%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU743^1 : 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 : n021.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 09:36:50 AM UTC 2026
% Result : Theorem 206.94s 30.98s
% Output : Refutation 206.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 42
% Syntax : Number of formulae : 235 ( 91 unt; 0 typ; 4 def)
% Number of atoms : 5409 (1544 equ; 0 cnn)
% Maximal formula atoms : 263 ( 23 avg)
% Number of connectives : 3831 ( 185 ~; 192 |; 853 &;1506 @)
% ( 19 <=>;1076 =>; 0 <=; 0 <~>)
% Maximal formula depth : 274 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 1789 (1786 usr; 290 con; 0-4 aty)
% Number of variables : 462 ( 0 ^; 381 !; 81 ?; 462 :)
% 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_311,type,
sP0: $i > $i > $o ).
thf(func_def_312,type,
sP1: $i > $o ).
thf(func_def_313,type,
sP2: $i > $i > $o ).
thf(func_def_314,type,
sP3: $i > $i > $o ).
thf(func_def_315,type,
sP4: $i > $i > $i > $o ).
thf(func_def_320,type,
sP9: $i > $i > $i > $i > $o ).
thf(func_def_322,type,
sP11: $i > $i > $i > $o > $o ).
thf(func_def_323,type,
sK12: $i > $o ).
thf(func_def_326,type,
sK15: $i > $o ).
thf(func_def_329,type,
sK18: $i > ( $i > $o ) > $i ).
thf(func_def_330,type,
sK19: $i > ( $i > $o ) > $i ).
thf(func_def_331,type,
sK20: $i > $o ).
thf(func_def_362,type,
sK51: $i > $o ).
thf(func_def_381,type,
sK70: $i > ( $i > $o ) > $i ).
thf(func_def_382,type,
sK71: $i > $o ).
thf(func_def_388,type,
sK77: $i > $i > $i ).
thf(func_def_395,type,
sK84: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_396,type,
sK85: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_399,type,
sK88: $i > $o ).
thf(func_def_400,type,
sK89: $i > $o ).
thf(func_def_416,type,
sK105: $i > $i > $i ).
thf(func_def_422,type,
sK111: $i > $o ).
thf(func_def_425,type,
sK114: $i > $i > $i ).
thf(func_def_426,type,
sK115: $i > $i > $i ).
thf(func_def_431,type,
sK120: $i > $i > $i ).
thf(func_def_438,type,
sK127: $i > $i > $i ).
thf(func_def_439,type,
sK128: $i > $i > $i ).
thf(func_def_440,type,
sK129: $i > $i > $i ).
thf(func_def_441,type,
sK130: $i > $i > $i ).
thf(func_def_442,type,
sK131: $i > $i > $i ).
thf(func_def_443,type,
sK132: $i > $i > $i > $i ).
thf(func_def_444,type,
sK133: $i > $i ).
thf(func_def_445,type,
sK134: $i > $i ).
thf(func_def_446,type,
sK135: $i > $i ).
thf(func_def_447,type,
sK136: $i > $i ).
thf(func_def_448,type,
sK137: $i > $i > $i ).
thf(func_def_449,type,
sK138: $i > $i > $i > $i ).
thf(func_def_450,type,
sK139: $i > $i > $i > $i ).
thf(func_def_451,type,
sK140: $i > $i > $i ).
thf(func_def_452,type,
sK141: $i > $i > $i ).
thf(func_def_453,type,
sK142: $i > $i ).
thf(func_def_455,type,
sK144: $i > $i ).
thf(func_def_456,type,
sK145: $i > $i ).
thf(func_def_465,type,
sK154: $i > $i > $o ).
thf(func_def_474,type,
sK163: $i > $i > $i ).
thf(func_def_495,type,
sK184: $i > ( $i > $i ) > $i > $i ).
thf(func_def_497,type,
sK186: $i > $i ).
thf(func_def_504,type,
sK193: $i > $i ).
thf(func_def_507,type,
sK196: $i > $i ).
thf(func_def_509,type,
sK198: $i > $i ).
thf(func_def_517,type,
sK206: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_518,type,
sK207: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_519,type,
sK208: $i > $o ).
thf(func_def_520,type,
sK209: $i > $o ).
thf(func_def_521,type,
sK210: $i > ( $i > $o ) > $i ).
thf(func_def_522,type,
sK211: $i > $o ).
thf(func_def_524,type,
sK213: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_525,type,
sK214: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_526,type,
sK215: $i > $o ).
thf(func_def_527,type,
sK216: $i > $o ).
thf(func_def_531,type,
sK220: $i > $i ).
thf(func_def_539,type,
sK228: $o > $i > $i > $i ).
thf(func_def_547,type,
sK236: $i > $i > $i > $i ).
thf(func_def_562,type,
sK251: $i > $i ).
thf(func_def_578,type,
sK267: $i > $o ).
thf(func_def_596,type,
sK285: $i > $i ).
thf(func_def_598,type,
sK287: ( $i > $i ) > $i > $i > $i ).
thf(func_def_601,type,
sK290: $i > $o ).
thf(func_def_602,type,
sK291: ( $i > $o ) > $i ).
thf(func_def_603,type,
sK292: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_604,type,
sK293: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_608,type,
sK297: $i > $o ).
thf(func_def_628,type,
sK317: $i > $o ).
thf(func_def_643,type,
sK332: $i > $i ).
thf(func_def_645,type,
sK334: $i > ( $i > $i ) > $i > $i ).
thf(func_def_656,type,
sK345: $i > $i > $i > $i ).
thf(func_def_660,type,
sK349: $i > $i > $i > $i ).
thf(func_def_661,type,
sK350: $i > $o ).
thf(func_def_664,type,
sK353: $i > $o ).
thf(func_def_666,type,
sK355: ( $i > $o ) > $i > $i ).
thf(func_def_667,type,
sK356: ( $i > $o ) > $i > $i ).
thf(func_def_672,type,
sK361: $i > $i > $o ).
thf(func_def_673,type,
sK362: $i > $i ).
thf(func_def_674,type,
sK363: $i > $i ).
thf(func_def_675,type,
sK364: ( $i > $i > $o ) > $i > $i ).
thf(func_def_676,type,
sK365: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_677,type,
sK366: ( $i > $i > $o ) > $i > $i ).
thf(func_def_690,type,
sK379: $i > $o ).
thf(func_def_692,type,
sK381: ( $i > $o ) > $i > $i ).
thf(func_def_693,type,
sK382: ( $i > $o ) > $i > $i ).
thf(func_def_694,type,
sK383: $i > $o ).
thf(func_def_701,type,
sK390: $i > $i > $o ).
thf(func_def_713,type,
sK402: $i > $o ).
thf(func_def_716,type,
sK405: $i > $i > $o ).
thf(func_def_725,type,
sK414: $i > ( $i > $o ) > $i ).
thf(func_def_726,type,
sK415: $i > $o ).
thf(func_def_734,type,
sK423: $i > $i ).
thf(func_def_741,type,
sK430: ( $i > $o ) > $i > $i ).
thf(func_def_743,type,
sK432: $i > $o ).
thf(func_def_751,type,
sK440: $i > $i > $o ).
thf(func_def_762,type,
sK451: $i > $i > $i ).
thf(func_def_772,type,
sK461: $i > $o ).
thf(func_def_790,type,
sK479: $i > $i > $i > $i ).
thf(func_def_792,type,
sK481: $i > $o ).
thf(func_def_795,type,
sK484: $i > $i > $o ).
thf(func_def_804,type,
sK493: $i > $o ).
thf(func_def_806,type,
sK495: ( $i > $o ) > $i > $i ).
thf(func_def_811,type,
sK500: $i > $o ).
thf(func_def_832,type,
sK521: $i > $i > $o ).
thf(func_def_842,type,
sK531: $i > $i > $i > $i > $i ).
thf(func_def_857,type,
sK546: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_858,type,
sK547: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_862,type,
sK551: $i > $o ).
thf(func_def_878,type,
sK567: $i > $i > $i > $i > $i ).
thf(func_def_879,type,
sK568: $i > $i > $i > $i > $i ).
thf(func_def_933,type,
sK622: $i > $i > $i > $i ).
thf(func_def_934,type,
sK623: $i > $i > $i > $i ).
thf(func_def_935,type,
sK624: ( $i > $o ) > $i ).
thf(func_def_936,type,
sK625: $i > $o ).
thf(func_def_937,type,
sK626: $i > $i ).
thf(func_def_943,type,
sK632: $i > $o ).
thf(func_def_946,type,
sK635: $i > $i > $i > $i > $i ).
thf(func_def_951,type,
sK640: $i > ( $i > $i ) > $i > $i ).
thf(func_def_953,type,
sK642: $i > $i ).
thf(func_def_970,type,
sK659: $i > $i > $i > $i > $i ).
thf(func_def_983,type,
sK672: $i > $o ).
thf(func_def_985,type,
sK674: ( $i > $o ) > $i ).
thf(func_def_986,type,
sK675: ( $i > $o ) > $i ).
thf(func_def_989,type,
sK678: $i > $i ).
thf(func_def_994,type,
sK683: ( $i > $i ) > $i > $i > $i ).
thf(func_def_997,type,
sK686: $i > $i ).
thf(func_def_1005,type,
sK694: $i > $i > $i ).
thf(func_def_1006,type,
sK695: $i > $o ).
thf(func_def_1009,type,
sK698: $i > $i > ( $i > $o ) > $i ).
thf(func_def_1014,type,
sK703: $i > $i > $i > $i > $i ).
thf(func_def_1015,type,
sK704: $i > $i > $i > $i > $i ).
thf(func_def_1016,type,
sK705: $i > $i > $i > $i > $i ).
thf(func_def_1017,type,
sK706: $i > $i > $i > $i > $i ).
thf(func_def_1028,type,
sK717: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1030,type,
sK719: $i > $i ).
thf(func_def_1045,type,
sK734: $i > $o ).
thf(func_def_1047,type,
sK736: $i > $o ).
thf(func_def_1048,type,
sK737: ( $i > $o ) > $i > $i ).
thf(func_def_1052,type,
sK741: $i > ( $i > $o ) > $i ).
thf(func_def_1053,type,
sK742: $i > $o ).
thf(func_def_1089,type,
sK778: $i > $i > $i ).
thf(func_def_1096,type,
sK785: $i > $i > $i ).
thf(func_def_1102,type,
sK791: $i > $i > $o ).
thf(func_def_1122,type,
sK811: $i > $o ).
thf(func_def_1123,type,
sK812: $i > $i ).
thf(func_def_1124,type,
sK813: ( $i > $o ) > $i ).
thf(func_def_1140,type,
sP829: $i > $o ).
thf(func_def_1141,type,
sP830: $o > $o ).
thf(func_def_1142,type,
sP831: $o > $o ).
thf(func_def_1143,type,
sP832: $o > $o ).
thf(func_def_1144,type,
sP833: $o > $o ).
thf(func_def_1145,type,
sP834: $o > $o ).
thf(func_def_1146,type,
sP835: $o > $o ).
thf(func_def_1147,type,
sP836: $o > $o ).
thf(func_def_1148,type,
sP837: $o > $o ).
thf(func_def_1149,type,
sP838: $o > $o ).
thf(func_def_1150,type,
sP839: $o > $o ).
thf(func_def_1151,type,
sP840: $o > $o ).
thf(func_def_1152,type,
sP841: $o > $o ).
thf(func_def_1153,type,
sP842: $o > $o ).
thf(func_def_1154,type,
sP843: $o > $o ).
thf(func_def_1155,type,
sP844: $o > $o ).
thf(func_def_1156,type,
sP845: $o > $o ).
thf(func_def_1157,type,
sP846: $o > $o ).
thf(func_def_1158,type,
sP847: $o > $o ).
thf(func_def_1159,type,
sP848: $o > $o ).
thf(func_def_1160,type,
sP849: $o > $o ).
thf(func_def_1161,type,
sP850: $o > $o ).
thf(func_def_1162,type,
sP851: $o > $o ).
thf(func_def_1163,type,
sP852: $o > $o ).
thf(func_def_1164,type,
sP853: $o > $o ).
thf(func_def_1165,type,
sP854: $o > $o ).
thf(func_def_1166,type,
sP855: $o > $o ).
thf(func_def_1167,type,
sP856: $o > $o ).
thf(func_def_1168,type,
sP857: $o > $o ).
thf(func_def_1169,type,
sP858: $o > $o ).
thf(func_def_1170,type,
sP859: $o > $o ).
thf(func_def_1171,type,
sP860: $o > $o ).
thf(func_def_1172,type,
sP861: $o > $o ).
thf(func_def_1173,type,
sP862: $i > $o ).
thf(func_def_1174,type,
sP863: $o > $o ).
thf(func_def_1175,type,
sP864: $o > $o ).
thf(func_def_1176,type,
sP865: $o > $o ).
thf(func_def_1177,type,
sP866: $o > $o ).
thf(func_def_1178,type,
sP867: $o > $o ).
thf(func_def_1179,type,
sP868: $o > $o ).
thf(func_def_1180,type,
sP869: $o > $o ).
thf(func_def_1181,type,
sP870: $o > $o ).
thf(func_def_1182,type,
sP871: $o > $o ).
thf(func_def_1183,type,
sP872: $o > $o ).
thf(func_def_1184,type,
sP873: $o > $o ).
thf(func_def_1185,type,
sP874: $o > $o ).
thf(func_def_1186,type,
sP875: $o > $o ).
thf(func_def_1187,type,
sP876: $o > $o ).
thf(func_def_1188,type,
sP877: $o > $o ).
thf(func_def_1189,type,
sP878: $o > $o ).
thf(func_def_1190,type,
sP879: $o > $o ).
thf(func_def_1191,type,
sP880: $o > $o ).
thf(func_def_1192,type,
sP881: $o > $o ).
thf(func_def_1193,type,
sP882: $o > $o ).
thf(func_def_1194,type,
sP883: $o > $o ).
thf(func_def_1195,type,
sP884: $o > $o ).
thf(func_def_1196,type,
sP885: $o > $o ).
thf(func_def_1197,type,
sP886: $o > $o ).
thf(func_def_1198,type,
sP887: $o > $o ).
thf(func_def_1199,type,
sP888: $o > $o ).
thf(func_def_1200,type,
sP889: $o > $o ).
thf(func_def_1201,type,
sP890: $o > $o ).
thf(func_def_1202,type,
sP891: $o > $o ).
thf(func_def_1203,type,
sP892: $o > $o ).
thf(func_def_1204,type,
sP893: $i > $o ).
thf(func_def_1205,type,
sP894: $o > $o ).
thf(func_def_1206,type,
sP895: $o > $o ).
thf(func_def_1207,type,
sP896: $o > $o ).
thf(func_def_1208,type,
sP897: $o > $o ).
thf(func_def_1209,type,
sP898: $o > $o ).
thf(func_def_1210,type,
sP899: $o > $o ).
thf(func_def_1211,type,
sP900: $o > $o ).
thf(func_def_1212,type,
sP901: $o > $o ).
thf(func_def_1213,type,
sP902: $o > $o ).
thf(func_def_1214,type,
sP903: $o > $o ).
thf(func_def_1215,type,
sP904: $o > $o ).
thf(func_def_1216,type,
sP905: $o > $o ).
thf(func_def_1217,type,
sP906: $o > $o ).
thf(func_def_1218,type,
sP907: $o > $o ).
thf(func_def_1219,type,
sP908: $o > $o ).
thf(func_def_1220,type,
sP909: $o > $o ).
thf(func_def_1221,type,
sP910: $o > $o ).
thf(func_def_1222,type,
sP911: $o > $o ).
thf(func_def_1223,type,
sP912: $o > $o ).
thf(func_def_1224,type,
sP913: $o > $o ).
thf(func_def_1225,type,
sP914: $o > $o ).
thf(func_def_1226,type,
sP915: $o > $o ).
thf(func_def_1227,type,
sP916: $o > $o ).
thf(func_def_1228,type,
sP917: $o > $o ).
thf(func_def_1229,type,
sP918: $o > $o ).
thf(func_def_1230,type,
sP919: $o > $o ).
thf(func_def_1231,type,
sP920: $o > $o ).
thf(func_def_1232,type,
sP921: $o > $o ).
thf(func_def_1233,type,
sP922: $o > $o ).
thf(func_def_1234,type,
sP923: $o > $o ).
thf(func_def_1235,type,
sP924: $i > $o ).
thf(func_def_1236,type,
sP925: $o > $o ).
thf(func_def_1237,type,
sP926: $o > $o ).
thf(func_def_1238,type,
sP927: $o > $o ).
thf(func_def_1239,type,
sP928: $o > $o ).
thf(func_def_1240,type,
sP929: $o > $o ).
thf(func_def_1241,type,
sP930: $o > $o ).
thf(func_def_1242,type,
sP931: $o > $o ).
thf(func_def_1243,type,
sP932: $o > $o ).
thf(func_def_1244,type,
sP933: $o > $o ).
thf(func_def_1245,type,
sP934: $o > $o ).
thf(func_def_1246,type,
sP935: $i > $o ).
thf(func_def_1247,type,
sP936: $o > $o ).
thf(func_def_1248,type,
sP937: $o > $o ).
thf(func_def_1249,type,
sP938: $o > $o ).
thf(func_def_1250,type,
sP939: $o > $o ).
thf(func_def_1251,type,
sP940: $o > $o ).
thf(func_def_1252,type,
sP941: $o > $o ).
thf(func_def_1253,type,
sP942: $i > $o ).
thf(func_def_1254,type,
sP943: $o > $o ).
thf(func_def_1255,type,
sP944: $o > $o ).
thf(func_def_1256,type,
sP945: $o > $o ).
thf(func_def_1257,type,
sP946: $o > $o ).
thf(func_def_1258,type,
sP947: $o > $o ).
thf(func_def_1259,type,
sP948: $o > $o ).
thf(func_def_1260,type,
sP949: $o > $o ).
thf(func_def_1261,type,
sP950: $o > $o ).
thf(func_def_1262,type,
sP951: $o > $o ).
thf(func_def_1263,type,
sP952: $o > $o ).
thf(func_def_1264,type,
sP953: $o > $o ).
thf(func_def_1265,type,
sP954: $o > $o ).
thf(func_def_1266,type,
sP955: $o > $o ).
thf(func_def_1267,type,
sP956: $o > $o ).
thf(func_def_1268,type,
sP957: $o > $o ).
thf(func_def_1269,type,
sP958: $o > $o ).
thf(func_def_1270,type,
sP959: $o > $o ).
thf(func_def_1271,type,
sP960: $o > $o ).
thf(func_def_1272,type,
sP961: $o > $o ).
thf(func_def_1273,type,
sP962: $o > $o ).
thf(func_def_1274,type,
sP963: $o > $o ).
thf(func_def_1275,type,
sP964: $o > $o ).
thf(func_def_1276,type,
sP965: $o > $o ).
thf(func_def_1277,type,
sP966: $o > $o ).
thf(func_def_1278,type,
sP967: $o > $o ).
thf(func_def_1279,type,
sP968: $o > $o ).
thf(func_def_1280,type,
sP969: $o > $o ).
thf(func_def_1281,type,
sP970: $o > $o ).
thf(func_def_1282,type,
sP971: $o > $o ).
thf(func_def_1283,type,
sP972: $o > $o ).
thf(func_def_1284,type,
sP973: $o > $o ).
thf(func_def_1285,type,
sP974: $o > $o ).
thf(func_def_1286,type,
sP975: $o > $o ).
thf(func_def_1287,type,
sP976: $o > $o ).
thf(func_def_1288,type,
sP977: $i > $o ).
thf(func_def_1289,type,
sP978: $o > $o ).
thf(func_def_1290,type,
sP979: $o > $o ).
thf(func_def_1291,type,
sP980: $o > $o ).
thf(func_def_1292,type,
sP981: $o > $o ).
thf(func_def_1293,type,
sP982: $o > $o ).
thf(func_def_1294,type,
sP983: $o > $o ).
thf(func_def_1295,type,
sP984: $o > $o ).
thf(func_def_1296,type,
sP985: $o > $o ).
thf(func_def_1297,type,
sP986: $i > $o ).
thf(func_def_1298,type,
sP987: $o > $o ).
thf(func_def_1299,type,
sP988: $o > $o ).
thf(func_def_1300,type,
sP989: $o > $o ).
thf(func_def_1301,type,
sP990: $o > $o ).
thf(func_def_1302,type,
sP991: $o > $o ).
thf(func_def_1303,type,
sP992: $o > $o ).
thf(func_def_1304,type,
sP993: $o > $o ).
thf(func_def_1305,type,
sP994: $o > $o ).
thf(func_def_1306,type,
sP995: $o > $o ).
thf(func_def_1307,type,
sP996: $o > $o ).
thf(func_def_1308,type,
sP997: $o > $o ).
thf(func_def_1309,type,
sP998: $o > $o ).
thf(func_def_1310,type,
sP999: $o > $o ).
thf(func_def_1311,type,
sP1000: $o > $o ).
thf(func_def_1312,type,
sP1001: $o > $o ).
thf(func_def_1313,type,
sP1002: $o > $o ).
thf(func_def_1314,type,
sP1003: $o > $o ).
thf(func_def_1315,type,
sP1004: $o > $o ).
thf(func_def_1316,type,
sP1005: $o > $o ).
thf(func_def_1317,type,
sP1006: $o > $o ).
thf(func_def_1318,type,
sP1007: $o > $o ).
thf(func_def_1319,type,
sP1008: $o > $o ).
thf(func_def_1320,type,
sP1009: $o > $o ).
thf(func_def_1321,type,
sP1010: $o > $o ).
thf(func_def_1322,type,
sP1011: $o > $o ).
thf(func_def_1323,type,
sP1012: $o > $o ).
thf(func_def_1324,type,
sP1013: $o > $o ).
thf(func_def_1325,type,
sP1014: $o > $o ).
thf(func_def_1326,type,
sP1015: $o > $o ).
thf(func_def_1327,type,
sP1016: $o > $o ).
thf(func_def_1328,type,
sP1017: $o > $o ).
thf(func_def_1329,type,
sP1018: $o > $o ).
thf(func_def_1330,type,
sP1019: $o > $o ).
thf(func_def_1331,type,
sP1020: $o > $o ).
thf(func_def_1332,type,
sP1021: $o > $o ).
thf(func_def_1333,type,
sP1022: $o > $o ).
thf(func_def_1334,type,
sP1023: $o > $o ).
thf(func_def_1335,type,
sP1024: $o > $o ).
thf(func_def_1336,type,
sP1025: $o > $o ).
thf(func_def_1337,type,
sP1026: $o > $o ).
thf(func_def_1338,type,
sP1027: $o > $o ).
thf(func_def_1339,type,
sP1028: $o > $o ).
thf(func_def_1340,type,
sP1029: $o > $o ).
thf(func_def_1341,type,
sP1030: $o > $o ).
thf(func_def_1342,type,
sP1031: $o > $o ).
thf(func_def_1343,type,
sP1032: $o > $o ).
thf(func_def_1344,type,
sP1033: $o > $o ).
thf(func_def_1345,type,
sP1034: $o > $o ).
thf(func_def_1346,type,
sP1035: $o > $o ).
thf(func_def_1347,type,
sP1036: $o > $o ).
thf(func_def_1348,type,
sP1037: $o > $o ).
thf(func_def_1349,type,
sP1038: $o > $o ).
thf(func_def_1350,type,
sP1039: $o > $o ).
thf(func_def_1351,type,
sP1040: $o > $o ).
thf(func_def_1352,type,
sP1041: $o > $o ).
thf(func_def_1353,type,
sP1042: $o > $o ).
thf(func_def_1354,type,
sP1043: $o > $o ).
thf(func_def_1355,type,
sP1044: $o > $o ).
thf(func_def_1356,type,
sP1045: $o > $o ).
thf(func_def_1357,type,
sP1046: $o > $o ).
thf(func_def_1358,type,
sP1047: $o > $o ).
thf(func_def_1359,type,
sP1048: $o > $o ).
thf(func_def_1360,type,
sP1049: $o > $o ).
thf(func_def_1361,type,
sP1050: $o > $o ).
thf(func_def_1362,type,
sP1051: $o > $o ).
thf(func_def_1363,type,
sP1052: $o > $o ).
thf(func_def_1364,type,
sP1053: $o > $o ).
thf(func_def_1365,type,
sP1054: $o > $o ).
thf(func_def_1366,type,
sP1055: $o > $o ).
thf(func_def_1367,type,
sP1056: $o > $o ).
thf(func_def_1368,type,
sP1057: $o > $o ).
thf(func_def_1369,type,
sP1058: $o > $o ).
thf(func_def_1370,type,
sP1059: $i > $o ).
thf(func_def_1371,type,
sP1060: $o > $o ).
thf(func_def_1372,type,
sP1061: $o > $o ).
thf(func_def_1373,type,
sP1062: $o > $o ).
thf(func_def_1374,type,
sP1063: $o > $o ).
thf(func_def_1375,type,
sP1064: $o > $o ).
thf(func_def_1376,type,
sP1065: $o > $o ).
thf(func_def_1377,type,
sP1066: $o > $o ).
thf(func_def_1378,type,
sP1067: $o > $o ).
thf(func_def_1379,type,
sP1068: $o > $o ).
thf(func_def_1380,type,
sP1069: $i > $o ).
thf(func_def_1381,type,
sP1070: $o > $o ).
thf(func_def_1382,type,
sP1071: $o > $o ).
thf(func_def_1383,type,
sP1072: $o > $o ).
thf(func_def_1384,type,
sP1073: $o > $o ).
thf(func_def_1385,type,
sP1074: $o > $o ).
thf(func_def_1386,type,
sP1075: $o > $o ).
thf(func_def_1387,type,
sP1076: $o > $o ).
thf(func_def_1388,type,
sP1077: $o > $o ).
thf(func_def_1389,type,
sP1078: $o > $o ).
thf(func_def_1390,type,
sP1079: $o > $o ).
thf(func_def_1391,type,
sP1080: $o > $o ).
thf(func_def_1392,type,
sP1081: $o > $o ).
thf(func_def_1393,type,
sP1082: $i > $o ).
thf(func_def_1394,type,
sP1083: $o > $o ).
thf(func_def_1395,type,
sP1084: $o > $o ).
thf(func_def_1396,type,
sP1085: $o > $o ).
thf(func_def_1397,type,
sP1086: $o > $o ).
thf(func_def_1398,type,
sP1087: $o > $o ).
thf(func_def_1399,type,
sP1088: $o > $o ).
thf(func_def_1400,type,
sP1089: $o > $o ).
thf(func_def_1401,type,
sP1090: $i > $o ).
thf(func_def_1402,type,
sP1091: $o > $o ).
thf(func_def_1403,type,
sP1092: $o > $o ).
thf(func_def_1404,type,
sP1093: $o > $o ).
thf(func_def_1405,type,
sP1094: $o > $o ).
thf(func_def_1406,type,
sP1095: $o > $o ).
thf(func_def_1407,type,
sP1096: $o > $o ).
thf(func_def_1408,type,
sP1097: $o > $o ).
thf(func_def_1409,type,
sP1098: $o > $o ).
thf(func_def_1410,type,
sP1099: $o > $o ).
thf(func_def_1411,type,
sP1100: $o > $o ).
thf(func_def_1412,type,
sP1101: $o > $o ).
thf(func_def_1413,type,
sP1102: $o > $o ).
thf(func_def_1414,type,
sP1103: $o > $o ).
thf(func_def_1415,type,
sP1104: $o > $o ).
thf(func_def_1416,type,
sP1105: $o > $o ).
thf(func_def_1417,type,
sP1106: $o > $o ).
thf(func_def_1418,type,
sP1107: $o > $o ).
thf(func_def_1419,type,
sP1108: $o > $o ).
thf(func_def_1420,type,
sP1109: $o > $o ).
thf(func_def_1421,type,
sP1110: $o > $o ).
thf(func_def_1422,type,
sP1111: $o > $o ).
thf(func_def_1423,type,
sP1112: $o > $o ).
thf(func_def_1424,type,
sP1113: $o > $o ).
thf(func_def_1425,type,
sP1114: $i > $o ).
thf(func_def_1426,type,
sP1115: $o > $o ).
thf(func_def_1427,type,
sP1116: $i > $o ).
thf(func_def_1428,type,
sP1117: $o > $o ).
thf(func_def_1429,type,
sP1118: $o > $o ).
thf(func_def_1430,type,
sP1119: $o > $o ).
thf(func_def_1431,type,
sP1120: $o > $o ).
thf(func_def_1432,type,
sP1121: $o > $o ).
thf(func_def_1433,type,
sP1122: $o > $o ).
thf(func_def_1434,type,
sP1123: $o > $o ).
thf(func_def_1435,type,
sP1124: $o > $o ).
thf(func_def_1436,type,
sP1125: $o > $o ).
thf(func_def_1437,type,
sP1126: $o > $o ).
thf(func_def_1438,type,
sP1127: $o > $o ).
thf(func_def_1439,type,
sP1128: $o > $o ).
thf(func_def_1440,type,
sP1129: $o > $o ).
thf(func_def_1441,type,
sP1130: $o > $o ).
thf(func_def_1442,type,
sP1131: $o > $o ).
thf(func_def_1443,type,
sP1132: $o > $o ).
thf(func_def_1444,type,
sP1133: $o > $o ).
thf(func_def_1445,type,
sP1134: $o > $o ).
thf(func_def_1446,type,
sP1135: $o > $o ).
thf(func_def_1447,type,
sP1136: $o > $o ).
thf(func_def_1448,type,
sP1137: $o > $o ).
thf(func_def_1449,type,
sP1138: $o > $o ).
thf(func_def_1450,type,
sP1139: $o > $o ).
thf(func_def_1451,type,
sP1140: $i > $o ).
thf(func_def_1452,type,
sP1141: $o > $o ).
thf(func_def_1453,type,
sP1142: $o > $o ).
thf(func_def_1454,type,
sP1143: $o > $o ).
thf(func_def_1455,type,
sP1144: $o > $o ).
thf(func_def_1456,type,
sP1145: $o > $o ).
thf(func_def_1457,type,
sP1146: $o > $o ).
thf(func_def_1458,type,
sP1147: $o > $o ).
thf(func_def_1459,type,
sP1148: $o > $o ).
thf(func_def_1460,type,
sP1149: $o > $o ).
thf(func_def_1461,type,
sP1150: $o > $o ).
thf(func_def_1462,type,
sP1151: $o > $o ).
thf(func_def_1463,type,
sP1152: $o > $o ).
thf(func_def_1464,type,
sP1153: $o > $o ).
thf(func_def_1465,type,
sP1154: $o > $o ).
thf(func_def_1466,type,
sP1155: $o > $o ).
thf(func_def_1467,type,
sP1156: $i > $o ).
thf(func_def_1468,type,
sP1157: $o > $o ).
thf(func_def_1469,type,
sP1158: $o > $o ).
thf(func_def_1470,type,
sP1159: $i > $o ).
thf(func_def_1471,type,
sP1160: $o > $o ).
thf(func_def_1472,type,
sP1161: $o > $o ).
thf(func_def_1473,type,
sP1162: $o > $o ).
thf(func_def_1474,type,
sP1163: $o > $o ).
thf(func_def_1475,type,
sP1164: $o > $o ).
thf(func_def_1476,type,
sP1165: $o > $o ).
thf(func_def_1477,type,
sP1166: $i > $o ).
thf(func_def_1478,type,
sP1167: $o > $o ).
thf(func_def_1479,type,
sP1168: $o > $o ).
thf(func_def_1480,type,
sP1169: $o > $o ).
thf(func_def_1481,type,
sP1170: $o > $o ).
thf(func_def_1482,type,
sP1171: $o > $o ).
thf(func_def_1483,type,
sP1172: $o > $o ).
thf(func_def_1484,type,
sP1173: $o > $o ).
thf(func_def_1485,type,
sP1174: $o > $o ).
thf(func_def_1486,type,
sP1175: $o > $o ).
thf(func_def_1487,type,
sP1176: $o > $o ).
thf(func_def_1488,type,
sP1177: $o > $o ).
thf(func_def_1489,type,
sP1178: $o > $o ).
thf(func_def_1490,type,
sP1179: $o > $o ).
thf(func_def_1491,type,
sP1180: $i > $o ).
thf(func_def_1492,type,
sP1181: $o > $o ).
thf(func_def_1493,type,
sP1182: $o > $o ).
thf(func_def_1494,type,
sP1183: $o > $o ).
thf(func_def_1495,type,
sP1184: $o > $o ).
thf(func_def_1496,type,
sP1185: $o > $o ).
thf(func_def_1497,type,
sP1186: $o > $o ).
thf(func_def_1498,type,
sP1187: $o > $o ).
thf(func_def_1499,type,
sP1188: $o > $o ).
thf(func_def_1500,type,
sP1189: $o > $o ).
thf(func_def_1501,type,
sP1190: $o > $o ).
thf(func_def_1502,type,
sP1191: $o > $o ).
thf(func_def_1503,type,
sP1192: $o > $o ).
thf(func_def_1504,type,
sP1193: $o > $o ).
thf(func_def_1505,type,
sP1194: $o > $o ).
thf(func_def_1506,type,
sP1195: $i > $o ).
thf(func_def_1507,type,
sP1196: $o > $o ).
thf(func_def_1508,type,
sP1197: $o > $o ).
thf(func_def_1509,type,
sP1198: $o > $o ).
thf(func_def_1510,type,
sP1199: $o > $o ).
thf(func_def_1511,type,
sP1200: $o > $o ).
thf(func_def_1512,type,
sP1201: $o > $o ).
thf(func_def_1513,type,
sP1202: $o > $o ).
thf(func_def_1514,type,
sP1203: $o > $o ).
thf(func_def_1515,type,
sP1204: $o > $o ).
thf(func_def_1516,type,
sP1205: $o > $o ).
thf(func_def_1517,type,
sP1206: $o > $o ).
thf(func_def_1518,type,
sP1207: $i > $o ).
thf(func_def_1519,type,
sP1208: $o > $o ).
thf(func_def_1520,type,
sP1209: $o > $o ).
thf(func_def_1521,type,
sP1210: $o > $o ).
thf(func_def_1522,type,
sP1211: $o > $o ).
thf(func_def_1523,type,
sP1212: $o > $o ).
thf(func_def_1524,type,
sP1213: $o > $o ).
thf(func_def_1525,type,
sP1214: $o > $o ).
thf(func_def_1526,type,
sP1215: $o > $o ).
thf(func_def_1527,type,
sP1216: $o > $o ).
thf(func_def_1528,type,
sP1217: $o > $o ).
thf(func_def_1529,type,
sP1218: $o > $o ).
thf(func_def_1530,type,
sP1219: $o > $o ).
thf(func_def_1531,type,
sP1220: $o > $o ).
thf(func_def_1532,type,
sP1221: $o > $o ).
thf(func_def_1533,type,
sP1222: $o > $o ).
thf(func_def_1534,type,
sP1223: $o > $o ).
thf(func_def_1535,type,
sP1224: $o > $o ).
thf(func_def_1536,type,
sP1225: $o > $o ).
thf(func_def_1537,type,
sP1226: $o > $o ).
thf(func_def_1538,type,
sP1227: $o > $o ).
thf(func_def_1539,type,
sP1228: $o > $o ).
thf(func_def_1540,type,
sP1229: $o > $o ).
thf(func_def_1541,type,
sP1230: $o > $o ).
thf(func_def_1542,type,
sP1231: $o > $o ).
thf(func_def_1543,type,
sP1232: $o > $o ).
thf(func_def_1544,type,
sP1233: $o > $o ).
thf(func_def_1545,type,
sP1234: $o > $o ).
thf(func_def_1546,type,
sP1235: $o > $o ).
thf(func_def_1547,type,
sP1236: $o > $o ).
thf(func_def_1548,type,
sP1237: $o > $o ).
thf(func_def_1549,type,
sP1238: $o > $o ).
thf(func_def_1550,type,
sP1239: $o > $o ).
thf(func_def_1551,type,
sP1240: $o > $o ).
thf(func_def_1552,type,
sP1241: $o > $o ).
thf(func_def_1553,type,
sP1242: $o > $o ).
thf(func_def_1554,type,
sP1243: $o > $o ).
thf(func_def_1555,type,
sP1244: $o > $o ).
thf(func_def_1556,type,
sP1245: $o > $o ).
thf(func_def_1557,type,
sP1246: $o > $o ).
thf(func_def_1558,type,
sP1247: $o > $o ).
thf(func_def_1559,type,
sP1248: $o > $o ).
thf(func_def_1560,type,
sP1249: $o > $o ).
thf(func_def_1561,type,
sP1250: $o > $o ).
thf(func_def_1562,type,
sP1251: $o > $o ).
thf(func_def_1563,type,
sP1252: $o > $o ).
thf(func_def_1564,type,
sP1253: $o > $o ).
thf(func_def_1565,type,
sP1254: $o > $o ).
thf(func_def_1566,type,
sP1255: $o > $o ).
thf(func_def_1567,type,
sP1256: $o > $o ).
thf(func_def_1568,type,
sP1257: $i > $o ).
thf(func_def_1569,type,
sP1258: $o > $o ).
thf(func_def_1570,type,
sP1259: $o > $o ).
thf(func_def_1571,type,
sP1260: $o > $o ).
thf(func_def_1572,type,
sP1261: $o > $o ).
thf(func_def_1573,type,
sP1262: $o > $o ).
thf(func_def_1574,type,
sP1263: $o > $o ).
thf(func_def_1575,type,
sP1264: $o > $o ).
thf(func_def_1576,type,
sP1265: $o > $o ).
thf(func_def_1577,type,
sP1266: $o > $o ).
thf(func_def_1578,type,
sP1267: $o > $o ).
thf(func_def_1579,type,
sP1268: $o > $o ).
thf(func_def_1580,type,
sP1269: $o > $o ).
thf(func_def_1581,type,
sP1270: $o > $o ).
thf(func_def_1582,type,
sP1271: $o > $o ).
thf(func_def_1583,type,
sP1272: $o > $o ).
thf(func_def_1584,type,
sP1273: $o > $o ).
thf(func_def_1585,type,
sP1274: $o > $o ).
thf(func_def_1586,type,
sP1275: $o > $o ).
thf(func_def_1587,type,
sP1276: $o > $o ).
thf(func_def_1588,type,
sP1277: $o > $o ).
thf(func_def_1589,type,
sP1278: $o > $o ).
thf(func_def_1590,type,
sP1279: $o > $o ).
thf(func_def_1591,type,
sP1280: $o > $o ).
thf(func_def_1592,type,
sP1281: $o > $o ).
thf(func_def_1593,type,
sP1282: $o > $o ).
thf(func_def_1594,type,
sP1283: $o > $o ).
thf(func_def_1595,type,
sP1284: $o > $o ).
thf(func_def_1596,type,
sP1285: $o > $o ).
thf(func_def_1597,type,
sP1286: $o > $o ).
thf(func_def_1598,type,
sP1287: $o > $o ).
thf(func_def_1599,type,
sP1288: $o > $o ).
thf(func_def_1600,type,
sP1289: $o > $o ).
thf(func_def_1601,type,
sP1290: $o > $o ).
thf(func_def_1602,type,
sP1291: $o > $o ).
thf(func_def_1603,type,
sP1292: $o > $o ).
thf(func_def_1604,type,
sP1293: $o > $o ).
thf(func_def_1605,type,
sP1294: $o > $o ).
thf(func_def_1606,type,
sP1295: $o > $o ).
thf(func_def_1607,type,
sP1296: $o > $o ).
thf(func_def_1608,type,
sP1297: $o > $o ).
thf(func_def_1609,type,
sP1298: $o > $o ).
thf(func_def_1610,type,
sP1299: $o > $o ).
thf(func_def_1611,type,
sP1300: $o > $o ).
thf(func_def_1612,type,
sP1301: $o > $o ).
thf(func_def_1613,type,
sP1302: $o > $o ).
thf(func_def_1614,type,
sP1303: $o > $o ).
thf(func_def_1615,type,
sP1304: $o > $o ).
thf(func_def_1616,type,
sP1305: $o > $o ).
thf(func_def_1617,type,
sP1306: $o > $o ).
thf(func_def_1618,type,
sP1307: $o > $o ).
thf(func_def_1619,type,
sP1308: $o > $o ).
thf(func_def_1620,type,
sP1309: $o > $o ).
thf(func_def_1621,type,
sP1310: $o > $o ).
thf(func_def_1622,type,
sP1311: $o > $o ).
thf(func_def_1623,type,
sP1312: $o > $o ).
thf(func_def_1624,type,
sP1313: $o > $o ).
thf(func_def_1625,type,
sP1314: $o > $o ).
thf(func_def_1626,type,
sP1315: $o > $o ).
thf(func_def_1627,type,
sP1316: $o > $o ).
thf(func_def_1628,type,
sP1317: $o > $o ).
thf(func_def_1629,type,
sP1318: $o > $o ).
thf(func_def_1630,type,
sP1319: $o > $o ).
thf(func_def_1631,type,
sP1320: $i > $o ).
thf(func_def_1632,type,
sP1321: $o > $o ).
thf(func_def_1633,type,
sP1322: $o > $o ).
thf(func_def_1634,type,
sP1323: $o > $o ).
thf(func_def_1635,type,
sP1324: $o > $o ).
thf(func_def_1636,type,
sP1325: $o > $o ).
thf(func_def_1637,type,
sP1326: $o > $o ).
thf(func_def_1638,type,
sP1327: $o > $o ).
thf(func_def_1639,type,
sP1328: $i > $o ).
thf(func_def_1640,type,
sP1329: $o > $o ).
thf(func_def_1641,type,
sP1330: $o > $o ).
thf(func_def_1642,type,
sP1331: $o > $o ).
thf(func_def_1643,type,
sP1332: $o > $o ).
thf(func_def_1644,type,
sP1333: $o > $o ).
thf(func_def_1645,type,
sP1334: $o > $o ).
thf(func_def_1646,type,
sP1335: $o > $o ).
thf(func_def_1647,type,
sP1336: $o > $o ).
thf(func_def_1648,type,
sP1337: $o > $o ).
thf(func_def_1649,type,
sP1338: $o > $o ).
thf(func_def_1650,type,
sP1339: $o > $o ).
thf(func_def_1651,type,
sP1340: $i > $o ).
thf(func_def_1652,type,
sP1341: $o > $o ).
thf(func_def_1653,type,
sP1342: $o > $o ).
thf(func_def_1654,type,
sP1343: $i > $o ).
thf(func_def_1655,type,
sP1344: $o > $o ).
thf(func_def_1656,type,
sP1345: $o > $o ).
thf(func_def_1657,type,
sP1346: $o > $o ).
thf(func_def_1658,type,
sP1347: $o > $o ).
thf(func_def_1659,type,
sP1348: $o > $o ).
thf(func_def_1660,type,
sP1349: $o > $o ).
thf(func_def_1661,type,
sP1350: $o > $o ).
thf(func_def_1662,type,
sP1351: $o > $o ).
thf(func_def_1663,type,
sP1352: $o > $o ).
thf(func_def_1664,type,
sP1353: $o > $o ).
thf(func_def_1665,type,
sP1354: $o > $o ).
thf(func_def_1666,type,
sP1355: $o > $o ).
thf(func_def_1667,type,
sP1356: $o > $o ).
thf(func_def_1668,type,
sP1357: $o > $o ).
thf(func_def_1669,type,
sP1358: $o > $o ).
thf(func_def_1670,type,
sP1359: $o > $o ).
thf(func_def_1671,type,
sP1360: $i > $o ).
thf(func_def_1672,type,
sP1361: $o > $o ).
thf(func_def_1673,type,
sP1362: $o > $o ).
thf(func_def_1674,type,
sP1363: $o > $o ).
thf(func_def_1675,type,
sP1364: $o > $o ).
thf(func_def_1676,type,
sP1365: $o > $o ).
thf(func_def_1677,type,
sP1366: $o > $o ).
thf(func_def_1678,type,
sP1367: $o > $o ).
thf(func_def_1679,type,
sP1368: $o > $o ).
thf(func_def_1680,type,
sP1369: $o > $o ).
thf(func_def_1681,type,
sP1370: $o > $o ).
thf(func_def_1682,type,
sP1371: $o > $o ).
thf(func_def_1683,type,
sP1372: $o > $o ).
thf(func_def_1684,type,
sP1373: $o > $o ).
thf(func_def_1685,type,
sP1374: $o > $o ).
thf(func_def_1686,type,
sP1375: $i > $o ).
thf(func_def_1687,type,
sP1376: $o > $o ).
thf(func_def_1688,type,
sP1377: $o > $o ).
thf(func_def_1689,type,
sP1378: $o > $o ).
thf(func_def_1690,type,
sP1379: $o > $o ).
thf(func_def_1691,type,
sP1380: $o > $o ).
thf(func_def_1692,type,
sP1381: $o > $o ).
thf(func_def_1693,type,
sP1382: $o > $o ).
thf(func_def_1694,type,
sP1383: $o > $o ).
thf(func_def_1695,type,
sP1384: $o > $o ).
thf(func_def_1696,type,
sP1385: $o > $o ).
thf(func_def_1697,type,
sP1386: $o > $o ).
thf(func_def_1698,type,
sP1387: $o > $o ).
thf(func_def_1699,type,
sP1388: $o > $o ).
thf(func_def_1700,type,
sP1389: $o > $o ).
thf(func_def_1701,type,
sP1390: $o > $o ).
thf(func_def_1702,type,
sP1391: $o > $o ).
thf(func_def_1703,type,
sP1392: $o > $o ).
thf(func_def_1704,type,
sP1393: $o > $o ).
thf(func_def_1705,type,
sP1394: $o > $o ).
thf(func_def_1706,type,
sP1395: $o > $o ).
thf(func_def_1707,type,
sP1396: $o > $o ).
thf(func_def_1708,type,
sP1397: $o > $o ).
thf(func_def_1709,type,
sP1398: $o > $o ).
thf(func_def_1710,type,
sP1399: $o > $o ).
thf(func_def_1711,type,
sP1400: $o > $o ).
thf(func_def_1712,type,
sP1401: $o > $o ).
thf(func_def_1713,type,
sP1402: $o > $o ).
thf(func_def_1714,type,
sP1403: $o > $o ).
thf(func_def_1715,type,
sP1404: $o > $o ).
thf(func_def_1716,type,
sP1405: $o > $o ).
thf(func_def_1717,type,
sP1406: $o > $o ).
thf(func_def_1718,type,
sP1407: $o > $o ).
thf(func_def_1719,type,
sP1408: $o > $o ).
thf(func_def_1720,type,
sP1409: $o > $o ).
thf(func_def_1721,type,
sP1410: $o > $o ).
thf(func_def_1722,type,
sP1411: $o > $o ).
thf(func_def_1723,type,
sP1412: $o > $o ).
thf(func_def_1724,type,
sP1413: $o > $o ).
thf(func_def_1725,type,
sP1414: $o > $o ).
thf(func_def_1726,type,
sP1415: $o > $o ).
thf(func_def_1727,type,
sP1416: $o > $o ).
thf(func_def_1728,type,
sP1417: $o > $o ).
thf(func_def_1729,type,
sP1418: $o > $o ).
thf(func_def_1730,type,
sP1419: $o > $o ).
thf(func_def_1731,type,
sP1420: $o > $o ).
thf(func_def_1732,type,
sP1421: $o > $o ).
thf(func_def_1733,type,
sP1422: $o > $o ).
thf(func_def_1734,type,
sP1423: $o > $o ).
thf(func_def_1735,type,
sP1424: $o > $o ).
thf(func_def_1736,type,
sP1425: $o > $o ).
thf(func_def_1737,type,
sP1426: $o > $o ).
thf(func_def_1738,type,
sP1427: $o > $o ).
thf(func_def_1739,type,
sP1428: $o > $o ).
thf(func_def_1740,type,
sP1429: $o > $o ).
thf(func_def_1741,type,
sP1430: $o > $o ).
thf(func_def_1742,type,
sP1431: $o > $o ).
thf(func_def_1743,type,
sP1432: $o > $o ).
thf(func_def_1744,type,
sP1433: $o > $o ).
thf(func_def_1745,type,
sP1434: $o > $o ).
thf(func_def_1746,type,
sP1435: $o > $o ).
thf(func_def_1747,type,
sP1436: $o > $o ).
thf(func_def_1748,type,
sP1437: $o > $o ).
thf(func_def_1749,type,
sP1438: $o > $o ).
thf(func_def_1750,type,
sP1439: $o > $o ).
thf(func_def_1751,type,
sP1440: $o > $o ).
thf(func_def_1752,type,
sP1441: $o > $o ).
thf(func_def_1753,type,
sP1442: $o > $o ).
thf(func_def_1754,type,
sP1443: $o > $o ).
thf(func_def_1755,type,
sP1444: $o > $o ).
thf(func_def_1756,type,
sP1445: $o > $o ).
thf(func_def_1757,type,
sP1446: $o > $o ).
thf(func_def_1758,type,
sP1447: $o > $o ).
thf(func_def_1759,type,
sP1448: $o > $o ).
thf(func_def_1760,type,
sP1449: $o > $o ).
thf(func_def_1761,type,
sP1450: $o > $o ).
thf(func_def_1762,type,
sP1451: $o > $o ).
thf(func_def_1763,type,
sP1452: $o > $o ).
thf(func_def_1764,type,
sP1453: $o > $o ).
thf(func_def_1765,type,
sP1454: $o > $o ).
thf(func_def_1766,type,
sP1455: $o > $o ).
thf(func_def_1767,type,
sP1456: $o > $o ).
thf(func_def_1768,type,
sP1457: $o > $o ).
thf(func_def_1769,type,
sP1458: $o > $o ).
thf(func_def_1770,type,
sP1459: $o > $o ).
thf(func_def_1771,type,
sP1460: $o > $o ).
thf(func_def_1772,type,
sP1461: $o > $o ).
thf(func_def_1773,type,
sP1462: $o > $o ).
thf(func_def_1774,type,
sP1463: $o > $o ).
thf(func_def_1775,type,
sP1464: $o > $o ).
thf(func_def_1776,type,
sP1465: $o > $o ).
thf(func_def_1777,type,
sP1466: $i > $o ).
thf(func_def_1778,type,
sP1467: $i > $o ).
thf(func_def_1779,type,
sP1468: $o > $o ).
thf(func_def_1780,type,
sP1469: $o > $o ).
thf(func_def_1781,type,
sP1470: $o > $o ).
thf(func_def_1782,type,
sP1471: $o > $o ).
thf(func_def_1783,type,
sP1472: $o > $o ).
thf(func_def_1784,type,
sP1473: $o > $o ).
thf(func_def_1785,type,
sP1474: $o > $o ).
thf(func_def_1786,type,
sP1475: $o > $o ).
thf(func_def_1787,type,
sP1476: $o > $o ).
thf(func_def_1788,type,
sP1477: $o > $o ).
thf(func_def_1789,type,
sP1478: $o > $o ).
thf(func_def_1790,type,
sP1479: $o > $o ).
thf(func_def_1791,type,
sP1480: $o > $o ).
thf(func_def_1792,type,
sP1481: $o > $o ).
thf(func_def_1793,type,
sP1482: $o > $o ).
thf(func_def_1794,type,
sP1483: $o > $o ).
thf(func_def_1795,type,
sP1484: $i > $o ).
thf(func_def_1796,type,
sP1485: $o > $o ).
thf(func_def_1797,type,
sP1486: $o > $o ).
thf(func_def_1798,type,
sP1487: $o > $o ).
thf(func_def_1799,type,
sP1488: $o > $o ).
thf(func_def_1800,type,
sP1489: $o > $o ).
thf(func_def_1801,type,
sP1490: $o > $o ).
thf(func_def_1802,type,
sP1491: $o > $o ).
thf(func_def_1803,type,
sP1492: $i > $o ).
thf(func_def_1804,type,
sP1493: $o > $o ).
thf(func_def_1805,type,
sP1494: $o > $o ).
thf(func_def_1806,type,
sP1495: $o > $o ).
thf(func_def_1807,type,
sP1496: $o > $o ).
thf(func_def_1808,type,
sP1497: $o > $o ).
thf(func_def_1809,type,
sP1498: $o > $o ).
thf(func_def_1810,type,
sP1499: $o > $o ).
thf(func_def_1811,type,
sP1500: $o > $o ).
thf(func_def_1812,type,
sP1501: $o > $o ).
thf(func_def_1813,type,
sP1502: $o > $o ).
thf(func_def_1814,type,
sP1503: $o > $o ).
thf(func_def_1815,type,
sP1504: $o > $o ).
thf(func_def_1816,type,
sP1505: $o > $o ).
thf(func_def_1817,type,
sP1506: $i > $o ).
thf(func_def_1818,type,
sP1507: $o > $o ).
thf(func_def_1819,type,
sP1508: $o > $o ).
thf(func_def_1820,type,
sP1509: $o > $o ).
thf(func_def_1821,type,
sP1510: $o > $o ).
thf(func_def_1822,type,
sP1511: $o > $o ).
thf(func_def_1823,type,
sP1512: $o > $o ).
thf(func_def_1824,type,
sP1513: $o > $o ).
thf(func_def_1825,type,
sP1514: $o > $o ).
thf(func_def_1826,type,
sP1515: $o > $o ).
thf(func_def_1827,type,
sP1516: $o > $o ).
thf(func_def_1828,type,
sP1517: $o > $o ).
thf(func_def_1829,type,
sP1518: $o > $o ).
thf(func_def_1830,type,
sP1519: $o > $o ).
thf(func_def_1831,type,
sP1520: $o > $o ).
thf(func_def_1832,type,
sP1521: $o > $o ).
thf(func_def_1833,type,
sP1522: $o > $o ).
thf(func_def_1834,type,
sP1523: $o > $o ).
thf(func_def_1835,type,
sP1524: $o > $o ).
thf(func_def_1836,type,
sP1525: $o > $o ).
thf(func_def_1837,type,
sP1526: $o > $o ).
thf(func_def_1838,type,
sP1527: $o > $o ).
thf(func_def_1839,type,
sP1528: $o > $o ).
thf(func_def_1840,type,
sP1529: $o > $o ).
thf(func_def_1841,type,
sP1530: $o > $o ).
thf(func_def_1842,type,
sP1531: $o > $o ).
thf(func_def_1843,type,
sP1532: $o > $o ).
thf(func_def_1844,type,
sP1533: $o > $o ).
thf(func_def_1845,type,
sP1534: $o > $o ).
thf(func_def_1846,type,
sP1535: $i > $o ).
thf(func_def_1847,type,
sP1536: $o > $o ).
thf(func_def_1848,type,
sP1537: $o > $o ).
thf(func_def_1849,type,
sP1538: $o > $o ).
thf(func_def_1850,type,
sP1539: $o > $o ).
thf(func_def_1851,type,
sP1540: $o > $o ).
thf(func_def_1852,type,
sP1541: $o > $o ).
thf(func_def_1853,type,
sP1542: $o > $o ).
thf(func_def_1854,type,
sP1543: $o > $o ).
thf(func_def_1855,type,
sP1544: $o > $o ).
thf(func_def_1856,type,
sP1545: $o > $o ).
thf(func_def_1857,type,
sP1546: $o > $o ).
thf(func_def_1858,type,
sP1547: $o > $o ).
thf(func_def_1859,type,
sP1548: $o > $o ).
thf(func_def_1860,type,
sP1549: $o > $o ).
thf(func_def_1861,type,
sP1550: $o > $o ).
thf(func_def_1862,type,
sP1551: $o > $o ).
thf(func_def_1863,type,
sP1552: $o > $o ).
thf(func_def_1864,type,
sP1553: $o > $o ).
thf(func_def_1865,type,
sP1554: $o > $o ).
thf(func_def_1866,type,
sP1555: $o > $o ).
thf(func_def_1867,type,
sP1556: $o > $o ).
thf(func_def_1868,type,
sP1557: $o > $o ).
thf(func_def_1869,type,
sP1558: $o > $o ).
thf(func_def_1870,type,
sP1559: $o > $o ).
thf(func_def_1871,type,
sP1560: $o > $o ).
thf(func_def_1872,type,
sP1561: $i > $o ).
thf(func_def_1873,type,
sP1562: $o > $o ).
thf(func_def_1874,type,
sP1563: $o > $o ).
thf(func_def_1875,type,
sP1564: $o > $o ).
thf(func_def_1876,type,
sP1565: $o > $o ).
thf(func_def_1877,type,
sP1566: $o > $o ).
thf(func_def_1878,type,
sP1567: $o > $o ).
thf(func_def_1879,type,
sP1568: $o > $o ).
thf(func_def_1880,type,
sP1569: $o > $o ).
thf(func_def_1881,type,
sP1570: $o > $o ).
thf(func_def_1882,type,
sP1571: $o > $o ).
thf(func_def_1883,type,
sP1572: $o > $o ).
thf(func_def_1884,type,
sP1573: $o > $o ).
thf(func_def_1885,type,
sP1574: $o > $o ).
thf(func_def_1886,type,
sP1575: $o > $o ).
thf(func_def_1887,type,
sP1576: $o > $o ).
thf(func_def_1888,type,
sP1577: $o > $o ).
thf(func_def_1889,type,
sP1578: $o > $o ).
thf(func_def_1890,type,
sP1579: $i > $o ).
thf(func_def_1891,type,
sP1580: $o > $o ).
thf(func_def_1892,type,
sP1581: $o > $o ).
thf(func_def_1893,type,
sP1582: $o > $o ).
thf(func_def_1894,type,
sP1583: $o > $o ).
thf(func_def_1895,type,
sP1584: $o > $o ).
thf(func_def_1896,type,
sP1585: $o > $o ).
thf(func_def_1897,type,
sP1586: $o > $o ).
thf(func_def_1898,type,
sP1587: $o > $o ).
thf(func_def_1899,type,
sP1588: $o > $o ).
thf(func_def_1900,type,
sP1589: $o > $o ).
thf(func_def_1901,type,
sP1590: $o > $o ).
thf(func_def_1902,type,
sP1591: $o > $o ).
thf(func_def_1903,type,
sP1592: $o > $o ).
thf(func_def_1904,type,
sP1593: $i > $o ).
thf(func_def_1905,type,
sP1594: $o > $o ).
thf(func_def_1906,type,
sP1595: $o > $o ).
thf(func_def_1907,type,
sP1596: $o > $o ).
thf(func_def_1908,type,
sP1597: $i > $o ).
thf(func_def_1909,type,
sP1598: $o > $o ).
thf(func_def_1910,type,
sP1599: $o > $o ).
thf(func_def_1911,type,
sP1600: $o > $o ).
thf(func_def_1912,type,
sP1601: $o > $o ).
thf(func_def_1913,type,
sP1602: $o > $o ).
thf(func_def_1914,type,
sP1603: $o > $o ).
thf(func_def_1915,type,
sP1604: $o > $o ).
thf(func_def_1916,type,
sP1605: $o > $o ).
thf(func_def_1917,type,
sP1606: $o > $o ).
thf(func_def_1918,type,
sP1607: $o > $o ).
thf(func_def_1919,type,
sP1608: $o > $o ).
thf(func_def_1920,type,
sP1609: $o > $o ).
thf(func_def_1921,type,
sP1610: $o > $o ).
thf(func_def_1922,type,
sP1611: $o > $o ).
thf(func_def_1923,type,
sP1612: $o > $o ).
thf(func_def_1924,type,
sP1613: $o > $o ).
thf(func_def_1925,type,
sP1614: $o > $o ).
thf(func_def_1926,type,
sP1615: $o > $o ).
thf(func_def_1927,type,
sP1616: $o > $o ).
thf(func_def_1928,type,
sP1617: $o > $o ).
thf(func_def_1929,type,
sP1618: $o > $o ).
thf(func_def_1930,type,
sP1619: $o > $o ).
thf(func_def_1931,type,
sP1620: $o > $o ).
thf(func_def_1932,type,
sP1621: $o > $o ).
thf(func_def_1933,type,
sP1622: $o > $o ).
thf(func_def_1934,type,
sP1623: $o > $o ).
thf(func_def_1935,type,
sP1624: $o > $o ).
thf(func_def_1936,type,
sP1625: $o > $o ).
thf(func_def_1937,type,
sP1626: $i > $o ).
thf(func_def_1938,type,
sP1627: $o > $o ).
thf(func_def_1939,type,
sP1628: $o > $o ).
thf(func_def_1940,type,
sP1629: $o > $o ).
thf(func_def_1941,type,
sP1630: $o > $o ).
thf(func_def_1942,type,
sP1631: $o > $o ).
thf(func_def_1943,type,
sP1632: $o > $o ).
thf(func_def_1944,type,
sP1633: $i > $o ).
thf(func_def_1945,type,
sP1634: $i > $o ).
thf(func_def_1946,type,
sP1635: $o > $o ).
thf(func_def_1947,type,
sP1636: $o > $o ).
thf(func_def_1948,type,
sP1637: $o > $o ).
thf(func_def_1949,type,
sP1638: $o > $o ).
thf(func_def_1950,type,
sP1639: $o > $o ).
thf(func_def_1951,type,
sP1640: $o > $o ).
thf(func_def_1952,type,
sP1641: $o > $o ).
thf(func_def_1953,type,
sP1642: $o > $o ).
thf(func_def_1954,type,
sP1643: $o > $o ).
thf(func_def_1955,type,
sP1644: $o > $o ).
thf(func_def_1956,type,
sP1645: $o > $o ).
thf(func_def_1957,type,
sP1646: $o > $o ).
thf(func_def_1958,type,
sP1647: $o > $o ).
thf(func_def_1959,type,
sP1648: $o > $o ).
thf(func_def_1960,type,
sP1649: $o > $o ).
thf(func_def_1961,type,
sP1650: $o > $o ).
thf(func_def_1962,type,
sP1651: $o > $o ).
thf(func_def_1963,type,
sP1652: $o > $o ).
thf(func_def_1964,type,
sP1653: $o > $o ).
thf(func_def_1965,type,
sP1654: $o > $o ).
thf(func_def_1966,type,
sP1655: $o > $o ).
thf(func_def_1967,type,
sP1656: $o > $o ).
thf(func_def_1968,type,
sP1657: $o > $o ).
thf(func_def_1969,type,
sP1658: $o > $o ).
thf(func_def_1970,type,
sP1659: $o > $o ).
thf(func_def_1971,type,
sP1660: $o > $o ).
thf(func_def_1972,type,
sP1661: $o > $o ).
thf(func_def_1973,type,
sP1662: $o > $o ).
thf(func_def_1974,type,
sP1663: $o > $o ).
thf(func_def_1975,type,
sP1664: $o > $o ).
thf(func_def_1976,type,
sP1665: $o > $o ).
thf(func_def_1977,type,
sP1666: $o > $o ).
thf(func_def_1978,type,
sP1667: $o > $o ).
thf(func_def_1979,type,
sP1668: $o > $o ).
thf(func_def_1980,type,
sP1669: $o > $o ).
thf(func_def_1981,type,
sP1670: $o > $o ).
thf(func_def_1982,type,
sP1671: $o > $o ).
thf(func_def_1983,type,
sP1672: $o > $o ).
thf(func_def_1984,type,
sP1673: $o > $o ).
thf(func_def_1985,type,
sP1674: $o > $o ).
thf(func_def_1986,type,
sP1675: $o > $o ).
thf(func_def_1987,type,
sP1676: $o > $o ).
thf(func_def_1988,type,
sP1677: $o > $o ).
thf(func_def_1989,type,
sP1678: $o > $o ).
thf(func_def_1990,type,
sP1679: $o > $o ).
thf(func_def_1991,type,
sP1680: $o > $o ).
thf(func_def_1992,type,
sP1681: $o > $o ).
thf(func_def_1993,type,
sP1682: $o > $o ).
thf(func_def_1994,type,
sP1683: $o > $o ).
thf(func_def_1995,type,
sP1684: $o > $o ).
thf(func_def_1996,type,
sP1685: $o > $o ).
thf(func_def_1997,type,
sP1686: $o > $o ).
thf(func_def_1998,type,
sP1687: $o > $o ).
thf(func_def_1999,type,
sP1688: $o > $o ).
thf(func_def_2000,type,
sP1689: $o > $o ).
thf(func_def_2001,type,
sP1690: $o > $o ).
thf(func_def_2002,type,
sP1691: $o > $o ).
thf(func_def_2003,type,
sP1692: $o > $o ).
thf(func_def_2004,type,
sP1693: $o > $o ).
thf(func_def_2005,type,
sP1694: $o > $o ).
thf(func_def_2006,type,
sP1695: $o > $o ).
thf(func_def_2007,type,
sP1696: $o > $o ).
thf(func_def_2008,type,
sP1697: $o > $o ).
thf(func_def_2009,type,
sP1698: $o > $o ).
thf(func_def_2010,type,
sP1699: $o > $o ).
thf(func_def_2011,type,
sP1700: $o > $o ).
thf(func_def_2012,type,
sP1701: $o > $o ).
thf(func_def_2013,type,
sP1702: $o > $o ).
thf(func_def_2014,type,
sP1703: $o > $o ).
thf(func_def_2015,type,
sP1704: $o > $o ).
thf(func_def_2016,type,
sP1705: $o > $o ).
thf(func_def_2017,type,
sP1706: $o > $o ).
thf(func_def_2018,type,
sP1707: $o > $o ).
thf(func_def_2019,type,
sP1708: $o > $o ).
thf(func_def_2020,type,
sP1709: $o > $o ).
thf(func_def_2021,type,
sP1710: $o > $o ).
thf(func_def_2022,type,
sP1711: $i > $o ).
thf(func_def_2023,type,
sP1712: $o > $o ).
thf(func_def_2024,type,
sP1713: $o > $o ).
thf(func_def_2025,type,
sP1714: $o > $o ).
thf(func_def_2026,type,
sP1715: $o > $o ).
thf(func_def_2027,type,
sP1716: $o > $o ).
thf(func_def_2028,type,
sP1717: $o > $o ).
thf(func_def_2029,type,
sP1718: $o > $o ).
thf(func_def_2030,type,
sP1719: $o > $o ).
thf(func_def_2031,type,
sP1720: $o > $o ).
thf(func_def_2032,type,
sP1721: $o > $o ).
thf(func_def_2033,type,
sP1722: $o > $o ).
thf(func_def_2034,type,
sP1723: $o > $o ).
thf(func_def_2035,type,
sP1724: $o > $o ).
thf(func_def_2036,type,
sP1725: $o > $o ).
thf(func_def_2037,type,
sP1726: $o > $o ).
thf(func_def_2038,type,
sP1727: $o > $o ).
thf(func_def_2039,type,
sP1728: $o > $o ).
thf(func_def_2040,type,
sP1729: $o > $o ).
thf(func_def_2041,type,
sP1730: $o > $o ).
thf(func_def_2042,type,
sP1731: $o > $o ).
thf(func_def_2043,type,
sP1732: $o > $o ).
thf(func_def_2044,type,
sP1733: $i > $o ).
thf(func_def_2045,type,
sP1734: $o > $o ).
thf(func_def_2046,type,
sP1735: $o > $o ).
thf(func_def_2047,type,
sP1736: $o > $o ).
thf(func_def_2048,type,
sP1737: $o > $o ).
thf(func_def_2049,type,
sP1738: $o > $o ).
thf(func_def_2050,type,
sP1739: $o > $o ).
thf(func_def_2051,type,
sP1740: $o > $o ).
thf(func_def_2052,type,
sP1741: $o > $o ).
thf(func_def_2053,type,
sP1742: $i > $o ).
thf(func_def_2054,type,
sP1743: $o > $o ).
thf(func_def_2055,type,
sP1744: $o > $o ).
thf(func_def_2056,type,
sP1745: $o > $o ).
thf(func_def_2057,type,
sP1746: $o > $o ).
thf(func_def_2058,type,
sP1747: $o > $o ).
thf(func_def_2059,type,
sP1748: $o > $o ).
thf(func_def_2060,type,
sP1749: $o > $o ).
thf(func_def_2061,type,
sP1750: $o > $o ).
thf(func_def_2062,type,
sP1751: $i > $o ).
thf(func_def_2063,type,
sP1752: $o > $o ).
thf(func_def_2064,type,
sP1753: $o > $o ).
thf(func_def_2065,type,
sP1754: $o > $o ).
thf(func_def_2066,type,
sP1755: $o > $o ).
thf(func_def_2067,type,
sP1756: $o > $o ).
thf(func_def_2068,type,
sP1757: $o > $o ).
thf(func_def_2069,type,
sP1758: $o > $o ).
thf(func_def_2070,type,
sP1759: $o > $o ).
thf(func_def_2071,type,
sP1760: $o > $o ).
thf(func_def_2072,type,
sP1761: $o > $o ).
thf(func_def_2073,type,
sP1762: $o > $o ).
thf(func_def_2074,type,
sP1763: $o > $o ).
thf(func_def_2075,type,
sP1764: $o > $o ).
thf(func_def_2076,type,
sP1765: $i > $o ).
thf(func_def_2077,type,
sP1766: $i > $o ).
thf(func_def_2078,type,
sP1767: $o > $o ).
thf(func_def_2079,type,
sP1768: $o > $o ).
thf(func_def_2080,type,
sP1769: $o > $o ).
thf(func_def_2081,type,
sP1770: $o > $o ).
thf(func_def_2082,type,
sP1771: $o > $o ).
thf(func_def_2083,type,
sP1772: $o > $o ).
thf(func_def_2084,type,
sP1773: $o > $o ).
thf(func_def_2085,type,
sP1774: $o > $o ).
thf(func_def_2086,type,
sP1775: $o > $o ).
thf(func_def_2087,type,
sP1776: $o > $o ).
thf(func_def_2088,type,
sP1777: $o > $o ).
thf(func_def_2089,type,
sP1778: $o > $o ).
thf(func_def_2090,type,
sP1779: $o > $o ).
thf(func_def_2091,type,
sP1780: $i > $o ).
thf(func_def_2092,type,
sP1781: $o > $o ).
thf(func_def_2093,type,
sP1782: $o > $o ).
thf(func_def_2094,type,
sP1783: $o > $o ).
thf(func_def_2095,type,
sP1784: $i > $o ).
thf(func_def_2096,type,
sP1785: $o > $o ).
thf(func_def_2097,type,
sP1786: $o > $o ).
thf(func_def_2098,type,
sP1787: $o > $o ).
thf(func_def_2099,type,
sP1788: $o > $o ).
thf(func_def_2100,type,
sP1789: $o > $o ).
thf(func_def_2101,type,
sP1790: $o > $o ).
thf(func_def_2102,type,
sP1791: $o > $o ).
thf(func_def_2103,type,
sP1792: $o > $o ).
thf(func_def_2104,type,
sP1793: $o > $o ).
thf(func_def_2105,type,
sP1794: $o > $o ).
thf(func_def_2106,type,
sP1795: $o > $o ).
thf(func_def_2107,type,
sP1796: $o > $o ).
thf(func_def_2108,type,
sP1797: $o > $o ).
thf(func_def_2109,type,
sP1798: $o > $o ).
thf(func_def_2110,type,
sP1799: $o > $o ).
thf(func_def_2111,type,
sP1800: $i > $o ).
thf(func_def_2112,type,
sP1801: $o > $o ).
thf(func_def_2113,type,
sP1802: $o > $o ).
thf(func_def_2114,type,
sP1803: $o > $o ).
thf(func_def_2115,type,
sP1804: $o > $o ).
thf(func_def_2116,type,
sP1805: $o > $o ).
thf(func_def_2117,type,
sP1806: $i > $o ).
thf(func_def_2118,type,
sP1807: $o > $o ).
thf(func_def_2119,type,
sP1808: $o > $o ).
thf(func_def_2120,type,
sP1809: $o > $o ).
thf(func_def_2121,type,
sP1810: $o > $o ).
thf(func_def_2122,type,
sP1811: $o > $o ).
thf(func_def_2123,type,
sP1812: $i > $o ).
thf(func_def_2124,type,
sP1813: $o > $o ).
thf(func_def_2125,type,
sP1814: $o > $o ).
thf(func_def_2126,type,
sP1815: $o > $o ).
thf(func_def_2127,type,
sP1816: $o > $o ).
thf(func_def_2128,type,
sP1817: $o > $o ).
thf(func_def_2129,type,
sP1818: $o > $o ).
thf(func_def_2130,type,
sP1819: $o > $o ).
thf(func_def_2131,type,
sP1820: $i > $o ).
thf(func_def_2132,type,
sP1821: $o > $o ).
thf(func_def_2133,type,
sP1822: $o > $o ).
thf(func_def_2134,type,
sP1823: $o > $o ).
thf(func_def_2135,type,
sP1824: $i > $o ).
thf(func_def_2136,type,
sP1825: $o > $o ).
thf(func_def_2137,type,
sP1826: $o > $o ).
thf(func_def_2138,type,
sP1827: $o > $o ).
thf(func_def_2139,type,
sP1828: $o > $o ).
thf(func_def_2140,type,
sP1829: $o > $o ).
thf(func_def_2141,type,
sP1830: $o > $o ).
thf(func_def_2142,type,
sP1831: $o > $o ).
thf(func_def_2143,type,
sP1832: $o > $o ).
thf(func_def_2144,type,
sP1833: $o > $o ).
thf(func_def_2145,type,
sP1834: $o > $o ).
thf(func_def_2146,type,
sP1835: $o > $o ).
thf(func_def_2147,type,
sP1836: $o > $o ).
thf(func_def_2148,type,
sP1837: $o > $o ).
thf(func_def_2149,type,
sP1838: $o > $o ).
thf(func_def_2150,type,
sP1839: $o > $o ).
thf(func_def_2151,type,
sP1840: $o > $o ).
thf(func_def_2152,type,
sP1841: $o > $o ).
thf(func_def_2153,type,
sP1842: $o > $o ).
thf(func_def_2154,type,
sP1843: $o > $o ).
thf(func_def_2155,type,
sP1844: $o > $o ).
thf(func_def_2156,type,
sP1845: $o > $o ).
thf(func_def_2157,type,
sP1846: $o > $o ).
thf(func_def_2158,type,
sP1847: $i > $o ).
thf(func_def_2159,type,
sP1848: $o > $o ).
thf(func_def_2160,type,
sP1849: $o > $o ).
thf(func_def_2161,type,
sP1850: $i > $o ).
thf(func_def_2162,type,
sP1851: $o > $o ).
thf(func_def_2163,type,
sP1852: $o > $o ).
thf(func_def_2164,type,
sP1853: $o > $o ).
thf(func_def_2165,type,
sP1854: $o > $o ).
thf(func_def_2166,type,
sP1855: $o > $o ).
thf(func_def_2167,type,
sP1856: $o > $o ).
thf(func_def_2168,type,
sP1857: $o > $o ).
thf(func_def_2169,type,
sP1858: $o > $o ).
thf(func_def_2170,type,
sP1859: $o > $o ).
thf(func_def_2171,type,
sP1860: $o > $o ).
thf(func_def_2172,type,
sP1861: $o > $o ).
thf(func_def_2173,type,
sP1862: $o > $o ).
thf(func_def_2174,type,
sP1863: $o > $o ).
thf(func_def_2175,type,
sP1864: $o > $o ).
thf(func_def_2176,type,
sP1865: $o > $o ).
thf(func_def_2177,type,
sP1866: $o > $o ).
thf(func_def_2178,type,
sP1867: $o > $o ).
thf(func_def_2179,type,
sP1868: $o > $o ).
thf(func_def_2180,type,
sP1869: $o > $o ).
thf(func_def_2181,type,
sP1870: $o > $o ).
thf(func_def_2182,type,
sP1871: $o > $o ).
thf(func_def_2183,type,
sP1872: $o > $o ).
thf(func_def_2184,type,
sP1873: $o > $o ).
thf(func_def_2185,type,
sP1874: $o > $o ).
thf(func_def_2186,type,
sP1875: $o > $o ).
thf(func_def_2187,type,
sP1876: $o > $o ).
thf(func_def_2188,type,
sP1877: $o > $o ).
thf(func_def_2189,type,
sP1878: $o > $o ).
thf(func_def_2190,type,
sP1879: $i > $o ).
thf(func_def_2191,type,
sP1880: $o > $o ).
thf(func_def_2192,type,
sP1881: $o > $o ).
thf(func_def_2193,type,
sP1882: $o > $o ).
thf(func_def_2194,type,
sP1883: $o > $o ).
thf(func_def_2195,type,
sP1884: $o > $o ).
thf(func_def_2196,type,
sP1885: $o > $o ).
thf(func_def_2197,type,
sP1886: $o > $o ).
thf(func_def_2198,type,
sP1887: $o > $o ).
thf(func_def_2199,type,
sP1888: $o > $o ).
thf(func_def_2200,type,
sP1889: $o > $o ).
thf(func_def_2201,type,
sP1890: $o > $o ).
thf(func_def_2202,type,
sP1891: $o > $o ).
thf(func_def_2203,type,
sP1892: $o > $o ).
thf(func_def_2204,type,
sP1893: $o > $o ).
thf(func_def_2205,type,
sP1894: $o > $o ).
thf(func_def_2206,type,
sP1895: $o > $o ).
thf(func_def_2207,type,
sP1896: $o > $o ).
thf(func_def_2208,type,
sP1897: $o > $o ).
thf(func_def_2209,type,
sP1898: $o > $o ).
thf(func_def_2210,type,
sP1899: $o > $o ).
thf(func_def_2211,type,
sP1900: $o > $o ).
thf(func_def_2212,type,
sP1901: $o > $o ).
thf(func_def_2213,type,
sP1902: $o > $o ).
thf(func_def_2214,type,
sP1903: $o > $o ).
thf(func_def_2215,type,
sP1904: $o > $o ).
thf(func_def_2216,type,
sP1905: $o > $o ).
thf(func_def_2217,type,
sP1906: $o > $o ).
thf(func_def_2218,type,
sP1907: $o > $o ).
thf(func_def_2219,type,
sP1908: $o > $o ).
thf(func_def_2220,type,
sP1909: $o > $o ).
thf(func_def_2221,type,
sP1910: $o > $o ).
thf(func_def_2222,type,
sP1911: $o > $o ).
thf(func_def_2223,type,
sP1912: $o > $o ).
thf(func_def_2224,type,
sP1913: $o > $o ).
thf(func_def_2225,type,
sP1914: $o > $o ).
thf(func_def_2226,type,
sP1915: $i > $o ).
thf(func_def_2227,type,
sP1916: $o > $o ).
thf(func_def_2228,type,
sP1917: $o > $o ).
thf(func_def_2229,type,
sP1918: $o > $o ).
thf(func_def_2230,type,
sP1919: $o > $o ).
thf(func_def_2231,type,
sP1920: $o > $o ).
thf(func_def_2232,type,
sP1921: $o > $o ).
thf(func_def_2233,type,
sP1922: $o > $o ).
thf(func_def_2234,type,
sP1923: $o > $o ).
thf(func_def_2235,type,
sP1924: $o > $o ).
thf(func_def_2236,type,
sP1925: $o > $o ).
thf(func_def_2237,type,
sP1926: $o > $o ).
thf(func_def_2238,type,
sP1927: $o > $o ).
thf(func_def_2239,type,
sP1928: $o > $o ).
thf(func_def_2240,type,
sP1929: $o > $o ).
thf(func_def_2241,type,
sP1930: $o > $o ).
thf(func_def_2242,type,
sP1931: $o > $o ).
thf(func_def_2243,type,
sP1932: $o > $o ).
