (21037)Time elapsed: 0.728 s
% 87.76/13.89 % (21037)Instructions burned: 2973 (million)
% 87.76/13.89 % (21037)------------------------------
% 87.76/13.89 % (21037)------------------------------
% 88.83/13.90 % (21040)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_20195 for (2873ds/3107Mi)
% 91.94/14.18 % (21033)Instruction limit reached!
% 91.94/14.18 % (21033)------------------------------
% 91.94/14.18 % (21033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.94/14.18 % (21033)Termination reason: Unknown
% 91.94/14.18 % (21033)Termination phase: Saturation
% 91.94/14.18
% 91.94/14.18 % (21033)Memory used [KB]: 13816
% 91.94/14.18 % (21033)Time elapsed: 1.656 s
% 91.94/14.18 % (21033)Instructions burned: 5475 (million)
% 91.94/14.18 % (21033)------------------------------
% 91.94/14.18 % (21033)------------------------------
% 91.94/14.19 % (21041)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_20195 for (2870ds/7967Mi)
% 95.51/14.78 % (21040)Instruction limit reached!
% 95.51/14.78 % (21040)------------------------------
% 95.51/14.78 % (21040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 95.51/14.78 % (21040)Termination reason: Unknown
% 95.51/14.78 % (21040)Termination phase: Saturation
% 95.51/14.78
% 95.51/14.78 % (21040)Memory used [KB]: 17782
% 95.51/14.78 % (21040)Time elapsed: 0.883 s
% 95.51/14.78 % (21040)Instructions burned: 3109 (million)
% 95.51/14.78 % (21040)------------------------------
% 95.51/14.78 % (21040)------------------------------
% 95.51/14.79 % (21191)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_20195 for (2864ds/3629Mi)
% 98.30/15.09 % (21031)Instruction limit reached!
% 98.30/15.09 % (21031)------------------------------
% 98.30/15.09 % (21031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.30/15.09 % (21031)Termination reason: Unknown
% 98.30/15.09 % (21031)Termination phase: Saturation
% 98.30/15.09
% 98.30/15.09 % (21031)Memory used [KB]: 19829
% 98.30/15.09 % (21031)Time elapsed: 2.735 s
% 98.30/15.09 % (21031)Instructions burned: 8787 (million)
% 98.30/15.09 % (21031)------------------------------
% 98.30/15.09 % (21031)------------------------------
% 98.30/15.10 % (21402)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_20195 for (2861ds/939Mi)
% 99.46/15.29 % (21035)Instruction limit reached!
% 99.46/15.29 % (21035)------------------------------
% 99.46/15.29 % (21035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 99.46/15.29 % (21035)Termination reason: Unknown
% 99.46/15.29 % (21035)Termination phase: Saturation
% 99.46/15.29
% 99.46/15.29 % (21035)Memory used [KB]: 14967
% 99.46/15.29 % (21035)Time elapsed: 2.253 s
% 99.46/15.29 % (21035)Instructions burned: 8382 (million)
% 99.46/15.29 % (21035)------------------------------
% 99.46/15.29 % (21035)------------------------------
% 100.05/15.30 % (21545)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_20195 for (2859ds/1188Mi)
% 100.05/15.39 % (21402)Instruction limit reached!
% 100.05/15.39 % (21402)------------------------------
% 100.05/15.39 % (21402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 100.05/15.39 % (21402)Termination reason: Unknown
% 100.05/15.39 % (21402)Termination phase: Saturation
% 100.05/15.39
% 100.05/15.39 % (21402)Memory used [KB]: 10362
% 100.05/15.39 % (21402)Time elapsed: 0.283 s
% 100.05/15.39 % (21402)Instructions burned: 941 (million)
% 100.05/15.39 % (21402)------------------------------
% 100.05/15.39 % (21402)------------------------------
% 100.05/15.40 % (21597)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_20195 for (2858ds/3205Mi)
% 101.85/15.60 % (21545)Instruction limit reached!
% 101.85/15.60 % (21545)------------------------------
% 101.85/15.60 % (21545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 101.85/15.60 % (21545)Termination reason: Unknown
% 101.85/15.60 % (21545)Termination phase: Saturation
% 101.85/15.60
% 101.85/15.60 % (21545)Memory used [KB]: 17270
% 101.85/15.60 % (21545)Time elapsed: 0.304 s
% 101.85/15.60 % (21545)Instructions burned: 1190 (million)
% 101.85/15.60 % (21545)------------------------------
% 101.85/15.60 % (21545)------------------------------
% 101.85/15.61 % (21636)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_20195 for (2856ds/865Mi)
% 102.66/15.70 % (21191)Instruction limit reached!
% 102.66/15.70 % (21191)------------------------------
% 102.66/15.70 % (21191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 102.66/15.70 % (21191)Termination reason: Unknown
% 102.66/15.70 % (21191)Termination phase: Saturation
% 102.66/15.70
% 102.66/15.70 % (21191)Memory used [KB]: 7931
% 102.66/15.70 % (21191)Time elapsed: 0.913 s
% 102.66/15.70 % (21191)Instructions burned: 3631 (million)
% 102.66/15.70 % (21191)------------------------------
% 102.66/15.70 % (21191)------------------------------
% 102.66/15.71 % (21637)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_20195 for (2855ds/7469Mi)
% 103.09/15.85 % (21636)Instruction limit reached!
% 103.09/15.85 % (21636)------------------------------
% 103.09/15.85 % (21636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 103.09/15.85 % (21636)Termination reason: Unknown
% 103.09/15.85 % (21636)Termination phase: Saturation
% 103.09/15.85
% 103.09/15.85 % (21636)Memory used [KB]: 7931
% 103.09/15.85 % (21636)Time elapsed: 0.239 s
% 103.09/15.85 % (21636)Instructions burned: 865 (million)
% 103.09/15.85 % (21636)------------------------------
% 103.09/15.85 % (21636)------------------------------
% 103.09/15.86 % (21638)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_20195 for (2854ds/4165Mi)
% 105.25/16.05 % (21038)Refutation not found, non-redundant clauses discarded% (21038)------------------------------
% 105.25/16.05 % (21038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 105.25/16.05 % (21038)Termination reason: Refutation not found, non-redundant clauses discarded
% 105.25/16.05
% 105.25/16.05 % (21038)Memory used [KB]: 22131
% 105.25/16.05 % (21038)Time elapsed: 2.813 s
% 105.25/16.05 % (21038)Instructions burned: 9217 (million)
% 105.25/16.05 % (21038)------------------------------
% 105.25/16.05 % (21038)------------------------------
% 105.25/16.06 % (21639)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_20195 for (2852ds/13468Mi)
% 105.88/16.19 % (21041)Instruction limit reached!
% 105.88/16.19 % (21041)------------------------------
% 105.88/16.19 % (21041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 105.88/16.19 % (21041)Termination reason: Unknown
% 105.88/16.19 % (21041)Termination phase: Saturation
% 105.88/16.19
% 105.88/16.19 % (21041)Memory used [KB]: 17142
% 105.88/16.19 % (21041)Time elapsed: 2.001 s
% 105.88/16.19 % (21041)Instructions burned: 7967 (million)
% 105.88/16.19 % (21041)------------------------------
% 105.88/16.19 % (21041)------------------------------
% 106.42/16.20 % (21640)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_20195 for (2850ds/2635Mi)
% 106.92/16.37 % (21039)Instruction limit reached!
% 106.92/16.37 % (21039)------------------------------
% 106.92/16.37 % (21039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 106.92/16.37 % (21039)Termination reason: Unknown
% 106.92/16.37 % (21039)Termination phase: Saturation
% 106.92/16.37
% 106.92/16.37 % (21039)Memory used [KB]: 12792
% 106.92/16.37 % (21039)Time elapsed: 2.534 s
% 106.92/16.37 % (21039)Instructions burned: 8425 (million)
% 106.92/16.37 % (21039)------------------------------
% 106.92/16.37 % (21039)------------------------------
% 106.92/16.38 % (21641)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_20195 for (2849ds/631Mi)
% 107.41/16.40 % (21597)Instruction limit reached!
% 107.41/16.40 % (21597)------------------------------
% 107.41/16.40 % (21597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 107.41/16.40 % (21597)Termination reason: Unknown
% 107.41/16.40 % (21597)Termination phase: Saturation
% 107.41/16.40
% 107.41/16.40 % (21597)Memory used [KB]: 16119
% 107.41/16.40 % (21597)Time elapsed: 1.009 s
% 107.41/16.40 % (21597)Instructions burned: 3205 (million)
% 107.41/16.40 % (21597)------------------------------
% 107.41/16.40 % (21597)------------------------------
% 107.41/16.41 % (21642)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_20195 for (2848ds/15557Mi)
% 107.73/16.54 % (21641)Instruction limit reached!
% 107.73/16.54 % (21641)------------------------------
% 107.73/16.54 % (21641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 107.73/16.54 % (21641)Termination reason: Unknown
% 107.73/16.54 % (21641)Termination phase: Saturation
% 107.73/16.54
% 107.73/16.54 % (21641)Memory used [KB]: 7675
% 107.73/16.54 % (21641)Time elapsed: 0.160 s
% 107.73/16.54 % (21641)Instructions burned: 631 (million)
% 107.73/16.54 % (21641)------------------------------
% 107.73/16.54 % (21641)------------------------------
% 107.73/16.55 % (21643)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_20195 for (2847ds/2142Mi)
% 109.08/17.01 % (21640)Instruction limit reached!
% 109.08/17.01 % (21640)------------------------------
% 109.08/17.01 % (21640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 109.08/17.01 % (21640)Termination reason: Unknown
% 109.08/17.01 % (21640)Termination phase: Saturation
% 109.08/17.01
% 109.08/17.01 % (21640)Memory used [KB]: 12409
% 109.08/17.01 % (21640)Time elapsed: 0.812 s
% 109.08/17.01 % (21640)Instructions burned: 2637 (million)
% 109.08/17.01 % (21640)------------------------------
% 109.08/17.01 % (21640)------------------------------
% 112.26/17.02 % (21644)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_20195 for (2842ds/5624Mi)
% 112.87/17.18 % (21638)Instruction limit reached!
% 112.87/17.18 % (21638)------------------------------
% 112.87/17.18 % (21638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 112.87/17.18 % (21638)Termination reason: Unknown
% 112.87/17.18 % (21638)Termination phase: Saturation
% 112.87/17.18
% 112.87/17.18 % (21638)Memory used [KB]: 25202
% 112.87/17.18 % (21638)Time elapsed: 1.324 s
% 112.87/17.18 % (21638)Instructions burned: 4167 (million)
% 112.87/17.18 % (21638)------------------------------
% 112.87/17.18 % (21638)------------------------------
% 112.87/17.19 % (21645)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_20195 for (2840ds/1665Mi)
% 112.87/17.19 % (21643)Instruction limit reached!
% 112.87/17.19 % (21643)------------------------------
% 112.87/17.19 % (21643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 112.87/17.19 % (21643)Termination reason: Unknown
% 112.87/17.19 % (21643)Termination phase: Saturation
% 112.87/17.19
% 112.87/17.19 % (21643)Memory used [KB]: 11385
% 112.87/17.19 % (21643)Time elapsed: 0.644 s
% 112.87/17.19 % (21643)Instructions burned: 2144 (million)
% 112.87/17.19 % (21643)------------------------------
% 112.87/17.19 % (21643)------------------------------
% 113.38/17.20 % (21646)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_20195 for (2840ds/64912Mi)
% 114.99/17.60 % (21645)Instruction limit reached!