thf(func_def_2244,type,
sP1933: $o > $o ).
thf(func_def_2245,type,
sP1934: $o > $o ).
thf(func_def_2246,type,
sP1935: $o > $o ).
thf(func_def_2247,type,
sP1936: $o > $o ).
thf(func_def_2248,type,
sP1937: $o > $o ).
thf(func_def_2249,type,
sP1938: $o > $o ).
thf(func_def_2250,type,
sP1939: $o > $o ).
thf(func_def_2251,type,
sP1940: $o > $o ).
thf(func_def_2252,type,
sP1941: $o > $o ).
thf(func_def_2253,type,
sP1942: $o > $o ).
thf(func_def_2254,type,
sP1943: $o > $o ).
thf(func_def_2255,type,
sP1944: $o > $o ).
thf(func_def_2256,type,
sP1945: $o > $o ).
thf(func_def_2257,type,
sP1946: $o > $o ).
thf(func_def_2258,type,
sP1947: $o > $o ).
thf(func_def_2259,type,
sP1948: $o > $o ).
thf(func_def_2260,type,
sP1949: $o > $o ).
thf(func_def_2261,type,
sP1950: $o > $o ).
thf(func_def_2262,type,
sP1951: $o > $o ).
thf(func_def_2263,type,
sP1952: $o > $o ).
thf(func_def_2264,type,
sP1953: $o > $o ).
thf(func_def_2265,type,
sP1954: $o > $o ).
thf(func_def_2266,type,
sP1955: $o > $o ).
thf(func_def_2267,type,
sP1956: $o > $o ).
thf(func_def_2268,type,
sP1957: $o > $o ).
thf(func_def_2269,type,
sP1958: $o > $o ).
thf(func_def_2270,type,
sP1959: $o > $o ).
thf(func_def_2271,type,
sP1960: $o > $o ).
thf(func_def_2272,type,
sP1961: $o > $o ).
thf(func_def_2273,type,
sP1962: $o > $o ).
thf(func_def_2274,type,
sP1963: $o > $o ).
thf(func_def_2275,type,
sP1964: $o > $o ).
thf(func_def_2276,type,
sP1965: $o > $o ).
thf(func_def_2277,type,
sP1966: $o > $o ).
thf(func_def_2278,type,
sP1967: $o > $o ).
thf(func_def_2279,type,
sP1968: $i > $o ).
thf(func_def_2280,type,
sP1969: $o > $o ).
thf(func_def_2281,type,
sP1970: $o > $o ).
thf(func_def_2282,type,
sP1971: $o > $o ).
thf(func_def_2283,type,
sP1972: $o > $o ).
thf(func_def_2284,type,
sP1973: $o > $o ).
thf(func_def_2285,type,
sP1974: $o > $o ).
thf(func_def_2286,type,
sP1975: $i > $o ).
thf(func_def_2287,type,
sP1976: $o > $o ).
thf(func_def_2288,type,
sP1977: $o > $o ).
thf(func_def_2289,type,
sP1978: $o > $o ).
thf(func_def_2290,type,
sP1979: $o > $o ).
thf(func_def_2291,type,
sP1980: $o > $o ).
thf(func_def_2292,type,
sP1981: $o > $o ).
thf(func_def_2293,type,
sP1982: $o > $o ).
thf(func_def_2294,type,
sP1983: $o > $o ).
thf(func_def_2295,type,
sP1984: $o > $o ).
thf(func_def_2296,type,
sP1985: $o > $o ).
thf(func_def_2297,type,
sP1986: $i > $o ).
thf(func_def_2298,type,
sP1987: $i > $o ).
thf(func_def_2299,type,
sP1988: $o > $o ).
thf(func_def_2300,type,
sP1989: $o > $o ).
thf(func_def_2301,type,
sP1990: $o > $o ).
thf(func_def_2302,type,
sP1991: $o > $o ).
thf(func_def_2303,type,
sP1992: $i > $o ).
thf(func_def_2304,type,
sP1993: $o > $o ).
thf(func_def_2305,type,
sP1994: $o > $o ).
thf(func_def_2306,type,
sP1995: $i > $o ).
thf(func_def_2307,type,
sP1996: $o > $o ).
thf(func_def_2308,type,
sP1997: $o > $o ).
thf(func_def_2309,type,
sP1998: $o > $o ).
thf(func_def_2310,type,
sP1999: $o > $o ).
thf(func_def_2311,type,
sP2000: $o > $o ).
thf(func_def_2312,type,
sP2001: $o > $o ).
thf(func_def_2313,type,
sP2002: $i > $o ).
thf(func_def_2314,type,
sP2003: $o > $o ).
thf(func_def_2315,type,
sP2004: $o > $o ).
thf(func_def_2316,type,
sP2005: $i > $o ).
thf(func_def_2317,type,
sP2006: $o > $o ).
thf(func_def_2318,type,
sP2007: $o > $o ).
thf(func_def_2319,type,
sP2008: $o > $o ).
thf(func_def_2320,type,
sP2009: $o > $o ).
thf(func_def_2321,type,
sP2010: $o > $o ).
thf(func_def_2322,type,
sP2011: $o > $o ).
thf(func_def_2323,type,
sP2012: $o > $o ).
thf(func_def_2324,type,
sP2013: $o > $o ).
thf(func_def_2325,type,
sP2014: $o > $o ).
thf(func_def_2326,type,
sP2015: $o > $o ).
thf(func_def_2327,type,
sP2016: $o > $o ).
thf(func_def_2328,type,
sP2017: $i > $o ).
thf(func_def_2329,type,
sP2018: $o > $o ).
thf(func_def_2330,type,
sP2019: $o > $o ).
thf(func_def_2331,type,
sP2020: $o > $o ).
thf(func_def_2332,type,
sP2021: $o > $o ).
thf(func_def_2333,type,
sP2022: $i > $o ).
thf(func_def_2334,type,
sP2023: $o > $o ).
thf(func_def_2335,type,
sP2024: $o > $o ).
thf(func_def_2336,type,
sP2025: $o > $o ).
thf(func_def_2337,type,
sP2026: $o > $o ).
thf(func_def_2338,type,
sP2027: $o > $o ).
thf(func_def_2339,type,
sP2028: $o > $o ).
thf(func_def_2340,type,
sP2029: $o > $o ).
thf(func_def_2341,type,
sP2030: $o > $o ).
thf(func_def_2342,type,
sP2031: $o > $o ).
thf(func_def_2343,type,
sP2032: $o > $o ).
thf(func_def_2344,type,
sP2033: $o > $o ).
thf(func_def_2345,type,
sP2034: $o > $o ).
thf(func_def_2346,type,
sP2035: $o > $o ).
thf(func_def_2347,type,
sP2036: $o > $o ).
thf(func_def_2348,type,
sP2037: $o > $o ).
thf(func_def_2349,type,
sP2038: $o > $o ).
thf(func_def_2350,type,
sP2039: $o > $o ).
thf(func_def_2351,type,
sP2040: $o > $o ).
thf(func_def_2352,type,
sP2041: $o > $o ).
thf(func_def_2353,type,
sP2042: $o > $o ).
thf(func_def_2354,type,
sP2043: $o > $o ).
thf(func_def_2355,type,
sP2044: $o > $o ).
thf(func_def_2356,type,
sP2045: $o > $o ).
thf(func_def_2357,type,
sP2046: $o > $o ).
thf(func_def_2358,type,
sP2047: $o > $o ).
thf(func_def_2359,type,
sP2048: $o > $o ).
thf(func_def_2360,type,
sP2049: $o > $o ).
thf(func_def_2361,type,
sP2050: $o > $o ).
thf(func_def_2362,type,
sP2051: $o > $o ).
thf(func_def_2363,type,
sP2052: $o > $o ).
thf(func_def_2364,type,
sP2053: $o > $o ).
thf(func_def_2365,type,
sP2054: $o > $o ).
thf(func_def_2366,type,
sP2055: $o > $o ).
thf(func_def_2367,type,
sP2056: $o > $o ).
thf(func_def_2368,type,
sP2057: $o > $o ).
thf(func_def_2369,type,
sP2058: $o > $o ).
thf(func_def_2370,type,
sP2059: $o > $o ).
thf(func_def_2371,type,
sP2060: $o > $o ).
thf(func_def_2372,type,
sP2061: $o > $o ).
thf(func_def_2373,type,
sP2062: $o > $o ).
thf(func_def_2374,type,
sP2063: $o > $o ).
thf(func_def_2375,type,
sP2064: $o > $o ).
thf(func_def_2376,type,
sP2065: $o > $o ).
thf(func_def_2377,type,
sP2066: $o > $o ).
thf(func_def_2378,type,
sP2067: $o > $o ).
thf(func_def_2379,type,
sP2068: $o > $o ).
thf(func_def_2380,type,
sP2069: $o > $o ).
thf(func_def_2381,type,
sP2070: $o > $o ).
thf(func_def_2382,type,
sP2071: $o > $o ).
thf(func_def_2383,type,
sP2072: $o > $o ).
thf(func_def_2384,type,
sP2073: $o > $o ).
thf(func_def_2385,type,
sP2074: $o > $o ).
thf(func_def_2386,type,
sP2075: $o > $o ).
thf(func_def_2387,type,
sP2076: $o > $o ).
thf(func_def_2388,type,
sP2077: $o > $o ).
thf(func_def_2389,type,
sP2078: $o > $o ).
thf(func_def_2390,type,
sP2079: $o > $o ).
thf(func_def_2391,type,
sP2080: $o > $o ).
thf(func_def_2392,type,
sP2081: $o > $o ).
thf(func_def_2393,type,
sP2082: $o > $o ).
thf(func_def_2394,type,
sP2083: $o > $o ).
thf(func_def_2395,type,
sP2084: $o > $o ).
thf(func_def_2396,type,
sP2085: $o > $o ).
thf(func_def_2397,type,
sP2086: $o > $o ).
thf(func_def_2398,type,
sP2087: $o > $o ).
thf(func_def_2399,type,
sP2088: $o > $o ).
thf(func_def_2400,type,
sP2089: $i > $o ).
thf(func_def_2401,type,
sP2090: $o > $o ).
thf(func_def_2402,type,
sP2091: $o > $o ).
thf(func_def_2403,type,
sP2092: $o > $o ).
thf(func_def_2404,type,
sP2093: $o > $o ).
thf(func_def_2405,type,
sP2094: $o > $o ).
thf(func_def_2406,type,
sP2095: $o > $o ).
thf(func_def_2407,type,
sP2096: $o > $o ).
thf(func_def_2408,type,
sP2097: $o > $o ).
thf(func_def_2409,type,
sP2098: $o > $o ).
thf(func_def_2410,type,
sP2099: $o > $o ).
thf(func_def_2411,type,
sP2100: $o > $o ).
thf(func_def_2412,type,
sP2101: $o > $o ).
thf(func_def_2413,type,
sP2102: $o > $o ).
thf(func_def_2414,type,
sP2103: $i > $o ).
thf(func_def_2415,type,
sP2104: $o > $o ).
thf(func_def_2416,type,
sP2105: $o > $o ).
thf(func_def_2417,type,
sP2106: $o > $o ).
thf(func_def_2418,type,
sP2107: $o > $o ).
thf(func_def_2419,type,
sP2108: $o > $o ).
thf(func_def_2420,type,
sP2109: $o > $o ).
thf(func_def_2421,type,
sP2110: $i > $o ).
thf(func_def_2422,type,
sP2111: $o > $o ).
thf(func_def_2423,type,
sP2112: $o > $o ).
thf(func_def_2424,type,
sP2113: $i > $o ).
thf(func_def_2425,type,
sP2114: $o > $o ).
thf(func_def_2426,type,
sP2115: $o > $o ).
thf(func_def_2427,type,
sP2116: $o > $o ).
thf(func_def_2428,type,
sP2117: $o > $o ).
thf(func_def_2429,type,
sP2118: $o > $o ).
thf(func_def_2431,type,
sK2120: ( $i > $o ) > $i ).
thf(func_def_2432,type,
sK2121: ( $i > $o ) > $i ).
thf(func_def_2433,type,
sK2122: ( $i > $o ) > $i ).
thf(func_def_2434,type,
sK2123: ( $i > $o ) > $i ).
thf(func_def_2435,type,
sK2124: ( $i > $o ) > $i ).
thf(func_def_2436,type,
sK2125: ( $i > $o ) > $i ).
thf(func_def_2437,type,
sK2126: ( $i > $o ) > $i ).
thf(func_def_2438,type,
sK2127: ( $i > $o ) > $i > $i ).
thf(func_def_2439,type,
sK2128: ( $i > $o ) > $i > $i ).
thf(func_def_2440,type,
sK2129: ( $i > $o ) > $i > $i ).
thf(func_def_2441,type,
sK2130: ( $i > $o ) > $i ).
thf(func_def_2442,type,
sK2131: ( $i > $o ) > $i ).
thf(func_def_2443,type,
sK2132: ( $i > $o ) > $i > $i ).
thf(func_def_2444,type,
sK2133: ( $i > $o ) > $i ).
thf(func_def_2445,type,
sK2134: $i > $i ).
thf(func_def_2446,type,
sK2135: ( $i > $o ) > $i ).
thf(func_def_2447,type,
sK2136: ( $i > $o ) > $i > $i ).
thf(func_def_2448,type,
sK2137: ( $i > $o ) > $i > $i ).
thf(func_def_2449,type,
sK2138: ( $i > $o ) > $i ).
thf(func_def_2450,type,
sK2139: ( $i > $o ) > $i > $i ).
thf(func_def_2451,type,
ph2140:
!>[X0: $tType] : X0 ).
thf(f47809,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f7421,f8431,f9194,f9546,f47531]) ).
thf(f47531,plain,
( ~ spl2119_70
| ~ spl2119_299 ),
inference(avatar_contradiction_clause,[status(thm)],[f47530]) ).
thf(f47530,plain,
( $false
| ~ spl2119_70
| ~ spl2119_299 ),
inference(subsumption_resolution,[status(thm)],[f47529,f46109]) ).
thf(f46109,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( binintersect @ X0 @ X1 )
= ( binintersect @ ( binintersect @ X0 @ X1 ) @ ( binunion @ X3 @ ( binintersect @ X1 @ ( binunion @ X0 @ X2 ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f41202,f46085]) ).
thf(f46085,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( binintersect @ X0 @ ( binunion @ X2 @ X1 ) )
= ( binintersect @ X0 @ ( binunion @ ( binintersect @ X2 @ X0 ) @ X1 ) ) ),
inference(backward_demodulation,[status(thm)],[f46071,f46084]) ).
thf(f46084,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( binunion @ ( binintersect @ X1 @ X0 ) @ ( binintersect @ X2 @ X0 ) )
= ( binintersect @ X0 @ ( binunion @ X1 @ X2 ) ) ),
inference(forward_demodulation,[status(thm)],[f45753,f45886]) ).
thf(f45886,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( binintersect @ X0 @ ( binunion @ X2 @ X1 ) )
= ( binintersect @ X0 @ ( binunion @ X2 @ ( binintersect @ X1 @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f31098,f41548]) ).
thf(f41548,plain,
! [X0: $i,X1: $i] :
( ( binintersect @ X1 @ X0 )
= ( binintersect @ X0 @ X1 ) ),
inference(forward_demodulation,[status(thm)],[f41547,f29976]) ).
thf(f29976,plain,
! [X0: $i,X1: $i] :
( ( binunion @ ( binintersect @ X0 @ X1 ) @ X0 )
= X0 ),
inference(forward_demodulation,[status(thm)],[f29947,f29004]) ).
thf(f29004,plain,
! [X0: $i,X1: $i] :
( ( binintersect @ X0 @ ( binunion @ X1 @ X0 ) )
= X0 ),
inference(trivial_inequality_removal,[status(thm)],[f29003]) ).
thf(f29003,plain,
! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ ( binunion @ X1 @ X0 ) )
= X0 )
| ( $false = $true ) ),
inference(forward_demodulation,[status(thm)],[f28998,f5926]) ).
thf(f5926,plain,
( $false
= ( sP1559 @ $true ) ),
introduced(definition,[new_symbols(naming,[sP1559])],[inequality_splitting_name_introduction]) ).
thf(f28998,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( sP1559 @ $true ) )
| ( ( binintersect @ X0 @ ( binunion @ X1 @ X0 ) )
= X0 ) ),
inference(superposition,[status(thm)],[f7865,f8122]) ).
thf(f8122,plain,
! [X2: $i,X3: $i] :
( ( subset @ X3 @ ( binunion @ X2 @ X3 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f8121]) ).
thf(f8121,plain,
! [X2: $i,X3: $i] :
( ( ( subset @ X3 @ ( binunion @ X2 @ X3 ) )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[status(thm)],[f6779,f6778]) ).
thf(f6778,plain,
( $false
= ( sP2108 @ $true ) ),
introduced(definition,[new_symbols(naming,[sP2108])],[inequality_splitting_name_introduction]) ).
thf(f6779,plain,
! [X2: $i,X3: $i] :
( ( $true
= ( sP2108 @ $true ) )
| ( ( subset @ X3 @ ( binunion @ X2 @ X3 ) )
= $true ) ),
inference(inequality_splitting,[status(thm)],[f4787,f6778]) ).
thf(f4787,plain,
! [X2: $i,X3: $i] :
( ( ( subset @ X3 @ ( binunion @ X2 @ X3 ) )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f3768,f2651]) ).
thf(f2651,plain,
binunionRsub = $true,
inference(cnf_transformation,[status(thm)],[f1190]) ).
thf(f1190,plain,
( ( setunion__Cong = $true )
& ( doubleComplementI1 = $true )
& ( ksndsingleton = $true )
& ( iftrueorfalse = $true )
& ( eta1 = $true )
& ( subset2powerset = $true )
& ( binunionE = $true )
& ( iffalse = $true )
& ( uniqinunit = $true )
& ( prop2setI = $true )
& ( apProp = $true )
& ( lamp = $true )
& ( iftrueProp1 = $true )
& ( upairsetIR = $true )
& ( notsubsetI = $true )
& ( inCongP = $true )
& ( contraSubsetComplement = $true )
& ( binunionIL = $true )
& ( descrp = $true )
& ( dpsetconstrI = $true )
& ( kpairiskpair = $true )
& ( cartprodsndin = $true )
& ( doubleComplementSub1 = $true )
& ( ifp = $true )
& ( symdiffIneg1 = $true )
& ( emptyE1 = $true )
& ( funcextLem = $true )
& ( setminusIRneg = $true )
& ( binunionTIRcontra = $true )
& ( theprop = $true )
& ( powersetE = $true )
& ( dsetconstrI = $true )
& ( funcinfuncset = $true )
& ( ubforcartprodlem3 = $true )
& ( iftrue = $true )
& ( complementTI1 = $true )
& ( subsetI2 = $true )
& ( inIntersectImpInUnion = $true )
& ( binunionLsub = $true )
& ( inIntersectImpInUnion2 = $true )
& ( dpsetconstrER = $true )
& ( setminusSubset2 = $true )
& ( funcext = $true )
& ( setadjoinIR = $true )
& ( funcImageSingleton = $true )
& ( setukpairIL = $true )
& ( complementTnotintersectT = $true )
& ( exuI2 = $true )
& ( emptyInPowerset = $true )
& ( binunionTILcontra = $true )
& ( cartprodfstin = $true )
& ( binintersectSubset2 = $true )
& ( binunionRsub = $true )
& ( funcGraphProp1 = $true )
& ( powersetsubset = $true )
& ( setminusSubset1 = $true )
& ( binintersectRsub = $true )
& ( contrasubsetT = $true )
& ( binunionEcases = $true )
& ( setunionsingleton2 = $true )
& ( binintersectSubset3 = $true )
& ( dpsetconstrSub = $true )
& ( eqimpsubset2 = $true )
& ( dsetconstrER = $true )
& ( setadjoinSub = $true )
& ( binintersectTERcontra = $true )
& ( foundationAx = $true )
& ( singletoninpowerset = $true )
& ( funcGraphProp3 = $true )
& ( setukpairinjR = $true )
& ( emptyI = $true )
& ( exu__Cong = $true )
& ( in__Cong = $true )
& ( setOfPairsIsBReln = $true )
& ( ubforcartprodlem2 = $true )
& ( powerset__Cong = $true )
& ( nonemptyE1 = $true )
& ( app = $true )
& ( complementTE1 = $true )
& ( contrasubsetT1 = $true )
& ( subsetTrans = $true )
& ( singletonsswitch = $true )
& ( lam2lamEq = $true )
& ( setunionE2 = $true )
& ( ksndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( exuEu = $true )
& ( quantDeMorgan1 = $true )
& ( infuncsetfunc = $true )
& ( upairset2E = $true )
& ( powersetTI1 = $true )
& ( setunionsingleton1 = $true )
& ( ex1I2 = $true )
& ( subsetE2 = $true )
& ( setadjoinIL = $true )
& ( lam2p = $true )
& ( symdiffIneg2 = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( binintersectLsub = $true )
& ( exuI1 = $true )
& ( setadjoinE = $true )
& ( setadjoinAx = $true )
& ( setunionE = $true )
& ( brelnall1 = $true )
& ( upairsetIL = $true )
& ( binintersectSubset1 = $true )
& ( subsetE = $true )
& ( replAx = $true )
& ( emptysetAx = $true )
& ( emptyinunitempty = $true )
& ( contrasubsetT2 = $true )
& ( setukpairinjL = $true )
& ( setminusERneg = $true )
& ( setminusT_lem = $true )
& ( powersetI1 = $true )
& ( kfstsingleton = $true )
& ( setminusILneg = $true )
& ( iffalseProp1 = $true )
& ( wellorderingAx = $true )
& ( ap2p = $true )
& ( exuE1 = $true )
& ( doubleComplementSub2 = $true )
& ( notinemptyset = $true )
& ( upairsetE = $true )
& ( powersetE1 = $true )
& ( ap2apEq2 = $true )
& ( singletonsubset = $true )
& ( subsetI1 = $true )
& ( complementT_lem = $true )
& ( inPowerset = $true )
& ( contrasubsetT3 = $true )
& ( exuE2 = $true )
& ( prop2set2propI = $true )
& ( brelnall2 = $true )
& ( omegaSAx = $true )
& ( nonemptyImpWitness = $true )
& ( binintersectSubset5 = $true )
& ( symdiffI2 = $true )
& ( ubforcartprodlem1 = $true )
& ( notequalI2 = $true )
& ( quantDeMorgan4 = $true )
& ( symdiffE = $true )
& ( kpairp = $true )
& ( ex1I = $true )
& ( cartprodsndpairEq = $true )
& ( secondinupair = $true )
& ( nonemptyI1 = $true )
& ( quantDeMorgan3 = $true )
& ( powersetT_lem = $true )
& ( setbeta = $true )
& ( iftrueProp2 = $true )
& ( setoftrueEq = $true )
& ( symdiffI1 = $true )
& ( powersetAx = $true )
& ( sepInPowerset = $true )
& ( binintersectSubset4 = $true )
& ( cartprodmempair = $true )
& ( binintersectT_lem = $true )
& ( subsetTI = $true )
& ( emptyset__Cong = $true )
& ( setukpairinjR1 = $true )
& ( funcGraphProp2 = $true )
& ( setextAx = $true )
& ( setminusEL = $true )
& ( disjointsetsI1 = $true )
& ( dpsetconstrEL1 = $true )
& ( subPowSU = $true )
& ( notdallE = $true )
& ( singletonprop = $true )
& ( binunionT_lem = $true )
& ( dsetconstr__Cong = $true )
& ( setminusER = $true )
& ( kpairsurjEq = $true )
& ( iffalseProp2 = $true )
& ( powersetI = $true )
& ( exuI3 = $true )
& ( complementTcontraSubset = $true )
& ( singletonsuniq = $true )
& ( setminusLsub = $true )
& ( ex1E1 = $true )
& ( prop2setE = $true )
& ( omegaIndAx = $true )
& ( dsetconstrEL = $true )
& ( emptysetE = $true )
& ( setadjoin__Cong = $true )
& ( binintersectTELcontra = $true )
& ( eqbreln = $true )
& ( exuE3e = $true )
& ( doubleComplementE1 = $true )
& ( setunionsingleton = $true )
& ( setext = $true )
& ( lamProp = $true )
& ( ap2apEq1 = $true )
& ( eqimpsubset1 = $true )
& ( subsetRefl = $true )
& ( upairsubunion = $true )
& ( upairinpowunion = $true )
& ( emptyinPowerset = $true )
& ( upairset2IR = $true )
& ( nonemptyI = $true )
& ( beta1 = $true )
& ( vacuousDall = $true )
& ( theeq = $true )
& ( notdexE = $true )
& ( quantDeMorgan2 = $true )
& ( singletoninpowunion = $true )
& ( setukpairinjR2 = $true )
& ( emptysetsubset = $true )
& ( setunionI = $true )
& ( upairequniteq = $true )
& ( dpsetconstrERa = $true )
& ( kfstpairEq = $true )
& ( descr__Cong = $true )
& ( subbreln = $true )
& ( omega0Ax = $true )
& ( bs114d = $true )
& ( setextsub = $true )
& ( setadjoinSub2 = $true )
& ( setukpairinjL1 = $true )
& ( cartprodpairin = $true )
& ( notequalI1 = $true )
& ( dpsetconstrEL2 = $true )
& ( $true
= ( in @ sK30 @ ( powerset @ sK27 ) ) )
& ( $true
!= ( in @ ( binintersect @ sK28 @ sK29 ) @ ( powerset @ ( binintersect @ ( binunion @ sK28 @ sK30 ) @ ( binunion @ sK29 @ sK30 ) ) ) ) )
& ( $true
= ( in @ sK29 @ ( powerset @ sK27 ) ) )
& ( $true
= ( in @ sK28 @ ( powerset @ sK27 ) ) )
& ( binintersectI = $true )
& ( powersetTE1 = $true )
& ( complementSubsetComplementIntersect = $true )
& ( setukpairinjR11 = $true )
& ( omega__Cong = $true )
& ( exuE3u = $true )
& ( cartprodpairmemEL = $true )
& ( eqinunit = $true )
& ( setminusI = $true )
& ( binunionIR = $true )
& ( setunionAx = $true )
& ( setukpairinjL2 = $true )
& ( sepSubset = $true )
& ( setminusELneg = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( funcGraphProp4 = $true )
& ( ex1E2 = $true )
& ( noeltsimpempty = $true )
& ( setukpairIR = $true )
& ( subsetemptysetimpeq = $true )
& ( beta2 = $true )
& ( setextT = $true )
& ( notinsingleton = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( eta2 = $true )
& ( binintersectER = $true )
& ( funcext2 = $true )
& ( cartprodpairsurjEq = $true )
& ( doubleComplementEq = $true )
& ( binintersectEL = $true )
& ( setukpairinjR12 = $true )
& ( setadjoinOr = $true )
& ( cartprodmempair1 = $true )
& ( ifSingleton = $true )
& ( emptysetimpfalse = $true )
& ( complementImpComplementIntersect = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27,sK28,sK29,sK30])],[f1025,f1189,f1188,f1187]) ).
thf(f1187,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
& ( ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X1 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) )
!= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) ) )
=> ( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( powerset @ sK27 ) ) )
& ( $true
!= ( in @ ( binintersect @ sK28 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ sK28 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK27 ) ) ) )
& ( $true
= ( in @ sK28 @ ( powerset @ sK27 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1188,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( powerset @ sK27 ) ) )
& ( $true
!= ( in @ ( binintersect @ sK28 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ sK28 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK27 ) ) ) )
=> ( ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( powerset @ sK27 ) ) )
& ( ( in @ ( binintersect @ sK28 @ sK29 ) @ ( powerset @ ( binintersect @ ( binunion @ sK28 @ X3 ) @ ( binunion @ sK29 @ X3 ) ) ) )
!= $true ) )
& ( $true
= ( in @ sK29 @ ( powerset @ sK27 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1189,plain,
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( powerset @ sK27 ) ) )
& ( ( in @ ( binintersect @ sK28 @ sK29 ) @ ( powerset @ ( binintersect @ ( binunion @ sK28 @ X3 ) @ ( binunion @ sK29 @ X3 ) ) ) )
!= $true ) )
=> ( ( $true
= ( in @ sK30 @ ( powerset @ sK27 ) ) )
& ( $true
!= ( in @ ( binintersect @ sK28 @ sK29 ) @ ( powerset @ ( binintersect @ ( binunion @ sK28 @ sK30 ) @ ( binunion @ sK29 @ sK30 ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1025,plain,
( ( setunion__Cong = $true )
& ( doubleComplementI1 = $true )
& ( ksndsingleton = $true )
& ( iftrueorfalse = $true )
& ( eta1 = $true )
& ( subset2powerset = $true )
& ( binunionE = $true )
& ( iffalse = $true )
& ( uniqinunit = $true )
& ( prop2setI = $true )
& ( apProp = $true )
& ( lamp = $true )
& ( iftrueProp1 = $true )
& ( upairsetIR = $true )
& ( notsubsetI = $true )
& ( inCongP = $true )
& ( contraSubsetComplement = $true )
& ( binunionIL = $true )
& ( descrp = $true )
& ( dpsetconstrI = $true )
& ( kpairiskpair = $true )
& ( cartprodsndin = $true )
& ( doubleComplementSub1 = $true )
& ( ifp = $true )
& ( symdiffIneg1 = $true )
& ( emptyE1 = $true )
& ( funcextLem = $true )
& ( setminusIRneg = $true )
& ( binunionTIRcontra = $true )
& ( theprop = $true )
& ( powersetE = $true )
& ( dsetconstrI = $true )
& ( funcinfuncset = $true )
& ( ubforcartprodlem3 = $true )
& ( iftrue = $true )
& ( complementTI1 = $true )
& ( subsetI2 = $true )
& ( inIntersectImpInUnion = $true )
& ( binunionLsub = $true )
& ( inIntersectImpInUnion2 = $true )
& ( dpsetconstrER = $true )
& ( setminusSubset2 = $true )
& ( funcext = $true )
& ( setadjoinIR = $true )
& ( funcImageSingleton = $true )
& ( setukpairIL = $true )
& ( complementTnotintersectT = $true )
& ( exuI2 = $true )
& ( emptyInPowerset = $true )
& ( binunionTILcontra = $true )
& ( cartprodfstin = $true )
& ( binintersectSubset2 = $true )
& ( binunionRsub = $true )
& ( funcGraphProp1 = $true )
& ( powersetsubset = $true )
& ( setminusSubset1 = $true )
& ( binintersectRsub = $true )
& ( contrasubsetT = $true )
& ( binunionEcases = $true )
& ( setunionsingleton2 = $true )
& ( binintersectSubset3 = $true )
& ( dpsetconstrSub = $true )
& ( eqimpsubset2 = $true )
& ( dsetconstrER = $true )
& ( setadjoinSub = $true )
& ( binintersectTERcontra = $true )
& ( foundationAx = $true )
& ( singletoninpowerset = $true )
& ( funcGraphProp3 = $true )
& ( setukpairinjR = $true )
& ( emptyI = $true )
& ( exu__Cong = $true )
& ( in__Cong = $true )
& ( setOfPairsIsBReln = $true )
& ( ubforcartprodlem2 = $true )
& ( powerset__Cong = $true )
& ( nonemptyE1 = $true )
& ( app = $true )
& ( complementTE1 = $true )
& ( contrasubsetT1 = $true )
& ( subsetTrans = $true )
& ( singletonsswitch = $true )
& ( lam2lamEq = $true )
& ( setunionE2 = $true )
& ( ksndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( exuEu = $true )
& ( quantDeMorgan1 = $true )
& ( infuncsetfunc = $true )
& ( upairset2E = $true )
& ( powersetTI1 = $true )
& ( setunionsingleton1 = $true )
& ( ex1I2 = $true )
& ( subsetE2 = $true )
& ( setadjoinIL = $true )
& ( lam2p = $true )
& ( symdiffIneg2 = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( binintersectLsub = $true )
& ( exuI1 = $true )
& ( setadjoinE = $true )
& ( setadjoinAx = $true )
& ( setunionE = $true )
& ( brelnall1 = $true )
& ( upairsetIL = $true )
& ( binintersectSubset1 = $true )
& ( subsetE = $true )
& ( replAx = $true )
& ( emptysetAx = $true )
& ( emptyinunitempty = $true )
& ( contrasubsetT2 = $true )
& ( setukpairinjL = $true )
& ( setminusERneg = $true )
& ( setminusT_lem = $true )
& ( powersetI1 = $true )
& ( kfstsingleton = $true )
& ( setminusILneg = $true )
& ( iffalseProp1 = $true )
& ( wellorderingAx = $true )
& ( ap2p = $true )
& ( exuE1 = $true )
& ( doubleComplementSub2 = $true )
& ( notinemptyset = $true )
& ( upairsetE = $true )
& ( powersetE1 = $true )
& ( ap2apEq2 = $true )
& ( singletonsubset = $true )
& ( subsetI1 = $true )
& ( complementT_lem = $true )
& ( inPowerset = $true )
& ( contrasubsetT3 = $true )
& ( exuE2 = $true )
& ( prop2set2propI = $true )
& ( brelnall2 = $true )
& ( omegaSAx = $true )
& ( nonemptyImpWitness = $true )
& ( binintersectSubset5 = $true )
& ( symdiffI2 = $true )
& ( ubforcartprodlem1 = $true )
& ( notequalI2 = $true )
& ( quantDeMorgan4 = $true )
& ( symdiffE = $true )
& ( kpairp = $true )
& ( ex1I = $true )
& ( cartprodsndpairEq = $true )
& ( secondinupair = $true )
& ( nonemptyI1 = $true )
& ( quantDeMorgan3 = $true )
& ( powersetT_lem = $true )
& ( setbeta = $true )
& ( iftrueProp2 = $true )
& ( setoftrueEq = $true )
& ( symdiffI1 = $true )
& ( powersetAx = $true )
& ( sepInPowerset = $true )
& ( binintersectSubset4 = $true )
& ( cartprodmempair = $true )
& ( binintersectT_lem = $true )
& ( subsetTI = $true )
& ( emptyset__Cong = $true )
& ( setukpairinjR1 = $true )
& ( funcGraphProp2 = $true )
& ( setextAx = $true )
& ( setminusEL = $true )
& ( disjointsetsI1 = $true )
& ( dpsetconstrEL1 = $true )
& ( subPowSU = $true )
& ( notdallE = $true )
& ( singletonprop = $true )
& ( binunionT_lem = $true )
& ( dsetconstr__Cong = $true )
& ( setminusER = $true )
& ( kpairsurjEq = $true )
& ( iffalseProp2 = $true )
& ( powersetI = $true )
& ( exuI3 = $true )
& ( complementTcontraSubset = $true )
& ( singletonsuniq = $true )
& ( setminusLsub = $true )
& ( ex1E1 = $true )
& ( prop2setE = $true )
& ( omegaIndAx = $true )
& ( dsetconstrEL = $true )
& ( emptysetE = $true )
& ( setadjoin__Cong = $true )
& ( binintersectTELcontra = $true )
& ( eqbreln = $true )
& ( exuE3e = $true )
& ( doubleComplementE1 = $true )
& ( setunionsingleton = $true )
& ( setext = $true )
& ( lamProp = $true )
& ( ap2apEq1 = $true )
& ( eqimpsubset1 = $true )
& ( subsetRefl = $true )
& ( upairsubunion = $true )
& ( upairinpowunion = $true )
& ( emptyinPowerset = $true )
& ( upairset2IR = $true )
& ( nonemptyI = $true )
& ( beta1 = $true )
& ( vacuousDall = $true )
& ( theeq = $true )
& ( notdexE = $true )
& ( quantDeMorgan2 = $true )
& ( singletoninpowunion = $true )
& ( setukpairinjR2 = $true )
& ( emptysetsubset = $true )
& ( setunionI = $true )
& ( upairequniteq = $true )
& ( dpsetconstrERa = $true )
& ( kfstpairEq = $true )
& ( descr__Cong = $true )
& ( subbreln = $true )
& ( omega0Ax = $true )
& ( bs114d = $true )
& ( setextsub = $true )
& ( setadjoinSub2 = $true )
& ( setukpairinjL1 = $true )
& ( cartprodpairin = $true )
& ( notequalI1 = $true )
& ( dpsetconstrEL2 = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
& ( ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X1 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) )
!= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) ) )
& ( binintersectI = $true )
& ( powersetTE1 = $true )
& ( complementSubsetComplementIntersect = $true )
& ( setukpairinjR11 = $true )
& ( omega__Cong = $true )
& ( exuE3u = $true )
& ( cartprodpairmemEL = $true )
& ( eqinunit = $true )
& ( setminusI = $true )
& ( binunionIR = $true )
& ( setunionAx = $true )
& ( setukpairinjL2 = $true )
& ( sepSubset = $true )
& ( setminusELneg = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( funcGraphProp4 = $true )
& ( ex1E2 = $true )
& ( noeltsimpempty = $true )
& ( setukpairIR = $true )
& ( subsetemptysetimpeq = $true )
& ( beta2 = $true )
& ( setextT = $true )
& ( notinsingleton = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( eta2 = $true )
& ( binintersectER = $true )
& ( funcext2 = $true )
& ( cartprodpairsurjEq = $true )
& ( doubleComplementEq = $true )
& ( binintersectEL = $true )
& ( setukpairinjR12 = $true )
& ( setadjoinOr = $true )
& ( cartprodmempair1 = $true )
& ( ifSingleton = $true )
& ( emptysetimpfalse = $true )
& ( complementImpComplementIntersect = $true ) ),
inference(flattening,[status(thm)],[f1024]) ).
thf(f1024,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
& ( ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X1 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) )
!= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) ) )
& ( 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)],[f557]) ).
thf(f557,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 )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X0 ) )
= $true )
=> ( ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X1 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f556]) ).
thf(f556,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
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ( in @ ( binintersect @ X1 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X1 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f265]) ).
thf(f265,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
=> ! [X3: $i,X11: $i] :
( ( in @ X11 @ ( powerset @ X3 ) )
=> ! [X16: $i] :
( ( in @ X16 @ ( powerset @ X3 ) )
=> ! [X17: $i] :
( ( in @ X17 @ ( powerset @ X3 ) )
=> ( in @ ( binintersect @ X11 @ X16 ) @ ( powerset @ ( binintersect @ ( binunion @ X11 @ X17 ) @ ( binunion @ X16 @ X17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f264]) ).
thf(f264,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
=> ! [X3: $i,X11: $i] :
( ( in @ X11 @ ( powerset @ X3 ) )
=> ! [X16: $i] :
( ( in @ X16 @ ( powerset @ X3 ) )
=> ! [X17: $i] :
( ( in @ X17 @ ( powerset @ X3 ) )
=> ( in @ ( binintersect @ X11 @ X16 ) @ ( powerset @ ( binintersect @ ( binunion @ X11 @ X17 ) @ ( binunion @ X16 @ X17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XapuwXWeE6/DTF2THF_1199.p',intersectInPowersetIntersectUnions) ).
thf(f3768,plain,
! [X2: $i,X3: $i] :
( ( ( subset @ X3 @ ( binunion @ X2 @ X3 ) )
= $true )
| ( binunionRsub != $true ) ),
inference(cnf_transformation,[status(thm)],[f2408]) ).
thf(f2408,plain,
( ( ( binunionRsub = $true )
| ( ( subset @ sK822 @ ( binunion @ sK821 @ sK822 ) )
!= $true ) )
& ( ! [X2: $i,X3: $i] :
( ( subset @ X3 @ ( binunion @ X2 @ X3 ) )
= $true )
| ( binunionRsub != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK821,sK822])],[f2406,f2407]) ).
thf(f2407,plain,
( ? [X0: $i,X1: $i] :
( $true
!= ( subset @ X1 @ ( binunion @ X0 @ X1 ) ) )
=> ( ( subset @ sK822 @ ( binunion @ sK821 @ sK822 ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2406,plain,
( ( ( binunionRsub = $true )
| ? [X0: $i,X1: $i] :
( $true
!= ( subset @ X1 @ ( binunion @ X0 @ X1 ) ) ) )
& ( ! [X2: $i,X3: $i] :
( ( subset @ X3 @ ( binunion @ X2 @ X3 ) )
= $true )
| ( binunionRsub != $true ) ) ),
inference(rectify,[status(thm)],[f2405]) ).
thf(f2405,plain,
( ( ( binunionRsub = $true )
| ? [X0: $i,X1: $i] :
( $true
!= ( subset @ X1 @ ( binunion @ X0 @ X1 ) ) ) )
& ( ! [X0: $i,X1: $i] :
( $true
= ( subset @ X1 @ ( binunion @ X0 @ X1 ) ) )
| ( binunionRsub != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f736]) ).
thf(f736,plain,
( ( binunionRsub = $true )
<=> ! [X0: $i,X1: $i] :
( $true
= ( subset @ X1 @ ( binunion @ X0 @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f735]) ).
thf(f735,plain,
! [X0: $i,X1: $i] :
( ( subset @ X1 @ ( binunion @ X0 @ X1 ) )
= binunionRsub ),
inference(rectify,[status(thm)],[f107]) ).
thf(f107,axiom,
! [X3: $i,X4: $i] :
( ( subset @ X4 @ ( binunion @ X3 @ X4 ) )
= binunionRsub ),
file('/export/starexec/sandbox/tmp/tmp.XapuwXWeE6/DTF2THF_1199.p',binunionRsub) ).
thf(f7865,plain,
! [X0: $i,X1: $i] :
( ( ( sP1559 @ ( subset @ X0 @ X1 ) )
= $true )
| ( ( binintersect @ X0 @ X1 )
= X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f7864]) ).
thf(f7864,plain,
! [X0: $i,X1: $i] :
( ( ( sP1559 @ ( subset @ X0 @ X1 ) )
= $true )
| ( $false = $true )
| ( ( binintersect @ X0 @ X1 )
= X0 ) ),
inference(forward_demodulation,[status(thm)],[f5928,f5927]) ).
thf(f5927,plain,
( $false
= ( sP1560 @ $true ) ),
introduced(definition,[new_symbols(naming,[sP1560])],[inequality_splitting_name_introduction]) ).
thf(f5928,plain,
! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X0 )
| ( $true
= ( sP1560 @ $true ) )
| ( ( sP1559 @ ( subset @ X0 @ X1 ) )
= $true ) ),
inference(inequality_splitting,[status(thm)],[f4331,f5927,f5926]) ).
thf(f4331,plain,
! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X0 )
| ( ( subset @ X0 @ X1 )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f3292,f2652]) ).
thf(f2652,plain,
binintersectSubset2 = $true,
inference(cnf_transformation,[status(thm)],[f1190]) ).
thf(f3292,plain,
! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X0 )
| ( ( subset @ X0 @ X1 )
!= $true )
| ( binintersectSubset2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f1863]) ).
thf(f1863,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X0 )
| ( ( subset @ X0 @ X1 )
!= $true ) )
| ( binintersectSubset2 != $true ) )
& ( ( binintersectSubset2 = $true )
| ( ( sK459
!= ( binintersect @ sK459 @ sK460 ) )
& ( ( subset @ sK459 @ sK460 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK459,sK460])],[f1861,f1862]) ).
thf(f1862,plain,
( ? [X2: $i,X3: $i] :
( ( ( binintersect @ X2 @ X3 )
!= X2 )
& ( $true
= ( subset @ X2 @ X3 ) ) )
=> ( ( sK459
!= ( binintersect @ sK459 @ sK460 ) )
& ( ( subset @ sK459 @ sK460 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1861,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X0 )
| ( ( subset @ X0 @ X1 )
!= $true ) )
| ( binintersectSubset2 != $true ) )
& ( ( binintersectSubset2 = $true )
| ? [X2: $i,X3: $i] :
( ( ( binintersect @ X2 @ X3 )
!= X2 )
& ( $true
= ( subset @ X2 @ X3 ) ) ) ) ),
inference(rectify,[status(thm)],[f1860]) ).
thf(f1860,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X0 )
| ( ( subset @ X0 @ X1 )
!= $true ) )
| ( binintersectSubset2 != $true ) )
& ( ( binintersectSubset2 = $true )
| ? [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
!= X0 )
& ( ( subset @ X0 @ X1 )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f969]) ).
thf(f969,plain,
( ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X0 )
| ( ( subset @ X0 @ X1 )
!= $true ) )
<=> ( binintersectSubset2 = $true ) ),
inference(ennf_transformation,[status(thm)],[f447]) ).
thf(f447,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
=> ( ( binintersect @ X0 @ X1 )
= X0 ) )
<=> ( binintersectSubset2 = $true ) ),
inference(fool_elimination,[status(thm)],[f446]) ).
thf(f446,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( binintersect @ X0 @ X1 )
= X0 ) )
= binintersectSubset2 ),
inference(rectify,[status(thm)],[f112]) ).
thf(f112,axiom,
! [X3: $i,X4: $i] :
( ( ( subset @ X3 @ X4 )
=> ( ( binintersect @ X3 @ X4 )
= X3 ) )
= binintersectSubset2 ),
file('/export/starexec/sandbox/tmp/tmp.XapuwXWeE6/DTF2THF_1199.p',binintersectSubset2) ).
thf(f29947,plain,
! [X0: $i,X1: $i] :
( ( binintersect @ X0 @ ( binunion @ X1 @ X0 ) )
= ( binunion @ ( binintersect @ X0 @ X1 ) @ X0 ) ),
inference(superposition,[status(thm)],[f9106,f28233]) ).
thf(f28233,plain,
! [X0: $i] :
( ( binintersect @ X0 @ X0 )
= X0 ),
inference(trivial_inequality_removal,[status(thm)],[f28232]) ).
thf(f28232,plain,
! [X0: $i] :
( ( ( binintersect @ X0 @ X0 )
= X0 )
| ( $false = $true ) ),
inference(forward_demodulation,[status(thm)],[f28229,f5812]) ).
thf(f5812,plain,
( $false
= ( sP1490 @ $true ) ),
introduced(definition,[new_symbols(naming,[sP1490])],[inequality_splitting_name_introduction]) ).
thf(f28229,plain,
! [X0: $i] :
( ( ( sP1490 @ $true )
= $true )
| ( ( binintersect @ X0 @ X0 )
= X0 ) ),
inference(superposition,[status(thm)],[f9027,f8209]) ).
thf(f8209,plain,
! [X3: $i] :
( ( subset @ X3 @ X3 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f8208]) ).
thf(f8208,plain,
! [X3: $i] :
( ( ( subset @ X3 @ X3 )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[status(thm)],[f6805,f5207]) ).
thf(f5207,plain,
( $false
= ( sP1092 @ $true ) ),
introduced(definition,[new_symbols(naming,[sP1092])],[inequality_splitting_name_introduction]) ).
thf(f6805,plain,
! [X3: $i] :
( ( ( subset @ X3 @ X3 )
= $true )
| ( $true
= ( sP1092 @ $true ) ) ),
inference(equality_resolution,[status(thm)],[f5208]) ).
thf(f5208,plain,
! [X2: $i,X3: $i] :
( ( $true
= ( subset @ X2 @ X3 ) )
| ( X2 != X3 )
| ( $true
= ( sP1092 @ $true ) ) ),
inference(inequality_splitting,[status(thm)],[f3962,f5207]) ).
thf(f3962,plain,
! [X2: $i,X3: $i] :
( ( $true
= ( subset @ X2 @ X3 ) )
| ( X2 != X3 )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f2895,f2510]) ).
thf(f2510,plain,
eqimpsubset1 = $true,
inference(cnf_transformation,[status(thm)],[f1190]) ).
thf(f2895,plain,
! [X2: $i,X3: $i] :
( ( $true
= ( subset @ X2 @ X3 ) )
| ( X2 != X3 )
| ( eqimpsubset1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f1408]) ).
thf(f1408,plain,
( ( ( eqimpsubset1 = $true )
| ( ( $true
!= ( subset @ sK170 @ sK171 ) )
& ( sK171 = sK170 ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
= ( subset @ X2 @ X3 ) )
| ( X2 != X3 ) )
| ( eqimpsubset1 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK170,sK171])],[f1406,f1407]) ).
thf(f1407,plain,
( ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
& ( X0 = X1 ) )
=> ( ( $true
!= ( subset @ sK170 @ sK171 ) )
& ( sK171 = sK170 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1406,plain,
( ( ( eqimpsubset1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
& ( X0 = X1 ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
= ( subset @ X2 @ X3 ) )
| ( X2 != X3 ) )
| ( eqimpsubset1 != $true ) ) ),
inference(rectify,[status(thm)],[f1405]) ).
thf(f1405,plain,
( ( ( eqimpsubset1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
& ( X0 = X1 ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( X0 != X1 ) )
| ( eqimpsubset1 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f1120]) ).
thf(f1120,plain,
( ( eqimpsubset1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( X0 != X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f607]) ).
thf(f607,plain,
( ( eqimpsubset1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( ( subset @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f606]) ).
thf(f606,plain,
( eqimpsubset1
= ( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( subset @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f80]) ).
thf(f80,axiom,
( eqimpsubset1
= ( ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( subset @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XapuwXWeE6/DTF2THF_1199.p',eqimpsubset1) ).
thf(f9027,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( sP1490 @ ( subset @ X0 @ X1 ) ) )
| ( ( binintersect @ X1 @ X0 )
= X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f9026]) ).
thf(f9026,plain,
! [X0: $i,X1: $i] :
( ( ( binintersect @ X1 @ X0 )
= X0 )
| ( $true
= ( sP1490 @ ( subset @ X0 @ X1 ) ) )
| ( $false = $true ) ),
inference(forward_demodulation,[status(thm)],[f5814,f5813]) ).
thf(f5813,plain,
( $false
= ( sP1491 @ $true ) ),
introduced(definition,[new_symbols(naming,[sP1491])],[inequality_splitting_name_introduction]) ).
thf(f5814,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( sP1491 @ $true ) )
| ( $true
= ( sP1490 @ ( subset @ X0 @ X1 ) ) )
| ( ( binintersect @ X1 @ X0 )
= X0 ) ),
inference(inequality_splitting,[status(thm)],[f4267,f5813,f5812]) ).
thf(f4267,plain,
! [X0: $i,X1: $i] :
( ( ( binintersect @ X1 @ X0 )
= X0 )
| ( ( subset @ X0 @ X1 )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f3228,f2548]) ).
thf(f2548,plain,
binintersectSubset4 = $true,
inference(cnf_transformation,[status(thm)],[f1190]) ).
thf(f3228,plain,
! [X0: $i,X1: $i] :
( ( ( binintersect @ X1 @ X0 )
= X0 )
| ( ( subset @ X0 @ X1 )
!= $true )
| ( binintersectSubset4 != $true ) ),
inference(cnf_transformation,[status(thm)],[f1776]) ).
thf(f1776,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( binintersect @ X1 @ X0 )
= X0 )
| ( ( subset @ X0 @ X1 )
!= $true ) )
| ( binintersectSubset4 != $true ) )
& ( ( binintersectSubset4 = $true )
| ( ( ( binintersect @ sK411 @ sK410 )
!= sK410 )
& ( $true
= ( subset @ sK410 @ sK411 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK410,sK411])],[f1774,f1775]) ).
thf(f1775,plain,
( ? [X2: $i,X3: $i] :
( ( ( binintersect @ X3 @ X2 )
!= X2 )
& ( $true
= ( subset @ X2 @ X3 ) ) )
=> ( ( ( binintersect @ sK411 @ sK410 )
!= sK410 )
& ( $true
= ( subset @ sK410 @ sK411 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1774,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( binintersect @ X1 @ X0 )
= X0 )
| ( ( subset @ X0 @ X1 )
!= $true ) )
| ( binintersectSubset4 != $true ) )
& ( ( binintersectSubset4 = $true )
| ? [X2: $i,X3: $i] :
( ( ( binintersect @ X3 @ X2 )
!= X2 )
& ( $true
= ( subset @ X2 @ X3 ) ) ) ) ),
inference(rectify,[status(thm)],[f1773]) ).
thf(f1773,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( binintersect @ X1 @ X0 )
= X0 )
| ( ( subset @ X0 @ X1 )
!= $true ) )
| ( binintersectSubset4 != $true ) )
& ( ( binintersectSubset4 = $true )
| ? [X0: $i,X1: $i] :
( ( ( binintersect @ X1 @ X0 )
!= X0 )
& ( ( subset @ X0 @ X1 )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f902]) ).
thf(f902,plain,
( ! [X0: $i,X1: $i] :
( ( ( binintersect @ X1 @ X0 )
= X0 )
| ( ( subset @ X0 @ X1 )
!= $true ) )
<=> ( binintersectSubset4 = $true ) ),
inference(ennf_transformation,[status(thm)],[f366]) ).
thf(f366,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
=> ( ( binintersect @ X1 @ X0 )
= X0 ) )
<=> ( binintersectSubset4 = $true ) ),
inference(fool_elimination,[status(thm)],[f365]) ).
thf(f365,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( binintersect @ X1 @ X0 )
= X0 ) )
= binintersectSubset4 ),
inference(rectify,[status(thm)],[f117]) ).
thf(f117,axiom,
! [X4: $i,X3: $i] :
( ( ( subset @ X4 @ X3 )
=> ( ( binintersect @ X3 @ X4 )
= X4 ) )
= binintersectSubset4 ),
file('/export/starexec/sandbox/tmp/tmp.XapuwXWeE6/DTF2THF_1199.p',binintersectSubset4) ).
thf(f9106,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( binintersect @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binunion @ ( binintersect @ X0 @ X1 ) @ ( binintersect @ X0 @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f9105]) ).
thf(f9105,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binunion @ ( binintersect @ X0 @ X1 ) @ ( binintersect @ X0 @ X2 ) ) )
| ( $false = $true ) ),
inference(forward_demodulation,[status(thm)],[f6595,f6594]) ).
thf(f6594,plain,
( $false
= ( sP1994 @ $true ) ),
introduced(definition,[new_symbols(naming,[sP1994])],[inequality_splitting_name_introduction]) ).
thf(f6595,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( sP1994 @ $true )
= $true )
| ( ( binintersect @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binunion @ ( binintersect @ X0 @ X1 ) @ ( binintersect @ X0 @ X2 ) ) ) ),
inference(inequality_splitting,[status(thm)],[f4681,f6594]) ).
thf(f4681,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binunion @ ( binintersect @ X0 @ X1 ) @ ( binintersect @ X0 @ X2 ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f3659,f2488]) ).
thf(f2488,plain,
bs114d = $true,
inference(cnf_transformation,[status(thm)],[f1190]) ).
thf(f3659,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binunion @ ( binintersect @ X0 @ X1 ) @ ( binintersect @ X0 @ X2 ) ) )
| ( bs114d != $true ) ),
inference(cnf_transformation,[status(thm)],[f2279]) ).
thf(f2279,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( binintersect @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binunion @ ( binintersect @ X0 @ X1 ) @ ( binintersect @ X0 @ X2 ) ) )
| ( bs114d != $true ) )
& ( ( bs114d = $true )
| ( ( binintersect @ sK744 @ ( binunion @ sK745 @ sK746 ) )
!= ( binunion @ ( binintersect @ sK744 @ sK745 ) @ ( binintersect @ sK744 @ sK746 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK744,sK745,sK746])],[f2277,f2278]) ).
thf(f2278,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( binintersect @ X3 @ ( binunion @ X4 @ X5 ) )
!= ( binunion @ ( binintersect @ X3 @ X4 ) @ ( binintersect @ X3 @ X5 ) ) )
=> ( ( binintersect @ sK744 @ ( binunion @ sK745 @ sK746 ) )
!= ( binunion @ ( binintersect @ sK744 @ sK745 ) @ ( binintersect @ sK744 @ sK746 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2277,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( binintersect @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binunion @ ( binintersect @ X0 @ X1 ) @ ( binintersect @ X0 @ X2 ) ) )
| ( bs114d != $true ) )
& ( ( bs114d = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( binintersect @ X3 @ ( binunion @ X4 @ X5 ) )
!= ( binunion @ ( binintersect @ X3 @ X4 ) @ ( binintersect @ X3 @ X5 ) ) ) ) ),
inference(rectify,[status(thm)],[f2276]) ).
thf(f2276,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( binintersect @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binunion @ ( binintersect @ X0 @ X1 ) @ ( binintersect @ X0 @ X2 ) ) )
| ( bs114d != $true ) )
& ( ( bs114d = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( binintersect @ X0 @ ( binunion @ X1 @ X2 ) )
!= ( binunion @ ( binintersect @ X0 @ X1 ) @ ( binintersect @ X0 @ X2 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f358]) ).
thf(f358,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( binintersect @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binunion @ ( binintersect @ X0 @ X1 ) @ ( binintersect @ X0 @ X2 ) ) )
<=> ( bs114d = $true ) ),
inference(fool_elimination,[status(thm)],[f357]) ).
thf(f357,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( binintersect @ X0 @ ( binunion @ X1 @ X2 ) )
= ( binunion @ ( binintersect @ X0 @ X1 ) @ ( binintersect @ X0 @ X2 ) ) )
= bs114d ),
inference(rectify,[status(thm)],[f119]) ).
thf(f119,axiom,
! [X3: $i,X4: $i,X5: $i] :
( ( ( binintersect @ X3 @ ( binunion @ X4 @ X5 ) )
= ( binunion @ ( binintersect @ X3 @ X4 ) @ ( binintersect @ X3 @ X5 ) ) )
= bs114d ),
file('/export/starexec/sandbox/tmp/tmp.XapuwXWeE6/DTF2THF_1199.p',bs114d) ).
thf(f41547,plain,
! [X0: $i,X1: $i] :
( ( binintersect @ X0 @ X1 )
= ( binintersect @ X1 @ ( binunion @ ( binintersect @ X0 @ X1 ) @ X0 ) ) ),
inference(forward_demodulation,[status(thm)],[f41474,f29974]) ).
thf(f29974,plain,
! [X0: $i,X1: $i] :
( ( binunion @ X0 @ ( binintersect @ X0 @ X1 ) )
= X0 ),
inference(forward_demodulation,[status(thm)],[f29956,f29029]) ).
thf(f29029,plain,
! [X0: $i,X1: $i] :
( ( binintersect @ X0 @ ( binunion @ X0 @ X1 ) )
= X0 ),
inference(trivial_inequality_removal,[status(thm)],[f29028]) ).
thf(f29028,plain,
! [X0: $i,X1: $i] :
( ( $false = $true )
| ( ( binintersect @ X0 @ ( binunion @ X0 @ X1 ) )
= X0 ) ),
inference(forward_demodulation,[status(thm)],[f29025,f5926]) ).
thf(f29025,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( sP1559 @ $true ) )
| ( ( binintersect @ X0 @ ( binunion @ X0 @ X1 ) )
= X0 ) ),
inference(superposition,[status(thm)],[f7865,f8573]) ).
thf(f8573,plain,
! [X0: $i,X1: $i] :
( $true
= ( subset @ X1 @ ( binunion @ X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f8572]) ).
thf(f8572,plain,
! [X0: $i,X1: $i] :
( ( $false = $true )
| ( $true
= ( subset @ X1 @ ( binunion @ X1 @ X0 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f5251,f5250]) ).
thf(f5250,plain,
( $false
= ( sP1119 @ $true ) ),
introduced(definition,[new_symbols(naming,[sP1119])],[inequality_splitting_name_introduction]) ).
thf(f5251,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ ( binunion @ X1 @ X0 ) ) )
| ( $true
= ( sP1119 @ $true ) ) ),
inference(inequality_splitting,[status(thm)],[f3987,f5250]) ).
thf(f3987,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ ( binunion @ X1 @ X0 ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f2923,f2665]) ).
thf(f2665,plain,
binunionLsub = $true,
inference(cnf_transformation,[status(thm)],[f1190]) ).
thf(f2923,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ ( binunion @ X1 @ X0 ) ) )
| ( binunionLsub != $true ) ),
inference(cnf_transformation,[status(thm)],[f1439]) ).
thf(f1439,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( subset @ X1 @ ( binunion @ X1 @ X0 ) ) )
| ( binunionLsub != $true ) )
& ( ( binunionLsub = $true )
| ( $true
!= ( subset @ sK192 @ ( binunion @ sK192 @ sK191 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK191,sK192])],[f1437,f1438]) ).
thf(f1438,plain,
( ? [X2: $i,X3: $i] :
( $true
!= ( subset @ X3 @ ( binunion @ X3 @ X2 ) ) )
=> ( $true
!= ( subset @ sK192 @ ( binunion @ sK192 @ sK191 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1437,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( subset @ X1 @ ( binunion @ X1 @ X0 ) ) )
| ( binunionLsub != $true ) )
& ( ( binunionLsub = $true )
| ? [X2: $i,X3: $i] :
( $true
!= ( subset @ X3 @ ( binunion @ X3 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f1436]) ).
thf(f1436,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( subset @ X1 @ ( binunion @ X1 @ X0 ) ) )
| ( binunionLsub != $true ) )
& ( ( binunionLsub = $true )
| ? [X0: $i,X1: $i] :
( $true
!= ( subset @ X1 @ ( binunion @ X1 @ X0 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f292]) ).
thf(f292,plain,
( ! [X0: $i,X1: $i] :
( $true
= ( subset @ X1 @ ( binunion @ X1 @ X0 ) ) )
<=> ( binunionLsub = $true ) ),
inference(fool_elimination,[status(thm)],[f291]) ).
thf(f291,plain,
( binunionLsub
= ( ! [X0: $i,X1: $i] : ( subset @ X1 @ ( binunion @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f106]) ).
thf(f106,axiom,
( binunionLsub
= ( ! [X4: $i,X3: $i] : ( subset @ X3 @ ( binunion @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XapuwXWeE6/DTF2THF_1199.p',binunionLsub) ).
thf(f29956,plain,
! [X0: $i,X1: $i] :
( ( binintersect @ X0 @ ( binunion @ X0 @ X1 ) )
= ( binunion @ X0 @ ( binintersect @ X0 @ X1 ) ) ),
inference(superposition,[status(thm)],[f9106,f28233]) ).
thf(f41474,plain,
! [X0: $i,X1: $i] :
( ( binintersect @ X1 @ ( binunion @ ( binintersect @ X0 @ X1 ) @ X0 ) )
= ( binintersect @ X0 @ ( binunion @ X1 @ ( binintersect @ X1 @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f31203,f31204]) ).
thf(f31204,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( binintersect @ X0 @ ( binunion @ X2 @ ( binintersect @ X1 @ X0 ) ) )
= ( binunion @ ( binintersect @ X0 @ X2 ) @ ( binintersect @ X1 @ X0 ) ) ),
inference(superposition,[status(thm)],[f9106,f29062]) ).
thf(f29062,plain,
! [X0: $i,X1: $i] :
( ( binintersect @ X1 @ ( binintersect @ X0 @ X1 ) )
= ( binintersect @ X0 @ X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f29061]) ).
thf(f29061,plain,
! [X0: $i,X1: $i] :
( ( ( binintersect @ X1 @ ( binintersect @ X0 @ X1 ) )
= ( binintersect @ X0 @ X1 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[status(thm)],[f29052,f5812]) ).
thf(f29052,plain,
! [X0: $i,X1: $i] :
( ( ( sP1490 @ $true )
= $true )
| ( ( binintersect @ X1 @ ( binintersect @ X0 @ X1 ) )
= ( binintersect @ X0 @ X1 ) ) ),
inference(superposition,[status(thm)],[f9027,f8991]) ).
thf(f8991,plain,
! [X0: $i,X1: $i] :
( $true
= ( subset @ ( binintersect @ X0 @ X1 ) @ X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f8990]) ).
thf(f8990,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ ( binintersect @ X0 @ X1 ) @ X1 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[status(thm)],[f6247,f6246]) ).
thf(f6246,plain,
( $false
= ( sP1769 @ $true ) ),
introduced(definition,[new_symbols(naming,[sP1769])],[inequality_splitting_name_introduction]) ).
thf(f6247,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ ( binintersect @ X0 @ X1 ) @ X1 ) )
| ( $true
= ( sP1769 @ $true ) ) ),
inference(inequality_splitting,[status(thm)],[f4509,f6246]) ).
thf(f4509,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ ( binintersect @ X0 @ X1 ) @ X1 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f3479,f2647]) ).
thf(f2647,plain,
binintersectRsub = $true,
inference(cnf_transformation,[status(thm)],[f1190]) ).
thf(f3479,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ ( binintersect @ X0 @ X1 ) @ X1 ) )
| ( binintersectRsub != $true ) ),
inference(cnf_transformation,[status(thm)],[f2076]) ).
thf(f2076,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( subset @ ( binintersect @ X0 @ X1 ) @ X1 ) )
| ( binintersectRsub != $true ) )
& ( ( binintersectRsub = $true )
| ( $true
!= ( subset @ ( binintersect @ sK606 @ sK607 ) @ sK607 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK606,sK607])],[f2074,f2075]) ).
thf(f2075,plain,
( ? [X2: $i,X3: $i] :
( $true
!= ( subset @ ( binintersect @ X2 @ X3 ) @ X3 ) )
=> ( $true
!= ( subset @ ( binintersect @ sK606 @ sK607 ) @ sK607 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2074,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( subset @ ( binintersect @ X0 @ X1 ) @ X1 ) )
| ( binintersectRsub != $true ) )
& ( ( binintersectRsub = $true )
| ? [X2: $i,X3: $i] :
( $true
!= ( subset @ ( binintersect @ X2 @ X3 ) @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f2073]) ).
thf(f2073,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( subset @ ( binintersect @ X0 @ X1 ) @ X1 ) )
| ( binintersectRsub != $true ) )
& ( ( binintersectRsub = $true )
| ? [X0: $i,X1: $i] :
( $true
!= ( subset @ ( binintersect @ X0 @ X1 ) @ X1 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f436]) ).
thf(f436,plain,
( ! [X0: $i,X1: $i] :
( $true
= ( subset @ ( binintersect @ X0 @ X1 ) @ X1 ) )
<=> ( binintersectRsub = $true ) ),
inference(fool_elimination,[status(thm)],[f435]) ).
thf(f435,plain,
! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X1 )
= binintersectRsub ),
inference(rectify,[status(thm)],[f116]) ).
thf(f116,axiom,
! [X3: $i,X4: $i] :
( ( subset @ ( binintersect @ X3 @ X4 ) @ X4 )
= binintersectRsub ),
file('/export/starexec/sandbox/tmp/tmp.XapuwXWeE6/DTF2THF_1199.p',binintersectRsub) ).
thf(f31203,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( binintersect @ X0 @ ( binunion @ ( binintersect @ X1 @ X0 ) @ X2 ) )
= ( binunion @ ( binintersect @ X1 @ X0 ) @ ( binintersect @ X0 @ X2 ) ) ),
inference(superposition,[status(thm)],[f9106,f29062]) ).
thf(f31098,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( binintersect @ X0 @ ( binunion @ X2 @ ( binintersect @ X0 @ X1 ) ) )
= ( binintersect @ X0 @ ( binunion @ X2 @ X1 ) ) ),
inference(forward_demodulation,[status(thm)],[f31082,f9106]) ).
thf(f31082,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( binintersect @ X0 @ ( binunion @ X2 @ ( binintersect @ X0 @ X1 ) ) )
= ( binunion @ ( binintersect @ X0 @ X2 ) @ ( binintersect @ X0 @ X1 ) ) ),
inference(superposition,[status(thm)],[f9106,f29045]) ).
thf(f29045,plain,
! [X0: $i,X1: $i] :
( ( binintersect @ X0 @ X1 )
= ( binintersect @ X0 @ ( binintersect @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f29044]) ).
thf(f29044,plain,
! [X0: $i,X1: $i] :
( ( $false = $true )
| ( ( binintersect @ X0 @ X1 )
= ( binintersect @ X0 @ ( binintersect @ X0 @ X1 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f29037,f5812]) ).
thf(f29037,plain,
! [X0: $i,X1: $i] :
( ( ( sP1490 @ $true )
= $true )
| ( ( binintersect @ X0 @ X1 )
= ( binintersect @ X0 @ ( binintersect @ X0 @ X1 ) ) ) ),
inference(superposition,[status(thm)],[f9027,f8886]) ).
thf(f8886,plain,
! [X2: $i,X3: $i] :
( $true
= ( subset @ ( binintersect @ X3 @ X2 ) @ X3 ) ),
inference(trivial_inequality_removal,[status(thm)],[f8885]) ).
thf(f8885,plain,
! [X2: $i,X3: $i] :
( ( $true
= ( subset @ ( binintersect @ X3 @ X2 ) @ X3 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[status(thm)],[f6196,f6195]) ).
thf(f6195,plain,
( $false
= ( sP1739 @ $true ) ),
introduced(definition,[new_symbols(naming,[sP1739])],[inequality_splitting_name_introduction]) ).
thf(f6196,plain,
! [X2: $i,X3: $i] :
( ( $true
= ( subset @ ( binintersect @ X3 @ X2 ) @ X3 ) )
| ( $true
= ( sP1739 @ $true ) ) ),
inference(inequality_splitting,[status(thm)],[f4478,f6195]) ).
thf(f4478,plain,
! [X2: $i,X3: $i] :
( ( $true
= ( subset @ ( binintersect @ X3 @ X2 ) @ X3 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f3445,f2605]) ).
thf(f2605,plain,
binintersectLsub = $true,
inference(cnf_transformation,[status(thm)],[f1190]) ).
thf(f3445,plain,
! [X2: $i,X3: $i] :
( ( $true
= ( subset @ ( binintersect @ X3 @ X2 ) @ X3 ) )
| ( binintersectLsub != $true ) ),
inference(cnf_transformation,[status(thm)],[f2035]) ).
thf(f2035,plain,
( ( ( binintersectLsub = $true )
| ( $true
!= ( subset @ ( binintersect @ sK581 @ sK580 ) @ sK581 ) ) )
& ( ! [X2: $i,X3: $i] :
( $true
= ( subset @ ( binintersect @ X3 @ X2 ) @ X3 ) )
| ( binintersectLsub != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK580,sK581])],[f2033,f2034]) ).
thf(f2034,plain,
( ? [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
!= $true )
=> ( $true
!= ( subset @ ( binintersect @ sK581 @ sK580 ) @ sK581 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2033,plain,
( ( ( binintersectLsub = $true )
| ? [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
!= $true ) )
& ( ! [X2: $i,X3: $i] :
( $true
= ( subset @ ( binintersect @ X3 @ X2 ) @ X3 ) )
| ( binintersectLsub != $true ) ) ),
inference(rectify,[status(thm)],[f2032]) ).
thf(f2032,plain,
( ( ( binintersectLsub = $true )
| ? [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
!= $true ) )
& ( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
= $true )
| ( binintersectLsub != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f330]) ).
thf(f330,plain,
( ( binintersectLsub = $true )
<=> ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f329]) ).
thf(f329,plain,
! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
= binintersectLsub ),
inference(rectify,[status(thm)],[f111]) ).
thf(f111,axiom,
! [X4: $i,X3: $i] :
( ( subset @ ( binintersect @ X3 @ X4 ) @ X3 )
= binintersectLsub ),
file('/export/starexec/sandbox/tmp/tmp.XapuwXWeE6/DTF2THF_1199.p',binintersectLsub) ).
thf(f45753,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( binintersect @ X0 @ ( binunion @ X1 @ ( binintersect @ X2 @ X0 ) ) )
= ( binunion @ ( binintersect @ X1 @ X0 ) @ ( binintersect @ X2 @ X0 ) ) ),
inference(superposition,[status(thm)],[f31204,f41548]) ).
thf(f46071,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( binunion @ ( binintersect @ X2 @ X0 ) @ ( binintersect @ X1 @ X0 ) )
= ( binintersect @ X0 @ ( binunion @ ( binintersect @ X2 @ X0 ) @ X1 ) ) ),
inference(backward_demodulation,[status(thm)],[f41047,f45886]) ).
thf(f41047,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( binintersect @ X0 @ ( binunion @ ( binintersect @ X2 @ X0 ) @ ( binintersect @ X1 @ X0 ) ) )
= ( binunion @ ( binintersect @ X2 @ X0 ) @ ( binintersect @ X1 @ X0 ) ) ),
inference(superposition,[status(thm)],[f31203,f29062]) ).
thf(f41202,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( binintersect @ ( binintersect @ X0 @ X1 ) @ ( binunion @ X3 @ ( binintersect @ X1 @ ( binunion @ ( binintersect @ X0 @ X1 ) @ X2 ) ) ) )
= ( binintersect @ X0 @ X1 ) ),
inference(superposition,[status(thm)],[f29982,f31203]) ).
thf(f29982,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( binintersect @ X0 @ ( binunion @ X2 @ ( binunion @ X0 @ X1 ) ) )
= X0 ),
inference(forward_demodulation,[status(thm)],[f29953,f29976]) ).
thf(f29953,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( binunion @ ( binintersect @ X0 @ X2 ) @ X0 )
= ( binintersect @ X0 @ ( binunion @ X2 @ ( binunion @ X0 @ X1 ) ) ) ),
inference(superposition,[status(thm)],[f9106,f29029]) ).
thf(f47529,plain,
( ( ( binintersect @ ( binintersect @ sK28 @ sK29 ) @ ( binunion @ sK30 @ ( binintersect @ sK29 @ ( binunion @ sK28 @ sK30 ) ) ) )
!= ( binintersect @ sK28 @ sK29 ) )
| ~ spl2119_70
| ~ spl2119_299 ),
inference(forward_demodulation,[status(thm)],[f47521,f41548]) ).
thf(f47521,plain,
( ( ( binintersect @ sK28 @ sK29 )
!= ( binintersect @ ( binintersect @ sK28 @ sK29 ) @ ( binunion @ sK30 @ ( binintersect @ ( binunion @ sK28 @ sK30 ) @ sK29 ) ) ) )
| ~ spl2119_70
| ~ spl2119_299 ),
inference(backward_demodulation,[status(thm)],[f30896,f47394]) ).
thf(f47394,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( binunion @ X1 @ ( binintersect @ ( binunion @ X0 @ X1 ) @ X2 ) )
= ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) ),
inference(backward_demodulation,[status(thm)],[f29949,f47385]) ).
thf(f47385,plain,
! [X0: $i,X1: $i] :
( ( binunion @ X0 @ X1 )
= ( binunion @ X1 @ X0 ) ),
inference(forward_demodulation,[status(thm)],[f47213,f29027]) ).
thf(f29027,plain,
! [X0: $i,X1: $i] :
( ( binintersect @ ( binunion @ X0 @ X1 ) @ X0 )
= X0 ),
inference(trivial_inequality_removal,[status(thm)],[f29026]) ).
thf(f29026,plain,
! [X0: $i,X1: $i] :
( ( $false = $true )
| ( ( binintersect @ ( binunion @ X0 @ X1 ) @ X0 )
= X0 ) ),
inference(forward_demodulation,[status(thm)],[f29024,f5812]) ).
thf(f29024,plain,
! [X0: $i,X1: $i] :
( ( ( binintersect @ ( binunion @ X0 @ X1 ) @ X0 )
= X0 )
| ( ( sP1490 @ $true )
= $true ) ),
inference(superposition,[status(thm)],[f9027,f8573]) ).
thf(f47213,plain,
! [X0: $i,X1: $i] :
( ( binunion @ X0 @ ( binintersect @ ( binunion @ X1 @ X0 ) @ X1 ) )
= ( binunion @ X1 @ X0 ) ),
inference(superposition,[status(thm)],[f45981,f29002]) ).
thf(f29002,plain,
! [X0: $i,X1: $i] :
( ( binintersect @ ( binunion @ X1 @ X0 ) @ X0 )
= X0 ),
inference(trivial_inequality_removal,[status(thm)],[f29001]) ).
thf(f29001,plain,
! [X0: $i,X1: $i] :
( ( $false = $true )
| ( ( binintersect @ ( binunion @ X1 @ X0 ) @ X0 )
= X0 ) ),
inference(forward_demodulation,[status(thm)],[f28997,f5812]) ).
thf(f28997,plain,
! [X0: $i,X1: $i] :
( ( ( binintersect @ ( binunion @ X1 @ X0 ) @ X0 )
= X0 )
| ( ( sP1490 @ $true )
= $true ) ),
inference(superposition,[status(thm)],[f9027,f8122]) ).
thf(f45981,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( binunion @ X0 @ ( binintersect @ ( binunion @ X2 @ X0 ) @ X1 ) )
= ( binunion @ ( binintersect @ ( binunion @ X0 @ X1 ) @ X2 ) @ X0 ) ),
inference(backward_demodulation,[status(thm)],[f29948,f45946]) ).
thf(f45946,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( binunion @ X1 @ ( binintersect @ ( binunion @ X0 @ X1 ) @ X2 ) )
= ( binintersect @ ( binunion @ X1 @ X2 ) @ ( binunion @ X0 @ X1 ) ) ),
inference(superposition,[status(thm)],[f29958,f41548]) ).
thf(f29958,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( binunion @ X1 @ ( binintersect @ ( binunion @ X0 @ X1 ) @ X2 ) )
= ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X1 @ X2 ) ) ),
inference(superposition,[status(thm)],[f9106,f29002]) ).
thf(f29948,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X0 ) )
= ( binunion @ ( binintersect @ ( binunion @ X0 @ X1 ) @ X2 ) @ X0 ) ),
inference(superposition,[status(thm)],[f9106,f29027]) ).
thf(f29949,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( binunion @ ( binintersect @ ( binunion @ X0 @ X1 ) @ X2 ) @ X1 )
= ( binintersect @ ( binunion @ X0 @ X1 ) @ ( binunion @ X2 @ X1 ) ) ),
inference(superposition,[status(thm)],[f9106,f29002]) ).
thf(f30896,plain,
( ( ( binintersect @ sK28 @ sK29 )
!= ( binintersect @ ( binintersect @ sK28 @ sK29 ) @ ( binintersect @ ( binunion @ sK28 @ sK30 ) @ ( binunion @ sK29 @ sK30 ) ) ) )
| ~ spl2119_70
| ~ spl2119_299 ),
inference(trivial_inequality_removal,[status(thm)],[f30895]) ).
thf(f30895,plain,
( ( $false = $true )
| ( ( binintersect @ sK28 @ sK29 )
!= ( binintersect @ ( binintersect @ sK28 @ sK29 ) @ ( binintersect @ ( binunion @ sK28 @ sK30 ) @ ( binunion @ sK29 @ sK30 ) ) ) )
| ~ spl2119_70
| ~ spl2119_299 ),
inference(forward_demodulation,[status(thm)],[f30886,f4835]) ).
thf(f4835,plain,
( $false
= ( sP854 @ $true ) ),
introduced(definition,[new_symbols(naming,[sP854])],[inequality_splitting_name_introduction]) ).
thf(f30886,plain,
( ( $true
= ( sP854 @ $true ) )
| ( ( binintersect @ sK28 @ sK29 )
!= ( binintersect @ ( binintersect @ sK28 @ sK29 ) @ ( binintersect @ ( binunion @ sK28 @ sK30 ) @ ( binunion @ sK29 @ sK30 ) ) ) )
| ~ spl2119_70
| ~ spl2119_299 ),
inference(superposition,[status(thm)],[f4836,f30133]) ).
thf(f30133,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( ( binintersect @ X0 @ X1 )
!= X0 ) )
| ~ spl2119_70
| ~ spl2119_299 ),
inference(trivial_inequality_removal,[status(thm)],[f30132]) ).
thf(f30132,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( ( binintersect @ X0 @ X1 )
!= X0 )
| ( $false = $true ) )
| ~ spl2119_70
| ~ spl2119_299 ),
inference(forward_demodulation,[status(thm)],[f30125,f5951]) ).
thf(f5951,plain,
( $false
= ( sP1575 @ $true ) ),
introduced(definition,[new_symbols(naming,[sP1575])],[inequality_splitting_name_introduction]) ).
thf(f30125,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( sP1575 @ $true ) )
| ( ( binintersect @ X0 @ X1 )
!= X0 )
| ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) ) )
| ~ spl2119_70
| ~ spl2119_299 ),
inference(superposition,[status(thm)],[f7420,f8430]) ).
thf(f8430,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( ( binintersect @ X0 @ X1 )
!= X0 ) )
| ~ spl2119_299 ),
inference(avatar_component_clause,[status(thm)],[f8429]) ).
thf(f8429,definition,
( spl2119_299
<=> ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( ( binintersect @ X0 @ X1 )
!= X0 ) ) ),
introduced(definition,[new_symbols(naming,[spl2119_299])],[avatar_definition]) ).
thf(f7420,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( sP1575 @ ( subset @ X1 @ X0 ) ) )
| ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) ) )
| ~ spl2119_70 ),
inference(avatar_component_clause,[status(thm)],[f7419]) ).
thf(f7419,definition,
( spl2119_70
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
| ( $true
= ( sP1575 @ ( subset @ X1 @ X0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2119_70])],[avatar_definition]) ).
thf(f4836,plain,
( ( sP854 @ ( in @ ( binintersect @ sK28 @ sK29 ) @ ( powerset @ ( binintersect @ ( binunion @ sK28 @ sK30 ) @ ( binunion @ sK29 @ sK30 ) ) ) ) )
= $true ),
inference(inequality_splitting,[status(thm)],[f2480,f4835]) ).
thf(f2480,plain,
( $true
!= ( in @ ( binintersect @ sK28 @ sK29 ) @ ( powerset @ ( binintersect @ ( binunion @ sK28 @ sK30 ) @ ( binunion @ sK29 @ sK30 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f1190]) ).
thf(f9546,plain,
~ spl2119_69,
inference(avatar_contradiction_clause,[status(thm)],[f9545]) ).
thf(f9545,plain,
( $false
| ~ spl2119_69 ),
inference(trivial_inequality_removal,[status(thm)],[f9544]) ).
thf(f9544,plain,
( ( $false = $true )
| ~ spl2119_69 ),
inference(forward_demodulation,[status(thm)],[f7417,f5952]) ).
thf(f5952,plain,
( $false
= ( sP1576 @ $true ) ),
introduced(definition,[new_symbols(naming,[sP1576])],[inequality_splitting_name_introduction]) ).
thf(f7417,plain,
( ( $true
= ( sP1576 @ $true ) )
| ~ spl2119_69 ),
inference(avatar_component_clause,[status(thm)],[f7415]) ).
thf(f7415,definition,
( spl2119_69
<=> ( $true
= ( sP1576 @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl2119_69])],[avatar_definition]) ).
thf(f9194,plain,
~ spl2119_298,
inference(avatar_contradiction_clause,[status(thm)],[f9193]) ).
thf(f9193,plain,
( $false
| ~ spl2119_298 ),
inference(trivial_inequality_removal,[status(thm)],[f9192]) ).
thf(f9192,plain,
( ( $false = $true )
| ~ spl2119_298 ),
inference(forward_demodulation,[status(thm)],[f8427,f5870]) ).
thf(f5870,plain,
( $false
= ( sP1526 @ $true ) ),
introduced(definition,[new_symbols(naming,[sP1526])],[inequality_splitting_name_introduction]) ).
thf(f8427,plain,
( ( ( sP1526 @ $true )
= $true )
| ~ spl2119_298 ),
inference(avatar_component_clause,[status(thm)],[f8425]) ).
thf(f8425,definition,
( spl2119_298
<=> ( ( sP1526 @ $true )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2119_298])],[avatar_definition]) ).
thf(f8431,plain,
( spl2119_298
| spl2119_299 ),
inference(avatar_split_clause,[status(thm)],[f5871,f8429,f8425]) ).
thf(f5871,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( ( sP1526 @ $true )
= $true )
| ( ( binintersect @ X0 @ X1 )
!= X0 ) ),
inference(inequality_splitting,[status(thm)],[f4301,f5870]) ).
thf(f4301,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( ( binintersect @ X0 @ X1 )
!= X0 )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f3262,f2598]) ).
thf(f2598,plain,
binintersectSubset1 = $true,
inference(cnf_transformation,[status(thm)],[f1190]) ).
thf(f3262,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( ( binintersect @ X0 @ X1 )
!= X0 )
| ( binintersectSubset1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f1820]) ).
thf(f1820,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( ( binintersect @ X0 @ X1 )
!= X0 ) )
| ( binintersectSubset1 != $true ) )
& ( ( binintersectSubset1 = $true )
| ( ( $true
!= ( subset @ sK434 @ sK435 ) )
& ( sK434
= ( binintersect @ sK434 @ sK435 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK434,sK435])],[f1818,f1819]) ).
thf(f1819,plain,
( ? [X2: $i,X3: $i] :
( ( $true
!= ( subset @ X2 @ X3 ) )
& ( ( binintersect @ X2 @ X3 )
= X2 ) )
=> ( ( $true
!= ( subset @ sK434 @ sK435 ) )
& ( sK434
= ( binintersect @ sK434 @ sK435 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1818,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( ( binintersect @ X0 @ X1 )
!= X0 ) )
| ( binintersectSubset1 != $true ) )
& ( ( binintersectSubset1 = $true )
| ? [X2: $i,X3: $i] :
( ( $true
!= ( subset @ X2 @ X3 ) )
& ( ( binintersect @ X2 @ X3 )
= X2 ) ) ) ),
inference(rectify,[status(thm)],[f1817]) ).
thf(f1817,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( ( binintersect @ X0 @ X1 )
!= X0 ) )
| ( binintersectSubset1 != $true ) )
& ( ( binintersectSubset1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
& ( ( binintersect @ X0 @ X1 )
= X0 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f1135]) ).
thf(f1135,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( ( binintersect @ X0 @ X1 )
!= X0 ) )
<=> ( binintersectSubset1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f681]) ).
thf(f681,plain,
( ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X0 )
=> ( ( subset @ X0 @ X1 )
= $true ) )
<=> ( binintersectSubset1 = $true ) ),
inference(fool_elimination,[status(thm)],[f680]) ).
thf(f680,plain,
( binintersectSubset1
= ( ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X0 )
=> ( subset @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f118]) ).
thf(f118,axiom,
( binintersectSubset1
= ( ! [X3: $i,X4: $i] :
( ( ( binintersect @ X3 @ X4 )
= X3 )
=> ( subset @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XapuwXWeE6/DTF2THF_1199.p',binintersectSubset1) ).
thf(f7421,plain,
( spl2119_69
| spl2119_70 ),
inference(avatar_split_clause,[status(thm)],[f5953,f7419,f7415]) ).
thf(f5953,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
| ( $true
= ( sP1575 @ ( subset @ X1 @ X0 ) ) )
| ( $true
= ( sP1576 @ $true ) ) ),
inference(inequality_splitting,[status(thm)],[f4347,f5952,f5951]) ).
thf(f4347,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f3308,f2589]) ).
thf(f2589,plain,
powersetI1 = $true,
inference(cnf_transformation,[status(thm)],[f1190]) ).
thf(f3308,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
| ( powersetI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f1880]) ).
thf(f1880,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) ) )
| ( powersetI1 != $true ) )
& ( ( powersetI1 = $true )
| ( ( ( subset @ sK471 @ sK470 )
= $true )
& ( ( in @ sK471 @ ( powerset @ sK470 ) )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK470,sK471])],[f1878,f1879]) ).
thf(f1879,plain,
( ? [X2: $i,X3: $i] :
( ( $true
= ( subset @ X3 @ X2 ) )
& ( ( in @ X3 @ ( powerset @ X2 ) )
!= $true ) )
=> ( ( ( subset @ sK471 @ sK470 )
= $true )
& ( ( in @ sK471 @ ( powerset @ sK470 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1878,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) ) )
| ( powersetI1 != $true ) )
& ( ( powersetI1 = $true )
| ? [X2: $i,X3: $i] :
( ( $true
= ( subset @ X3 @ X2 ) )
& ( ( in @ X3 @ ( powerset @ X2 ) )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f1877]) ).
thf(f1877,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) ) )
| ( powersetI1 != $true ) )
& ( ( powersetI1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
& ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f905]) ).
thf(f905,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) ) )
<=> ( powersetI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f338]) ).
thf(f338,plain,
( ( powersetI1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
=> ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f337]) ).
thf(f337,plain,
( powersetI1
= ( ! [X0: $i,X1: $i] :
( ( subset @ X1 @ X0 )
=> ( in @ X1 @ ( powerset @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f95]) ).
thf(f95,axiom,
( powersetI1
= ( ! [X3: $i,X4: $i] :
( ( subset @ X4 @ X3 )
=> ( in @ X4 @ ( powerset @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XapuwXWeE6/DTF2THF_1199.p',powersetI1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU743^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n021.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:32:39 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.45 ---- Original DTF file ---
% 0.20/0.45 thf(spec,logic,$$dhol).
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 % File : SEU743^1 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.45 % Domain : Set Theory
% 0.20/0.45 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.20/0.45 % Version : Especial.
% 0.20/0.45 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.20/0.45 % (! Z:i.in Z (powerset A) -> in (binintersect X Y)
% 0.20/0.45 % (powerset (binintersect (binunion X Z) (binunion Y Z))))))
% 0.20/0.45
% 0.20/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.20/0.45 % Source : [Bro08]
% 0.20/0.45 % Names : ZFC245g [Bro08]
% 0.20/0.45
% 0.20/0.45 % Status : Theorem
% 0.20/0.45 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.40 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.57 v7.4.0, 0.78 v7.2.0, 0.75 v7.1.0, 0.88 v7.0.0, 1.00 v6.2.0, 0.86 v6.1.0, 1.00 v5.5.0, 0.83 v5.4.0, 0.60 v5.2.0, 1.00 v3.7.0
% 0.20/0.45 % Syntax : Number of formulae : 561 ( 263 unt; 297 typ; 263 def)
% 0.20/0.45 % Number of atoms : 1533 ( 389 equ; 0 cnn)
% 0.20/0.45 % Maximal formula atoms : 263 ( 5 avg)
% 0.20/0.45 % Number of connectives : 3117 ( 69 ~; 12 |; 44 &;2225 @)
% 0.20/0.45 % ( 14 <=>; 753 =>; 0 <=; 0 <~>)
% 0.20/0.45 % Maximal formula depth : 273 ( 2 avg)
% 0.20/0.45 % Number of types : 2 ( 0 usr)
% 0.20/0.45 % Number of type conns : 132 ( 132 >; 0 *; 0 +; 0 <<)
% 0.20/0.45 % Number of symbols : 300 ( 297 usr; 263 con; 0-4 aty)
% 0.20/0.45 % Number of variables : 890 ( 74 ^; 781 !; 35 ?; 890 :)
% 0.20/0.45 % SPC : TH0_THM_EQU_NAR
% 0.20/0.45
% 0.20/0.45 % Comments : http://mathgate.info/detsetitem.php?id=305
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 thf(in_type,type,
% 0.20/0.45 in: $i > $i > $o ).
% 0.20/0.45
% 0.20/0.45 thf(exu_type,type,
% 0.20/0.45 exu: ( $i > $o ) > $o ).
% 0.20/0.45
% 0.20/0.45 thf(exu,definition,
% 0.20/0.45 ( exu
% 0.20/0.45 = ( ^ [Xphi: $i > $o] :
% 0.20/0.45 ? [Xx: $i] :
% 0.20/0.45 ( ( Xphi @ Xx )
% 0.20/0.45 & ! [Xy: $i] :
% 0.20/0.45 ( ( Xphi @ Xy )
% 0.20/0.45 => ( Xx = Xy ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(setextAx_type,type,
% 0.20/0.45 setextAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(setextAx,definition,
% 0.20/0.45 ( setextAx
% 0.20/0.45 = ( ! [A: $i,B: $i] :
% 0.20/0.45 ( ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ A )
% 0.20/0.45 <=> ( in @ Xx @ B ) )
% 0.20/0.45 => ( A = B ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(emptyset_type,type,
% 0.20/0.45 emptyset: $i ).
% 0.20/0.45
% 0.20/0.45 thf(emptysetAx_type,type,
% 0.20/0.45 emptysetAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(emptysetAx,definition,
% 0.20/0.45 ( emptysetAx
% 0.20/0.45 = ( ! [Xx: $i] :
% 0.20/0.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(setadjoin_type,type,
% 0.20/0.45 setadjoin: $i > $i > $i ).
% 0.20/0.45
% 0.20/0.45 thf(setadjoinAx_type,type,
% 0.20/0.45 setadjoinAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(setadjoinAx,definition,
% 0.20/0.45 ( setadjoinAx
% 0.20/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.45 <=> ( ( Xy = Xx )
% 0.20/0.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(powerset_type,type,
% 0.20/0.45 powerset: $i > $i ).
% 0.20/0.45
% 0.20/0.45 thf(powersetAx_type,type,
% 0.20/0.45 powersetAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(powersetAx,definition,
% 0.20/0.45 ( powersetAx
% 0.20/0.45 = ( ! [A: $i,B: $i] :
% 0.20/0.45 ( ( in @ B @ ( powerset @ A ) )
% 0.20/0.45 <=> ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ B )
% 0.20/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(setunion_type,type,
% 0.20/0.45 setunion: $i > $i ).
% 0.20/0.45
% 0.20/0.45 thf(setunionAx_type,type,
% 0.20/0.45 setunionAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(setunionAx,definition,
% 0.20/0.45 ( setunionAx
% 0.20/0.45 = ( ! [A: $i,Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ ( setunion @ A ) )
% 0.20/0.45 <=> ? [B: $i] :
% 0.20/0.45 ( ( in @ Xx @ B )
% 0.20/0.45 & ( in @ B @ A ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(omega_type,type,
% 0.20/0.45 omega: $i ).
% 0.20/0.45
% 0.20/0.45 thf(omega0Ax_type,type,
% 0.20/0.45 omega0Ax: $o ).
% 0.20/0.45
% 0.20/0.45 thf(omega0Ax,definition,
% 0.20/0.45 ( omega0Ax
% 0.20/0.45 = ( in @ emptyset @ omega ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(omegaSAx_type,type,
% 0.20/0.45 omegaSAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(omegaSAx,definition,
% 0.20/0.45 ( omegaSAx
% 0.20/0.45 = ( ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ omega )
% 0.20/0.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(omegaIndAx_type,type,
% 0.20/0.45 omegaIndAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(omegaIndAx,definition,
% 0.20/0.45 ( omegaIndAx
% 0.20/0.45 = ( ! [A: $i] :
% 0.20/0.45 ( ( ( in @ emptyset @ A )
% 0.20/0.45 & ! [Xx: $i] :
% 0.20/0.45 ( ( ( in @ Xx @ omega )
% 0.20/0.45 & ( in @ Xx @ A ) )
% 0.20/0.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.20/0.45 => ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ omega )
% 0.20/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(replAx_type,type,
% 0.20/0.45 replAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(replAx,definition,
% 0.20/0.45 ( replAx
% 0.20/0.45 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.20/0.45 ( ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ A )
% 0.20/0.45 => ( exu
% 0.20/0.45 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.20/0.45 => ? [B: $i] :
% 0.20/0.45 ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ B )
% 0.20/0.45 <=> ? [Xy: $i] :
% 0.20/0.45 ( ( in @ Xy @ A )
% 0.20/0.45 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(foundationAx_type,type,
% 0.20/0.45 foundationAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(foundationAx,definition,
% 0.20/0.45 ( foundationAx
% 0.20/0.45 = ( ! [A: $i] :
% 0.20/0.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.20/0.45 => ? [B: $i] :
% 0.20/0.45 ( ( in @ B @ A )
% 0.20/0.45 & ~ ? [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ B )
% 0.20/0.45 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(wellorderingAx_type,type,
% 0.20/0.45 wellorderingAx: $o ).
% 0.20/0.45
% 0.20/0.45 thf(wellorderingAx,definition,
% 0.20/0.45 ( wellorderingAx
% 0.20/0.45 = ( ! [A: $i] :
% 0.20/0.45 ? [B: $i] :
% 0.20/0.45 ( ! [C: $i] :
% 0.20/0.45 ( ( in @ C @ B )
% 0.20/0.45 => ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ C )
% 0.20/0.45 => ( in @ Xx @ A ) ) )
% 0.20/0.45 & ! [Xx: $i,Xy: $i] :
% 0.20/0.45 ( ( ( in @ Xx @ A )
% 0.20/0.45 & ( in @ Xy @ A ) )
% 0.20/0.45 => ( ! [C: $i] :
% 0.20/0.45 ( ( in @ C @ B )
% 0.20/0.45 => ( ( in @ Xx @ C )
% 0.20/0.45 <=> ( in @ Xy @ C ) ) )
% 0.20/0.45 => ( Xx = Xy ) ) )
% 0.20/0.45 & ! [C: $i,D: $i] :
% 0.20/0.45 ( ( ( in @ C @ B )
% 0.20/0.45 & ( in @ D @ B ) )
% 0.20/0.45 => ( ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ C )
% 0.20/0.45 => ( in @ Xx @ D ) )
% 0.20/0.45 | ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ D )
% 0.20/0.45 => ( in @ Xx @ C ) ) ) )
% 0.20/0.45 & ! [C: $i] :
% 0.20/0.45 ( ( ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ C )
% 0.20/0.45 => ( in @ Xx @ A ) )
% 0.20/0.45 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.20/0.45 => ? [D: $i,Xx: $i] :
% 0.20/0.45 ( ( in @ D @ B )
% 0.20/0.45 & ( in @ Xx @ C )
% 0.20/0.45 & ~ ? [Xy: $i] :
% 0.20/0.45 ( ( in @ Xy @ D )
% 0.20/0.45 & ( in @ Xy @ C ) )
% 0.20/0.45 & ! [E: $i] :
% 0.20/0.45 ( ( in @ E @ B )
% 0.20/0.45 => ( ! [Xy: $i] :
% 0.20/0.45 ( ( in @ Xy @ E )
% 0.20/0.45 => ( in @ Xy @ D ) )
% 0.20/0.45 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(descr_type,type,
% 0.20/0.45 descr: ( $i > $o ) > $i ).
% 0.20/0.45
% 0.20/0.45 thf(descrp_type,type,
% 0.20/0.45 descrp: $o ).
% 0.20/0.45
% 0.20/0.45 thf(descrp,definition,
% 0.20/0.45 ( descrp
% 0.20/0.45 = ( ! [Xphi: $i > $o] :
% 0.20/0.45 ( ( exu
% 0.20/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.45 => ( Xphi
% 0.20/0.45 @ ( descr
% 0.20/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(dsetconstr_type,type,
% 0.20/0.45 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.20/0.45
% 0.20/0.45 thf(dsetconstrI_type,type,
% 0.20/0.45 dsetconstrI: $o ).
% 0.20/0.45
% 0.20/0.45 thf(dsetconstrI,definition,
% 0.20/0.45 ( dsetconstrI
% 0.20/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ A )
% 0.20/0.45 => ( ( Xphi @ Xx )
% 0.20/0.45 => ( in @ Xx
% 0.20/0.45 @ ( dsetconstr @ A
% 0.20/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(dsetconstrEL_type,type,
% 0.20/0.45 dsetconstrEL: $o ).
% 0.20/0.45
% 0.20/0.45 thf(dsetconstrEL,definition,
% 0.20/0.45 ( dsetconstrEL
% 0.20/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.45 ( ( in @ Xx
% 0.20/0.45 @ ( dsetconstr @ A
% 0.20/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.45 => ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(dsetconstrER_type,type,
% 0.20/0.45 dsetconstrER: $o ).
% 0.20/0.45
% 0.20/0.45 thf(dsetconstrER,definition,
% 0.20/0.45 ( dsetconstrER
% 0.20/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.45 ( ( in @ Xx
% 0.20/0.45 @ ( dsetconstr @ A
% 0.20/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.45 => ( Xphi @ Xx ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(exuE1_type,type,
% 0.20/0.45 exuE1: $o ).
% 0.20/0.45
% 0.20/0.45 thf(exuE1,definition,
% 0.20/0.45 ( exuE1
% 0.20/0.45 = ( ! [Xphi: $i > $o] :
% 0.20/0.45 ( ( exu
% 0.20/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.45 => ? [Xx: $i] :
% 0.20/0.45 ( ( Xphi @ Xx )
% 0.20/0.45 & ! [Xy: $i] :
% 0.20/0.45 ( ( Xphi @ Xy )
% 0.20/0.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(prop2set_type,type,
% 0.20/0.45 prop2set: $o > $i ).
% 0.20/0.45
% 0.20/0.45 thf(prop2setE_type,type,
% 0.20/0.45 prop2setE: $o ).
% 0.20/0.45
% 0.20/0.45 thf(prop2setE,definition,
% 0.20/0.45 ( prop2setE
% 0.20/0.45 = ( ! [Xphi: $o,Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.20/0.45 => Xphi ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(emptysetE_type,type,
% 0.20/0.45 emptysetE: $o ).
% 0.20/0.45
% 0.20/0.45 thf(emptysetE,definition,
% 0.20/0.45 ( emptysetE
% 0.20/0.45 = ( ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ emptyset )
% 0.20/0.45 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(emptysetimpfalse_type,type,
% 0.20/0.45 emptysetimpfalse: $o ).
% 0.20/0.45
% 0.20/0.45 thf(emptysetimpfalse,definition,
% 0.20/0.45 ( emptysetimpfalse
% 0.20/0.45 = ( ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ emptyset )
% 0.20/0.45 => $false ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(notinemptyset_type,type,
% 0.20/0.45 notinemptyset: $o ).
% 0.20/0.45
% 0.20/0.45 thf(notinemptyset,definition,
% 0.20/0.45 ( notinemptyset
% 0.20/0.45 = ( ! [Xx: $i] :
% 0.20/0.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(exuE3e_type,type,
% 0.20/0.45 exuE3e: $o ).
% 0.20/0.45
% 0.20/0.45 thf(exuE3e,definition,
% 0.20/0.45 ( exuE3e
% 0.20/0.45 = ( ! [Xphi: $i > $o] :
% 0.20/0.45 ( ( exu
% 0.20/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.45 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf(setext_type,type,
% 0.20/0.45 setext: $o ).
% 0.20/0.45
% 0.20/0.45 thf(setext,definition,
% 0.20/0.45 ( setext
% 0.20/0.45 = ( ! [A: $i,B: $i] :
% 0.20/0.45 ( ! [Xx: $i] :
% 0.20/0.45 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ B ) )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ A ) )
% 0.20/0.46 => ( A = B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptyI_type,type,
% 0.20/0.46 emptyI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptyI,definition,
% 0.20/0.46 ( emptyI
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ~ ( in @ Xx @ A )
% 0.20/0.46 => ( A = emptyset ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(noeltsimpempty_type,type,
% 0.20/0.46 noeltsimpempty: $o ).
% 0.20/0.46
% 0.20/0.46 thf(noeltsimpempty,definition,
% 0.20/0.46 ( noeltsimpempty
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ~ ( in @ Xx @ A )
% 0.20/0.46 => ( A = emptyset ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setbeta_type,type,
% 0.20/0.46 setbeta: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setbeta,definition,
% 0.20/0.46 ( setbeta
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(nonempty_type,type,
% 0.20/0.46 nonempty: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(nonempty,definition,
% 0.20/0.46 ( nonempty
% 0.20/0.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyE1_type,type,
% 0.20/0.46 nonemptyE1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyE1,definition,
% 0.20/0.46 ( nonemptyE1
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ( nonempty @ A )
% 0.20/0.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyI_type,type,
% 0.20/0.46 nonemptyI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyI,definition,
% 0.20/0.46 ( nonemptyI
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 => ( nonempty
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyI1_type,type,
% 0.20/0.46 nonemptyI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyI1,definition,
% 0.20/0.46 ( nonemptyI1
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.20/0.46 => ( nonempty @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinIL_type,type,
% 0.20/0.46 setadjoinIL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinIL,definition,
% 0.20/0.46 ( setadjoinIL
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptyinunitempty_type,type,
% 0.20/0.46 emptyinunitempty: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptyinunitempty,definition,
% 0.20/0.46 ( emptyinunitempty
% 0.20/0.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinIR_type,type,
% 0.20/0.46 setadjoinIR: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinIR,definition,
% 0.20/0.46 ( setadjoinIR
% 0.20/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinE_type,type,
% 0.20/0.46 setadjoinE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinE,definition,
% 0.20/0.46 ( setadjoinE
% 0.20/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.46 => ! [Xphi: $o] :
% 0.20/0.46 ( ( ( Xy = Xx )
% 0.20/0.46 => Xphi )
% 0.20/0.46 => ( ( ( in @ Xy @ A )
% 0.20/0.46 => Xphi )
% 0.20/0.46 => Xphi ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinOr_type,type,
% 0.20/0.46 setadjoinOr: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinOr,definition,
% 0.20/0.46 ( setadjoinOr
% 0.20/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.46 => ( ( Xy = Xx )
% 0.20/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setoftrueEq_type,type,
% 0.20/0.46 setoftrueEq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setoftrueEq,definition,
% 0.20/0.46 ( setoftrueEq
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xx: $i] : $true )
% 0.20/0.46 = A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powersetI_type,type,
% 0.20/0.46 powersetI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetI,definition,
% 0.20/0.46 ( powersetI
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ A ) )
% 0.20/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptyinPowerset_type,type,
% 0.20/0.46 emptyinPowerset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptyinPowerset,definition,
% 0.20/0.46 ( emptyinPowerset
% 0.20/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptyInPowerset_type,type,
% 0.20/0.46 emptyInPowerset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptyInPowerset,definition,
% 0.20/0.46 ( emptyInPowerset
% 0.20/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powersetE_type,type,
% 0.20/0.46 powersetE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetE,definition,
% 0.20/0.46 ( powersetE
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.20/0.46 => ( ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setunionI_type,type,
% 0.20/0.46 setunionI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setunionI,definition,
% 0.20/0.46 ( setunionI
% 0.20/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 => ( ( in @ B @ A )
% 0.20/0.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setunionE_type,type,
% 0.20/0.46 setunionE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setunionE,definition,
% 0.20/0.46 ( setunionE
% 0.20/0.46 = ( ! [A: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.20/0.46 => ! [Xphi: $o] :
% 0.20/0.46 ( ! [B: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 => ( ( in @ B @ A )
% 0.20/0.46 => Xphi ) )
% 0.20/0.46 => Xphi ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subPowSU_type,type,
% 0.20/0.46 subPowSU: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subPowSU,definition,
% 0.20/0.46 ( subPowSU
% 0.20/0.46 = ( ! [A: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuE2_type,type,
% 0.20/0.46 exuE2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuE2,definition,
% 0.20/0.46 ( exuE2
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ? [Xx: $i] :
% 0.20/0.46 ! [Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xy )
% 0.20/0.46 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyImpWitness_type,type,
% 0.20/0.46 nonemptyImpWitness: $o ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyImpWitness,definition,
% 0.20/0.46 ( nonemptyImpWitness
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ( nonempty @ A )
% 0.20/0.46 => ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & $true ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(uniqinunit_type,type,
% 0.20/0.46 uniqinunit: $o ).
% 0.20/0.46
% 0.20/0.46 thf(uniqinunit,definition,
% 0.20/0.46 ( uniqinunit
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(notinsingleton_type,type,
% 0.20/0.46 notinsingleton: $o ).
% 0.20/0.46
% 0.20/0.46 thf(notinsingleton,definition,
% 0.20/0.46 ( notinsingleton
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx != Xy )
% 0.20/0.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(eqinunit_type,type,
% 0.20/0.46 eqinunit: $o ).
% 0.20/0.46
% 0.20/0.46 thf(eqinunit,definition,
% 0.20/0.46 ( eqinunit
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(singletonsswitch_type,type,
% 0.20/0.46 singletonsswitch: $o ).
% 0.20/0.46
% 0.20/0.46 thf(singletonsswitch,definition,
% 0.20/0.46 ( singletonsswitch
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.20/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(upairsetE_type,type,
% 0.20/0.46 upairsetE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairsetE,definition,
% 0.20/0.46 ( upairsetE
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.20/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.20/0.46 => ( ( Xz = Xx )
% 0.20/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(upairsetIL_type,type,
% 0.20/0.46 upairsetIL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairsetIL,definition,
% 0.20/0.46 ( upairsetIL
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(upairsetIR_type,type,
% 0.20/0.46 upairsetIR: $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairsetIR,definition,
% 0.20/0.46 ( upairsetIR
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptyE1_type,type,
% 0.20/0.46 emptyE1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptyE1,definition,
% 0.20/0.46 ( emptyE1
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( Xphi @ Xx ) )
% 0.20/0.46 => ( ( ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 = emptyset )
% 0.20/0.46 => $false ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(vacuousDall_type,type,
% 0.20/0.46 vacuousDall: $o ).
% 0.20/0.46
% 0.20/0.46 thf(vacuousDall,definition,
% 0.20/0.46 ( vacuousDall
% 0.20/0.46 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ emptyset )
% 0.20/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan1_type,type,
% 0.20/0.46 quantDeMorgan1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan1,definition,
% 0.20/0.46 ( quantDeMorgan1
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ~ ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( Xphi @ Xx ) )
% 0.20/0.46 => ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan2_type,type,
% 0.20/0.46 quantDeMorgan2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan2,definition,
% 0.20/0.46 ( quantDeMorgan2
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ~ ( Xphi @ Xx ) )
% 0.20/0.46 => ~ ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan3_type,type,
% 0.20/0.46 quantDeMorgan3: $o ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan3,definition,
% 0.20/0.46 ( quantDeMorgan3
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ~ ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( Xphi @ Xx ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan4_type,type,
% 0.20/0.46 quantDeMorgan4: $o ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan4,definition,
% 0.20/0.46 ( quantDeMorgan4
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ~ ( Xphi @ Xx ) )
% 0.20/0.46 => ~ ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(prop2setI_type,type,
% 0.20/0.46 prop2setI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(prop2setI,definition,
% 0.20/0.46 ( prop2setI
% 0.20/0.46 = ( ! [Xphi: $o] :
% 0.20/0.46 ( Xphi
% 0.20/0.46 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(set2prop_type,type,
% 0.20/0.46 set2prop: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(prop2set2propI_type,type,
% 0.20/0.46 prop2set2propI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(prop2set2propI,definition,
% 0.20/0.46 ( prop2set2propI
% 0.20/0.46 = ( ! [Xphi: $o] :
% 0.20/0.46 ( Xphi
% 0.20/0.46 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(notdexE_type,type,
% 0.20/0.46 notdexE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(notdexE,definition,
% 0.20/0.46 ( notdexE
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ~ ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( Xphi @ Xx ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(notdallE_type,type,
% 0.20/0.46 notdallE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(notdallE,definition,
% 0.20/0.46 ( notdallE
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ~ ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( Xphi @ Xx ) )
% 0.20/0.46 => ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuI1_type,type,
% 0.20/0.46 exuI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuI1,definition,
% 0.20/0.46 ( exuI1
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ? [Xx: $i] :
% 0.20/0.46 ( ( Xphi @ Xx )
% 0.20/0.46 & ! [Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) )
% 0.20/0.46 => ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuI3_type,type,
% 0.20/0.46 exuI3: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuI3,definition,
% 0.20/0.46 ( exuI3
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.20/0.46 => ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xx )
% 0.20/0.46 => ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) )
% 0.20/0.46 => ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuI2_type,type,
% 0.20/0.46 exuI2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuI2,definition,
% 0.20/0.46 ( exuI2
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ? [Xx: $i] :
% 0.20/0.46 ! [Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xy )
% 0.20/0.46 <=> ( Xy = Xx ) )
% 0.20/0.46 => ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(inCongP_type,type,
% 0.20/0.46 inCongP: $o ).
% 0.20/0.46
% 0.20/0.46 thf(inCongP,definition,
% 0.20/0.46 ( inCongP
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(in__Cong_type,type,
% 0.20/0.46 in__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(in__Cong,definition,
% 0.20/0.46 ( in__Cong
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ( ( in @ Xx @ A )
% 0.20/0.46 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuE3u_type,type,
% 0.20/0.46 exuE3u: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuE3u,definition,
% 0.20/0.46 ( exuE3u
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xx )
% 0.20/0.46 => ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exu__Cong_type,type,
% 0.20/0.46 exu__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exu__Cong,definition,
% 0.20/0.46 ( exu__Cong
% 0.20/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.20/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.20/0.46 => ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 <=> ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptyset__Cong_type,type,
% 0.20/0.46 emptyset__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptyset__Cong,definition,
% 0.20/0.46 ( emptyset__Cong
% 0.20/0.46 = ( emptyset = emptyset ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoin__Cong_type,type,
% 0.20/0.46 setadjoin__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoin__Cong,definition,
% 0.20/0.46 ( setadjoin__Cong
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ! [Xz: $i,Xu: $i] :
% 0.20/0.46 ( ( Xz = Xu )
% 0.20/0.46 => ( ( setadjoin @ Xx @ Xz )
% 0.20/0.46 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powerset__Cong_type,type,
% 0.20/0.46 powerset__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powerset__Cong,definition,
% 0.20/0.46 ( powerset__Cong
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ( ( powerset @ A )
% 0.20/0.46 = ( powerset @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setunion__Cong_type,type,
% 0.20/0.46 setunion__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setunion__Cong,definition,
% 0.20/0.46 ( setunion__Cong
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ( ( setunion @ A )
% 0.20/0.46 = ( setunion @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(omega__Cong_type,type,
% 0.20/0.46 omega__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(omega__Cong,definition,
% 0.20/0.46 ( omega__Cong
% 0.20/0.46 = ( omega = omega ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuEu_type,type,
% 0.20/0.46 exuEu: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuEu,definition,
% 0.20/0.46 ( exuEu
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xx )
% 0.20/0.46 => ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(descr__Cong_type,type,
% 0.20/0.46 descr__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(descr__Cong,definition,
% 0.20/0.46 ( descr__Cong
% 0.20/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.20/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.20/0.46 => ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.20/0.46 => ( ( descr
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 = ( descr
% 0.20/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstr__Cong_type,type,
% 0.20/0.46 dsetconstr__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstr__Cong,definition,
% 0.20/0.46 ( dsetconstr__Cong
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( Xx = Xy )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.20/0.46 => ( ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 = ( dsetconstr @ B
% 0.20/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subset_type,type,
% 0.20/0.46 subset: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(disjoint_type,type,
% 0.20/0.46 disjoint: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(setsmeet_type,type,
% 0.20/0.46 setsmeet: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetI1_type,type,
% 0.20/0.46 subsetI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetI1,definition,
% 0.20/0.46 ( subsetI1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ B ) )
% 0.20/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(eqimpsubset2_type,type,
% 0.20/0.46 eqimpsubset2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(eqimpsubset2,definition,
% 0.20/0.46 ( eqimpsubset2
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(eqimpsubset1_type,type,
% 0.20/0.46 eqimpsubset1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(eqimpsubset1,definition,
% 0.20/0.46 ( eqimpsubset1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subsetI2_type,type,
% 0.20/0.46 subsetI2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetI2,definition,
% 0.20/0.46 ( subsetI2
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ B ) )
% 0.20/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptysetsubset_type,type,
% 0.20/0.46 emptysetsubset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptysetsubset,definition,
% 0.20/0.46 ( emptysetsubset
% 0.20/0.46 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subsetE_type,type,
% 0.20/0.46 subsetE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetE,definition,
% 0.20/0.46 ( subsetE
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subsetE2_type,type,
% 0.20/0.46 subsetE2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetE2,definition,
% 0.20/0.46 ( subsetE2
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(notsubsetI_type,type,
% 0.20/0.46 notsubsetI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(notsubsetI,definition,
% 0.20/0.46 ( notsubsetI
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(notequalI1_type,type,
% 0.20/0.46 notequalI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(notequalI1,definition,
% 0.20/0.46 ( notequalI1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ~ ( subset @ A @ B )
% 0.20/0.46 => ( A != B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(notequalI2_type,type,
% 0.20/0.46 notequalI2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(notequalI2,definition,
% 0.20/0.46 ( notequalI2
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => ( A != B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subsetRefl_type,type,
% 0.20/0.46 subsetRefl: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetRefl,definition,
% 0.20/0.46 ( subsetRefl
% 0.20/0.46 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subsetTrans_type,type,
% 0.20/0.46 subsetTrans: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetTrans,definition,
% 0.20/0.46 ( subsetTrans
% 0.20/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( ( subset @ B @ C )
% 0.20/0.46 => ( subset @ A @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinSub_type,type,
% 0.20/0.46 setadjoinSub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinSub,definition,
% 0.20/0.46 ( setadjoinSub
% 0.20/0.46 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinSub2_type,type,
% 0.20/0.46 setadjoinSub2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinSub2,definition,
% 0.20/0.46 ( setadjoinSub2
% 0.20/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subset2powerset_type,type,
% 0.20/0.46 subset2powerset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subset2powerset,definition,
% 0.20/0.46 ( subset2powerset
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setextsub_type,type,
% 0.20/0.46 setextsub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setextsub,definition,
% 0.20/0.46 ( setextsub
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( ( subset @ B @ A )
% 0.20/0.46 => ( A = B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subsetemptysetimpeq_type,type,
% 0.20/0.46 subsetemptysetimpeq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetemptysetimpeq,definition,
% 0.20/0.46 ( subsetemptysetimpeq
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ( subset @ A @ emptyset )
% 0.20/0.46 => ( A = emptyset ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powersetI1_type,type,
% 0.20/0.46 powersetI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetI1,definition,
% 0.20/0.46 ( powersetI1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( subset @ B @ A )
% 0.20/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powersetE1_type,type,
% 0.20/0.46 powersetE1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetE1,definition,
% 0.20/0.46 ( powersetE1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.20/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(inPowerset_type,type,
% 0.20/0.46 inPowerset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(inPowerset,definition,
% 0.20/0.46 ( inPowerset
% 0.20/0.46 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powersetsubset_type,type,
% 0.20/0.46 powersetsubset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetsubset,definition,
% 0.20/0.46 ( powersetsubset
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sepInPowerset_type,type,
% 0.20/0.46 sepInPowerset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(sepInPowerset,definition,
% 0.20/0.46 ( sepInPowerset
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( in
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 @ ( powerset @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sepSubset_type,type,
% 0.20/0.46 sepSubset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(sepSubset,definition,
% 0.20/0.46 ( sepSubset
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( subset
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunion_type,type,
% 0.20/0.46 binunion: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(binunionIL_type,type,
% 0.20/0.46 binunionIL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionIL,definition,
% 0.20/0.46 ( binunionIL
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(upairset2IR_type,type,
% 0.20/0.46 upairset2IR: $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairset2IR,definition,
% 0.20/0.46 ( upairset2IR
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunionIR_type,type,
% 0.20/0.46 binunionIR: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionIR,definition,
% 0.20/0.46 ( binunionIR
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunionEcases_type,type,
% 0.20/0.46 binunionEcases: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionEcases,definition,
% 0.20/0.46 ( binunionEcases
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.20/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.20/0.46 => ( ( ( in @ Xx @ A )
% 0.20/0.46 => Xphi )
% 0.20/0.46 => ( ( ( in @ Xx @ B )
% 0.20/0.46 => Xphi )
% 0.20/0.46 => Xphi ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunionE_type,type,
% 0.20/0.46 binunionE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionE,definition,
% 0.20/0.46 ( binunionE
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.20/0.46 => ( ( in @ Xx @ A )
% 0.20/0.46 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunionLsub_type,type,
% 0.20/0.46 binunionLsub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionLsub,definition,
% 0.20/0.46 ( binunionLsub
% 0.20/0.46 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunionRsub_type,type,
% 0.20/0.46 binunionRsub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionRsub,definition,
% 0.20/0.46 ( binunionRsub
% 0.20/0.46 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersect_type,type,
% 0.20/0.46 binintersect: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectI_type,type,
% 0.20/0.46 binintersectI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectI,definition,
% 0.20/0.46 ( binintersectI
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset5_type,type,
% 0.20/0.46 binintersectSubset5: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset5,definition,
% 0.20/0.46 ( binintersectSubset5
% 0.20/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.20/0.46 ( ( subset @ C @ A )
% 0.20/0.46 => ( ( subset @ C @ B )
% 0.20/0.46 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectEL_type,type,
% 0.20/0.46 binintersectEL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectEL,definition,
% 0.20/0.46 ( binintersectEL
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.20/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectLsub_type,type,
% 0.20/0.46 binintersectLsub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectLsub,definition,
% 0.20/0.46 ( binintersectLsub
% 0.20/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset2_type,type,
% 0.20/0.46 binintersectSubset2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset2,definition,
% 0.20/0.46 ( binintersectSubset2
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( ( binintersect @ A @ B )
% 0.20/0.46 = A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset3_type,type,
% 0.20/0.46 binintersectSubset3: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset3,definition,
% 0.20/0.46 ( binintersectSubset3
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( ( binintersect @ A @ B )
% 0.20/0.46 = B )
% 0.20/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectER_type,type,
% 0.20/0.46 binintersectER: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectER,definition,
% 0.20/0.46 ( binintersectER
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.20/0.46 => ( in @ Xx @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(disjointsetsI1_type,type,
% 0.20/0.46 disjointsetsI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(disjointsetsI1,definition,
% 0.20/0.46 ( disjointsetsI1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ~ ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( in @ Xx @ B ) )
% 0.20/0.46 => ( ( binintersect @ A @ B )
% 0.20/0.46 = emptyset ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectRsub_type,type,
% 0.20/0.46 binintersectRsub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectRsub,definition,
% 0.20/0.46 ( binintersectRsub
% 0.20/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset4_type,type,
% 0.20/0.46 binintersectSubset4: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset4,definition,
% 0.20/0.46 ( binintersectSubset4
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( subset @ B @ A )
% 0.20/0.46 => ( ( binintersect @ A @ B )
% 0.20/0.46 = B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset1_type,type,
% 0.20/0.46 binintersectSubset1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset1,definition,
% 0.20/0.46 ( binintersectSubset1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( ( binintersect @ A @ B )
% 0.20/0.46 = A )
% 0.20/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(bs114d_type,type,
% 0.20/0.46 bs114d: $o ).
% 0.20/0.46
% 0.20/0.46 thf(bs114d,definition,
% 0.20/0.46 ( bs114d
% 0.20/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.20/0.46 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.20/0.46 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(regular_type,type,
% 0.20/0.46 regular: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminus_type,type,
% 0.20/0.46 setminus: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(setminusI_type,type,
% 0.20/0.46 setminusI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusI,definition,
% 0.20/0.46 ( setminusI
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusEL_type,type,
% 0.20/0.46 setminusEL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusEL,definition,
% 0.20/0.46 ( setminusEL
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.20/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusER_type,type,
% 0.20/0.46 setminusER: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusER,definition,
% 0.20/0.46 ( setminusER
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.20/0.46 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusSubset2_type,type,
% 0.20/0.46 setminusSubset2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusSubset2,definition,
% 0.20/0.46 ( setminusSubset2
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( ( setminus @ A @ B )
% 0.20/0.46 = emptyset ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusERneg_type,type,
% 0.20/0.46 setminusERneg: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusERneg,definition,
% 0.20/0.46 ( setminusERneg
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.20/0.46 => ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusELneg_type,type,
% 0.20/0.46 setminusELneg: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusELneg,definition,
% 0.20/0.46 ( setminusELneg
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusILneg_type,type,
% 0.20/0.46 setminusILneg: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusILneg,definition,
% 0.20/0.46 ( setminusILneg
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ~ ( in @ Xx @ A )
% 0.20/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusIRneg_type,type,
% 0.20/0.46 setminusIRneg: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusIRneg,definition,
% 0.20/0.46 ( setminusIRneg
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusLsub_type,type,
% 0.20/0.46 setminusLsub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusLsub,definition,
% 0.20/0.46 ( setminusLsub
% 0.20/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusSubset1_type,type,
% 0.20/0.46 setminusSubset1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusSubset1,definition,
% 0.20/0.46 ( setminusSubset1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( ( setminus @ A @ B )
% 0.20/0.46 = emptyset )
% 0.20/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(symdiff_type,type,
% 0.20/0.46 symdiff: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffE_type,type,
% 0.20/0.46 symdiffE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffE,definition,
% 0.20/0.46 ( symdiffE
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.20/0.46 => ! [Xphi: $o] :
% 0.20/0.46 ( ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => Xphi ) )
% 0.20/0.46 => ( ( ~ ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ B )
% 0.20/0.46 => Xphi ) )
% 0.20/0.46 => Xphi ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffI1_type,type,
% 0.20/0.46 symdiffI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffI1,definition,
% 0.20/0.46 ( symdiffI1
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffI2_type,type,
% 0.20/0.46 symdiffI2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffI2,definition,
% 0.20/0.46 ( symdiffI2
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ~ ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffIneg1_type,type,
% 0.20/0.46 symdiffIneg1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffIneg1,definition,
% 0.20/0.46 ( symdiffIneg1
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ B )
% 0.20/0.46 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffIneg2_type,type,
% 0.20/0.46 symdiffIneg2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffIneg2,definition,
% 0.20/0.46 ( symdiffIneg2
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ~ ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(iskpair_type,type,
% 0.20/0.46 iskpair: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(secondinupair_type,type,
% 0.20/0.46 secondinupair: $o ).
% 0.20/0.46
% 0.20/0.46 thf(secondinupair,definition,
% 0.20/0.46 ( secondinupair
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairIL_type,type,
% 0.20/0.46 setukpairIL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairIL,definition,
% 0.20/0.46 ( setukpairIL
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairIR_type,type,
% 0.20/0.46 setukpairIR: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairIR,definition,
% 0.20/0.46 ( setukpairIR
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(kpairiskpair_type,type,
% 0.20/0.46 kpairiskpair: $o ).
% 0.20/0.46
% 0.20/0.46 thf(kpairiskpair,definition,
% 0.20/0.46 ( kpairiskpair
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(kpair_type,type,
% 0.20/0.46 kpair: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(kpairp_type,type,
% 0.20/0.46 kpairp: $o ).
% 0.20/0.46
% 0.20/0.46 thf(kpairp,definition,
% 0.20/0.46 ( kpairp
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cartprod_type,type,
% 0.20/0.46 cartprod: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(singletonsubset_type,type,
% 0.20/0.46 singletonsubset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(singletonsubset,definition,
% 0.20/0.46 ( singletonsubset
% 0.20/0.46 = ( ! [A: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(singletoninpowerset_type,type,
% 0.20/0.46 singletoninpowerset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(singletoninpowerset,definition,
% 0.20/0.46 ( singletoninpowerset
% 0.20/0.46 = ( ! [A: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(singletoninpowunion_type,type,
% 0.20/0.46 singletoninpowunion: $o ).
% 0.20/0.46
% 0.20/0.46 thf(singletoninpowunion,definition,
% 0.20/0.46 ( singletoninpowunion
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(upairset2E_type,type,
% 0.20/0.46 upairset2E: $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairset2E,definition,
% 0.20/0.46 ( upairset2E
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.20/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.20/0.46 => ( ( Xz = Xx )
% 0.20/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(upairsubunion_type,type,
% 0.20/0.46 upairsubunion: $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairsubunion,definition,
% 0.20/0.46 ( upairsubunion
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(upairinpowunion_type,type,
% 0.20/0.46 upairinpowunion: $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairinpowunion,definition,
% 0.20/0.46 ( upairinpowunion
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ubforcartprodlem1_type,type,
% 0.20/0.46 ubforcartprodlem1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ubforcartprodlem1,definition,
% 0.20/0.46 ( ubforcartprodlem1
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ubforcartprodlem2_type,type,
% 0.20/0.46 ubforcartprodlem2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ubforcartprodlem2,definition,
% 0.20/0.46 ( ubforcartprodlem2
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ubforcartprodlem3_type,type,
% 0.20/0.46 ubforcartprodlem3: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ubforcartprodlem3,definition,
% 0.20/0.46 ( ubforcartprodlem3
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodpairin_type,type,
% 0.20/0.46 cartprodpairin: $o ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodpairin,definition,
% 0.20/0.46 ( cartprodpairin
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodmempair1_type,type,
% 0.20/0.46 cartprodmempair1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodmempair1,definition,
% 0.20/0.46 ( cartprodmempair1
% 0.20/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.20/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.20/0.46 => ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ? [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 & ( Xu
% 0.20/0.46 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodmempair_type,type,
% 0.20/0.46 cartprodmempair: $o ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodmempair,definition,
% 0.20/0.46 ( cartprodmempair
% 0.20/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.20/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.20/0.46 => ( iskpair @ Xu ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setunionE2_type,type,
% 0.20/0.46 setunionE2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setunionE2,definition,
% 0.20/0.46 ( setunionE2
% 0.20/0.46 = ( ! [A: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.20/0.46 => ? [X: $i] :
% 0.20/0.46 ( ( in @ X @ A )
% 0.20/0.46 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setunionsingleton1_type,type,
% 0.20/0.46 setunionsingleton1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setunionsingleton1,definition,
% 0.20/0.46 ( setunionsingleton1
% 0.20/0.46 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setunionsingleton2_type,type,
% 0.20/0.46 setunionsingleton2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setunionsingleton2,definition,
% 0.20/0.46 ( setunionsingleton2
% 0.20/0.46 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setunionsingleton_type,type,
% 0.20/0.46 setunionsingleton: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setunionsingleton,definition,
% 0.20/0.46 ( setunionsingleton
% 0.20/0.46 = ( ! [Xx: $i] :
% 0.20/0.46 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.20/0.46 = Xx ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(singleton_type,type,
% 0.20/0.46 singleton: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(singletonprop_type,type,
% 0.20/0.46 singletonprop: $o ).
% 0.20/0.46
% 0.20/0.46 thf(singletonprop,definition,
% 0.20/0.46 ( singletonprop
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 => ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) )
% 0.20/0.46 => ( ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( Xphi @ Xx ) )
% 0.20/0.46 => ( singleton
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ex1_type,type,
% 0.20/0.46 ex1: $i > ( $i > $o ) > $o ).
% 0.20/0.46
% 0.20/0.46 thf(ex1,definition,
% 0.20/0.46 ( ex1
% 0.20/0.46 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( singleton
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ex1E1_type,type,
% 0.20/0.46 ex1E1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ex1E1,definition,
% 0.20/0.46 ( ex1E1
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ( ex1 @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ex1I_type,type,
% 0.20/0.46 ex1I: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ex1I,definition,
% 0.20/0.46 ( ex1I
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 => ( ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xy = Xx ) ) )
% 0.20/0.46 => ( ex1 @ A
% 0.20/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ex1I2_type,type,
% 0.20/0.46 ex1I2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ex1I2,definition,
% 0.20/0.46 ( ex1I2
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 => ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) )
% 0.20/0.46 => ( ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( Xphi @ Xx ) )
% 0.20/0.46 => ( ex1 @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(singletonsuniq_type,type,
% 0.20/0.46 singletonsuniq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(singletonsuniq,definition,
% 0.20/0.46 ( singletonsuniq
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( ( setadjoin @ Xx @ emptyset )
% 0.20/0.46 = ( setadjoin @ Xy @ emptyset ) )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(atmost1p_type,type,
% 0.20/0.46 atmost1p: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(atleast2p_type,type,
% 0.20/0.46 atleast2p: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(atmost2p_type,type,
% 0.20/0.46 atmost2p: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairsetp_type,type,
% 0.20/0.46 upairsetp: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjL1_type,type,
% 0.20/0.46 setukpairinjL1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjL1,definition,
% 0.20/0.46 ( setukpairinjL1
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.20/0.46 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.20/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(kfstsingleton_type,type,
% 0.20/0.46 kfstsingleton: $o ).
% 0.20/0.46
% 0.20/0.46 thf(kfstsingleton,definition,
% 0.20/0.46 ( kfstsingleton
% 0.20/0.46 = ( ! [Xu: $i] :
% 0.20/0.46 ( ( iskpair @ Xu )
% 0.20/0.46 => ( singleton
% 0.20/0.46 @ ( dsetconstr @ ( setunion @ Xu )
% 0.20/0.46 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(theprop_type,type,
% 0.20/0.46 theprop: $o ).
% 0.20/0.46
% 0.20/0.46 thf(theprop,definition,
% 0.20/0.46 ( theprop
% 0.20/0.46 = ( ! [X: $i] :
% 0.20/0.46 ( ( singleton @ X )
% 0.20/0.46 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(kfst_type,type,
% 0.20/0.46 kfst: $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(kfstpairEq_type,type,
% 0.20/0.46 kfstpairEq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(kfstpairEq,definition,
% 0.20/0.46 ( kfstpairEq
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.20/0.46 = Xx ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodfstin_type,type,
% 0.20/0.46 cartprodfstin: $o ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodfstin,definition,
% 0.20/0.46 ( cartprodfstin
% 0.20/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.20/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.20/0.46 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjL2_type,type,
% 0.20/0.46 setukpairinjL2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjL2,definition,
% 0.20/0.46 ( setukpairinjL2
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.20/0.46 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.20/0.46 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.20/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjL_type,type,
% 0.20/0.46 setukpairinjL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjL,definition,
% 0.20/0.46 ( setukpairinjL
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.20/0.46 ( ( ( kpair @ Xx @ Xy )
% 0.20/0.46 = ( kpair @ Xz @ Xu ) )
% 0.20/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR11_type,type,
% 0.20/0.46 setukpairinjR11: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR11,definition,
% 0.20/0.46 ( setukpairinjR11
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.20/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR12_type,type,
% 0.20/0.46 setukpairinjR12: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR12,definition,
% 0.20/0.46 ( setukpairinjR12
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.20/0.46 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR1_type,type,
% 0.20/0.46 setukpairinjR1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR1,definition,
% 0.20/0.46 ( setukpairinjR1
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.20/0.46 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.20/0.46 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.20/0.46 => ( ( Xz = Xu )
% 0.20/0.46 => ( Xy = Xu ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(upairequniteq_type,type,
% 0.20/0.46 upairequniteq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairequniteq,definition,
% 0.20/0.46 ( upairequniteq
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.20/0.46 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.20/0.46 = ( setadjoin @ Xz @ emptyset ) )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR2_type,type,
% 0.20/0.46 setukpairinjR2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR2,definition,
% 0.20/0.46 ( setukpairinjR2
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.20/0.46 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.20/0.46 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.20/0.46 => ( Xy = Xu ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR_type,type,
% 0.20/0.46 setukpairinjR: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR,definition,
% 0.20/0.46 ( setukpairinjR
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.20/0.46 ( ( ( kpair @ Xx @ Xy )
% 0.20/0.46 = ( kpair @ Xz @ Xu ) )
% 0.20/0.46 => ( Xy = Xu ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ksndsingleton_type,type,
% 0.20/0.46 ksndsingleton: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ksndsingleton,definition,
% 0.20/0.46 ( ksndsingleton
% 0.20/0.46 = ( ! [Xu: $i] :
% 0.20/0.46 ( ( iskpair @ Xu )
% 0.20/0.46 => ( singleton
% 0.20/0.46 @ ( dsetconstr @ ( setunion @ Xu )
% 0.20/0.46 @ ^ [Xx: $i] :
% 0.20/0.46 ( Xu
% 0.20/0.46 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ksnd_type,type,
% 0.20/0.46 ksnd: $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(ksndpairEq_type,type,
% 0.20/0.46 ksndpairEq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ksndpairEq,definition,
% 0.20/0.46 ( ksndpairEq
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.20/0.46 = Xy ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(kpairsurjEq_type,type,
% 0.20/0.46 kpairsurjEq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(kpairsurjEq,definition,
% 0.20/0.46 ( kpairsurjEq
% 0.20/0.46 = ( ! [Xu: $i] :
% 0.20/0.46 ( ( iskpair @ Xu )
% 0.20/0.46 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.20/0.46 = Xu ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodsndin_type,type,
% 0.20/0.46 cartprodsndin: $o ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodsndin,definition,
% 0.20/0.46 ( cartprodsndin
% 0.20/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.20/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.20/0.46 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodpairmemEL_type,type,
% 0.20/0.46 cartprodpairmemEL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodpairmemEL,definition,
% 0.20/0.46 ( cartprodpairmemEL
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.20/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodpairmemER_type,type,
% 0.20/0.46 cartprodpairmemER: $o ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodpairmemER,definition,
% 0.20/0.46 ( cartprodpairmemER
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.20/0.46 => ( in @ Xy @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodmempaircEq_type,type,
% 0.20/0.46 cartprodmempaircEq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodmempaircEq,definition,
% 0.20/0.46 ( cartprodmempaircEq
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( kpair @ Xx @ Xy )
% 0.20/0.46 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodfstpairEq_type,type,
% 0.20/0.46 cartprodfstpairEq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodfstpairEq,definition,
% 0.20/0.46 ( cartprodfstpairEq
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.20/0.46 = Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodsndpairEq_type,type,
% 0.20/0.46 cartprodsndpairEq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodsndpairEq,definition,
% 0.20/0.46 ( cartprodsndpairEq
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.20/0.46 = Xy ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodpairsurjEq_type,type,
% 0.20/0.46 cartprodpairsurjEq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodpairsurjEq,definition,
% 0.20/0.46 ( cartprodpairsurjEq
% 0.20/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.20/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.20/0.46 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.20/0.46 = Xu ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(breln_type,type,
% 0.20/0.46 breln: $i > $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(breln,definition,
% 0.20/0.46 ( breln
% 0.20/0.46 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(dpsetconstr_type,type,
% 0.20/0.46 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.20/0.46
% 0.20/0.46 thf(dpsetconstrI_type,type,
% 0.20/0.46 dpsetconstrI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(dpsetconstrI,definition,
% 0.20/0.46 ( dpsetconstrI
% 0.20/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( Xphi @ Xx @ Xy )
% 0.20/0.46 => ( in @ ( kpair @ Xx @ Xy )
% 0.20/0.46 @ ( dpsetconstr @ A @ B
% 0.20/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(dpsetconstrSub_type,type,
% 0.20/0.46 dpsetconstrSub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(dpsetconstrSub,definition,
% 0.20/0.46 ( dpsetconstrSub
% 0.20/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.20/0.46 ( subset
% 0.20/0.46 @ ( dpsetconstr @ A @ B
% 0.20/0.46 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.20/0.46 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setOfPairsIsBReln_type,type,
% 0.20/0.46 setOfPairsIsBReln: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setOfPairsIsBReln,definition,
% 0.20/0.46 ( setOfPairsIsBReln
% 0.20/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.20/0.46 ( breln @ A @ B
% 0.20/0.46 @ ( dpsetconstr @ A @ B
% 0.20/0.46 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(dpsetconstrERa_type,type,
% 0.20/0.46 dpsetconstrERa: $o ).
% 0.20/0.46
% 0.20/0.46 thf(dpsetconstrERa,definition,
% 0.20/0.46 ( dpsetconstrERa
% 0.20/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.20/0.46 @ ( dpsetconstr @ A @ B
% 0.20/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.20/0.46 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(dpsetconstrEL1_type,type,
% 0.20/0.46 dpsetconstrEL1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(dpsetconstrEL1,definition,
% 0.20/0.46 ( dpsetconstrEL1
% 0.20/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ ( kpair @ Xx @ Xy )
% 0.20/0.46 @ ( dpsetconstr @ A @ B
% 0.20/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.20/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(dpsetconstrEL2_type,type,
% 0.20/0.46 dpsetconstrEL2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(dpsetconstrEL2,definition,
% 0.20/0.46 ( dpsetconstrEL2
% 0.20/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ ( kpair @ Xx @ Xy )
% 0.20/0.46 @ ( dpsetconstr @ A @ B
% 0.20/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.20/0.46 => ( in @ Xy @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(dpsetconstrER_type,type,
% 0.20/0.46 dpsetconstrER: $o ).
% 0.20/0.46
% 0.20/0.46 thf(dpsetconstrER,definition,
% 0.20/0.46 ( dpsetconstrER
% 0.20/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ ( kpair @ Xx @ Xy )
% 0.20/0.46 @ ( dpsetconstr @ A @ B
% 0.20/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.20/0.46 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(func_type,type,
% 0.20/0.46 func: $i > $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(funcSet_type,type,
% 0.20/0.46 funcSet: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(funcImageSingleton_type,type,
% 0.20/0.46 funcImageSingleton: $o ).
% 0.20/0.46
% 0.20/0.46 thf(funcImageSingleton,definition,
% 0.20/0.46 ( funcImageSingleton
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( func @ A @ B @ Xf )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( singleton
% 0.20/0.46 @ ( dsetconstr @ B
% 0.20/0.46 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(apProp_type,type,
% 0.20/0.46 apProp: $o ).
% 0.20/0.46
% 0.20/0.46 thf(apProp,definition,
% 0.20/0.46 ( apProp
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( func @ A @ B @ Xf )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in
% 0.20/0.46 @ ( setunion
% 0.20/0.46 @ ( dsetconstr @ B
% 0.20/0.46 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.20/0.46 @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ap_type,type,
% 0.20/0.46 ap: $i > $i > $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(app_type,type,
% 0.20/0.46 app: $o ).
% 0.20/0.46
% 0.20/0.46 thf(app,definition,
% 0.20/0.46 ( app
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( func @ A @ B @ Xf )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(infuncsetfunc_type,type,
% 0.20/0.46 infuncsetfunc: $o ).
% 0.20/0.46
% 0.20/0.46 thf(infuncsetfunc,definition,
% 0.20/0.46 ( infuncsetfunc
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.20/0.46 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ap2p_type,type,
% 0.20/0.46 ap2p: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ap2p,definition,
% 0.20/0.46 ( ap2p
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(funcinfuncset_type,type,
% 0.20/0.46 funcinfuncset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(funcinfuncset,definition,
% 0.20/0.46 ( funcinfuncset
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( func @ A @ B @ Xf )
% 0.20/0.46 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(lamProp_type,type,
% 0.20/0.46 lamProp: $o ).
% 0.20/0.46
% 0.20/0.46 thf(lamProp,definition,
% 0.20/0.46 ( lamProp
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.20/0.46 => ( func @ A @ B
% 0.20/0.46 @ ( dpsetconstr @ A @ B
% 0.20/0.46 @ ^ [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xf @ Xx )
% 0.20/0.46 = Xy ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(lam_type,type,
% 0.20/0.46 lam: $i > $i > ( $i > $i ) > $i ).
% 0.20/0.46
% 0.20/0.46 thf(lamp_type,type,
% 0.20/0.46 lamp: $o ).
% 0.20/0.46
% 0.20/0.46 thf(lamp,definition,
% 0.20/0.46 ( lamp
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.20/0.46 => ( func @ A @ B
% 0.20/0.46 @ ( lam @ A @ B
% 0.20/0.46 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(lam2p_type,type,
% 0.20/0.46 lam2p: $o ).
% 0.20/0.46
% 0.20/0.46 thf(lam2p,definition,
% 0.20/0.46 ( lam2p
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.20/0.46 => ( in
% 0.20/0.46 @ ( lam @ A @ B
% 0.20/0.46 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.20/0.46 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(brelnall1_type,type,
% 0.20/0.46 brelnall1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(brelnall1,definition,
% 0.20/0.46 ( brelnall1
% 0.20/0.46 = ( ! [A: $i,B: $i,R: $i] :
% 0.20/0.46 ( ( breln @ A @ B @ R )
% 0.20/0.46 => ! [Xphi: $i > $o] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.20/0.46 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ R )
% 0.20/0.46 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(brelnall2_type,type,
% 0.20/0.46 brelnall2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(brelnall2,definition,
% 0.20/0.46 ( brelnall2
% 0.20/0.46 = ( ! [A: $i,B: $i,R: $i] :
% 0.20/0.46 ( ( breln @ A @ B @ R )
% 0.20/0.46 => ! [Xphi: $i > $o] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.20/0.46 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ R )
% 0.20/0.46 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ex1E2_type,type,
% 0.20/0.46 ex1E2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ex1E2,definition,
% 0.20/0.46 ( ex1E2
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ( ex1 @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 => ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(funcGraphProp1_type,type,
% 0.20/0.46 funcGraphProp1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(funcGraphProp1,definition,
% 0.20/0.46 ( funcGraphProp1
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( func @ A @ B @ Xf )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(funcGraphProp3_type,type,
% 0.20/0.46 funcGraphProp3: $o ).
% 0.20/0.46
% 0.20/0.46 thf(funcGraphProp3,definition,
% 0.20/0.46 ( funcGraphProp3
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(funcGraphProp2_type,type,
% 0.20/0.46 funcGraphProp2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(funcGraphProp2,definition,
% 0.20/0.46 ( funcGraphProp2
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( func @ A @ B @ Xf )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.20/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.20/0.46 = Xy ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(funcextLem_type,type,
% 0.20/0.46 funcextLem: $o ).
% 0.20/0.46
% 0.20/0.46 thf(funcextLem,definition,
% 0.20/0.46 ( funcextLem
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( func @ A @ B @ Xf )
% 0.20/0.46 => ! [Xg: $i] :
% 0.20/0.46 ( ( func @ A @ B @ Xg )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.20/0.46 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 0.20/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(funcGraphProp4_type,type,
% 0.20/0.46 funcGraphProp4: $o ).
% 0.20/0.46
% 0.20/0.46 thf(funcGraphProp4,definition,
% 0.20/0.46 ( funcGraphProp4
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.20/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.20/0.46 = Xy ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subbreln_type,type,
% 0.20/0.46 subbreln: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subbreln,definition,
% 0.20/0.46 ( subbreln
% 0.20/0.46 = ( ! [A: $i,B: $i,R: $i] :
% 0.20/0.46 ( ( breln @ A @ B @ R )
% 0.20/0.46 => ! [S: $i] :
% 0.20/0.46 ( ( breln @ A @ B @ S )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.20/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.20/0.46 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(eqbreln_type,type,
% 0.20/0.46 eqbreln: $o ).
% 0.20/0.46
% 0.20/0.46 thf(eqbreln,definition,
% 0.20/0.46 ( eqbreln
% 0.20/0.46 = ( ! [A: $i,B: $i,R: $i] :
% 0.20/0.46 ( ( breln @ A @ B @ R )
% 0.20/0.46 => ! [S: $i] :
% 0.20/0.46 ( ( breln @ A @ B @ S )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.20/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.20/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.20/0.46 => ( R = S ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(funcext_type,type,
% 0.20/0.46 funcext: $o ).
% 0.20/0.46
% 0.20/0.46 thf(funcext,definition,
% 0.20/0.46 ( funcext
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( func @ A @ B @ Xf )
% 0.20/0.46 => ! [Xg: $i] :
% 0.20/0.46 ( ( func @ A @ B @ Xg )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.20/0.46 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.20/0.46 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(funcext2_type,type,
% 0.20/0.46 funcext2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(funcext2,definition,
% 0.20/0.46 ( funcext2
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.20/0.46 => ! [Xg: $i] :
% 0.20/0.46 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.20/0.46 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.20/0.46 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ap2apEq1_type,type,
% 0.20/0.46 ap2apEq1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ap2apEq1,definition,
% 0.20/0.46 ( ap2apEq1
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.20/0.46 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ap2apEq2_type,type,
% 0.20/0.46 ap2apEq2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ap2apEq2,definition,
% 0.20/0.46 ( ap2apEq2
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( func @ A @ B @ Xf )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.20/0.46 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(beta1_type,type,
% 0.20/0.46 beta1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(beta1,definition,
% 0.20/0.46 ( beta1
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( ap @ A @ B
% 0.20/0.46 @ ( lam @ A @ B
% 0.20/0.46 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.20/0.46 @ Xx )
% 0.20/0.46 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(eta1_type,type,
% 0.20/0.46 eta1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(eta1,definition,
% 0.20/0.46 ( eta1
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( func @ A @ B @ Xf )
% 0.20/0.46 => ( ( lam @ A @ B
% 0.20/0.46 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.20/0.46 = Xf ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(lam2lamEq_type,type,
% 0.20/0.46 lam2lamEq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(lam2lamEq,definition,
% 0.20/0.46 ( lam2lamEq
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.20/0.46 => ( ( lam @ A @ B
% 0.20/0.46 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.20/0.46 = ( lam @ A @ B
% 0.20/0.46 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(beta2_type,type,
% 0.20/0.46 beta2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(beta2,definition,
% 0.20/0.46 ( beta2
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( ap @ A @ B
% 0.20/0.46 @ ( lam @ A @ B
% 0.20/0.46 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.20/0.46 @ Xx )
% 0.20/0.46 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(eta2_type,type,
% 0.20/0.46 eta2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(eta2,definition,
% 0.20/0.46 ( eta2
% 0.20/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.20/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.20/0.46 => ( ( lam @ A @ B
% 0.20/0.46 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.20/0.46 = Xf ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(iffalseProp1_type,type,
% 0.20/0.46 iffalseProp1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(iffalseProp1,definition,
% 0.20/0.46 ( iffalseProp1
% 0.20/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( ~ Xphi
% 0.20/0.46 => ( in @ Xy
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xz: $i] :
% 0.20/0.46 ( ( Xphi
% 0.20/0.46 & ( Xz = Xx ) )
% 0.20/0.46 | ( ~ Xphi
% 0.20/0.46 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(iffalseProp2_type,type,
% 0.20/0.46 iffalseProp2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(iffalseProp2,definition,
% 0.20/0.46 ( iffalseProp2
% 0.20/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( ~ Xphi
% 0.20/0.46 => ( ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xz: $i] :
% 0.20/0.46 ( ( Xphi
% 0.20/0.46 & ( Xz = Xx ) )
% 0.20/0.46 | ( ~ Xphi
% 0.20/0.46 & ( Xz = Xy ) ) ) )
% 0.20/0.46 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(iftrueProp1_type,type,
% 0.20/0.46 iftrueProp1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(iftrueProp1,definition,
% 0.20/0.46 ( iftrueProp1
% 0.20/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( Xphi
% 0.20/0.46 => ( in @ Xx
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xz: $i] :
% 0.20/0.46 ( ( Xphi
% 0.20/0.46 & ( Xz = Xx ) )
% 0.20/0.46 | ( ~ Xphi
% 0.20/0.46 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(iftrueProp2_type,type,
% 0.20/0.46 iftrueProp2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(iftrueProp2,definition,
% 0.20/0.46 ( iftrueProp2
% 0.20/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( Xphi
% 0.20/0.46 => ( ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xz: $i] :
% 0.20/0.46 ( ( Xphi
% 0.20/0.46 & ( Xz = Xx ) )
% 0.20/0.46 | ( ~ Xphi
% 0.20/0.46 & ( Xz = Xy ) ) ) )
% 0.20/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ifSingleton_type,type,
% 0.20/0.46 ifSingleton: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ifSingleton,definition,
% 0.20/0.46 ( ifSingleton
% 0.20/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( singleton
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xz: $i] :
% 0.20/0.46 ( ( Xphi
% 0.20/0.46 & ( Xz = Xx ) )
% 0.20/0.46 | ( ~ Xphi
% 0.20/0.46 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(if_type,type,
% 0.20/0.46 if: $i > $o > $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(ifp_type,type,
% 0.20/0.46 ifp: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ifp,definition,
% 0.20/0.46 ( ifp
% 0.20/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(theeq_type,type,
% 0.20/0.46 theeq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(theeq,definition,
% 0.20/0.46 ( theeq
% 0.20/0.46 = ( ! [X: $i] :
% 0.20/0.46 ( ( singleton @ X )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ X )
% 0.20/0.46 => ( ( setunion @ X )
% 0.20/0.46 = Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(iftrue_type,type,
% 0.20/0.46 iftrue: $o ).
% 0.20/0.46
% 0.20/0.46 thf(iftrue,definition,
% 0.20/0.46 ( iftrue
% 0.20/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( Xphi
% 0.20/0.46 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.20/0.46 = Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(iffalse_type,type,
% 0.20/0.46 iffalse: $o ).
% 0.20/0.46
% 0.20/0.46 thf(iffalse,definition,
% 0.20/0.46 ( iffalse
% 0.20/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( ~ Xphi
% 0.20/0.46 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.20/0.46 = Xy ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(iftrueorfalse_type,type,
% 0.20/0.46 iftrueorfalse: $o ).
% 0.20/0.46
% 0.20/0.46 thf(iftrueorfalse,definition,
% 0.20/0.46 ( iftrueorfalse
% 0.20/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectT_lem_type,type,
% 0.20/0.46 binintersectT_lem: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectT_lem,definition,
% 0.20/0.46 ( binintersectT_lem
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunionT_lem_type,type,
% 0.20/0.46 binunionT_lem: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionT_lem,definition,
% 0.20/0.46 ( binunionT_lem
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powersetT_lem_type,type,
% 0.20/0.46 powersetT_lem: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetT_lem,definition,
% 0.20/0.46 ( powersetT_lem
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusT_lem_type,type,
% 0.20/0.46 setminusT_lem: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusT_lem,definition,
% 0.20/0.46 ( setminusT_lem
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(complementT_lem_type,type,
% 0.20/0.46 complementT_lem: $o ).
% 0.20/0.46
% 0.20/0.46 thf(complementT_lem,definition,
% 0.20/0.46 ( complementT_lem
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setextT_type,type,
% 0.20/0.46 setextT: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setextT,definition,
% 0.20/0.46 ( setextT
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ X )
% 0.20/0.46 => ( in @ Xx @ Y ) ) )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ Y )
% 0.20/0.46 => ( in @ Xx @ X ) ) )
% 0.20/0.46 => ( X = Y ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subsetTI_type,type,
% 0.20/0.46 subsetTI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetTI,definition,
% 0.20/0.46 ( subsetTI
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ X )
% 0.20/0.46 => ( in @ Xx @ Y ) ) )
% 0.20/0.46 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powersetTI1_type,type,
% 0.20/0.46 powersetTI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetTI1,definition,
% 0.20/0.46 ( powersetTI1
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ X )
% 0.20/0.46 => ( in @ Xx @ Y ) ) )
% 0.20/0.46 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powersetTE1_type,type,
% 0.20/0.46 powersetTE1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetTE1,definition,
% 0.20/0.46 ( powersetTE1
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ X @ ( powerset @ Y ) )
% 0.20/0.46 => ( ( in @ Xx @ X )
% 0.20/0.46 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(complementTI1_type,type,
% 0.20/0.46 complementTI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(complementTI1,definition,
% 0.20/0.46 ( complementTI1
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ X )
% 0.20/0.46 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(complementTE1_type,type,
% 0.20/0.46 complementTE1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(complementTE1,definition,
% 0.20/0.46 ( complementTE1
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 0.20/0.46 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectTELcontra_type,type,
% 0.20/0.46 binintersectTELcontra: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectTELcontra,definition,
% 0.20/0.46 ( binintersectTELcontra
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ X )
% 0.20/0.46 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectTERcontra_type,type,
% 0.20/0.46 binintersectTERcontra: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectTERcontra,definition,
% 0.20/0.46 ( binintersectTERcontra
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ Y )
% 0.20/0.46 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(contrasubsetT_type,type,
% 0.20/0.46 contrasubsetT: $o ).
% 0.20/0.46
% 0.20/0.46 thf(contrasubsetT,definition,
% 0.20/0.46 ( contrasubsetT
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.20/0.46 => ( ( in @ Xx @ Y )
% 0.20/0.46 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(contrasubsetT1_type,type,
% 0.20/0.46 contrasubsetT1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(contrasubsetT1,definition,
% 0.20/0.46 ( contrasubsetT1
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( subset @ X @ Y )
% 0.20/0.46 => ( ~ ( in @ Xx @ Y )
% 0.20/0.46 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(contrasubsetT2_type,type,
% 0.20/0.46 contrasubsetT2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(contrasubsetT2,definition,
% 0.20/0.46 ( contrasubsetT2
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( ( subset @ X @ Y )
% 0.20/0.46 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(contrasubsetT3_type,type,
% 0.20/0.46 contrasubsetT3: $o ).
% 0.20/0.46
% 0.20/0.46 thf(contrasubsetT3,definition,
% 0.20/0.46 ( contrasubsetT3
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 0.20/0.46 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(doubleComplementI1_type,type,
% 0.20/0.46 doubleComplementI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(doubleComplementI1,definition,
% 0.20/0.46 ( doubleComplementI1
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ X )
% 0.20/0.46 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(doubleComplementE1_type,type,
% 0.20/0.46 doubleComplementE1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(doubleComplementE1,definition,
% 0.20/0.46 ( doubleComplementE1
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 0.20/0.46 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(doubleComplementSub1_type,type,
% 0.20/0.46 doubleComplementSub1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(doubleComplementSub1,definition,
% 0.20/0.46 ( doubleComplementSub1
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(doubleComplementSub2_type,type,
% 0.20/0.46 doubleComplementSub2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(doubleComplementSub2,definition,
% 0.20/0.46 ( doubleComplementSub2
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(doubleComplementEq_type,type,
% 0.20/0.46 doubleComplementEq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(doubleComplementEq,definition,
% 0.20/0.46 ( doubleComplementEq
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ( X
% 0.20/0.46 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(complementTnotintersectT_type,type,
% 0.20/0.46 complementTnotintersectT: $o ).
% 0.20/0.46
% 0.20/0.46 thf(complementTnotintersectT,definition,
% 0.20/0.46 ( complementTnotintersectT
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.20/0.46 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(complementImpComplementIntersect_type,type,
% 0.20/0.46 complementImpComplementIntersect: $o ).
% 0.20/0.46
% 0.20/0.46 thf(complementImpComplementIntersect,definition,
% 0.20/0.46 ( complementImpComplementIntersect
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.20/0.46 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(complementSubsetComplementIntersect_type,type,
% 0.20/0.46 complementSubsetComplementIntersect: $o ).
% 0.20/0.46
% 0.20/0.46 thf(complementSubsetComplementIntersect,definition,
% 0.20/0.46 ( complementSubsetComplementIntersect
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(complementInPowersetComplementIntersect_type,type,
% 0.20/0.46 complementInPowersetComplementIntersect: $o ).
% 0.20/0.46
% 0.20/0.46 thf(complementInPowersetComplementIntersect,definition,
% 0.20/0.46 ( complementInPowersetComplementIntersect
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(contraSubsetComplement_type,type,
% 0.20/0.46 contraSubsetComplement: $o ).
% 0.20/0.46
% 0.20/0.46 thf(contraSubsetComplement,definition,
% 0.20/0.46 ( contraSubsetComplement
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ Y )
% 0.20/0.46 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(complementTcontraSubset_type,type,
% 0.20/0.46 complementTcontraSubset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(complementTcontraSubset,definition,
% 0.20/0.46 ( complementTcontraSubset
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.20/0.46 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunionTILcontra_type,type,
% 0.20/0.46 binunionTILcontra: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionTILcontra,definition,
% 0.20/0.46 ( binunionTILcontra
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.20/0.46 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunionTIRcontra_type,type,
% 0.20/0.46 binunionTIRcontra: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionTIRcontra,definition,
% 0.20/0.46 ( binunionTIRcontra
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.20/0.46 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(inIntersectImpInUnion_type,type,
% 0.20/0.46 inIntersectImpInUnion: $o ).