% 114.99/17.60 % (21645)------------------------------
% 114.99/17.60 % (21645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 114.99/17.60 % (21645)Termination reason: Unknown
% 114.99/17.60 % (21645)Termination phase: Saturation
% 114.99/17.60
% 114.99/17.60 % (21645)Memory used [KB]: 17014
% 114.99/17.60 % (21645)Time elapsed: 0.412 s
% 114.99/17.60 % (21645)Instructions burned: 1668 (million)
% 114.99/17.60 % (21645)------------------------------
% 114.99/17.60 % (21645)------------------------------
% 114.99/17.61 % (21647)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_20195 for (2836ds/7801Mi)
% 115.81/17.70 % (21637)Instruction limit reached!
% 115.81/17.70 % (21637)------------------------------
% 115.81/17.70 % (21637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 115.81/17.70 % (21637)Termination reason: Unknown
% 115.81/17.70 % (21637)Termination phase: Saturation
% 115.81/17.70
% 115.81/17.70 % (21637)Memory used [KB]: 11257
% 115.81/17.70 % (21637)Time elapsed: 1.989 s
% 115.81/17.70 % (21637)Instructions burned: 7470 (million)
% 115.81/17.70 % (21637)------------------------------
% 115.81/17.70 % (21637)------------------------------
% 115.81/17.71 % (21648)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_20195 for (2835ds/15194Mi)
% 124.07/18.75 % (21644)Instruction limit reached!
% 124.07/18.75 % (21644)------------------------------
% 124.07/18.75 % (21644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 124.07/18.75 % (21644)Termination reason: Unknown
% 124.07/18.75 % (21644)Termination phase: Saturation
% 124.07/18.75
% 124.07/18.75 % (21644)Memory used [KB]: 14072
% 124.07/18.75 % (21644)Time elapsed: 1.732 s
% 124.07/18.75 % (21644)Instructions burned: 5626 (million)
% 124.07/18.75 % (21644)------------------------------
% 124.07/18.75 % (21644)------------------------------
% 124.07/18.76 % (21649)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_20195 for (2825ds/6753Mi)
% 127.59/19.22 % (21639)Instruction limit reached!
% 127.59/19.22 % (21639)------------------------------
% 127.59/19.22 % (21639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 127.59/19.22 % (21639)Termination reason: Unknown
% 127.59/19.22 % (21639)Termination phase: Saturation
% 127.59/19.22
% 127.59/19.22 % (21639)Memory used [KB]: 8827
% 127.59/19.22 % (21639)Time elapsed: 3.158 s
% 127.59/19.22 % (21639)Instructions burned: 13472 (million)
% 127.59/19.22 % (21639)------------------------------
% 127.59/19.22 % (21639)------------------------------
% 127.59/19.23 % (21650)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_20195 for (2820ds/1003Mi)
% 128.82/19.48 % (21650)Instruction limit reached!
% 128.82/19.48 % (21650)------------------------------
% 128.82/19.48 % (21650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 128.82/19.48 % (21650)Termination reason: Unknown
% 128.82/19.48 % (21650)Termination phase: Saturation
% 128.82/19.48
% 128.82/19.48 % (21650)Memory used [KB]: 7803
% 128.82/19.48 % (21650)Time elapsed: 0.251 s
% 128.82/19.48 % (21650)Instructions burned: 1003 (million)
% 128.82/19.48 % (21650)------------------------------
% 128.82/19.48 % (21650)------------------------------
% 128.82/19.49 % (21651)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_20195 for (2818ds/13018Mi)
% 130.88/19.78 % (21647)Instruction limit reached!
% 130.88/19.78 % (21647)------------------------------
% 130.88/19.78 % (21647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 130.88/19.78 % (21647)Termination reason: Unknown
% 130.88/19.78 % (21647)Termination phase: Saturation
% 130.88/19.78
% 130.88/19.78 % (21647)Memory used [KB]: 13304
% 130.88/19.78 % (21647)Time elapsed: 2.163 s
% 130.88/19.78 % (21647)Instructions burned: 7801 (million)
% 130.88/19.78 % (21647)------------------------------
% 130.88/19.78 % (21647)------------------------------
% 130.88/19.79 % (21652)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_20195 for (2815ds/1267Mi)
% 133.97/20.17 % (21652)Instruction limit reached!
% 133.97/20.17 % (21652)------------------------------
% 133.97/20.17 % (21652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 133.97/20.17 % (21652)Termination reason: Unknown
% 133.97/20.17 % (21652)Termination phase: Saturation
% 133.97/20.17
% 133.97/20.17 % (21652)Memory used [KB]: 12281
% 133.97/20.17 % (21652)Time elapsed: 0.387 s
% 133.97/20.17 % (21652)Instructions burned: 1269 (million)
% 133.97/20.17 % (21652)------------------------------
% 133.97/20.17 % (21652)------------------------------
% 133.97/20.18 % (21653)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_20195 for (2811ds/2570Mi)
% 133.97/20.19 % (21642)Instruction limit reached!
% 133.97/20.19 % (21642)------------------------------
% 133.97/20.19 % (21642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 133.97/20.19 % (21642)Termination reason: Unknown
% 133.97/20.19 % (21642)Termination phase: Saturation
% 133.97/20.19
% 133.97/20.19 % (21642)Memory used [KB]: 18166
% 133.97/20.19 % (21642)Time elapsed: 3.774 s
% 133.97/20.19 % (21642)Instructions burned: 15561 (million)
% 133.97/20.19 % (21642)------------------------------
% 133.97/20.19 % (21642)------------------------------
% 134.58/20.20 % (21654)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=13163:si=on:rtra=on_0 on DTF2THF_20195 for (2810ds/13163Mi)
% 137.09/20.78 % (21649)Instruction limit reached!
% 137.09/20.78 % (21649)------------------------------
% 137.09/20.78 % (21649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 137.09/20.78 % (21649)Termination reason: Unknown
% 137.09/20.78 % (21649)Termination phase: Saturation
% 137.09/20.78
% 137.09/20.78 % (21649)Memory used [KB]: 21108
% 137.09/20.78 % (21649)Time elapsed: 2.020 s
% 137.09/20.78 % (21649)Instructions burned: 6753 (million)
% 137.09/20.78 % (21649)------------------------------
% 137.09/20.78 % (21649)------------------------------
% 137.09/20.79 % (21655)lrs+1666_1:1_au=on:s2a=on:sd=2:ss=axioms:st=5.0:i=5087:si=on:rtra=on_0 on DTF2THF_20195 for (2805ds/5087Mi)
% 137.58/20.80 % (21653)Instruction limit reached!
% 137.58/20.80 % (21653)------------------------------
% 137.58/20.80 % (21653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 137.58/20.80 % (21653)Termination reason: Unknown
% 137.58/20.80 % (21653)Termination phase: Saturation
% 137.58/20.80
% 137.58/20.80 % (21653)Memory used [KB]: 26737
% 137.58/20.80 % (21653)Time elapsed: 0.617 s
% 137.58/20.80 % (21653)Instructions burned: 2571 (million)
% 137.58/20.80 % (21653)------------------------------
% 137.58/20.80 % (21653)------------------------------
% 137.58/20.81 % (21656)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_20195 for (2804ds/10380Mi)
% 148.01/22.18 % (21648)Instruction limit reached!
% 148.01/22.18 % (21648)------------------------------
% 148.01/22.18 % (21648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 148.01/22.18 % (21648)Termination reason: Unknown
% 148.01/22.18 % (21648)Termination phase: Saturation
% 148.01/22.18
% 148.01/22.18 % (21648)Memory used [KB]: 23155
% 148.01/22.18 % (21648)Time elapsed: 4.470 s
% 148.01/22.18 % (21648)Instructions burned: 15194 (million)
% 148.01/22.18 % (21648)------------------------------
% 148.01/22.18 % (21648)------------------------------
% 148.01/22.19 % (21657)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_20195 for (2791ds/4218Mi)
% 149.21/22.35 % (21655)Instruction limit reached!
% 149.21/22.35 % (21655)------------------------------
% 149.21/22.35 % (21655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 149.21/22.35 % (21655)Termination reason: Unknown
% 149.21/22.35 % (21655)Termination phase: Saturation
% 149.21/22.35
% 149.21/22.35 % (21655)Memory used [KB]: 14200
% 149.21/22.35 % (21655)Time elapsed: 1.558 s
% 149.21/22.35 % (21655)Instructions burned: 5090 (million)
% 149.21/22.35 % (21655)------------------------------
% 149.21/22.35 % (21655)------------------------------
% 149.21/22.36 % (21658)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_20195 for (2789ds/3971Mi)
% 156.33/23.34 % (21656)Instruction limit reached!
% 156.33/23.34 % (21656)------------------------------
% 156.33/23.34 % (21656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 156.33/23.34 % (21656)Termination reason: Unknown
% 156.33/23.34 % (21656)Termination phase: Saturation
% 156.33/23.34
% 156.33/23.34 % (21656)Memory used [KB]: 7803
% 156.33/23.34 % (21656)Time elapsed: 2.534 s
% 156.33/23.34 % (21656)Instructions burned: 10382 (million)
% 156.33/23.34 % (21656)------------------------------
% 156.33/23.34 % (21656)------------------------------
% 156.33/23.35 % (21659)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_20195 for (2779ds/14014Mi)
% 156.98/23.47 % (21657)Instruction limit reached!
% 156.98/23.47 % (21657)------------------------------
% 156.98/23.47 % (21657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 156.98/23.47 % (21657)Termination reason: Unknown
% 156.98/23.47 % (21657)Termination phase: Saturation
% 156.98/23.47
% 156.98/23.47 % (21657)Memory used [KB]: 13816
% 156.98/23.47 % (21657)Time elapsed: 1.299 s
% 156.98/23.47 % (21657)Instructions burned: 4220 (million)
% 156.98/23.47 % (21657)------------------------------
% 156.98/23.47 % (21657)------------------------------
% 156.98/23.48 % (21660)lrs+10_1:1_ins=1:sgt=8:ss=axioms:i=8517:si=on:rtra=on_0 on DTF2THF_20195 for (2778ds/8517Mi)
% 157.56/23.53 % (21658)Instruction limit reached!
% 157.56/23.53 % (21658)------------------------------
% 157.56/23.53 % (21658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 157.56/23.53 % (21658)Termination reason: Unknown
% 157.56/23.53 % (21658)Termination phase: Saturation
% 157.56/23.53
% 157.56/23.53 % (21658)Memory used [KB]: 18549
% 157.56/23.53 % (21658)Time elapsed: 1.191 s
% 157.56/23.53 % (21658)Instructions burned: 3971 (million)
% 157.56/23.53 % (21658)------------------------------
% 157.56/23.53 % (21658)------------------------------
% 157.56/23.54 % (21661)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=10148:si=on:rtra=on_0 on DTF2THF_20195 for (2777ds/10148Mi)
% 157.99/23.62 % (21651)Instruction limit reached!