% 0.20/0.46
% 0.20/0.46 thf(inIntersectImpInUnion,definition,
% 0.20/0.46 ( inIntersectImpInUnion
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Z: $i] :
% 0.20/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.20/0.46 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(inIntersectImpInUnion2_type,type,
% 0.20/0.46 inIntersectImpInUnion2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(inIntersectImpInUnion2,definition,
% 0.20/0.46 ( inIntersectImpInUnion2
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Z: $i] :
% 0.20/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.20/0.46 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(inIntersectImpInIntersectUnions_type,type,
% 0.20/0.46 inIntersectImpInIntersectUnions: $o ).
% 0.20/0.46
% 0.20/0.46 thf(inIntersectImpInIntersectUnions,definition,
% 0.20/0.46 ( inIntersectImpInIntersectUnions
% 0.20/0.46 = ( ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Z: $i] :
% 0.20/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.20/0.46 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(intersectInPowersetIntersectUnions,conjecture,
% 0.20/0.46 ( setextAx
% 0.20/0.46 => ( emptysetAx
% 0.20/0.46 => ( setadjoinAx
% 0.20/0.46 => ( powersetAx
% 0.20/0.46 => ( setunionAx
% 0.20/0.46 => ( omega0Ax
% 0.20/0.46 => ( omegaSAx
% 0.20/0.46 => ( omegaIndAx
% 0.20/0.46 => ( replAx
% 0.20/0.46 => ( foundationAx
% 0.20/0.46 => ( wellorderingAx
% 0.20/0.46 => ( descrp
% 0.20/0.46 => ( dsetconstrI
% 0.20/0.46 => ( dsetconstrEL
% 0.20/0.46 => ( dsetconstrER
% 0.20/0.46 => ( exuE1
% 0.20/0.46 => ( prop2setE
% 0.20/0.46 => ( emptysetE
% 0.20/0.46 => ( emptysetimpfalse
% 0.20/0.46 => ( notinemptyset
% 0.20/0.46 => ( exuE3e
% 0.20/0.46 => ( setext
% 0.20/0.46 => ( emptyI
% 0.20/0.46 => ( noeltsimpempty
% 0.20/0.46 => ( setbeta
% 0.20/0.46 => ( nonemptyE1
% 0.20/0.46 => ( nonemptyI
% 0.20/0.46 => ( nonemptyI1
% 0.20/0.46 => ( setadjoinIL
% 0.20/0.46 => ( emptyinunitempty
% 0.20/0.46 => ( setadjoinIR
% 0.20/0.46 => ( setadjoinE
% 0.20/0.46 => ( setadjoinOr
% 0.20/0.46 => ( setoftrueEq
% 0.20/0.46 => ( powersetI
% 0.20/0.46 => ( emptyinPowerset
% 0.20/0.46 => ( emptyInPowerset
% 0.20/0.46 => ( powersetE
% 0.20/0.46 => ( setunionI
% 0.20/0.46 => ( setunionE
% 0.20/0.46 => ( subPowSU
% 0.20/0.46 => ( exuE2
% 0.20/0.46 => ( nonemptyImpWitness
% 0.20/0.46 => ( uniqinunit
% 0.20/0.46 => ( notinsingleton
% 0.20/0.46 => ( eqinunit
% 0.20/0.46 => ( singletonsswitch
% 0.20/0.46 => ( upairsetE
% 0.20/0.46 => ( upairsetIL
% 0.20/0.46 => ( upairsetIR
% 0.20/0.46 => ( emptyE1
% 0.20/0.46 => ( vacuousDall
% 0.20/0.46 => ( quantDeMorgan1
% 0.20/0.46 => ( quantDeMorgan2
% 0.20/0.46 => ( quantDeMorgan3
% 0.20/0.46 => ( quantDeMorgan4
% 0.20/0.46 => ( prop2setI
% 0.20/0.46 => ( prop2set2propI
% 0.20/0.46 => ( notdexE
% 0.20/0.46 => ( notdallE
% 0.20/0.46 => ( exuI1
% 0.20/0.46 => ( exuI3
% 0.20/0.46 => ( exuI2
% 0.20/0.46 => ( inCongP
% 0.20/0.46 => ( in__Cong
% 0.20/0.46 => ( exuE3u
% 0.20/0.46 => ( exu__Cong
% 0.20/0.46 => ( emptyset__Cong
% 0.20/0.46 => ( setadjoin__Cong
% 0.20/0.46 => ( powerset__Cong
% 0.20/0.46 => ( setunion__Cong
% 0.20/0.46 => ( omega__Cong
% 0.20/0.46 => ( exuEu
% 0.20/0.46 => ( descr__Cong
% 0.20/0.46 => ( dsetconstr__Cong
% 0.20/0.46 => ( subsetI1
% 0.20/0.46 => ( eqimpsubset2
% 0.20/0.46 => ( eqimpsubset1
% 0.20/0.46 => ( subsetI2
% 0.20/0.46 => ( emptysetsubset
% 0.20/0.46 => ( subsetE
% 0.20/0.46 => ( subsetE2
% 0.20/0.46 => ( notsubsetI
% 0.20/0.46 => ( notequalI1
% 0.20/0.46 => ( notequalI2
% 0.20/0.46 => ( subsetRefl
% 0.20/0.46 => ( subsetTrans
% 0.20/0.46 => ( setadjoinSub
% 0.20/0.46 => ( setadjoinSub2
% 0.20/0.46 => ( subset2powerset
% 0.20/0.46 => ( setextsub
% 0.20/0.46 => ( subsetemptysetimpeq
% 0.20/0.46 => ( powersetI1
% 0.20/0.46 => ( powersetE1
% 0.20/0.46 => ( inPowerset
% 0.20/0.46 => ( powersetsubset
% 0.20/0.46 => ( sepInPowerset
% 0.20/0.46 => ( sepSubset
% 0.20/0.46 => ( binunionIL
% 0.20/0.46 => ( upairset2IR
% 0.20/0.46 => ( binunionIR
% 0.20/0.46 => ( binunionEcases
% 0.20/0.46 => ( binunionE
% 0.20/0.46 => ( binunionLsub
% 0.20/0.46 => ( binunionRsub
% 0.20/0.46 => ( binintersectI
% 0.20/0.46 => ( binintersectSubset5
% 0.20/0.46 => ( binintersectEL
% 0.20/0.46 => ( binintersectLsub
% 0.20/0.46 => ( binintersectSubset2
% 0.20/0.46 => ( binintersectSubset3
% 0.20/0.46 => ( binintersectER
% 0.20/0.46 => ( disjointsetsI1
% 0.20/0.46 => ( binintersectRsub
% 0.20/0.46 => ( binintersectSubset4
% 0.20/0.46 => ( binintersectSubset1
% 0.20/0.46 => ( bs114d
% 0.20/0.46 => ( setminusI
% 0.20/0.46 => ( setminusEL
% 0.20/0.46 => ( setminusER
% 0.20/0.46 => ( setminusSubset2
% 0.20/0.46 => ( setminusERneg
% 0.20/0.46 => ( setminusELneg
% 0.20/0.46 => ( setminusILneg
% 0.20/0.46 => ( setminusIRneg
% 0.20/0.46 => ( setminusLsub
% 0.20/0.46 => ( setminusSubset1
% 0.20/0.46 => ( symdiffE
% 0.20/0.46 => ( symdiffI1
% 0.20/0.46 => ( symdiffI2
% 0.20/0.46 => ( symdiffIneg1
% 0.20/0.46 => ( symdiffIneg2
% 0.20/0.46 => ( secondinupair
% 0.20/0.46 => ( setukpairIL
% 0.20/0.46 => ( setukpairIR
% 0.20/0.46 => ( kpairiskpair
% 0.20/0.46 => ( kpairp
% 0.20/0.46 => ( singletonsubset
% 0.20/0.46 => ( singletoninpowerset
% 0.20/0.46 => ( singletoninpowunion
% 0.20/0.46 => ( upairset2E
% 0.20/0.46 => ( upairsubunion
% 0.20/0.46 => ( upairinpowunion
% 0.20/0.46 => ( ubforcartprodlem1
% 0.20/0.46 => ( ubforcartprodlem2
% 0.20/0.46 => ( ubforcartprodlem3
% 0.20/0.46 => ( cartprodpairin
% 0.20/0.46 => ( cartprodmempair1
% 0.20/0.46 => ( cartprodmempair
% 0.20/0.46 => ( setunionE2
% 0.20/0.46 => ( setunionsingleton1
% 0.20/0.46 => ( setunionsingleton2
% 0.20/0.46 => ( setunionsingleton
% 0.20/0.46 => ( singletonprop
% 0.20/0.46 => ( ex1E1
% 0.20/0.46 => ( ex1I
% 0.20/0.46 => ( ex1I2
% 0.20/0.46 => ( singletonsuniq
% 0.20/0.46 => ( setukpairinjL1
% 0.20/0.46 => ( kfstsingleton
% 0.20/0.46 => ( theprop
% 0.20/0.46 => ( kfstpairEq
% 0.20/0.46 => ( cartprodfstin
% 0.20/0.46 => ( setukpairinjL2
% 0.20/0.46 => ( setukpairinjL
% 0.20/0.46 => ( setukpairinjR11
% 0.20/0.46 => ( setukpairinjR12
% 0.20/0.46 => ( setukpairinjR1
% 0.20/0.46 => ( upairequniteq
% 0.20/0.46 => ( setukpairinjR2
% 0.20/0.46 => ( setukpairinjR
% 0.20/0.46 => ( ksndsingleton
% 0.20/0.46 => ( ksndpairEq
% 0.20/0.46 => ( kpairsurjEq
% 0.20/0.46 => ( cartprodsndin
% 0.20/0.46 => ( cartprodpairmemEL
% 0.20/0.46 => ( cartprodpairmemER
% 0.20/0.46 => ( cartprodmempaircEq
% 0.20/0.46 => ( cartprodfstpairEq
% 0.20/0.46 => ( cartprodsndpairEq
% 0.20/0.46 => ( cartprodpairsurjEq
% 0.20/0.46 => ( dpsetconstrI
% 0.20/0.46 => ( dpsetconstrSub
% 0.20/0.46 => ( setOfPairsIsBReln
% 0.20/0.46 => ( dpsetconstrERa
% 0.20/0.46 => ( dpsetconstrEL1
% 0.20/0.46 => ( dpsetconstrEL2
% 0.20/0.46 => ( dpsetconstrER
% 0.20/0.46 => ( funcImageSingleton
% 0.20/0.46 => ( apProp
% 0.20/0.46 => ( app
% 0.20/0.46 => ( infuncsetfunc
% 0.20/0.46 => ( ap2p
% 0.20/0.46 => ( funcinfuncset
% 0.20/0.46 => ( lamProp
% 0.20/0.46 => ( lamp
% 0.20/0.46 => ( lam2p
% 0.20/0.46 => ( brelnall1
% 0.20/0.46 => ( brelnall2
% 0.20/0.46 => ( ex1E2
% 0.20/0.46 => ( funcGraphProp1
% 0.20/0.46 => ( funcGraphProp3
% 0.20/0.46 => ( funcGraphProp2
% 0.20/0.46 => ( funcextLem
% 0.20/0.46 => ( funcGraphProp4
% 0.20/0.46 => ( subbreln
% 0.20/0.46 => ( eqbreln
% 0.20/0.46 => ( funcext
% 0.20/0.46 => ( funcext2
% 0.20/0.46 => ( ap2apEq1
% 0.20/0.46 => ( ap2apEq2
% 0.20/0.46 => ( beta1
% 0.20/0.46 => ( eta1
% 0.20/0.46 => ( lam2lamEq
% 0.20/0.46 => ( beta2
% 0.20/0.46 => ( eta2
% 0.20/0.46 => ( iffalseProp1
% 0.20/0.46 => ( iffalseProp2
% 0.20/0.46 => ( iftrueProp1
% 0.20/0.46 => ( iftrueProp2
% 0.20/0.46 => ( ifSingleton
% 0.20/0.46 => ( ifp
% 0.20/0.46 => ( theeq
% 0.20/0.46 => ( iftrue
% 0.20/0.46 => ( iffalse
% 0.20/0.46 => ( iftrueorfalse
% 0.20/0.46 => ( binintersectT_lem
% 0.20/0.46 => ( binunionT_lem
% 0.20/0.46 => ( powersetT_lem
% 0.20/0.46 => ( setminusT_lem
% 0.20/0.46 => ( complementT_lem
% 0.20/0.46 => ( setextT
% 0.20/0.46 => ( subsetTI
% 0.20/0.46 => ( powersetTI1
% 0.20/0.46 => ( powersetTE1
% 0.20/0.46 => ( complementTI1
% 0.20/0.46 => ( complementTE1
% 0.20/0.46 => ( binintersectTELcontra
% 0.20/0.46 => ( binintersectTERcontra
% 0.20/0.46 => ( contrasubsetT
% 0.20/0.46 => ( contrasubsetT1
% 0.20/0.46 => ( contrasubsetT2
% 0.20/0.46 => ( contrasubsetT3
% 0.20/0.46 => ( doubleComplementI1
% 0.20/0.46 => ( doubleComplementE1
% 0.20/0.46 => ( doubleComplementSub1
% 0.20/0.46 => ( doubleComplementSub2
% 0.20/0.46 => ( doubleComplementEq
% 0.20/0.46 => ( complementTnotintersectT
% 0.20/0.46 => ( complementImpComplementIntersect
% 0.20/0.46 => ( complementSubsetComplementIntersect
% 0.20/0.46 => ( complementInPowersetComplementIntersect
% 0.20/0.46 => ( contraSubsetComplement
% 0.20/0.46 => ( complementTcontraSubset
% 0.20/0.46 => ( binunionTILcontra
% 0.20/0.46 => ( binunionTIRcontra
% 0.20/0.46 => ( inIntersectImpInUnion
% 0.20/0.46 => ( inIntersectImpInUnion2
% 0.20/0.46 => ( inIntersectImpInIntersectUnions
% 0.20/0.46 => ! [A: $i,X: $i] :
% 0.20/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.20/0.46 => ! [Y: $i] :
% 0.20/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.20/0.46 => ! [Z: $i] :
% 0.20/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.20/0.46 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 3.28/1.73 ---- Embedded in THF ---
% 3.28/1.73 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.28/1.73 %%% Generated on Tue Feb 24 12:32:40 EST 2026
% 3.28/1.73 %%% using '$$dhol' embedding, version 1.3.0.
% 3.28/1.73 %%% Logic specification used:
% 3.28/1.73 %%% thf(spec, logic, $$dhol).
% 3.28/1.73
% 3.28/1.73 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.XapuwXWeE6/DTF2DTF1199.p
% See solution above
% 3.28/1.73 ------------------------
% 3.28/1.79 ---- Cleaned THF ---
% 3.28/1.79 thf(in_type,type,
% 3.28/1.79 in: $i > $i > $o ).
% 3.28/1.79
% 3.28/1.79 thf(exu_type,type,
% 3.28/1.79 exu: ( $i > $o ) > $o ).
% 3.28/1.79
% 3.28/1.79 thf(exu,definition,
% 3.28/1.79 ( exu
% 3.28/1.79 = ( ^ [Xphi: $i > $o] :
% 3.28/1.79 ? [Xx: $i] :
% 3.28/1.79 ( ( Xphi @ Xx )
% 3.28/1.79 & ! [Xy: $i] :
% 3.28/1.79 ( ( Xphi @ Xy )
% 3.28/1.79 => ( Xx = Xy ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setextAx_type,type,
% 3.28/1.79 setextAx: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setextAx,definition,
% 3.28/1.79 ( setextAx
% 3.28/1.79 = ( ! [A: $i,B: $i] :
% 3.28/1.79 ( ! [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 <=> ( in @ Xx @ B ) )
% 3.28/1.79 => ( A = B ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(emptyset_type,type,
% 3.28/1.79 emptyset: $i ).
% 3.28/1.79
% 3.28/1.79 thf(emptysetAx_type,type,
% 3.28/1.79 emptysetAx: $o ).
% 3.28/1.79
% 3.28/1.79 thf(emptysetAx,definition,
% 3.28/1.79 ( emptysetAx
% 3.28/1.79 = ( ! [Xx: $i] :
% 3.28/1.79 ~ ( in @ Xx @ emptyset ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setadjoin_type,type,
% 3.28/1.79 setadjoin: $i > $i > $i ).
% 3.28/1.79
% 3.28/1.79 thf(setadjoinAx_type,type,
% 3.28/1.79 setadjoinAx: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setadjoinAx,definition,
% 3.28/1.79 ( setadjoinAx
% 3.28/1.79 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.28/1.79 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.28/1.79 <=> ( ( Xy = Xx )
% 3.28/1.79 | ( in @ Xy @ A ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(powerset_type,type,
% 3.28/1.79 powerset: $i > $i ).
% 3.28/1.79
% 3.28/1.79 thf(powersetAx_type,type,
% 3.28/1.79 powersetAx: $o ).
% 3.28/1.79
% 3.28/1.79 thf(powersetAx,definition,
% 3.28/1.79 ( powersetAx
% 3.28/1.79 = ( ! [A: $i,B: $i] :
% 3.28/1.79 ( ( in @ B @ ( powerset @ A ) )
% 3.28/1.79 <=> ! [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ B )
% 3.28/1.79 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setunion_type,type,
% 3.28/1.79 setunion: $i > $i ).
% 3.28/1.79
% 3.28/1.79 thf(setunionAx_type,type,
% 3.28/1.79 setunionAx: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setunionAx,definition,
% 3.28/1.79 ( setunionAx
% 3.28/1.79 = ( ! [A: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ ( setunion @ A ) )
% 3.28/1.79 <=> ? [B: $i] :
% 3.28/1.79 ( ( in @ Xx @ B )
% 3.28/1.79 & ( in @ B @ A ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(omega_type,type,
% 3.28/1.79 omega: $i ).
% 3.28/1.79
% 3.28/1.79 thf(omega0Ax_type,type,
% 3.28/1.79 omega0Ax: $o ).
% 3.28/1.79
% 3.28/1.79 thf(omega0Ax,definition,
% 3.28/1.79 ( omega0Ax
% 3.28/1.79 = ( in @ emptyset @ omega ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(omegaSAx_type,type,
% 3.28/1.79 omegaSAx: $o ).
% 3.28/1.79
% 3.28/1.79 thf(omegaSAx,definition,
% 3.28/1.79 ( omegaSAx
% 3.28/1.79 = ( ! [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ omega )
% 3.28/1.79 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(omegaIndAx_type,type,
% 3.28/1.79 omegaIndAx: $o ).
% 3.28/1.79
% 3.28/1.79 thf(omegaIndAx,definition,
% 3.28/1.79 ( omegaIndAx
% 3.28/1.79 = ( ! [A: $i] :
% 3.28/1.79 ( ( ( in @ emptyset @ A )
% 3.28/1.79 & ! [Xx: $i] :
% 3.28/1.79 ( ( ( in @ Xx @ omega )
% 3.28/1.79 & ( in @ Xx @ A ) )
% 3.28/1.79 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 3.28/1.79 => ! [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ omega )
% 3.28/1.79 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(replAx_type,type,
% 3.28/1.79 replAx: $o ).
% 3.28/1.79
% 3.28/1.79 thf(replAx,definition,
% 3.28/1.79 ( replAx
% 3.28/1.79 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 3.28/1.79 ( ! [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ( exu
% 3.28/1.79 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 3.28/1.79 => ? [B: $i] :
% 3.28/1.79 ! [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ B )
% 3.28/1.79 <=> ? [Xy: $i] :
% 3.28/1.79 ( ( in @ Xy @ A )
% 3.28/1.79 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(foundationAx_type,type,
% 3.28/1.79 foundationAx: $o ).
% 3.28/1.79
% 3.28/1.79 thf(foundationAx,definition,
% 3.28/1.79 ( foundationAx
% 3.28/1.79 = ( ! [A: $i] :
% 3.28/1.79 ( ? [Xx: $i] : ( in @ Xx @ A )
% 3.28/1.79 => ? [B: $i] :
% 3.28/1.79 ( ( in @ B @ A )
% 3.28/1.79 & ~ ? [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ B )
% 3.28/1.79 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(wellorderingAx_type,type,
% 3.28/1.79 wellorderingAx: $o ).
% 3.28/1.79
% 3.28/1.79 thf(wellorderingAx,definition,
% 3.28/1.79 ( wellorderingAx
% 3.28/1.79 = ( ! [A: $i] :
% 3.28/1.79 ? [B: $i] :
% 3.28/1.79 ( ! [C: $i] :
% 3.28/1.79 ( ( in @ C @ B )
% 3.28/1.79 => ! [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ C )
% 3.28/1.79 => ( in @ Xx @ A ) ) )
% 3.28/1.79 & ! [Xx: $i,Xy: $i] :
% 3.28/1.79 ( ( ( in @ Xx @ A )
% 3.28/1.79 & ( in @ Xy @ A ) )
% 3.28/1.79 => ( ! [C: $i] :
% 3.28/1.79 ( ( in @ C @ B )
% 3.28/1.79 => ( ( in @ Xx @ C )
% 3.28/1.79 <=> ( in @ Xy @ C ) ) )
% 3.28/1.79 => ( Xx = Xy ) ) )
% 3.28/1.79 & ! [C: $i,D: $i] :
% 3.28/1.79 ( ( ( in @ C @ B )
% 3.28/1.79 & ( in @ D @ B ) )
% 3.28/1.79 => ( ! [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ C )
% 3.28/1.79 => ( in @ Xx @ D ) )
% 3.28/1.79 | ! [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ D )
% 3.28/1.79 => ( in @ Xx @ C ) ) ) )
% 3.28/1.79 & ! [C: $i] :
% 3.28/1.79 ( ( ! [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ C )
% 3.28/1.79 => ( in @ Xx @ A ) )
% 3.28/1.79 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 3.28/1.79 => ? [D: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ D @ B )
% 3.28/1.79 & ( in @ Xx @ C )
% 3.28/1.79 & ~ ? [Xy: $i] :
% 3.28/1.79 ( ( in @ Xy @ D )
% 3.28/1.79 & ( in @ Xy @ C ) )
% 3.28/1.79 & ! [E: $i] :
% 3.28/1.79 ( ( in @ E @ B )
% 3.28/1.79 => ( ! [Xy: $i] :
% 3.28/1.79 ( ( in @ Xy @ E )
% 3.28/1.79 => ( in @ Xy @ D ) )
% 3.28/1.79 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(descr_type,type,
% 3.28/1.79 descr: ( $i > $o ) > $i ).
% 3.28/1.79
% 3.28/1.79 thf(descrp_type,type,
% 3.28/1.79 descrp: $o ).
% 3.28/1.79
% 3.28/1.79 thf(descrp,definition,
% 3.28/1.79 ( descrp
% 3.28/1.79 = ( ! [Xphi: $i > $o] :
% 3.28/1.79 ( ( exu
% 3.28/1.79 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.28/1.79 => ( Xphi
% 3.28/1.79 @ ( descr
% 3.28/1.79 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(dsetconstr_type,type,
% 3.28/1.79 dsetconstr: $i > ( $i > $o ) > $i ).
% 3.28/1.79
% 3.28/1.79 thf(dsetconstrI_type,type,
% 3.28/1.79 dsetconstrI: $o ).
% 3.28/1.79
% 3.28/1.79 thf(dsetconstrI,definition,
% 3.28/1.79 ( dsetconstrI
% 3.28/1.79 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ( ( Xphi @ Xx )
% 3.28/1.79 => ( in @ Xx
% 3.28/1.79 @ ( dsetconstr @ A
% 3.28/1.79 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(dsetconstrEL_type,type,
% 3.28/1.79 dsetconstrEL: $o ).
% 3.28/1.79
% 3.28/1.79 thf(dsetconstrEL,definition,
% 3.28/1.79 ( dsetconstrEL
% 3.28/1.79 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx
% 3.28/1.79 @ ( dsetconstr @ A
% 3.28/1.79 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.28/1.79 => ( in @ Xx @ A ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(dsetconstrER_type,type,
% 3.28/1.79 dsetconstrER: $o ).
% 3.28/1.79
% 3.28/1.79 thf(dsetconstrER,definition,
% 3.28/1.79 ( dsetconstrER
% 3.28/1.79 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx
% 3.28/1.79 @ ( dsetconstr @ A
% 3.28/1.79 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.28/1.79 => ( Xphi @ Xx ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(exuE1_type,type,
% 3.28/1.79 exuE1: $o ).
% 3.28/1.79
% 3.28/1.79 thf(exuE1,definition,
% 3.28/1.79 ( exuE1
% 3.28/1.79 = ( ! [Xphi: $i > $o] :
% 3.28/1.79 ( ( exu
% 3.28/1.79 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.28/1.79 => ? [Xx: $i] :
% 3.28/1.79 ( ( Xphi @ Xx )
% 3.28/1.79 & ! [Xy: $i] :
% 3.28/1.79 ( ( Xphi @ Xy )
% 3.28/1.79 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(prop2set_type,type,
% 3.28/1.79 prop2set: $o > $i ).
% 3.28/1.79
% 3.28/1.79 thf(prop2setE_type,type,
% 3.28/1.79 prop2setE: $o ).
% 3.28/1.79
% 3.28/1.79 thf(prop2setE,definition,
% 3.28/1.79 ( prop2setE
% 3.28/1.79 = ( ! [Xphi: $o,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 3.28/1.79 => Xphi ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(emptysetE_type,type,
% 3.28/1.79 emptysetE: $o ).
% 3.28/1.79
% 3.28/1.79 thf(emptysetE,definition,
% 3.28/1.79 ( emptysetE
% 3.28/1.79 = ( ! [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ emptyset )
% 3.28/1.79 => ! [Xphi: $o] : Xphi ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(emptysetimpfalse_type,type,
% 3.28/1.79 emptysetimpfalse: $o ).
% 3.28/1.79
% 3.28/1.79 thf(emptysetimpfalse,definition,
% 3.28/1.79 ( emptysetimpfalse
% 3.28/1.79 = ( ! [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ emptyset )
% 3.28/1.79 => $false ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(notinemptyset_type,type,
% 3.28/1.79 notinemptyset: $o ).
% 3.28/1.79
% 3.28/1.79 thf(notinemptyset,definition,
% 3.28/1.79 ( notinemptyset
% 3.28/1.79 = ( ! [Xx: $i] :
% 3.28/1.79 ~ ( in @ Xx @ emptyset ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(exuE3e_type,type,
% 3.28/1.79 exuE3e: $o ).
% 3.28/1.79
% 3.28/1.79 thf(exuE3e,definition,
% 3.28/1.79 ( exuE3e
% 3.28/1.79 = ( ! [Xphi: $i > $o] :
% 3.28/1.79 ( ( exu
% 3.28/1.79 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.28/1.79 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setext_type,type,
% 3.28/1.79 setext: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setext,definition,
% 3.28/1.79 ( setext
% 3.28/1.79 = ( ! [A: $i,B: $i] :
% 3.28/1.79 ( ! [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ( in @ Xx @ B ) )
% 3.28/1.79 => ( ! [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ B )
% 3.28/1.79 => ( in @ Xx @ A ) )
% 3.28/1.79 => ( A = B ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(emptyI_type,type,
% 3.28/1.79 emptyI: $o ).
% 3.28/1.79
% 3.28/1.79 thf(emptyI,definition,
% 3.28/1.79 ( emptyI
% 3.28/1.79 = ( ! [A: $i] :
% 3.28/1.79 ( ! [Xx: $i] :
% 3.28/1.79 ~ ( in @ Xx @ A )
% 3.28/1.79 => ( A = emptyset ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(noeltsimpempty_type,type,
% 3.28/1.79 noeltsimpempty: $o ).
% 3.28/1.79
% 3.28/1.79 thf(noeltsimpempty,definition,
% 3.28/1.79 ( noeltsimpempty
% 3.28/1.79 = ( ! [A: $i] :
% 3.28/1.79 ( ! [Xx: $i] :
% 3.28/1.79 ~ ( in @ Xx @ A )
% 3.28/1.79 => ( A = emptyset ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setbeta_type,type,
% 3.28/1.79 setbeta: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setbeta,definition,
% 3.28/1.79 ( setbeta
% 3.28/1.79 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ( ( in @ Xx
% 3.28/1.79 @ ( dsetconstr @ A
% 3.28/1.79 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.28/1.79 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(nonempty_type,type,
% 3.28/1.79 nonempty: $i > $o ).
% 3.28/1.79
% 3.28/1.79 thf(nonempty,definition,
% 3.28/1.79 ( nonempty
% 3.28/1.79 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(nonemptyE1_type,type,
% 3.28/1.79 nonemptyE1: $o ).
% 3.28/1.79
% 3.28/1.79 thf(nonemptyE1,definition,
% 3.28/1.79 ( nonemptyE1
% 3.28/1.79 = ( ! [A: $i] :
% 3.28/1.79 ( ( nonempty @ A )
% 3.28/1.79 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(nonemptyI_type,type,
% 3.28/1.79 nonemptyI: $o ).
% 3.28/1.79
% 3.28/1.79 thf(nonemptyI,definition,
% 3.28/1.79 ( nonemptyI
% 3.28/1.79 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ( ( Xphi @ Xx )
% 3.28/1.79 => ( nonempty
% 3.28/1.79 @ ( dsetconstr @ A
% 3.28/1.79 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(nonemptyI1_type,type,
% 3.28/1.79 nonemptyI1: $o ).
% 3.28/1.79
% 3.28/1.79 thf(nonemptyI1,definition,
% 3.28/1.79 ( nonemptyI1
% 3.28/1.79 = ( ! [A: $i] :
% 3.28/1.79 ( ? [Xx: $i] : ( in @ Xx @ A )
% 3.28/1.79 => ( nonempty @ A ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setadjoinIL_type,type,
% 3.28/1.79 setadjoinIL: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setadjoinIL,definition,
% 3.28/1.79 ( setadjoinIL
% 3.28/1.79 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(emptyinunitempty_type,type,
% 3.28/1.79 emptyinunitempty: $o ).
% 3.28/1.79
% 3.28/1.79 thf(emptyinunitempty,definition,
% 3.28/1.79 ( emptyinunitempty
% 3.28/1.79 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setadjoinIR_type,type,
% 3.28/1.79 setadjoinIR: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setadjoinIR,definition,
% 3.28/1.79 ( setadjoinIR
% 3.28/1.79 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.28/1.79 ( ( in @ Xy @ A )
% 3.28/1.79 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setadjoinE_type,type,
% 3.28/1.79 setadjoinE: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setadjoinE,definition,
% 3.28/1.79 ( setadjoinE
% 3.28/1.79 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.28/1.79 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.28/1.79 => ! [Xphi: $o] :
% 3.28/1.79 ( ( ( Xy = Xx )
% 3.28/1.79 => Xphi )
% 3.28/1.79 => ( ( ( in @ Xy @ A )
% 3.28/1.79 => Xphi )
% 3.28/1.79 => Xphi ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setadjoinOr_type,type,
% 3.28/1.79 setadjoinOr: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setadjoinOr,definition,
% 3.28/1.79 ( setadjoinOr
% 3.28/1.79 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.28/1.79 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.28/1.79 => ( ( Xy = Xx )
% 3.28/1.79 | ( in @ Xy @ A ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setoftrueEq_type,type,
% 3.28/1.79 setoftrueEq: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setoftrueEq,definition,
% 3.28/1.79 ( setoftrueEq
% 3.28/1.79 = ( ! [A: $i] :
% 3.28/1.79 ( ( dsetconstr @ A
% 3.28/1.79 @ ^ [Xx: $i] : $true )
% 3.28/1.79 = A ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(powersetI_type,type,
% 3.28/1.79 powersetI: $o ).
% 3.28/1.79
% 3.28/1.79 thf(powersetI,definition,
% 3.28/1.79 ( powersetI
% 3.28/1.79 = ( ! [A: $i,B: $i] :
% 3.28/1.79 ( ! [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ B )
% 3.28/1.79 => ( in @ Xx @ A ) )
% 3.28/1.79 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(emptyinPowerset_type,type,
% 3.28/1.79 emptyinPowerset: $o ).
% 3.28/1.79
% 3.28/1.79 thf(emptyinPowerset,definition,
% 3.28/1.79 ( emptyinPowerset
% 3.28/1.79 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(emptyInPowerset_type,type,
% 3.28/1.79 emptyInPowerset: $o ).
% 3.28/1.79
% 3.28/1.79 thf(emptyInPowerset,definition,
% 3.28/1.79 ( emptyInPowerset
% 3.28/1.79 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(powersetE_type,type,
% 3.28/1.79 powersetE: $o ).
% 3.28/1.79
% 3.28/1.79 thf(powersetE,definition,
% 3.28/1.79 ( powersetE
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ B @ ( powerset @ A ) )
% 3.28/1.79 => ( ( in @ Xx @ B )
% 3.28/1.79 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setunionI_type,type,
% 3.28/1.79 setunionI: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setunionI,definition,
% 3.28/1.79 ( setunionI
% 3.28/1.79 = ( ! [A: $i,Xx: $i,B: $i] :
% 3.28/1.79 ( ( in @ Xx @ B )
% 3.28/1.79 => ( ( in @ B @ A )
% 3.28/1.79 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setunionE_type,type,
% 3.28/1.79 setunionE: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setunionE,definition,
% 3.28/1.79 ( setunionE
% 3.28/1.79 = ( ! [A: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ ( setunion @ A ) )
% 3.28/1.79 => ! [Xphi: $o] :
% 3.28/1.79 ( ! [B: $i] :
% 3.28/1.79 ( ( in @ Xx @ B )
% 3.28/1.79 => ( ( in @ B @ A )
% 3.28/1.79 => Xphi ) )
% 3.28/1.79 => Xphi ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(subPowSU_type,type,
% 3.28/1.79 subPowSU: $o ).
% 3.28/1.79
% 3.28/1.79 thf(subPowSU,definition,
% 3.28/1.79 ( subPowSU
% 3.28/1.79 = ( ! [A: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(exuE2_type,type,
% 3.28/1.79 exuE2: $o ).
% 3.28/1.79
% 3.28/1.79 thf(exuE2,definition,
% 3.28/1.79 ( exuE2
% 3.28/1.79 = ( ! [Xphi: $i > $o] :
% 3.28/1.79 ( ( exu
% 3.28/1.79 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.28/1.79 => ? [Xx: $i] :
% 3.28/1.79 ! [Xy: $i] :
% 3.28/1.79 ( ( Xphi @ Xy )
% 3.28/1.79 <=> ( Xy = Xx ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(nonemptyImpWitness_type,type,
% 3.28/1.79 nonemptyImpWitness: $o ).
% 3.28/1.79
% 3.28/1.79 thf(nonemptyImpWitness,definition,
% 3.28/1.79 ( nonemptyImpWitness
% 3.28/1.79 = ( ! [A: $i] :
% 3.28/1.79 ( ( nonempty @ A )
% 3.28/1.79 => ? [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 & $true ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(uniqinunit_type,type,
% 3.28/1.79 uniqinunit: $o ).
% 3.28/1.79
% 3.28/1.79 thf(uniqinunit,definition,
% 3.28/1.79 ( uniqinunit
% 3.28/1.79 = ( ! [Xx: $i,Xy: $i] :
% 3.28/1.79 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.28/1.79 => ( Xx = Xy ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(notinsingleton_type,type,
% 3.28/1.79 notinsingleton: $o ).
% 3.28/1.79
% 3.28/1.79 thf(notinsingleton,definition,
% 3.28/1.79 ( notinsingleton
% 3.28/1.79 = ( ! [Xx: $i,Xy: $i] :
% 3.28/1.79 ( ( Xx != Xy )
% 3.28/1.79 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(eqinunit_type,type,
% 3.28/1.79 eqinunit: $o ).
% 3.28/1.79
% 3.28/1.79 thf(eqinunit,definition,
% 3.28/1.79 ( eqinunit
% 3.28/1.79 = ( ! [Xx: $i,Xy: $i] :
% 3.28/1.79 ( ( Xx = Xy )
% 3.28/1.79 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(singletonsswitch_type,type,
% 3.28/1.79 singletonsswitch: $o ).
% 3.28/1.79
% 3.28/1.79 thf(singletonsswitch,definition,
% 3.28/1.79 ( singletonsswitch
% 3.28/1.79 = ( ! [Xx: $i,Xy: $i] :
% 3.28/1.79 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.28/1.79 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(upairsetE_type,type,
% 3.28/1.79 upairsetE: $o ).
% 3.28/1.79
% 3.28/1.79 thf(upairsetE,definition,
% 3.28/1.79 ( upairsetE
% 3.28/1.79 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.28/1.79 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 3.28/1.79 => ( ( Xz = Xx )
% 3.28/1.79 | ( Xz = Xy ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(upairsetIL_type,type,
% 3.28/1.79 upairsetIL: $o ).
% 3.28/1.79
% 3.28/1.79 thf(upairsetIL,definition,
% 3.28/1.79 ( upairsetIL
% 3.28/1.79 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(upairsetIR_type,type,
% 3.28/1.79 upairsetIR: $o ).
% 3.28/1.79
% 3.28/1.79 thf(upairsetIR,definition,
% 3.28/1.79 ( upairsetIR
% 3.28/1.79 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(emptyE1_type,type,
% 3.28/1.79 emptyE1: $o ).
% 3.28/1.79
% 3.28/1.79 thf(emptyE1,definition,
% 3.28/1.79 ( emptyE1
% 3.28/1.79 = ( ! [A: $i,Xphi: $i > $o] :
% 3.28/1.79 ( ? [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 & ( Xphi @ Xx ) )
% 3.28/1.79 => ( ( ( dsetconstr @ A
% 3.28/1.79 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.28/1.79 = emptyset )
% 3.28/1.79 => $false ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(vacuousDall_type,type,
% 3.28/1.79 vacuousDall: $o ).
% 3.28/1.79
% 3.28/1.79 thf(vacuousDall,definition,
% 3.28/1.79 ( vacuousDall
% 3.28/1.79 = ( ! [Xphi: $i > $o,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ emptyset )
% 3.28/1.79 => ( Xphi @ Xx ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(quantDeMorgan1_type,type,
% 3.28/1.79 quantDeMorgan1: $o ).
% 3.28/1.79
% 3.28/1.79 thf(quantDeMorgan1,definition,
% 3.28/1.79 ( quantDeMorgan1
% 3.28/1.79 = ( ! [A: $i,Xphi: $i > $o] :
% 3.28/1.79 ( ~ ! [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ( Xphi @ Xx ) )
% 3.28/1.79 => ? [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(quantDeMorgan2_type,type,
% 3.28/1.79 quantDeMorgan2: $o ).
% 3.28/1.79
% 3.28/1.79 thf(quantDeMorgan2,definition,
% 3.28/1.79 ( quantDeMorgan2
% 3.28/1.79 = ( ! [A: $i,Xphi: $i > $o] :
% 3.28/1.79 ( ! [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ~ ( Xphi @ Xx ) )
% 3.28/1.79 => ~ ? [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 & ( Xphi @ Xx ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(quantDeMorgan3_type,type,
% 3.28/1.79 quantDeMorgan3: $o ).
% 3.28/1.79
% 3.28/1.79 thf(quantDeMorgan3,definition,
% 3.28/1.79 ( quantDeMorgan3
% 3.28/1.79 = ( ! [A: $i,Xphi: $i > $o] :
% 3.28/1.79 ( ~ ? [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 & ( Xphi @ Xx ) )
% 3.28/1.79 => ! [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(quantDeMorgan4_type,type,
% 3.28/1.79 quantDeMorgan4: $o ).
% 3.28/1.79
% 3.28/1.79 thf(quantDeMorgan4,definition,
% 3.28/1.79 ( quantDeMorgan4
% 3.28/1.79 = ( ! [A: $i,Xphi: $i > $o] :
% 3.28/1.79 ( ? [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 & ~ ( Xphi @ Xx ) )
% 3.28/1.79 => ~ ! [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ( Xphi @ Xx ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(prop2setI_type,type,
% 3.28/1.79 prop2setI: $o ).
% 3.28/1.79
% 3.28/1.79 thf(prop2setI,definition,
% 3.28/1.79 ( prop2setI
% 3.28/1.79 = ( ! [Xphi: $o] :
% 3.28/1.79 ( Xphi
% 3.28/1.79 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(set2prop_type,type,
% 3.28/1.79 set2prop: $i > $o ).
% 3.28/1.79
% 3.28/1.79 thf(prop2set2propI_type,type,
% 3.28/1.79 prop2set2propI: $o ).
% 3.28/1.79
% 3.28/1.79 thf(prop2set2propI,definition,
% 3.28/1.79 ( prop2set2propI
% 3.28/1.79 = ( ! [Xphi: $o] :
% 3.28/1.79 ( Xphi
% 3.28/1.79 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(notdexE_type,type,
% 3.28/1.79 notdexE: $o ).
% 3.28/1.79
% 3.28/1.79 thf(notdexE,definition,
% 3.28/1.79 ( notdexE
% 3.28/1.79 = ( ! [A: $i,Xphi: $i > $o] :
% 3.28/1.79 ( ~ ? [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 & ( Xphi @ Xx ) )
% 3.28/1.79 => ! [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(notdallE_type,type,
% 3.28/1.79 notdallE: $o ).
% 3.28/1.79
% 3.28/1.79 thf(notdallE,definition,
% 3.28/1.79 ( notdallE
% 3.28/1.79 = ( ! [A: $i,Xphi: $i > $o] :
% 3.28/1.79 ( ~ ! [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ( Xphi @ Xx ) )
% 3.28/1.79 => ? [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(exuI1_type,type,
% 3.28/1.79 exuI1: $o ).
% 3.28/1.79
% 3.28/1.79 thf(exuI1,definition,
% 3.28/1.79 ( exuI1
% 3.28/1.79 = ( ! [Xphi: $i > $o] :
% 3.28/1.79 ( ? [Xx: $i] :
% 3.28/1.79 ( ( Xphi @ Xx )
% 3.28/1.79 & ! [Xy: $i] :
% 3.28/1.79 ( ( Xphi @ Xy )
% 3.28/1.79 => ( Xx = Xy ) ) )
% 3.28/1.79 => ( exu
% 3.28/1.79 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(exuI3_type,type,
% 3.28/1.79 exuI3: $o ).
% 3.28/1.79
% 3.28/1.79 thf(exuI3,definition,
% 3.28/1.79 ( exuI3
% 3.28/1.79 = ( ! [Xphi: $i > $o] :
% 3.28/1.79 ( ? [Xx: $i] : ( Xphi @ Xx )
% 3.28/1.79 => ( ! [Xx: $i,Xy: $i] :
% 3.28/1.79 ( ( Xphi @ Xx )
% 3.28/1.79 => ( ( Xphi @ Xy )
% 3.28/1.79 => ( Xx = Xy ) ) )
% 3.28/1.79 => ( exu
% 3.28/1.79 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(exuI2_type,type,
% 3.28/1.79 exuI2: $o ).
% 3.28/1.79
% 3.28/1.79 thf(exuI2,definition,
% 3.28/1.79 ( exuI2
% 3.28/1.79 = ( ! [Xphi: $i > $o] :
% 3.28/1.79 ( ? [Xx: $i] :
% 3.28/1.79 ! [Xy: $i] :
% 3.28/1.79 ( ( Xphi @ Xy )
% 3.28/1.79 <=> ( Xy = Xx ) )
% 3.28/1.79 => ( exu
% 3.28/1.79 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(inCongP_type,type,
% 3.28/1.79 inCongP: $o ).
% 3.28/1.79
% 3.28/1.79 thf(inCongP,definition,
% 3.28/1.79 ( inCongP
% 3.28/1.79 = ( ! [A: $i,B: $i] :
% 3.28/1.79 ( ( A = B )
% 3.28/1.79 => ! [Xx: $i,Xy: $i] :
% 3.28/1.79 ( ( Xx = Xy )
% 3.28/1.79 => ( ( in @ Xx @ A )
% 3.28/1.79 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(in__Cong_type,type,
% 3.28/1.79 in__Cong: $o ).
% 3.28/1.79
% 3.28/1.79 thf(in__Cong,definition,
% 3.28/1.79 ( in__Cong
% 3.28/1.79 = ( ! [A: $i,B: $i] :
% 3.28/1.79 ( ( A = B )
% 3.28/1.79 => ! [Xx: $i,Xy: $i] :
% 3.28/1.79 ( ( Xx = Xy )
% 3.28/1.79 => ( ( in @ Xx @ A )
% 3.28/1.79 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(exuE3u_type,type,
% 3.28/1.79 exuE3u: $o ).
% 3.28/1.79
% 3.28/1.79 thf(exuE3u,definition,
% 3.28/1.79 ( exuE3u
% 3.28/1.79 = ( ! [Xphi: $i > $o] :
% 3.28/1.79 ( ( exu
% 3.28/1.79 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.28/1.79 => ! [Xx: $i,Xy: $i] :
% 3.28/1.79 ( ( Xphi @ Xx )
% 3.28/1.79 => ( ( Xphi @ Xy )
% 3.28/1.79 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(exu__Cong_type,type,
% 3.28/1.79 exu__Cong: $o ).
% 3.28/1.79
% 3.28/1.79 thf(exu__Cong,definition,
% 3.28/1.79 ( exu__Cong
% 3.28/1.79 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.28/1.79 ( ! [Xx: $i,Xy: $i] :
% 3.28/1.79 ( ( Xx = Xy )
% 3.28/1.79 => ( ( Xphi @ Xx )
% 3.28/1.79 <=> ( Xpsi @ Xy ) ) )
% 3.28/1.79 => ( ( exu
% 3.28/1.79 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.28/1.79 <=> ( exu
% 3.28/1.79 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(emptyset__Cong_type,type,
% 3.28/1.79 emptyset__Cong: $o ).
% 3.28/1.79
% 3.28/1.79 thf(emptyset__Cong,definition,
% 3.28/1.79 ( emptyset__Cong
% 3.28/1.79 = ( emptyset = emptyset ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setadjoin__Cong_type,type,
% 3.28/1.79 setadjoin__Cong: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setadjoin__Cong,definition,
% 3.28/1.79 ( setadjoin__Cong
% 3.28/1.79 = ( ! [Xx: $i,Xy: $i] :
% 3.28/1.79 ( ( Xx = Xy )
% 3.28/1.79 => ! [Xz: $i,Xu: $i] :
% 3.28/1.79 ( ( Xz = Xu )
% 3.28/1.79 => ( ( setadjoin @ Xx @ Xz )
% 3.28/1.79 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(powerset__Cong_type,type,
% 3.28/1.79 powerset__Cong: $o ).
% 3.28/1.79
% 3.28/1.79 thf(powerset__Cong,definition,
% 3.28/1.79 ( powerset__Cong
% 3.28/1.79 = ( ! [A: $i,B: $i] :
% 3.28/1.79 ( ( A = B )
% 3.28/1.79 => ( ( powerset @ A )
% 3.28/1.79 = ( powerset @ B ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setunion__Cong_type,type,
% 3.28/1.79 setunion__Cong: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setunion__Cong,definition,
% 3.28/1.79 ( setunion__Cong
% 3.28/1.79 = ( ! [A: $i,B: $i] :
% 3.28/1.79 ( ( A = B )
% 3.28/1.79 => ( ( setunion @ A )
% 3.28/1.79 = ( setunion @ B ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(omega__Cong_type,type,
% 3.28/1.79 omega__Cong: $o ).
% 3.28/1.79
% 3.28/1.79 thf(omega__Cong,definition,
% 3.28/1.79 ( omega__Cong
% 3.28/1.79 = ( omega = omega ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(exuEu_type,type,
% 3.28/1.79 exuEu: $o ).
% 3.28/1.79
% 3.28/1.79 thf(exuEu,definition,
% 3.28/1.79 ( exuEu
% 3.28/1.79 = ( ! [Xphi: $i > $o] :
% 3.28/1.79 ( ( exu
% 3.28/1.79 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.28/1.79 => ! [Xx: $i,Xy: $i] :
% 3.28/1.79 ( ( Xphi @ Xx )
% 3.28/1.79 => ( ( Xphi @ Xy )
% 3.28/1.79 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(descr__Cong_type,type,
% 3.28/1.79 descr__Cong: $o ).
% 3.28/1.79
% 3.28/1.79 thf(descr__Cong,definition,
% 3.28/1.79 ( descr__Cong
% 3.28/1.79 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.28/1.79 ( ! [Xx: $i,Xy: $i] :
% 3.28/1.79 ( ( Xx = Xy )
% 3.28/1.79 => ( ( Xphi @ Xx )
% 3.28/1.79 <=> ( Xpsi @ Xy ) ) )
% 3.28/1.79 => ( ( exu
% 3.28/1.79 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.28/1.79 => ( ( exu
% 3.28/1.79 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 3.28/1.79 => ( ( descr
% 3.28/1.79 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.28/1.79 = ( descr
% 3.28/1.79 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(dsetconstr__Cong_type,type,
% 3.28/1.79 dsetconstr__Cong: $o ).
% 3.28/1.79
% 3.28/1.79 thf(dsetconstr__Cong,definition,
% 3.28/1.79 ( dsetconstr__Cong
% 3.28/1.79 = ( ! [A: $i,B: $i] :
% 3.28/1.79 ( ( A = B )
% 3.28/1.79 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.28/1.79 ( ! [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ! [Xy: $i] :
% 3.28/1.79 ( ( in @ Xy @ B )
% 3.28/1.79 => ( ( Xx = Xy )
% 3.28/1.79 => ( ( Xphi @ Xx )
% 3.28/1.79 <=> ( Xpsi @ Xy ) ) ) ) )
% 3.28/1.79 => ( ( dsetconstr @ A
% 3.28/1.79 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.28/1.79 = ( dsetconstr @ B
% 3.28/1.79 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(subset_type,type,
% 3.28/1.79 subset: $i > $i > $o ).
% 3.28/1.79
% 3.28/1.79 thf(disjoint_type,type,
% 3.28/1.79 disjoint: $i > $i > $o ).
% 3.28/1.79
% 3.28/1.79 thf(setsmeet_type,type,
% 3.28/1.79 setsmeet: $i > $i > $o ).
% 3.28/1.79
% 3.28/1.79 thf(subsetI1_type,type,
% 3.28/1.79 subsetI1: $o ).
% 3.28/1.79
% 3.28/1.79 thf(subsetI1,definition,
% 3.28/1.79 ( subsetI1
% 3.28/1.79 = ( ! [A: $i,B: $i] :
% 3.28/1.79 ( ! [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ( in @ Xx @ B ) )
% 3.28/1.79 => ( subset @ A @ B ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(eqimpsubset2_type,type,
% 3.28/1.79 eqimpsubset2: $o ).
% 3.28/1.79
% 3.28/1.79 thf(eqimpsubset2,definition,
% 3.28/1.79 ( eqimpsubset2
% 3.28/1.79 = ( ! [A: $i,B: $i] :
% 3.28/1.79 ( ( A = B )
% 3.28/1.79 => ( subset @ B @ A ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(eqimpsubset1_type,type,
% 3.28/1.79 eqimpsubset1: $o ).
% 3.28/1.79
% 3.28/1.79 thf(eqimpsubset1,definition,
% 3.28/1.79 ( eqimpsubset1
% 3.28/1.79 = ( ! [A: $i,B: $i] :
% 3.28/1.79 ( ( A = B )
% 3.28/1.79 => ( subset @ A @ B ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(subsetI2_type,type,
% 3.28/1.79 subsetI2: $o ).
% 3.28/1.79
% 3.28/1.79 thf(subsetI2,definition,
% 3.28/1.79 ( subsetI2
% 3.28/1.79 = ( ! [A: $i,B: $i] :
% 3.28/1.79 ( ! [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ( in @ Xx @ B ) )
% 3.28/1.79 => ( subset @ A @ B ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(emptysetsubset_type,type,
% 3.28/1.79 emptysetsubset: $o ).
% 3.28/1.79
% 3.28/1.79 thf(emptysetsubset,definition,
% 3.28/1.79 ( emptysetsubset
% 3.28/1.79 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(subsetE_type,type,
% 3.28/1.79 subsetE: $o ).
% 3.28/1.79
% 3.28/1.79 thf(subsetE,definition,
% 3.28/1.79 ( subsetE
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ( subset @ A @ B )
% 3.28/1.79 => ( ( in @ Xx @ A )
% 3.28/1.79 => ( in @ Xx @ B ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(subsetE2_type,type,
% 3.28/1.79 subsetE2: $o ).
% 3.28/1.79
% 3.28/1.79 thf(subsetE2,definition,
% 3.28/1.79 ( subsetE2
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ( subset @ A @ B )
% 3.28/1.79 => ( ~ ( in @ Xx @ B )
% 3.28/1.79 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(notsubsetI_type,type,
% 3.28/1.79 notsubsetI: $o ).
% 3.28/1.79
% 3.28/1.79 thf(notsubsetI,definition,
% 3.28/1.79 ( notsubsetI
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ( ~ ( in @ Xx @ B )
% 3.28/1.79 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(notequalI1_type,type,
% 3.28/1.79 notequalI1: $o ).
% 3.28/1.79
% 3.28/1.79 thf(notequalI1,definition,
% 3.28/1.79 ( notequalI1
% 3.28/1.79 = ( ! [A: $i,B: $i] :
% 3.28/1.79 ( ~ ( subset @ A @ B )
% 3.28/1.79 => ( A != B ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(notequalI2_type,type,
% 3.28/1.79 notequalI2: $o ).
% 3.28/1.79
% 3.28/1.79 thf(notequalI2,definition,
% 3.28/1.79 ( notequalI2
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ( ~ ( in @ Xx @ B )
% 3.28/1.79 => ( A != B ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(subsetRefl_type,type,
% 3.28/1.79 subsetRefl: $o ).
% 3.28/1.79
% 3.28/1.79 thf(subsetRefl,definition,
% 3.28/1.79 ( subsetRefl
% 3.28/1.79 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(subsetTrans_type,type,
% 3.28/1.79 subsetTrans: $o ).
% 3.28/1.79
% 3.28/1.79 thf(subsetTrans,definition,
% 3.28/1.79 ( subsetTrans
% 3.28/1.79 = ( ! [A: $i,B: $i,C: $i] :
% 3.28/1.79 ( ( subset @ A @ B )
% 3.28/1.79 => ( ( subset @ B @ C )
% 3.28/1.79 => ( subset @ A @ C ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setadjoinSub_type,type,
% 3.28/1.79 setadjoinSub: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setadjoinSub,definition,
% 3.28/1.79 ( setadjoinSub
% 3.28/1.79 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setadjoinSub2_type,type,
% 3.28/1.79 setadjoinSub2: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setadjoinSub2,definition,
% 3.28/1.79 ( setadjoinSub2
% 3.28/1.79 = ( ! [A: $i,Xx: $i,B: $i] :
% 3.28/1.79 ( ( subset @ A @ B )
% 3.28/1.79 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(subset2powerset_type,type,
% 3.28/1.79 subset2powerset: $o ).
% 3.28/1.79
% 3.28/1.79 thf(subset2powerset,definition,
% 3.28/1.79 ( subset2powerset
% 3.28/1.79 = ( ! [A: $i,B: $i] :
% 3.28/1.79 ( ( subset @ A @ B )
% 3.28/1.79 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setextsub_type,type,
% 3.28/1.79 setextsub: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setextsub,definition,
% 3.28/1.79 ( setextsub
% 3.28/1.79 = ( ! [A: $i,B: $i] :
% 3.28/1.79 ( ( subset @ A @ B )
% 3.28/1.79 => ( ( subset @ B @ A )
% 3.28/1.79 => ( A = B ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(subsetemptysetimpeq_type,type,
% 3.28/1.79 subsetemptysetimpeq: $o ).
% 3.28/1.79
% 3.28/1.79 thf(subsetemptysetimpeq,definition,
% 3.28/1.79 ( subsetemptysetimpeq
% 3.28/1.79 = ( ! [A: $i] :
% 3.28/1.79 ( ( subset @ A @ emptyset )
% 3.28/1.79 => ( A = emptyset ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(powersetI1_type,type,
% 3.28/1.79 powersetI1: $o ).
% 3.28/1.79
% 3.28/1.79 thf(powersetI1,definition,
% 3.28/1.79 ( powersetI1
% 3.28/1.79 = ( ! [A: $i,B: $i] :
% 3.28/1.79 ( ( subset @ B @ A )
% 3.28/1.79 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(powersetE1_type,type,
% 3.28/1.79 powersetE1: $o ).
% 3.28/1.79
% 3.28/1.79 thf(powersetE1,definition,
% 3.28/1.79 ( powersetE1
% 3.28/1.79 = ( ! [A: $i,B: $i] :
% 3.28/1.79 ( ( in @ B @ ( powerset @ A ) )
% 3.28/1.79 => ( subset @ B @ A ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(inPowerset_type,type,
% 3.28/1.79 inPowerset: $o ).
% 3.28/1.79
% 3.28/1.79 thf(inPowerset,definition,
% 3.28/1.79 ( inPowerset
% 3.28/1.79 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(powersetsubset_type,type,
% 3.28/1.79 powersetsubset: $o ).
% 3.28/1.79
% 3.28/1.79 thf(powersetsubset,definition,
% 3.28/1.79 ( powersetsubset
% 3.28/1.79 = ( ! [A: $i,B: $i] :
% 3.28/1.79 ( ( subset @ A @ B )
% 3.28/1.79 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(sepInPowerset_type,type,
% 3.28/1.79 sepInPowerset: $o ).
% 3.28/1.79
% 3.28/1.79 thf(sepInPowerset,definition,
% 3.28/1.79 ( sepInPowerset
% 3.28/1.79 = ( ! [A: $i,Xphi: $i > $o] :
% 3.28/1.79 ( in
% 3.28/1.79 @ ( dsetconstr @ A
% 3.28/1.79 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.28/1.79 @ ( powerset @ A ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(sepSubset_type,type,
% 3.28/1.79 sepSubset: $o ).
% 3.28/1.79
% 3.28/1.79 thf(sepSubset,definition,
% 3.28/1.79 ( sepSubset
% 3.28/1.79 = ( ! [A: $i,Xphi: $i > $o] :
% 3.28/1.79 ( subset
% 3.28/1.79 @ ( dsetconstr @ A
% 3.28/1.79 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.28/1.79 @ A ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(binunion_type,type,
% 3.28/1.79 binunion: $i > $i > $i ).
% 3.28/1.79
% 3.28/1.79 thf(binunionIL_type,type,
% 3.28/1.79 binunionIL: $o ).
% 3.28/1.79
% 3.28/1.79 thf(binunionIL,definition,
% 3.28/1.79 ( binunionIL
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(upairset2IR_type,type,
% 3.28/1.79 upairset2IR: $o ).
% 3.28/1.79
% 3.28/1.79 thf(upairset2IR,definition,
% 3.28/1.79 ( upairset2IR
% 3.28/1.79 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(binunionIR_type,type,
% 3.28/1.79 binunionIR: $o ).
% 3.28/1.79
% 3.28/1.79 thf(binunionIR,definition,
% 3.28/1.79 ( binunionIR
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ B )
% 3.28/1.79 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(binunionEcases_type,type,
% 3.28/1.79 binunionEcases: $o ).
% 3.28/1.79
% 3.28/1.79 thf(binunionEcases,definition,
% 3.28/1.79 ( binunionEcases
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 3.28/1.79 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 3.28/1.79 => ( ( ( in @ Xx @ A )
% 3.28/1.79 => Xphi )
% 3.28/1.79 => ( ( ( in @ Xx @ B )
% 3.28/1.79 => Xphi )
% 3.28/1.79 => Xphi ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(binunionE_type,type,
% 3.28/1.79 binunionE: $o ).
% 3.28/1.79
% 3.28/1.79 thf(binunionE,definition,
% 3.28/1.79 ( binunionE
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 3.28/1.79 => ( ( in @ Xx @ A )
% 3.28/1.79 | ( in @ Xx @ B ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(binunionLsub_type,type,
% 3.28/1.79 binunionLsub: $o ).
% 3.28/1.79
% 3.28/1.79 thf(binunionLsub,definition,
% 3.28/1.79 ( binunionLsub
% 3.28/1.79 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(binunionRsub_type,type,
% 3.28/1.79 binunionRsub: $o ).
% 3.28/1.79
% 3.28/1.79 thf(binunionRsub,definition,
% 3.28/1.79 ( binunionRsub
% 3.28/1.79 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(binintersect_type,type,
% 3.28/1.79 binintersect: $i > $i > $i ).
% 3.28/1.79
% 3.28/1.79 thf(binintersectI_type,type,
% 3.28/1.79 binintersectI: $o ).
% 3.28/1.79
% 3.28/1.79 thf(binintersectI,definition,
% 3.28/1.79 ( binintersectI
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ( ( in @ Xx @ B )
% 3.28/1.79 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(binintersectSubset5_type,type,
% 3.28/1.79 binintersectSubset5: $o ).
% 3.28/1.79
% 3.28/1.79 thf(binintersectSubset5,definition,
% 3.28/1.79 ( binintersectSubset5
% 3.28/1.79 = ( ! [A: $i,B: $i,C: $i] :
% 3.28/1.79 ( ( subset @ C @ A )
% 3.28/1.79 => ( ( subset @ C @ B )
% 3.28/1.79 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(binintersectEL_type,type,
% 3.28/1.79 binintersectEL: $o ).
% 3.28/1.79
% 3.28/1.79 thf(binintersectEL,definition,
% 3.28/1.79 ( binintersectEL
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 3.28/1.79 => ( in @ Xx @ A ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(binintersectLsub_type,type,
% 3.28/1.79 binintersectLsub: $o ).
% 3.28/1.79
% 3.28/1.79 thf(binintersectLsub,definition,
% 3.28/1.79 ( binintersectLsub
% 3.28/1.79 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(binintersectSubset2_type,type,
% 3.28/1.79 binintersectSubset2: $o ).
% 3.28/1.79
% 3.28/1.79 thf(binintersectSubset2,definition,
% 3.28/1.79 ( binintersectSubset2
% 3.28/1.79 = ( ! [A: $i,B: $i] :
% 3.28/1.79 ( ( subset @ A @ B )
% 3.28/1.79 => ( ( binintersect @ A @ B )
% 3.28/1.79 = A ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(binintersectSubset3_type,type,
% 3.28/1.79 binintersectSubset3: $o ).
% 3.28/1.79
% 3.28/1.79 thf(binintersectSubset3,definition,
% 3.28/1.79 ( binintersectSubset3
% 3.28/1.79 = ( ! [A: $i,B: $i] :
% 3.28/1.79 ( ( ( binintersect @ A @ B )
% 3.28/1.79 = B )
% 3.28/1.79 => ( subset @ B @ A ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(binintersectER_type,type,
% 3.28/1.79 binintersectER: $o ).
% 3.28/1.79
% 3.28/1.79 thf(binintersectER,definition,
% 3.28/1.79 ( binintersectER
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 3.28/1.79 => ( in @ Xx @ B ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(disjointsetsI1_type,type,
% 3.28/1.79 disjointsetsI1: $o ).
% 3.28/1.79
% 3.28/1.79 thf(disjointsetsI1,definition,
% 3.28/1.79 ( disjointsetsI1
% 3.28/1.79 = ( ! [A: $i,B: $i] :
% 3.28/1.79 ( ~ ? [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 & ( in @ Xx @ B ) )
% 3.28/1.79 => ( ( binintersect @ A @ B )
% 3.28/1.79 = emptyset ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(binintersectRsub_type,type,
% 3.28/1.79 binintersectRsub: $o ).
% 3.28/1.79
% 3.28/1.79 thf(binintersectRsub,definition,
% 3.28/1.79 ( binintersectRsub
% 3.28/1.79 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(binintersectSubset4_type,type,
% 3.28/1.79 binintersectSubset4: $o ).
% 3.28/1.79
% 3.28/1.79 thf(binintersectSubset4,definition,
% 3.28/1.79 ( binintersectSubset4
% 3.28/1.79 = ( ! [A: $i,B: $i] :
% 3.28/1.79 ( ( subset @ B @ A )
% 3.28/1.79 => ( ( binintersect @ A @ B )
% 3.28/1.79 = B ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(binintersectSubset1_type,type,
% 3.28/1.79 binintersectSubset1: $o ).
% 3.28/1.79
% 3.28/1.79 thf(binintersectSubset1,definition,
% 3.28/1.79 ( binintersectSubset1
% 3.28/1.79 = ( ! [A: $i,B: $i] :
% 3.28/1.79 ( ( ( binintersect @ A @ B )
% 3.28/1.79 = A )
% 3.28/1.79 => ( subset @ A @ B ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(bs114d_type,type,
% 3.28/1.79 bs114d: $o ).
% 3.28/1.79
% 3.28/1.79 thf(bs114d,definition,
% 3.28/1.79 ( bs114d
% 3.28/1.79 = ( ! [A: $i,B: $i,C: $i] :
% 3.28/1.79 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 3.28/1.79 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(regular_type,type,
% 3.28/1.79 regular: $i > $o ).
% 3.28/1.79
% 3.28/1.79 thf(setminus_type,type,
% 3.28/1.79 setminus: $i > $i > $i ).
% 3.28/1.79
% 3.28/1.79 thf(setminusI_type,type,
% 3.28/1.79 setminusI: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setminusI,definition,
% 3.28/1.79 ( setminusI
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ( ~ ( in @ Xx @ B )
% 3.28/1.79 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setminusEL_type,type,
% 3.28/1.79 setminusEL: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setminusEL,definition,
% 3.28/1.79 ( setminusEL
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 3.28/1.79 => ( in @ Xx @ A ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setminusER_type,type,
% 3.28/1.79 setminusER: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setminusER,definition,
% 3.28/1.79 ( setminusER
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 3.28/1.79 => ~ ( in @ Xx @ B ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setminusSubset2_type,type,
% 3.28/1.79 setminusSubset2: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setminusSubset2,definition,
% 3.28/1.79 ( setminusSubset2
% 3.28/1.79 = ( ! [A: $i,B: $i] :
% 3.28/1.79 ( ( subset @ A @ B )
% 3.28/1.79 => ( ( setminus @ A @ B )
% 3.28/1.79 = emptyset ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setminusERneg_type,type,
% 3.28/1.79 setminusERneg: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setminusERneg,definition,
% 3.28/1.79 ( setminusERneg
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 3.28/1.79 => ( ( in @ Xx @ A )
% 3.28/1.79 => ( in @ Xx @ B ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setminusELneg_type,type,
% 3.28/1.79 setminusELneg: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setminusELneg,definition,
% 3.28/1.79 ( setminusELneg
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 3.28/1.79 => ( ~ ( in @ Xx @ B )
% 3.28/1.79 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setminusILneg_type,type,
% 3.28/1.79 setminusILneg: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setminusILneg,definition,
% 3.28/1.79 ( setminusILneg
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ~ ( in @ Xx @ A )
% 3.28/1.79 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setminusIRneg_type,type,
% 3.28/1.79 setminusIRneg: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setminusIRneg,definition,
% 3.28/1.79 ( setminusIRneg
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ B )
% 3.28/1.79 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setminusLsub_type,type,
% 3.28/1.79 setminusLsub: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setminusLsub,definition,
% 3.28/1.79 ( setminusLsub
% 3.28/1.79 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setminusSubset1_type,type,
% 3.28/1.79 setminusSubset1: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setminusSubset1,definition,
% 3.28/1.79 ( setminusSubset1
% 3.28/1.79 = ( ! [A: $i,B: $i] :
% 3.28/1.79 ( ( ( setminus @ A @ B )
% 3.28/1.79 = emptyset )
% 3.28/1.79 => ( subset @ A @ B ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(symdiff_type,type,
% 3.28/1.79 symdiff: $i > $i > $i ).
% 3.28/1.79
% 3.28/1.79 thf(symdiffE_type,type,
% 3.28/1.79 symdiffE: $o ).
% 3.28/1.79
% 3.28/1.79 thf(symdiffE,definition,
% 3.28/1.79 ( symdiffE
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 3.28/1.79 => ! [Xphi: $o] :
% 3.28/1.79 ( ( ( in @ Xx @ A )
% 3.28/1.79 => ( ~ ( in @ Xx @ B )
% 3.28/1.79 => Xphi ) )
% 3.28/1.79 => ( ( ~ ( in @ Xx @ A )
% 3.28/1.79 => ( ( in @ Xx @ B )
% 3.28/1.79 => Xphi ) )
% 3.28/1.79 => Xphi ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(symdiffI1_type,type,
% 3.28/1.79 symdiffI1: $o ).
% 3.28/1.79
% 3.28/1.79 thf(symdiffI1,definition,
% 3.28/1.79 ( symdiffI1
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ( ~ ( in @ Xx @ B )
% 3.28/1.79 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(symdiffI2_type,type,
% 3.28/1.79 symdiffI2: $o ).
% 3.28/1.79
% 3.28/1.79 thf(symdiffI2,definition,
% 3.28/1.79 ( symdiffI2
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ~ ( in @ Xx @ A )
% 3.28/1.79 => ( ( in @ Xx @ B )
% 3.28/1.79 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(symdiffIneg1_type,type,
% 3.28/1.79 symdiffIneg1: $o ).
% 3.28/1.79
% 3.28/1.79 thf(symdiffIneg1,definition,
% 3.28/1.79 ( symdiffIneg1
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ( ( in @ Xx @ B )
% 3.28/1.79 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(symdiffIneg2_type,type,
% 3.28/1.79 symdiffIneg2: $o ).
% 3.28/1.79
% 3.28/1.79 thf(symdiffIneg2,definition,
% 3.28/1.79 ( symdiffIneg2
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ~ ( in @ Xx @ A )
% 3.28/1.79 => ( ~ ( in @ Xx @ B )
% 3.28/1.79 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(iskpair_type,type,
% 3.28/1.79 iskpair: $i > $o ).
% 3.28/1.79
% 3.28/1.79 thf(secondinupair_type,type,
% 3.28/1.79 secondinupair: $o ).
% 3.28/1.79
% 3.28/1.79 thf(secondinupair,definition,
% 3.28/1.79 ( secondinupair
% 3.28/1.79 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setukpairIL_type,type,
% 3.28/1.79 setukpairIL: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setukpairIL,definition,
% 3.28/1.79 ( setukpairIL
% 3.28/1.79 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setukpairIR_type,type,
% 3.28/1.79 setukpairIR: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setukpairIR,definition,
% 3.28/1.79 ( setukpairIR
% 3.28/1.79 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(kpairiskpair_type,type,
% 3.28/1.79 kpairiskpair: $o ).
% 3.28/1.79
% 3.28/1.79 thf(kpairiskpair,definition,
% 3.28/1.79 ( kpairiskpair
% 3.28/1.79 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(kpair_type,type,
% 3.28/1.79 kpair: $i > $i > $i ).
% 3.28/1.79
% 3.28/1.79 thf(kpairp_type,type,
% 3.28/1.79 kpairp: $o ).
% 3.28/1.79
% 3.28/1.79 thf(kpairp,definition,
% 3.28/1.79 ( kpairp
% 3.28/1.79 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(cartprod_type,type,
% 3.28/1.79 cartprod: $i > $i > $i ).
% 3.28/1.79
% 3.28/1.79 thf(singletonsubset_type,type,
% 3.28/1.79 singletonsubset: $o ).
% 3.28/1.79
% 3.28/1.79 thf(singletonsubset,definition,
% 3.28/1.79 ( singletonsubset
% 3.28/1.79 = ( ! [A: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(singletoninpowerset_type,type,
% 3.28/1.79 singletoninpowerset: $o ).
% 3.28/1.79
% 3.28/1.79 thf(singletoninpowerset,definition,
% 3.28/1.79 ( singletoninpowerset
% 3.28/1.79 = ( ! [A: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(singletoninpowunion_type,type,
% 3.28/1.79 singletoninpowunion: $o ).
% 3.28/1.79
% 3.28/1.79 thf(singletoninpowunion,definition,
% 3.28/1.79 ( singletoninpowunion
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(upairset2E_type,type,
% 3.28/1.79 upairset2E: $o ).
% 3.28/1.79
% 3.28/1.79 thf(upairset2E,definition,
% 3.28/1.79 ( upairset2E
% 3.28/1.79 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.28/1.79 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 3.28/1.79 => ( ( Xz = Xx )
% 3.28/1.79 | ( Xz = Xy ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(upairsubunion_type,type,
% 3.28/1.79 upairsubunion: $o ).
% 3.28/1.79
% 3.28/1.79 thf(upairsubunion,definition,
% 3.28/1.79 ( upairsubunion
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ! [Xy: $i] :
% 3.28/1.79 ( ( in @ Xy @ B )
% 3.28/1.79 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(upairinpowunion_type,type,
% 3.28/1.79 upairinpowunion: $o ).
% 3.28/1.79
% 3.28/1.79 thf(upairinpowunion,definition,
% 3.28/1.79 ( upairinpowunion
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ! [Xy: $i] :
% 3.28/1.79 ( ( in @ Xy @ B )
% 3.28/1.79 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(ubforcartprodlem1_type,type,
% 3.28/1.79 ubforcartprodlem1: $o ).
% 3.28/1.79
% 3.28/1.79 thf(ubforcartprodlem1,definition,
% 3.28/1.79 ( ubforcartprodlem1
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ! [Xy: $i] :
% 3.28/1.79 ( ( in @ Xy @ B )
% 3.28/1.79 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(ubforcartprodlem2_type,type,
% 3.28/1.79 ubforcartprodlem2: $o ).
% 3.28/1.79
% 3.28/1.79 thf(ubforcartprodlem2,definition,
% 3.28/1.79 ( ubforcartprodlem2
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ! [Xy: $i] :
% 3.28/1.79 ( ( in @ Xy @ B )
% 3.28/1.79 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(ubforcartprodlem3_type,type,
% 3.28/1.79 ubforcartprodlem3: $o ).
% 3.28/1.79
% 3.28/1.79 thf(ubforcartprodlem3,definition,
% 3.28/1.79 ( ubforcartprodlem3
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ! [Xy: $i] :
% 3.28/1.79 ( ( in @ Xy @ B )
% 3.28/1.79 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(cartprodpairin_type,type,
% 3.28/1.79 cartprodpairin: $o ).
% 3.28/1.79
% 3.28/1.79 thf(cartprodpairin,definition,
% 3.28/1.79 ( cartprodpairin
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ! [Xy: $i] :
% 3.28/1.79 ( ( in @ Xy @ B )
% 3.28/1.79 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(cartprodmempair1_type,type,
% 3.28/1.79 cartprodmempair1: $o ).
% 3.28/1.79
% 3.28/1.79 thf(cartprodmempair1,definition,
% 3.28/1.79 ( cartprodmempair1
% 3.28/1.79 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.28/1.79 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.28/1.79 => ? [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 & ? [Xy: $i] :
% 3.28/1.79 ( ( in @ Xy @ B )
% 3.28/1.79 & ( Xu
% 3.28/1.79 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(cartprodmempair_type,type,
% 3.28/1.79 cartprodmempair: $o ).
% 3.28/1.79
% 3.28/1.79 thf(cartprodmempair,definition,
% 3.28/1.79 ( cartprodmempair
% 3.28/1.79 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.28/1.79 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.28/1.79 => ( iskpair @ Xu ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setunionE2_type,type,
% 3.28/1.79 setunionE2: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setunionE2,definition,
% 3.28/1.79 ( setunionE2
% 3.28/1.79 = ( ! [A: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ ( setunion @ A ) )
% 3.28/1.79 => ? [X: $i] :
% 3.28/1.79 ( ( in @ X @ A )
% 3.28/1.79 & ( in @ Xx @ X ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setunionsingleton1_type,type,
% 3.28/1.79 setunionsingleton1: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setunionsingleton1,definition,
% 3.28/1.79 ( setunionsingleton1
% 3.28/1.79 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setunionsingleton2_type,type,
% 3.28/1.79 setunionsingleton2: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setunionsingleton2,definition,
% 3.28/1.79 ( setunionsingleton2
% 3.28/1.79 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setunionsingleton_type,type,
% 3.28/1.79 setunionsingleton: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setunionsingleton,definition,
% 3.28/1.79 ( setunionsingleton
% 3.28/1.79 = ( ! [Xx: $i] :
% 3.28/1.79 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 3.28/1.79 = Xx ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(singleton_type,type,
% 3.28/1.79 singleton: $i > $o ).
% 3.28/1.79
% 3.28/1.79 thf(singletonprop_type,type,
% 3.28/1.79 singletonprop: $o ).
% 3.28/1.79
% 3.28/1.79 thf(singletonprop,definition,
% 3.28/1.79 ( singletonprop
% 3.28/1.79 = ( ! [A: $i,Xphi: $i > $o] :
% 3.28/1.79 ( ! [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ! [Xy: $i] :
% 3.28/1.79 ( ( in @ Xy @ A )
% 3.28/1.79 => ( ( Xphi @ Xx )
% 3.28/1.79 => ( ( Xphi @ Xy )
% 3.28/1.79 => ( Xx = Xy ) ) ) ) )
% 3.28/1.79 => ( ? [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 & ( Xphi @ Xx ) )
% 3.28/1.79 => ( singleton
% 3.28/1.79 @ ( dsetconstr @ A
% 3.28/1.79 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(ex1_type,type,
% 3.28/1.79 ex1: $i > ( $i > $o ) > $o ).
% 3.28/1.79
% 3.28/1.79 thf(ex1,definition,
% 3.28/1.79 ( ex1
% 3.28/1.79 = ( ^ [A: $i,Xphi: $i > $o] :
% 3.28/1.79 ( singleton
% 3.28/1.79 @ ( dsetconstr @ A
% 3.28/1.79 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(ex1E1_type,type,
% 3.28/1.79 ex1E1: $o ).
% 3.28/1.79
% 3.28/1.79 thf(ex1E1,definition,
% 3.28/1.79 ( ex1E1
% 3.28/1.79 = ( ! [A: $i,Xphi: $i > $o] :
% 3.28/1.79 ( ( ex1 @ A
% 3.28/1.79 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.28/1.79 => ? [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 & ( Xphi @ Xx ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(ex1I_type,type,
% 3.28/1.79 ex1I: $o ).
% 3.28/1.79
% 3.28/1.79 thf(ex1I,definition,
% 3.28/1.79 ( ex1I
% 3.28/1.79 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ( ( Xphi @ Xx )
% 3.28/1.79 => ( ! [Xy: $i] :
% 3.28/1.79 ( ( in @ Xy @ A )
% 3.28/1.79 => ( ( Xphi @ Xy )
% 3.28/1.79 => ( Xy = Xx ) ) )
% 3.28/1.79 => ( ex1 @ A
% 3.28/1.79 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(ex1I2_type,type,
% 3.28/1.79 ex1I2: $o ).
% 3.28/1.79
% 3.28/1.79 thf(ex1I2,definition,
% 3.28/1.79 ( ex1I2
% 3.28/1.79 = ( ! [A: $i,Xphi: $i > $o] :
% 3.28/1.79 ( ! [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ! [Xy: $i] :
% 3.28/1.79 ( ( in @ Xy @ A )
% 3.28/1.79 => ( ( Xphi @ Xx )
% 3.28/1.79 => ( ( Xphi @ Xy )
% 3.28/1.79 => ( Xx = Xy ) ) ) ) )
% 3.28/1.79 => ( ? [Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 & ( Xphi @ Xx ) )
% 3.28/1.79 => ( ex1 @ A
% 3.28/1.79 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(singletonsuniq_type,type,
% 3.28/1.79 singletonsuniq: $o ).