% 157.99/23.62 % (21651)------------------------------
% 157.99/23.62 % (21651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 157.99/23.62 % (21651)Termination reason: Unknown
% 157.99/23.62 % (21651)Termination phase: Saturation
% 157.99/23.62
% 157.99/23.62 % (21651)Memory used [KB]: 37611
% 157.99/23.62 % (21651)Time elapsed: 4.132 s
% 157.99/23.62 % (21651)Instructions burned: 13018 (million)
% 157.99/23.62 % (21651)------------------------------
% 157.99/23.62 % (21651)------------------------------
% 157.99/23.63 % (21662)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_20195 for (2776ds/9078Mi)
% 162.04/24.15 % (21654)Instruction limit reached!
% 162.04/24.15 % (21654)------------------------------
% 162.04/24.15 % (21654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 162.04/24.15 % (21654)Termination reason: Unknown
% 162.04/24.15 % (21654)Termination phase: Saturation
% 162.04/24.15
% 162.04/24.15 % (21654)Memory used [KB]: 26737
% 162.04/24.15 % (21654)Time elapsed: 3.954 s
% 162.04/24.15 % (21654)Instructions burned: 13163 (million)
% 162.04/24.15 % (21654)------------------------------
% 162.04/24.15 % (21654)------------------------------
% 162.04/24.16 % (21663)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_20195 for (2771ds/16164Mi)
% 169.05/25.17 % (21661)First to succeed.
% 169.05/25.17 % (21661)Refutation found. Thanks to Tanya!
% 169.05/25.17 % SZS status Theorem for DTF2THF_20195
% 169.05/25.17 % SZS output start Proof for DTF2THF_20195
% 169.05/25.17 thf(func_def_0, type, in: $i > $i > $o).
% 169.05/25.17 thf(func_def_1, type, exu: ($i > $o) > $o).
% 169.05/25.17 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 169.05/25.17 thf(func_def_8, type, powerset: $i > $i).
% 169.05/25.17 thf(func_def_10, type, setunion: $i > $i).
% 169.05/25.17 thf(func_def_19, type, descr: ($i > $o) > $i).
% 169.05/25.17 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 169.05/25.17 thf(func_def_26, type, prop2set: $o > $i).
% 169.05/25.17 thf(func_def_36, type, nonempty: $i > $o).
% 169.05/25.17 thf(func_def_69, type, set2prop: $i > $o).
% 169.05/25.17 thf(func_def_88, type, subset: $i > $i > $o).
% 169.05/25.17 thf(func_def_89, type, disjoint: $i > $i > $o).
% 169.05/25.17 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 169.05/25.17 thf(func_def_114, type, binunion: $i > $i > $i).
% 169.05/25.17 thf(func_def_122, type, binintersect: $i > $i > $i).
% 169.05/25.17 thf(func_def_135, type, regular: $i > $o).
% 169.05/25.17 thf(func_def_136, type, setminus: $i > $i > $i).
% 169.05/25.17 thf(func_def_147, type, symdiff: $i > $i > $i).
% 169.05/25.17 thf(func_def_153, type, iskpair: $i > $o).
% 169.05/25.17 thf(func_def_158, type, kpair: $i > $i > $i).
% 169.05/25.17 thf(func_def_160, type, cartprod: $i > $i > $i).
% 169.05/25.17 thf(func_def_177, type, singleton: $i > $o).
% 169.05/25.17 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 169.05/25.17 thf(func_def_184, type, atmost1p: $i > $o).
% 169.05/25.17 thf(func_def_185, type, atleast2p: $i > $o).
% 169.05/25.17 thf(func_def_186, type, atmost2p: $i > $o).
% 169.05/25.17 thf(func_def_187, type, upairsetp: $i > $o).
% 169.05/25.17 thf(func_def_191, type, kfst: $i > $i).
% 169.05/25.17 thf(func_def_203, type, ksnd: $i > $i).
% 169.05/25.17 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 169.05/25.17 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 169.05/25.17 thf(func_def_222, type, func: $i > $i > $i > $o).
% 169.05/25.17 thf(func_def_223, type, funcSet: $i > $i > $i).
% 169.05/25.17 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 169.05/25.17 thf(func_def_259, type, if: $i > $o > $i > $i > $i).
% 169.05/25.17 thf(func_def_323, type, breln1: $i > $i > $o).
% 169.05/25.17 thf(func_def_325, type, breln1Set: $i > $i).
% 169.05/25.17 thf(func_def_327, type, transitive: $i > $i > $o).
% 169.05/25.17 thf(func_def_328, type, antisymmetric: $i > $i > $o).
% 169.05/25.17 thf(func_def_329, type, reflexive: $i > $i > $o).
% 169.05/25.17 thf(func_def_330, type, refltransitive: $i > $i > $o).
% 169.05/25.17 thf(func_def_331, type, refllinearorder: $i > $i > $o).
% 169.05/25.17 thf(func_def_332, type, reflwellordering: $i > $i > $o).
% 169.05/25.17 thf(func_def_338, type, breln1invset: $i > $i > $i).
% 169.05/25.17 thf(func_def_342, type, breln1compset: $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_364, type, sP3: $i > ($i > $i > $o) > $o).
% 169.05/25.17 thf(func_def_376, type, sP15: $i > $i > $i > $i > $o).
% 169.05/25.17 thf(func_def_384, type, sP23: $i > $o > $i > $i > $o).
% 169.05/25.17 thf(func_def_390, type, sP29: $i > $i > $i > $o).
% 169.05/25.17 thf(func_def_391, type, sP30: $i > $i > $o).
% 169.05/25.17 thf(func_def_392, type, sP31: ($i > $o) > $i > $o).
% 169.05/25.17 thf(func_def_396, type, sP35: $i > $i > $i > $i > $o).
% 169.05/25.17 thf(func_def_397, type, sP36: $i > $i > $i > $o).
% 169.05/25.17 thf(func_def_402, type, sP41: $i > $i > ($i > $i > $o) > $o).
% 169.05/25.17 thf(func_def_407, type, sP46: ($i > $o) > $i > $o).
% 169.05/25.17 thf(func_def_410, type, sP49: $i > $i > $i > $o).
% 169.05/25.17 thf(func_def_411, type, sP50: $i > $i > $i > $o).
% 169.05/25.17 thf(func_def_412, type, sP51: $i > $i > $o).
% 169.05/25.17 thf(func_def_413, type, sP52: $i > $i > $i > $o).
% 169.05/25.17 thf(func_def_414, type, sP53: $i > $i > $o).
% 169.05/25.17 thf(func_def_415, type, sP54: $i > $o).
% 169.05/25.17 thf(func_def_416, type, sP55: $i > $i > $o).
% 169.05/25.17 thf(func_def_417, type, sP56: $i > $i > $o).
% 169.05/25.17 thf(func_def_418, type, sP57: $i > $i > $o).
% 169.05/25.17 thf(func_def_432, type, sK71: $i > $o).
% 169.05/25.17 thf(func_def_434, type, sK73: $i > ($i > $o) > $i).
% 169.05/25.17 thf(func_def_438, type, sK77: $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_439, type, sK78: $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_442, type, sK81: $i > $i).
% 169.05/25.17 thf(func_def_443, type, sK82: $i > $i).
% 169.05/25.17 thf(func_def_453, type, sK92: $i > $o).
% 169.05/25.17 thf(func_def_482, type, sK121: $i > $i > ($i > $i > $o) > $i).
% 169.05/25.17 thf(func_def_483, type, sK122: $i > $i > ($i > $i > $o) > $i).
% 169.05/25.17 thf(func_def_484, type, sK123: $i > ($i > $i > $o) > $i).
% 169.05/25.17 thf(func_def_485, type, sK124: $i > $i > ($i > $i > $o) > $i).
% 169.05/25.17 thf(func_def_486, type, sK125: $i > $i > $o).
% 169.05/25.17 thf(func_def_488, type, sK127: $i > ($i > $i > $o) > $i).
% 169.05/25.17 thf(func_def_493, type, sK132: $i > $o).
% 169.05/25.17 thf(func_def_494, type, sK133: ($i > $o) > $i > $i > $i).
% 169.05/25.17 thf(func_def_495, type, sK134: $i > $o).
% 169.05/25.17 thf(func_def_497, type, sK136: $i > ($i > $o) > $i).
% 169.05/25.17 thf(func_def_517, type, sK156: $i > $i > $i).
% 169.05/25.17 thf(func_def_519, type, sK158: $i > $o).
% 169.05/25.17 thf(func_def_521, type, sK160: ($i > $o) > $i > $i).
% 169.05/25.17 thf(func_def_534, type, sK173: $i > $i > $o).
% 169.05/25.17 thf(func_def_542, type, sK181: $i > $o).
% 169.05/25.17 thf(func_def_544, type, sK183: ($i > $o) > $i > $i).
% 169.05/25.17 thf(func_def_569, type, sK208: $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_596, type, sK235: $i > $i > $o).
% 169.05/25.17 thf(func_def_603, type, sK242: $i > $o).
% 169.05/25.17 thf(func_def_604, type, sK243: $i > $o).
% 169.05/25.17 thf(func_def_605, type, sK244: ($i > $o) > ($i > $o) > $i > $i > $i).
% 169.05/25.17 thf(func_def_606, type, sK245: ($i > $o) > ($i > $o) > $i > $i > $i).
% 169.05/25.17 thf(func_def_625, type, sK264: $i > $i > $o).
% 169.05/25.17 thf(func_def_630, type, sK269: $i > $o).
% 169.05/25.17 thf(func_def_644, type, sK283: $i > $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_664, type, sK303: $i > $o).
% 169.05/25.17 thf(func_def_666, type, sK305: ($i > $o) > $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_667, type, sK306: ($i > $o) > $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_671, type, sK310: $i > $i).
% 169.05/25.17 thf(func_def_675, type, sK314: $i > $i > ($i > $i) > $i).
% 169.05/25.17 thf(func_def_679, type, sK318: $i > $i > $i).
% 169.05/25.17 thf(func_def_712, type, sK351: $i > $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_713, type, sK352: $i > $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_714, type, sK353: $i > $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_716, type, sK355: $i > $o).
% 169.05/25.17 thf(func_def_745, type, sK384: $i > $o).
% 169.05/25.17 thf(func_def_746, type, sK385: $i > $i).
% 169.05/25.17 thf(func_def_747, type, sK386: ($i > $o) > $i).
% 169.05/25.17 thf(func_def_788, type, sK427: $i > $i > $i).
% 169.05/25.17 thf(func_def_805, type, sK444: $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_806, type, sK445: $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_816, type, sK455: $i > $i).
% 169.05/25.17 thf(func_def_820, type, sK459: $i > $o).
% 169.05/25.17 thf(func_def_821, type, sK460: ($i > $i) > $i > $i > $i).
% 169.05/25.17 thf(func_def_824, type, sK463: $i > $i).
% 169.05/25.17 thf(func_def_826, type, sK465: $i > $o).
% 169.05/25.17 thf(func_def_828, type, sK467: ($i > $o) > $i > $i).
% 169.05/25.17 thf(func_def_831, type, sK470: $i > $o).