% 3.28/1.79
% 3.28/1.79 thf(singletonsuniq,definition,
% 3.28/1.79 ( singletonsuniq
% 3.28/1.79 = ( ! [Xx: $i,Xy: $i] :
% 3.28/1.79 ( ( ( setadjoin @ Xx @ emptyset )
% 3.28/1.79 = ( setadjoin @ Xy @ emptyset ) )
% 3.28/1.79 => ( Xx = Xy ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(atmost1p_type,type,
% 3.28/1.79 atmost1p: $i > $o ).
% 3.28/1.79
% 3.28/1.79 thf(atleast2p_type,type,
% 3.28/1.79 atleast2p: $i > $o ).
% 3.28/1.79
% 3.28/1.79 thf(atmost2p_type,type,
% 3.28/1.79 atmost2p: $i > $o ).
% 3.28/1.79
% 3.28/1.79 thf(upairsetp_type,type,
% 3.28/1.79 upairsetp: $i > $o ).
% 3.28/1.79
% 3.28/1.79 thf(setukpairinjL1_type,type,
% 3.28/1.79 setukpairinjL1: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setukpairinjL1,definition,
% 3.28/1.79 ( setukpairinjL1
% 3.28/1.79 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.28/1.79 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 3.28/1.79 => ( Xx = Xz ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(kfstsingleton_type,type,
% 3.28/1.79 kfstsingleton: $o ).
% 3.28/1.79
% 3.28/1.79 thf(kfstsingleton,definition,
% 3.28/1.79 ( kfstsingleton
% 3.28/1.79 = ( ! [Xu: $i] :
% 3.28/1.79 ( ( iskpair @ Xu )
% 3.28/1.79 => ( singleton
% 3.28/1.79 @ ( dsetconstr @ ( setunion @ Xu )
% 3.28/1.79 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(theprop_type,type,
% 3.28/1.79 theprop: $o ).
% 3.28/1.79
% 3.28/1.79 thf(theprop,definition,
% 3.28/1.79 ( theprop
% 3.28/1.79 = ( ! [X: $i] :
% 3.28/1.79 ( ( singleton @ X )
% 3.28/1.79 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(kfst_type,type,
% 3.28/1.79 kfst: $i > $i ).
% 3.28/1.79
% 3.28/1.79 thf(kfstpairEq_type,type,
% 3.28/1.79 kfstpairEq: $o ).
% 3.28/1.79
% 3.28/1.79 thf(kfstpairEq,definition,
% 3.28/1.79 ( kfstpairEq
% 3.28/1.79 = ( ! [Xx: $i,Xy: $i] :
% 3.28/1.79 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 3.28/1.79 = Xx ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(cartprodfstin_type,type,
% 3.28/1.79 cartprodfstin: $o ).
% 3.28/1.79
% 3.28/1.79 thf(cartprodfstin,definition,
% 3.28/1.79 ( cartprodfstin
% 3.28/1.79 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.28/1.79 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.28/1.79 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setukpairinjL2_type,type,
% 3.28/1.79 setukpairinjL2: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setukpairinjL2,definition,
% 3.28/1.79 ( setukpairinjL2
% 3.28/1.79 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.28/1.79 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.28/1.79 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.28/1.79 => ( Xx = Xz ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setukpairinjL_type,type,
% 3.28/1.79 setukpairinjL: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setukpairinjL,definition,
% 3.28/1.79 ( setukpairinjL
% 3.28/1.79 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.28/1.79 ( ( ( kpair @ Xx @ Xy )
% 3.28/1.79 = ( kpair @ Xz @ Xu ) )
% 3.28/1.79 => ( Xx = Xz ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setukpairinjR11_type,type,
% 3.28/1.79 setukpairinjR11: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setukpairinjR11,definition,
% 3.28/1.79 ( setukpairinjR11
% 3.28/1.79 = ( ! [Xx: $i,Xy: $i] :
% 3.28/1.79 ( ( Xx = Xy )
% 3.28/1.79 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.28/1.79 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setukpairinjR12_type,type,
% 3.28/1.79 setukpairinjR12: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setukpairinjR12,definition,
% 3.28/1.79 ( setukpairinjR12
% 3.28/1.79 = ( ! [Xx: $i,Xy: $i] :
% 3.28/1.79 ( ( Xx = Xy )
% 3.28/1.79 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.28/1.79 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setukpairinjR1_type,type,
% 3.28/1.79 setukpairinjR1: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setukpairinjR1,definition,
% 3.28/1.79 ( setukpairinjR1
% 3.28/1.79 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.28/1.79 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.28/1.79 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.28/1.79 => ( ( Xz = Xu )
% 3.28/1.79 => ( Xy = Xu ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(upairequniteq_type,type,
% 3.28/1.79 upairequniteq: $o ).
% 3.28/1.79
% 3.28/1.79 thf(upairequniteq,definition,
% 3.28/1.79 ( upairequniteq
% 3.28/1.79 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.28/1.79 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.28/1.79 = ( setadjoin @ Xz @ emptyset ) )
% 3.28/1.79 => ( Xx = Xy ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setukpairinjR2_type,type,
% 3.28/1.79 setukpairinjR2: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setukpairinjR2,definition,
% 3.28/1.79 ( setukpairinjR2
% 3.28/1.79 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.28/1.79 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.28/1.79 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.28/1.79 => ( Xy = Xu ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(setukpairinjR_type,type,
% 3.28/1.79 setukpairinjR: $o ).
% 3.28/1.79
% 3.28/1.79 thf(setukpairinjR,definition,
% 3.28/1.79 ( setukpairinjR
% 3.28/1.79 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.28/1.79 ( ( ( kpair @ Xx @ Xy )
% 3.28/1.79 = ( kpair @ Xz @ Xu ) )
% 3.28/1.79 => ( Xy = Xu ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(ksndsingleton_type,type,
% 3.28/1.79 ksndsingleton: $o ).
% 3.28/1.79
% 3.28/1.79 thf(ksndsingleton,definition,
% 3.28/1.79 ( ksndsingleton
% 3.28/1.79 = ( ! [Xu: $i] :
% 3.28/1.79 ( ( iskpair @ Xu )
% 3.28/1.79 => ( singleton
% 3.28/1.79 @ ( dsetconstr @ ( setunion @ Xu )
% 3.28/1.79 @ ^ [Xx: $i] :
% 3.28/1.79 ( Xu
% 3.28/1.79 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(ksnd_type,type,
% 3.28/1.79 ksnd: $i > $i ).
% 3.28/1.79
% 3.28/1.79 thf(ksndpairEq_type,type,
% 3.28/1.79 ksndpairEq: $o ).
% 3.28/1.79
% 3.28/1.79 thf(ksndpairEq,definition,
% 3.28/1.79 ( ksndpairEq
% 3.28/1.79 = ( ! [Xx: $i,Xy: $i] :
% 3.28/1.79 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 3.28/1.79 = Xy ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(kpairsurjEq_type,type,
% 3.28/1.79 kpairsurjEq: $o ).
% 3.28/1.79
% 3.28/1.79 thf(kpairsurjEq,definition,
% 3.28/1.79 ( kpairsurjEq
% 3.28/1.79 = ( ! [Xu: $i] :
% 3.28/1.79 ( ( iskpair @ Xu )
% 3.28/1.79 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 3.28/1.79 = Xu ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(cartprodsndin_type,type,
% 3.28/1.79 cartprodsndin: $o ).
% 3.28/1.79
% 3.28/1.79 thf(cartprodsndin,definition,
% 3.28/1.79 ( cartprodsndin
% 3.28/1.79 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.28/1.79 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.28/1.79 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(cartprodpairmemEL_type,type,
% 3.28/1.79 cartprodpairmemEL: $o ).
% 3.28/1.79
% 3.28/1.79 thf(cartprodpairmemEL,definition,
% 3.28/1.79 ( cartprodpairmemEL
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 3.28/1.79 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 3.28/1.79 => ( in @ Xx @ A ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(cartprodpairmemER_type,type,
% 3.28/1.79 cartprodpairmemER: $o ).
% 3.28/1.79
% 3.28/1.79 thf(cartprodpairmemER,definition,
% 3.28/1.79 ( cartprodpairmemER
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 3.28/1.79 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 3.28/1.79 => ( in @ Xy @ B ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(cartprodmempaircEq_type,type,
% 3.28/1.79 cartprodmempaircEq: $o ).
% 3.28/1.79
% 3.28/1.79 thf(cartprodmempaircEq,definition,
% 3.28/1.79 ( cartprodmempaircEq
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ! [Xy: $i] :
% 3.28/1.79 ( ( in @ Xy @ B )
% 3.28/1.79 => ( ( kpair @ Xx @ Xy )
% 3.28/1.79 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(cartprodfstpairEq_type,type,
% 3.28/1.79 cartprodfstpairEq: $o ).
% 3.28/1.79
% 3.28/1.79 thf(cartprodfstpairEq,definition,
% 3.28/1.79 ( cartprodfstpairEq
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ! [Xy: $i] :
% 3.28/1.79 ( ( in @ Xy @ B )
% 3.28/1.79 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 3.28/1.79 = Xx ) ) ) ) ) ).
% 3.28/1.79
% 3.28/1.79 thf(cartprodsndpairEq_type,type,
% 3.28/1.79 cartprodsndpairEq: $o ).
% 3.28/1.79
% 3.28/1.79 thf(cartprodsndpairEq,definition,
% 3.28/1.79 ( cartprodsndpairEq
% 3.28/1.79 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.28/1.79 ( ( in @ Xx @ A )
% 3.28/1.79 => ! [Xy: $i] :
% 3.28/1.79 ( ( in @ Xy @ B )
% 3.28/1.79 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 3.28/1.79 = Xy ) ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(cartprodpairsurjEq_type,type,
% 3.28/1.80 cartprodpairsurjEq: $o ).
% 3.28/1.80
% 3.28/1.80 thf(cartprodpairsurjEq,definition,
% 3.28/1.80 ( cartprodpairsurjEq
% 3.28/1.80 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.28/1.80 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.28/1.80 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 3.28/1.80 = Xu ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(breln_type,type,
% 3.28/1.80 breln: $i > $i > $i > $o ).
% 3.28/1.80
% 3.28/1.80 thf(breln,definition,
% 3.28/1.80 ( breln
% 3.28/1.80 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(dpsetconstr_type,type,
% 3.28/1.80 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 3.28/1.80
% 3.28/1.80 thf(dpsetconstrI_type,type,
% 3.28/1.80 dpsetconstrI: $o ).
% 3.28/1.80
% 3.28/1.80 thf(dpsetconstrI,definition,
% 3.28/1.80 ( dpsetconstrI
% 3.28/1.80 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ! [Xy: $i] :
% 3.28/1.80 ( ( in @ Xy @ B )
% 3.28/1.80 => ( ( Xphi @ Xx @ Xy )
% 3.28/1.80 => ( in @ ( kpair @ Xx @ Xy )
% 3.28/1.80 @ ( dpsetconstr @ A @ B
% 3.28/1.80 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(dpsetconstrSub_type,type,
% 3.28/1.80 dpsetconstrSub: $o ).
% 3.28/1.80
% 3.28/1.80 thf(dpsetconstrSub,definition,
% 3.28/1.80 ( dpsetconstrSub
% 3.28/1.80 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.28/1.80 ( subset
% 3.28/1.80 @ ( dpsetconstr @ A @ B
% 3.28/1.80 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 3.28/1.80 @ ( cartprod @ A @ B ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(setOfPairsIsBReln_type,type,
% 3.28/1.80 setOfPairsIsBReln: $o ).
% 3.28/1.80
% 3.28/1.80 thf(setOfPairsIsBReln,definition,
% 3.28/1.80 ( setOfPairsIsBReln
% 3.28/1.80 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.28/1.80 ( breln @ A @ B
% 3.28/1.80 @ ( dpsetconstr @ A @ B
% 3.28/1.80 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(dpsetconstrERa_type,type,
% 3.28/1.80 dpsetconstrERa: $o ).
% 3.28/1.80
% 3.28/1.80 thf(dpsetconstrERa,definition,
% 3.28/1.80 ( dpsetconstrERa
% 3.28/1.80 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ! [Xy: $i] :
% 3.28/1.80 ( ( in @ Xy @ B )
% 3.28/1.80 => ( ( in @ ( kpair @ Xx @ Xy )
% 3.28/1.80 @ ( dpsetconstr @ A @ B
% 3.28/1.80 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.28/1.80 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(dpsetconstrEL1_type,type,
% 3.28/1.80 dpsetconstrEL1: $o ).
% 3.28/1.80
% 3.28/1.80 thf(dpsetconstrEL1,definition,
% 3.28/1.80 ( dpsetconstrEL1
% 3.28/1.80 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.28/1.80 ( ( in @ ( kpair @ Xx @ Xy )
% 3.28/1.80 @ ( dpsetconstr @ A @ B
% 3.28/1.80 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.28/1.80 => ( in @ Xx @ A ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(dpsetconstrEL2_type,type,
% 3.28/1.80 dpsetconstrEL2: $o ).
% 3.28/1.80
% 3.28/1.80 thf(dpsetconstrEL2,definition,
% 3.28/1.80 ( dpsetconstrEL2
% 3.28/1.80 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.28/1.80 ( ( in @ ( kpair @ Xx @ Xy )
% 3.28/1.80 @ ( dpsetconstr @ A @ B
% 3.28/1.80 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.28/1.80 => ( in @ Xy @ B ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(dpsetconstrER_type,type,
% 3.28/1.80 dpsetconstrER: $o ).
% 3.28/1.80
% 3.28/1.80 thf(dpsetconstrER,definition,
% 3.28/1.80 ( dpsetconstrER
% 3.28/1.80 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.28/1.80 ( ( in @ ( kpair @ Xx @ Xy )
% 3.28/1.80 @ ( dpsetconstr @ A @ B
% 3.28/1.80 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.28/1.80 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(func_type,type,
% 3.28/1.80 func: $i > $i > $i > $o ).
% 3.28/1.80
% 3.28/1.80 thf(funcSet_type,type,
% 3.28/1.80 funcSet: $i > $i > $i ).
% 3.28/1.80
% 3.28/1.80 thf(funcImageSingleton_type,type,
% 3.28/1.80 funcImageSingleton: $o ).
% 3.28/1.80
% 3.28/1.80 thf(funcImageSingleton,definition,
% 3.28/1.80 ( funcImageSingleton
% 3.28/1.80 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.28/1.80 ( ( func @ A @ B @ Xf )
% 3.28/1.80 => ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ( singleton
% 3.28/1.80 @ ( dsetconstr @ B
% 3.28/1.80 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(apProp_type,type,
% 3.28/1.80 apProp: $o ).
% 3.28/1.80
% 3.28/1.80 thf(apProp,definition,
% 3.28/1.80 ( apProp
% 3.28/1.80 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.28/1.80 ( ( func @ A @ B @ Xf )
% 3.28/1.80 => ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ( in
% 3.28/1.80 @ ( setunion
% 3.28/1.80 @ ( dsetconstr @ B
% 3.28/1.80 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 3.28/1.80 @ B ) ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(ap_type,type,
% 3.28/1.80 ap: $i > $i > $i > $i > $i ).
% 3.28/1.80
% 3.28/1.80 thf(app_type,type,
% 3.28/1.80 app: $o ).
% 3.28/1.80
% 3.28/1.80 thf(app,definition,
% 3.28/1.80 ( app
% 3.28/1.80 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.28/1.80 ( ( func @ A @ B @ Xf )
% 3.28/1.80 => ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(infuncsetfunc_type,type,
% 3.28/1.80 infuncsetfunc: $o ).
% 3.28/1.80
% 3.28/1.80 thf(infuncsetfunc,definition,
% 3.28/1.80 ( infuncsetfunc
% 3.28/1.80 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.28/1.80 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.28/1.80 => ( func @ A @ B @ Xf ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(ap2p_type,type,
% 3.28/1.80 ap2p: $o ).
% 3.28/1.80
% 3.28/1.80 thf(ap2p,definition,
% 3.28/1.80 ( ap2p
% 3.28/1.80 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.28/1.80 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.28/1.80 => ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(funcinfuncset_type,type,
% 3.28/1.80 funcinfuncset: $o ).
% 3.28/1.80
% 3.28/1.80 thf(funcinfuncset,definition,
% 3.28/1.80 ( funcinfuncset
% 3.28/1.80 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.28/1.80 ( ( func @ A @ B @ Xf )
% 3.28/1.80 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(lamProp_type,type,
% 3.28/1.80 lamProp: $o ).
% 3.28/1.80
% 3.28/1.80 thf(lamProp,definition,
% 3.28/1.80 ( lamProp
% 3.28/1.80 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.28/1.80 ( ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.28/1.80 => ( func @ A @ B
% 3.28/1.80 @ ( dpsetconstr @ A @ B
% 3.28/1.80 @ ^ [Xx: $i,Xy: $i] :
% 3.28/1.80 ( ( Xf @ Xx )
% 3.28/1.80 = Xy ) ) ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(lam_type,type,
% 3.28/1.80 lam: $i > $i > ( $i > $i ) > $i ).
% 3.28/1.80
% 3.28/1.80 thf(lamp_type,type,
% 3.28/1.80 lamp: $o ).
% 3.28/1.80
% 3.28/1.80 thf(lamp,definition,
% 3.28/1.80 ( lamp
% 3.28/1.80 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.28/1.80 ( ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.28/1.80 => ( func @ A @ B
% 3.28/1.80 @ ( lam @ A @ B
% 3.28/1.80 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(lam2p_type,type,
% 3.28/1.80 lam2p: $o ).
% 3.28/1.80
% 3.28/1.80 thf(lam2p,definition,
% 3.28/1.80 ( lam2p
% 3.28/1.80 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.28/1.80 ( ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.28/1.80 => ( in
% 3.28/1.80 @ ( lam @ A @ B
% 3.28/1.80 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 3.28/1.80 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(brelnall1_type,type,
% 3.28/1.80 brelnall1: $o ).
% 3.28/1.80
% 3.28/1.80 thf(brelnall1,definition,
% 3.28/1.80 ( brelnall1
% 3.28/1.80 = ( ! [A: $i,B: $i,R: $i] :
% 3.28/1.80 ( ( breln @ A @ B @ R )
% 3.28/1.80 => ! [Xphi: $i > $o] :
% 3.28/1.80 ( ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ! [Xy: $i] :
% 3.28/1.80 ( ( in @ Xy @ B )
% 3.28/1.80 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.28/1.80 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.28/1.80 => ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ R )
% 3.28/1.80 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(brelnall2_type,type,
% 3.28/1.80 brelnall2: $o ).
% 3.28/1.80
% 3.28/1.80 thf(brelnall2,definition,
% 3.28/1.80 ( brelnall2
% 3.28/1.80 = ( ! [A: $i,B: $i,R: $i] :
% 3.28/1.80 ( ( breln @ A @ B @ R )
% 3.28/1.80 => ! [Xphi: $i > $o] :
% 3.28/1.80 ( ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ! [Xy: $i] :
% 3.28/1.80 ( ( in @ Xy @ B )
% 3.28/1.80 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.28/1.80 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.28/1.80 => ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ R )
% 3.28/1.80 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(ex1E2_type,type,
% 3.28/1.80 ex1E2: $o ).
% 3.28/1.80
% 3.28/1.80 thf(ex1E2,definition,
% 3.28/1.80 ( ex1E2
% 3.28/1.80 = ( ! [A: $i,Xphi: $i > $o] :
% 3.28/1.80 ( ( ex1 @ A
% 3.28/1.80 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.28/1.80 => ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ! [Xy: $i] :
% 3.28/1.80 ( ( in @ Xy @ A )
% 3.28/1.80 => ( ( Xphi @ Xx )
% 3.28/1.80 => ( ( Xphi @ Xy )
% 3.28/1.80 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(funcGraphProp1_type,type,
% 3.28/1.80 funcGraphProp1: $o ).
% 3.28/1.80
% 3.28/1.80 thf(funcGraphProp1,definition,
% 3.28/1.80 ( funcGraphProp1
% 3.28/1.80 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.28/1.80 ( ( func @ A @ B @ Xf )
% 3.28/1.80 => ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(funcGraphProp3_type,type,
% 3.28/1.80 funcGraphProp3: $o ).
% 3.28/1.80
% 3.28/1.80 thf(funcGraphProp3,definition,
% 3.28/1.80 ( funcGraphProp3
% 3.28/1.80 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.28/1.80 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.28/1.80 => ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(funcGraphProp2_type,type,
% 3.28/1.80 funcGraphProp2: $o ).
% 3.28/1.80
% 3.28/1.80 thf(funcGraphProp2,definition,
% 3.28/1.80 ( funcGraphProp2
% 3.28/1.80 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.28/1.80 ( ( func @ A @ B @ Xf )
% 3.28/1.80 => ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ! [Xy: $i] :
% 3.28/1.80 ( ( in @ Xy @ B )
% 3.28/1.80 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 3.28/1.80 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.28/1.80 = Xy ) ) ) ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(funcextLem_type,type,
% 3.28/1.80 funcextLem: $o ).
% 3.28/1.80
% 3.28/1.80 thf(funcextLem,definition,
% 3.28/1.80 ( funcextLem
% 3.28/1.80 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.28/1.80 ( ( func @ A @ B @ Xf )
% 3.28/1.80 => ! [Xg: $i] :
% 3.28/1.80 ( ( func @ A @ B @ Xg )
% 3.28/1.80 => ( ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.28/1.80 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.28/1.80 => ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ! [Xy: $i] :
% 3.28/1.80 ( ( in @ Xy @ B )
% 3.28/1.80 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 3.28/1.80 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(funcGraphProp4_type,type,
% 3.28/1.80 funcGraphProp4: $o ).
% 3.28/1.80
% 3.28/1.80 thf(funcGraphProp4,definition,
% 3.28/1.80 ( funcGraphProp4
% 3.28/1.80 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.28/1.80 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.28/1.80 => ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ! [Xy: $i] :
% 3.28/1.80 ( ( in @ Xy @ B )
% 3.28/1.80 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 3.28/1.80 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.28/1.80 = Xy ) ) ) ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(subbreln_type,type,
% 3.28/1.80 subbreln: $o ).
% 3.28/1.80
% 3.28/1.80 thf(subbreln,definition,
% 3.28/1.80 ( subbreln
% 3.28/1.80 = ( ! [A: $i,B: $i,R: $i] :
% 3.28/1.80 ( ( breln @ A @ B @ R )
% 3.28/1.80 => ! [S: $i] :
% 3.28/1.80 ( ( breln @ A @ B @ S )
% 3.28/1.80 => ( ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ! [Xy: $i] :
% 3.28/1.80 ( ( in @ Xy @ B )
% 3.28/1.80 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.28/1.80 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.28/1.80 => ( subset @ R @ S ) ) ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(eqbreln_type,type,
% 3.28/1.80 eqbreln: $o ).
% 3.28/1.80
% 3.28/1.80 thf(eqbreln,definition,
% 3.28/1.80 ( eqbreln
% 3.28/1.80 = ( ! [A: $i,B: $i,R: $i] :
% 3.28/1.80 ( ( breln @ A @ B @ R )
% 3.28/1.80 => ! [S: $i] :
% 3.28/1.80 ( ( breln @ A @ B @ S )
% 3.28/1.80 => ( ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ! [Xy: $i] :
% 3.28/1.80 ( ( in @ Xy @ B )
% 3.28/1.80 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.28/1.80 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.28/1.80 => ( ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ! [Xy: $i] :
% 3.28/1.80 ( ( in @ Xy @ B )
% 3.28/1.80 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.28/1.80 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 3.28/1.80 => ( R = S ) ) ) ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(funcext_type,type,
% 3.28/1.80 funcext: $o ).
% 3.28/1.80
% 3.28/1.80 thf(funcext,definition,
% 3.28/1.80 ( funcext
% 3.28/1.80 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.28/1.80 ( ( func @ A @ B @ Xf )
% 3.28/1.80 => ! [Xg: $i] :
% 3.28/1.80 ( ( func @ A @ B @ Xg )
% 3.28/1.80 => ( ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.28/1.80 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.28/1.80 => ( Xf = Xg ) ) ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(funcext2_type,type,
% 3.28/1.80 funcext2: $o ).
% 3.28/1.80
% 3.28/1.80 thf(funcext2,definition,
% 3.28/1.80 ( funcext2
% 3.28/1.80 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.28/1.80 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.28/1.80 => ! [Xg: $i] :
% 3.28/1.80 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 3.28/1.80 => ( ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.28/1.80 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.28/1.80 => ( Xf = Xg ) ) ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(ap2apEq1_type,type,
% 3.28/1.80 ap2apEq1: $o ).
% 3.28/1.80
% 3.28/1.80 thf(ap2apEq1,definition,
% 3.28/1.80 ( ap2apEq1
% 3.28/1.80 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.28/1.80 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.28/1.80 => ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.28/1.80 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(ap2apEq2_type,type,
% 3.28/1.80 ap2apEq2: $o ).
% 3.28/1.80
% 3.28/1.80 thf(ap2apEq2,definition,
% 3.28/1.80 ( ap2apEq2
% 3.28/1.80 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.28/1.80 ( ( func @ A @ B @ Xf )
% 3.28/1.80 => ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.28/1.80 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(beta1_type,type,
% 3.28/1.80 beta1: $o ).
% 3.28/1.80
% 3.28/1.80 thf(beta1,definition,
% 3.28/1.80 ( beta1
% 3.28/1.80 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.28/1.80 ( ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.28/1.80 => ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ( ( ap @ A @ B
% 3.28/1.80 @ ( lam @ A @ B
% 3.28/1.80 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 3.28/1.80 @ Xx )
% 3.28/1.80 = ( Xf @ Xx ) ) ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(eta1_type,type,
% 3.28/1.80 eta1: $o ).
% 3.28/1.80
% 3.28/1.80 thf(eta1,definition,
% 3.28/1.80 ( eta1
% 3.28/1.80 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.28/1.80 ( ( func @ A @ B @ Xf )
% 3.28/1.80 => ( ( lam @ A @ B
% 3.28/1.80 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 3.28/1.80 = Xf ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(lam2lamEq_type,type,
% 3.28/1.80 lam2lamEq: $o ).
% 3.28/1.80
% 3.28/1.80 thf(lam2lamEq,definition,
% 3.28/1.80 ( lam2lamEq
% 3.28/1.80 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.28/1.80 ( ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.28/1.80 => ( ( lam @ A @ B
% 3.28/1.80 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 3.28/1.80 = ( lam @ A @ B
% 3.28/1.80 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(beta2_type,type,
% 3.28/1.80 beta2: $o ).
% 3.28/1.80
% 3.28/1.80 thf(beta2,definition,
% 3.28/1.80 ( beta2
% 3.28/1.80 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.28/1.80 ( ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.28/1.80 => ! [Xx: $i] :
% 3.28/1.80 ( ( in @ Xx @ A )
% 3.28/1.80 => ( ( ap @ A @ B
% 3.28/1.80 @ ( lam @ A @ B
% 3.28/1.80 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 3.28/1.80 @ Xx )
% 3.28/1.80 = ( Xf @ Xx ) ) ) ) ) ) ).
% 3.28/1.80
% 3.28/1.80 thf(eta2_type,type,
% 3.28/1.80 eta2: $o ).
% 3.28/1.80
% 3.28/1.80 thf(eta2,definition,
% 3.39/1.80 ( eta2
% 3.39/1.80 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.39/1.80 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.39/1.80 => ( ( lam @ A @ B
% 3.39/1.80 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 3.39/1.80 = Xf ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(iffalseProp1_type,type,
% 3.39/1.80 iffalseProp1: $o ).
% 3.39/1.80
% 3.39/1.80 thf(iffalseProp1,definition,
% 3.39/1.80 ( iffalseProp1
% 3.39/1.80 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ! [Xy: $i] :
% 3.39/1.80 ( ( in @ Xy @ A )
% 3.39/1.80 => ( ~ Xphi
% 3.39/1.80 => ( in @ Xy
% 3.39/1.80 @ ( dsetconstr @ A
% 3.39/1.80 @ ^ [Xz: $i] :
% 3.39/1.80 ( ( Xphi
% 3.39/1.80 & ( Xz = Xx ) )
% 3.39/1.80 | ( ~ Xphi
% 3.39/1.80 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(iffalseProp2_type,type,
% 3.39/1.80 iffalseProp2: $o ).
% 3.39/1.80
% 3.39/1.80 thf(iffalseProp2,definition,
% 3.39/1.80 ( iffalseProp2
% 3.39/1.80 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ! [Xy: $i] :
% 3.39/1.80 ( ( in @ Xy @ A )
% 3.39/1.80 => ( ~ Xphi
% 3.39/1.80 => ( ( dsetconstr @ A
% 3.39/1.80 @ ^ [Xz: $i] :
% 3.39/1.80 ( ( Xphi
% 3.39/1.80 & ( Xz = Xx ) )
% 3.39/1.80 | ( ~ Xphi
% 3.39/1.80 & ( Xz = Xy ) ) ) )
% 3.39/1.80 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(iftrueProp1_type,type,
% 3.39/1.80 iftrueProp1: $o ).
% 3.39/1.80
% 3.39/1.80 thf(iftrueProp1,definition,
% 3.39/1.80 ( iftrueProp1
% 3.39/1.80 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ! [Xy: $i] :
% 3.39/1.80 ( ( in @ Xy @ A )
% 3.39/1.80 => ( Xphi
% 3.39/1.80 => ( in @ Xx
% 3.39/1.80 @ ( dsetconstr @ A
% 3.39/1.80 @ ^ [Xz: $i] :
% 3.39/1.80 ( ( Xphi
% 3.39/1.80 & ( Xz = Xx ) )
% 3.39/1.80 | ( ~ Xphi
% 3.39/1.80 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(iftrueProp2_type,type,
% 3.39/1.80 iftrueProp2: $o ).
% 3.39/1.80
% 3.39/1.80 thf(iftrueProp2,definition,
% 3.39/1.80 ( iftrueProp2
% 3.39/1.80 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ! [Xy: $i] :
% 3.39/1.80 ( ( in @ Xy @ A )
% 3.39/1.80 => ( Xphi
% 3.39/1.80 => ( ( dsetconstr @ A
% 3.39/1.80 @ ^ [Xz: $i] :
% 3.39/1.80 ( ( Xphi
% 3.39/1.80 & ( Xz = Xx ) )
% 3.39/1.80 | ( ~ Xphi
% 3.39/1.80 & ( Xz = Xy ) ) ) )
% 3.39/1.80 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(ifSingleton_type,type,
% 3.39/1.80 ifSingleton: $o ).
% 3.39/1.80
% 3.39/1.80 thf(ifSingleton,definition,
% 3.39/1.80 ( ifSingleton
% 3.39/1.80 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ! [Xy: $i] :
% 3.39/1.80 ( ( in @ Xy @ A )
% 3.39/1.80 => ( singleton
% 3.39/1.80 @ ( dsetconstr @ A
% 3.39/1.80 @ ^ [Xz: $i] :
% 3.39/1.80 ( ( Xphi
% 3.39/1.80 & ( Xz = Xx ) )
% 3.39/1.80 | ( ~ Xphi
% 3.39/1.80 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(if_type,type,
% 3.39/1.80 if: $i > $o > $i > $i > $i ).
% 3.39/1.80
% 3.39/1.80 thf(ifp_type,type,
% 3.39/1.80 ifp: $o ).
% 3.39/1.80
% 3.39/1.80 thf(ifp,definition,
% 3.39/1.80 ( ifp
% 3.39/1.80 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ! [Xy: $i] :
% 3.39/1.80 ( ( in @ Xy @ A )
% 3.39/1.80 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(theeq_type,type,
% 3.39/1.80 theeq: $o ).
% 3.39/1.80
% 3.39/1.80 thf(theeq,definition,
% 3.39/1.80 ( theeq
% 3.39/1.80 = ( ! [X: $i] :
% 3.39/1.80 ( ( singleton @ X )
% 3.39/1.80 => ! [Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ X )
% 3.39/1.80 => ( ( setunion @ X )
% 3.39/1.80 = Xx ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(iftrue_type,type,
% 3.39/1.80 iftrue: $o ).
% 3.39/1.80
% 3.39/1.80 thf(iftrue,definition,
% 3.39/1.80 ( iftrue
% 3.39/1.80 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ! [Xy: $i] :
% 3.39/1.80 ( ( in @ Xy @ A )
% 3.39/1.80 => ( Xphi
% 3.39/1.80 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 3.39/1.80 = Xx ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(iffalse_type,type,
% 3.39/1.80 iffalse: $o ).
% 3.39/1.80
% 3.39/1.80 thf(iffalse,definition,
% 3.39/1.80 ( iffalse
% 3.39/1.80 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ! [Xy: $i] :
% 3.39/1.80 ( ( in @ Xy @ A )
% 3.39/1.80 => ( ~ Xphi
% 3.39/1.80 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 3.39/1.80 = Xy ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(iftrueorfalse_type,type,
% 3.39/1.80 iftrueorfalse: $o ).
% 3.39/1.80
% 3.39/1.80 thf(iftrueorfalse,definition,
% 3.39/1.80 ( iftrueorfalse
% 3.39/1.80 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ! [Xy: $i] :
% 3.39/1.80 ( ( in @ Xy @ A )
% 3.39/1.80 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(binintersectT_lem_type,type,
% 3.39/1.80 binintersectT_lem: $o ).
% 3.39/1.80
% 3.39/1.80 thf(binintersectT_lem,definition,
% 3.39/1.80 ( binintersectT_lem
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ! [Y: $i] :
% 3.39/1.80 ( ( in @ Y @ ( powerset @ A ) )
% 3.39/1.80 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(binunionT_lem_type,type,
% 3.39/1.80 binunionT_lem: $o ).
% 3.39/1.80
% 3.39/1.80 thf(binunionT_lem,definition,
% 3.39/1.80 ( binunionT_lem
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ! [Y: $i] :
% 3.39/1.80 ( ( in @ Y @ ( powerset @ A ) )
% 3.39/1.80 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(powersetT_lem_type,type,
% 3.39/1.80 powersetT_lem: $o ).
% 3.39/1.80
% 3.39/1.80 thf(powersetT_lem,definition,
% 3.39/1.80 ( powersetT_lem
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(setminusT_lem_type,type,
% 3.39/1.80 setminusT_lem: $o ).
% 3.39/1.80
% 3.39/1.80 thf(setminusT_lem,definition,
% 3.39/1.80 ( setminusT_lem
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ! [Y: $i] :
% 3.39/1.80 ( ( in @ Y @ ( powerset @ A ) )
% 3.39/1.80 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(complementT_lem_type,type,
% 3.39/1.80 complementT_lem: $o ).
% 3.39/1.80
% 3.39/1.80 thf(complementT_lem,definition,
% 3.39/1.80 ( complementT_lem
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(setextT_type,type,
% 3.39/1.80 setextT: $o ).
% 3.39/1.80
% 3.39/1.80 thf(setextT,definition,
% 3.39/1.80 ( setextT
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ! [Y: $i] :
% 3.39/1.80 ( ( in @ Y @ ( powerset @ A ) )
% 3.39/1.80 => ( ! [Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ( ( in @ Xx @ X )
% 3.39/1.80 => ( in @ Xx @ Y ) ) )
% 3.39/1.80 => ( ! [Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ( ( in @ Xx @ Y )
% 3.39/1.80 => ( in @ Xx @ X ) ) )
% 3.39/1.80 => ( X = Y ) ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(subsetTI_type,type,
% 3.39/1.80 subsetTI: $o ).
% 3.39/1.80
% 3.39/1.80 thf(subsetTI,definition,
% 3.39/1.80 ( subsetTI
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ! [Y: $i] :
% 3.39/1.80 ( ( in @ Y @ ( powerset @ A ) )
% 3.39/1.80 => ( ! [Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ( ( in @ Xx @ X )
% 3.39/1.80 => ( in @ Xx @ Y ) ) )
% 3.39/1.80 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(powersetTI1_type,type,
% 3.39/1.80 powersetTI1: $o ).
% 3.39/1.80
% 3.39/1.80 thf(powersetTI1,definition,
% 3.39/1.80 ( powersetTI1
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ! [Y: $i] :
% 3.39/1.80 ( ( in @ Y @ ( powerset @ A ) )
% 3.39/1.80 => ( ! [Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ( ( in @ Xx @ X )
% 3.39/1.80 => ( in @ Xx @ Y ) ) )
% 3.39/1.80 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(powersetTE1_type,type,
% 3.39/1.80 powersetTE1: $o ).
% 3.39/1.80
% 3.39/1.80 thf(powersetTE1,definition,
% 3.39/1.80 ( powersetTE1
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ! [Y: $i] :
% 3.39/1.80 ( ( in @ Y @ ( powerset @ A ) )
% 3.39/1.80 => ! [Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ( ( in @ X @ ( powerset @ Y ) )
% 3.39/1.80 => ( ( in @ Xx @ X )
% 3.39/1.80 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(complementTI1_type,type,
% 3.39/1.80 complementTI1: $o ).
% 3.39/1.80
% 3.39/1.80 thf(complementTI1,definition,
% 3.39/1.80 ( complementTI1
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ! [Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ( ( in @ Xx @ X )
% 3.39/1.80 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(complementTE1_type,type,
% 3.39/1.80 complementTE1: $o ).
% 3.39/1.80
% 3.39/1.80 thf(complementTE1,definition,
% 3.39/1.80 ( complementTE1
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ! [Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 3.39/1.80 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(binintersectTELcontra_type,type,
% 3.39/1.80 binintersectTELcontra: $o ).
% 3.39/1.80
% 3.39/1.80 thf(binintersectTELcontra,definition,
% 3.39/1.80 ( binintersectTELcontra
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ! [Y: $i] :
% 3.39/1.80 ( ( in @ Y @ ( powerset @ A ) )
% 3.39/1.80 => ! [Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ( ~ ( in @ Xx @ X )
% 3.39/1.80 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(binintersectTERcontra_type,type,
% 3.39/1.80 binintersectTERcontra: $o ).
% 3.39/1.80
% 3.39/1.80 thf(binintersectTERcontra,definition,
% 3.39/1.80 ( binintersectTERcontra
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ! [Y: $i] :
% 3.39/1.80 ( ( in @ Y @ ( powerset @ A ) )
% 3.39/1.80 => ! [Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ( ~ ( in @ Xx @ Y )
% 3.39/1.80 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(contrasubsetT_type,type,
% 3.39/1.80 contrasubsetT: $o ).
% 3.39/1.80
% 3.39/1.80 thf(contrasubsetT,definition,
% 3.39/1.80 ( contrasubsetT
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ! [Y: $i] :
% 3.39/1.80 ( ( in @ Y @ ( powerset @ A ) )
% 3.39/1.80 => ! [Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.39/1.80 => ( ( in @ Xx @ Y )
% 3.39/1.80 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(contrasubsetT1_type,type,
% 3.39/1.80 contrasubsetT1: $o ).
% 3.39/1.80
% 3.39/1.80 thf(contrasubsetT1,definition,
% 3.39/1.80 ( contrasubsetT1
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ! [Y: $i] :
% 3.39/1.80 ( ( in @ Y @ ( powerset @ A ) )
% 3.39/1.80 => ! [Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ( ( subset @ X @ Y )
% 3.39/1.80 => ( ~ ( in @ Xx @ Y )
% 3.39/1.80 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(contrasubsetT2_type,type,
% 3.39/1.80 contrasubsetT2: $o ).
% 3.39/1.80
% 3.39/1.80 thf(contrasubsetT2,definition,
% 3.39/1.80 ( contrasubsetT2
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ! [Y: $i] :
% 3.39/1.80 ( ( in @ Y @ ( powerset @ A ) )
% 3.39/1.80 => ( ( subset @ X @ Y )
% 3.39/1.80 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(contrasubsetT3_type,type,
% 3.39/1.80 contrasubsetT3: $o ).
% 3.39/1.80
% 3.39/1.80 thf(contrasubsetT3,definition,
% 3.39/1.80 ( contrasubsetT3
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ! [Y: $i] :
% 3.39/1.80 ( ( in @ Y @ ( powerset @ A ) )
% 3.39/1.80 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 3.39/1.80 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(doubleComplementI1_type,type,
% 3.39/1.80 doubleComplementI1: $o ).
% 3.39/1.80
% 3.39/1.80 thf(doubleComplementI1,definition,
% 3.39/1.80 ( doubleComplementI1
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ! [Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ( ( in @ Xx @ X )
% 3.39/1.80 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(doubleComplementE1_type,type,
% 3.39/1.80 doubleComplementE1: $o ).
% 3.39/1.80
% 3.39/1.80 thf(doubleComplementE1,definition,
% 3.39/1.80 ( doubleComplementE1
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ! [Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 3.39/1.80 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(doubleComplementSub1_type,type,
% 3.39/1.80 doubleComplementSub1: $o ).
% 3.39/1.80
% 3.39/1.80 thf(doubleComplementSub1,definition,
% 3.39/1.80 ( doubleComplementSub1
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(doubleComplementSub2_type,type,
% 3.39/1.80 doubleComplementSub2: $o ).
% 3.39/1.80
% 3.39/1.80 thf(doubleComplementSub2,definition,
% 3.39/1.80 ( doubleComplementSub2
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(doubleComplementEq_type,type,
% 3.39/1.80 doubleComplementEq: $o ).
% 3.39/1.80
% 3.39/1.80 thf(doubleComplementEq,definition,
% 3.39/1.80 ( doubleComplementEq
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ( X
% 3.39/1.80 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(complementTnotintersectT_type,type,
% 3.39/1.80 complementTnotintersectT: $o ).
% 3.39/1.80
% 3.39/1.80 thf(complementTnotintersectT,definition,
% 3.39/1.80 ( complementTnotintersectT
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ! [Y: $i] :
% 3.39/1.80 ( ( in @ Y @ ( powerset @ A ) )
% 3.39/1.80 => ! [Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.39/1.80 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(complementImpComplementIntersect_type,type,
% 3.39/1.80 complementImpComplementIntersect: $o ).
% 3.39/1.80
% 3.39/1.80 thf(complementImpComplementIntersect,definition,
% 3.39/1.80 ( complementImpComplementIntersect
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ! [Y: $i] :
% 3.39/1.80 ( ( in @ Y @ ( powerset @ A ) )
% 3.39/1.80 => ! [Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.39/1.80 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(complementSubsetComplementIntersect_type,type,
% 3.39/1.80 complementSubsetComplementIntersect: $o ).
% 3.39/1.80
% 3.39/1.80 thf(complementSubsetComplementIntersect,definition,
% 3.39/1.80 ( complementSubsetComplementIntersect
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ! [Y: $i] :
% 3.39/1.80 ( ( in @ Y @ ( powerset @ A ) )
% 3.39/1.80 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(complementInPowersetComplementIntersect_type,type,
% 3.39/1.80 complementInPowersetComplementIntersect: $o ).
% 3.39/1.80
% 3.39/1.80 thf(complementInPowersetComplementIntersect,definition,
% 3.39/1.80 ( complementInPowersetComplementIntersect
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ! [Y: $i] :
% 3.39/1.80 ( ( in @ Y @ ( powerset @ A ) )
% 3.39/1.80 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(contraSubsetComplement_type,type,
% 3.39/1.80 contraSubsetComplement: $o ).
% 3.39/1.80
% 3.39/1.80 thf(contraSubsetComplement,definition,
% 3.39/1.80 ( contraSubsetComplement
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ! [Y: $i] :
% 3.39/1.80 ( ( in @ Y @ ( powerset @ A ) )
% 3.39/1.80 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.39/1.80 => ! [Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ( ( in @ Xx @ Y )
% 3.39/1.80 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(complementTcontraSubset_type,type,
% 3.39/1.80 complementTcontraSubset: $o ).
% 3.39/1.80
% 3.39/1.80 thf(complementTcontraSubset,definition,
% 3.39/1.80 ( complementTcontraSubset
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ! [Y: $i] :
% 3.39/1.80 ( ( in @ Y @ ( powerset @ A ) )
% 3.39/1.80 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.39/1.80 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(binunionTILcontra_type,type,
% 3.39/1.80 binunionTILcontra: $o ).
% 3.39/1.80
% 3.39/1.80 thf(binunionTILcontra,definition,
% 3.39/1.80 ( binunionTILcontra
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ! [Y: $i] :
% 3.39/1.80 ( ( in @ Y @ ( powerset @ A ) )
% 3.39/1.80 => ! [Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.39/1.80 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(binunionTIRcontra_type,type,
% 3.39/1.80 binunionTIRcontra: $o ).
% 3.39/1.80
% 3.39/1.80 thf(binunionTIRcontra,definition,
% 3.39/1.80 ( binunionTIRcontra
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ! [Y: $i] :
% 3.39/1.80 ( ( in @ Y @ ( powerset @ A ) )
% 3.39/1.80 => ! [Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.39/1.80 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(inIntersectImpInUnion_type,type,
% 3.39/1.80 inIntersectImpInUnion: $o ).
% 3.39/1.80
% 3.39/1.80 thf(inIntersectImpInUnion,definition,
% 3.39/1.80 ( inIntersectImpInUnion
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ! [Y: $i] :
% 3.39/1.80 ( ( in @ Y @ ( powerset @ A ) )
% 3.39/1.80 => ! [Z: $i] :
% 3.39/1.80 ( ( in @ Z @ ( powerset @ A ) )
% 3.39/1.80 => ! [Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.39/1.80 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(inIntersectImpInUnion2_type,type,
% 3.39/1.80 inIntersectImpInUnion2: $o ).
% 3.39/1.80
% 3.39/1.80 thf(inIntersectImpInUnion2,definition,
% 3.39/1.80 ( inIntersectImpInUnion2
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ! [Y: $i] :
% 3.39/1.80 ( ( in @ Y @ ( powerset @ A ) )
% 3.39/1.80 => ! [Z: $i] :
% 3.39/1.80 ( ( in @ Z @ ( powerset @ A ) )
% 3.39/1.80 => ! [Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.39/1.80 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(inIntersectImpInIntersectUnions_type,type,
% 3.39/1.80 inIntersectImpInIntersectUnions: $o ).
% 3.39/1.80
% 3.39/1.80 thf(inIntersectImpInIntersectUnions,definition,
% 3.39/1.80 ( inIntersectImpInIntersectUnions
% 3.39/1.80 = ( ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ! [Y: $i] :
% 3.39/1.80 ( ( in @ Y @ ( powerset @ A ) )
% 3.39/1.80 => ! [Z: $i] :
% 3.39/1.80 ( ( in @ Z @ ( powerset @ A ) )
% 3.39/1.80 => ! [Xx: $i] :
% 3.39/1.80 ( ( in @ Xx @ A )
% 3.39/1.80 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.39/1.80 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(intersectInPowersetIntersectUnions,conjecture,
% 3.39/1.80 ( setextAx
% 3.39/1.80 => ( emptysetAx
% 3.39/1.80 => ( setadjoinAx
% 3.39/1.80 => ( powersetAx
% 3.39/1.80 => ( setunionAx
% 3.39/1.80 => ( omega0Ax
% 3.39/1.80 => ( omegaSAx
% 3.39/1.80 => ( omegaIndAx
% 3.39/1.80 => ( replAx
% 3.39/1.80 => ( foundationAx
% 3.39/1.80 => ( wellorderingAx
% 3.39/1.80 => ( descrp
% 3.39/1.80 => ( dsetconstrI
% 3.39/1.80 => ( dsetconstrEL
% 3.39/1.80 => ( dsetconstrER
% 3.39/1.80 => ( exuE1
% 3.39/1.80 => ( prop2setE
% 3.39/1.80 => ( emptysetE
% 3.39/1.80 => ( emptysetimpfalse
% 3.39/1.80 => ( notinemptyset
% 3.39/1.80 => ( exuE3e
% 3.39/1.80 => ( setext
% 3.39/1.80 => ( emptyI
% 3.39/1.80 => ( noeltsimpempty
% 3.39/1.80 => ( setbeta
% 3.39/1.80 => ( nonemptyE1
% 3.39/1.80 => ( nonemptyI
% 3.39/1.80 => ( nonemptyI1
% 3.39/1.80 => ( setadjoinIL
% 3.39/1.80 => ( emptyinunitempty
% 3.39/1.80 => ( setadjoinIR
% 3.39/1.80 => ( setadjoinE
% 3.39/1.80 => ( setadjoinOr
% 3.39/1.80 => ( setoftrueEq
% 3.39/1.80 => ( powersetI
% 3.39/1.80 => ( emptyinPowerset
% 3.39/1.80 => ( emptyInPowerset
% 3.39/1.80 => ( powersetE
% 3.39/1.80 => ( setunionI
% 3.39/1.80 => ( setunionE
% 3.39/1.80 => ( subPowSU
% 3.39/1.80 => ( exuE2
% 3.39/1.80 => ( nonemptyImpWitness
% 3.39/1.80 => ( uniqinunit
% 3.39/1.80 => ( notinsingleton
% 3.39/1.80 => ( eqinunit
% 3.39/1.80 => ( singletonsswitch
% 3.39/1.80 => ( upairsetE
% 3.39/1.80 => ( upairsetIL
% 3.39/1.80 => ( upairsetIR
% 3.39/1.80 => ( emptyE1
% 3.39/1.80 => ( vacuousDall
% 3.39/1.80 => ( quantDeMorgan1
% 3.39/1.80 => ( quantDeMorgan2
% 3.39/1.80 => ( quantDeMorgan3
% 3.39/1.80 => ( quantDeMorgan4
% 3.39/1.80 => ( prop2setI
% 3.39/1.80 => ( prop2set2propI
% 3.39/1.80 => ( notdexE
% 3.39/1.80 => ( notdallE
% 3.39/1.80 => ( exuI1
% 3.39/1.80 => ( exuI3
% 3.39/1.80 => ( exuI2
% 3.39/1.80 => ( inCongP
% 3.39/1.80 => ( in__Cong
% 3.39/1.80 => ( exuE3u
% 3.39/1.80 => ( exu__Cong
% 3.39/1.80 => ( emptyset__Cong
% 3.39/1.80 => ( setadjoin__Cong
% 3.39/1.80 => ( powerset__Cong
% 3.39/1.80 => ( setunion__Cong
% 3.39/1.80 => ( omega__Cong
% 3.39/1.80 => ( exuEu
% 3.39/1.80 => ( descr__Cong
% 3.39/1.80 => ( dsetconstr__Cong
% 3.39/1.80 => ( subsetI1
% 3.39/1.80 => ( eqimpsubset2
% 3.39/1.80 => ( eqimpsubset1
% 3.39/1.80 => ( subsetI2
% 3.39/1.80 => ( emptysetsubset
% 3.39/1.80 => ( subsetE
% 3.39/1.80 => ( subsetE2
% 3.39/1.80 => ( notsubsetI
% 3.39/1.80 => ( notequalI1
% 3.39/1.80 => ( notequalI2
% 3.39/1.80 => ( subsetRefl
% 3.39/1.80 => ( subsetTrans
% 3.39/1.80 => ( setadjoinSub
% 3.39/1.80 => ( setadjoinSub2
% 3.39/1.80 => ( subset2powerset
% 3.39/1.80 => ( setextsub
% 3.39/1.80 => ( subsetemptysetimpeq
% 3.39/1.80 => ( powersetI1
% 3.39/1.80 => ( powersetE1
% 3.39/1.80 => ( inPowerset
% 3.39/1.80 => ( powersetsubset
% 3.39/1.80 => ( sepInPowerset
% 3.39/1.80 => ( sepSubset
% 3.39/1.80 => ( binunionIL
% 3.39/1.80 => ( upairset2IR
% 3.39/1.80 => ( binunionIR
% 3.39/1.80 => ( binunionEcases
% 3.39/1.80 => ( binunionE
% 3.39/1.80 => ( binunionLsub
% 3.39/1.80 => ( binunionRsub
% 3.39/1.80 => ( binintersectI
% 3.39/1.80 => ( binintersectSubset5
% 3.39/1.80 => ( binintersectEL
% 3.39/1.80 => ( binintersectLsub
% 3.39/1.80 => ( binintersectSubset2
% 3.39/1.80 => ( binintersectSubset3
% 3.39/1.80 => ( binintersectER
% 3.39/1.80 => ( disjointsetsI1
% 3.39/1.80 => ( binintersectRsub
% 3.39/1.80 => ( binintersectSubset4
% 3.39/1.80 => ( binintersectSubset1
% 3.39/1.80 => ( bs114d
% 3.39/1.80 => ( setminusI
% 3.39/1.80 => ( setminusEL
% 3.39/1.80 => ( setminusER
% 3.39/1.80 => ( setminusSubset2
% 3.39/1.80 => ( setminusERneg
% 3.39/1.80 => ( setminusELneg
% 3.39/1.80 => ( setminusILneg
% 3.39/1.80 => ( setminusIRneg
% 3.39/1.80 => ( setminusLsub
% 3.39/1.80 => ( setminusSubset1
% 3.39/1.80 => ( symdiffE
% 3.39/1.80 => ( symdiffI1
% 3.39/1.80 => ( symdiffI2
% 3.39/1.80 => ( symdiffIneg1
% 3.39/1.80 => ( symdiffIneg2
% 3.39/1.80 => ( secondinupair
% 3.39/1.80 => ( setukpairIL
% 3.39/1.80 => ( setukpairIR
% 3.39/1.80 => ( kpairiskpair
% 3.39/1.80 => ( kpairp
% 3.39/1.80 => ( singletonsubset
% 3.39/1.80 => ( singletoninpowerset
% 3.39/1.80 => ( singletoninpowunion
% 3.39/1.80 => ( upairset2E
% 3.39/1.80 => ( upairsubunion
% 3.39/1.80 => ( upairinpowunion
% 3.39/1.80 => ( ubforcartprodlem1
% 3.39/1.80 => ( ubforcartprodlem2
% 3.39/1.80 => ( ubforcartprodlem3
% 3.39/1.80 => ( cartprodpairin
% 3.39/1.80 => ( cartprodmempair1
% 3.39/1.80 => ( cartprodmempair
% 3.39/1.80 => ( setunionE2
% 3.39/1.80 => ( setunionsingleton1
% 3.39/1.80 => ( setunionsingleton2
% 3.39/1.80 => ( setunionsingleton
% 3.39/1.80 => ( singletonprop
% 3.39/1.80 => ( ex1E1
% 3.39/1.80 => ( ex1I
% 3.39/1.80 => ( ex1I2
% 3.39/1.80 => ( singletonsuniq
% 3.39/1.80 => ( setukpairinjL1
% 3.39/1.80 => ( kfstsingleton
% 3.39/1.80 => ( theprop
% 3.39/1.80 => ( kfstpairEq
% 3.39/1.80 => ( cartprodfstin
% 3.39/1.80 => ( setukpairinjL2
% 3.39/1.80 => ( setukpairinjL
% 3.39/1.80 => ( setukpairinjR11
% 3.39/1.80 => ( setukpairinjR12
% 3.39/1.80 => ( setukpairinjR1
% 3.39/1.80 => ( upairequniteq
% 3.39/1.80 => ( setukpairinjR2
% 3.39/1.80 => ( setukpairinjR
% 3.39/1.80 => ( ksndsingleton
% 3.39/1.80 => ( ksndpairEq
% 3.39/1.80 => ( kpairsurjEq
% 3.39/1.80 => ( cartprodsndin
% 3.39/1.80 => ( cartprodpairmemEL
% 3.39/1.80 => ( cartprodpairmemER
% 3.39/1.80 => ( cartprodmempaircEq
% 3.39/1.80 => ( cartprodfstpairEq
% 3.39/1.80 => ( cartprodsndpairEq
% 3.39/1.80 => ( cartprodpairsurjEq
% 3.39/1.80 => ( dpsetconstrI
% 3.39/1.80 => ( dpsetconstrSub
% 3.39/1.80 => ( setOfPairsIsBReln
% 3.39/1.80 => ( dpsetconstrERa
% 3.39/1.80 => ( dpsetconstrEL1
% 3.39/1.80 => ( dpsetconstrEL2
% 3.39/1.80 => ( dpsetconstrER
% 3.39/1.80 => ( funcImageSingleton
% 3.39/1.80 => ( apProp
% 3.39/1.80 => ( app
% 3.39/1.80 => ( infuncsetfunc
% 3.39/1.80 => ( ap2p
% 3.39/1.80 => ( funcinfuncset
% 3.39/1.80 => ( lamProp
% 3.39/1.80 => ( lamp
% 3.39/1.80 => ( lam2p
% 3.39/1.80 => ( brelnall1
% 3.39/1.80 => ( brelnall2
% 3.39/1.80 => ( ex1E2
% 3.39/1.80 => ( funcGraphProp1
% 3.39/1.80 => ( funcGraphProp3
% 3.39/1.80 => ( funcGraphProp2
% 3.39/1.80 => ( funcextLem
% 3.39/1.80 => ( funcGraphProp4
% 3.39/1.80 => ( subbreln
% 3.39/1.80 => ( eqbreln
% 3.39/1.80 => ( funcext
% 3.39/1.80 => ( funcext2
% 3.39/1.80 => ( ap2apEq1
% 3.39/1.80 => ( ap2apEq2
% 3.39/1.80 => ( beta1
% 3.39/1.80 => ( eta1
% 3.39/1.80 => ( lam2lamEq
% 3.39/1.80 => ( beta2
% 3.39/1.80 => ( eta2
% 3.39/1.80 => ( iffalseProp1
% 3.39/1.80 => ( iffalseProp2
% 3.39/1.80 => ( iftrueProp1
% 3.39/1.80 => ( iftrueProp2
% 3.39/1.80 => ( ifSingleton
% 3.39/1.80 => ( ifp
% 3.39/1.80 => ( theeq
% 3.39/1.80 => ( iftrue
% 3.39/1.80 => ( iffalse
% 3.39/1.80 => ( iftrueorfalse
% 3.39/1.80 => ( binintersectT_lem
% 3.39/1.80 => ( binunionT_lem
% 3.39/1.80 => ( powersetT_lem
% 3.39/1.80 => ( setminusT_lem
% 3.39/1.80 => ( complementT_lem
% 3.39/1.80 => ( setextT
% 3.39/1.80 => ( subsetTI
% 3.39/1.80 => ( powersetTI1
% 3.39/1.80 => ( powersetTE1
% 3.39/1.80 => ( complementTI1
% 3.39/1.80 => ( complementTE1
% 3.39/1.80 => ( binintersectTELcontra
% 3.39/1.80 => ( binintersectTERcontra
% 3.39/1.80 => ( contrasubsetT
% 3.39/1.80 => ( contrasubsetT1
% 3.39/1.80 => ( contrasubsetT2
% 3.39/1.80 => ( contrasubsetT3
% 3.39/1.80 => ( doubleComplementI1
% 3.39/1.80 => ( doubleComplementE1
% 3.39/1.80 => ( doubleComplementSub1
% 3.39/1.80 => ( doubleComplementSub2
% 3.39/1.80 => ( doubleComplementEq
% 3.39/1.80 => ( complementTnotintersectT
% 3.39/1.80 => ( complementImpComplementIntersect
% 3.39/1.80 => ( complementSubsetComplementIntersect
% 3.39/1.80 => ( complementInPowersetComplementIntersect
% 3.39/1.80 => ( contraSubsetComplement
% 3.39/1.80 => ( complementTcontraSubset
% 3.39/1.80 => ( binunionTILcontra
% 3.39/1.80 => ( binunionTIRcontra
% 3.39/1.80 => ( inIntersectImpInUnion
% 3.39/1.80 => ( inIntersectImpInUnion2
% 3.39/1.80 => ( inIntersectImpInIntersectUnions
% 3.39/1.80 => ! [A: $i,X: $i] :
% 3.39/1.80 ( ( in @ X @ ( powerset @ A ) )
% 3.39/1.80 => ! [Y: $i] :
% 3.39/1.80 ( ( in @ Y @ ( powerset @ A ) )
% 3.39/1.80 => ! [Z: $i] :
% 3.39/1.80 ( ( in @ Z @ ( powerset @ A ) )
% 3.39/1.80 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.39/1.80 ------------------------
% 3.39/1.84 % (1302)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1199 for (2999ds/2Mi)
% 3.39/1.84 % (1300)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_1199 for (2999ds/4Mi)
% 3.39/1.84 % (1301)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_1199 for (2999ds/27Mi)
% 3.39/1.84 % (1299)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1199 for (2999ds/183Mi)
% 3.39/1.84 % (1303)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_1199 for (2999ds/2Mi)
% 3.39/1.84 % (1304)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_1199 for (2999ds/275Mi)
% 3.39/1.84 % (1305)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1199 for (2999ds/18Mi)
% 3.39/1.84 % (1302)Instruction limit reached!
% 3.39/1.84 % (1302)------------------------------
% 3.39/1.84 % (1302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.84 % (1302)Termination reason: Unknown
% 3.39/1.84 % (1302)Termination phase: shuffling
% 3.39/1.84
% 3.39/1.84 % (1303)Instruction limit reached!
% 3.39/1.84 % (1303)------------------------------
% 3.39/1.84 % (1303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.84 % (1302)Memory used [KB]: 1407
% 3.39/1.84 % (1302)Time elapsed: 0.003 s
% 3.39/1.84 % (1302)Instructions burned: 2 (million)
% 3.39/1.84 % (1302)------------------------------
% 3.39/1.84 % (1302)------------------------------
% 3.39/1.84 % (1303)Termination reason: Unknown
% 3.39/1.84 % (1303)Termination phase: shuffling
% 3.39/1.84
% 3.39/1.84 % (1303)Memory used [KB]: 1407
% 3.39/1.84 % (1303)Time elapsed: 0.003 s
% 3.39/1.84 % (1303)Instructions burned: 2 (million)
% 3.39/1.84 % (1303)------------------------------
% 3.39/1.84 % (1303)------------------------------
% 3.39/1.84 % (1300)Instruction limit reached!
% 3.39/1.84 % (1300)------------------------------
% 3.39/1.84 % (1300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.84 % (1300)Termination reason: Unknown
% 3.39/1.84 % (1300)Termination phase: shuffling
% 3.39/1.84
% 3.39/1.84 % (1300)Memory used [KB]: 1535
% 3.39/1.84 % (1300)Time elapsed: 0.004 s
% 3.39/1.84 % (1300)Instructions burned: 4 (million)
% 3.39/1.84 % (1300)------------------------------
% 3.39/1.84 % (1300)------------------------------
% 3.39/1.85 % (1305)Instruction limit reached!
% 3.39/1.85 % (1305)------------------------------
% 3.39/1.85 % (1305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.85 % (1305)Termination reason: Unknown
% 3.39/1.85 % (1305)Termination phase: shuffling
% 3.39/1.85
% 3.39/1.85 % (1305)Memory used [KB]: 1791
% 3.39/1.85 % (1305)Time elapsed: 0.011 s
% 3.39/1.85 % (1305)Instructions burned: 18 (million)
% 3.39/1.85 % (1305)------------------------------
% 3.39/1.85 % (1305)------------------------------
% 3.39/1.85 % (1301)Instruction limit reached!
% 3.39/1.85 % (1301)------------------------------
% 3.39/1.85 % (1301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.85 % (1301)Termination reason: Unknown
% 3.39/1.85 % (1301)Termination phase: shuffling
% 3.39/1.85
% 3.39/1.85 % (1301)Memory used [KB]: 2046
% 3.39/1.85 % (1301)Time elapsed: 0.015 s
% 3.39/1.85 % (1301)Instructions burned: 28 (million)
% 3.39/1.85 % (1301)------------------------------
% 3.39/1.85 % (1301)------------------------------
% 3.39/1.86 % (1306)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1199 for (2999ds/3Mi)
% 3.39/1.86 % (1307)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_1199 for (2999ds/37Mi)
% 3.39/1.86 % (1308)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_1199 for (2999ds/15Mi)
% 3.39/1.86 % (1306)Instruction limit reached!
% 3.39/1.86 % (1306)------------------------------
% 3.39/1.86 % (1306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.86 % (1306)Termination reason: Unknown
% 3.39/1.86 % (1306)Termination phase: shuffling
% 3.39/1.86
% 3.39/1.86 % (1306)Memory used [KB]: 1407
% 3.39/1.86 % (1306)Time elapsed: 0.003 s
% 3.39/1.86 % (1306)Instructions burned: 3 (million)
% 3.39/1.86 % (1306)------------------------------
% 3.39/1.86 % (1306)------------------------------
% 3.39/1.86 % (1308)Instruction limit reached!
% 3.39/1.86 % (1308)------------------------------
% 3.39/1.86 % (1308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.86 % (1308)Termination reason: Unknown
% 3.39/1.86 % (1308)Termination phase: shuffling
% 3.39/1.86
% 3.39/1.86 % (1308)Memory used [KB]: 1663
% 3.39/1.86 % (1308)Time elapsed: 0.009 s
% 3.39/1.86 % (1308)Instructions burned: 15 (million)
% 3.39/1.86 % (1308)------------------------------
% 3.39/1.86 % (1308)------------------------------
% 3.39/1.86 % (1309)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_1199 for (2999ds/3Mi)
% 3.39/1.87 % (1309)Instruction limit reached!
% 3.39/1.87 % (1309)------------------------------
% 3.39/1.87 % (1309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.87 % (1309)Termination reason: Unknown
% 3.39/1.87 % (1309)Termination phase: shuffling
% 3.39/1.87
% 3.39/1.87 % (1309)Memory used [KB]: 1407
% 3.39/1.87 % (1309)Time elapsed: 0.003 s
% 3.39/1.87 % (1309)Instructions burned: 3 (million)
% 3.39/1.87 % (1309)------------------------------
% 3.39/1.87 % (1309)------------------------------
% 3.39/1.87 % (1310)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_1199 for (2999ds/1041Mi)
% 3.39/1.87 % (1307)Instruction limit reached!
% 3.39/1.87 % (1307)------------------------------
% 3.39/1.87 % (1307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.87 % (1307)Termination reason: Unknown
% 3.39/1.87 % (1307)Termination phase: shuffling
% 3.39/1.87
% 3.39/1.87 % (1307)Memory used [KB]: 2302
% 3.39/1.87 % (1307)Time elapsed: 0.019 s
% 3.39/1.87 % (1307)Instructions burned: 38 (million)
% 3.39/1.87 % (1307)------------------------------
% 3.39/1.87 % (1307)------------------------------
% 3.39/1.87 % (1311)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_1199 for (2999ds/7Mi)
% 3.39/1.88 % (1311)Instruction limit reached!
% 3.39/1.88 % (1311)------------------------------
% 3.39/1.88 % (1311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.88 % (1311)Termination reason: Unknown
% 3.39/1.88 % (1311)Termination phase: shuffling
% 3.39/1.88
% 3.39/1.88 % (1311)Memory used [KB]: 1535
% 3.39/1.88 % (1311)Time elapsed: 0.005 s
% 3.39/1.88 % (1311)Instructions burned: 7 (million)
% 3.39/1.88 % (1311)------------------------------
% 3.39/1.88 % (1311)------------------------------
% 3.39/1.88 % (1312)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_1199 for (2999ds/16Mi)
% 3.39/1.88 % (1313)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_1199 for (2999ds/3Mi)
% 3.39/1.88 % (1313)Instruction limit reached!
% 3.39/1.88 % (1313)------------------------------
% 3.39/1.88 % (1313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.88 % (1313)Termination reason: Unknown
% 3.39/1.88 % (1313)Termination phase: shuffling
% 3.39/1.88
% 3.39/1.88 % (1313)Memory used [KB]: 1407
% 3.39/1.88 % (1313)Time elapsed: 0.003 s
% 3.39/1.88 % (1313)Instructions burned: 3 (million)
% 3.39/1.88 % (1313)------------------------------
% 3.39/1.88 % (1313)------------------------------
% 3.39/1.89 % (1312)Instruction limit reached!
% 3.39/1.89 % (1312)------------------------------
% 3.39/1.89 % (1312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.89 % (1312)Termination reason: Unknown
% 3.39/1.89 % (1312)Termination phase: shuffling
% 3.39/1.89
% 3.39/1.89 % (1312)Memory used [KB]: 1791
% 3.39/1.89 % (1312)Time elapsed: 0.009 s
% 3.39/1.89 % (1312)Instructions burned: 16 (million)
% 3.39/1.89 % (1312)------------------------------
% 3.39/1.89 % (1312)------------------------------
% 3.39/1.89 % (1314)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_1199 for (2999ds/3Mi)
% 3.39/1.89 % (1314)Instruction limit reached!
% 3.39/1.89 % (1314)------------------------------
% 3.39/1.89 % (1314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.89 % (1314)Termination reason: Unknown
% 3.39/1.89 % (1314)Termination phase: shuffling
% 3.39/1.89
% 3.39/1.89 % (1314)Memory used [KB]: 1407
% 3.39/1.89 % (1314)Time elapsed: 0.003 s
% 3.39/1.89 % (1314)Instructions burned: 3 (million)
% 3.39/1.89 % (1314)------------------------------
% 3.39/1.89 % (1314)------------------------------
% 3.39/1.89 % (1315)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_1199 for (2999ds/7Mi)
% 3.39/1.90 % (1315)Instruction limit reached!
% 3.39/1.90 % (1315)------------------------------
% 3.39/1.90 % (1315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.90 % (1315)Termination reason: Unknown
% 3.39/1.90 % (1315)Termination phase: shuffling
% 3.39/1.90
% 3.39/1.90 % (1315)Memory used [KB]: 1535
% 3.39/1.90 % (1315)Time elapsed: 0.005 s
% 3.39/1.90 % (1315)Instructions burned: 8 (million)
% 3.39/1.90 % (1315)------------------------------
% 3.39/1.90 % (1315)------------------------------
% 3.39/1.90 % (1316)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_1199 for (2999ds/3Mi)
% 3.39/1.90 % (1316)Instruction limit reached!
% 3.39/1.90 % (1316)------------------------------
% 3.39/1.90 % (1316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.90 % (1316)Termination reason: Unknown
% 3.39/1.90 % (1316)Termination phase: shuffling
% 3.39/1.90
% 3.39/1.90 % (1316)Memory used [KB]: 1535
% 3.39/1.90 % (1316)Time elapsed: 0.003 s
% 3.39/1.90 % (1316)Instructions burned: 3 (million)
% 3.39/1.90 % (1316)------------------------------
% 3.39/1.90 % (1316)------------------------------
% 3.39/1.90 % (1317)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_1199 for (2999ds/4Mi)
% 3.39/1.91 % (1317)Instruction limit reached!
% 3.39/1.91 % (1317)------------------------------
% 3.39/1.91 % (1317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.91 % (1317)Termination reason: Unknown
% 3.39/1.91 % (1317)Termination phase: shuffling
% 3.39/1.91
% 3.39/1.91 % (1317)Memory used [KB]: 1535
% 3.39/1.91 % (1317)Time elapsed: 0.004 s
% 3.39/1.91 % (1317)Instructions burned: 5 (million)
% 3.39/1.91 % (1317)------------------------------
% 3.39/1.91 % (1317)------------------------------
% 3.39/1.91 % (1318)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_1199 for (2999ds/18Mi)
% 3.39/1.91 % (1319)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_1199 for (2999ds/710Mi)
% 3.39/1.92 % (1318)Instruction limit reached!
% 3.39/1.92 % (1318)------------------------------
% 3.39/1.92 % (1318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.92 % (1318)Termination reason: Unknown
% 3.39/1.92 % (1318)Termination phase: shuffling
% 3.39/1.92
% 3.39/1.92 % (1318)Memory used [KB]: 1791
% 3.39/1.92 % (1318)Time elapsed: 0.010 s
% 3.39/1.92 % (1318)Instructions burned: 18 (million)
% 3.39/1.92 % (1318)------------------------------
% 3.39/1.92 % (1318)------------------------------
% 3.39/1.92 % (1320)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_1199 for (2999ds/6Mi)
% 3.39/1.92 % (1299)Instruction limit reached!
% 3.39/1.92 % (1299)------------------------------
% 3.39/1.92 % (1299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.92 % (1299)Termination reason: Unknown
% 3.39/1.92 % (1299)Termination phase: Saturation
% 3.39/1.92
% 3.39/1.92 % (1299)Memory used [KB]: 7419
% 3.39/1.92 % (1299)Time elapsed: 0.083 s
% 3.39/1.92 % (1299)Instructions burned: 183 (million)
% 3.39/1.92 % (1299)------------------------------
% 3.39/1.92 % (1299)------------------------------
% 3.39/1.92 % (1320)Instruction limit reached!
% 3.39/1.92 % (1320)------------------------------
% 3.39/1.92 % (1320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.92 % (1320)Termination reason: Unknown
% 3.39/1.92 % (1320)Termination phase: shuffling
% 3.39/1.92
% 3.39/1.92 % (1320)Memory used [KB]: 1535
% 3.39/1.92 % (1320)Time elapsed: 0.005 s
% 3.39/1.92 % (1320)Instructions burned: 7 (million)
% 3.39/1.92 % (1320)------------------------------
% 3.39/1.92 % (1320)------------------------------
% 3.39/1.92 % (1321)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_1199 for (2999ds/902Mi)
% 3.39/1.93 % (1322)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_1199 for (2998ds/21Mi)
% 3.39/1.94 % (1323)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_1199 for (2998ds/5Mi)
% 3.39/1.94 % (1324)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_1199 for (2998ds/6Mi)
% 3.39/1.94 % (1323)Instruction limit reached!
% 3.39/1.94 % (1323)------------------------------
% 3.39/1.94 % (1323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.94 % (1323)Termination reason: Unknown
% 3.39/1.94 % (1323)Termination phase: shuffling
% 3.39/1.94
% 3.39/1.94 % (1323)Memory used [KB]: 1535
% 3.39/1.94 % (1323)Time elapsed: 0.004 s
% 3.39/1.94 % (1323)Instructions burned: 5 (million)
% 3.39/1.94 % (1323)------------------------------
% 3.39/1.94 % (1323)------------------------------
% 3.39/1.94 % (1324)Instruction limit reached!
% 3.39/1.94 % (1324)------------------------------
% 3.39/1.94 % (1324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.94 % (1324)Termination reason: Unknown
% 3.39/1.94 % (1324)Termination phase: shuffling
% 3.39/1.94
% 3.39/1.94 % (1324)Memory used [KB]: 1535
% 3.39/1.94 % (1324)Time elapsed: 0.005 s
% 3.39/1.94 % (1324)Instructions burned: 7 (million)
% 3.39/1.94 % (1324)------------------------------
% 3.39/1.94 % (1324)------------------------------
% 3.39/1.94 % (1322)Instruction limit reached!
% 3.39/1.94 % (1322)------------------------------
% 3.39/1.94 % (1322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.94 % (1322)Termination reason: Unknown
% 3.39/1.94 % (1322)Termination phase: shuffling
% 3.39/1.94
% 3.39/1.94 % (1322)Memory used [KB]: 1918
% 3.39/1.94 % (1322)Time elapsed: 0.012 s
% 3.39/1.94 % (1322)Instructions burned: 22 (million)
% 3.39/1.94 % (1322)------------------------------
% 3.39/1.94 % (1322)------------------------------
% 3.39/1.95 % (1325)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_1199 for (2998ds/377Mi)
% 3.39/1.96 % (1326)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_1199 for (2998ds/779Mi)
% 3.39/1.96 % (1327)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_1199 for (2998ds/19Mi)
% 3.39/1.97 % (1327)Instruction limit reached!
% 3.39/1.97 % (1327)------------------------------
% 3.39/1.97 % (1327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.97 % (1327)Termination reason: Unknown
% 3.39/1.97 % (1327)Termination phase: shuffling
% 3.39/1.97
% 3.39/1.97 % (1327)Memory used [KB]: 1791
% 3.39/1.97 % (1327)Time elapsed: 0.010 s
% 3.39/1.97 % (1327)Instructions burned: 19 (million)
% 3.39/1.97 % (1327)------------------------------
% 3.39/1.97 % (1327)------------------------------
% 3.39/1.97 % (1304)Instruction limit reached!
% 3.39/1.97 % (1304)------------------------------
% 3.39/1.97 % (1304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.97 % (1304)Termination reason: Unknown
% 3.39/1.97 % (1304)Termination phase: Saturation
% 3.39/1.97
% 3.39/1.97 % (1304)Memory used [KB]: 9722
% 3.39/1.97 % (1304)Time elapsed: 0.131 s
% 3.39/1.97 % (1304)Instructions burned: 275 (million)
% 3.39/1.97 % (1304)------------------------------
% 3.39/1.97 % (1304)------------------------------
% 3.39/1.98 % (1328)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_1199 for (2998ds/879Mi)
% 3.39/1.98 % (1329)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_1199 for (2998ds/17Mi)
% 3.39/1.99 % (1329)Instruction limit reached!
% 3.39/1.99 % (1329)------------------------------
% 3.39/1.99 % (1329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.99 % (1329)Termination reason: Unknown
% 3.39/1.99 % (1329)Termination phase: shuffling
% 3.39/1.99
% 3.39/1.99 % (1329)Memory used [KB]: 1918
% 3.39/1.99 % (1329)Time elapsed: 0.010 s
% 3.39/1.99 % (1329)Instructions burned: 18 (million)
% 3.39/1.99 % (1329)------------------------------
% 3.39/1.99 % (1329)------------------------------
% 3.39/2.01 % (1330)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_1199 for (2998ds/3Mi)
% 3.39/2.01 % (1330)Instruction limit reached!
% 3.39/2.01 % (1330)------------------------------
% 3.39/2.01 % (1330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/2.01 % (1330)Termination reason: Unknown
% 3.39/2.01 % (1330)Termination phase: shuffling
% 3.39/2.01
% 3.39/2.01 % (1330)Memory used [KB]: 1407
% 3.39/2.01 % (1330)Time elapsed: 0.003 s
% 3.39/2.01 % (1330)Instructions burned: 3 (million)
% 3.39/2.01 % (1330)------------------------------
% 3.39/2.01 % (1330)------------------------------
% 4.70/2.03 % (1331)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_1199 for (2998ds/30Mi)
% 4.70/2.04 % (1331)Instruction limit reached!
% 4.70/2.04 % (1331)------------------------------
% 4.70/2.04 % (1331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.70/2.04 % (1331)Termination reason: Unknown
% 4.70/2.04 % (1331)Termination phase: shuffling
% 4.70/2.04
% 4.70/2.04 % (1331)Memory used [KB]: 2046
% 4.70/2.04 % (1331)Time elapsed: 0.016 s
% 4.70/2.04 % (1331)Instructions burned: 30 (million)
% 4.70/2.04 % (1331)------------------------------
% 4.70/2.04 % (1331)------------------------------
% 4.70/2.06 % (1332)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_1199 for (2997ds/127Mi)
% 4.70/2.11 % (1332)Instruction limit reached!
% 4.70/2.11 % (1332)------------------------------
% 4.70/2.11 % (1332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.70/2.11 % (1332)Termination reason: Unknown
% 4.70/2.11 % (1332)Termination phase: Function definition elimination
% 4.70/2.11
% 4.70/2.11 % (1332)Memory used [KB]: 2686
% 4.70/2.11 % (1332)Time elapsed: 0.057 s
% 4.70/2.11 % (1332)Instructions burned: 128 (million)
% 4.70/2.11 % (1332)------------------------------
% 4.70/2.11 % (1332)------------------------------
% 4.70/2.13 % (1325)Instruction limit reached!