% 169.05/25.17 thf(func_def_832, type, sK471: ($i > $o) > $i).
% 169.05/25.17 thf(func_def_836, type, sK475: $i > $o).
% 169.05/25.17 thf(func_def_838, type, sK477: ($i > $o) > $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_839, type, sK478: ($i > $o) > $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_842, type, sK481: $i > $o).
% 169.05/25.17 thf(func_def_844, type, sK483: ($i > $o) > $i > $i > $i).
% 169.05/25.17 thf(func_def_845, type, sK484: ($i > $o) > $i > $i > $i).
% 169.05/25.17 thf(func_def_880, type, sK519: $i > $i > $i).
% 169.05/25.17 thf(func_def_886, type, sK525: $i > $i > $i).
% 169.05/25.17 thf(func_def_904, type, sK543: $i > $o).
% 169.05/25.17 thf(func_def_939, type, sK578: $i > $i > $i).
% 169.05/25.17 thf(func_def_940, type, sK579: $i > $i > $i).
% 169.05/25.17 thf(func_def_947, type, sK586: $i > $o).
% 169.05/25.17 thf(func_def_952, type, sK591: $i > $i > $i).
% 169.05/25.17 thf(func_def_962, type, sK601: $i > $o).
% 169.05/25.17 thf(func_def_967, type, sK606: $i > $i).
% 169.05/25.17 thf(func_def_969, type, sK608: $i > $o).
% 169.05/25.17 thf(func_def_971, type, sK610: ($i > $o) > $i > $i).
% 169.05/25.17 thf(func_def_972, type, sK611: ($i > $o) > ($i > $o) > $i).
% 169.05/25.17 thf(func_def_973, type, sK612: ($i > $o) > ($i > $o) > $i).
% 169.05/25.17 thf(func_def_974, type, sK613: $i > $o).
% 169.05/25.17 thf(func_def_975, type, sK614: $i > $o).
% 169.05/25.17 thf(func_def_989, type, sK628: $i > $i).
% 169.05/25.17 thf(func_def_998, type, sK637: $i > $o).
% 169.05/25.17 thf(func_def_1001, type, sK640: $i > ($i > $o) > $i).
% 169.05/25.17 thf(func_def_1009, type, sK648: $i > $i > $i).
% 169.05/25.17 thf(func_def_1010, type, sK649: $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_1011, type, sK650: $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_1012, type, sK651: $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_1013, type, sK652: $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_1017, type, sK656: $i > $o).
% 169.05/25.17 thf(func_def_1018, type, sK657: ($i > $o) > $i > $i).
% 169.05/25.17 thf(func_def_1024, type, sK663: $i > $i).
% 169.05/25.17 thf(func_def_1051, type, sK690: $i > $i > $o).
% 169.05/25.17 thf(func_def_1053, type, sK692: ($i > $o) > $i > $i).
% 169.05/25.17 thf(func_def_1054, type, sK693: ($i > $o) > $i > $i).
% 169.05/25.17 thf(func_def_1055, type, sK694: $i > $o).
% 169.05/25.17 thf(func_def_1059, type, sK698: $i > $o).
% 169.05/25.17 thf(func_def_1076, type, sK715: $i > $o).
% 169.05/25.17 thf(func_def_1077, type, sK716: $i > $o).
% 169.05/25.17 thf(func_def_1078, type, sK717: ($i > $o) > ($i > $o) > $i).
% 169.05/25.17 thf(func_def_1079, type, sK718: ($i > $o) > ($i > $o) > $i).
% 169.05/25.17 thf(func_def_1084, type, sK723: $i > $o).
% 169.05/25.17 thf(func_def_1085, type, sK724: $i > $o).
% 169.05/25.17 thf(func_def_1093, type, sK732: $i > $i > $o).
% 169.05/25.17 thf(func_def_1094, type, sK733: $i > $i > ($i > $i) > $i).
% 169.05/25.17 thf(func_def_1095, type, sK734: $i > $i).
% 169.05/25.17 thf(func_def_1098, type, sK737: $i > $i).
% 169.05/25.17 thf(func_def_1111, type, sK750: $i > $o).
% 169.05/25.17 thf(func_def_1112, type, sK751: $i > $i).
% 169.05/25.17 thf(func_def_1113, type, sK752: ($i > $o) > $i).
% 169.05/25.17 thf(func_def_1114, type, sK753: $i > $o).
% 169.05/25.17 thf(func_def_1117, type, sK756: $i > ($i > $o) > $i).
% 169.05/25.17 thf(func_def_1120, type, sK759: $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_1121, type, sK760: $i > $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_1122, type, sK761: $i > $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_1123, type, sK762: $i > $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_1124, type, sK763: $i > $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_1161, type, sK800: $i > $i > $i).
% 169.05/25.17 thf(func_def_1162, type, sK801: $i > $i > $i).
% 169.05/25.17 thf(func_def_1163, type, sK802: $i > $o).
% 169.05/25.17 thf(func_def_1165, type, sK804: ($i > $o) > $i).
% 169.05/25.17 thf(func_def_1166, type, sK805: ($i > $o) > $i).
% 169.05/25.17 thf(func_def_1171, type, sK810: $i > $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_1172, type, sK811: $i > $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_1178, type, sK817: $i > $o).
% 169.05/25.17 thf(func_def_1180, type, sK819: ($i > $o) > $i > $i > $i).
% 169.05/25.17 thf(func_def_1181, type, sK820: ($i > $o) > $i > $i > $i).
% 169.05/25.17 thf(func_def_1182, type, sK821: $i > $i > ($i > $i) > $i).
% 169.05/25.17 thf(func_def_1183, type, sK822: $i > $i).
% 169.05/25.17 thf(func_def_1190, type, sK829: $i > $i > $o).
% 169.05/25.17 thf(func_def_1192, type, sK831: $i > $i).
% 169.05/25.17 thf(func_def_1193, type, sK832: $i > ($i > $i > $o) > $i > $i).
% 169.05/25.17 thf(func_def_1194, type, sK833: $i > $i > ($i > $i > $o) > $i).
% 169.05/25.17 thf(func_def_1195, type, sK834: $i > $i > ($i > $i > $o) > $i).
% 169.05/25.17 thf(func_def_1219, type, sK858: $i > $i > $o).
% 169.05/25.17 thf(func_def_1225, type, sK864: $i > $i).
% 169.05/25.17 thf(func_def_1227, type, sK866: $i > ($i > $i) > $i > $i).
% 169.05/25.17 thf(func_def_1229, type, sK868: $i > $i > $o).
% 169.05/25.17 thf(func_def_1242, type, sK881: $i > $i).
% 169.05/25.17 thf(func_def_1244, type, sK883: ($i > $i) > $i > $i > $i).
% 169.05/25.17 thf(func_def_1252, type, sK891: $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_1256, type, sK895: ($i > $o) > $i > $i).
% 169.05/25.17 thf(func_def_1257, type, sK896: ($i > $o) > $i > $i).
% 169.05/25.17 thf(func_def_1258, type, sK897: $i > $o).
% 169.05/25.17 thf(func_def_1286, type, sK925: $i > $o).
% 169.05/25.17 thf(func_def_1297, type, sK936: $i > $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_1327, type, sK966: $i > $i > $o).
% 169.05/25.17 thf(func_def_1331, type, sK970: $i > $o).
% 169.05/25.17 thf(func_def_1332, type, sK971: $i > $o).
% 169.05/25.17 thf(func_def_1340, type, sK979: $o > $i > $i > $i).
% 169.05/25.17 thf(func_def_1356, type, sK995: $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_1357, type, sK996: $i > $i > $i > $o).
% 169.05/25.17 thf(func_def_1361, type, sK1000: $i > $i > $i).
% 169.05/25.17 thf(func_def_1362, type, sK1001: $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_1363, type, sK1002: $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_1368, type, sK1007: $i > $i > $i).
% 169.05/25.17 thf(func_def_1369, type, sK1008: $i > $i > $i).
% 169.05/25.17 thf(func_def_1370, type, sK1009: $i > $i > $i).
% 169.05/25.17 thf(func_def_1371, type, sK1010: $i > $i > $i).
% 169.05/25.17 thf(func_def_1372, type, sK1011: $i > $i > $i).
% 169.05/25.17 thf(func_def_1373, type, sK1012: $i > $i > $i).
% 169.05/25.17 thf(func_def_1374, type, sK1013: $i > $i > $i).
% 169.05/25.17 thf(func_def_1375, type, sK1014: $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_1376, type, sK1015: $i > $i).
% 169.05/25.17 thf(func_def_1377, type, sK1016: $i > $i).
% 169.05/25.17 thf(func_def_1378, type, sK1017: $i > $i).
% 169.05/25.17 thf(func_def_1379, type, sK1018: $i > $i).
% 169.05/25.17 thf(func_def_1380, type, sK1019: $i > $i > $i).
% 169.05/25.17 thf(func_def_1381, type, sK1020: $i > $i > $i).
% 169.05/25.17 thf(func_def_1382, type, sK1021: $i > $i > $i).
% 169.05/25.17 thf(func_def_1383, type, sK1022: $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_1384, type, sK1023: $i > $i > $i > $i).
% 169.05/25.17 thf(func_def_1386, type, sK1025: $i > $i).
% 169.05/25.17 thf(func_def_1388, type, sK1027: ($i > $o) > $i).
% 169.05/25.17 thf(func_def_1389, type, sK1028: ($i > $o) > $i > $i).
% 169.05/25.17 thf(func_def_1391, type, sK1030: ($i > $o) > $i).
% 169.05/25.17 thf(func_def_1392, type, sK1031: ($i > $o) > $i > $i).
% 169.05/25.17 thf(func_def_1393, type, sK1032: ($i > $o) > $i).
% 169.05/25.17 thf(func_def_1394, type, sK1033: ($i > $o) > $i).
% 169.05/25.17 thf(func_def_1395, type, sK1034: ($i > $o) > $i > $i).
% 169.05/25.17 thf(func_def_1396, type, sK1035: ($i > $o) > $i > $i).
% 169.05/25.17 thf(func_def_1397, type, sK1036: ($i > $o) > $i).
% 169.05/25.17 thf(func_def_1398, type, sK1037: ($i > $o) > $i > $i).
% 169.05/25.17 thf(func_def_1399, type, sK1038: ($i > $o) > $i > $i).
% 169.05/25.17 thf(func_def_1400, type, sK1039: ($i > $o) > $i).
% 169.05/25.17 thf(func_def_1401, type, sK1040: ($i > $o) > $i > $i).
% 169.05/25.17 thf(func_def_1402, type, sK1041: ($i > $o) > $i).
% 169.05/25.17 thf(func_def_1404, type, sK1043: ($i > $o) > $i > $i).
% 169.05/25.17 thf(func_def_1405, type, sK1044: $i > $i).
% 169.05/25.17 thf(func_def_1407, type, sK1046: ($i > $o) > $i > $i).
% 169.05/25.17 thf(func_def_1408, type, sK1047: $i > ($i > $o) > $i).
% 169.05/25.17 thf(func_def_1409, type, sK1048: $i > ($i > $o) > $i).
% 169.05/25.17 thf(func_def_1410, type, sK1049: $i > ($i > $o) > $i).
% 169.05/25.17 thf(func_def_1411, type, sK1050: $i > ($i > $o) > $i).
% 169.05/25.17 thf(func_def_1412, type, sK1051: $i > ($i > $o) > $i).
% 169.05/25.17 thf(func_def_1413, type, sK1052: ($i > $o) > $i > $i).
% 169.05/25.17 thf(func_def_1414, type, sK1053: ($i > $o) > $i > $i).
% 169.05/25.17 thf(func_def_1416, type, sK1055: ($i > $o) > $i).
% 169.05/25.17 thf(func_def_1417, type, sK1056: ($i > $o) > $i > $i).
% 169.05/25.17 thf(func_def_1418, type, sK1057: $i > ($i > $o) > $i).
% 169.05/25.17 thf(func_def_1419, type, sK1058: ($i > $o) > $i > $i).
% 169.05/25.17 thf(func_def_1420, type, sK1059: ($i > $o) > $i > $i).
% 169.05/25.17 thf(func_def_1421, type, sK1060: ($i > $o) > $i).
% 169.05/25.17 thf(func_def_1422, type, sK1061: $i > $i).
% 169.05/25.17 thf(func_def_1423, type, sK1062: $i > ($i > $o) > $i).
% 169.05/25.17 thf(func_def_1424, type, sK1063: ($i > $o) > $i).
% 169.05/25.17 thf(func_def_1425, type, sK1064: $i > $i).
% 169.05/25.17 thf(func_def_1426, type, sK1065: ($i > $o) > $i).
% 169.05/25.17 thf(func_def_1427, type, sK1066: ($i > $o) > $i > $i).
% 169.05/25.17 thf(func_def_1428, type, sK1067: ($i > $o) > $i > $i).
% 169.05/25.17 thf(func_def_1429, type, sK1068: ($i > $o) > $i > $i).
% 169.05/25.17 thf(func_def_1430, type, sK1069: ($i > $o) > $i).
% 169.05/25.17 thf(func_def_1431, type, sK1070: ($i > $o) > $i).
% 169.05/25.17 thf(func_def_1432, type, sK1071: ($i > $i > $o) > $i > $i > $i).
% 169.05/25.17 thf(func_def_1433, type, ph1072: !>[X0: $tType]:(X0)).
% 169.05/25.17 thf(f17672,plain,(
% 169.05/25.17 $false),
% 169.05/25.17 inference(subsumption_resolution,[status(thm)],[f17671,f15292])).
% 169.05/25.17 thf(f15292,plain,(
% 169.05/25.17 ($true = (in @ sK1073 @ sK338))),
% 169.05/25.17 inference(binary_proxy_clausification,[status(thm)],[f15290])).
% 169.05/25.17 thf(f15290,plain,(
% 169.05/25.17 (((in @ sK1073 @ sK338) & (in @ (kpair @ sK340 @ sK1073) @ sK337)) = $true)),
% 169.05/25.17 inference(binary_proxy_clausification,[status(thm)],[f15288])).
% 169.05/25.17 thf(f15288,plain,(
% 169.05/25.17 ((((in @ sK1073 @ sK338) & (in @ (kpair @ sK340 @ sK1073) @ sK337)) & (in @ (kpair @ sK1073 @ sK341) @ sK339)) = $true)),
% 169.05/25.17 inference(beta_eta_normalization,[status(thm)],[f15287])).
% 169.05/25.17 thf(f15287,plain,(
% 169.05/25.17 (((^[Y0 : $i]: (((in @ Y0 @ sK338) & (in @ (kpair @ sK340 @ Y0) @ sK337)) & (in @ (kpair @ Y0 @ sK341) @ sK339))) @ sK1073) = $true)),
% 169.05/25.17 inference(sigma_clausification,[status(thm)],[f15286])).
% 169.05/25.17 thf(f15286,plain,(
% 169.05/25.17 ((?? @ $i @ (^[Y0 : $i]: (((in @ Y0 @ sK338) & (in @ (kpair @ sK340 @ Y0) @ sK337)) & (in @ (kpair @ Y0 @ sK341) @ sK339)))) = $true)),
% 169.05/25.17 inference(beta_eta_normalization,[status(thm)],[f15285])).
% 169.05/25.17 thf(f15285,plain,(
% 169.05/25.17 (((^[Y0 : $i]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ sK338) & (in @ (kpair @ Y0 @ Y2) @ sK337)) & (in @ (kpair @ Y2 @ Y1) @ sK339))))))) @ sK340 @ sK341) = $true)),
% 169.05/25.17 inference(trivial_inequality_removal,[status(thm)],[f15213])).
% 169.05/25.17 thf(f15213,plain,(
% 169.05/25.17 (((^[Y0 : $i]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ sK338) & (in @ (kpair @ Y0 @ Y2) @ sK337)) & (in @ (kpair @ Y2 @ Y1) @ sK339))))))) @ sK340 @ sK341) = $true) | ($true != $true)),
% 169.05/25.17 inference(superposition,[status(thm)],[f6172,f6416])).
% 169.05/25.17 thf(f6416,plain,(
% 169.05/25.17 ((in @ (kpair @ sK340 @ sK341) @ (dpsetconstr @ sK338 @ sK338 @ (^[Y0 : $i]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ sK338) & (in @ (kpair @ Y0 @ Y2) @ sK337)) & (in @ (kpair @ Y2 @ Y1) @ sK339))))))))) = $true)),
% 169.05/25.17 inference(beta_eta_normalization,[status(thm)],[f5012])).
% 169.05/25.17 thf(f5012,plain,(
% 169.05/25.17 ((in @ (kpair @ sK340 @ sK341) @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y0) & (in @ (kpair @ Y3 @ Y5) @ Y1)) & (in @ (kpair @ Y5 @ Y4) @ Y2))))))))))))) @ sK338 @ sK337 @ sK339)) = $true)),
% 169.05/25.17 inference(definition_unfolding,[status(thm)],[f3456,f2992])).
% 169.05/25.17 thf(f2992,plain,(
% 169.05/25.17 (breln1compset = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y0) & (in @ (kpair @ Y3 @ Y5) @ Y1)) & (in @ (kpair @ Y5 @ Y4) @ Y2))))))))))))))),
% 169.05/25.17 inference(cnf_transformation,[status(thm)],[f818])).
% 169.05/25.17 thf(f818,plain,(
% 169.05/25.17 (breln1compset = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y0) & (in @ (kpair @ Y3 @ Y5) @ Y1)) & (in @ (kpair @ Y5 @ Y4) @ Y2))))))))))))))),
% 169.05/25.17 inference(fool_elimination,[status(thm)],[f817])).
% 169.05/25.17 thf(f817,plain,(
% 169.05/25.17 ((^[X0 : $i, X1 : $i, X2 : $i] : (dpsetconstr @ X0 @ X0 @ (^[X3 : $i, X4 : $i] : (? [X5 : $i] : ((in @ (kpair @ X5 @ X4) @ X2) & (in @ (kpair @ X3 @ X5) @ X1) & (in @ X5 @ X0)))))) = breln1compset)),
% 169.05/25.17 inference(rectify,[status(thm)],[f299])).
% 169.05/25.17 thf(f299,axiom,(
% 169.05/25.17 ((^[X3 : $i, X13 : $i, X15 : $i] : (dpsetconstr @ X3 @ X3 @ (^[X1 : $i, X2 : $i] : (? [X8 : $i] : ((in @ (kpair @ X8 @ X2) @ X15) & (in @ (kpair @ X1 @ X8) @ X13) & (in @ X8 @ X3)))))) = breln1compset)),
% 169.05/25.17 file('/export/starexec/sandbox/tmp/tmp.uVZj498QyD/DTF2THF_20195.p',breln1compset)).
% 169.05/25.17 thf(f3456,plain,(
% 169.05/25.17 ((in @ (kpair @ sK340 @ sK341) @ (breln1compset @ sK338 @ sK337 @ sK339)) = $true)),
% 169.05/25.17 inference(cnf_transformation,[status(thm)],[f1868])).