% 4.70/2.13 % (1325)------------------------------
% 4.70/2.13 % (1325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.70/2.13 % (1325)Termination reason: Unknown
% 4.70/2.13 % (1325)Termination phase: Saturation
% 4.70/2.13
% 4.70/2.13 % (1325)Memory used [KB]: 9338
% 4.70/2.13 % (1325)Time elapsed: 0.173 s
% 4.70/2.13 % (1325)Instructions burned: 377 (million)
% 4.70/2.13 % (1325)------------------------------
% 4.70/2.13 % (1325)------------------------------
% 5.28/2.13 % (1333)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_1199 for (2996ds/100Mi)
% 5.28/2.14 % (1334)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_1199 for (2996ds/3Mi)
% 5.28/2.14 % (1334)Instruction limit reached!
% 5.28/2.14 % (1334)------------------------------
% 5.28/2.14 % (1334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.28/2.14 % (1334)Termination reason: Unknown
% 5.28/2.14 % (1334)Termination phase: shuffling
% 5.28/2.14
% 5.28/2.14 % (1334)Memory used [KB]: 1535
% 5.28/2.14 % (1334)Time elapsed: 0.003 s
% 5.28/2.14 % (1334)Instructions burned: 3 (million)
% 5.28/2.14 % (1334)------------------------------
% 5.28/2.14 % (1334)------------------------------
% 5.28/2.16 % (1335)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_1199 for (2996ds/20Mi)
% 5.28/2.17 % (1335)Instruction limit reached!
% 5.28/2.17 % (1335)------------------------------
% 5.28/2.17 % (1335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.28/2.17 % (1335)Termination reason: Unknown
% 5.28/2.17 % (1335)Termination phase: shuffling
% 5.28/2.17
% 5.28/2.17 % (1335)Memory used [KB]: 1918
% 5.28/2.17 % (1335)Time elapsed: 0.011 s
% 5.28/2.17 % (1335)Instructions burned: 20 (million)
% 5.28/2.17 % (1335)------------------------------
% 5.28/2.17 % (1335)------------------------------
% 5.28/2.17 % (1333)Instruction limit reached!
% 5.28/2.17 % (1333)------------------------------
% 5.28/2.17 % (1333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.28/2.17 % (1333)Termination reason: Unknown
% 5.28/2.17 % (1333)Termination phase: Property scanning
% 5.28/2.17
% 5.28/2.17 % (1333)Memory used [KB]: 2558
% 5.28/2.17 % (1333)Time elapsed: 0.046 s
% 5.28/2.17 % (1333)Instructions burned: 101 (million)
% 5.28/2.17 % (1333)------------------------------
% 5.28/2.17 % (1333)------------------------------
% 5.28/2.19 % (1336)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_1199 for (2996ds/86Mi)
% 5.28/2.19 % (1337)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_1199 for (2996ds/107Mi)
% 5.92/2.23 % (1336)Instruction limit reached!
% 5.92/2.23 % (1336)------------------------------
% 5.92/2.23 % (1336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.23 % (1336)Termination reason: Unknown
% 5.92/2.23 % (1336)Termination phase: Property scanning
% 5.92/2.23
% 5.92/2.23 % (1336)Memory used [KB]: 2558
% 5.92/2.23 % (1336)Time elapsed: 0.042 s
% 5.92/2.23 % (1336)Instructions burned: 87 (million)
% 5.92/2.23 % (1336)------------------------------
% 5.92/2.23 % (1336)------------------------------
% 5.92/2.24 % (1337)Instruction limit reached!
% 5.92/2.24 % (1337)------------------------------
% 5.92/2.24 % (1337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.24 % (1337)Termination reason: Unknown
% 5.92/2.24 % (1337)Termination phase: Property scanning
% 5.92/2.24
% 5.92/2.24 % (1337)Memory used [KB]: 2558
% 5.92/2.24 % (1337)Time elapsed: 0.048 s
% 5.92/2.24 % (1337)Instructions burned: 107 (million)
% 5.92/2.24 % (1337)------------------------------
% 5.92/2.24 % (1337)------------------------------
% 5.92/2.24 % (1338)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_1199 for (2995ds/39Mi)
% 5.92/2.25 % (1326)Instruction limit reached!
% 5.92/2.25 % (1326)------------------------------
% 5.92/2.25 % (1326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.25 % (1326)Termination reason: Unknown
% 5.92/2.25 % (1326)Termination phase: Saturation
% 5.92/2.25
% 5.92/2.25 % (1326)Memory used [KB]: 7547
% 5.92/2.25 % (1326)Time elapsed: 0.299 s
% 5.92/2.25 % (1326)Instructions burned: 780 (million)
% 5.92/2.25 % (1326)------------------------------
% 5.92/2.25 % (1326)------------------------------
% 5.92/2.25 % (1339)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_1199 for (2995ds/448Mi)
% 5.92/2.26 % (1338)Instruction limit reached!
% 5.92/2.26 % (1338)------------------------------
% 5.92/2.26 % (1338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.26 % (1338)Termination reason: Unknown
% 5.92/2.26 % (1338)Termination phase: shuffling
% 5.92/2.26
% 5.92/2.26 % (1338)Memory used [KB]: 2302
% 5.92/2.26 % (1338)Time elapsed: 0.020 s
% 5.92/2.26 % (1338)Instructions burned: 40 (million)
% 5.92/2.26 % (1338)------------------------------
% 5.92/2.26 % (1338)------------------------------
% 5.92/2.27 % (1319)Instruction limit reached!
% 5.92/2.27 % (1319)------------------------------
% 5.92/2.27 % (1319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.27 % (1319)Termination reason: Unknown
% 5.92/2.27 % (1319)Termination phase: Saturation
% 5.92/2.27
% 5.92/2.27 % (1319)Memory used [KB]: 10618
% 5.92/2.27 % (1319)Time elapsed: 0.356 s
% 5.92/2.27 % (1319)Instructions burned: 710 (million)
% 5.92/2.27 % (1319)------------------------------
% 5.92/2.27 % (1319)------------------------------
% 5.92/2.27 % (1310)Instruction limit reached!
% 5.92/2.27 % (1310)------------------------------
% 5.92/2.27 % (1310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.27 % (1310)Termination reason: Unknown
% 5.92/2.27 % (1310)Termination phase: Saturation
% 5.92/2.27
% 5.92/2.27 % (1310)Memory used [KB]: 15223
% 5.92/2.27 % (1310)Time elapsed: 0.401 s
% 5.92/2.27 % (1310)Instructions burned: 1042 (million)
% 5.92/2.27 % (1310)------------------------------
% 5.92/2.27 % (1310)------------------------------
% 5.92/2.27 % (1340)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_1199 for (2995ds/46Mi)
% 5.92/2.28 % (1341)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_1199 for (2995ds/98Mi)
% 5.92/2.28 % (1342)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_1199 for (2995ds/507Mi)
% 5.92/2.28 % (1343)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_1199 for (2995ds/149Mi)
% 5.92/2.29 % (1340)Instruction limit reached!
% 5.92/2.29 % (1340)------------------------------
% 5.92/2.29 % (1340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.29 % (1340)Termination reason: Unknown
% 5.92/2.29 % (1340)Termination phase: shuffling
% 5.92/2.29
% 5.92/2.29 % (1340)Memory used [KB]: 2430
% 5.92/2.29 % (1340)Time elapsed: 0.024 s
% 5.92/2.29 % (1340)Instructions burned: 47 (million)
% 5.92/2.29 % (1340)------------------------------
% 5.92/2.29 % (1340)------------------------------
% 6.54/2.31 % (1344)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_1199 for (2995ds/39Mi)
% 6.54/2.32 % (1341)Instruction limit reached!
% 6.54/2.32 % (1341)------------------------------
% 6.54/2.32 % (1341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.32 % (1341)Termination reason: Unknown
% 6.54/2.32 % (1341)Termination phase: Property scanning
% 6.54/2.32
% 6.54/2.32 % (1341)Memory used [KB]: 2430
% 6.54/2.32 % (1341)Time elapsed: 0.045 s
% 6.54/2.32 % (1341)Instructions burned: 98 (million)
% 6.54/2.32 % (1341)------------------------------
% 6.54/2.32 % (1341)------------------------------
% 6.54/2.33 % (1344)Instruction limit reached!
% 6.54/2.33 % (1344)------------------------------
% 6.54/2.33 % (1344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.33 % (1344)Termination reason: Unknown
% 6.54/2.33 % (1344)Termination phase: shuffling
% 6.54/2.33
% 6.54/2.33 % (1344)Memory used [KB]: 2302
% 6.54/2.33 % (1344)Time elapsed: 0.020 s
% 6.54/2.33 % (1344)Instructions burned: 40 (million)
% 6.54/2.33 % (1344)------------------------------
% 6.54/2.33 % (1344)------------------------------
% 6.54/2.34 % (1345)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_1199 for (2994ds/6Mi)
% 6.54/2.34 % (1345)Instruction limit reached!
% 6.54/2.34 % (1345)------------------------------
% 6.54/2.34 % (1345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.34 % (1345)Termination reason: Unknown
% 6.54/2.34 % (1345)Termination phase: shuffling
% 6.54/2.34
% 6.54/2.34 % (1345)Memory used [KB]: 1535
% 6.54/2.34 % (1345)Time elapsed: 0.005 s
% 6.54/2.34 % (1345)Instructions burned: 7 (million)
% 6.54/2.34 % (1345)------------------------------
% 6.54/2.34 % (1345)------------------------------
% 6.54/2.34 % (1346)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_1199 for (2994ds/1087Mi)
% 6.54/2.35 % (1343)Instruction limit reached!
% 6.54/2.35 % (1343)------------------------------
% 6.54/2.35 % (1343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.35 % (1343)Termination reason: Unknown
% 6.54/2.35 % (1343)Termination phase: Property scanning
% 6.54/2.35
% 6.54/2.35 % (1343)Memory used [KB]: 3454
% 6.54/2.35 % (1343)Time elapsed: 0.068 s
% 6.54/2.35 % (1343)Instructions burned: 149 (million)
% 6.54/2.35 % (1343)------------------------------
% 6.54/2.35 % (1343)------------------------------
% 6.54/2.36 % (1321)Instruction limit reached!
% 6.54/2.36 % (1321)------------------------------
% 6.54/2.36 % (1321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.36 % (1321)Termination reason: Unknown
% 6.54/2.36 % (1321)Termination phase: Saturation
% 6.54/2.36
% 6.54/2.36 % (1321)Memory used [KB]: 12537
% 6.54/2.36 % (1321)Time elapsed: 0.434 s
% 6.54/2.36 % (1321)Instructions burned: 903 (million)
% 6.54/2.36 % (1321)------------------------------
% 6.54/2.36 % (1321)------------------------------
% 6.54/2.36 % (1347)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_1199 for (2994ds/47Mi)
% 6.54/2.37 % (1348)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_1199 for (2994ds/44Mi)
% 6.54/2.37 % (1349)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_1199 for (2994ds/432Mi)
% 6.54/2.38 % (1347)Instruction limit reached!
% 6.54/2.38 % (1347)------------------------------
% 6.54/2.38 % (1347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.38 % (1347)Termination reason: Unknown
% 6.54/2.38 % (1347)Termination phase: shuffling
% 6.54/2.38
% 6.54/2.38 % (1347)Memory used [KB]: 2430
% 6.54/2.38 % (1347)Time elapsed: 0.023 s
% 6.54/2.38 % (1347)Instructions burned: 47 (million)
% 6.54/2.38 % (1347)------------------------------
% 6.54/2.38 % (1347)------------------------------
% 6.54/2.39 % (1348)Instruction limit reached!
% 6.54/2.39 % (1348)------------------------------
% 6.54/2.39 % (1348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.39 % (1348)Termination reason: Unknown
% 6.54/2.39 % (1348)Termination phase: shuffling
% 6.54/2.39
% 6.54/2.39 % (1348)Memory used [KB]: 2302
% 6.54/2.39 % (1348)Time elapsed: 0.022 s
% 6.54/2.39 % (1348)Instructions burned: 45 (million)
% 6.54/2.39 % (1348)------------------------------
% 6.54/2.39 % (1348)------------------------------
% 6.54/2.39 % (1350)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_1199 for (2994ds/62Mi)
% 6.98/2.40 % (1351)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_1199 for (2994ds/31Mi)
% 6.98/2.41 % (1328)Instruction limit reached!
% 6.98/2.41 % (1328)------------------------------
% 6.98/2.41 % (1328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.98/2.41 % (1328)Termination reason: Unknown
% 6.98/2.41 % (1328)Termination phase: Saturation
% 6.98/2.41
% 6.98/2.41 % (1328)Memory used [KB]: 9850
% 6.98/2.41 % (1328)Time elapsed: 0.427 s
% 6.98/2.41 % (1328)Instructions burned: 879 (million)
% 6.98/2.41 % (1328)------------------------------
% 6.98/2.41 % (1328)------------------------------
% 6.98/2.42 % (1351)Instruction limit reached!
% 6.98/2.42 % (1351)------------------------------
% 6.98/2.42 % (1351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.98/2.42 % (1351)Termination reason: Unknown
% 6.98/2.42 % (1351)Termination phase: shuffling
% 6.98/2.42
% 6.98/2.42 % (1351)Memory used [KB]: 2046
% 6.98/2.42 % (1351)Time elapsed: 0.016 s
% 6.98/2.42 % (1351)Instructions burned: 31 (million)
% 6.98/2.42 % (1351)------------------------------
% 6.98/2.42 % (1351)------------------------------
% 6.98/2.42 % (1350)Instruction limit reached!
% 6.98/2.42 % (1350)------------------------------
% 6.98/2.42 % (1350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.98/2.42 % (1350)Termination reason: Unknown
% 6.98/2.42 % (1350)Termination phase: Property scanning
% 6.98/2.42
% 6.98/2.42 % (1350)Memory used [KB]: 2430
% 6.98/2.42 % (1350)Time elapsed: 0.030 s
% 6.98/2.42 % (1350)Instructions burned: 62 (million)
% 6.98/2.42 % (1350)------------------------------
% 6.98/2.42 % (1350)------------------------------
% 6.98/2.43 % (1352)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_1199 for (2993ds/96Mi)
% 6.98/2.43 % (1339)Instruction limit reached!
% 6.98/2.43 % (1339)------------------------------
% 6.98/2.43 % (1339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.98/2.43 % (1339)Termination reason: Unknown
% 6.98/2.43 % (1339)Termination phase: Saturation
% 6.98/2.43
% 6.98/2.43 % (1339)Memory used [KB]: 7419
% 6.98/2.43 % (1339)Time elapsed: 0.182 s
% 6.98/2.43 % (1339)Instructions burned: 448 (million)
% 6.98/2.43 % (1339)------------------------------
% 6.98/2.43 % (1339)------------------------------
% 6.98/2.43 % (1353)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_1199 for (2993ds/453Mi)
% 6.98/2.44 % (1354)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_1199 for (2993ds/71Mi)
% 6.98/2.45 % (1355)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_1199 for (2993ds/83Mi)
% 6.98/2.47 % (1352)Instruction limit reached!
% 6.98/2.47 % (1352)------------------------------
% 6.98/2.47 % (1352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.98/2.47 % (1352)Termination reason: Unknown
% 6.98/2.47 % (1352)Termination phase: Property scanning
% 6.98/2.47
% 6.98/2.47 % (1352)Memory used [KB]: 2558
% 6.98/2.47 % (1352)Time elapsed: 0.045 s
% 6.98/2.47 % (1352)Instructions burned: 96 (million)
% 6.98/2.47 % (1352)------------------------------
% 6.98/2.47 % (1352)------------------------------
% 6.98/2.47 % (1354)Instruction limit reached!
% 6.98/2.47 % (1354)------------------------------
% 6.98/2.47 % (1354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.98/2.47 % (1354)Termination reason: Unknown
% 6.98/2.47 % (1354)Termination phase: Property scanning
% 6.98/2.47
% 6.98/2.47 % (1354)Memory used [KB]: 2430
% 6.98/2.47 % (1354)Time elapsed: 0.034 s
% 6.98/2.47 % (1354)Instructions burned: 72 (million)
% 6.98/2.47 % (1354)------------------------------
% 6.98/2.47 % (1354)------------------------------
% 6.98/2.49 % (1356)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_1199 for (2993ds/11Mi)
% 6.98/2.49 % (1357)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_1199 for (2993ds/41Mi)
% 6.98/2.49 % (1355)Instruction limit reached!
% 6.98/2.49 % (1355)------------------------------
% 6.98/2.49 % (1355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.98/2.49 % (1355)Termination reason: Unknown
% 6.98/2.49 % (1355)Termination phase: SInE selection
% 6.98/2.49
% 6.98/2.49 % (1355)Memory used [KB]: 2430
% 6.98/2.49 % (1355)Time elapsed: 0.039 s
% 6.98/2.49 % (1355)Instructions burned: 85 (million)
% 6.98/2.49 % (1355)------------------------------
% 6.98/2.49 % (1355)------------------------------
% 6.98/2.49 % (1356)Instruction limit reached!
% 6.98/2.49 % (1356)------------------------------
% 6.98/2.49 % (1356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.98/2.49 % (1356)Termination reason: Unknown
% 6.98/2.49 % (1356)Termination phase: shuffling
% 6.98/2.49
% 6.98/2.49 % (1356)Memory used [KB]: 1663
% 6.98/2.49 % (1356)Time elapsed: 0.007 s
% 6.98/2.49 % (1356)Instructions burned: 11 (million)
% 6.98/2.49 % (1356)------------------------------
% 6.98/2.49 % (1356)------------------------------
% 7.46/2.50 % (1358)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_1199 for (2993ds/6Mi)
% 7.46/2.51 % (1357)Instruction limit reached!
% 7.46/2.51 % (1357)------------------------------
% 7.46/2.51 % (1357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.46/2.51 % (1357)Termination reason: Unknown
% 7.46/2.51 % (1357)Termination phase: shuffling
% 7.46/2.51
% 7.46/2.51 % (1357)Memory used [KB]: 2302
% 7.46/2.51 % (1357)Time elapsed: 0.020 s
% 7.46/2.51 % (1357)Instructions burned: 41 (million)
% 7.46/2.51 % (1357)------------------------------
% 7.46/2.51 % (1357)------------------------------
% 7.46/2.51 % (1359)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_1199 for (2993ds/150Mi)
% 7.46/2.51 % (1358)Instruction limit reached!
% 7.46/2.51 % (1358)------------------------------
% 7.46/2.51 % (1358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.46/2.51 % (1358)Termination reason: Unknown
% 7.46/2.51 % (1358)Termination phase: shuffling
% 7.46/2.51
% 7.46/2.51 % (1358)Memory used [KB]: 1535
% 7.46/2.51 % (1358)Time elapsed: 0.005 s
% 7.46/2.51 % (1358)Instructions burned: 7 (million)
% 7.46/2.51 % (1358)------------------------------
% 7.46/2.51 % (1358)------------------------------
% 7.46/2.52 % (1360)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_1199 for (2993ds/343Mi)
% 7.46/2.52 % (1342)Instruction limit reached!
% 7.46/2.52 % (1342)------------------------------
% 7.46/2.52 % (1342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.46/2.52 % (1342)Termination reason: Unknown
% 7.46/2.52 % (1342)Termination phase: Saturation
% 7.46/2.52
% 7.46/2.52 % (1342)Memory used [KB]: 8059
% 7.46/2.52 % (1342)Time elapsed: 0.240 s
% 7.46/2.52 % (1342)Instructions burned: 507 (million)
% 7.46/2.52 % (1342)------------------------------
% 7.46/2.52 % (1342)------------------------------
% 7.46/2.52 % (1361)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_1199 for (2993ds/109Mi)
% 7.46/2.54 % (1362)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_1199 for (2992ds/253Mi)
% 7.46/2.55 % (1349)Instruction limit reached!
% 7.46/2.55 % (1349)------------------------------
% 7.46/2.55 % (1349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.46/2.55 % (1349)Termination reason: Unknown
% 7.46/2.55 % (1349)Termination phase: Saturation
% 7.46/2.55
% 7.46/2.55 % (1349)Memory used [KB]: 2942
% 7.46/2.55 % (1349)Time elapsed: 0.178 s
% 7.46/2.55 % (1349)Instructions burned: 432 (million)
% 7.46/2.55 % (1349)------------------------------
% 7.46/2.55 % (1349)------------------------------
% 7.46/2.57 % (1363)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_1199 for (2992ds/140Mi)
% 7.46/2.57 % (1361)Instruction limit reached!
% 7.46/2.57 % (1361)------------------------------
% 7.46/2.57 % (1361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.46/2.57 % (1361)Termination reason: Unknown
% 7.46/2.57 % (1361)Termination phase: Property scanning
% 7.46/2.57
% 7.46/2.57 % (1361)Memory used [KB]: 2558
% 7.46/2.57 % (1361)Time elapsed: 0.049 s
% 7.46/2.57 % (1361)Instructions burned: 110 (million)
% 7.46/2.57 % (1361)------------------------------
% 7.46/2.57 % (1361)------------------------------
% 7.46/2.58 % (1359)Instruction limit reached!
% 7.46/2.58 % (1359)------------------------------
% 7.46/2.58 % (1359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.46/2.58 % (1359)Termination reason: Unknown
% 7.46/2.58 % (1359)Termination phase: Function definition elimination
% 7.46/2.58
% 7.46/2.58 % (1359)Memory used [KB]: 4477
% 7.46/2.58 % (1359)Time elapsed: 0.072 s
% 7.46/2.58 % (1359)Instructions burned: 151 (million)
% 7.46/2.58 % (1359)------------------------------
% 7.46/2.58 % (1359)------------------------------
% 7.46/2.59 % (1364)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_1199 for (2992ds/614Mi)
% 7.46/2.59 % (1365)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_1199 for (2992ds/202Mi)
% 8.11/2.62 % (1353)Instruction limit reached!
% 8.11/2.62 % (1353)------------------------------
% 8.11/2.62 % (1353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.11/2.62 % (1353)Termination reason: Unknown
% 8.11/2.62 % (1353)Termination phase: Saturation
% 8.11/2.62
% 8.11/2.62 % (1353)Memory used [KB]: 7419
% 8.11/2.62 % (1353)Time elapsed: 0.186 s
% 8.11/2.62 % (1353)Instructions burned: 454 (million)
% 8.11/2.62 % (1353)------------------------------
% 8.11/2.62 % (1353)------------------------------
% 8.11/2.63 % (1363)Instruction limit reached!
% 8.11/2.63 % (1363)------------------------------
% 8.11/2.63 % (1363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.11/2.63 % (1363)Termination reason: Unknown
% 8.11/2.63 % (1363)Termination phase: Property scanning
% 8.11/2.63
% 8.11/2.63 % (1363)Memory used [KB]: 2686
% 8.11/2.63 % (1363)Time elapsed: 0.063 s
% 8.11/2.63 % (1363)Instructions burned: 141 (million)
% 8.11/2.63 % (1363)------------------------------
% 8.11/2.63 % (1363)------------------------------
% 8.11/2.64 % (1366)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_1199 for (2991ds/339Mi)
% 8.11/2.64 % (1367)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_1199 for (2991ds/283Mi)
% 8.11/2.66 % (1362)Instruction limit reached!
% 8.11/2.66 % (1362)------------------------------
% 8.11/2.66 % (1362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.11/2.66 % (1362)Termination reason: Unknown
% 8.11/2.66 % (1362)Termination phase: Saturation
% 8.11/2.66
% 8.11/2.66 % (1362)Memory used [KB]: 9850
% 8.11/2.66 % (1362)Time elapsed: 0.120 s
% 8.11/2.66 % (1362)Instructions burned: 253 (million)
% 8.11/2.66 % (1362)------------------------------
% 8.11/2.66 % (1362)------------------------------
% 8.11/2.67 % (1360)Instruction limit reached!
% 8.11/2.67 % (1360)------------------------------
% 8.11/2.67 % (1360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.11/2.67 % (1360)Termination reason: Unknown
% 8.11/2.67 % (1360)Termination phase: Saturation
% 8.11/2.67
% 8.11/2.67 % (1360)Memory used [KB]: 8571
% 8.11/2.67 % (1360)Time elapsed: 0.152 s
% 8.11/2.67 % (1360)Instructions burned: 343 (million)
% 8.11/2.67 % (1360)------------------------------
% 8.11/2.67 % (1360)------------------------------
% 8.11/2.67 % (1368)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_1199 for (2991ds/134Mi)
% 8.11/2.69 % (1365)Instruction limit reached!
% 8.11/2.69 % (1365)------------------------------
% 8.11/2.69 % (1365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.11/2.69 % (1365)Termination reason: Unknown
% 8.11/2.69 % (1365)Termination phase: Saturation
% 8.11/2.69
% 8.11/2.69 % (1365)Memory used [KB]: 4733
% 8.11/2.69 % (1365)Time elapsed: 0.095 s
% 8.11/2.69 % (1365)Instructions burned: 203 (million)
% 8.11/2.69 % (1365)------------------------------
% 8.11/2.69 % (1365)------------------------------
% 8.11/2.69 % (1369)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_1199 for (2991ds/298Mi)
% 8.80/2.70 % (1370)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_1199 for (2991ds/192Mi)
% 8.80/2.73 % (1368)Instruction limit reached!
% 8.80/2.73 % (1368)------------------------------
% 8.80/2.73 % (1368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.80/2.73 % (1368)Termination reason: Unknown
% 8.80/2.73 % (1368)Termination phase: Property scanning
% 8.80/2.73
% 8.80/2.73 % (1368)Memory used [KB]: 2686
% 8.80/2.73 % (1368)Time elapsed: 0.061 s
% 8.80/2.73 % (1368)Instructions burned: 135 (million)
% 8.80/2.73 % (1368)------------------------------
% 8.80/2.73 % (1368)------------------------------
% 8.80/2.75 % (1371)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_1199 for (2990ds/258Mi)
% 8.80/2.76 % (1367)Instruction limit reached!
% 8.80/2.76 % (1367)------------------------------
% 8.80/2.76 % (1367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.80/2.76 % (1367)Termination reason: Unknown
% 8.80/2.76 % (1367)Termination phase: Saturation
% 8.80/2.76
% 8.80/2.76 % (1367)Memory used [KB]: 7419
% 8.80/2.76 % (1367)Time elapsed: 0.119 s
% 8.80/2.76 % (1367)Instructions burned: 284 (million)
% 8.80/2.76 % (1367)------------------------------
% 8.80/2.76 % (1367)------------------------------
% 8.80/2.78 % (1372)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_1199 for (2990ds/90Mi)
% 8.80/2.79 % (1366)Instruction limit reached!
% 8.80/2.79 % (1366)------------------------------
% 8.80/2.79 % (1366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.80/2.79 % (1366)Termination reason: Unknown
% 8.80/2.79 % (1366)Termination phase: Saturation
% 8.80/2.79
% 8.80/2.79 % (1366)Memory used [KB]: 7931
% 8.80/2.79 % (1366)Time elapsed: 0.154 s
% 8.80/2.79 % (1366)Instructions burned: 340 (million)
% 8.80/2.79 % (1366)------------------------------
% 8.80/2.79 % (1366)------------------------------
% 8.80/2.79 % (1370)Instruction limit reached!
% 8.80/2.79 % (1370)------------------------------
% 8.80/2.79 % (1370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.80/2.79 % (1370)Termination reason: Unknown
% 8.80/2.79 % (1370)Termination phase: Saturation
% 8.80/2.79
% 8.80/2.79 % (1370)Memory used [KB]: 7675
% 8.80/2.79 % (1370)Time elapsed: 0.087 s
% 8.80/2.79 % (1370)Instructions burned: 192 (million)
% 8.80/2.79 % (1370)------------------------------
% 8.80/2.79 % (1370)------------------------------
% 9.28/2.80 % (1373)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_1199 for (2990ds/231Mi)
% 9.28/2.81 % (1374)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_1199 for (2990ds/458Mi)
% 9.28/2.81 % (1369)Instruction limit reached!
% 9.28/2.81 % (1369)------------------------------
% 9.28/2.81 % (1369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.28/2.81 % (1369)Termination reason: Unknown
% 9.28/2.81 % (1369)Termination phase: Saturation
% 9.28/2.81
% 9.28/2.81 % (1369)Memory used [KB]: 7419
% 9.28/2.81 % (1369)Time elapsed: 0.126 s
% 9.28/2.81 % (1369)Instructions burned: 299 (million)
% 9.28/2.81 % (1369)------------------------------
% 9.28/2.81 % (1369)------------------------------
% 9.28/2.82 % (1372)Instruction limit reached!
% 9.28/2.82 % (1372)------------------------------
% 9.28/2.82 % (1372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.28/2.82 % (1372)Termination reason: Unknown
% 9.28/2.82 % (1372)Termination phase: Property scanning
% 9.28/2.82
% 9.28/2.82 % (1372)Memory used [KB]: 2558
% 9.28/2.82 % (1372)Time elapsed: 0.042 s
% 9.28/2.82 % (1372)Instructions burned: 90 (million)
% 9.28/2.82 % (1372)------------------------------
% 9.28/2.82 % (1372)------------------------------
% 9.28/2.83 % (1375)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_1199 for (2989ds/31Mi)
% 9.28/2.83 % (1376)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_1199 for (2989ds/297Mi)
% 9.28/2.84 % (1375)Instruction limit reached!
% 9.28/2.84 % (1375)------------------------------
% 9.28/2.84 % (1375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.28/2.84 % (1375)Termination reason: Unknown
% 9.28/2.84 % (1375)Termination phase: shuffling
% 9.28/2.84
% 9.28/2.84 % (1375)Memory used [KB]: 2046
% 9.28/2.84 % (1375)Time elapsed: 0.016 s
% 9.28/2.84 % (1375)Instructions burned: 31 (million)
% 9.28/2.84 % (1375)------------------------------
% 9.28/2.84 % (1375)------------------------------
% 9.28/2.86 % (1377)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_1199 for (2989ds/987Mi)
% 9.28/2.86 % (1371)Instruction limit reached!
% 9.28/2.86 % (1371)------------------------------
% 9.28/2.86 % (1371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.28/2.86 % (1371)Termination reason: Unknown
% 9.28/2.86 % (1371)Termination phase: Saturation
% 9.28/2.86
% 9.28/2.86 % (1371)Memory used [KB]: 7931
% 9.28/2.86 % (1371)Time elapsed: 0.116 s
% 9.28/2.86 % (1371)Instructions burned: 259 (million)
% 9.28/2.86 % (1371)------------------------------
% 9.28/2.86 % (1371)------------------------------
% 9.28/2.88 % (1364)Instruction limit reached!
% 9.28/2.88 % (1364)------------------------------
% 9.28/2.88 % (1364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.28/2.88 % (1364)Termination reason: Unknown
% 9.28/2.88 % (1364)Termination phase: Saturation
% 9.28/2.88
% 9.28/2.88 % (1364)Memory used [KB]: 9850
% 9.28/2.88 % (1364)Time elapsed: 0.313 s
% 9.28/2.88 % (1364)Instructions burned: 614 (million)
% 9.28/2.88 % (1364)------------------------------
% 9.28/2.88 % (1364)------------------------------
% 9.28/2.88 % (1378)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_1199 for (2989ds/182Mi)
% 9.28/2.89 % (1346)Instruction limit reached!
% 9.28/2.89 % (1346)------------------------------
% 9.28/2.89 % (1346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.28/2.89 % (1346)Termination reason: Unknown
% 9.28/2.89 % (1346)Termination phase: Saturation
% 9.28/2.89
% 9.28/2.89 % (1346)Memory used [KB]: 12153
% 9.28/2.89 % (1346)Time elapsed: 0.544 s
% 9.28/2.89 % (1346)Instructions burned: 1088 (million)
% 9.28/2.89 % (1346)------------------------------
% 9.28/2.89 % (1346)------------------------------
% 9.28/2.89 % (1379)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_1199 for (2989ds/182Mi)
% 10.50/2.90 % (1380)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_1199 for (2989ds/154Mi)
% 10.50/2.91 % (1373)Instruction limit reached!
% 10.50/2.91 % (1373)------------------------------
% 10.50/2.91 % (1373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.50/2.91 % (1373)Termination reason: Unknown
% 10.50/2.91 % (1373)Termination phase: Saturation
% 10.50/2.91
% 10.50/2.91 % (1373)Memory used [KB]: 8443
% 10.50/2.91 % (1373)Time elapsed: 0.104 s
% 10.50/2.91 % (1373)Instructions burned: 232 (million)
% 10.50/2.91 % (1373)------------------------------
% 10.50/2.91 % (1373)------------------------------
% 10.50/2.92 % (1381)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_1199 for (2988ds/79Mi)
% 10.50/2.96 % (1376)Instruction limit reached!
% 10.50/2.96 % (1376)------------------------------
% 10.50/2.96 % (1376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.50/2.96 % (1376)Termination reason: Unknown
% 10.50/2.96 % (1376)Termination phase: Saturation
% 10.50/2.96
% 10.50/2.96 % (1376)Memory used [KB]: 7419
% 10.50/2.96 % (1376)Time elapsed: 0.124 s
% 10.50/2.96 % (1376)Instructions burned: 299 (million)
% 10.50/2.96 % (1376)------------------------------
% 10.50/2.96 % (1376)------------------------------
% 10.50/2.96 % (1381)Instruction limit reached!
% 10.50/2.96 % (1381)------------------------------
% 10.50/2.96 % (1381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.50/2.96 % (1381)Termination reason: Unknown
% 10.50/2.96 % (1381)Termination phase: Property scanning
% 10.50/2.96
% 10.50/2.96 % (1381)Memory used [KB]: 2558
% 10.50/2.96 % (1381)Time elapsed: 0.038 s
% 10.50/2.96 % (1381)Instructions burned: 80 (million)
% 10.50/2.96 % (1381)------------------------------
% 10.50/2.96 % (1381)------------------------------
% 10.50/2.96 % (1378)Instruction limit reached!
% 10.50/2.96 % (1378)------------------------------
% 10.50/2.96 % (1378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.50/2.96 % (1378)Termination reason: Unknown
% 10.50/2.96 % (1378)Termination phase: Saturation
% 10.50/2.96
% 10.50/2.96 % (1378)Memory used [KB]: 7675
% 10.50/2.96 % (1378)Time elapsed: 0.082 s
% 10.50/2.96 % (1378)Instructions burned: 182 (million)
% 10.50/2.96 % (1378)------------------------------
% 10.50/2.96 % (1378)------------------------------
% 10.50/2.97 % (1380)Instruction limit reached!
% 10.50/2.97 % (1380)------------------------------
% 10.50/2.97 % (1380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.50/2.97 % (1380)Termination reason: Unknown
% 10.50/2.97 % (1380)Termination phase: Saturation
% 10.50/2.97
% 10.50/2.97 % (1380)Memory used [KB]: 7036
% 10.50/2.97 % (1380)Time elapsed: 0.068 s
% 10.50/2.97 % (1380)Instructions burned: 154 (million)
% 10.50/2.97 % (1380)------------------------------
% 10.50/2.97 % (1380)------------------------------
% 10.50/2.97 % (1382)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_1199 for (2988ds/216Mi)
% 10.50/2.98 % (1383)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_1199 for (2988ds/114Mi)
% 10.50/2.98 % (1384)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_1199 for (2988ds/922Mi)
% 10.50/2.98 % (1379)Instruction limit reached!
% 10.50/2.98 % (1379)------------------------------
% 10.50/2.98 % (1379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.50/2.98 % (1379)Termination reason: Unknown
% 10.50/2.98 % (1379)Termination phase: Property scanning
% 10.50/2.98
% 10.50/2.98 % (1379)Memory used [KB]: 4349
% 10.50/2.98 % (1379)Time elapsed: 0.086 s
% 10.50/2.98 % (1379)Instructions burned: 183 (million)
% 10.50/2.98 % (1379)------------------------------
% 10.50/2.98 % (1379)------------------------------
% 10.50/2.99 % (1385)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_1199 for (2988ds/182Mi)
% 10.50/3.00 % (1386)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_1199 for (2988ds/164Mi)
% 10.50/3.01 % (1374)Instruction limit reached!
% 10.50/3.01 % (1374)------------------------------
% 10.50/3.01 % (1374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.50/3.01 % (1374)Termination reason: Unknown
% 10.50/3.01 % (1374)Termination phase: Saturation
% 10.50/3.01
% 10.50/3.01 % (1374)Memory used [KB]: 9466
% 10.50/3.01 % (1374)Time elapsed: 0.210 s
% 10.50/3.01 % (1374)Instructions burned: 459 (million)
% 10.50/3.01 % (1374)------------------------------
% 10.50/3.01 % (1374)------------------------------
% 10.50/3.03 % (1383)Instruction limit reached!
% 10.50/3.03 % (1383)------------------------------
% 10.50/3.03 % (1383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.50/3.03 % (1383)Termination reason: Unknown
% 10.50/3.03 % (1383)Termination phase: Function definition elimination
% 10.50/3.03
% 10.50/3.03 % (1383)Memory used [KB]: 2686
% 10.50/3.03 % (1383)Time elapsed: 0.052 s
% 10.50/3.03 % (1383)Instructions burned: 114 (million)
% 10.50/3.03 % (1383)------------------------------
% 10.50/3.03 % (1383)------------------------------
% 11.73/3.03 % (1387)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_1199 for (2987ds/50Mi)
% 11.73/3.04 % (1388)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_1199 for (2987ds/368Mi)
% 11.73/3.05 % (1387)Instruction limit reached!
% 11.73/3.05 % (1387)------------------------------
% 11.73/3.05 % (1387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.73/3.05 % (1387)Termination reason: Unknown
% 11.73/3.05 % (1387)Termination phase: Property scanning
% 11.73/3.05
% 11.73/3.05 % (1387)Memory used [KB]: 2430
% 11.73/3.05 % (1387)Time elapsed: 0.025 s
% 11.73/3.05 % (1387)Instructions burned: 51 (million)
% 11.73/3.05 % (1387)------------------------------
% 11.73/3.05 % (1387)------------------------------
% 11.73/3.06 % (1382)Instruction limit reached!
% 11.73/3.06 % (1382)------------------------------
% 11.73/3.06 % (1382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.73/3.06 % (1382)Termination reason: Unknown
% 11.73/3.06 % (1382)Termination phase: Saturation
% 11.73/3.06
% 11.73/3.06 % (1382)Memory used [KB]: 7419
% 11.73/3.06 % (1382)Time elapsed: 0.092 s
% 11.73/3.06 % (1382)Instructions burned: 217 (million)
% 11.73/3.06 % (1382)------------------------------
% 11.73/3.06 % (1382)------------------------------
% 11.73/3.06 % (1385)Instruction limit reached!
% 11.73/3.06 % (1385)------------------------------
% 11.73/3.06 % (1385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.73/3.06 % (1385)Termination reason: Unknown
% 11.73/3.06 % (1385)Termination phase: Saturation
% 11.73/3.06
% 11.73/3.06 % (1385)Memory used [KB]: 7419
% 11.73/3.06 % (1385)Time elapsed: 0.080 s
% 11.73/3.06 % (1385)Instructions burned: 184 (million)
% 11.73/3.06 % (1385)------------------------------
% 11.73/3.06 % (1385)------------------------------
% 11.73/3.07 % (1386)Instruction limit reached!
% 11.73/3.07 % (1386)------------------------------
% 11.73/3.07 % (1386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.73/3.07 % (1386)Termination reason: Unknown
% 11.73/3.07 % (1386)Termination phase: Property scanning
% 11.73/3.07
% 11.73/3.07 % (1386)Memory used [KB]: 2686
% 11.73/3.07 % (1386)Time elapsed: 0.072 s
% 11.73/3.07 % (1386)Instructions burned: 164 (million)
% 11.73/3.07 % (1386)------------------------------
% 11.73/3.07 % (1386)------------------------------
% 11.73/3.07 % (1389)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_1199 for (2987ds/1021Mi)
% 11.73/3.08 % (1390)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_1199 for (2987ds/267Mi)
% 11.73/3.08 % (1391)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_1199 for (2987ds/204Mi)
% 11.73/3.08 % (1392)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_1199 for (2987ds/26Mi)
% 11.73/3.09 % (1392)Instruction limit reached!
% 11.73/3.09 % (1392)------------------------------
% 11.73/3.09 % (1392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.73/3.09 % (1392)Termination reason: Unknown
% 11.73/3.10 % (1392)Termination phase: shuffling
% 11.73/3.10
% 11.73/3.10 % (1392)Memory used [KB]: 1918
% 11.73/3.10 % (1392)Time elapsed: 0.014 s
% 11.73/3.10 % (1392)Instructions burned: 27 (million)
% 11.73/3.10 % (1392)------------------------------
% 11.73/3.10 % (1392)------------------------------
% 11.73/3.11 % (1393)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_1199 for (2987ds/53Mi)
% 12.17/3.14 % (1393)Instruction limit reached!
% 12.17/3.14 % (1393)------------------------------
% 12.17/3.14 % (1393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.17/3.14 % (1393)Termination reason: Unknown
% 12.17/3.14 % (1393)Termination phase: Property scanning
% 12.17/3.14
% 12.17/3.14 % (1393)Memory used [KB]: 2430
% 12.17/3.14 % (1393)Time elapsed: 0.026 s
% 12.17/3.14 % (1393)Instructions burned: 54 (million)
% 12.17/3.14 % (1393)------------------------------
% 12.17/3.14 % (1393)------------------------------
% 12.17/3.15 % (1394)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_1199 for (2986ds/4436Mi)
% 12.17/3.17 % (1391)Instruction limit reached!
% 12.17/3.17 % (1391)------------------------------
% 12.17/3.17 % (1391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.17/3.17 % (1391)Termination reason: Unknown
% 12.17/3.17 % (1391)Termination phase: Saturation
% 12.17/3.17
% 12.17/3.17 % (1391)Memory used [KB]: 7291
% 12.17/3.17 % (1391)Time elapsed: 0.088 s
% 12.17/3.17 % (1391)Instructions burned: 204 (million)
% 12.17/3.17 % (1391)------------------------------
% 12.17/3.17 % (1391)------------------------------
% 12.17/3.18 % (1395)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_1199 for (2986ds/1539Mi)
% 12.17/3.19 % (1390)Instruction limit reached!
% 12.17/3.19 % (1390)------------------------------
% 12.17/3.19 % (1390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.17/3.19 % (1390)Termination reason: Unknown
% 12.17/3.19 % (1390)Termination phase: Saturation
% 12.17/3.19
% 12.17/3.19 % (1390)Memory used [KB]: 7419
% 12.17/3.19 % (1390)Time elapsed: 0.113 s
% 12.17/3.19 % (1390)Instructions burned: 268 (million)
% 12.17/3.19 % (1390)------------------------------
% 12.17/3.19 % (1390)------------------------------
% 12.58/3.21 % (1396)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_1199 for (2986ds/408Mi)
% 12.58/3.21 % (1388)Instruction limit reached!
% 12.58/3.21 % (1388)------------------------------
% 12.58/3.21 % (1388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.58/3.21 % (1388)Termination reason: Unknown
% 12.58/3.21 % (1388)Termination phase: Saturation
% 12.58/3.21
% 12.58/3.21 % (1388)Memory used [KB]: 8827
% 12.58/3.21 % (1388)Time elapsed: 0.170 s
% 12.58/3.21 % (1388)Instructions burned: 369 (million)
% 12.58/3.21 % (1388)------------------------------
% 12.58/3.21 % (1388)------------------------------
% 12.58/3.23 % (1397)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_1199 for (2985ds/5205Mi)
% 12.58/3.24 % (1377)Instruction limit reached!
% 12.58/3.24 % (1377)------------------------------
% 12.58/3.24 % (1377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.58/3.24 % (1377)Termination reason: Unknown
% 12.58/3.24 % (1377)Termination phase: Saturation
% 12.58/3.24
% 12.58/3.24 % (1377)Memory used [KB]: 14839
% 12.58/3.24 % (1377)Time elapsed: 0.383 s
% 12.58/3.24 % (1377)Instructions burned: 988 (million)
% 12.58/3.24 % (1377)------------------------------
% 12.58/3.24 % (1377)------------------------------
% 12.58/3.26 % (1398)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_1199 for (2985ds/1913Mi)
% 13.03/3.41 % (1396)Instruction limit reached!
% 13.03/3.41 % (1396)------------------------------
% 13.03/3.41 % (1396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.03/3.41 % (1396)Termination reason: Unknown
% 13.03/3.41 % (1396)Termination phase: Saturation
% 13.03/3.41
% 13.03/3.41 % (1396)Memory used [KB]: 10618
% 13.03/3.41 % (1396)Time elapsed: 0.201 s
% 13.03/3.41 % (1396)Instructions burned: 408 (million)
% 13.03/3.41 % (1396)------------------------------
% 13.03/3.41 % (1396)------------------------------
% 13.03/3.42 % (1399)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_1199 for (2984ds/4350Mi)
% 13.03/3.43 % (1384)Instruction limit reached!
% 13.03/3.43 % (1384)------------------------------
% 13.03/3.43 % (1384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.03/3.43 % (1384)Termination reason: Unknown
% 13.03/3.43 % (1384)Termination phase: Saturation
% 13.03/3.43
% 13.03/3.43 % (1384)Memory used [KB]: 11385
% 13.03/3.43 % (1384)Time elapsed: 0.457 s
% 13.03/3.43 % (1384)Instructions burned: 922 (million)
% 13.03/3.43 % (1384)------------------------------
% 13.03/3.43 % (1384)------------------------------
% 13.03/3.45 % (1400)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_1199 for (2983ds/68Mi)
% 13.03/3.48 % (1400)Instruction limit reached!
% 13.03/3.48 % (1400)------------------------------
% 13.03/3.48 % (1400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.03/3.48 % (1400)Termination reason: Unknown
% 13.03/3.48 % (1400)Termination phase: Property scanning
% 13.03/3.48
% 13.03/3.48 % (1400)Memory used [KB]: 2430
% 13.03/3.48 % (1400)Time elapsed: 0.033 s
% 13.03/3.48 % (1400)Instructions burned: 69 (million)
% 13.03/3.48 % (1400)------------------------------
% 13.03/3.48 % (1400)------------------------------
% 13.33/3.50 % (1401)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_1199 for (2983ds/358Mi)
% 13.33/3.58 % (1389)Instruction limit reached!
% 13.33/3.58 % (1389)------------------------------
% 13.33/3.58 % (1389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.33/3.58 % (1389)Termination reason: Unknown
% 13.33/3.58 % (1389)Termination phase: Saturation
% 13.33/3.58
% 13.33/3.58 % (1389)Memory used [KB]: 12281
% 13.33/3.58 % (1389)Time elapsed: 0.512 s
% 13.33/3.58 % (1389)Instructions burned: 1021 (million)
% 13.33/3.58 % (1389)------------------------------
% 13.33/3.58 % (1389)------------------------------
% 13.86/3.60 % (1402)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_1199 for (2982ds/31Mi)
% 13.86/3.61 % (1402)Instruction limit reached!
% 13.86/3.61 % (1402)------------------------------
% 13.86/3.61 % (1402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.86/3.61 % (1402)Termination reason: Unknown
% 13.86/3.61 % (1402)Termination phase: shuffling
% 13.86/3.61
% 13.86/3.61 % (1402)Memory used [KB]: 1918
% 13.86/3.61 % (1402)Time elapsed: 0.016 s
% 13.86/3.61 % (1402)Instructions burned: 31 (million)
% 13.86/3.61 % (1402)------------------------------
% 13.86/3.61 % (1402)------------------------------
% 13.86/3.63 % (1403)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_1199 for (2981ds/279Mi)
% 13.86/3.65 % (1401)Instruction limit reached!
% 13.86/3.65 % (1401)------------------------------
% 13.86/3.65 % (1401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.86/3.65 % (1401)Termination reason: Unknown
% 13.86/3.65 % (1401)Termination phase: Saturation
% 13.86/3.65
% 13.86/3.65 % (1401)Memory used [KB]: 8571
% 13.86/3.65 % (1401)Time elapsed: 0.158 s
% 13.86/3.65 % (1401)Instructions burned: 359 (million)
% 13.86/3.65 % (1401)------------------------------
% 13.86/3.65 % (1401)------------------------------
% 13.86/3.67 % (1404)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_1199 for (2981ds/258Mi)
% 14.07/3.75 % (1403)Instruction limit reached!
% 14.07/3.75 % (1403)------------------------------
% 14.07/3.75 % (1403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.07/3.75 % (1403)Termination reason: Unknown
% 14.07/3.75 % (1403)Termination phase: Saturation
% 14.07/3.75
% 14.07/3.75 % (1403)Memory used [KB]: 7419
% 14.07/3.75 % (1403)Time elapsed: 0.118 s
% 14.07/3.75 % (1403)Instructions burned: 281 (million)
% 14.07/3.75 % (1403)------------------------------
% 14.07/3.75 % (1403)------------------------------
% 14.07/3.76 % (1405)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_1199 for (2980ds/26Mi)
% 14.07/3.77 % (1405)Instruction limit reached!
% 14.07/3.77 % (1405)------------------------------
% 14.07/3.77 % (1405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.07/3.77 % (1405)Termination reason: Unknown
% 14.07/3.77 % (1405)Termination phase: shuffling
% 14.07/3.77
% 14.07/3.77 % (1405)Memory used [KB]: 1918
% 14.07/3.77 % (1405)Time elapsed: 0.014 s
% 14.07/3.77 % (1405)Instructions burned: 27 (million)
% 14.07/3.77 % (1405)------------------------------
% 14.07/3.77 % (1405)------------------------------
% 14.07/3.79 % (1404)Instruction limit reached!
% 14.07/3.79 % (1404)------------------------------
% 14.07/3.79 % (1404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.07/3.79 % (1404)Termination reason: Unknown
% 14.07/3.79 % (1404)Termination phase: Saturation
% 14.07/3.79
% 14.07/3.79 % (1404)Memory used [KB]: 8059
% 14.07/3.79 % (1404)Time elapsed: 0.117 s
% 14.07/3.79 % (1404)Instructions burned: 258 (million)
% 14.07/3.79 % (1404)------------------------------
% 14.07/3.79 % (1404)------------------------------
% 14.07/3.79 % (1406)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_1199 for (2980ds/995Mi)
% 14.37/3.80 % (1407)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_1199 for (2980ds/373Mi)
% 14.37/3.94 % (1395)Instruction limit reached!
% 14.37/3.94 % (1395)------------------------------
% 14.37/3.94 % (1395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.37/3.94 % (1395)Termination reason: Unknown
% 14.37/3.94 % (1395)Termination phase: Saturation
% 14.37/3.94
% 14.37/3.94 % (1395)Memory used [KB]: 10618
% 14.37/3.94 % (1395)Time elapsed: 0.758 s
% 14.37/3.94 % (1395)Instructions burned: 1539 (million)
% 14.37/3.94 % (1395)------------------------------
% 14.37/3.94 % (1395)------------------------------
% 14.37/3.96 % (1408)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_1199 for (2978ds/253Mi)
% 14.37/3.97 % (1407)Instruction limit reached!
% 14.37/3.97 % (1407)------------------------------
% 14.37/3.97 % (1407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.37/3.97 % (1407)Termination reason: Unknown
% 14.37/3.97 % (1407)Termination phase: Saturation
% 14.37/3.97
% 14.37/3.97 % (1407)Memory used [KB]: 8827
% 14.37/3.97 % (1407)Time elapsed: 0.195 s
% 14.37/3.97 % (1407)Instructions burned: 374 (million)
% 14.37/3.97 % (1407)------------------------------
% 14.37/3.97 % (1407)------------------------------
% 14.37/3.99 % (1409)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_1199 for (2978ds/832Mi)
% 18.70/4.06 % (1408)Instruction limit reached!
% 18.70/4.06 % (1408)------------------------------
% 18.70/4.06 % (1408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.70/4.06 % (1408)Termination reason: Unknown
% 18.70/4.06 % (1408)Termination phase: Saturation
% 18.70/4.06
% 18.70/4.06 % (1408)Memory used [KB]: 7419
% 18.70/4.06 % (1408)Time elapsed: 0.108 s
% 18.70/4.06 % (1408)Instructions burned: 253 (million)
% 18.70/4.06 % (1408)------------------------------
% 18.70/4.06 % (1408)------------------------------
% 18.70/4.08 % (1410)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_1199 for (2977ds/668Mi)
% 19.40/4.17 % (1406)Instruction limit reached!
% 19.40/4.17 % (1406)------------------------------
% 19.40/4.17 % (1406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.40/4.17 % (1406)Termination reason: Unknown
% 19.40/4.17 % (1406)Termination phase: Saturation
% 19.40/4.17
% 19.40/4.17 % (1406)Memory used [KB]: 14711
% 19.40/4.17 % (1406)Time elapsed: 0.383 s
% 19.40/4.17 % (1406)Instructions burned: 996 (million)
% 19.40/4.17 % (1406)------------------------------
% 19.40/4.17 % (1406)------------------------------
% 19.40/4.18 % (1398)Instruction limit reached!
% 19.40/4.18 % (1398)------------------------------
% 19.40/4.18 % (1398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.40/4.18 % (1398)Termination reason: Unknown
% 19.40/4.18 % (1398)Termination phase: Saturation
% 19.40/4.18
% 19.40/4.18 % (1398)Memory used [KB]: 6140
% 19.40/4.18 % (1398)Time elapsed: 0.922 s
% 19.40/4.18 % (1398)Instructions burned: 1913 (million)
% 19.40/4.18 % (1398)------------------------------
% 19.40/4.18 % (1398)------------------------------
% 19.40/4.19 % (1411)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_1199 for (2976ds/40Mi)
% 19.40/4.20 % (1412)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_1199 for (2976ds/294Mi)
% 19.80/4.21 % (1411)Instruction limit reached!
% 19.80/4.21 % (1411)------------------------------
% 19.80/4.21 % (1411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.80/4.21 % (1411)Termination reason: Unknown
% 19.80/4.21 % (1411)Termination phase: shuffling
% 19.80/4.21
% 19.80/4.21 % (1411)Memory used [KB]: 2302
% 19.80/4.21 % (1411)Time elapsed: 0.019 s
% 19.80/4.21 % (1411)Instructions burned: 40 (million)
% 19.80/4.21 % (1411)------------------------------
% 19.80/4.21 % (1411)------------------------------
% 19.80/4.22 % (1413)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_1199 for (2975ds/187Mi)
% 20.23/4.31 % (1413)Instruction limit reached!
% 20.23/4.31 % (1413)------------------------------
% 20.23/4.31 % (1413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.23/4.31 % (1413)Termination reason: Unknown
% 20.23/4.31 % (1413)Termination phase: Saturation
% 20.23/4.31
% 20.23/4.31 % (1413)Memory used [KB]: 7675
% 20.23/4.31 % (1413)Time elapsed: 0.084 s
% 20.23/4.31 % (1413)Instructions burned: 187 (million)
% 20.23/4.31 % (1413)------------------------------
% 20.23/4.31 % (1413)------------------------------
% 20.23/4.32 % (1412)Instruction limit reached!
% 20.23/4.32 % (1412)------------------------------
% 20.23/4.32 % (1412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.23/4.32 % (1412)Termination reason: Unknown
% 20.23/4.32 % (1412)Termination phase: Saturation
% 20.23/4.32
% 20.23/4.32 % (1412)Memory used [KB]: 7419
% 20.23/4.32 % (1412)Time elapsed: 0.123 s
% 20.23/4.32 % (1412)Instructions burned: 295 (million)
% 20.23/4.32 % (1412)------------------------------
% 20.23/4.32 % (1412)------------------------------
% 20.23/4.32 % (1414)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_1199 for (2974ds/371Mi)
% 20.23/4.33 % (1415)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_1199 for (2974ds/1827Mi)
% 20.23/4.35 % (1410)Instruction limit reached!
% 20.23/4.35 % (1410)------------------------------
% 20.23/4.35 % (1410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.23/4.35 % (1410)Termination reason: Unknown
% 20.23/4.35 % (1410)Termination phase: Saturation
% 20.23/4.35
% 20.23/4.35 % (1410)Memory used [KB]: 18933
% 20.23/4.35 % (1410)Time elapsed: 0.269 s
% 20.23/4.35 % (1410)Instructions burned: 668 (million)
% 20.23/4.35 % (1410)------------------------------
% 20.23/4.35 % (1410)------------------------------
% 20.23/4.37 % (1416)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_1199 for (2974ds/70Mi)
% 21.15/4.40 % (1416)Instruction limit reached!
% 21.15/4.40 % (1416)------------------------------
% 21.15/4.40 % (1416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.15/4.40 % (1416)Termination reason: Unknown
% 21.15/4.40 % (1416)Termination phase: Property scanning
% 21.15/4.40
% 21.15/4.40 % (1416)Memory used [KB]: 2430
% 21.15/4.40 % (1416)Time elapsed: 0.034 s
% 21.15/4.40 % (1416)Instructions burned: 70 (million)
% 21.15/4.40 % (1416)------------------------------
% 21.15/4.40 % (1416)------------------------------
% 21.15/4.40 % (1409)Instruction limit reached!
% 21.15/4.40 % (1409)------------------------------
% 21.15/4.40 % (1409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.15/4.40 % (1409)Termination reason: Unknown
% 21.15/4.40 % (1409)Termination phase: Saturation
% 21.15/4.40
% 21.15/4.40 % (1409)Memory used [KB]: 11129
% 21.15/4.40 % (1409)Time elapsed: 0.412 s
% 21.15/4.40 % (1409)Instructions burned: 833 (million)
% 21.15/4.40 % (1409)------------------------------
% 21.15/4.40 % (1409)------------------------------
% 21.15/4.41 % (1417)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_1199 for (2974ds/316Mi)
% 21.15/4.42 % (1418)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_1199 for (2973ds/932Mi)
% 21.15/4.49 % (1414)Instruction limit reached!
% 21.15/4.49 % (1414)------------------------------
% 21.15/4.49 % (1414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.15/4.49 % (1414)Termination reason: Unknown
% 21.15/4.49 % (1414)Termination phase: Saturation
% 21.15/4.49
% 21.15/4.49 % (1414)Memory used [KB]: 9338
% 21.15/4.49 % (1414)Time elapsed: 0.169 s
% 21.15/4.49 % (1414)Instructions burned: 372 (million)
% 21.15/4.49 % (1414)------------------------------
% 21.15/4.49 % (1414)------------------------------
% 21.69/4.51 % (1419)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_1199 for (2973ds/4714Mi)
% 21.69/4.55 % (1417)Instruction limit reached!
% 21.69/4.55 % (1417)------------------------------
% 21.69/4.55 % (1417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.69/4.55 % (1417)Termination reason: Unknown
% 21.69/4.55 % (1417)Termination phase: Saturation
% 21.69/4.55
% 21.69/4.55 % (1417)Memory used [KB]: 7419
% 21.69/4.55 % (1417)Time elapsed: 0.134 s
% 21.69/4.55 % (1417)Instructions burned: 318 (million)
% 21.69/4.55 % (1417)------------------------------
% 21.69/4.55 % (1417)------------------------------
% 21.69/4.56 % (1420)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_1199 for (2972ds/8250Mi)
% 22.45/4.79 % (1418)Instruction limit reached!
% 22.45/4.79 % (1418)------------------------------
% 22.45/4.79 % (1418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.45/4.79 % (1418)Termination reason: Unknown
% 22.45/4.79 % (1418)Termination phase: Saturation
% 22.45/4.79
% 22.45/4.79 % (1418)Memory used [KB]: 16247
% 22.45/4.79 % (1418)Time elapsed: 0.372 s
% 22.45/4.79 % (1418)Instructions burned: 933 (million)
% 22.45/4.79 % (1418)------------------------------
% 22.45/4.79 % (1418)------------------------------
% 23.13/4.81 % (1421)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_1199 for (2970ds/770Mi)
% 25.67/5.13 % (1397)Instruction limit reached!
% 25.67/5.13 % (1397)------------------------------
% 25.67/5.13 % (1397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.67/5.13 % (1397)Termination reason: Unknown
% 25.67/5.13 % (1397)Termination phase: Saturation
% 25.67/5.13
% 25.67/5.13 % (1397)Memory used [KB]: 15607
% 25.67/5.13 % (1397)Time elapsed: 1.902 s
% 25.67/5.13 % (1397)Instructions burned: 5205 (million)
% 25.67/5.13 % (1397)------------------------------
% 25.67/5.13 % (1397)------------------------------
% 24.55/5.14 % (1421)Instruction limit reached!
% 24.55/5.14 % (1421)------------------------------
% 24.55/5.14 % (1421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.55/5.14 % (1421)Termination reason: Unknown
% 24.55/5.14 % (1421)Termination phase: Saturation
% 24.55/5.14
% 24.55/5.14 % (1421)Memory used [KB]: 7547
% 24.55/5.14 % (1421)Time elapsed: 0.340 s
% 24.55/5.14 % (1421)Instructions burned: 770 (million)
% 24.55/5.14 % (1421)------------------------------
% 24.55/5.14 % (1421)------------------------------
% 24.55/5.15 % (1422)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_1199 for (2966ds/794Mi)
% 24.55/5.16 % (1423)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_1199 for (2966ds/464Mi)
% 24.55/5.19 % (1415)Instruction limit reached!
% 24.55/5.19 % (1415)------------------------------
% 24.55/5.19 % (1415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.55/5.19 % (1415)Termination reason: Unknown
% 24.55/5.19 % (1415)Termination phase: Saturation
% 24.55/5.19
% 24.55/5.19 % (1415)Memory used [KB]: 20212
% 24.55/5.19 % (1415)Time elapsed: 0.857 s
% 24.55/5.19 % (1415)Instructions burned: 1827 (million)
% 24.55/5.19 % (1415)------------------------------
% 24.55/5.19 % (1415)------------------------------
% 26.82/5.21 % (1424)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_1199 for (2966ds/1376Mi)
% 27.22/5.36 % (1394)Instruction limit reached!
% 27.22/5.36 % (1394)------------------------------
% 27.22/5.36 % (1394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.22/5.36 % (1394)Termination reason: Unknown
% 27.22/5.36 % (1394)Termination phase: Saturation
% 27.22/5.36
% 27.22/5.36 % (1394)Memory used [KB]: 15863
% 27.22/5.36 % (1394)Time elapsed: 2.206 s
% 27.22/5.36 % (1394)Instructions burned: 4437 (million)
% 27.22/5.36 % (1394)------------------------------
% 27.22/5.36 % (1394)------------------------------
% 27.22/5.37 % (1425)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_1199 for (2964ds/906Mi)
% 27.22/5.38 % (1423)Instruction limit reached!
% 27.22/5.38 % (1423)------------------------------
% 27.22/5.38 % (1423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.22/5.38 % (1423)Termination reason: Unknown
% 27.22/5.38 % (1423)Termination phase: Saturation
% 27.22/5.38
% 27.22/5.38 % (1423)Memory used [KB]: 9466
% 27.22/5.38 % (1423)Time elapsed: 0.223 s
% 27.22/5.38 % (1423)Instructions burned: 464 (million)
% 27.22/5.38 % (1423)------------------------------
% 27.22/5.38 % (1423)------------------------------
% 27.83/5.40 % (1426)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_1199 for (2964ds/434Mi)
% 27.83/5.48 % (1399)Refutation not found, non-redundant clauses discarded% (1399)------------------------------
% 27.83/5.48 % (1399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.83/5.48 % (1399)Termination reason: Refutation not found, non-redundant clauses discarded
% 27.83/5.48
% 27.83/5.48 % (1399)Memory used [KB]: 13560
% 27.83/5.48 % (1399)Time elapsed: 2.063 s
% 27.83/5.48 % (1399)Instructions burned: 4215 (million)
% 27.83/5.49 % (1399)------------------------------
% 27.83/5.49 % (1399)------------------------------
% 28.14/5.50 % (1427)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_1199 for (2963ds/865Mi)
% 28.14/5.53 % (1422)Instruction limit reached!
% 28.14/5.53 % (1422)------------------------------
% 28.14/5.53 % (1422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.14/5.53 % (1422)Termination reason: Unknown
% 28.14/5.53 % (1422)Termination phase: Saturation
% 28.14/5.53
% 28.14/5.53 % (1422)Memory used [KB]: 5884
% 28.14/5.53 % (1422)Time elapsed: 0.390 s
% 28.14/5.53 % (1422)Instructions burned: 795 (million)
% 28.14/5.53 % (1422)------------------------------
% 28.14/5.53 % (1422)------------------------------
% 28.14/5.55 % (1428)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_1199 for (2962ds/593Mi)
% 28.73/5.61 % (1426)Instruction limit reached!
% 28.73/5.61 % (1426)------------------------------
% 28.73/5.61 % (1426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.73/5.61 % (1426)Termination reason: Unknown
% 28.73/5.61 % (1426)Termination phase: Saturation
% 28.73/5.61
% 28.73/5.61 % (1426)Memory used [KB]: 10746
% 28.73/5.61 % (1426)Time elapsed: 0.210 s
% 28.73/5.61 % (1426)Instructions burned: 434 (million)
% 28.73/5.61 % (1426)------------------------------
% 28.73/5.61 % (1426)------------------------------
% 28.73/5.62 % (1429)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_1199 for (2962ds/443Mi)
% 29.16/5.75 % (1424)Instruction limit reached!
% 29.16/5.75 % (1424)------------------------------
% 29.16/5.75 % (1424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.16/5.75 % (1424)Termination reason: Unknown
% 29.16/5.75 % (1424)Termination phase: Saturation
% 29.16/5.75
% 29.16/5.75 % (1424)Memory used [KB]: 9594
% 29.16/5.75 % (1424)Time elapsed: 0.546 s
% 29.16/5.75 % (1424)Instructions burned: 1376 (million)
% 29.16/5.75 % (1424)------------------------------
% 29.16/5.75 % (1424)------------------------------
% 29.16/5.77 % (1430)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_1199 for (2960ds/594Mi)
% 29.16/5.78 % (1428)Instruction limit reached!
% 29.16/5.78 % (1428)------------------------------
% 29.16/5.78 % (1428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.16/5.78 % (1428)Termination reason: Unknown
% 29.16/5.78 % (1428)Termination phase: Saturation
% 29.16/5.78
% 29.16/5.78 % (1428)Memory used [KB]: 7547
% 29.16/5.78 % (1428)Time elapsed: 0.234 s
% 29.16/5.78 % (1428)Instructions burned: 593 (million)
% 29.16/5.78 % (1428)------------------------------
% 29.16/5.78 % (1428)------------------------------
% 30.17/5.80 % (1431)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_1199 for (2960ds/327Mi)
% 30.17/5.81 % (1425)Instruction limit reached!
% 30.17/5.81 % (1425)------------------------------
% 30.17/5.81 % (1425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.17/5.81 % (1425)Termination reason: Unknown
% 30.17/5.81 % (1425)Termination phase: Saturation
% 30.17/5.81
% 30.17/5.81 % (1425)Memory used [KB]: 11001
% 30.17/5.81 % (1425)Time elapsed: 0.442 s
% 30.17/5.81 % (1425)Instructions burned: 908 (million)
% 30.17/5.81 % (1425)------------------------------
% 30.17/5.81 % (1425)------------------------------
% 30.17/5.83 % (1429)Instruction limit reached!
% 30.17/5.83 % (1429)------------------------------
% 30.17/5.83 % (1429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.17/5.83 % (1429)Termination reason: Unknown
% 30.17/5.83 % (1429)Termination phase: Saturation
% 30.17/5.83
% 30.17/5.83 % (1429)Memory used [KB]: 9466
% 30.17/5.83 % (1429)Time elapsed: 0.204 s
% 30.17/5.83 % (1429)Instructions burned: 444 (million)
% 30.17/5.83 % (1429)------------------------------
% 30.17/5.83 % (1429)------------------------------
% 30.17/5.83 % (1432)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_1199 for (2959ds/5411Mi)
% 30.17/5.84 % (1433)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_1199 for (2959ds/1762Mi)
% 30.17/5.87 % (1427)Instruction limit reached!
% 30.17/5.87 % (1427)------------------------------
% 30.17/5.87 % (1427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.17/5.87 % (1427)Termination reason: Unknown
% 30.17/5.87 % (1427)Termination phase: Saturation
% 30.17/5.87
% 30.17/5.87 % (1427)Memory used [KB]: 8315
% 30.17/5.87 % (1427)Time elapsed: 0.365 s
% 30.17/5.87 % (1427)Instructions burned: 866 (million)
% 30.17/5.87 % (1427)------------------------------
% 30.17/5.87 % (1427)------------------------------
% 30.17/5.88 % (1434)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_1199 for (2959ds/96Mi)
% 31.43/5.93 % (1434)Instruction limit reached!
% 31.43/5.93 % (1434)------------------------------
% 31.43/5.93 % (1434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.43/5.93 % (1434)Termination reason: Unknown
% 31.43/5.93 % (1434)Termination phase: Property scanning
% 31.43/5.93
% 31.43/5.93 % (1434)Memory used [KB]: 2430
% 31.43/5.93 % (1434)Time elapsed: 0.045 s
% 31.43/5.93 % (1434)Instructions burned: 96 (million)
% 31.43/5.93 % (1434)------------------------------
% 31.43/5.93 % (1434)------------------------------
% 31.43/5.94 % (1435)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_1199 for (2958ds/503Mi)
% 31.43/5.96 % (1431)Instruction limit reached!
% 31.43/5.96 % (1431)------------------------------
% 31.43/5.96 % (1431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.43/5.96 % (1431)Termination reason: Unknown
% 31.43/5.96 % (1431)Termination phase: Saturation
% 31.43/5.96
% 31.43/5.96 % (1431)Memory used [KB]: 11129
% 31.43/5.96 % (1431)Time elapsed: 0.163 s
% 31.43/5.96 % (1431)Instructions burned: 328 (million)
% 31.43/5.96 % (1431)------------------------------
% 31.43/5.96 % (1431)------------------------------
% 31.43/5.98 % (1436)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_1199 for (2958ds/90Mi)
% 31.43/6.02 % (1436)Instruction limit reached!
% 31.43/6.02 % (1436)------------------------------
% 31.43/6.02 % (1436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.43/6.02 % (1436)Termination reason: Unknown
% 31.43/6.02 % (1436)Termination phase: Property scanning
% 31.43/6.02
% 31.43/6.02 % (1436)Memory used [KB]: 2558
% 31.43/6.02 % (1436)Time elapsed: 0.042 s
% 31.43/6.02 % (1436)Instructions burned: 90 (million)
% 31.43/6.02 % (1436)------------------------------
% 31.43/6.02 % (1436)------------------------------
% 32.67/6.04 % (1437)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_1199 for (2957ds/593Mi)
% 32.67/6.05 % (1430)Instruction limit reached!
% 32.67/6.05 % (1430)------------------------------
% 32.67/6.05 % (1430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.67/6.05 % (1430)Termination reason: Unknown
% 32.67/6.05 % (1430)Termination phase: Saturation
% 32.67/6.05
% 32.67/6.05 % (1430)Memory used [KB]: 9594
% 32.67/6.05 % (1430)Time elapsed: 0.282 s
% 32.67/6.05 % (1430)Instructions burned: 594 (million)
% 32.67/6.05 % (1430)------------------------------
% 32.67/6.05 % (1430)------------------------------
% 32.67/6.07 % (1438)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_1199 for (2957ds/1512Mi)
% 33.26/6.18 % (1435)Instruction limit reached!
% 33.26/6.18 % (1435)------------------------------
% 33.26/6.18 % (1435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.26/6.18 % (1435)Termination reason: Unknown
% 33.26/6.18 % (1435)Termination phase: Saturation
% 33.26/6.18
% 33.26/6.18 % (1435)Memory used [KB]: 9722
% 33.26/6.18 % (1435)Time elapsed: 0.235 s
% 33.26/6.18 % (1435)Instructions burned: 503 (million)
% 33.26/6.18 % (1435)------------------------------
% 33.26/6.18 % (1435)------------------------------
% 33.26/6.19 % (1439)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_1199 for (2956ds/569Mi)
% 33.61/6.26 % (1419)Instruction limit reached!
% 33.61/6.26 % (1419)------------------------------
% 33.61/6.26 % (1419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.61/6.26 % (1419)Termination reason: Unknown
% 33.61/6.26 % (1419)Termination phase: Saturation
% 33.61/6.26
% 33.61/6.26 % (1419)Memory used [KB]: 7547
% 33.61/6.26 % (1419)Time elapsed: 1.747 s
% 33.61/6.26 % (1419)Instructions burned: 4716 (million)
% 33.61/6.26 % (1419)------------------------------
% 33.61/6.26 % (1419)------------------------------
% 33.61/6.28 % (1440)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_1199 for (2955ds/501Mi)
% 33.98/6.32 % (1437)Instruction limit reached!
% 33.98/6.32 % (1437)------------------------------
% 33.98/6.32 % (1437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.98/6.32 % (1437)Termination reason: Unknown
% 33.98/6.32 % (1437)Termination phase: Saturation
% 33.98/6.32
% 33.98/6.32 % (1437)Memory used [KB]: 9850
% 33.98/6.32 % (1437)Time elapsed: 0.283 s
% 33.98/6.32 % (1437)Instructions burned: 594 (million)
% 33.98/6.32 % (1437)------------------------------
% 33.98/6.32 % (1437)------------------------------
% 33.98/6.34 % (1441)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_1199 for (2954ds/562Mi)
% 34.58/6.42 % (1439)Instruction limit reached!
% 34.58/6.42 % (1439)------------------------------
% 34.58/6.42 % (1439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.58/6.42 % (1439)Termination reason: Unknown
% 34.58/6.42 % (1439)Termination phase: Saturation
% 34.58/6.42
% 34.58/6.42 % (1439)Memory used [KB]: 10362
% 34.58/6.42 % (1439)Time elapsed: 0.229 s
% 34.58/6.42 % (1439)Instructions burned: 570 (million)
% 34.58/6.42 % (1439)------------------------------
% 34.58/6.42 % (1439)------------------------------
% 34.58/6.44 % (1442)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_1199 for (2953ds/406Mi)
% 35.13/6.50 % (1433)Instruction limit reached!
% 35.13/6.50 % (1433)------------------------------
% 35.13/6.50 % (1433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.13/6.50 % (1433)Termination reason: Unknown
% 35.13/6.50 % (1433)Termination phase: Saturation
% 35.13/6.50
% 35.13/6.50 % (1433)Memory used [KB]: 22899
% 35.13/6.50 % (1433)Time elapsed: 0.657 s
% 35.13/6.50 % (1433)Instructions burned: 1763 (million)
% 35.13/6.50 % (1433)------------------------------
% 35.13/6.50 % (1433)------------------------------
% 35.13/6.52 % (1443)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_1199 for (2952ds/582Mi)
% 35.13/6.52 % (1440)Instruction limit reached!
% 35.13/6.52 % (1440)------------------------------
% 35.13/6.52 % (1440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.13/6.52 % (1440)Termination reason: Unknown
% 35.13/6.52 % (1440)Termination phase: Saturation
% 35.13/6.52
% 35.13/6.52 % (1440)Memory used [KB]: 10234
% 35.13/6.52 % (1440)Time elapsed: 0.244 s
% 35.13/6.52 % (1440)Instructions burned: 501 (million)
% 35.13/6.52 % (1440)------------------------------
% 35.13/6.52 % (1440)------------------------------
% 35.13/6.54 % (1444)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_1199 for (2952ds/456Mi)
% 35.13/6.59 % (1441)Instruction limit reached!
% 35.13/6.59 % (1441)------------------------------
% 35.13/6.59 % (1441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.13/6.59 % (1441)Termination reason: Unknown
% 35.13/6.59 % (1441)Termination phase: Saturation
% 35.13/6.59
% 35.13/6.59 % (1441)Memory used [KB]: 8315
% 35.13/6.59 % (1441)Time elapsed: 0.257 s
% 35.13/6.59 % (1441)Instructions burned: 563 (million)
% 35.13/6.59 % (1441)------------------------------
% 35.13/6.59 % (1441)------------------------------
% 35.87/6.61 % (1445)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_1199 for (2952ds/393Mi)
% 35.87/6.63 % (1442)Instruction limit reached!
% 35.87/6.63 % (1442)------------------------------
% 35.87/6.63 % (1442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.87/6.63 % (1442)Termination reason: Unknown
% 35.87/6.63 % (1442)Termination phase: Saturation
% 35.87/6.63
% 35.87/6.63 % (1442)Memory used [KB]: 7675
% 35.87/6.63 % (1442)Time elapsed: 0.189 s
% 35.87/6.63 % (1442)Instructions burned: 406 (million)
% 35.87/6.63 % (1442)------------------------------
% 35.87/6.63 % (1442)------------------------------
% 35.87/6.64 % (1446)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_1199 for (2951ds/1335Mi)
% 36.27/6.75 % (1444)Instruction limit reached!
% 36.27/6.75 % (1444)------------------------------
% 36.27/6.75 % (1444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.27/6.75 % (1444)Termination reason: Unknown
% 36.27/6.75 % (1444)Termination phase: Saturation
% 36.27/6.75
% 36.27/6.75 % (1444)Memory used [KB]: 9466
% 36.27/6.75 % (1444)Time elapsed: 0.210 s
% 36.27/6.75 % (1444)Instructions burned: 456 (million)
% 36.27/6.75 % (1444)------------------------------
% 36.27/6.75 % (1444)------------------------------
% 36.27/6.77 % (1447)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_1199 for (2950ds/3373Mi)
% 36.27/6.78 % (1445)Instruction limit reached!
% 36.27/6.78 % (1445)------------------------------
% 36.27/6.78 % (1445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.27/6.78 % (1445)Termination reason: Unknown
% 36.27/6.78 % (1445)Termination phase: Saturation
% 36.27/6.78
% 36.27/6.78 % (1445)Memory used [KB]: 9466
% 36.27/6.78 % (1445)Time elapsed: 0.177 s
% 36.27/6.78 % (1445)Instructions burned: 394 (million)
% 36.27/6.78 % (1445)------------------------------
% 36.27/6.78 % (1445)------------------------------
% 36.89/6.80 % (1448)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_1199 for (2950ds/474Mi)
% 36.89/6.80 % (1443)Instruction limit reached!
% 36.89/6.80 % (1443)------------------------------
% 36.89/6.80 % (1443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.89/6.80 % (1443)Termination reason: Unknown
% 36.89/6.80 % (1443)Termination phase: Saturation
% 36.89/6.80
% 36.89/6.80 % (1443)Memory used [KB]: 10362
% 36.89/6.80 % (1443)Time elapsed: 0.289 s
% 36.89/6.80 % (1443)Instructions burned: 582 (million)
% 36.89/6.80 % (1443)------------------------------
% 36.89/6.80 % (1443)------------------------------
% 36.89/6.81 % (1438)Instruction limit reached!
% 36.89/6.81 % (1438)------------------------------
% 36.89/6.81 % (1438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.89/6.81 % (1438)Termination reason: Unknown
% 36.89/6.81 % (1438)Termination phase: Saturation
% 36.89/6.81
% 36.89/6.81 % (1438)Memory used [KB]: 13304
% 36.89/6.81 % (1438)Time elapsed: 0.767 s
% 36.89/6.81 % (1438)Instructions burned: 1513 (million)
% 36.89/6.81 % (1438)------------------------------
% 36.89/6.81 % (1438)------------------------------
% 36.89/6.82 % (1449)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_1199 for (2949ds/157Mi)
% 36.89/6.83 % (1450)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_1199 for (2949ds/590Mi)
% 36.89/6.89 % (1449)Instruction limit reached!