% 169.05/25.17 thf(f1868,plain,(
% 169.05/25.17 (exuI3 = $true) & (setukpairIL = $true) & (prop2setE = $true) & (setadjoinSub2 = $true) & (funcGraphProp2 = $true) & (woz1_3 = $true) & (ex1I = $true) & (setminusLsub = $true) & (cartprodmempaircEq = $true) & (omega__Cong = $true) & (binintersectSubset3 = $true) & (breln1invprop = $true) & (setadjoinIL = $true) & (exuE3e = $true) & (setunionsingleton = $true) & (ubforcartprodlem1 = $true) & (nonemptyE1 = $true) & (complementTE1 = $true) & (notinsingleton = $true) & (binintersectSubset5 = $true) & (setukpairinjR12 = $true) & (ap2p = $true) & (lamp = $true) & (theprop = $true) & (binunionTIRcontra = $true) & (dpsetconstrER = $true) & (emptysetimpfalse = $true) & (notinemptyset = $true) & (dsetconstr__Cong = $true) & (symdiffI1 = $true) & (setunionE = $true) & (replAx = $true) & (infuncsetfunc = $true) & (iffalse = $true) & (eqimpsubset2 = $true) & (emptysetE = $true) & (cartprodsndpairEq = $true) & (funcGraphProp3 = $true) & (emptyI = $true) & (setbeta = $true) & (subPowSU = $true) & (demorgan2b2 = $true) & (demorgan1a = $true) & (demorgan2 = $true) & (setext = $true) & (funcGraphProp4 = $true) & (secondinupair = $true) & (funcGraphProp1 = $true) & (binintersectTERcontra = $true) & (binintersectLsub = $true) & (setunionAx = $true) & (powersetsubset = $true) & (descr__Cong = $true) & (exu__Cong = $true) & (upairset2IR = $true) & (symdiffI2 = $true) & (emptyinPowerset = $true) & (demorgan2a1 = $true) & (upairset2E = $true) & (complementTI1 = $true) & (woz13rule4 = $true) & (setOfPairsIsBReln = $true) & (inComplementUnionImpNotIn1 = $true) & (binintersectI = $true) & (sepInPowerset = $true) & (eta1 = $true) & (subsetRefl = $true) & (ap2apEq1 = $true) & (binintersectER = $true) & (powersetTI1 = $true) & (setunion__Cong = $true) & (doubleComplementEq = $true) & (powerset__Cong = $true) & (symdiffIneg1 = $true) & (contrasubsetT = $true) & (setadjoinSub = $true) & (exuEu = $true) & (ex1E2 = $true) & (setukpairinjR = $true) & (emptyinunitempty = $true) & (powersetE1 = $true) & (beta1 = $true) & (woz13rule1 = $true) & (setukpairinjR1 = $true) & (setukpairIR = $true) & (nonemptyI1 = $true) & (cartprodmempair = $true) & (dsetconstrI = $true) & (powersetAx = $true) & (setadjoinIR = $true) & (notequalI2 = $true) & (ksndpairEq = $true) & (exuE2 = $true) & (cartprodfstin = $true) & (brelnall1 = $true) & (cartprodpairmemER = $true) & (powersetI1 = $true) & (iffalseProp1 = $true) & (setminusIRneg = $true) & (funcextLem = $true) & (setOfPairsIsBReln1 = $true) & (lam2lamEq = $true) & (upairsetIL = $true) & (funcinfuncset = $true) & (in__Cong = $true) & (demorgan1b = $true) & (woz1_2 = $true) & (setukpairinjL1 = $true) & (breln1invI = $true) & (nonemptyI = $true) & (binunionLsub = $true) & (quantDeMorgan1 = $true) & (kpairp = $true) & (subsetTrans = $true) & (singletonsswitch = $true) & (setukpairinjR2 = $true) & (upairsubunion = $true) & (notdexE = $true) & (breln1SetBreln1 = $true) & (eqimpsubset1 = $true) & (eqbreln = $true) & (woz13rule3 = $true) & (breln1compI = $true) & (ubforcartprodlem2 = $true) & (ubforcartprodlem3 = $true) & (notdallE = $true) & (inPowerset = $true) & (iftrueProp1 = $true) & (binunionEcases = $true) & (setunionE2 = $true) & (ifp = $true) & (woz13rule0 = $true) & (quantDeMorgan2 = $true) & (upairequniteq = $true) & (ifSingleton = $true) & (breln1invE = $true) & (app = $true) & (iftrue = $true) & (demorgan2b = $true) & (setukpairinjL = $true) & (exuE1 = $true) & (doubleComplementI1 = $true) & (complementInPowersetComplementIntersect = $true) & (contrasubsetT2 = $true) & (iftrueorfalse = $true) & (setadjoin__Cong = $true) & (singletoninpowunion = $true) & (subset2powerset = $true) & (powersetTE1 = $true) & (setukpairinjR11 = $true) & (inIntersectImpInUnion2 = $true) & (exuE3u = $true) & (cartprodpairin = $true) & (theeq = $true) & (doubleComplementSub1 = $true) & (notsubsetI = $true) & (descrp = $true) & (sepSubset = $true) & (ex1I2 = $true) & (disjointsetsI1 = $true) & (ap2apEq2 = $true) & (binintersectEL = $true) & (setextT = $true) & (iffalseProp2 = $true) & (setminusI = $true) & (subsetI2 = $true) & (emptysetAx = $true) & (powersetE = $true) & (complementTcontraSubset = $true) & (breln1compprop = $true) & (binunionT_lem = $true) & (setunionsingleton2 = $true) & (quantDeMorgan4 = $true) & (uniqinunit = $true) & (setextAx = $true) & (woz13rule2 = $true) & (singletonsuniq = $true) & (doubleComplementE1 = $true) & (demorgan1 = $true) & (setadjoinOr = $true) & (binintersectT_lem = $true) & (dpsetconstrSub = $true) & (cartprodmempair1 = $true) & (demorgan2a2 = $true) & (quantDeMorgan3 = $true) & (setminusELneg = $true) & (binunionE = $true) & (kpairiskpair = $true) & (powersetI = $true) & (setminusT_lem = $true) & (setminusILneg = $true) & (binunionIL = $true) & (dpsetconstrI = $true) & (setminusSubset1 = $true) & (exuI2 = $true) & (setoftrueEq = $true) & (inIntersectImpInUnion = $true) & (setminusSubset2 = $true) & (cartprodpairmemEL = $true) & (ex1E1 = $true) & (complementUnionInPowersetComplement = $true) & (setminusER = $true) & (eta2 = $true) & (cartprodfstpairEq = $true) & (dsetconstrEL = $true) & (subsetemptysetimpeq = $true) & (kfstsingleton = $true) & (setadjoinE = $true) & (nonemptyImpWitness = $true) & (binintersectRsub = $true) & (breln1all2 = $true) & (cartprodpairsurjEq = $true) & (prop2setI = $true) & (apProp = $true) & (setukpairinjL2 = $true) & (beta2 = $true) & (emptyE1 = $true) & (complementTnotintersectT = $true) & (binunionTEcontra = $true) & (inCongP = $true) & (funcext = $true) & (doubleComplementSub2 = $true) & (setunionI = $true) & (cartprodsndin = $true) & (contrasubsetT1 = $true) & (exuI1 = $true) & ((((breln1 @ sK338 @ sK339) = $true) & (((in @ sK340 @ sK338) = $true) & (((in @ sK341 @ sK338) = $true) & ! [X5 : $i] : (((in @ X5 @ sK338) != $true) | ((in @ (kpair @ sK340 @ X5) @ sK337) != $true) | ((in @ (kpair @ X5 @ sK341) @ sK339) != $true)) & ((in @ (kpair @ sK340 @ sK341) @ (breln1compset @ sK338 @ sK337 @ sK339)) = $true)))) & ((breln1 @ sK338 @ sK337) = $true)) & (lam2p = $true) & (binintersectSubset4 = $true) & (omega0Ax = $true) & (eqinunit = $true) & (kpairsurjEq = $true) & (breln1all1 = $true) & (binintersectSubset1 = $true) & (omegaSAx = $true) & (dpsetconstrEL2 = $true) & (inComplementUnionImpInComplement1 = $true) & (lamProp = $true) & (woz1_1 = $true) & (emptyset__Cong = $true) & (binunionIR = $true) & (funcImageSingleton = $true) & (singletoninpowerset = $true) & (woz1_4 = $true) & (singletonsubset = $true) & (vacuousDall = $true) & (subsetE2 = $true) & (ksndsingleton = $true) & (brelnall2 = $true) & (complementSubsetComplementIntersect = $true) & (binunionTE = $true) & (dpsetconstrERa = $true) & (binintersectTELcontra = $true) & (setminusEL = $true) & (prop2set2propI = $true) & (emptysetsubset = $true) & (eqbreln1 = $true) & (upairsetIR = $true) & (upairsetE = $true) & (intersectInPowersetIntersectUnions = $true) & (bs114d = $true) & (emptyInPowerset = $true) & (binintersectSubset2 = $true) & (choice2fnsingleton = $true) & (binunionTILcontra = $true) & (inIntersectImpInIntersectUnions = $true) & (symdiffIneg2 = $true) & (omegaIndAx = $true) & (dsetconstrER = $true) & (setminusERneg = $true) & (symdiffE = $true) & (setunionsingleton1 = $true) & (subsetTI = $true) & (subsetI1 = $true) & (complementT_lem = $true) & (binunionRsub = $true) & (contraSubsetComplement = $true) & (woz1_5 = $true) & (contrasubsetT3 = $true) & (iftrueProp2 = $true) & (wellorderingAx = $true) & (setadjoinAx = $true) & (foundationAx = $true) & (singletonprop = $true) & (subbreln = $true) & (noeltsimpempty = $true) & (upairinpowunion = $true) & (setextsub = $true) & (powersetT_lem = $true) & (kfstpairEq = $true) & (notequalI1 = $true) & (subsetE = $true) & (subbreln1 = $true) & (complementImpComplementIntersect = $true) & (funcext2 = $true) & (demorgan2a = $true) & (dpsetconstrEL1 = $true)),
% 169.05/25.17 inference(skolemisation,[status(esa),new_symbols(skolem,[sK337,sK338,sK339,sK340,sK341])],[f1134,f1867,f1866,f1865,f1864])).
% 169.05/25.17 thf(f1864,plain,(
% 169.05/25.17 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (breln1 @ X1 @ X2)) & ? [X3 : $i] : (((in @ X3 @ X1) = $true) & ? [X4 : $i] : (((in @ X4 @ X1) = $true) & ! [X5 : $i] : (((in @ X5 @ X1) != $true) | ($true != (in @ (kpair @ X3 @ X5) @ X0)) | ((in @ (kpair @ X5 @ X4) @ X2) != $true)) & ((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) = $true)))) & ((breln1 @ X1 @ X0) = $true)) => (? [X2 : $i] : (((breln1 @ sK338 @ X2) = $true) & ? [X3 : $i] : (((in @ X3 @ sK338) = $true) & ? [X4 : $i] : (((in @ X4 @ sK338) = $true) & ! [X5 : $i] : (((in @ X5 @ sK338) != $true) | ((in @ (kpair @ X3 @ X5) @ sK337) != $true) | ((in @ (kpair @ X5 @ X4) @ X2) != $true)) & ((in @ (kpair @ X3 @ X4) @ (breln1compset @ sK338 @ sK337 @ X2)) = $true)))) & ((breln1 @ sK338 @ sK337) = $true))),
% 169.05/25.17 introduced(definition,[],[choice_axiom])).
% 169.05/25.17 thf(f1865,plain,(
% 169.05/25.17 ? [X2 : $i] : (((breln1 @ sK338 @ X2) = $true) & ? [X3 : $i] : (((in @ X3 @ sK338) = $true) & ? [X4 : $i] : (((in @ X4 @ sK338) = $true) & ! [X5 : $i] : (((in @ X5 @ sK338) != $true) | ((in @ (kpair @ X3 @ X5) @ sK337) != $true) | ((in @ (kpair @ X5 @ X4) @ X2) != $true)) & ((in @ (kpair @ X3 @ X4) @ (breln1compset @ sK338 @ sK337 @ X2)) = $true)))) => (((breln1 @ sK338 @ sK339) = $true) & ? [X3 : $i] : (((in @ X3 @ sK338) = $true) & ? [X4 : $i] : (((in @ X4 @ sK338) = $true) & ! [X5 : $i] : (((in @ X5 @ sK338) != $true) | ((in @ (kpair @ X3 @ X5) @ sK337) != $true) | ((in @ (kpair @ X5 @ X4) @ sK339) != $true)) & ((in @ (kpair @ X3 @ X4) @ (breln1compset @ sK338 @ sK337 @ sK339)) = $true))))),
% 169.05/25.17 introduced(definition,[],[choice_axiom])).
% 169.05/25.17 thf(f1866,plain,(
% 169.05/25.17 ? [X3 : $i] : (((in @ X3 @ sK338) = $true) & ? [X4 : $i] : (((in @ X4 @ sK338) = $true) & ! [X5 : $i] : (((in @ X5 @ sK338) != $true) | ((in @ (kpair @ X3 @ X5) @ sK337) != $true) | ((in @ (kpair @ X5 @ X4) @ sK339) != $true)) & ((in @ (kpair @ X3 @ X4) @ (breln1compset @ sK338 @ sK337 @ sK339)) = $true))) => (((in @ sK340 @ sK338) = $true) & ? [X4 : $i] : (((in @ X4 @ sK338) = $true) & ! [X5 : $i] : (((in @ X5 @ sK338) != $true) | ((in @ (kpair @ sK340 @ X5) @ sK337) != $true) | ((in @ (kpair @ X5 @ X4) @ sK339) != $true)) & ((in @ (kpair @ sK340 @ X4) @ (breln1compset @ sK338 @ sK337 @ sK339)) = $true)))),
% 169.05/25.17 introduced(definition,[],[choice_axiom])).
% 169.05/25.17 thf(f1867,plain,(
% 169.05/25.17 ? [X4 : $i] : (((in @ X4 @ sK338) = $true) & ! [X5 : $i] : (((in @ X5 @ sK338) != $true) | ((in @ (kpair @ sK340 @ X5) @ sK337) != $true) | ((in @ (kpair @ X5 @ X4) @ sK339) != $true)) & ((in @ (kpair @ sK340 @ X4) @ (breln1compset @ sK338 @ sK337 @ sK339)) = $true)) => (((in @ sK341 @ sK338) = $true) & ! [X5 : $i] : (((in @ X5 @ sK338) != $true) | ((in @ (kpair @ sK340 @ X5) @ sK337) != $true) | ((in @ (kpair @ X5 @ sK341) @ sK339) != $true)) & ((in @ (kpair @ sK340 @ sK341) @ (breln1compset @ sK338 @ sK337 @ sK339)) = $true))),
% 169.05/25.17 introduced(definition,[],[choice_axiom])).
% 169.05/25.17 thf(f1134,plain,(
% 169.05/25.17 (exuI3 = $true) & (setukpairIL = $true) & (prop2setE = $true) & (setadjoinSub2 = $true) & (funcGraphProp2 = $true) & (woz1_3 = $true) & (ex1I = $true) & (setminusLsub = $true) & (cartprodmempaircEq = $true) & (omega__Cong = $true) & (binintersectSubset3 = $true) & (breln1invprop = $true) & (setadjoinIL = $true) & (exuE3e = $true) & (setunionsingleton = $true) & (ubforcartprodlem1 = $true) & (nonemptyE1 = $true) & (complementTE1 = $true) & (notinsingleton = $true) & (binintersectSubset5 = $true) & (setukpairinjR12 = $true) & (ap2p = $true) & (lamp = $true) & (theprop = $true) & (binunionTIRcontra = $true) & (dpsetconstrER = $true) & (emptysetimpfalse = $true) & (notinemptyset = $true) & (dsetconstr__Cong = $true) & (symdiffI1 = $true) & (setunionE = $true) & (replAx = $true) & (infuncsetfunc = $true) & (iffalse = $true) & (eqimpsubset2 = $true) & (emptysetE = $true) & (cartprodsndpairEq = $true) & (funcGraphProp3 = $true) & (emptyI = $true) & (setbeta = $true) & (subPowSU = $true) & (demorgan2b2 = $true) & (demorgan1a = $true) & (demorgan2 = $true) & (setext = $true) & (funcGraphProp4 = $true) & (secondinupair = $true) & (funcGraphProp1 = $true) & (binintersectTERcontra = $true) & (binintersectLsub = $true) & (setunionAx = $true) & (powersetsubset = $true) & (descr__Cong = $true) & (exu__Cong = $true) & (upairset2IR = $true) & (symdiffI2 = $true) & (emptyinPowerset = $true) & (demorgan2a1 = $true) & (upairset2E = $true) & (complementTI1 = $true) & (woz13rule4 = $true) & (setOfPairsIsBReln = $true) & (inComplementUnionImpNotIn1 = $true) & (binintersectI = $true) & (sepInPowerset = $true) & (eta1 = $true) & (subsetRefl = $true) & (ap2apEq1 = $true) & (binintersectER = $true) & (powersetTI1 = $true) & (setunion__Cong = $true) & (doubleComplementEq = $true) & (powerset__Cong = $true) & (symdiffIneg1 = $true) & (contrasubsetT = $true) & (setadjoinSub = $true) & (exuEu = $true) & (ex1E2 = $true) & (setukpairinjR = $true) & (emptyinunitempty = $true) & (powersetE1 = $true) & (beta1 = $true) & (woz13rule1 = $true) & (setukpairinjR1 = $true) & (setukpairIR = $true) & (nonemptyI1 = $true) & (cartprodmempair = $true) & (dsetconstrI = $true) & (powersetAx = $true) & (setadjoinIR = $true) & (notequalI2 = $true) & (ksndpairEq = $true) & (exuE2 = $true) & (cartprodfstin = $true) & (brelnall1 = $true) & (cartprodpairmemER = $true) & (powersetI1 = $true) & (iffalseProp1 = $true) & (setminusIRneg = $true) & (funcextLem = $true) & (setOfPairsIsBReln1 = $true) & (lam2lamEq = $true) & (upairsetIL = $true) & (funcinfuncset = $true) & (in__Cong = $true) & (demorgan1b = $true) & (woz1_2 = $true) & (setukpairinjL1 = $true) & (breln1invI = $true) & (nonemptyI = $true) & (binunionLsub = $true) & (quantDeMorgan1 = $true) & (kpairp = $true) & (subsetTrans = $true) & (singletonsswitch = $true) & (setukpairinjR2 = $true) & (upairsubunion = $true) & (notdexE = $true) & (breln1SetBreln1 = $true) & (eqimpsubset1 = $true) & (eqbreln = $true) & (woz13rule3 = $true) & (breln1compI = $true) & (ubforcartprodlem2 = $true) & (ubforcartprodlem3 = $true) & (notdallE = $true) & (inPowerset = $true) & (iftrueProp1 = $true) & (binunionEcases = $true) & (setunionE2 = $true) & (ifp = $true) & (woz13rule0 = $true) & (quantDeMorgan2 = $true) & (upairequniteq = $true) & (ifSingleton = $true) & (breln1invE = $true) & (app = $true) & (iftrue = $true) & (demorgan2b = $true) & (setukpairinjL = $true) & (exuE1 = $true) & (doubleComplementI1 = $true) & (complementInPowersetComplementIntersect = $true) & (contrasubsetT2 = $true) & (iftrueorfalse = $true) & (setadjoin__Cong = $true) & (singletoninpowunion = $true) & (subset2powerset = $true) & (powersetTE1 = $true) & (setukpairinjR11 = $true) & (inIntersectImpInUnion2 = $true) & (exuE3u = $true) & (cartprodpairin = $true) & (theeq = $true) & (doubleComplementSub1 = $true) & (notsubsetI = $true) & (descrp = $true) & (sepSubset = $true) & (ex1I2 = $true) & (disjointsetsI1 = $true) & (ap2apEq2 = $true) & (binintersectEL = $true) & (setextT = $true) & (iffalseProp2 = $true) & (setminusI = $true) & (subsetI2 = $true) & (emptysetAx = $true) & (powersetE = $true) & (complementTcontraSubset = $true) & (breln1compprop = $true) & (binunionT_lem = $true) & (setunionsingleton2 = $true) & (quantDeMorgan4 = $true) & (uniqinunit = $true) & (setextAx = $true) & (woz13rule2 = $true) & (singletonsuniq = $true) & (doubleComplementE1 = $true) & (demorgan1 = $true) & (setadjoinOr = $true) & (binintersectT_lem = $true) & (dpsetconstrSub = $true) & (cartprodmempair1 = $true) & (demorgan2a2 = $true) & (quantDeMorgan3 = $true) & (setminusELneg = $true) & (binunionE = $true) & (kpairiskpair = $true) & (powersetI = $true) & (setminusT_lem = $true) & (setminusILneg = $true) & (binunionIL = $true) & (dpsetconstrI = $true) & (setminusSubset1 = $true) & (exuI2 = $true) & (setoftrueEq = $true) & (inIntersectImpInUnion = $true) & (setminusSubset2 = $true) & (cartprodpairmemEL = $true) & (ex1E1 = $true) & (complementUnionInPowersetComplement = $true) & (setminusER = $true) & (eta2 = $true) & (cartprodfstpairEq = $true) & (dsetconstrEL = $true) & (subsetemptysetimpeq = $true) & (kfstsingleton = $true) & (setadjoinE = $true) & (nonemptyImpWitness = $true) & (binintersectRsub = $true) & (breln1all2 = $true) & (cartprodpairsurjEq = $true) & (prop2setI = $true) & (apProp = $true) & (setukpairinjL2 = $true) & (beta2 = $true) & (emptyE1 = $true) & (complementTnotintersectT = $true) & (binunionTEcontra = $true) & (inCongP = $true) & (funcext = $true) & (doubleComplementSub2 = $true) & (setunionI = $true) & (cartprodsndin = $true) & (contrasubsetT1 = $true) & (exuI1 = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (breln1 @ X1 @ X2)) & ? [X3 : $i] : (((in @ X3 @ X1) = $true) & ? [X4 : $i] : (((in @ X4 @ X1) = $true) & ! [X5 : $i] : (((in @ X5 @ X1) != $true) | ($true != (in @ (kpair @ X3 @ X5) @ X0)) | ((in @ (kpair @ X5 @ X4) @ X2) != $true)) & ((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) = $true)))) & ((breln1 @ X1 @ X0) = $true)) & (lam2p = $true) & (binintersectSubset4 = $true) & (omega0Ax = $true) & (eqinunit = $true) & (kpairsurjEq = $true) & (breln1all1 = $true) & (binintersectSubset1 = $true) & (omegaSAx = $true) & (dpsetconstrEL2 = $true) & (inComplementUnionImpInComplement1 = $true) & (lamProp = $true) & (woz1_1 = $true) & (emptyset__Cong = $true) & (binunionIR = $true) & (funcImageSingleton = $true) & (singletoninpowerset = $true) & (woz1_4 = $true) & (singletonsubset = $true) & (vacuousDall = $true) & (subsetE2 = $true) & (ksndsingleton = $true) & (brelnall2 = $true) & (complementSubsetComplementIntersect = $true) & (binunionTE = $true) & (dpsetconstrERa = $true) & (binintersectTELcontra = $true) & (setminusEL = $true) & (prop2set2propI = $true) & (emptysetsubset = $true) & (eqbreln1 = $true) & (upairsetIR = $true) & (upairsetE = $true) & (intersectInPowersetIntersectUnions = $true) & (bs114d = $true) & (emptyInPowerset = $true) & (binintersectSubset2 = $true) & (choice2fnsingleton = $true) & (binunionTILcontra = $true) & (inIntersectImpInIntersectUnions = $true) & (symdiffIneg2 = $true) & (omegaIndAx = $true) & (dsetconstrER = $true) & (setminusERneg = $true) & (symdiffE = $true) & (setunionsingleton1 = $true) & (subsetTI = $true) & (subsetI1 = $true) & (complementT_lem = $true) & (binunionRsub = $true) & (contraSubsetComplement = $true) & (woz1_5 = $true) & (contrasubsetT3 = $true) & (iftrueProp2 = $true) & (wellorderingAx = $true) & (setadjoinAx = $true) & (foundationAx = $true) & (singletonprop = $true) & (subbreln = $true) & (noeltsimpempty = $true) & (upairinpowunion = $true) & (setextsub = $true) & (powersetT_lem = $true) & (kfstpairEq = $true) & (notequalI1 = $true) & (subsetE = $true) & (subbreln1 = $true) & (complementImpComplementIntersect = $true) & (funcext2 = $true) & (demorgan2a = $true) & (dpsetconstrEL1 = $true)),
% 169.05/25.17 inference(flattening,[status(thm)],[f1133])).
% 169.05/25.17 thf(f1133,plain,(
% 169.05/25.17 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : ((! [X5 : $i] : (((in @ X5 @ X1) != $true) | ($true != (in @ (kpair @ X3 @ X5) @ X0)) | ((in @ (kpair @ X5 @ X4) @ X2) != $true)) & ((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) = $true)) & ((in @ X4 @ X1) = $true)) & ((in @ X3 @ X1) = $true)) & ($true = (breln1 @ X1 @ X2))) & ((breln1 @ X1 @ X0) = $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)),
% 169.05/25.17 inference(ennf_transformation,[status(thm)],[f872])).