% 36.89/6.89 % (1449)------------------------------
% 36.89/6.89 % (1449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.89/6.89 % (1449)Termination reason: Unknown
% 36.89/6.89 % (1449)Termination phase: Property scanning
% 36.89/6.89
% 36.89/6.89 % (1449)Memory used [KB]: 2558
% 36.89/6.89 % (1449)Time elapsed: 0.069 s
% 36.89/6.89 % (1449)Instructions burned: 159 (million)
% 36.89/6.89 % (1449)------------------------------
% 36.89/6.89 % (1449)------------------------------
% 38.25/6.91 % (1451)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_1199 for (2949ds/104Mi)
% 38.25/6.95 % (1451)Instruction limit reached!
% 38.25/6.95 % (1451)------------------------------
% 38.25/6.95 % (1451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.25/6.95 % (1451)Termination reason: Unknown
% 38.25/6.95 % (1451)Termination phase: Property scanning
% 38.25/6.95
% 38.25/6.95 % (1451)Memory used [KB]: 2558
% 38.25/6.95 % (1451)Time elapsed: 0.048 s
% 38.25/6.95 % (1451)Instructions burned: 105 (million)
% 38.25/6.95 % (1451)------------------------------
% 38.25/6.95 % (1451)------------------------------
% 38.25/6.97 % (1452)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_1199 for (2948ds/414Mi)
% 38.25/6.99 % (1448)Instruction limit reached!
% 38.25/6.99 % (1448)------------------------------
% 38.25/6.99 % (1448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.25/6.99 % (1448)Termination reason: Unknown
% 38.25/6.99 % (1448)Termination phase: Saturation
% 38.25/6.99
% 38.25/6.99 % (1448)Memory used [KB]: 7419
% 38.25/6.99 % (1448)Time elapsed: 0.193 s
% 38.25/6.99 % (1448)Instructions burned: 476 (million)
% 38.25/6.99 % (1448)------------------------------
% 38.25/6.99 % (1448)------------------------------
% 38.25/7.01 % (1453)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_1199 for (2948ds/715Mi)
% 39.69/7.10 % (1450)Instruction limit reached!
% 39.69/7.10 % (1450)------------------------------
% 39.69/7.10 % (1450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.69/7.10 % (1450)Termination reason: Unknown
% 39.69/7.10 % (1450)Termination phase: Saturation
% 39.69/7.10
% 39.69/7.10 % (1450)Memory used [KB]: 9338
% 39.69/7.10 % (1450)Time elapsed: 0.272 s
% 39.69/7.10 % (1450)Instructions burned: 592 (million)
% 39.69/7.10 % (1450)------------------------------
% 39.69/7.10 % (1450)------------------------------
% 39.69/7.11 % (1454)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_1199 for (2947ds/961Mi)
% 40.41/7.14 % (1452)Instruction limit reached!
% 40.41/7.14 % (1452)------------------------------
% 40.41/7.14 % (1452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.41/7.14 % (1452)Termination reason: Unknown
% 40.41/7.14 % (1452)Termination phase: Saturation
% 40.41/7.14
% 40.41/7.14 % (1452)Memory used [KB]: 7419
% 40.41/7.14 % (1452)Time elapsed: 0.170 s
% 40.41/7.14 % (1452)Instructions burned: 414 (million)
% 40.41/7.14 % (1452)------------------------------
% 40.41/7.14 % (1452)------------------------------
% 40.41/7.15 % (1455)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_1199 for (2946ds/1213Mi)
% 40.78/7.22 % (1446)Instruction limit reached!
% 40.78/7.22 % (1446)------------------------------
% 40.78/7.22 % (1446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.78/7.22 % (1446)Termination reason: Unknown
% 40.78/7.22 % (1446)Termination phase: Saturation
% 40.78/7.22
% 40.78/7.22 % (1446)Memory used [KB]: 9466
% 40.78/7.22 % (1446)Time elapsed: 0.583 s
% 40.78/7.22 % (1446)Instructions burned: 1336 (million)
% 40.78/7.22 % (1446)------------------------------
% 40.78/7.22 % (1446)------------------------------
% 40.78/7.24 % (1456)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_1199 for (2945ds/1979Mi)
% 41.21/7.35 % (1453)Instruction limit reached!
% 41.21/7.35 % (1453)------------------------------
% 41.21/7.35 % (1453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.21/7.35 % (1453)Termination reason: Unknown
% 41.21/7.35 % (1453)Termination phase: Saturation
% 41.21/7.35
% 41.21/7.35 % (1453)Memory used [KB]: 5373
% 41.21/7.35 % (1453)Time elapsed: 0.343 s
% 41.21/7.35 % (1453)Instructions burned: 715 (million)
% 41.21/7.35 % (1453)------------------------------
% 41.21/7.35 % (1453)------------------------------
% 41.21/7.37 % (1457)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_1199 for (2944ds/481Mi)
% 41.88/7.56 % (1457)Instruction limit reached!
% 41.88/7.56 % (1457)------------------------------
% 41.88/7.56 % (1457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.88/7.56 % (1457)Termination reason: Unknown
% 41.88/7.56 % (1457)Termination phase: Saturation
% 41.88/7.56
% 41.88/7.56 % (1457)Memory used [KB]: 7419
% 41.88/7.56 % (1457)Time elapsed: 0.196 s
% 41.88/7.56 % (1457)Instructions burned: 481 (million)
% 41.88/7.56 % (1457)------------------------------
% 41.88/7.56 % (1457)------------------------------
% 41.88/7.58 % (1454)Instruction limit reached!
% 41.88/7.58 % (1454)------------------------------
% 41.88/7.58 % (1454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.88/7.58 % (1454)Termination reason: Unknown
% 41.88/7.58 % (1454)Termination phase: Saturation
% 41.88/7.58
% 41.88/7.58 % (1454)Memory used [KB]: 10106
% 41.88/7.58 % (1454)Time elapsed: 0.465 s
% 41.88/7.58 % (1454)Instructions burned: 961 (million)
% 41.88/7.58 % (1454)------------------------------
% 41.88/7.58 % (1454)------------------------------
% 41.88/7.58 % (1458)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_1199 for (2942ds/783Mi)
% 41.88/7.59 % (1459)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_1199 for (2942ds/432Mi)
% 43.18/7.76 % (1455)Instruction limit reached!
% 43.18/7.76 % (1455)------------------------------
% 43.18/7.76 % (1455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.18/7.76 % (1455)Termination reason: Unknown
% 43.18/7.76 % (1455)Termination phase: Saturation
% 43.18/7.76
% 43.18/7.76 % (1455)Memory used [KB]: 14583
% 43.18/7.76 % (1455)Time elapsed: 0.606 s
% 43.18/7.76 % (1455)Instructions burned: 1215 (million)
% 43.18/7.76 % (1455)------------------------------
% 43.18/7.76 % (1455)------------------------------
% 43.18/7.78 % (1460)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_1199 for (2940ds/1670Mi)
% 43.18/7.79 % (1459)Instruction limit reached!
% 43.18/7.79 % (1459)------------------------------
% 43.18/7.79 % (1459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.18/7.79 % (1459)Termination reason: Unknown
% 43.18/7.79 % (1459)Termination phase: Saturation
% 43.18/7.79
% 43.18/7.79 % (1459)Memory used [KB]: 9338
% 43.18/7.79 % (1459)Time elapsed: 0.200 s
% 43.18/7.79 % (1459)Instructions burned: 432 (million)
% 43.18/7.79 % (1459)------------------------------
% 43.18/7.79 % (1459)------------------------------
% 44.31/7.81 % (1461)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_1199 for (2940ds/90Mi)
% 44.31/7.85 % (1461)Instruction limit reached!
% 44.31/7.85 % (1461)------------------------------
% 44.31/7.85 % (1461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.31/7.85 % (1461)Termination reason: Unknown
% 44.31/7.85 % (1461)Termination phase: Property scanning
% 44.31/7.85
% 44.31/7.85 % (1461)Memory used [KB]: 2558
% 44.31/7.85 % (1461)Time elapsed: 0.042 s
% 44.31/7.85 % (1461)Instructions burned: 90 (million)
% 44.31/7.85 % (1461)------------------------------
% 44.31/7.85 % (1461)------------------------------
% 44.31/7.87 % (1462)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_1199 for (2939ds/346Mi)
% 44.66/7.97 % (1458)Instruction limit reached!
% 44.66/7.97 % (1458)------------------------------
% 44.66/7.97 % (1458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.66/7.97 % (1458)Termination reason: Unknown
% 44.66/7.97 % (1458)Termination phase: Saturation
% 44.66/7.97
% 44.66/7.97 % (1458)Memory used [KB]: 11513
% 44.66/7.97 % (1458)Time elapsed: 0.393 s
% 44.66/7.97 % (1458)Instructions burned: 784 (million)
% 44.66/7.97 % (1458)------------------------------
% 44.66/7.97 % (1458)------------------------------
% 44.66/7.99 % (1463)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_1199 for (2938ds/401Mi)
% 44.66/8.01 % (1462)Instruction limit reached!
% 44.66/8.01 % (1462)------------------------------
% 44.66/8.01 % (1462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.66/8.01 % (1462)Termination reason: Unknown
% 44.66/8.01 % (1462)Termination phase: Saturation
% 44.66/8.01
% 44.66/8.01 % (1462)Memory used [KB]: 7419
% 44.66/8.01 % (1462)Time elapsed: 0.144 s
% 44.66/8.01 % (1462)Instructions burned: 348 (million)
% 44.66/8.01 % (1462)------------------------------
% 44.66/8.01 % (1462)------------------------------
% 44.66/8.03 % (1464)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_1199 for (2937ds/6454Mi)
% 47.31/8.15 % (1463)Instruction limit reached!
% 47.31/8.15 % (1463)------------------------------
% 47.31/8.15 % (1463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.31/8.15 % (1463)Termination reason: Unknown
% 47.31/8.15 % (1463)Termination phase: Saturation
% 47.31/8.15
% 47.31/8.15 % (1463)Memory used [KB]: 7419
% 47.31/8.15 % (1463)Time elapsed: 0.166 s
% 47.31/8.15 % (1463)Instructions burned: 401 (million)
% 47.31/8.15 % (1463)------------------------------
% 47.31/8.15 % (1463)------------------------------
% 47.31/8.17 % (1465)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_1199 for (2936ds/283Mi)
% 47.31/8.19 % (1456)Instruction limit reached!
% 47.31/8.19 % (1456)------------------------------
% 47.31/8.19 % (1456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.31/8.19 % (1456)Termination reason: Unknown
% 47.31/8.19 % (1456)Termination phase: Saturation
% 47.31/8.19
% 47.31/8.19 % (1456)Memory used [KB]: 10362
% 47.31/8.19 % (1456)Time elapsed: 0.955 s
% 47.31/8.19 % (1456)Instructions burned: 1979 (million)
% 47.31/8.19 % (1456)------------------------------
% 47.31/8.19 % (1456)------------------------------
% 47.70/8.21 % (1466)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_1199 for (2936ds/865Mi)
% 47.70/8.29 % (1465)Instruction limit reached!
% 47.70/8.29 % (1465)------------------------------
% 47.70/8.29 % (1465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.70/8.29 % (1465)Termination reason: Unknown
% 47.70/8.29 % (1465)Termination phase: Saturation
% 47.70/8.29
% 47.70/8.29 % (1465)Memory used [KB]: 8187
% 47.70/8.29 % (1465)Time elapsed: 0.129 s
% 47.70/8.29 % (1465)Instructions burned: 283 (million)
% 47.70/8.29 % (1465)------------------------------
% 47.70/8.29 % (1465)------------------------------
% 48.25/8.31 % (1467)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_1199 for (2935ds/4528Mi)
% 48.25/8.39 % (1447)Instruction limit reached!
% 48.25/8.39 % (1447)------------------------------
% 48.25/8.39 % (1447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.25/8.39 % (1447)Termination reason: Unknown
% 48.25/8.39 % (1447)Termination phase: Saturation
% 48.25/8.39
% 48.25/8.39 % (1447)Memory used [KB]: 12409
% 48.25/8.39 % (1447)Time elapsed: 1.625 s
% 48.25/8.39 % (1447)Instructions burned: 3374 (million)
% 48.25/8.39 % (1447)------------------------------
% 48.25/8.39 % (1447)------------------------------
% 48.67/8.41 % (1468)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_1199 for (2934ds/1001Mi)
% 48.67/8.43 % (1460)Instruction limit reached!
% 48.67/8.43 % (1460)------------------------------
% 48.67/8.43 % (1460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.67/8.43 % (1460)Termination reason: Unknown
% 48.67/8.43 % (1460)Termination phase: Saturation
% 48.67/8.43
% 48.67/8.43 % (1460)Memory used [KB]: 16375
% 48.67/8.43 % (1460)Time elapsed: 0.655 s
% 48.67/8.43 % (1460)Instructions burned: 1671 (million)
% 48.67/8.43 % (1460)------------------------------
% 48.67/8.43 % (1460)------------------------------
% 48.67/8.45 % (1469)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_1199 for (2933ds/102Mi)
% 48.67/8.49 % (1469)Instruction limit reached!
% 48.67/8.49 % (1469)------------------------------
% 48.67/8.49 % (1469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.67/8.49 % (1469)Termination reason: Unknown
% 48.67/8.49 % (1469)Termination phase: Property scanning
% 48.67/8.49
% 48.67/8.49 % (1469)Memory used [KB]: 2558
% 48.67/8.49 % (1469)Time elapsed: 0.047 s
% 48.67/8.49 % (1469)Instructions burned: 102 (million)
% 48.67/8.49 % (1469)------------------------------
% 48.67/8.49 % (1469)------------------------------
% 48.97/8.51 % (1470)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_1199 for (2933ds/952Mi)
% 48.97/8.52 % (1432)Refutation not found, non-redundant clauses discarded% (1432)------------------------------
% 48.97/8.52 % (1432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.97/8.52 % (1432)Termination reason: Refutation not found, non-redundant clauses discarded
% 48.97/8.52
% 48.97/8.52 % (1432)Memory used [KB]: 16119
% 48.97/8.52 % (1432)Time elapsed: 2.693 s
% 48.97/8.52 % (1432)Instructions burned: 5396 (million)
% 48.97/8.52 % (1432)------------------------------
% 48.97/8.52 % (1432)------------------------------
% 48.97/8.54 % (1471)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_1199 for (2932ds/578Mi)
% 48.97/8.58 % (1467)Refutation not found, incomplete strategy
% 48.97/8.58 % (1467)------------------------------
% 48.97/8.58 % (1467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.97/8.58 % (1467)Termination reason: Refutation not found, incomplete strategy
% 48.97/8.58
% 48.97/8.58
% 48.97/8.58 % (1467)Memory used [KB]: 2942
% 48.97/8.58 % (1467)Time elapsed: 0.271 s
% 48.97/8.58 % (1467)Instructions burned: 639 (million)
% 48.97/8.58 % (1467)------------------------------
% 48.97/8.58 % (1467)------------------------------
% 48.97/8.59 % (1466)Instruction limit reached!
% 48.97/8.59 % (1466)------------------------------
% 48.97/8.59 % (1466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.97/8.59 % (1466)Termination reason: Unknown
% 48.97/8.59 % (1466)Termination phase: Saturation
% 48.97/8.59
% 48.97/8.59 % (1466)Memory used [KB]: 7931
% 48.97/8.59 % (1466)Time elapsed: 0.383 s
% 48.97/8.59 % (1466)Instructions burned: 866 (million)
% 48.97/8.59 % (1466)------------------------------
% 48.97/8.59 % (1466)------------------------------
% 49.78/8.60 % (1472)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_1199 for (2932ds/643Mi)
% 49.78/8.61 % (1473)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_1199 for (2932ds/865Mi)
% 49.88/8.76 % (1420)Instruction limit reached!
% 49.88/8.76 % (1420)------------------------------
% 49.88/8.76 % (1420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.88/8.76 % (1420)Termination reason: Unknown
% 49.88/8.76 % (1420)Termination phase: Saturation
% 49.88/8.76
% 49.88/8.76 % (1420)Memory used [KB]: 25330
% 49.88/8.76 % (1420)Time elapsed: 4.196 s
% 49.88/8.76 % (1420)Instructions burned: 8251 (million)
% 49.88/8.76 % (1420)------------------------------
% 49.88/8.76 % (1420)------------------------------
% 49.88/8.76 % (1471)Instruction limit reached!
% 49.88/8.76 % (1471)------------------------------
% 49.88/8.76 % (1471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.88/8.76 % (1471)Termination reason: Unknown
% 49.88/8.77 % (1471)Termination phase: Saturation
% 49.88/8.77
% 49.88/8.77 % (1471)Memory used [KB]: 9978
% 49.88/8.77 % (1471)Time elapsed: 0.225 s
% 49.88/8.77 % (1471)Instructions burned: 578 (million)
% 49.88/8.77 % (1471)------------------------------
% 49.88/8.77 % (1471)------------------------------
% 49.88/8.78 % (1474)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_1199 for (2930ds/1174Mi)
% 49.88/8.78 % (1475)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_1199 for (2930ds/644Mi)
% 50.21/8.85 % (1472)Instruction limit reached!
% 50.21/8.85 % (1472)------------------------------
% 50.21/8.85 % (1472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.21/8.85 % (1472)Termination reason: Unknown
% 50.21/8.85 % (1472)Termination phase: Saturation
% 50.21/8.85
% 50.21/8.85 % (1472)Memory used [KB]: 9466
% 50.21/8.85 % (1472)Time elapsed: 0.253 s
% 50.21/8.85 % (1472)Instructions burned: 643 (million)
% 50.21/8.85 % (1472)------------------------------
% 50.21/8.85 % (1472)------------------------------
% 50.21/8.87 % (1476)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_1199 for (2929ds/1201Mi)
% 50.47/8.90 % (1468)Instruction limit reached!
% 50.47/8.90 % (1468)------------------------------
% 50.47/8.90 % (1468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.47/8.90 % (1468)Termination reason: Unknown
% 50.47/8.90 % (1468)Termination phase: Saturation
% 50.47/8.90
% 50.47/8.90 % (1468)Memory used [KB]: 11385
% 50.47/8.90 % (1468)Time elapsed: 0.494 s
% 50.47/8.90 % (1468)Instructions burned: 1002 (million)
% 50.47/8.90 % (1468)------------------------------
% 50.47/8.90 % (1468)------------------------------
% 50.47/8.92 % (1477)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_1199 for (2929ds/1046Mi)
% 50.47/8.97 % (1470)Instruction limit reached!
% 50.47/8.97 % (1470)------------------------------
% 50.47/8.97 % (1470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.47/8.97 % (1470)Termination reason: Unknown
% 50.47/8.97 % (1470)Termination phase: Saturation
% 50.47/8.97
% 50.47/8.97 % (1470)Memory used [KB]: 10234
% 50.47/8.97 % (1470)Time elapsed: 0.461 s
% 50.47/8.97 % (1470)Instructions burned: 952 (million)
% 50.47/8.97 % (1470)------------------------------
% 50.47/8.97 % (1470)------------------------------
% 50.47/8.98 % (1478)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_1199 for (2928ds/222Mi)
% 50.47/8.99 % (1473)Instruction limit reached!
% 50.47/8.99 % (1473)------------------------------
% 50.47/8.99 % (1473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.47/8.99 % (1473)Termination reason: Unknown
% 50.47/8.99 % (1473)Termination phase: Saturation
% 50.47/8.99
% 50.47/8.99 % (1473)Memory used [KB]: 7675
% 50.47/8.99 % (1473)Time elapsed: 0.381 s
% 50.47/8.99 % (1473)Instructions burned: 866 (million)
% 50.47/8.99 % (1473)------------------------------
% 50.47/8.99 % (1473)------------------------------
% 50.47/9.00 % (1479)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_1199 for (2928ds/68Mi)
% 53.67/9.04 % (1479)Instruction limit reached!
% 53.67/9.04 % (1479)------------------------------
% 53.67/9.04 % (1479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.67/9.04 % (1479)Termination reason: Unknown
% 53.67/9.04 % (1479)Termination phase: Property scanning
% 53.67/9.04
% 53.67/9.04 % (1479)Memory used [KB]: 2430
% 53.67/9.04 % (1479)Time elapsed: 0.033 s
% 53.67/9.04 % (1479)Instructions burned: 69 (million)
% 53.67/9.04 % (1479)------------------------------
% 53.67/9.04 % (1479)------------------------------
% 53.67/9.05 % (1480)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_1199 for (2927ds/454Mi)
% 53.67/9.08 % (1478)Instruction limit reached!
% 53.67/9.08 % (1478)------------------------------
% 53.67/9.08 % (1478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.67/9.08 % (1478)Termination reason: Unknown
% 53.67/9.08 % (1478)Termination phase: Saturation
% 53.67/9.08
% 53.67/9.08 % (1478)Memory used [KB]: 7419
% 53.67/9.08 % (1478)Time elapsed: 0.096 s
% 53.67/9.08 % (1478)Instructions burned: 224 (million)
% 53.67/9.08 % (1478)------------------------------
% 53.67/9.08 % (1478)------------------------------
% 53.67/9.09 % (1475)Instruction limit reached!
% 53.67/9.09 % (1475)------------------------------
% 53.67/9.09 % (1475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.67/9.09 % (1475)Termination reason: Unknown
% 53.67/9.09 % (1475)Termination phase: Saturation
% 53.67/9.09
% 53.67/9.09 % (1475)Memory used [KB]: 8059
% 53.67/9.09 % (1475)Time elapsed: 0.306 s
% 53.67/9.09 % (1475)Instructions burned: 646 (million)
% 53.67/9.09 % (1475)------------------------------
% 53.67/9.09 % (1475)------------------------------
% 53.67/9.10 % (1481)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_1199 for (2927ds/360Mi)
% 53.67/9.10 % (1482)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_1199 for (2927ds/157Mi)
% 54.28/9.17 % (1482)Instruction limit reached!
% 54.28/9.17 % (1482)------------------------------
% 54.28/9.17 % (1482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.28/9.17 % (1482)Termination reason: Unknown
% 54.28/9.17 % (1482)Termination phase: Property scanning
% 54.28/9.17
% 54.28/9.17 % (1482)Memory used [KB]: 2558
% 54.28/9.17 % (1482)Time elapsed: 0.069 s
% 54.28/9.17 % (1482)Instructions burned: 158 (million)
% 54.28/9.17 % (1482)------------------------------
% 54.28/9.17 % (1482)------------------------------
% 54.28/9.19 % (1483)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_1199 for (2926ds/5061Mi)
% 54.64/9.24 % (1480)Instruction limit reached!
% 54.64/9.24 % (1480)------------------------------
% 54.64/9.24 % (1480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.64/9.24 % (1480)Termination reason: Unknown
% 54.64/9.24 % (1480)Termination phase: Saturation
% 54.64/9.24
% 54.64/9.24 % (1480)Memory used [KB]: 11897
% 54.64/9.24 % (1480)Time elapsed: 0.189 s
% 54.64/9.24 % (1480)Instructions burned: 456 (million)
% 54.64/9.24 % (1480)------------------------------
% 54.64/9.24 % (1480)------------------------------
% 54.64/9.24 % (1481)Instruction limit reached!
% 54.64/9.24 % (1481)------------------------------
% 54.64/9.24 % (1481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.64/9.24 % (1481)Termination reason: Unknown
% 54.64/9.24 % (1481)Termination phase: Saturation
% 54.64/9.24
% 54.64/9.24 % (1481)Memory used [KB]: 7419
% 54.64/9.24 % (1481)Time elapsed: 0.150 s
% 54.64/9.24 % (1481)Instructions burned: 360 (million)
% 54.64/9.24 % (1481)------------------------------
% 54.64/9.24 % (1481)------------------------------
% 54.64/9.26 % (1484)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_1199 for (2925ds/2401Mi)
% 54.64/9.26 % (1485)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_1199 for (2925ds/5798Mi)
% 55.40/9.31 % (1477)Instruction limit reached!
% 55.40/9.31 % (1477)------------------------------
% 55.40/9.31 % (1477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.40/9.31 % (1477)Termination reason: Unknown
% 55.40/9.31 % (1477)Termination phase: Saturation
% 55.40/9.31
% 55.40/9.31 % (1477)Memory used [KB]: 7547
% 55.40/9.31 % (1477)Time elapsed: 0.399 s
% 55.40/9.31 % (1477)Instructions burned: 1048 (million)
% 55.40/9.31 % (1477)------------------------------
% 55.40/9.31 % (1477)------------------------------
% 55.40/9.32 % (1474)Refutation not found, non-redundant clauses discarded% (1474)------------------------------
% 55.40/9.32 % (1474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.40/9.32 % (1474)Termination reason: Refutation not found, non-redundant clauses discarded
% 55.40/9.32
% 55.40/9.32 % (1474)Memory used [KB]: 10106
% 55.40/9.32 % (1474)Time elapsed: 0.541 s
% 55.40/9.32 % (1474)Instructions burned: 1111 (million)
% 55.40/9.32 % (1474)------------------------------
% 55.40/9.32 % (1474)------------------------------
% 55.40/9.33 % (1486)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_1199 for (2924ds/346Mi)
% 55.40/9.33 % (1487)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_1199 for (2924ds/1321Mi)
% 55.67/9.41 % (1476)Instruction limit reached!
% 55.67/9.41 % (1476)------------------------------
% 55.67/9.41 % (1476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.67/9.41 % (1476)Termination reason: Unknown
% 55.67/9.41 % (1476)Termination phase: Saturation
% 55.67/9.41
% 55.67/9.41 % (1476)Memory used [KB]: 10618
% 55.67/9.41 % (1476)Time elapsed: 0.542 s
% 55.67/9.41 % (1476)Instructions burned: 1202 (million)
% 55.67/9.41 % (1476)------------------------------
% 55.67/9.41 % (1476)------------------------------
% 55.67/9.42 % (1488)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_1199 for (2923ds/1312Mi)
% 55.67/9.47 % (1486)Instruction limit reached!
% 55.67/9.47 % (1486)------------------------------
% 55.67/9.47 % (1486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.67/9.47 % (1486)Termination reason: Unknown
% 55.67/9.47 % (1486)Termination phase: Saturation
% 55.67/9.47
% 55.67/9.47 % (1486)Memory used [KB]: 7419
% 55.67/9.47 % (1486)Time elapsed: 0.144 s
% 55.67/9.47 % (1486)Instructions burned: 346 (million)
% 55.67/9.47 % (1486)------------------------------
% 55.67/9.47 % (1486)------------------------------
% 55.67/9.49 % (1489)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_1199 for (2923ds/672Mi)
% 56.26/9.82 % (1489)Instruction limit reached!
% 56.26/9.82 % (1489)------------------------------
% 56.26/9.82 % (1489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.26/9.82 % (1489)Termination reason: Unknown
% 56.26/9.82 % (1489)Termination phase: Saturation
% 56.26/9.82
% 56.26/9.82 % (1489)Memory used [KB]: 10746
% 56.26/9.82 % (1489)Time elapsed: 0.331 s
% 56.26/9.82 % (1489)Instructions burned: 673 (million)
% 56.26/9.82 % (1489)------------------------------
% 56.26/9.82 % (1489)------------------------------
% 56.26/9.83 % (1490)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_1199 for (2919ds/1897Mi)
% 56.70/9.92 % (1488)Instruction limit reached!
% 56.70/9.92 % (1488)------------------------------
% 56.70/9.92 % (1488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.70/9.92 % (1488)Termination reason: Unknown
% 56.70/9.92 % (1488)Termination phase: Saturation
% 56.70/9.92
% 56.70/9.92 % (1488)Memory used [KB]: 15095
% 56.70/9.92 % (1488)Time elapsed: 0.499 s
% 56.70/9.92 % (1488)Instructions burned: 1314 (million)
% 56.70/9.92 % (1488)------------------------------
% 56.70/9.92 % (1488)------------------------------
% 56.70/9.94 % (1491)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_1199 for (2918ds/1202Mi)
% 56.70/9.98 % (1487)Instruction limit reached!
% 56.70/9.98 % (1487)------------------------------
% 56.70/9.98 % (1487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.70/9.98 % (1487)Termination reason: Unknown
% 56.70/9.98 % (1487)Termination phase: Saturation
% 56.70/9.98
% 56.70/9.98 % (1487)Memory used [KB]: 7931
% 56.70/9.98 % (1487)Time elapsed: 0.649 s
% 56.70/9.98 % (1487)Instructions burned: 1322 (million)
% 56.70/9.98 % (1487)------------------------------
% 56.70/9.98 % (1487)------------------------------
% 56.70/10.00 % (1492)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_1199 for (2918ds/1493Mi)
% 63.33/10.42 % (1484)Instruction limit reached!
% 63.33/10.42 % (1484)------------------------------
% 63.33/10.42 % (1484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.33/10.42 % (1484)Termination reason: Unknown
% 63.33/10.42 % (1484)Termination phase: Saturation
% 63.33/10.42
% 63.33/10.42 % (1484)Memory used [KB]: 9978
% 63.33/10.42 % (1484)Time elapsed: 1.184 s
% 63.33/10.42 % (1484)Instructions burned: 2401 (million)
% 63.33/10.42 % (1484)------------------------------
% 63.33/10.42 % (1484)------------------------------
% 63.33/10.44 % (1493)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_1199 for (2913ds/7679Mi)
% 63.96/10.50 % (1491)Instruction limit reached!
% 63.96/10.50 % (1491)------------------------------
% 63.96/10.50 % (1491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.96/10.50 % (1491)Termination reason: Unknown
% 63.96/10.50 % (1491)Termination phase: Saturation
% 63.96/10.50
% 63.96/10.50 % (1491)Memory used [KB]: 9083
% 63.96/10.50 % (1491)Time elapsed: 0.568 s
% 63.96/10.50 % (1491)Instructions burned: 1202 (million)
% 63.96/10.50 % (1491)------------------------------
% 63.96/10.50 % (1491)------------------------------
% 63.96/10.52 % (1494)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_1199 for (2912ds/340Mi)
% 63.96/10.55 % (1492)Instruction limit reached!
% 63.96/10.55 % (1492)------------------------------
% 63.96/10.55 % (1492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.96/10.55 % (1492)Termination reason: Unknown
% 63.96/10.55 % (1492)Termination phase: Saturation
% 63.96/10.55
% 63.96/10.55 % (1492)Memory used [KB]: 7675
% 63.96/10.55 % (1492)Time elapsed: 0.550 s
% 63.96/10.55 % (1492)Instructions burned: 1493 (million)
% 63.96/10.55 % (1492)------------------------------
% 63.96/10.55 % (1492)------------------------------
% 63.96/10.56 % (1495)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_1199 for (2912ds/3672Mi)
% 64.44/10.68 % (1494)Instruction limit reached!
% 64.44/10.68 % (1494)------------------------------
% 64.44/10.68 % (1494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.44/10.68 % (1494)Termination reason: Unknown
% 64.44/10.68 % (1494)Termination phase: Saturation
% 64.44/10.68
% 64.44/10.68 % (1494)Memory used [KB]: 10618
% 64.44/10.68 % (1494)Time elapsed: 0.162 s
% 64.44/10.68 % (1494)Instructions burned: 340 (million)
% 64.44/10.68 % (1494)------------------------------
% 64.44/10.68 % (1494)------------------------------
% 65.01/10.70 % (1496)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_1199 for (2911ds/1535Mi)
% 65.01/10.77 % (1490)Instruction limit reached!
% 65.01/10.77 % (1490)------------------------------
% 65.01/10.77 % (1490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.01/10.77 % (1490)Termination reason: Unknown
% 65.01/10.77 % (1490)Termination phase: Saturation
% 65.01/10.77
% 65.01/10.77 % (1490)Memory used [KB]: 13432
% 65.01/10.77 % (1490)Time elapsed: 0.939 s
% 65.01/10.77 % (1490)Instructions burned: 1898 (million)
% 65.01/10.77 % (1490)------------------------------
% 65.01/10.77 % (1490)------------------------------
% 65.01/10.79 % (1497)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_1199 for (2910ds/4637Mi)
% 65.70/11.03 % (1483)Instruction limit reached!
% 65.70/11.03 % (1483)------------------------------
% 65.70/11.03 % (1483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.70/11.03 % (1483)Termination reason: Unknown
% 65.70/11.03 % (1483)Termination phase: Saturation
% 65.70/11.03
% 65.70/11.03 % (1483)Memory used [KB]: 7803
% 65.70/11.03 % (1483)Time elapsed: 1.842 s
% 65.70/11.03 % (1483)Instructions burned: 5063 (million)
% 65.70/11.03 % (1483)------------------------------
% 65.70/11.03 % (1483)------------------------------
% 67.71/11.04 % (1498)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_1199 for (2907ds/3174Mi)
% 68.74/11.26 % (1464)Instruction limit reached!
% 68.74/11.26 % (1464)------------------------------
% 68.74/11.26 % (1464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 68.74/11.26 % (1464)Termination reason: Unknown
% 68.74/11.26 % (1464)Termination phase: Saturation
% 68.74/11.26
% 68.74/11.26 % (1464)Memory used [KB]: 14839
% 68.74/11.26 % (1464)Time elapsed: 3.243 s
% 68.74/11.27 % (1464)Instructions burned: 6455 (million)
% 68.74/11.27 % (1464)------------------------------
% 68.74/11.27 % (1464)------------------------------
% 68.74/11.28 % (1499)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_1199 for (2905ds/307Mi)
% 69.31/11.30 % (1496)Instruction limit reached!
% 69.31/11.30 % (1496)------------------------------
% 69.31/11.30 % (1496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.31/11.30 % (1496)Termination reason: Unknown
% 69.31/11.30 % (1496)Termination phase: Saturation
% 69.31/11.30
% 69.31/11.30 % (1496)Memory used [KB]: 15863
% 69.31/11.30 % (1496)Time elapsed: 0.600 s
% 69.31/11.30 % (1496)Instructions burned: 1535 (million)
% 69.31/11.30 % (1496)------------------------------
% 69.31/11.30 % (1496)------------------------------
% 69.31/11.32 % (1500)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_1199 for (2905ds/3619Mi)
% 69.73/11.41 % (1499)Instruction limit reached!
% 69.73/11.41 % (1499)------------------------------
% 69.73/11.41 % (1499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.73/11.41 % (1499)Termination reason: Unknown
% 69.73/11.41 % (1499)Termination phase: Saturation
% 69.73/11.41
% 69.73/11.41 % (1499)Memory used [KB]: 7419
% 69.73/11.41 % (1499)Time elapsed: 0.130 s
% 69.73/11.41 % (1499)Instructions burned: 308 (million)
% 69.73/11.41 % (1499)------------------------------
% 69.73/11.41 % (1499)------------------------------
% 69.73/11.43 % (1501)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_1199 for (2903ds/2325Mi)
% 75.39/12.15 % (1485)Instruction limit reached!
% 75.39/12.15 % (1485)------------------------------
% 75.39/12.15 % (1485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.39/12.15 % (1485)Termination reason: Unknown
% 75.39/12.15 % (1485)Termination phase: Saturation
% 75.39/12.15
% 75.39/12.15 % (1485)Memory used [KB]: 13688
% 75.39/12.15 % (1485)Time elapsed: 2.911 s
% 75.39/12.15 % (1485)Instructions burned: 5799 (million)
% 75.39/12.15 % (1485)------------------------------
% 75.39/12.15 % (1485)------------------------------
% 75.39/12.17 % (1502)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_1199 for (2896ds/2341Mi)
% 76.44/12.37 % (1495)Instruction limit reached!
% 76.44/12.37 % (1495)------------------------------
% 76.44/12.37 % (1495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.44/12.37 % (1495)Termination reason: Unknown
% 76.44/12.37 % (1495)Termination phase: Saturation
% 76.44/12.37
% 76.44/12.37 % (1495)Memory used [KB]: 13560
% 76.44/12.37 % (1495)Time elapsed: 1.806 s
% 76.44/12.37 % (1495)Instructions burned: 3673 (million)
% 76.44/12.37 % (1495)------------------------------
% 76.44/12.37 % (1495)------------------------------
% 76.44/12.38 % (1503)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_1199 for (2894ds/7257Mi)
% 77.02/12.46 % (1498)Refutation not found, non-redundant clauses discarded% (1498)------------------------------
% 77.02/12.46 % (1498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.02/12.46 % (1498)Termination reason: Refutation not found, non-redundant clauses discarded
% 77.02/12.46
% 77.02/12.46 % (1498)Memory used [KB]: 18933
% 77.02/12.46 % (1498)Time elapsed: 1.412 s
% 77.02/12.46 % (1498)Instructions burned: 2878 (million)
% 77.02/12.46 % (1498)------------------------------
% 77.02/12.46 % (1498)------------------------------
% 77.02/12.47 % (1504)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_1199 for (2893ds/3710Mi)
% 77.49/12.57 % (1501)Instruction limit reached!
% 77.49/12.57 % (1501)------------------------------
% 77.49/12.57 % (1501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.49/12.57 % (1501)Termination reason: Unknown
% 77.49/12.57 % (1501)Termination phase: Saturation
% 77.49/12.57
% 77.49/12.57 % (1501)Memory used [KB]: 18038
% 77.49/12.57 % (1501)Time elapsed: 1.142 s
% 77.49/12.57 % (1501)Instructions burned: 2326 (million)
% 77.49/12.57 % (1501)------------------------------
% 77.49/12.57 % (1501)------------------------------
% 77.49/12.59 % (1505)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_1199 for (2892ds/326Mi)
% 78.17/12.73 % (1505)Instruction limit reached!
% 78.17/12.73 % (1505)------------------------------
% 78.17/12.73 % (1505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.17/12.73 % (1505)Termination reason: Unknown
% 78.17/12.73 % (1505)Termination phase: Saturation
% 78.17/12.73
% 78.17/12.73 % (1505)Memory used [KB]: 8571
% 78.17/12.73 % (1505)Time elapsed: 0.148 s
% 78.17/12.73 % (1505)Instructions burned: 326 (million)
% 78.17/12.73 % (1505)------------------------------
% 78.17/12.73 % (1505)------------------------------
% 78.17/12.75 % (1506)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_1199 for (2890ds/1100Mi)
% 81.64/13.04 % (1497)Instruction limit reached!
% 81.64/13.04 % (1497)------------------------------
% 81.64/13.04 % (1497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 81.64/13.04 % (1497)Termination reason: Unknown
% 81.64/13.04 % (1497)Termination phase: Saturation
% 81.64/13.04
% 81.64/13.04 % (1497)Memory used [KB]: 11513
% 81.64/13.04 % (1497)Time elapsed: 2.248 s
% 81.64/13.04 % (1497)Instructions burned: 4637 (million)
% 81.64/13.04 % (1497)------------------------------
% 81.64/13.04 % (1497)------------------------------
% 81.64/13.05 % (1507)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_1199 for (2887ds/406Mi)
% 81.64/13.07 % (1500)Instruction limit reached!
% 81.64/13.07 % (1500)------------------------------
% 81.64/13.07 % (1500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 81.64/13.07 % (1500)Termination reason: Unknown
% 81.64/13.07 % (1500)Termination phase: Saturation
% 81.64/13.07
% 81.64/13.07 % (1500)Memory used [KB]: 20212
% 81.64/13.07 % (1500)Time elapsed: 1.753 s
% 81.64/13.07 % (1500)Instructions burned: 3619 (million)
% 81.64/13.07 % (1500)------------------------------
% 81.64/13.07 % (1500)------------------------------
% 81.64/13.09 % (1508)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_1199 for (2887ds/1871Mi)
% 82.59/13.24 % (1507)Instruction limit reached!
% 82.59/13.24 % (1507)------------------------------
% 82.59/13.24 % (1507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 82.59/13.24 % (1507)Termination reason: Unknown
% 82.59/13.24 % (1507)Termination phase: Saturation
% 82.59/13.24
% 82.59/13.24 % (1507)Memory used [KB]: 7803
% 82.59/13.24 % (1507)Time elapsed: 0.191 s
% 82.59/13.24 % (1507)Instructions burned: 407 (million)
% 82.59/13.24 % (1507)------------------------------
% 82.59/13.24 % (1507)------------------------------
% 82.59/13.26 % (1509)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_1199 for (2885ds/1194Mi)
% 83.30/13.30 % (1502)Instruction limit reached!
% 83.30/13.30 % (1502)------------------------------
% 83.30/13.30 % (1502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.30/13.30 % (1502)Termination reason: Unknown
% 83.30/13.30 % (1502)Termination phase: Saturation
% 83.30/13.30
% 83.30/13.30 % (1502)Memory used [KB]: 11129
% 83.30/13.30 % (1502)Time elapsed: 1.133 s
% 83.30/13.30 % (1502)Instructions burned: 2341 (million)
% 83.30/13.30 % (1502)------------------------------
% 83.30/13.30 % (1502)------------------------------
% 83.30/13.30 % (1506)Instruction limit reached!
% 83.30/13.30 % (1506)------------------------------
% 83.30/13.30 % (1506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.30/13.30 % (1506)Termination reason: Unknown
% 83.30/13.30 % (1506)Termination phase: Saturation
% 83.30/13.30
% 83.30/13.30 % (1506)Memory used [KB]: 14456
% 83.30/13.30 % (1506)Time elapsed: 0.557 s
% 83.30/13.30 % (1506)Instructions burned: 1101 (million)
% 83.30/13.30 % (1506)------------------------------
% 83.30/13.30 % (1506)------------------------------
% 83.30/13.32 % (1510)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_1199 for (2885ds/474Mi)
% 83.30/13.32 % (1511)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_1199 for (2885ds/3115Mi)
% 83.94/13.51 % (1510)Instruction limit reached!
% 83.94/13.51 % (1510)------------------------------
% 83.94/13.51 % (1510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.94/13.51 % (1510)Termination reason: Unknown
% 83.94/13.51 % (1510)Termination phase: Saturation
% 83.94/13.51
% 83.94/13.51 % (1510)Memory used [KB]: 7419
% 83.94/13.51 % (1510)Time elapsed: 0.195 s
% 83.94/13.51 % (1510)Instructions burned: 475 (million)
% 83.94/13.51 % (1510)------------------------------
% 83.94/13.51 % (1510)------------------------------
% 83.94/13.53 % (1512)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_1199 for (2883ds/831Mi)
% 85.04/13.86 % (1509)Instruction limit reached!
% 85.04/13.86 % (1509)------------------------------
% 85.04/13.86 % (1509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.04/13.86 % (1509)Termination reason: Unknown
% 85.04/13.86 % (1509)Termination phase: Saturation
% 85.04/13.86
% 85.04/13.86 % (1509)Memory used [KB]: 12537
% 85.04/13.86 % (1509)Time elapsed: 0.621 s
% 85.04/13.86 % (1509)Instructions burned: 1195 (million)
% 85.04/13.86 % (1509)------------------------------
% 85.04/13.86 % (1509)------------------------------
% 85.04/13.87 % (1513)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_1199 for (2879ds/1188Mi)
% 85.97/13.93 % (1512)Instruction limit reached!
% 85.97/13.93 % (1512)------------------------------
% 85.97/13.93 % (1512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.97/13.93 % (1512)Termination reason: Unknown
% 85.97/13.93 % (1512)Termination phase: Saturation
% 85.97/13.93
% 85.97/13.93 % (1512)Memory used [KB]: 9850
% 85.97/13.93 % (1512)Time elapsed: 0.427 s
% 85.97/13.93 % (1512)Instructions burned: 832 (million)
% 85.97/13.93 % (1512)------------------------------
% 85.97/13.93 % (1512)------------------------------
% 85.97/13.93 % (1504)Instruction limit reached!
% 85.97/13.93 % (1504)------------------------------
% 85.97/13.93 % (1504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.97/13.93 % (1504)Termination reason: Unknown
% 85.97/13.93 % (1504)Termination phase: Saturation
% 85.97/13.93
% 85.97/13.93 % (1504)Memory used [KB]: 17142
% 85.97/13.93 % (1504)Time elapsed: 1.458 s
% 85.97/13.93 % (1504)Instructions burned: 3712 (million)
% 85.97/13.93 % (1504)------------------------------
% 85.97/13.93 % (1504)------------------------------
% 85.97/13.94 % (1514)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_1199 for (2878ds/2868Mi)
% 85.97/13.95 % (1515)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_1199 for (2878ds/1516Mi)
% 85.97/14.01 % (1508)Instruction limit reached!
% 85.97/14.01 % (1508)------------------------------
% 85.97/14.01 % (1508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.97/14.01 % (1508)Termination reason: Unknown
% 85.97/14.01 % (1508)Termination phase: Saturation
% 85.97/14.01
% 85.97/14.01 % (1508)Memory used [KB]: 19445
% 85.97/14.01 % (1508)Time elapsed: 0.951 s
% 85.97/14.01 % (1508)Instructions burned: 1871 (million)
% 85.97/14.01 % (1508)------------------------------
% 85.97/14.01 % (1508)------------------------------
% 88.64/14.03 % (1516)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_1199 for (2877ds/2321Mi)
% 88.64/14.10 % (1493)Instruction limit reached!
% 88.64/14.10 % (1493)------------------------------
% 88.64/14.10 % (1493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 88.64/14.10 % (1493)Termination reason: Unknown
% 88.64/14.10 % (1493)Termination phase: Saturation
% 88.64/14.10
% 88.64/14.10 % (1493)Memory used [KB]: 17910
% 88.64/14.10 % (1493)Time elapsed: 3.657 s
% 88.64/14.10 % (1493)Instructions burned: 7680 (million)
% 88.64/14.10 % (1493)------------------------------
% 88.64/14.10 % (1493)------------------------------
% 88.64/14.12 % (1518)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_1199 for (2876ds/2812Mi)
% 90.12/14.34 % (1513)Instruction limit reached!
% 90.12/14.34 % (1513)------------------------------
% 90.12/14.34 % (1513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.12/14.34 % (1513)Termination reason: Unknown
% 90.12/14.34 % (1513)Termination phase: Saturation
% 90.12/14.34
% 90.12/14.34 % (1513)Memory used [KB]: 16375
% 90.12/14.34 % (1513)Time elapsed: 0.495 s
% 90.12/14.34 % (1513)Instructions burned: 1189 (million)
% 90.12/14.34 % (1513)------------------------------
% 90.12/14.34 % (1513)------------------------------
% 90.12/14.36 % (1519)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_1199 for (2874ds/4604Mi)
% 90.56/14.49 % (1511)Instruction limit reached!
% 90.56/14.49 % (1511)------------------------------
% 90.56/14.49 % (1511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.56/14.49 % (1511)Termination reason: Unknown
% 90.56/14.49 % (1511)Termination phase: Saturation
% 90.56/14.49
% 90.56/14.49 % (1511)Memory used [KB]: 15095
% 90.56/14.49 % (1511)Time elapsed: 1.179 s
% 90.56/14.49 % (1511)Instructions burned: 3117 (million)
% 90.56/14.49 % (1511)------------------------------
% 90.56/14.49 % (1511)------------------------------
% 90.97/14.51 % (1521)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_1199 for (2873ds/2678Mi)
% 91.27/14.70 % (1515)Instruction limit reached!
% 91.27/14.70 % (1515)------------------------------
% 91.27/14.70 % (1515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.27/14.70 % (1515)Termination reason: Unknown
% 91.27/14.70 % (1515)Termination phase: Saturation
% 91.27/14.70
% 91.27/14.70 % (1515)Memory used [KB]: 12153
% 91.27/14.70 % (1515)Time elapsed: 0.772 s
% 91.27/14.70 % (1515)Instructions burned: 1517 (million)
% 91.27/14.70 % (1515)------------------------------
% 91.27/14.70 % (1515)------------------------------
% 90.82/14.71 % (1522)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_1199 for (2871ds/643Mi)
% 91.79/14.88 % (1516)Instruction limit reached!
% 91.79/14.88 % (1516)------------------------------
% 91.79/14.88 % (1516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.79/14.88 % (1516)Termination reason: Unknown
% 91.79/14.88 % (1516)Termination phase: Saturation
% 91.79/14.88
% 91.79/14.88 % (1516)Memory used [KB]: 14456
% 91.79/14.88 % (1516)Time elapsed: 0.853 s
% 91.79/14.88 % (1516)Instructions burned: 2322 (million)
% 91.79/14.88 % (1516)------------------------------
% 91.79/14.88 % (1516)------------------------------
% 92.86/14.90 % (1523)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_1199 for (2869ds/458Mi)
% 92.86/14.96 % (1522)Instruction limit reached!
% 92.86/14.96 % (1522)------------------------------
% 92.86/14.96 % (1522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 92.86/14.96 % (1522)Termination reason: Unknown
% 92.86/14.96 % (1522)Termination phase: Saturation
% 92.86/14.96
% 92.86/14.96 % (1522)Memory used [KB]: 9466
% 92.86/14.96 % (1522)Time elapsed: 0.253 s
% 92.86/14.96 % (1522)Instructions burned: 645 (million)
% 92.86/14.96 % (1522)------------------------------
% 92.86/14.96 % (1522)------------------------------
% 92.86/14.98 % (1524)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_1199 for (2868ds/2546Mi)
% 92.86/15.01 % (1514)Instruction limit reached!
% 92.86/15.01 % (1514)------------------------------
% 92.86/15.01 % (1514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 92.86/15.01 % (1514)Termination reason: Unknown
% 92.86/15.01 % (1514)Termination phase: Saturation
% 92.86/15.01
% 92.86/15.01 % (1514)Memory used [KB]: 7547
% 92.86/15.01 % (1514)Time elapsed: 1.066 s
% 92.86/15.01 % (1514)Instructions burned: 2870 (million)
% 92.86/15.01 % (1514)------------------------------
% 92.86/15.01 % (1514)------------------------------
% 92.86/15.03 % (1525)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_1199 for (2867ds/1432Mi)
% 95.63/15.09 % (1523)Instruction limit reached!
% 95.63/15.09 % (1523)------------------------------
% 95.63/15.09 % (1523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 95.63/15.09 % (1523)Termination reason: Unknown
% 95.63/15.09 % (1523)Termination phase: Saturation
% 95.63/15.09
% 95.63/15.09 % (1523)Memory used [KB]: 7419
% 95.63/15.09 % (1523)Time elapsed: 0.187 s
% 95.63/15.09 % (1523)Instructions burned: 458 (million)
% 95.63/15.09 % (1523)------------------------------
% 95.63/15.09 % (1523)------------------------------
% 95.63/15.10 % (1526)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_1199 for (2867ds/386Mi)
% 96.58/15.25 % (1526)Instruction limit reached!
% 96.58/15.25 % (1526)------------------------------
% 96.58/15.25 % (1526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 96.58/15.25 % (1526)Termination reason: Unknown
% 96.58/15.25 % (1526)Termination phase: Saturation
% 96.58/15.25
% 96.58/15.25 % (1526)Memory used [KB]: 7419
% 96.58/15.25 % (1526)Time elapsed: 0.150 s
% 96.58/15.25 % (1526)Instructions burned: 387 (million)
% 96.58/15.25 % (1526)------------------------------
% 96.58/15.25 % (1526)------------------------------
% 96.58/15.27 % (1527)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_1199 for (2865ds/360Mi)
% 97.73/15.42 % (1527)Instruction limit reached!
% 97.73/15.42 % (1527)------------------------------
% 97.73/15.42 % (1527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 97.73/15.42 % (1527)Termination reason: Unknown
% 97.73/15.42 % (1527)Termination phase: Saturation
% 97.73/15.42
% 97.73/15.42 % (1527)Memory used [KB]: 7419
% 97.73/15.42 % (1527)Time elapsed: 0.153 s
% 97.73/15.42 % (1527)Instructions burned: 362 (million)
% 97.73/15.42 % (1527)------------------------------
% 97.73/15.42 % (1527)------------------------------
% 97.73/15.44 % (1528)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_1199 for (2863ds/5446Mi)
% 98.40/15.50 % (1518)Instruction limit reached!
% 98.40/15.50 % (1518)------------------------------
% 98.40/15.50 % (1518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.40/15.50 % (1518)Termination reason: Unknown
% 98.40/15.50 % (1518)Termination phase: Saturation
% 98.40/15.50
% 98.40/15.50 % (1518)Memory used [KB]: 12025
% 98.40/15.50 % (1518)Time elapsed: 1.381 s
% 98.40/15.50 % (1518)Instructions burned: 2813 (million)
% 98.40/15.50 % (1518)------------------------------
% 98.40/15.50 % (1518)------------------------------
% 98.40/15.52 % (1529)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_1199 for (2863ds/2573Mi)
% 98.40/15.53 % (1521)Instruction limit reached!
% 98.40/15.53 % (1521)------------------------------
% 98.40/15.53 % (1521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.40/15.53 % (1521)Termination reason: Unknown
% 98.40/15.53 % (1521)Termination phase: Saturation
% 98.40/15.53
% 98.40/15.53 % (1521)Memory used [KB]: 23155
% 98.40/15.53 % (1521)Time elapsed: 1.027 s
% 98.40/15.53 % (1521)Instructions burned: 2679 (million)
% 98.40/15.53 % (1521)------------------------------
% 98.40/15.53 % (1521)------------------------------
% 98.40/15.55 % (1530)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_1199 for (2862ds/2655Mi)
% 98.40/15.56 % (1525)Instruction limit reached!
% 98.40/15.56 % (1525)------------------------------
% 98.40/15.56 % (1525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.40/15.56 % (1525)Termination reason: Unknown
% 98.40/15.56 % (1525)Termination phase: Saturation
% 98.40/15.56
% 98.40/15.56 % (1525)Memory used [KB]: 20980
% 98.40/15.56 % (1525)Time elapsed: 0.539 s
% 98.40/15.56 % (1525)Instructions burned: 1433 (million)
% 98.40/15.56 % (1525)------------------------------
% 98.40/15.56 % (1525)------------------------------
% 98.40/15.58 % (1531)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_1199 for (2862ds/2781Mi)
% 99.92/15.85 % (1503)Instruction limit reached!
% 99.92/15.85 % (1503)------------------------------
% 99.92/15.85 % (1503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 99.92/15.85 % (1503)Termination reason: Unknown
% 99.92/15.85 % (1503)Termination phase: Saturation
% 99.92/15.85
% 99.92/15.85 % (1503)Memory used [KB]: 11001
% 99.92/15.85 % (1503)Time elapsed: 3.471 s
% 99.92/15.85 % (1503)Instructions burned: 7257 (million)
% 99.92/15.85 % (1503)------------------------------
% 99.92/15.85 % (1503)------------------------------
% 99.92/15.87 % (1532)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_1199 for (2859ds/307Mi)
% 100.20/16.00 % (1532)Instruction limit reached!
% 100.20/16.00 % (1532)------------------------------
% 100.20/16.00 % (1532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 100.20/16.00 % (1532)Termination reason: Unknown
% 100.20/16.00 % (1532)Termination phase: Saturation
% 100.20/16.00
% 100.20/16.00 % (1532)Memory used [KB]: 7419
% 100.20/16.00 % (1532)Time elapsed: 0.128 s
% 100.20/16.00 % (1532)Instructions burned: 307 (million)
% 100.20/16.00 % (1532)------------------------------
% 100.20/16.00 % (1532)------------------------------
% 100.20/16.01 % (1533)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_1199 for (2858ds/1548Mi)
% 103.24/16.17 % (1524)Instruction limit reached!
% 103.24/16.17 % (1524)------------------------------
% 103.24/16.17 % (1524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 103.24/16.17 % (1524)Termination reason: Unknown
% 103.24/16.17 % (1524)Termination phase: Saturation
% 103.24/16.17
% 103.24/16.17 % (1524)Memory used [KB]: 10490
% 103.24/16.17 % (1524)Time elapsed: 1.193 s
% 103.24/16.17 % (1524)Instructions burned: 2547 (million)
% 103.24/16.17 % (1524)------------------------------
% 103.24/16.17 % (1524)------------------------------
% 103.24/16.19 % (1534)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_1199 for (2856ds/5214Mi)
% 105.14/16.52 % (1529)Instruction limit reached!
% 105.14/16.52 % (1529)------------------------------
% 105.14/16.52 % (1529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 105.14/16.52 % (1529)Termination reason: Unknown
% 105.14/16.52 % (1529)Termination phase: Saturation
% 105.14/16.52
% 105.14/16.52 % (1529)Memory used [KB]: 17398
% 105.14/16.52 % (1529)Time elapsed: 1.008 s
% 105.14/16.52 % (1529)Instructions burned: 2574 (million)
% 105.14/16.52 % (1529)------------------------------
% 105.14/16.52 % (1529)------------------------------
% 105.14/16.54 % (1535)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_1199 for (2852ds/3201Mi)
% 105.57/16.60 % (1530)Instruction limit reached!
% 105.57/16.60 % (1530)------------------------------
% 105.57/16.60 % (1530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 105.57/16.60 % (1530)Termination reason: Unknown
% 105.57/16.60 % (1530)Termination phase: Saturation
% 105.57/16.60
% 105.57/16.60 % (1530)Memory used [KB]: 5756
% 105.57/16.60 % (1530)Time elapsed: 1.055 s
% 105.57/16.60 % (1530)Instructions burned: 2656 (million)
% 105.57/16.60 % (1530)------------------------------
% 105.57/16.60 % (1530)------------------------------
% 105.57/16.62 % (1536)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_1199 for (2852ds/454Mi)
% 105.57/16.63 % (1519)Instruction limit reached!
% 105.57/16.63 % (1519)------------------------------
% 105.57/16.63 % (1519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 105.57/16.63 % (1519)Termination reason: Unknown
% 105.57/16.63 % (1519)Termination phase: Saturation
% 105.57/16.63
% 105.57/16.63 % (1519)Memory used [KB]: 14456
% 105.57/16.63 % (1519)Time elapsed: 2.270 s
% 105.57/16.63 % (1519)Instructions burned: 4605 (million)
% 105.57/16.63 % (1519)------------------------------
% 105.57/16.63 % (1519)------------------------------
% 105.57/16.65 % (1537)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_1199 for (2851ds/3049Mi)
% 105.83/16.78 % (1533)Instruction limit reached!
% 105.83/16.78 % (1533)------------------------------
% 105.83/16.78 % (1533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 105.83/16.78 % (1533)Termination reason: Unknown
% 105.83/16.78 % (1533)Termination phase: Saturation
% 105.83/16.78
% 105.83/16.78 % (1533)Memory used [KB]: 10106
% 105.83/16.78 % (1533)Time elapsed: 0.767 s
% 105.83/16.78 % (1533)Instructions burned: 1548 (million)
% 105.83/16.78 % (1533)------------------------------
% 105.83/16.78 % (1533)------------------------------
% 106.83/16.80 % (1538)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_1199 for (2850ds/7311Mi)
% 106.83/16.81 % (1536)Instruction limit reached!
% 106.83/16.81 % (1536)------------------------------
% 106.83/16.81 % (1536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 106.83/16.81 % (1536)Termination reason: Unknown
% 106.83/16.81 % (1536)Termination phase: Saturation
% 106.83/16.81
% 106.83/16.81 % (1536)Memory used [KB]: 11897
% 106.83/16.81 % (1536)Time elapsed: 0.187 s
% 106.83/16.81 % (1536)Instructions burned: 455 (million)
% 106.83/16.81 % (1536)------------------------------
% 106.83/16.81 % (1536)------------------------------
% 106.83/16.82 % (1539)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_1199 for (2850ds/6804Mi)
% 107.23/16.92 % (1531)Instruction limit reached!
% 107.23/16.92 % (1531)------------------------------
% 107.23/16.92 % (1531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 107.23/16.92 % (1531)Termination reason: Unknown
% 107.23/16.92 % (1531)Termination phase: Saturation
% 107.23/16.92
% 107.23/16.92 % (1531)Memory used [KB]: 8827
% 107.23/16.92 % (1531)Time elapsed: 1.344 s
% 107.23/16.92 % (1531)Instructions burned: 2783 (million)
% 107.23/16.92 % (1531)------------------------------
% 107.23/16.92 % (1531)------------------------------
% 107.23/16.94 % (1540)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_1199 for (2848ds/1683Mi)
% 114.29/17.71 % (1540)Instruction limit reached!
% 114.29/17.71 % (1540)------------------------------
% 114.29/17.71 % (1540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 114.29/17.71 % (1540)Termination reason: Unknown
% 114.29/17.71 % (1540)Termination phase: Saturation
% 114.29/17.71
% 114.29/17.71 % (1540)Memory used [KB]: 19829
% 114.29/17.71 % (1540)Time elapsed: 0.775 s
% 114.29/17.71 % (1540)Instructions burned: 1684 (million)
% 114.29/17.71 % (1540)------------------------------
% 114.29/17.71 % (1540)------------------------------
% 114.29/17.73 % (1541)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_1199 for (2840ds/4688Mi)
% 116.57/18.11 % (1537)Instruction limit reached!
% 116.57/18.11 % (1537)------------------------------
% 116.57/18.11 % (1537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 116.57/18.11 % (1537)Termination reason: Unknown
% 116.57/18.11 % (1537)Termination phase: Saturation
% 116.57/18.11
% 116.57/18.11 % (1537)Memory used [KB]: 11129
% 116.57/18.11 % (1537)Time elapsed: 1.463 s
% 116.57/18.11 % (1537)Instructions burned: 3050 (million)
% 116.57/18.11 % (1537)------------------------------
% 116.57/18.11 % (1537)------------------------------
% 116.57/18.12 % (1535)Instruction limit reached!
% 116.57/18.12 % (1535)------------------------------
% 116.57/18.12 % (1535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 116.57/18.12 % (1535)Termination reason: Unknown
% 116.57/18.12 % (1535)Termination phase: Saturation
% 116.57/18.12
% 116.57/18.12 % (1535)Memory used [KB]: 12281
% 116.57/18.12 % (1535)Time elapsed: 1.578 s
% 116.57/18.12 % (1535)Instructions burned: 3201 (million)
% 116.57/18.12 % (1535)------------------------------
% 116.57/18.12 % (1535)------------------------------
% 117.33/18.13 % (1542)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_1199 for (2836ds/2207Mi)
% 117.33/18.14 % (1543)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_1199 for (2836ds/8216Mi)
% 117.33/18.17 % (1528)Instruction limit reached!
% 117.33/18.17 % (1528)------------------------------
% 117.33/18.17 % (1528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 117.33/18.17 % (1528)Termination reason: Unknown
% 117.33/18.17 % (1528)Termination phase: Saturation
% 117.33/18.17
% 117.33/18.17 % (1528)Memory used [KB]: 14328
% 117.33/18.17 % (1528)Time elapsed: 2.740 s
% 117.33/18.17 % (1528)Instructions burned: 5446 (million)
% 117.33/18.17 % (1528)------------------------------
% 117.33/18.17 % (1528)------------------------------
% 117.33/18.19 % (1544)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_1199 for (2836ds/430Mi)
% 118.06/18.37 % (1544)Instruction limit reached!
% 118.06/18.37 % (1544)------------------------------
% 118.06/18.37 % (1544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 118.06/18.37 % (1544)Termination reason: Unknown
% 118.06/18.37 % (1544)Termination phase: Saturation
% 118.06/18.37
% 118.06/18.37 % (1544)Memory used [KB]: 7419
% 118.06/18.37 % (1544)Time elapsed: 0.181 s
% 118.06/18.37 % (1544)Instructions burned: 432 (million)
% 118.06/18.37 % (1544)------------------------------
% 118.06/18.37 % (1544)------------------------------
% 118.06/18.38 % (1545)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_1199 for (2834ds/2012Mi)
% 119.46/18.62 % (1534)Instruction limit reached!
% 119.46/18.62 % (1534)------------------------------
% 119.46/18.62 % (1534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 119.46/18.62 % (1534)Termination reason: Unknown
% 119.46/18.62 % (1534)Termination phase: Saturation
% 119.46/18.62
% 119.46/18.62 % (1534)Memory used [KB]: 11001
% 119.46/18.62 % (1534)Time elapsed: 2.429 s
% 119.46/18.62 % (1534)Instructions burned: 5214 (million)
% 119.46/18.62 % (1534)------------------------------
% 119.46/18.62 % (1534)------------------------------
% 119.46/18.64 % (1546)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_1199 for (2831ds/631Mi)
% 120.38/18.93 % (1546)Instruction limit reached!
% 120.38/18.93 % (1546)------------------------------
% 120.38/18.93 % (1546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 120.38/18.93 % (1546)Termination reason: Unknown
% 120.38/18.93 % (1546)Termination phase: Saturation
% 120.38/18.93
% 120.38/18.93 % (1546)Memory used [KB]: 8059
% 120.38/18.93 % (1546)Time elapsed: 0.302 s
% 120.38/18.93 % (1546)Instructions burned: 631 (million)
% 120.38/18.93 % (1546)------------------------------
% 120.38/18.93 % (1546)------------------------------
% 120.38/18.95 % (1547)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_1199 for (2828ds/8785Mi)
% 124.32/19.13 % (1545)Instruction limit reached!
% 124.32/19.13 % (1545)------------------------------
% 124.32/19.13 % (1545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 124.32/19.13 % (1545)Termination reason: Unknown
% 124.32/19.13 % (1545)Termination phase: Saturation
% 124.32/19.13
% 124.32/19.13 % (1545)Memory used [KB]: 12025
% 124.32/19.13 % (1545)Time elapsed: 0.749 s
% 124.32/19.13 % (1545)Instructions burned: 2012 (million)
% 124.32/19.13 % (1545)------------------------------
% 124.32/19.13 % (1545)------------------------------
% 124.32/19.15 % (1548)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_1199 for (2826ds/739Mi)
% 124.75/19.21 % (1542)Instruction limit reached!
% 124.75/19.21 % (1542)------------------------------
% 124.75/19.21 % (1542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 124.75/19.21 % (1542)Termination reason: Unknown
% 124.75/19.21 % (1542)Termination phase: Saturation
% 124.75/19.21
% 124.75/19.21 % (1542)Memory used [KB]: 11001
% 124.75/19.21 % (1542)Time elapsed: 1.083 s
% 124.75/19.21 % (1542)Instructions burned: 2208 (million)
% 124.75/19.21 % (1542)------------------------------
% 124.75/19.21 % (1542)------------------------------
% 124.75/19.23 % (1549)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_1199 for (2826ds/5473Mi)
% 126.29/19.51 % (1548)Instruction limit reached!
% 126.29/19.51 % (1548)------------------------------
% 126.29/19.51 % (1548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 126.29/19.51 % (1548)Termination reason: Unknown
% 126.29/19.51 % (1548)Termination phase: Saturation
% 126.29/19.51
% 126.29/19.51 % (1548)Memory used [KB]: 12792
% 126.29/19.51 % (1548)Time elapsed: 0.370 s
% 126.29/19.51 % (1548)Instructions burned: 739 (million)
% 126.29/19.51 % (1548)------------------------------
% 126.29/19.51 % (1548)------------------------------
% 126.29/19.53 % (1550)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_1199 for (2822ds/43570Mi)
% 128.67/19.96 % (1541)Instruction limit reached!
% 128.67/19.96 % (1541)------------------------------
% 128.67/19.96 % (1541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 128.67/19.96 % (1541)Termination reason: Unknown
% 128.67/19.96 % (1541)Termination phase: Saturation
% 128.67/19.96
% 128.67/19.96 % (1541)Memory used [KB]: 14328
% 128.67/19.96 % (1541)Time elapsed: 2.230 s
% 128.67/19.96 % (1541)Instructions burned: 4688 (million)
% 128.67/19.96 % (1541)------------------------------
% 128.67/19.96 % (1541)------------------------------
% 128.67/19.98 % (1551)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_1199 for (2818ds/8382Mi)
% 131.81/20.23 % (1539)Instruction limit reached!
% 131.81/20.23 % (1539)------------------------------
% 131.81/20.23 % (1539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 131.81/20.23 % (1539)Termination reason: Unknown
% 131.81/20.23 % (1539)Termination phase: Saturation
% 131.81/20.23
% 131.81/20.23 % (1539)Memory used [KB]: 17526
% 131.81/20.23 % (1539)Time elapsed: 3.413 s
% 131.81/20.23 % (1539)Instructions burned: 6804 (million)
% 131.81/20.23 % (1539)------------------------------
% 131.81/20.23 % (1539)------------------------------
% 131.81/20.25 % (1552)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_1199 for (2815ds/407Mi)
% 133.07/20.44 % (1552)Instruction limit reached!
% 133.07/20.44 % (1552)------------------------------
% 133.07/20.44 % (1552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 133.07/20.44 % (1552)Termination reason: Unknown
% 133.07/20.44 % (1552)Termination phase: Saturation
% 133.07/20.44
% 133.07/20.44 % (1552)Memory used [KB]: 8827
% 133.07/20.44 % (1552)Time elapsed: 0.210 s
% 133.07/20.44 % (1552)Instructions burned: 407 (million)
% 133.07/20.44 % (1552)------------------------------
% 133.07/20.44 % (1552)------------------------------
% 133.07/20.45 % (1553)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_1199 for (2813ds/2971Mi)
% 133.88/20.53 % (1538)Instruction limit reached!
% 133.88/20.53 % (1538)------------------------------
% 133.88/20.53 % (1538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 133.88/20.53 % (1538)Termination reason: Unknown
% 133.88/20.53 % (1538)Termination phase: Saturation
% 133.88/20.53
% 133.88/20.53 % (1538)Memory used [KB]: 21236
% 133.88/20.53 % (1538)Time elapsed: 3.734 s
% 133.88/20.53 % (1538)Instructions burned: 7311 (million)
% 133.88/20.53 % (1538)------------------------------
% 133.88/20.53 % (1538)------------------------------
% 133.88/20.55 % (1554)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_1199 for (2812ds/9822Mi)
% 135.91/21.02 % (1543)Instruction limit reached!
% 135.91/21.02 % (1543)------------------------------
% 135.91/21.02 % (1543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 135.91/21.02 % (1543)Termination reason: Unknown
% 135.91/21.02 % (1543)Termination phase: Saturation
% 135.91/21.02
% 135.91/21.02 % (1543)Memory used [KB]: 7803
% 135.91/21.02 % (1543)Time elapsed: 2.884 s
% 135.91/21.02 % (1543)Instructions burned: 8216 (million)
% 135.91/21.02 % (1543)------------------------------
% 135.91/21.02 % (1543)------------------------------
% 134.67/21.04 % (1556)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_1199 for (2807ds/8425Mi)
% 139.86/21.49 % (1553)Instruction limit reached!
% 139.86/21.49 % (1553)------------------------------
% 139.86/21.49 % (1553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 139.86/21.49 % (1553)Termination reason: Unknown
% 139.86/21.49 % (1553)Termination phase: Saturation
% 139.86/21.49
% 139.86/21.49 % (1553)Memory used [KB]: 7547
% 139.86/21.49 % (1553)Time elapsed: 1.039 s
% 139.86/21.49 % (1553)Instructions burned: 2973 (million)
% 139.86/21.49 % (1553)------------------------------
% 139.86/21.49 % (1553)------------------------------
% 140.45/21.50 % (1557)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_1199 for (2803ds/3107Mi)
% 141.45/21.71 % (1549)Instruction limit reached!
% 141.45/21.71 % (1549)------------------------------
% 141.45/21.71 % (1549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 141.45/21.71 % (1549)Termination reason: Unknown
% 141.45/21.71 % (1549)Termination phase: Saturation
% 141.45/21.71
% 141.45/21.71 % (1549)Memory used [KB]: 13304
% 141.45/21.71 % (1549)Time elapsed: 2.512 s
% 141.45/21.71 % (1549)Instructions burned: 5473 (million)
% 141.45/21.71 % (1549)------------------------------
% 141.45/21.71 % (1549)------------------------------
% 141.45/21.73 % (1558)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_1199 for (2800ds/7967Mi)
% 146.50/22.39 % (1557)Instruction limit reached!
% 146.50/22.39 % (1557)------------------------------
% 146.50/22.39 % (1557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 146.50/22.39 % (1557)Termination reason: Unknown
% 146.50/22.39 % (1557)Termination phase: Saturation
% 146.50/22.39
% 146.50/22.39 % (1557)Memory used [KB]: 19445
% 146.50/22.39 % (1557)Time elapsed: 0.893 s
% 146.50/22.39 % (1557)Instructions burned: 3108 (million)
% 146.50/22.39 % (1557)------------------------------
% 146.50/22.39 % (1557)------------------------------
% 147.21/22.40 % (1792)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_1199 for (2794ds/3629Mi)
% 148.42/22.60 % (1547)Instruction limit reached!
% 148.42/22.60 % (1547)------------------------------
% 148.42/22.60 % (1547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 148.42/22.60 % (1547)Termination reason: Unknown
% 148.42/22.60 % (1547)Termination phase: Saturation
% 148.42/22.60
% 148.42/22.60 % (1547)Memory used [KB]: 21364
% 148.42/22.60 % (1547)Time elapsed: 3.654 s
% 148.42/22.60 % (1547)Instructions burned: 8786 (million)
% 148.42/22.60 % (1547)------------------------------
% 148.42/22.60 % (1547)------------------------------
% 148.42/22.62 % (1799)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_1199 for (2791ds/939Mi)
% 148.94/22.79 % (1551)Instruction limit reached!
% 148.94/22.79 % (1551)------------------------------
% 148.94/22.79 % (1551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 148.94/22.79 % (1551)Termination reason: Unknown
% 148.94/22.79 % (1551)Termination phase: Saturation
% 148.94/22.79
% 148.94/22.79 % (1551)Memory used [KB]: 14583
% 148.94/22.79 % (1551)Time elapsed: 2.829 s
% 148.94/22.79 % (1551)Instructions burned: 8383 (million)
% 148.94/22.79 % (1551)------------------------------
% 148.94/22.79 % (1551)------------------------------
% 148.94/22.80 % (1800)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_1199 for (2790ds/1188Mi)
% 149.44/22.90 % (1799)Instruction limit reached!
% 149.44/22.90 % (1799)------------------------------
% 149.44/22.90 % (1799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 149.44/22.90 % (1799)Termination reason: Unknown
% 149.44/22.90 % (1799)Termination phase: Saturation
% 149.44/22.90
% 149.44/22.90 % (1799)Memory used [KB]: 9978
% 149.44/22.90 % (1799)Time elapsed: 0.282 s
% 149.44/22.90 % (1799)Instructions burned: 941 (million)
% 149.44/22.90 % (1799)------------------------------
% 149.44/22.90 % (1799)------------------------------
% 150.14/22.91 % (1801)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_1199 for (2789ds/3205Mi)
% 151.57/23.10 % (1800)Instruction limit reached!
% 151.57/23.10 % (1800)------------------------------
% 151.57/23.10 % (1800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 151.57/23.10 % (1800)Termination reason: Unknown
% 151.57/23.10 % (1800)Termination phase: Saturation
% 151.57/23.10
% 151.57/23.10 % (1800)Memory used [KB]: 16758
% 151.57/23.10 % (1800)Time elapsed: 0.304 s
% 151.57/23.10 % (1800)Instructions burned: 1190 (million)
% 151.57/23.10 % (1800)------------------------------
% 151.57/23.10 % (1800)------------------------------
% 151.57/23.11 % (1802)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_1199 for (2787ds/865Mi)
% 153.36/23.31 % (1792)Instruction limit reached!
% 153.36/23.31 % (1792)------------------------------
% 153.36/23.31 % (1792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 153.36/23.31 % (1792)Termination reason: Unknown
% 153.36/23.31 % (1792)Termination phase: Saturation
% 153.36/23.31
% 153.36/23.31 % (1792)Memory used [KB]: 7803
% 153.36/23.31 % (1792)Time elapsed: 0.905 s
% 153.36/23.31 % (1792)Instructions burned: 3633 (million)
% 153.36/23.31 % (1792)------------------------------
% 153.36/23.31 % (1792)------------------------------
% 153.36/23.32 % (1803)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_1199 for (2784ds/7469Mi)
% 153.36/23.35 % (1802)Instruction limit reached!
% 153.36/23.35 % (1802)------------------------------
% 153.36/23.35 % (1802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 153.36/23.35 % (1802)Termination reason: Unknown
% 153.36/23.35 % (1802)Termination phase: Saturation
% 153.36/23.35
% 153.36/23.35 % (1802)Memory used [KB]: 7675
% 153.36/23.35 % (1802)Time elapsed: 0.241 s
% 153.36/23.35 % (1802)Instructions burned: 866 (million)
% 153.36/23.35 % (1802)------------------------------
% 153.36/23.35 % (1802)------------------------------
% 153.36/23.36 % (1804)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_1199 for (2784ds/4165Mi)
% 155.14/23.63 % (1554)Refutation not found, non-redundant clauses discarded% (1554)------------------------------
% 155.14/23.63 % (1554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 155.14/23.63 % (1554)Termination reason: Refutation not found, non-redundant clauses discarded
% 155.14/23.63
% 155.14/23.63 % (1554)Memory used [KB]: 20340
% 155.14/23.63 % (1554)Time elapsed: 3.109 s
% 155.14/23.63 % (1554)Instructions burned: 8773 (million)
% 155.14/23.63 % (1554)------------------------------
% 155.14/23.63 % (1554)------------------------------
% 155.14/23.65 % (1805)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_1199 for (2781ds/13468Mi)
% 155.59/23.73 % (1556)Instruction limit reached!
% 155.59/23.73 % (1556)------------------------------
% 155.59/23.73 % (1556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 155.59/23.73 % (1556)Termination reason: Unknown
% 155.59/23.73 % (1556)Termination phase: Saturation
% 155.59/23.73
% 155.59/23.73 % (1556)Memory used [KB]: 12281
% 155.59/23.73 % (1556)Time elapsed: 2.719 s
% 155.59/23.73 % (1556)Instructions burned: 8426 (million)
% 155.59/23.73 % (1556)------------------------------
% 155.59/23.73 % (1556)------------------------------
% 155.59/23.74 % (1806)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_1199 for (2780ds/2635Mi)
% 155.59/23.74 % (1558)Instruction limit reached!
% 155.59/23.74 % (1558)------------------------------
% 155.59/23.74 % (1558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 155.59/23.74 % (1558)Termination reason: Unknown
% 155.59/23.74 % (1558)Termination phase: Saturation
% 155.59/23.74
% 155.59/23.74 % (1558)Memory used [KB]: 15095
% 155.59/23.74 % (1558)Time elapsed: 2.018 s
% 155.59/23.74 % (1558)Instructions burned: 7968 (million)
% 155.59/23.74 % (1558)------------------------------
% 155.59/23.74 % (1558)------------------------------
% 155.59/23.75 % (1807)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_1199 for (2780ds/631Mi)
% 156.09/23.91 % (1801)Instruction limit reached!
% 156.09/23.91 % (1801)------------------------------
% 156.09/23.91 % (1801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 156.09/23.91 % (1801)Termination reason: Unknown
% 156.09/23.91 % (1801)Termination phase: Saturation
% 156.09/23.91
% 156.09/23.91 % (1801)Memory used [KB]: 15351
% 156.09/23.91 % (1801)Time elapsed: 1.001 s
% 156.09/23.91 % (1801)Instructions burned: 3206 (million)
% 156.09/23.91 % (1801)------------------------------
% 156.09/23.91 % (1801)------------------------------
% 156.09/23.91 % (1807)Instruction limit reached!