% 169.05/25.17 thf(f872,plain,(
% 169.05/25.17 ~((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) => ! [X0 : $i,X1 : $i] : (((breln1 @ X1 @ X0) = $true) => ! [X2 : $i] : (($true = (breln1 @ X1 @ X2)) => ! [X3 : $i] : (((in @ X3 @ X1) = $true) => ! [X4 : $i] : (((in @ X4 @ X1) = $true) => (((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) = $true) => ? [X5 : $i] : (((in @ (kpair @ X5 @ X4) @ X2) = $true) & ($true = (in @ (kpair @ X3 @ X5) @ X0)) & ((in @ X5 @ X1) = $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 169.05/25.17 inference(fool_elimination,[status(thm)],[f871])).
% 169.05/25.17 thf(f871,plain,(
% 169.05/25.17 ~(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 => ! [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 : $i] : ((in @ (kpair @ X5 @ X4) @ X2) & (in @ (kpair @ X3 @ X5) @ X0) & (in @ X5 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 169.05/25.17 inference(rectify,[status(thm)],[f303])).
% 169.05/25.17 thf(f303,negated_conjecture,(
% 169.05/25.17 ~(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 => ! [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)) => ? [X8 : $i] : ((in @ (kpair @ X8 @ X2) @ X15) & (in @ (kpair @ X1 @ X8) @ X13) & (in @ X8 @ X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 169.05/25.17 inference(negated_conjecture,[status(cth)],[f302])).
% 169.05/25.17 thf(f302,conjecture,(
% 169.05/25.17 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 => ! [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)) => ? [X8 : $i] : ((in @ (kpair @ X8 @ X2) @ X15) & (in @ (kpair @ X1 @ X8) @ X13) & (in @ X8 @ X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 169.05/25.17 file('/export/starexec/sandbox/tmp/tmp.uVZj498QyD/DTF2THF_20195.p',breln1compE)).
% 169.05/25.17 thf(f6172,plain,(
% 169.05/25.17 ( ! [X8 : $i > $i > $o,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (((in @ (kpair @ X7 @ X5) @ (dpsetconstr @ X9 @ X6 @ X8)) != $true) | ((X8 @ X7 @ X5) = $true)) )),
% 169.05/25.17 inference(beta_eta_normalization,[status(thm)],[f6171])).
% 169.05/25.17 thf(f6171,plain,(
% 169.05/25.17 ( ! [X8 : $i > $i > $o,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (((in @ (kpair @ X7 @ X5) @ (dpsetconstr @ X9 @ X6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X8 @ Y0 @ Y1)))))) != $true) | ((X8 @ X7 @ X5) = $true)) )),
% 169.05/25.17 inference(trivial_inequality_removal,[status(thm)],[f5428])).
% 169.05/25.17 thf(f5428,plain,(
% 169.05/25.17 ( ! [X8 : $i > $i > $o,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (($true != $true) | ((X8 @ X7 @ X5) = $true) | ((in @ (kpair @ X7 @ X5) @ (dpsetconstr @ X9 @ X6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X8 @ Y0 @ Y1)))))) != $true)) )),
% 169.05/25.17 inference(definition_unfolding,[status(thm)],[f4176,f3661])).
% 169.05/25.17 thf(f3661,plain,(
% 169.05/25.17 (dpsetconstrER = $true)),
% 169.05/25.17 inference(cnf_transformation,[status(thm)],[f1868])).
% 169.05/25.17 thf(f4176,plain,(
% 169.05/25.17 ( ! [X8 : $i > $i > $o,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (((X8 @ X7 @ X5) = $true) | ((in @ (kpair @ X7 @ X5) @ (dpsetconstr @ X9 @ X6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X8 @ Y0 @ Y1)))))) != $true) | (dpsetconstrER != $true)) )),
% 169.05/25.17 inference(cnf_transformation,[status(thm)],[f2426])).
% 169.05/25.17 thf(f2426,plain,(
% 169.05/25.17 ((dpsetconstrER = $true) | (((sK690 @ sK689 @ sK687) != $true) & ($true = (in @ (kpair @ sK689 @ sK687) @ (dpsetconstr @ sK691 @ sK688 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK690 @ Y0 @ Y1))))))))) & (! [X5 : $i,X6 : $i,X7 : $i,X8 : $i > $i > $o,X9 : $i] : (((X8 @ X7 @ X5) = $true) | ((in @ (kpair @ X7 @ X5) @ (dpsetconstr @ X9 @ X6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X8 @ Y0 @ Y1)))))) != $true)) | (dpsetconstrER != $true))),
% 169.05/25.17 inference(skolemisation,[status(esa),new_symbols(skolem,[sK687,sK688,sK689,sK690,sK691])],[f2424,f2425])).
% 169.05/25.17 thf(f2425,plain,(
% 169.05/25.17 ? [X0 : $i,X1 : $i,X2 : $i,X3 : $i > $i > $o,X4 : $i] : (((X3 @ X2 @ X0) != $true) & ((in @ (kpair @ X2 @ X0) @ (dpsetconstr @ X4 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X3 @ Y0 @ Y1)))))) = $true)) => (((sK690 @ sK689 @ sK687) != $true) & ($true = (in @ (kpair @ sK689 @ sK687) @ (dpsetconstr @ sK691 @ sK688 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK690 @ Y0 @ Y1))))))))),
% 169.05/25.17 introduced(definition,[],[choice_axiom])).
% 169.05/25.17 thf(f2424,plain,(
% 169.05/25.17 ((dpsetconstrER = $true) | ? [X0 : $i,X1 : $i,X2 : $i,X3 : $i > $i > $o,X4 : $i] : (((X3 @ X2 @ X0) != $true) & ((in @ (kpair @ X2 @ X0) @ (dpsetconstr @ X4 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X3 @ Y0 @ Y1)))))) = $true))) & (! [X5 : $i,X6 : $i,X7 : $i,X8 : $i > $i > $o,X9 : $i] : (((X8 @ X7 @ X5) = $true) | ((in @ (kpair @ X7 @ X5) @ (dpsetconstr @ X9 @ X6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X8 @ Y0 @ Y1)))))) != $true)) | (dpsetconstrER != $true))),
% 169.05/25.17 inference(rectify,[status(thm)],[f2423])).
% 169.05/25.17 thf(f2423,plain,(
% 169.05/25.17 ((dpsetconstrER = $true) | ? [X0 : $i,X1 : $i,X2 : $i,X3 : $i > $i > $o,X4 : $i] : (((X3 @ X2 @ X0) != $true) & ((in @ (kpair @ X2 @ X0) @ (dpsetconstr @ X4 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X3 @ Y0 @ Y1)))))) = $true))) & (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i > $i > $o,X4 : $i] : (((X3 @ X2 @ X0) = $true) | ((in @ (kpair @ X2 @ X0) @ (dpsetconstr @ X4 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X3 @ Y0 @ Y1)))))) != $true)) | (dpsetconstrER != $true))),
% 169.05/25.17 inference(nnf_transformation,[status(thm)],[f1132])).
% 169.05/25.17 thf(f1132,plain,(
% 169.05/25.17 (dpsetconstrER = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i > $i > $o,X4 : $i] : (((X3 @ X2 @ X0) = $true) | ((in @ (kpair @ X2 @ X0) @ (dpsetconstr @ X4 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X3 @ Y0 @ Y1)))))) != $true))),
% 169.05/25.17 inference(ennf_transformation,[status(thm)],[f674])).
% 169.05/25.17 thf(f674,plain,(
% 169.05/25.17 ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i > $i > $o,X4 : $i] : (((in @ (kpair @ X2 @ X0) @ (dpsetconstr @ X4 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X3 @ Y0 @ Y1)))))) = $true) => ((X3 @ X2 @ X0) = $true)) <=> (dpsetconstrER = $true)),
% 169.05/25.17 inference(fool_elimination,[status(thm)],[f673])).
% 169.05/25.17 thf(f673,plain,(
% 169.05/25.17 (dpsetconstrER = ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i > $i > $o,X4 : $i] : ((in @ (kpair @ X2 @ X0) @ (dpsetconstr @ X4 @ X1 @ (^[X5 : $i, X6 : $i] : (X3 @ X5 @ X6)))) => (X3 @ X2 @ X0)))),
% 169.05/25.17 inference(rectify,[status(thm)],[f191])).
% 169.05/25.17 thf(f191,axiom,(
% 169.05/25.17 (dpsetconstrER = ! [X2 : $i,X4 : $i,X1 : $i,X0 : $i > $i > $o,X3 : $i] : ((in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10)))) => (X0 @ X1 @ X2)))),
% 169.05/25.17 file('/export/starexec/sandbox/tmp/tmp.uVZj498QyD/DTF2THF_20195.p',dpsetconstrER)).
% 169.05/25.17 thf(f17671,plain,(
% 169.05/25.17 ($true != (in @ sK1073 @ sK338))),
% 169.05/25.17 inference(subsumption_resolution,[status(thm)],[f17649,f15289])).
% 169.05/25.17 thf(f15289,plain,(
% 169.05/25.17 ((in @ (kpair @ sK1073 @ sK341) @ sK339) = $true)),
% 169.05/25.17 inference(binary_proxy_clausification,[status(thm)],[f15288])).
% 169.05/25.17 thf(f17649,plain,(
% 169.05/25.17 ((in @ (kpair @ sK1073 @ sK341) @ sK339) != $true) | ($true != (in @ sK1073 @ sK338))),
% 169.05/25.17 inference(trivial_inequality_removal,[status(thm)],[f17588])).
% 169.05/25.17 thf(f17588,plain,(
% 169.05/25.17 ($true != $true) | ($true != (in @ sK1073 @ sK338)) | ((in @ (kpair @ sK1073 @ sK341) @ sK339) != $true)),
% 169.05/25.17 inference(superposition,[status(thm)],[f3457,f15291])).
% 169.05/25.17 thf(f15291,plain,(
% 169.05/25.17 ($true = (in @ (kpair @ sK340 @ sK1073) @ sK337))),
% 169.05/25.17 inference(binary_proxy_clausification,[status(thm)],[f15290])).
% 169.05/25.17 thf(f3457,plain,(
% 169.05/25.17 ( ! [X5 : $i] : (((in @ (kpair @ sK340 @ X5) @ sK337) != $true) | ((in @ (kpair @ X5 @ sK341) @ sK339) != $true) | ((in @ X5 @ sK338) != $true)) )),
% 169.05/25.17 inference(cnf_transformation,[status(thm)],[f1868])).
% 169.05/25.17 % SZS output end Proof for DTF2THF_20195
% 169.05/25.17 % (21661)------------------------------
% 169.05/25.17 % (21661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 169.05/25.17 % (21661)Termination reason: Refutation
% 169.05/25.17
% 169.05/25.17 % (21661)Memory used [KB]: 13176
% 169.05/25.17 % (21661)Time elapsed: 1.660 s
% 169.05/25.17 % (21661)Instructions burned: 5302 (million)
% 169.05/25.17 % (21661)------------------------------
% 169.05/25.17 % (21661)------------------------------
% 169.05/25.17 % (20434)Success in time 23.886 s
%------------------------------------------------------------------------------