% 156.09/23.91 % (1807)------------------------------
% 156.09/23.91 % (1807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 156.09/23.91 % (1807)Termination reason: Unknown
% 156.09/23.91 % (1807)Termination phase: Saturation
% 156.09/23.91
% 156.09/23.91 % (1807)Memory used [KB]: 9722
% 156.09/23.91 % (1807)Time elapsed: 0.158 s
% 156.09/23.91 % (1807)Instructions burned: 631 (million)
% 156.09/23.91 % (1807)------------------------------
% 156.09/23.91 % (1807)------------------------------
% 156.09/23.92 % (1808)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_1199 for (2778ds/15557Mi)
% 156.09/23.92 % (1809)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_1199 for (2778ds/2142Mi)
% 161.97/24.55 % (1806)Instruction limit reached!
% 161.97/24.55 % (1806)------------------------------
% 161.97/24.55 % (1806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 161.97/24.55 % (1806)Termination reason: Unknown
% 161.97/24.55 % (1806)Termination phase: Saturation
% 161.97/24.55
% 161.97/24.55 % (1806)Memory used [KB]: 12153
% 161.97/24.55 % (1806)Time elapsed: 0.814 s
% 161.97/24.55 % (1806)Instructions burned: 2636 (million)
% 161.97/24.55 % (1806)------------------------------
% 161.97/24.55 % (1806)------------------------------
% 161.97/24.56 % (1809)Instruction limit reached!
% 161.97/24.56 % (1809)------------------------------
% 161.97/24.56 % (1809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 161.97/24.56 % (1809)Termination reason: Unknown
% 161.97/24.56 % (1809)Termination phase: Saturation
% 161.97/24.56
% 161.97/24.56 % (1809)Memory used [KB]: 11001
% 161.97/24.56 % (1809)Time elapsed: 0.641 s
% 161.97/24.56 % (1809)Instructions burned: 2144 (million)
% 161.97/24.56 % (1809)------------------------------
% 161.97/24.56 % (1809)------------------------------
% 161.97/24.56 % (1810)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_1199 for (2772ds/5624Mi)
% 161.97/24.57 % (1811)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_1199 for (2772ds/1665Mi)
% 162.61/24.66 % (1804)Instruction limit reached!
% 162.61/24.66 % (1804)------------------------------
% 162.61/24.66 % (1804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 162.61/24.66 % (1804)Termination reason: Unknown
% 162.61/24.66 % (1804)Termination phase: Saturation
% 162.61/24.66
% 162.61/24.66 % (1804)Memory used [KB]: 24434
% 162.61/24.66 % (1804)Time elapsed: 1.299 s
% 162.61/24.66 % (1804)Instructions burned: 4166 (million)
% 162.61/24.66 % (1804)------------------------------
% 162.61/24.66 % (1804)------------------------------
% 162.61/24.67 % (1812)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_1199 for (2771ds/64912Mi)
% 163.90/25.00 % (1811)Instruction limit reached!
% 163.90/25.00 % (1811)------------------------------
% 163.90/25.00 % (1811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 163.90/25.00 % (1811)Termination reason: Unknown
% 163.90/25.00 % (1811)Termination phase: Saturation
% 163.90/25.00
% 163.90/25.00 % (1811)Memory used [KB]: 14839
% 163.90/25.00 % (1811)Time elapsed: 0.428 s
% 163.90/25.00 % (1811)Instructions burned: 1666 (million)
% 163.90/25.00 % (1811)------------------------------
% 163.90/25.00 % (1811)------------------------------
% 163.90/25.01 % (1813)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_1199 for (2767ds/7801Mi)
% 167.32/25.36 % (1803)Instruction limit reached!
% 167.32/25.36 % (1803)------------------------------
% 167.32/25.36 % (1803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 167.32/25.36 % (1803)Termination reason: Unknown
% 167.32/25.36 % (1803)Termination phase: Saturation
% 167.32/25.36
% 167.32/25.36 % (1803)Memory used [KB]: 11257
% 167.32/25.36 % (1803)Time elapsed: 2.041 s
% 167.32/25.36 % (1803)Instructions burned: 7472 (million)
% 167.32/25.36 % (1803)------------------------------
% 167.32/25.36 % (1803)------------------------------
% 167.32/25.37 % (1814)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_1199 for (2764ds/15194Mi)
% 174.63/26.34 % (1810)Instruction limit reached!
% 174.63/26.34 % (1810)------------------------------
% 174.63/26.34 % (1810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 174.63/26.34 % (1810)Termination reason: Unknown
% 174.63/26.34 % (1810)Termination phase: Saturation
% 174.63/26.34
% 174.63/26.34 % (1810)Memory used [KB]: 14072
% 174.63/26.34 % (1810)Time elapsed: 1.781 s
% 174.63/26.34 % (1810)Instructions burned: 5626 (million)
% 174.63/26.34 % (1810)------------------------------
% 174.63/26.34 % (1810)------------------------------
% 174.63/26.35 % (1815)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_1199 for (2754ds/6753Mi)
% 179.68/27.12 % (1805)Instruction limit reached!
% 179.68/27.12 % (1805)------------------------------
% 179.68/27.12 % (1805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 179.68/27.12 % (1805)Termination reason: Unknown
% 179.68/27.12 % (1805)Termination phase: Saturation
% 179.68/27.12
% 179.68/27.12 % (1805)Memory used [KB]: 15223
% 179.68/27.12 % (1805)Time elapsed: 3.477 s
% 179.68/27.12 % (1805)Instructions burned: 13469 (million)
% 179.68/27.12 % (1805)------------------------------
% 179.68/27.12 % (1805)------------------------------
% 180.43/27.13 % (1816)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_1199 for (2746ds/1003Mi)
% 181.46/27.31 % (1813)Instruction limit reached!
% 181.46/27.31 % (1813)------------------------------
% 181.46/27.31 % (1813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 181.46/27.31 % (1813)Termination reason: Unknown
% 181.46/27.31 % (1813)Termination phase: Saturation
% 181.46/27.31
% 181.46/27.31 % (1813)Memory used [KB]: 12920
% 181.46/27.31 % (1813)Time elapsed: 2.303 s
% 181.46/27.31 % (1813)Instructions burned: 7802 (million)
% 181.46/27.31 % (1813)------------------------------
% 181.46/27.31 % (1813)------------------------------
% 181.46/27.32 % (1817)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_1199 for (2744ds/13018Mi)
% 181.46/27.39 % (1816)Instruction limit reached!
% 181.46/27.39 % (1816)------------------------------
% 181.46/27.39 % (1816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 181.46/27.39 % (1816)Termination reason: Unknown
% 181.46/27.39 % (1816)Termination phase: Saturation
% 181.46/27.39
% 181.46/27.39 % (1816)Memory used [KB]: 7547
% 181.46/27.39 % (1816)Time elapsed: 0.258 s
% 181.46/27.39 % (1816)Instructions burned: 1007 (million)
% 181.46/27.39 % (1816)------------------------------
% 181.46/27.39 % (1816)------------------------------
% 182.27/27.40 % (1818)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_1199 for (2744ds/1267Mi)
% 183.77/27.74 % (1808)Instruction limit reached!
% 183.77/27.74 % (1808)------------------------------
% 183.77/27.74 % (1808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 183.77/27.74 % (1808)Termination reason: Unknown
% 183.77/27.74 % (1808)Termination phase: Saturation
% 183.77/27.74
% 183.77/27.74 % (1808)Memory used [KB]: 16502
% 183.77/27.74 % (1808)Time elapsed: 3.827 s
% 183.77/27.74 % (1808)Instructions burned: 15558 (million)
% 183.77/27.74 % (1808)------------------------------
% 183.77/27.74 % (1808)------------------------------
% 183.77/27.75 % (1819)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_1199 for (2740ds/2570Mi)
% 183.77/27.79 % (1818)Instruction limit reached!
% 183.77/27.79 % (1818)------------------------------
% 183.77/27.79 % (1818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 183.77/27.79 % (1818)Termination reason: Unknown
% 183.77/27.79 % (1818)Termination phase: Saturation
% 183.77/27.79
% 183.77/27.79 % (1818)Memory used [KB]: 11641
% 183.77/27.79 % (1818)Time elapsed: 0.393 s
% 183.77/27.79 % (1818)Instructions burned: 1267 (million)
% 183.77/27.79 % (1818)------------------------------
% 183.77/27.79 % (1818)------------------------------
% 184.63/27.80 % (1820)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=13163:si=on:rtra=on_0 on DTF2THF_1199 for (2740ds/13163Mi)
% 188.65/28.38 % (1819)Instruction limit reached!
% 188.65/28.38 % (1819)------------------------------
% 188.65/28.38 % (1819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 188.65/28.38 % (1819)Termination reason: Unknown
% 188.65/28.38 % (1819)Termination phase: Saturation
% 188.65/28.38
% 188.65/28.38 % (1819)Memory used [KB]: 22899
% 188.65/28.38 % (1819)Time elapsed: 0.629 s
% 188.65/28.38 % (1819)Instructions burned: 2573 (million)
% 188.65/28.38 % (1819)------------------------------
% 188.65/28.38 % (1819)------------------------------
% 188.65/28.39 % (1821)lrs+1666_1:1_au=on:s2a=on:sd=2:ss=axioms:st=5.0:i=5087:si=on:rtra=on_0 on DTF2THF_1199 for (2734ds/5087Mi)
% 189.34/28.42 % (1815)Instruction limit reached!
% 189.34/28.42 % (1815)------------------------------
% 189.34/28.42 % (1815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 189.34/28.42 % (1815)Termination reason: Unknown
% 189.34/28.42 % (1815)Termination phase: Saturation
% 189.34/28.42
% 189.34/28.42 % (1815)Memory used [KB]: 20596
% 189.34/28.42 % (1815)Time elapsed: 2.070 s
% 189.34/28.42 % (1815)Instructions burned: 6755 (million)
% 189.34/28.42 % (1815)------------------------------
% 189.34/28.42 % (1815)------------------------------
% 189.34/28.43 % (1822)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_1199 for (2733ds/10380Mi)
% 199.20/29.86 % (1814)Instruction limit reached!
% 199.20/29.86 % (1814)------------------------------
% 199.20/29.86 % (1814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 199.20/29.86 % (1814)Termination reason: Unknown
% 199.20/29.86 % (1814)Termination phase: Saturation
% 199.20/29.86
% 199.20/29.86 % (1814)Memory used [KB]: 22131
% 199.20/29.86 % (1814)Time elapsed: 4.491 s
% 199.20/29.86 % (1814)Instructions burned: 15196 (million)
% 199.20/29.86 % (1814)------------------------------
% 199.20/29.86 % (1814)------------------------------
% 199.20/29.87 % (2094)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_1199 for (2719ds/4218Mi)
% 199.88/29.99 % (1821)Instruction limit reached!
% 199.88/29.99 % (1821)------------------------------
% 199.88/29.99 % (1821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 199.88/29.99 % (1821)Termination reason: Unknown
% 199.88/29.99 % (1821)Termination phase: Saturation
% 199.88/29.99
% 199.88/29.99 % (1821)Memory used [KB]: 12281
% 199.88/29.99 % (1821)Time elapsed: 1.599 s
% 199.88/29.99 % (1821)Instructions burned: 5089 (million)
% 199.88/29.99 % (1821)------------------------------
% 199.88/29.99 % (1821)------------------------------
% 199.88/30.00 % (2181)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_1199 for (2718ds/3971Mi)
% 206.94/30.96 % (1817)First to succeed.
% 206.94/30.98 % (1817)Refutation found. Thanks to Tanya!
% 206.94/30.98 % SZS status Theorem for DTF2THF_1199
% 206.94/30.98 % SZS output start Proof for DTF2THF_1199
% 206.94/30.98 thf(func_def_0, type, in: $i > $i > $o).
% 206.94/30.98 thf(func_def_1, type, exu: ($i > $o) > $o).
% 206.94/30.98 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 206.94/30.98 thf(func_def_8, type, powerset: $i > $i).
% 206.94/30.98 thf(func_def_10, type, setunion: $i > $i).
% 206.94/30.98 thf(func_def_19, type, descr: ($i > $o) > $i).
% 206.94/30.98 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 206.94/30.98 thf(func_def_26, type, prop2set: $o > $i).
% 206.94/30.98 thf(func_def_36, type, nonempty: $i > $o).
% 206.94/30.98 thf(func_def_69, type, set2prop: $i > $o).
% 206.94/30.98 thf(func_def_88, type, subset: $i > $i > $o).
% 206.94/30.98 thf(func_def_89, type, disjoint: $i > $i > $o).
% 206.94/30.98 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 206.94/30.98 thf(func_def_114, type, binunion: $i > $i > $i).
% 206.94/30.98 thf(func_def_122, type, binintersect: $i > $i > $i).
% 206.94/30.98 thf(func_def_135, type, regular: $i > $o).
% 206.94/30.98 thf(func_def_136, type, setminus: $i > $i > $i).
% 206.94/30.98 thf(func_def_147, type, symdiff: $i > $i > $i).
% 206.94/30.98 thf(func_def_153, type, iskpair: $i > $o).
% 206.94/30.98 thf(func_def_158, type, kpair: $i > $i > $i).
% 206.94/30.98 thf(func_def_160, type, cartprod: $i > $i > $i).
% 206.94/30.98 thf(func_def_177, type, singleton: $i > $o).
% 206.94/30.98 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 206.94/30.98 thf(func_def_184, type, atmost1p: $i > $o).
% 206.94/30.98 thf(func_def_185, type, atleast2p: $i > $o).
% 206.94/30.98 thf(func_def_186, type, atmost2p: $i > $o).
% 206.94/30.98 thf(func_def_187, type, upairsetp: $i > $o).
% 206.94/30.98 thf(func_def_191, type, kfst: $i > $i).
% 206.94/30.98 thf(func_def_203, type, ksnd: $i > $i).
% 206.94/30.98 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 206.94/30.98 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 206.94/30.98 thf(func_def_222, type, func: $i > $i > $i > $o).
% 206.94/30.98 thf(func_def_223, type, funcSet: $i > $i > $i).
% 206.94/30.98 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 206.94/30.98 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 206.94/30.98 thf(func_def_259, type, if: $i > $o > $i > $i > $i).
% 206.94/30.98 thf(func_def_311, type, sP0: $i > $i > $o).
% 206.94/30.98 thf(func_def_312, type, sP1: $i > $o).
% 206.94/30.98 thf(func_def_313, type, sP2: $i > $i > $o).
% 206.94/30.98 thf(func_def_314, type, sP3: $i > $i > $o).
% 206.94/30.98 thf(func_def_315, type, sP4: $i > $i > $i > $o).
% 206.94/30.98 thf(func_def_320, type, sP9: $i > $i > $i > $i > $o).
% 206.94/30.98 thf(func_def_322, type, sP11: $i > $i > $i > $o > $o).
% 206.94/30.98 thf(func_def_323, type, sK12: $i > $o).
% 206.94/30.98 thf(func_def_326, type, sK15: $i > $o).
% 206.94/30.98 thf(func_def_329, type, sK18: $i > ($i > $o) > $i).
% 206.94/30.98 thf(func_def_330, type, sK19: $i > ($i > $o) > $i).
% 206.94/30.98 thf(func_def_331, type, sK20: $i > $o).
% 206.94/30.98 thf(func_def_362, type, sK51: $i > $o).
% 206.94/30.98 thf(func_def_381, type, sK70: $i > ($i > $o) > $i).
% 206.94/30.98 thf(func_def_382, type, sK71: $i > $o).
% 206.94/30.98 thf(func_def_388, type, sK77: $i > $i > $i).
% 206.94/30.98 thf(func_def_395, type, sK84: ($i > $o) > ($i > $o) > $i > $i > $i).
% 206.94/30.98 thf(func_def_396, type, sK85: ($i > $o) > ($i > $o) > $i > $i > $i).
% 206.94/30.98 thf(func_def_399, type, sK88: $i > $o).
% 206.94/30.98 thf(func_def_400, type, sK89: $i > $o).
% 206.94/30.98 thf(func_def_416, type, sK105: $i > $i > $i).
% 206.94/30.98 thf(func_def_422, type, sK111: $i > $o).
% 206.94/30.98 thf(func_def_425, type, sK114: $i > $i > $i).
% 206.94/30.98 thf(func_def_426, type, sK115: $i > $i > $i).
% 206.94/30.98 thf(func_def_431, type, sK120: $i > $i > $i).
% 206.94/30.98 thf(func_def_438, type, sK127: $i > $i > $i).
% 206.94/30.98 thf(func_def_439, type, sK128: $i > $i > $i).
% 206.94/30.98 thf(func_def_440, type, sK129: $i > $i > $i).
% 206.94/30.98 thf(func_def_441, type, sK130: $i > $i > $i).
% 206.94/30.98 thf(func_def_442, type, sK131: $i > $i > $i).
% 206.94/30.98 thf(func_def_443, type, sK132: $i > $i > $i > $i).
% 206.94/30.98 thf(func_def_444, type, sK133: $i > $i).
% 206.94/30.98 thf(func_def_445, type, sK134: $i > $i).
% 206.94/30.98 thf(func_def_446, type, sK135: $i > $i).
% 206.94/30.98 thf(func_def_447, type, sK136: $i > $i).
% 206.94/30.98 thf(func_def_448, type, sK137: $i > $i > $i).
% 206.94/30.98 thf(func_def_449, type, sK138: $i > $i > $i > $i).
% 206.94/30.98 thf(func_def_450, type, sK139: $i > $i > $i > $i).
% 206.94/30.98 thf(func_def_451, type, sK140: $i > $i > $i).
% 206.94/30.98 thf(func_def_452, type, sK141: $i > $i > $i).
% 206.94/30.98 thf(func_def_453, type, sK142: $i > $i).
% 206.94/30.98 thf(func_def_455, type, sK144: $i > $i).
% 206.94/30.98 thf(func_def_456, type, sK145: $i > $i).
% 206.94/30.98 thf(func_def_465, type, sK154: $i > $i > $o).
% 206.94/30.98 thf(func_def_474, type, sK163: $i > $i > $i).
% 206.94/30.98 thf(func_def_495, type, sK184: $i > ($i > $i) > $i > $i).
% 206.94/30.98 thf(func_def_497, type, sK186: $i > $i).
% 206.94/30.98 thf(func_def_504, type, sK193: $i > $i).
% 206.94/30.98 thf(func_def_507, type, sK196: $i > $i).
% 206.94/30.98 thf(func_def_509, type, sK198: $i > $i).
% 206.94/30.98 thf(func_def_517, type, sK206: ($i > $o) > ($i > $o) > $i).
% 206.94/30.98 thf(func_def_518, type, sK207: ($i > $o) > ($i > $o) > $i).
% 206.94/30.98 thf(func_def_519, type, sK208: $i > $o).
% 206.94/30.98 thf(func_def_520, type, sK209: $i > $o).
% 206.94/30.98 thf(func_def_521, type, sK210: $i > ($i > $o) > $i).
% 206.94/30.98 thf(func_def_522, type, sK211: $i > $o).
% 206.94/30.98 thf(func_def_524, type, sK213: ($i > $o) > ($i > $o) > $i).
% 206.94/30.98 thf(func_def_525, type, sK214: ($i > $o) > ($i > $o) > $i).
% 206.94/30.98 thf(func_def_526, type, sK215: $i > $o).
% 206.94/30.98 thf(func_def_527, type, sK216: $i > $o).
% 206.94/30.98 thf(func_def_531, type, sK220: $i > $i).
% 206.94/30.98 thf(func_def_539, type, sK228: $o > $i > $i > $i).
% 206.94/30.98 thf(func_def_547, type, sK236: $i > $i > $i > $i).
% 206.94/30.98 thf(func_def_562, type, sK251: $i > $i).
% 206.94/30.98 thf(func_def_578, type, sK267: $i > $o).
% 206.94/30.98 thf(func_def_596, type, sK285: $i > $i).
% 206.94/30.98 thf(func_def_598, type, sK287: ($i > $i) > $i > $i > $i).
% 206.94/30.98 thf(func_def_601, type, sK290: $i > $o).
% 206.94/30.98 thf(func_def_602, type, sK291: ($i > $o) > $i).
% 206.94/30.98 thf(func_def_603, type, sK292: ($i > $o) > $i > $i > $i > $i).
% 206.94/30.98 thf(func_def_604, type, sK293: ($i > $o) > $i > $i > $i > $i).
% 206.94/30.98 thf(func_def_608, type, sK297: $i > $o).
% 206.94/30.98 thf(func_def_628, type, sK317: $i > $o).
% 206.94/30.98 thf(func_def_643, type, sK332: $i > $i).
% 206.94/30.98 thf(func_def_645, type, sK334: $i > ($i > $i) > $i > $i).
% 206.94/30.98 thf(func_def_656, type, sK345: $i > $i > $i > $i).
% 206.94/30.98 thf(func_def_660, type, sK349: $i > $i > $i > $i).
% 206.94/30.98 thf(func_def_661, type, sK350: $i > $o).
% 206.94/30.98 thf(func_def_664, type, sK353: $i > $o).
% 206.94/30.98 thf(func_def_666, type, sK355: ($i > $o) > $i > $i).
% 206.94/30.98 thf(func_def_667, type, sK356: ($i > $o) > $i > $i).
% 206.94/30.98 thf(func_def_672, type, sK361: $i > $i > $o).
% 206.94/30.98 thf(func_def_673, type, sK362: $i > $i).
% 206.94/30.98 thf(func_def_674, type, sK363: $i > $i).
% 206.94/30.98 thf(func_def_675, type, sK364: ($i > $i > $o) > $i > $i).
% 206.94/30.98 thf(func_def_676, type, sK365: $i > ($i > $i > $o) > $i > $i).
% 206.94/30.98 thf(func_def_677, type, sK366: ($i > $i > $o) > $i > $i).
% 206.94/30.98 thf(func_def_690, type, sK379: $i > $o).
% 206.94/30.98 thf(func_def_692, type, sK381: ($i > $o) > $i > $i).
% 206.94/30.98 thf(func_def_693, type, sK382: ($i > $o) > $i > $i).
% 206.94/30.98 thf(func_def_694, type, sK383: $i > $o).
% 206.94/30.98 thf(func_def_701, type, sK390: $i > $i > $o).
% 206.94/30.98 thf(func_def_713, type, sK402: $i > $o).
% 206.94/30.98 thf(func_def_716, type, sK405: $i > $i > $o).
% 206.94/30.98 thf(func_def_725, type, sK414: $i > ($i > $o) > $i).
% 206.94/30.98 thf(func_def_726, type, sK415: $i > $o).
% 206.94/30.98 thf(func_def_734, type, sK423: $i > $i).
% 206.94/30.98 thf(func_def_741, type, sK430: ($i > $o) > $i > $i).
% 206.94/30.98 thf(func_def_743, type, sK432: $i > $o).
% 206.94/30.98 thf(func_def_751, type, sK440: $i > $i > $o).
% 206.94/30.98 thf(func_def_762, type, sK451: $i > $i > $i).
% 206.94/30.98 thf(func_def_772, type, sK461: $i > $o).
% 206.94/30.98 thf(func_def_790, type, sK479: $i > $i > $i > $i).
% 206.94/30.98 thf(func_def_792, type, sK481: $i > $o).
% 206.94/30.98 thf(func_def_795, type, sK484: $i > $i > $o).
% 206.94/30.98 thf(func_def_804, type, sK493: $i > $o).
% 206.94/30.98 thf(func_def_806, type, sK495: ($i > $o) > $i > $i).
% 206.94/30.98 thf(func_def_811, type, sK500: $i > $o).
% 206.94/30.98 thf(func_def_832, type, sK521: $i > $i > $o).
% 206.94/30.98 thf(func_def_842, type, sK531: $i > $i > $i > $i > $i).
% 206.94/30.98 thf(func_def_857, type, sK546: ($i > $o) > $i > $i > $i > $i).
% 206.94/30.98 thf(func_def_858, type, sK547: ($i > $o) > $i > $i > $i > $i).
% 206.94/30.98 thf(func_def_862, type, sK551: $i > $o).
% 206.94/30.98 thf(func_def_878, type, sK567: $i > $i > $i > $i > $i).
% 206.94/30.98 thf(func_def_879, type, sK568: $i > $i > $i > $i > $i).
% 206.94/30.98 thf(func_def_933, type, sK622: $i > $i > $i > $i).
% 206.94/30.98 thf(func_def_934, type, sK623: $i > $i > $i > $i).
% 206.94/30.98 thf(func_def_935, type, sK624: ($i > $o) > $i).
% 206.94/30.98 thf(func_def_936, type, sK625: $i > $o).
% 206.94/30.98 thf(func_def_937, type, sK626: $i > $i).
% 206.94/30.98 thf(func_def_943, type, sK632: $i > $o).
% 206.94/30.98 thf(func_def_946, type, sK635: $i > $i > $i > $i > $i).
% 206.94/30.98 thf(func_def_951, type, sK640: $i > ($i > $i) > $i > $i).
% 206.94/30.98 thf(func_def_953, type, sK642: $i > $i).
% 206.94/30.98 thf(func_def_970, type, sK659: $i > $i > $i > $i > $i).
% 206.94/30.98 thf(func_def_983, type, sK672: $i > $o).
% 206.94/30.98 thf(func_def_985, type, sK674: ($i > $o) > $i).
% 206.94/30.98 thf(func_def_986, type, sK675: ($i > $o) > $i).
% 206.94/30.98 thf(func_def_989, type, sK678: $i > $i).
% 206.94/30.98 thf(func_def_994, type, sK683: ($i > $i) > $i > $i > $i).
% 206.94/30.98 thf(func_def_997, type, sK686: $i > $i).
% 206.94/30.98 thf(func_def_1005, type, sK694: $i > $i > $i).
% 206.94/30.98 thf(func_def_1006, type, sK695: $i > $o).
% 206.94/30.98 thf(func_def_1009, type, sK698: $i > $i > ($i > $o) > $i).
% 206.94/30.98 thf(func_def_1014, type, sK703: $i > $i > $i > $i > $i).
% 206.94/30.98 thf(func_def_1015, type, sK704: $i > $i > $i > $i > $i).
% 206.94/30.98 thf(func_def_1016, type, sK705: $i > $i > $i > $i > $i).
% 206.94/30.98 thf(func_def_1017, type, sK706: $i > $i > $i > $i > $i).
% 206.94/30.98 thf(func_def_1028, type, sK717: $i > ($i > $i) > $i > $i).
% 206.94/30.98 thf(func_def_1030, type, sK719: $i > $i).
% 206.94/30.98 thf(func_def_1045, type, sK734: $i > $o).
% 206.94/30.98 thf(func_def_1047, type, sK736: $i > $o).
% 206.94/30.98 thf(func_def_1048, type, sK737: ($i > $o) > $i > $i).
% 206.94/30.98 thf(func_def_1052, type, sK741: $i > ($i > $o) > $i).
% 206.94/30.98 thf(func_def_1053, type, sK742: $i > $o).
% 206.94/30.98 thf(func_def_1089, type, sK778: $i > $i > $i).
% 206.94/30.98 thf(func_def_1096, type, sK785: $i > $i > $i).
% 206.94/30.98 thf(func_def_1102, type, sK791: $i > $i > $o).
% 206.94/30.98 thf(func_def_1122, type, sK811: $i > $o).
% 206.94/30.98 thf(func_def_1123, type, sK812: $i > $i).
% 206.94/30.98 thf(func_def_1124, type, sK813: ($i > $o) > $i).
% 206.94/30.98 thf(func_def_1140, type, sP829: $i > $o).
% 206.94/30.98 thf(func_def_1141, type, sP830: $o > $o).
% 206.94/30.98 thf(func_def_1142, type, sP831: $o > $o).
% 206.94/30.98 thf(func_def_1143, type, sP832: $o > $o).
% 206.94/30.98 thf(func_def_1144, type, sP833: $o > $o).
% 206.94/30.98 thf(func_def_1145, type, sP834: $o > $o).
% 206.94/30.98 thf(func_def_1146, type, sP835: $o > $o).
% 206.94/30.98 thf(func_def_1147, type, sP836: $o > $o).
% 206.94/30.98 thf(func_def_1148, type, sP837: $o > $o).
% 206.94/30.98 thf(func_def_1149, type, sP838: $o > $o).
% 206.94/30.98 thf(func_def_1150, type, sP839: $o > $o).
% 206.94/30.98 thf(func_def_1151, type, sP840: $o > $o).
% 206.94/30.98 thf(func_def_1152, type, sP841: $o > $o).
% 206.94/30.98 thf(func_def_1153, type, sP842: $o > $o).
% 206.94/30.98 thf(func_def_1154, type, sP843: $o > $o).
% 206.94/30.98 thf(func_def_1155, type, sP844: $o > $o).
% 206.94/30.98 thf(func_def_1156, type, sP845: $o > $o).
% 206.94/30.98 thf(func_def_1157, type, sP846: $o > $o).
% 206.94/30.98 thf(func_def_1158, type, sP847: $o > $o).
% 206.94/30.98 thf(func_def_1159, type, sP848: $o > $o).
% 206.94/30.98 thf(func_def_1160, type, sP849: $o > $o).
% 206.94/30.98 thf(func_def_1161, type, sP850: $o > $o).
% 206.94/30.98 thf(func_def_1162, type, sP851: $o > $o).
% 206.94/30.98 thf(func_def_1163, type, sP852: $o > $o).
% 206.94/30.98 thf(func_def_1164, type, sP853: $o > $o).
% 206.94/30.98 thf(func_def_1165, type, sP854: $o > $o).
% 206.94/30.98 thf(func_def_1166, type, sP855: $o > $o).
% 206.94/30.98 thf(func_def_1167, type, sP856: $o > $o).
% 206.94/30.98 thf(func_def_1168, type, sP857: $o > $o).
% 206.94/30.98 thf(func_def_1169, type, sP858: $o > $o).
% 206.94/30.98 thf(func_def_1170, type, sP859: $o > $o).
% 206.94/30.98 thf(func_def_1171, type, sP860: $o > $o).
% 206.94/30.98 thf(func_def_1172, type, sP861: $o > $o).
% 206.94/30.98 thf(func_def_1173, type, sP862: $i > $o).
% 206.94/30.98 thf(func_def_1174, type, sP863: $o > $o).
% 206.94/30.98 thf(func_def_1175, type, sP864: $o > $o).
% 206.94/30.98 thf(func_def_1176, type, sP865: $o > $o).
% 206.94/30.98 thf(func_def_1177, type, sP866: $o > $o).
% 206.94/30.98 thf(func_def_1178, type, sP867: $o > $o).
% 206.94/30.98 thf(func_def_1179, type, sP868: $o > $o).
% 206.94/30.98 thf(func_def_1180, type, sP869: $o > $o).
% 206.94/30.98 thf(func_def_1181, type, sP870: $o > $o).
% 206.94/30.98 thf(func_def_1182, type, sP871: $o > $o).
% 206.94/30.98 thf(func_def_1183, type, sP872: $o > $o).
% 206.94/30.98 thf(func_def_1184, type, sP873: $o > $o).
% 206.94/30.98 thf(func_def_1185, type, sP874: $o > $o).
% 206.94/30.98 thf(func_def_1186, type, sP875: $o > $o).
% 206.94/30.98 thf(func_def_1187, type, sP876: $o > $o).
% 206.94/30.98 thf(func_def_1188, type, sP877: $o > $o).
% 206.94/30.98 thf(func_def_1189, type, sP878: $o > $o).
% 206.94/30.98 thf(func_def_1190, type, sP879: $o > $o).
% 206.94/30.98 thf(func_def_1191, type, sP880: $o > $o).
% 206.94/30.98 thf(func_def_1192, type, sP881: $o > $o).
% 206.94/30.98 thf(func_def_1193, type, sP882: $o > $o).
% 206.94/30.98 thf(func_def_1194, type, sP883: $o > $o).
% 206.94/30.98 thf(func_def_1195, type, sP884: $o > $o).
% 206.94/30.98 thf(func_def_1196, type, sP885: $o > $o).
% 206.94/30.98 thf(func_def_1197, type, sP886: $o > $o).
% 206.94/30.98 thf(func_def_1198, type, sP887: $o > $o).
% 206.94/30.98 thf(func_def_1199, type, sP888: $o > $o).
% 206.94/30.98 thf(func_def_1200, type, sP889: $o > $o).
% 206.94/30.98 thf(func_def_1201, type, sP890: $o > $o).
% 206.94/30.98 thf(func_def_1202, type, sP891: $o > $o).
% 206.94/30.98 thf(func_def_1203, type, sP892: $o > $o).
% 206.94/30.98 thf(func_def_1204, type, sP893: $i > $o).
% 206.94/30.98 thf(func_def_1205, type, sP894: $o > $o).
% 206.94/30.98 thf(func_def_1206, type, sP895: $o > $o).
% 206.94/30.98 thf(func_def_1207, type, sP896: $o > $o).
% 206.94/30.98 thf(func_def_1208, type, sP897: $o > $o).
% 206.94/30.98 thf(func_def_1209, type, sP898: $o > $o).
% 206.94/30.98 thf(func_def_1210, type, sP899: $o > $o).
% 206.94/30.98 thf(func_def_1211, type, sP900: $o > $o).
% 206.94/30.98 thf(func_def_1212, type, sP901: $o > $o).
% 206.94/30.98 thf(func_def_1213, type, sP902: $o > $o).
% 206.94/30.98 thf(func_def_1214, type, sP903: $o > $o).
% 206.94/30.98 thf(func_def_1215, type, sP904: $o > $o).
% 206.94/30.98 thf(func_def_1216, type, sP905: $o > $o).
% 206.94/30.98 thf(func_def_1217, type, sP906: $o > $o).
% 206.94/30.98 thf(func_def_1218, type, sP907: $o > $o).
% 206.94/30.98 thf(func_def_1219, type, sP908: $o > $o).
% 206.94/30.98 thf(func_def_1220, type, sP909: $o > $o).
% 206.94/30.98 thf(func_def_1221, type, sP910: $o > $o).
% 206.94/30.98 thf(func_def_1222, type, sP911: $o > $o).
% 206.94/30.98 thf(func_def_1223, type, sP912: $o > $o).
% 206.94/30.98 thf(func_def_1224, type, sP913: $o > $o).
% 206.94/30.98 thf(func_def_1225, type, sP914: $o > $o).
% 206.94/30.98 thf(func_def_1226, type, sP915: $o > $o).
% 206.94/30.98 thf(func_def_1227, type, sP916: $o > $o).
% 206.94/30.98 thf(func_def_1228, type, sP917: $o > $o).
% 206.94/30.98 thf(func_def_1229, type, sP918: $o > $o).
% 206.94/30.98 thf(func_def_1230, type, sP919: $o > $o).
% 206.94/30.98 thf(func_def_1231, type, sP920: $o > $o).
% 206.94/30.98 thf(func_def_1232, type, sP921: $o > $o).
% 206.94/30.98 thf(func_def_1233, type, sP922: $o > $o).
% 206.94/30.98 thf(func_def_1234, type, sP923: $o > $o).
% 206.94/30.98 thf(func_def_1235, type, sP924: $i > $o).
% 206.94/30.98 thf(func_def_1236, type, sP925: $o > $o).
% 206.94/30.98 thf(func_def_1237, type, sP926: $o > $o).
% 206.94/30.98 thf(func_def_1238, type, sP927: $o > $o).
% 206.94/30.98 thf(func_def_1239, type, sP928: $o > $o).
% 206.94/30.98 thf(func_def_1240, type, sP929: $o > $o).
% 206.94/30.98 thf(func_def_1241, type, sP930: $o > $o).
% 206.94/30.98 thf(func_def_1242, type, sP931: $o > $o).
% 206.94/30.98 thf(func_def_1243, type, sP932: $o > $o).
% 206.94/30.98 thf(func_def_1244, type, sP933: $o > $o).
% 206.94/30.98 thf(func_def_1245, type, sP934: $o > $o).
% 206.94/30.98 thf(func_def_1246, type, sP935: $i > $o).
% 206.94/30.98 thf(func_def_1247, type, sP936: $o > $o).
% 206.94/30.98 thf(func_def_1248, type, sP937: $o > $o).
% 206.94/30.98 thf(func_def_1249, type, sP938: $o > $o).
% 206.94/30.98 thf(func_def_1250, type, sP939: $o > $o).
% 206.94/30.98 thf(func_def_1251, type, sP940: $o > $o).
% 206.94/30.98 thf(func_def_1252, type, sP941: $o > $o).
% 206.94/30.98 thf(func_def_1253, type, sP942: $i > $o).
% 206.94/30.98 thf(func_def_1254, type, sP943: $o > $o).
% 206.94/30.98 thf(func_def_1255, type, sP944: $o > $o).
% 206.94/30.98 thf(func_def_1256, type, sP945: $o > $o).
% 206.94/30.98 thf(func_def_1257, type, sP946: $o > $o).
% 206.94/30.98 thf(func_def_1258, type, sP947: $o > $o).
% 206.94/30.98 thf(func_def_1259, type, sP948: $o > $o).
% 206.94/30.98 thf(func_def_1260, type, sP949: $o > $o).
% 206.94/30.98 thf(func_def_1261, type, sP950: $o > $o).
% 206.94/30.98 thf(func_def_1262, type, sP951: $o > $o).
% 206.94/30.98 thf(func_def_1263, type, sP952: $o > $o).
% 206.94/30.98 thf(func_def_1264, type, sP953: $o > $o).
% 206.94/30.98 thf(func_def_1265, type, sP954: $o > $o).
% 206.94/30.98 thf(func_def_1266, type, sP955: $o > $o).
% 206.94/30.98 thf(func_def_1267, type, sP956: $o > $o).
% 206.94/30.98 thf(func_def_1268, type, sP957: $o > $o).
% 206.94/30.98 thf(func_def_1269, type, sP958: $o > $o).
% 206.94/30.98 thf(func_def_1270, type, sP959: $o > $o).
% 206.94/30.98 thf(func_def_1271, type, sP960: $o > $o).
% 206.94/30.98 thf(func_def_1272, type, sP961: $o > $o).
% 206.94/30.98 thf(func_def_1273, type, sP962: $o > $o).
% 206.94/30.98 thf(func_def_1274, type, sP963: $o > $o).
% 206.94/30.98 thf(func_def_1275, type, sP964: $o > $o).
% 206.94/30.98 thf(func_def_1276, type, sP965: $o > $o).
% 206.94/30.98 thf(func_def_1277, type, sP966: $o > $o).
% 206.94/30.98 thf(func_def_1278, type, sP967: $o > $o).
% 206.94/30.98 thf(func_def_1279, type, sP968: $o > $o).
% 206.94/30.98 thf(func_def_1280, type, sP969: $o > $o).
% 206.94/30.98 thf(func_def_1281, type, sP970: $o > $o).
% 206.94/30.98 thf(func_def_1282, type, sP971: $o > $o).
% 206.94/30.98 thf(func_def_1283, type, sP972: $o > $o).
% 206.94/30.98 thf(func_def_1284, type, sP973: $o > $o).
% 206.94/30.98 thf(func_def_1285, type, sP974: $o > $o).
% 206.94/30.98 thf(func_def_1286, type, sP975: $o > $o).
% 206.94/30.98 thf(func_def_1287, type, sP976: $o > $o).
% 206.94/30.98 thf(func_def_1288, type, sP977: $i > $o).
% 206.94/30.98 thf(func_def_1289, type, sP978: $o > $o).
% 206.94/30.98 thf(func_def_1290, type, sP979: $o > $o).
% 206.94/30.98 thf(func_def_1291, type, sP980: $o > $o).
% 206.94/30.98 thf(func_def_1292, type, sP981: $o > $o).
% 206.94/30.98 thf(func_def_1293, type, sP982: $o > $o).
% 206.94/30.98 thf(func_def_1294, type, sP983: $o > $o).
% 206.94/30.98 thf(func_def_1295, type, sP984: $o > $o).
% 206.94/30.98 thf(func_def_1296, type, sP985: $o > $o).
% 206.94/30.98 thf(func_def_1297, type, sP986: $i > $o).
% 206.94/30.98 thf(func_def_1298, type, sP987: $o > $o).
% 206.94/30.98 thf(func_def_1299, type, sP988: $o > $o).
% 206.94/30.98 thf(func_def_1300, type, sP989: $o > $o).
% 206.94/30.98 thf(func_def_1301, type, sP990: $o > $o).
% 206.94/30.98 thf(func_def_1302, type, sP991: $o > $o).
% 206.94/30.98 thf(func_def_1303, type, sP992: $o > $o).
% 206.94/30.98 thf(func_def_1304, type, sP993: $o > $o).
% 206.94/30.98 thf(func_def_1305, type, sP994: $o > $o).
% 206.94/30.98 thf(func_def_1306, type, sP995: $o > $o).
% 206.94/30.98 thf(func_def_1307, type, sP996: $o > $o).
% 206.94/30.98 thf(func_def_1308, type, sP997: $o > $o).
% 206.94/30.98 thf(func_def_1309, type, sP998: $o > $o).
% 206.94/30.98 thf(func_def_1310, type, sP999: $o > $o).
% 206.94/30.98 thf(func_def_1311, type, sP1000: $o > $o).
% 206.94/30.98 thf(func_def_1312, type, sP1001: $o > $o).
% 206.94/30.98 thf(func_def_1313, type, sP1002: $o > $o).
% 206.94/30.98 thf(func_def_1314, type, sP1003: $o > $o).
% 206.94/30.98 thf(func_def_1315, type, sP1004: $o > $o).
% 206.94/30.98 thf(func_def_1316, type, sP1005: $o > $o).
% 206.94/30.98 thf(func_def_1317, type, sP1006: $o > $o).
% 206.94/30.98 thf(func_def_1318, type, sP1007: $o > $o).
% 206.94/30.98 thf(func_def_1319, type, sP1008: $o > $o).
% 206.94/30.98 thf(func_def_1320, type, sP1009: $o > $o).
% 206.94/30.98 thf(func_def_1321, type, sP1010: $o > $o).
% 206.94/30.98 thf(func_def_1322, type, sP1011: $o > $o).
% 206.94/30.98 thf(func_def_1323, type, sP1012: $o > $o).
% 206.94/30.98 thf(func_def_1324, type, sP1013: $o > $o).
% 206.94/30.98 thf(func_def_1325, type, sP1014: $o > $o).
% 206.94/30.98 thf(func_def_1326, type, sP1015: $o > $o).
% 206.94/30.98 thf(func_def_1327, type, sP1016: $o > $o).
% 206.94/30.98 thf(func_def_1328, type, sP1017: $o > $o).
% 206.94/30.98 thf(func_def_1329, type, sP1018: $o > $o).
% 206.94/30.98 thf(func_def_1330, type, sP1019: $o > $o).
% 206.94/30.98 thf(func_def_1331, type, sP1020: $o > $o).
% 206.94/30.98 thf(func_def_1332, type, sP1021: $o > $o).
% 206.94/30.98 thf(func_def_1333, type, sP1022: $o > $o).
% 206.94/30.98 thf(func_def_1334, type, sP1023: $o > $o).
% 206.94/30.98 thf(func_def_1335, type, sP1024: $o > $o).
% 206.94/30.98 thf(func_def_1336, type, sP1025: $o > $o).
% 206.94/30.98 thf(func_def_1337, type, sP1026: $o > $o).
% 206.94/30.98 thf(func_def_1338, type, sP1027: $o > $o).
% 206.94/30.98 thf(func_def_1339, type, sP1028: $o > $o).
% 206.94/30.98 thf(func_def_1340, type, sP1029: $o > $o).
% 206.94/30.98 thf(func_def_1341, type, sP1030: $o > $o).
% 206.94/30.98 thf(func_def_1342, type, sP1031: $o > $o).
% 206.94/30.98 thf(func_def_1343, type, sP1032: $o > $o).
% 206.94/30.98 thf(func_def_1344, type, sP1033: $o > $o).
% 206.94/30.98 thf(func_def_1345, type, sP1034: $o > $o).
% 206.94/30.98 thf(func_def_1346, type, sP1035: $o > $o).
% 206.94/30.98 thf(func_def_1347, type, sP1036: $o > $o).
% 206.94/30.98 thf(func_def_1348, type, sP1037: $o > $o).
% 206.94/30.98 thf(func_def_1349, type, sP1038: $o > $o).
% 206.94/30.98 thf(func_def_1350, type, sP1039: $o > $o).
% 206.94/30.98 thf(func_def_1351, type, sP1040: $o > $o).
% 206.94/30.98 thf(func_def_1352, type, sP1041: $o > $o).
% 206.94/30.98 thf(func_def_1353, type, sP1042: $o > $o).
% 206.94/30.98 thf(func_def_1354, type, sP1043: $o > $o).
% 206.94/30.98 thf(func_def_1355, type, sP1044: $o > $o).
% 206.94/30.98 thf(func_def_1356, type, sP1045: $o > $o).
% 206.94/30.98 thf(func_def_1357, type, sP1046: $o > $o).
% 206.94/30.98 thf(func_def_1358, type, sP1047: $o > $o).
% 206.94/30.98 thf(func_def_1359, type, sP1048: $o > $o).
% 206.94/30.98 thf(func_def_1360, type, sP1049: $o > $o).
% 206.94/30.98 thf(func_def_1361, type, sP1050: $o > $o).
% 206.94/30.98 thf(func_def_1362, type, sP1051: $o > $o).
% 206.94/30.98 thf(func_def_1363, type, sP1052: $o > $o).
% 206.94/30.98 thf(func_def_1364, type, sP1053: $o > $o).
% 206.94/30.98 thf(func_def_1365, type, sP1054: $o > $o).
% 206.94/30.98 thf(func_def_1366, type, sP1055: $o > $o).
% 206.94/30.98 thf(func_def_1367, type, sP1056: $o > $o).
% 206.94/30.98 thf(func_def_1368, type, sP1057: $o > $o).
% 206.94/30.98 thf(func_def_1369, type, sP1058: $o > $o).
% 206.94/30.98 thf(func_def_1370, type, sP1059: $i > $o).
% 206.94/30.98 thf(func_def_1371, type, sP1060: $o > $o).
% 206.94/30.98 thf(func_def_1372, type, sP1061: $o > $o).
% 206.94/30.98 thf(func_def_1373, type, sP1062: $o > $o).
% 206.94/30.98 thf(func_def_1374, type, sP1063: $o > $o).
% 206.94/30.98 thf(func_def_1375, type, sP1064: $o > $o).
% 206.94/30.98 thf(func_def_1376, type, sP1065: $o > $o).
% 206.94/30.98 thf(func_def_1377, type, sP1066: $o > $o).
% 206.94/30.98 thf(func_def_1378, type, sP1067: $o > $o).
% 206.94/30.98 thf(func_def_1379, type, sP1068: $o > $o).
% 206.94/30.98 thf(func_def_1380, type, sP1069: $i > $o).
% 206.94/30.98 thf(func_def_1381, type, sP1070: $o > $o).
% 206.94/30.98 thf(func_def_1382, type, sP1071: $o > $o).
% 206.94/30.98 thf(func_def_1383, type, sP1072: $o > $o).
% 206.94/30.98 thf(func_def_1384, type, sP1073: $o > $o).
% 206.94/30.98 thf(func_def_1385, type, sP1074: $o > $o).
% 206.94/30.98 thf(func_def_1386, type, sP1075: $o > $o).
% 206.94/30.98 thf(func_def_1387, type, sP1076: $o > $o).
% 206.94/30.98 thf(func_def_1388, type, sP1077: $o > $o).
% 206.94/30.98 thf(func_def_1389, type, sP1078: $o > $o).
% 206.94/30.98 thf(func_def_1390, type, sP1079: $o > $o).
% 206.94/30.98 thf(func_def_1391, type, sP1080: $o > $o).
% 206.94/30.98 thf(func_def_1392, type, sP1081: $o > $o).
% 206.94/30.98 thf(func_def_1393, type, sP1082: $i > $o).
% 206.94/30.98 thf(func_def_1394, type, sP1083: $o > $o).
% 206.94/30.98 thf(func_def_1395, type, sP1084: $o > $o).
% 206.94/30.98 thf(func_def_1396, type, sP1085: $o > $o).
% 206.94/30.98 thf(func_def_1397, type, sP1086: $o > $o).
% 206.94/30.98 thf(func_def_1398, type, sP1087: $o > $o).
% 206.94/30.98 thf(func_def_1399, type, sP1088: $o > $o).
% 206.94/30.98 thf(func_def_1400, type, sP1089: $o > $o).
% 206.94/30.98 thf(func_def_1401, type, sP1090: $i > $o).
% 206.94/30.98 thf(func_def_1402, type, sP1091: $o > $o).
% 206.94/30.98 thf(func_def_1403, type, sP1092: $o > $o).
% 206.94/30.98 thf(func_def_1404, type, sP1093: $o > $o).
% 206.94/30.98 thf(func_def_1405, type, sP1094: $o > $o).
% 206.94/30.98 thf(func_def_1406, type, sP1095: $o > $o).
% 206.94/30.98 thf(func_def_1407, type, sP1096: $o > $o).
% 206.94/30.98 thf(func_def_1408, type, sP1097: $o > $o).
% 206.94/30.98 thf(func_def_1409, type, sP1098: $o > $o).
% 206.94/30.98 thf(func_def_1410, type, sP1099: $o > $o).
% 206.94/30.98 thf(func_def_1411, type, sP1100: $o > $o).
% 206.94/30.98 thf(func_def_1412, type, sP1101: $o > $o).
% 206.94/30.98 thf(func_def_1413, type, sP1102: $o > $o).
% 206.94/30.98 thf(func_def_1414, type, sP1103: $o > $o).
% 206.94/30.98 thf(func_def_1415, type, sP1104: $o > $o).
% 206.94/30.98 thf(func_def_1416, type, sP1105: $o > $o).
% 206.94/30.98 thf(func_def_1417, type, sP1106: $o > $o).
% 206.94/30.98 thf(func_def_1418, type, sP1107: $o > $o).
% 206.94/30.98 thf(func_def_1419, type, sP1108: $o > $o).
% 206.94/30.98 thf(func_def_1420, type, sP1109: $o > $o).
% 206.94/30.98 thf(func_def_1421, type, sP1110: $o > $o).
% 206.94/30.98 thf(func_def_1422, type, sP1111: $o > $o).
% 206.94/30.98 thf(func_def_1423, type, sP1112: $o > $o).
% 206.94/30.98 thf(func_def_1424, type, sP1113: $o > $o).
% 206.94/30.98 thf(func_def_1425, type, sP1114: $i > $o).
% 206.94/30.98 thf(func_def_1426, type, sP1115: $o > $o).
% 206.94/30.98 thf(func_def_1427, type, sP1116: $i > $o).
% 206.94/30.98 thf(func_def_1428, type, sP1117: $o > $o).
% 206.94/30.98 thf(func_def_1429, type, sP1118: $o > $o).
% 206.94/30.98 thf(func_def_1430, type, sP1119: $o > $o).
% 206.94/30.98 thf(func_def_1431, type, sP1120: $o > $o).
% 206.94/30.98 thf(func_def_1432, type, sP1121: $o > $o).
% 206.94/30.98 thf(func_def_1433, type, sP1122: $o > $o).
% 206.94/30.98 thf(func_def_1434, type, sP1123: $o > $o).
% 206.94/30.98 thf(func_def_1435, type, sP1124: $o > $o).
% 206.94/30.98 thf(func_def_1436, type, sP1125: $o > $o).
% 206.94/30.98 thf(func_def_1437, type, sP1126: $o > $o).
% 206.94/30.98 thf(func_def_1438, type, sP1127: $o > $o).
% 206.94/30.98 thf(func_def_1439, type, sP1128: $o > $o).
% 206.94/30.98 thf(func_def_1440, type, sP1129: $o > $o).
% 206.94/30.98 thf(func_def_1441, type, sP1130: $o > $o).
% 206.94/30.98 thf(func_def_1442, type, sP1131: $o > $o).
% 206.94/30.98 thf(func_def_1443, type, sP1132: $o > $o).
% 206.94/30.98 thf(func_def_1444, type, sP1133: $o > $o).
% 206.94/30.98 thf(func_def_1445, type, sP1134: $o > $o).
% 206.94/30.98 thf(func_def_1446, type, sP1135: $o > $o).
% 206.94/30.98 thf(func_def_1447, type, sP1136: $o > $o).
% 206.94/30.98 thf(func_def_1448, type, sP1137: $o > $o).
% 206.94/30.98 thf(func_def_1449, type, sP1138: $o > $o).
% 206.94/30.98 thf(func_def_1450, type, sP1139: $o > $o).
% 206.94/30.98 thf(func_def_1451, type, sP1140: $i > $o).
% 206.94/30.98 thf(func_def_1452, type, sP1141: $o > $o).
% 206.94/30.98 thf(func_def_1453, type, sP1142: $o > $o).
% 206.94/30.98 thf(func_def_1454, type, sP1143: $o > $o).
% 206.94/30.98 thf(func_def_1455, type, sP1144: $o > $o).
% 206.94/30.98 thf(func_def_1456, type, sP1145: $o > $o).
% 206.94/30.98 thf(func_def_1457, type, sP1146: $o > $o).
% 206.94/30.98 thf(func_def_1458, type, sP1147: $o > $o).
% 206.94/30.98 thf(func_def_1459, type, sP1148: $o > $o).
% 206.94/30.98 thf(func_def_1460, type, sP1149: $o > $o).
% 206.94/30.98 thf(func_def_1461, type, sP1150: $o > $o).
% 206.94/30.98 thf(func_def_1462, type, sP1151: $o > $o).
% 206.94/30.98 thf(func_def_1463, type, sP1152: $o > $o).
% 206.94/30.98 thf(func_def_1464, type, sP1153: $o > $o).
% 206.94/30.98 thf(func_def_1465, type, sP1154: $o > $o).
% 206.94/30.98 thf(func_def_1466, type, sP1155: $o > $o).
% 206.94/30.98 thf(func_def_1467, type, sP1156: $i > $o).
% 206.94/30.98 thf(func_def_1468, type, sP1157: $o > $o).
% 206.94/30.98 thf(func_def_1469, type, sP1158: $o > $o).
% 206.94/30.98 thf(func_def_1470, type, sP1159: $i > $o).
% 206.94/30.98 thf(func_def_1471, type, sP1160: $o > $o).
% 206.94/30.98 thf(func_def_1472, type, sP1161: $o > $o).
% 206.94/30.98 thf(func_def_1473, type, sP1162: $o > $o).
% 206.94/30.98 thf(func_def_1474, type, sP1163: $o > $o).
% 206.94/30.98 thf(func_def_1475, type, sP1164: $o > $o).
% 206.94/30.98 thf(func_def_1476, type, sP1165: $o > $o).
% 206.94/30.98 thf(func_def_1477, type, sP1166: $i > $o).
% 206.94/30.98 thf(func_def_1478, type, sP1167: $o > $o).
% 206.94/30.98 thf(func_def_1479, type, sP1168: $o > $o).
% 206.94/30.98 thf(func_def_1480, type, sP1169: $o > $o).
% 206.94/30.98 thf(func_def_1481, type, sP1170: $o > $o).
% 206.94/30.98 thf(func_def_1482, type, sP1171: $o > $o).
% 206.94/30.98 thf(func_def_1483, type, sP1172: $o > $o).
% 206.94/30.98 thf(func_def_1484, type, sP1173: $o > $o).
% 206.94/30.98 thf(func_def_1485, type, sP1174: $o > $o).
% 206.94/30.98 thf(func_def_1486, type, sP1175: $o > $o).
% 206.94/30.98 thf(func_def_1487, type, sP1176: $o > $o).
% 206.94/30.98 thf(func_def_1488, type, sP1177: $o > $o).
% 206.94/30.98 thf(func_def_1489, type, sP1178: $o > $o).
% 206.94/30.98 thf(func_def_1490, type, sP1179: $o > $o).
% 206.94/30.98 thf(func_def_1491, type, sP1180: $i > $o).
% 206.94/30.98 thf(func_def_1492, type, sP1181: $o > $o).
% 206.94/30.98 thf(func_def_1493, type, sP1182: $o > $o).
% 206.94/30.98 thf(func_def_1494, type, sP1183: $o > $o).
% 206.94/30.98 thf(func_def_1495, type, sP1184: $o > $o).
% 206.94/30.98 thf(func_def_1496, type, sP1185: $o > $o).
% 206.94/30.98 thf(func_def_1497, type, sP1186: $o > $o).
% 206.94/30.98 thf(func_def_1498, type, sP1187: $o > $o).
% 206.94/30.98 thf(func_def_1499, type, sP1188: $o > $o).
% 206.94/30.98 thf(func_def_1500, type, sP1189: $o > $o).
% 206.94/30.98 thf(func_def_1501, type, sP1190: $o > $o).
% 206.94/30.98 thf(func_def_1502, type, sP1191: $o > $o).
% 206.94/30.98 thf(func_def_1503, type, sP1192: $o > $o).
% 206.94/30.98 thf(func_def_1504, type, sP1193: $o > $o).
% 206.94/30.98 thf(func_def_1505, type, sP1194: $o > $o).
% 206.94/30.98 thf(func_def_1506, type, sP1195: $i > $o).
% 206.94/30.98 thf(func_def_1507, type, sP1196: $o > $o).
% 206.94/30.98 thf(func_def_1508, type, sP1197: $o > $o).
% 206.94/30.98 thf(func_def_1509, type, sP1198: $o > $o).
% 206.94/30.98 thf(func_def_1510, type, sP1199: $o > $o).
% 206.94/30.98 thf(func_def_1511, type, sP1200: $o > $o).
% 206.94/30.98 thf(func_def_1512, type, sP1201: $o > $o).
% 206.94/30.98 thf(func_def_1513, type, sP1202: $o > $o).
% 206.94/30.98 thf(func_def_1514, type, sP1203: $o > $o).
% 206.94/30.98 thf(func_def_1515, type, sP1204: $o > $o).
% 206.94/30.98 thf(func_def_1516, type, sP1205: $o > $o).
% 206.94/30.98 thf(func_def_1517, type, sP1206: $o > $o).
% 206.94/30.98 thf(func_def_1518, type, sP1207: $i > $o).
% 206.94/30.98 thf(func_def_1519, type, sP1208: $o > $o).
% 206.94/30.98 thf(func_def_1520, type, sP1209: $o > $o).
% 206.94/30.98 thf(func_def_1521, type, sP1210: $o > $o).
% 206.94/30.98 thf(func_def_1522, type, sP1211: $o > $o).
% 206.94/30.98 thf(func_def_1523, type, sP1212: $o > $o).
% 206.94/30.98 thf(func_def_1524, type, sP1213: $o > $o).
% 206.94/30.98 thf(func_def_1525, type, sP1214: $o > $o).
% 206.94/30.98 thf(func_def_1526, type, sP1215: $o > $o).
% 206.94/30.98 thf(func_def_1527, type, sP1216: $o > $o).
% 206.94/30.98 thf(func_def_1528, type, sP1217: $o > $o).
% 206.94/30.98 thf(func_def_1529, type, sP1218: $o > $o).
% 206.94/30.98 thf(func_def_1530, type, sP1219: $o > $o).
% 206.94/30.98 thf(func_def_1531, type, sP1220: $o > $o).
% 206.94/30.98 thf(func_def_1532, type, sP1221: $o > $o).
% 206.94/30.98 thf(func_def_1533, type, sP1222: $o > $o).
% 206.94/30.98 thf(func_def_1534, type, sP1223: $o > $o).
% 206.94/30.98 thf(func_def_1535, type, sP1224: $o > $o).
% 206.94/30.98 thf(func_def_1536, type, sP1225: $o > $o).
% 206.94/30.98 thf(func_def_1537, type, sP1226: $o > $o).
% 206.94/30.98 thf(func_def_1538, type, sP1227: $o > $o).
% 206.94/30.98 thf(func_def_1539, type, sP1228: $o > $o).
% 206.94/30.98 thf(func_def_1540, type, sP1229: $o > $o).
% 206.94/30.98 thf(func_def_1541, type, sP1230: $o > $o).
% 206.94/30.98 thf(func_def_1542, type, sP1231: $o > $o).
% 206.94/30.98 thf(func_def_1543, type, sP1232: $o > $o).
% 206.94/30.98 thf(func_def_1544, type, sP1233: $o > $o).
% 206.94/30.98 thf(func_def_1545, type, sP1234: $o > $o).
% 206.94/30.98 thf(func_def_1546, type, sP1235: $o > $o).
% 206.94/30.98 thf(func_def_1547, type, sP1236: $o > $o).
% 206.94/30.98 thf(func_def_1548, type, sP1237: $o > $o).
% 206.94/30.98 thf(func_def_1549, type, sP1238: $o > $o).
% 206.94/30.98 thf(func_def_1550, type, sP1239: $o > $o).
% 206.94/30.98 thf(func_def_1551, type, sP1240: $o > $o).
% 206.94/30.98 thf(func_def_1552, type, sP1241: $o > $o).
% 206.94/30.98 thf(func_def_1553, type, sP1242: $o > $o).
% 206.94/30.98 thf(func_def_1554, type, sP1243: $o > $o).
% 206.94/30.98 thf(func_def_1555, type, sP1244: $o > $o).
% 206.94/30.98 thf(func_def_1556, type, sP1245: $o > $o).
% 206.94/30.98 thf(func_def_1557, type, sP1246: $o > $o).
% 206.94/30.98 thf(func_def_1558, type, sP1247: $o > $o).
% 206.94/30.98 thf(func_def_1559, type, sP1248: $o > $o).
% 206.94/30.98 thf(func_def_1560, type, sP1249: $o > $o).
% 206.94/30.98 thf(func_def_1561, type, sP1250: $o > $o).
% 206.94/30.98 thf(func_def_1562, type, sP1251: $o > $o).
% 206.94/30.98 thf(func_def_1563, type, sP1252: $o > $o).
% 206.94/30.98 thf(func_def_1564, type, sP1253: $o > $o).
% 206.94/30.98 thf(func_def_1565, type, sP1254: $o > $o).
% 206.94/30.98 thf(func_def_1566, type, sP1255: $o > $o).
% 206.94/30.98 thf(func_def_1567, type, sP1256: $o > $o).
% 206.94/30.98 thf(func_def_1568, type, sP1257: $i > $o).
% 206.94/30.98 thf(func_def_1569, type, sP1258: $o > $o).
% 206.94/30.98 thf(func_def_1570, type, sP1259: $o > $o).
% 206.94/30.98 thf(func_def_1571, type, sP1260: $o > $o).
% 206.94/30.98 thf(func_def_1572, type, sP1261: $o > $o).
% 206.94/30.98 thf(func_def_1573, type, sP1262: $o > $o).
% 206.94/30.98 thf(func_def_1574, type, sP1263: $o > $o).
% 206.94/30.98 thf(func_def_1575, type, sP1264: $o > $o).
% 206.94/30.98 thf(func_def_1576, type, sP1265: $o > $o).
% 206.94/30.98 thf(func_def_1577, type, sP1266: $o > $o).
% 206.94/30.98 thf(func_def_1578, type, sP1267: $o > $o).
% 206.94/30.98 thf(func_def_1579, type, sP1268: $o > $o).
% 206.94/30.98 thf(func_def_1580, type, sP1269: $o > $o).
% 206.94/30.98 thf(func_def_1581, type, sP1270: $o > $o).
% 206.94/30.98 thf(func_def_1582, type, sP1271: $o > $o).
% 206.94/30.98 thf(func_def_1583, type, sP1272: $o > $o).
% 206.94/30.98 thf(func_def_1584, type, sP1273: $o > $o).
% 206.94/30.98 thf(func_def_1585, type, sP1274: $o > $o).
% 206.94/30.98 thf(func_def_1586, type, sP1275: $o > $o).
% 206.94/30.98 thf(func_def_1587, type, sP1276: $o > $o).
% 206.94/30.98 thf(func_def_1588, type, sP1277: $o > $o).
% 206.94/30.98 thf(func_def_1589, type, sP1278: $o > $o).
% 206.94/30.98 thf(func_def_1590, type, sP1279: $o > $o).
% 206.94/30.98 thf(func_def_1591, type, sP1280: $o > $o).
% 206.94/30.98 thf(func_def_1592, type, sP1281: $o > $o).
% 206.94/30.98 thf(func_def_1593, type, sP1282: $o > $o).
% 206.94/30.98 thf(func_def_1594, type, sP1283: $o > $o).
% 206.94/30.98 thf(func_def_1595, type, sP1284: $o > $o).
% 206.94/30.98 thf(func_def_1596, type, sP1285: $o > $o).
% 206.94/30.98 thf(func_def_1597, type, sP1286: $o > $o).
% 206.94/30.98 thf(func_def_1598, type, sP1287: $o > $o).
% 206.94/30.98 thf(func_def_1599, type, sP1288: $o > $o).
% 206.94/30.98 thf(func_def_1600, type, sP1289: $o > $o).
% 206.94/30.98 thf(func_def_1601, type, sP1290: $o > $o).
% 206.94/30.98 thf(func_def_1602, type, sP1291: $o > $o).
% 206.94/30.98 thf(func_def_1603, type, sP1292: $o > $o).
% 206.94/30.98 thf(func_def_1604, type, sP1293: $o > $o).
% 206.94/30.98 thf(func_def_1605, type, sP1294: $o > $o).
% 206.94/30.98 thf(func_def_1606, type, sP1295: $o > $o).
% 206.94/30.98 thf(func_def_1607, type, sP1296: $o > $o).
% 206.94/30.98 thf(func_def_1608, type, sP1297: $o > $o).
% 206.94/30.98 thf(func_def_1609, type, sP1298: $o > $o).
% 206.94/30.98 thf(func_def_1610, type, sP1299: $o > $o).
% 206.94/30.98 thf(func_def_1611, type, sP1300: $o > $o).
% 206.94/30.98 thf(func_def_1612, type, sP1301: $o > $o).
% 206.94/30.98 thf(func_def_1613, type, sP1302: $o > $o).
% 206.94/30.98 thf(func_def_1614, type, sP1303: $o > $o).
% 206.94/30.98 thf(func_def_1615, type, sP1304: $o > $o).
% 206.94/30.98 thf(func_def_1616, type, sP1305: $o > $o).
% 206.94/30.98 thf(func_def_1617, type, sP1306: $o > $o).
% 206.94/30.98 thf(func_def_1618, type, sP1307: $o > $o).
% 206.94/30.98 thf(func_def_1619, type, sP1308: $o > $o).
% 206.94/30.98 thf(func_def_1620, type, sP1309: $o > $o).
% 206.94/30.98 thf(func_def_1621, type, sP1310: $o > $o).
% 206.94/30.98 thf(func_def_1622, type, sP1311: $o > $o).
% 206.94/30.98 thf(func_def_1623, type, sP1312: $o > $o).
% 206.94/30.98 thf(func_def_1624, type, sP1313: $o > $o).
% 206.94/30.98 thf(func_def_1625, type, sP1314: $o > $o).
% 206.94/30.98 thf(func_def_1626, type, sP1315: $o > $o).
% 206.94/30.98 thf(func_def_1627, type, sP1316: $o > $o).
% 206.94/30.98 thf(func_def_1628, type, sP1317: $o > $o).
% 206.94/30.98 thf(func_def_1629, type, sP1318: $o > $o).
% 206.94/30.98 thf(func_def_1630, type, sP1319: $o > $o).
% 206.94/30.98 thf(func_def_1631, type, sP1320: $i > $o).
% 206.94/30.98 thf(func_def_1632, type, sP1321: $o > $o).
% 206.94/30.98 thf(func_def_1633, type, sP1322: $o > $o).
% 206.94/30.98 thf(func_def_1634, type, sP1323: $o > $o).
% 206.94/30.98 thf(func_def_1635, type, sP1324: $o > $o).
% 206.94/30.98 thf(func_def_1636, type, sP1325: $o > $o).
% 206.94/30.98 thf(func_def_1637, type, sP1326: $o > $o).
% 206.94/30.98 thf(func_def_1638, type, sP1327: $o > $o).
% 206.94/30.98 thf(func_def_1639, type, sP1328: $i > $o).
% 206.94/30.98 thf(func_def_1640, type, sP1329: $o > $o).
% 206.94/30.98 thf(func_def_1641, type, sP1330: $o > $o).
% 206.94/30.98 thf(func_def_1642, type, sP1331: $o > $o).
% 206.94/30.98 thf(func_def_1643, type, sP1332: $o > $o).
% 206.94/30.98 thf(func_def_1644, type, sP1333: $o > $o).
% 206.94/30.98 thf(func_def_1645, type, sP1334: $o > $o).
% 206.94/30.98 thf(func_def_1646, type, sP1335: $o > $o).
% 206.94/30.98 thf(func_def_1647, type, sP1336: $o > $o).
% 206.94/30.98 thf(func_def_1648, type, sP1337: $o > $o).
% 206.94/30.98 thf(func_def_1649, type, sP1338: $o > $o).
% 206.94/30.98 thf(func_def_1650, type, sP1339: $o > $o).
% 206.94/30.98 thf(func_def_1651, type, sP1340: $i > $o).
% 206.94/30.98 thf(func_def_1652, type, sP1341: $o > $o).
% 206.94/30.98 thf(func_def_1653, type, sP1342: $o > $o).
% 206.94/30.98 thf(func_def_1654, type, sP1343: $i > $o).
% 206.94/30.98 thf(func_def_1655, type, sP1344: $o > $o).
% 206.94/30.98 thf(func_def_1656, type, sP1345: $o > $o).
% 206.94/30.98 thf(func_def_1657, type, sP1346: $o > $o).
% 206.94/30.98 thf(func_def_1658, type, sP1347: $o > $o).
% 206.94/30.98 thf(func_def_1659, type, sP1348: $o > $o).
% 206.94/30.98 thf(func_def_1660, type, sP1349: $o > $o).
% 206.94/30.98 thf(func_def_1661, type, sP1350: $o > $o).
% 206.94/30.98 thf(func_def_1662, type, sP1351: $o > $o).
% 206.94/30.98 thf(func_def_1663, type, sP1352: $o > $o).
% 206.94/30.98 thf(func_def_1664, type, sP1353: $o > $o).
% 206.94/30.98 thf(func_def_1665, type, sP1354: $o > $o).
% 206.94/30.98 thf(func_def_1666, type, sP1355: $o > $o).
% 206.94/30.98 thf(func_def_1667, type, sP1356: $o > $o).
% 206.94/30.98 thf(func_def_1668, type, sP1357: $o > $o).
% 206.94/30.98 thf(func_def_1669, type, sP1358: $o > $o).
% 206.94/30.98 thf(func_def_1670, type, sP1359: $o > $o).
% 206.94/30.98 thf(func_def_1671, type, sP1360: $i > $o).
% 206.94/30.98 thf(func_def_1672, type, sP1361: $o > $o).
% 206.94/30.98 thf(func_def_1673, type, sP1362: $o > $o).
% 206.94/30.98 thf(func_def_1674, type, sP1363: $o > $o).
% 206.94/30.98 thf(func_def_1675, type, sP1364: $o > $o).
% 206.94/30.98 thf(func_def_1676, type, sP1365: $o > $o).
% 206.94/30.98 thf(func_def_1677, type, sP1366: $o > $o).
% 206.94/30.98 thf(func_def_1678, type, sP1367: $o > $o).
% 206.94/30.98 thf(func_def_1679, type, sP1368: $o > $o).
% 206.94/30.98 thf(func_def_1680, type, sP1369: $o > $o).
% 206.94/30.98 thf(func_def_1681, type, sP1370: $o > $o).
% 206.94/30.98 thf(func_def_1682, type, sP1371: $o > $o).
% 206.94/30.98 thf(func_def_1683, type, sP1372: $o > $o).
% 206.94/30.98 thf(func_def_1684, type, sP1373: $o > $o).
% 206.94/30.98 thf(func_def_1685, type, sP1374: $o > $o).
% 206.94/30.98 thf(func_def_1686, type, sP1375: $i > $o).
% 206.94/30.98 thf(func_def_1687, type, sP1376: $o > $o).
% 206.94/30.98 thf(func_def_1688, type, sP1377: $o > $o).
% 206.94/30.98 thf(func_def_1689, type, sP1378: $o > $o).
% 206.94/30.98 thf(func_def_1690, type, sP1379: $o > $o).
% 206.94/30.98 thf(func_def_1691, type, sP1380: $o > $o).
% 206.94/30.98 thf(func_def_1692, type, sP1381: $o > $o).
% 206.94/30.98 thf(func_def_1693, type, sP1382: $o > $o).
% 206.94/30.98 thf(func_def_1694, type, sP1383: $o > $o).
% 206.94/30.98 thf(func_def_1695, type, sP1384: $o > $o).
% 206.94/30.98 thf(func_def_1696, type, sP1385: $o > $o).
% 206.94/30.98 thf(func_def_1697, type, sP1386: $o > $o).
% 206.94/30.98 thf(func_def_1698, type, sP1387: $o > $o).
% 206.94/30.98 thf(func_def_1699, type, sP1388: $o > $o).
% 206.94/30.98 thf(func_def_1700, type, sP1389: $o > $o).
% 206.94/30.98 thf(func_def_1701, type, sP1390: $o > $o).
% 206.94/30.98 thf(func_def_1702, type, sP1391: $o > $o).
% 206.94/30.98 thf(func_def_1703, type, sP1392: $o > $o).
% 206.94/30.98 thf(func_def_1704, type, sP1393: $o > $o).
% 206.94/30.98 thf(func_def_1705, type, sP1394: $o > $o).
% 206.94/30.98 thf(func_def_1706, type, sP1395: $o > $o).
% 206.94/30.98 thf(func_def_1707, type, sP1396: $o > $o).
% 206.94/30.98 thf(func_def_1708, type, sP1397: $o > $o).
% 206.94/30.98 thf(func_def_1709, type, sP1398: $o > $o).
% 206.94/30.98 thf(func_def_1710, type, sP1399: $o > $o).
% 206.94/30.98 thf(func_def_1711, type, sP1400: $o > $o).
% 206.94/30.98 thf(func_def_1712, type, sP1401: $o > $o).
% 206.94/30.98 thf(func_def_1713, type, sP1402: $o > $o).
% 206.94/30.98 thf(func_def_1714, type, sP1403: $o > $o).
% 206.94/30.98 thf(func_def_1715, type, sP1404: $o > $o).
% 206.94/30.98 thf(func_def_1716, type, sP1405: $o > $o).
% 206.94/30.98 thf(func_def_1717, type, sP1406: $o > $o).
% 206.94/30.98 thf(func_def_1718, type, sP1407: $o > $o).
% 206.94/30.98 thf(func_def_1719, type, sP1408: $o > $o).
% 206.94/30.98 thf(func_def_1720, type, sP1409: $o > $o).
% 206.94/30.98 thf(func_def_1721, type, sP1410: $o > $o).
% 206.94/30.98 thf(func_def_1722, type, sP1411: $o > $o).
% 206.94/30.98 thf(func_def_1723, type, sP1412: $o > $o).
% 206.94/30.98 thf(func_def_1724, type, sP1413: $o > $o).
% 206.94/30.98 thf(func_def_1725, type, sP1414: $o > $o).
% 206.94/30.98 thf(func_def_1726, type, sP1415: $o > $o).
% 206.94/30.98 thf(func_def_1727, type, sP1416: $o > $o).
% 206.94/30.98 thf(func_def_1728, type, sP1417: $o > $o).
% 206.94/30.98 thf(func_def_1729, type, sP1418: $o > $o).
% 206.94/30.98 thf(func_def_1730, type, sP1419: $o > $o).
% 206.94/30.98 thf(func_def_1731, type, sP1420: $o > $o).
% 206.94/30.98 thf(func_def_1732, type, sP1421: $o > $o).
% 206.94/30.98 thf(func_def_1733, type, sP1422: $o > $o).
% 206.94/30.98 thf(func_def_1734, type, sP1423: $o > $o).
% 206.94/30.98 thf(func_def_1735, type, sP1424: $o > $o).
% 206.94/30.98 thf(func_def_1736, type, sP1425: $o > $o).
% 206.94/30.98 thf(func_def_1737, type, sP1426: $o > $o).
% 206.94/30.98 thf(func_def_1738, type, sP1427: $o > $o).
% 206.94/30.98 thf(func_def_1739, type, sP1428: $o > $o).
% 206.94/30.98 thf(func_def_1740, type, sP1429: $o > $o).
% 206.94/30.98 thf(func_def_1741, type, sP1430: $o > $o).
% 206.94/30.98 thf(func_def_1742, type, sP1431: $o > $o).
% 206.94/30.98 thf(func_def_1743, type, sP1432: $o > $o).
% 206.94/30.98 thf(func_def_1744, type, sP1433: $o > $o).
% 206.94/30.98 thf(func_def_1745, type, sP1434: $o > $o).
% 206.94/30.98 thf(func_def_1746, type, sP1435: $o > $o).
% 206.94/30.98 thf(func_def_1747, type, sP1436: $o > $o).
% 206.94/30.98 thf(func_def_1748, type, sP1437: $o > $o).
% 206.94/30.98 thf(func_def_1749, type, sP1438: $o > $o).
% 206.94/30.98 thf(func_def_1750, type, sP1439: $o > $o).
% 206.94/30.98 thf(func_def_1751, type, sP1440: $o > $o).
% 206.94/30.98 thf(func_def_1752, type, sP1441: $o > $o).
% 206.94/30.98 thf(func_def_1753, type, sP1442: $o > $o).
% 206.94/30.98 thf(func_def_1754, type, sP1443: $o > $o).
% 206.94/30.98 thf(func_def_1755, type, sP1444: $o > $o).
% 206.94/30.98 thf(func_def_1756, type, sP1445: $o > $o).
% 206.94/30.98 thf(func_def_1757, type, sP1446: $o > $o).
% 206.94/30.98 thf(func_def_1758, type, sP1447: $o > $o).
% 206.94/30.98 thf(func_def_1759, type, sP1448: $o > $o).
% 206.94/30.98 thf(func_def_1760, type, sP1449: $o > $o).
% 206.94/30.98 thf(func_def_1761, type, sP1450: $o > $o).
% 206.94/30.98 thf(func_def_1762, type, sP1451: $o > $o).
% 206.94/30.98 thf(func_def_1763, type, sP1452: $o > $o).
% 206.94/30.98 thf(func_def_1764, type, sP1453: $o > $o).
% 206.94/30.98 thf(func_def_1765, type, sP1454: $o > $o).
% 206.94/30.98 thf(func_def_1766, type, sP1455: $o > $o).
% 206.94/30.98 thf(func_def_1767, type, sP1456: $o > $o).
% 206.94/30.98 thf(func_def_1768, type, sP1457: $o > $o).
% 206.94/30.98 thf(func_def_1769, type, sP1458: $o > $o).
% 206.94/30.98 thf(func_def_1770, type, sP1459: $o > $o).
% 206.94/30.98 thf(func_def_1771, type, sP1460: $o > $o).
% 206.94/30.98 thf(func_def_1772, type, sP1461: $o > $o).
% 206.94/30.98 thf(func_def_1773, type, sP1462: $o > $o).
% 206.94/30.98 thf(func_def_1774, type, sP1463: $o > $o).
% 206.94/30.98 thf(func_def_1775, type, sP1464: $o > $o).
% 206.94/30.98 thf(func_def_1776, type, sP1465: $o > $o).
% 206.94/30.98 thf(func_def_1777, type, sP1466: $i > $o).
% 206.94/30.98 thf(func_def_1778, type, sP1467: $i > $o).
% 206.94/30.98 thf(func_def_1779, type, sP1468: $o > $o).
% 206.94/30.98 thf(func_def_1780, type, sP1469: $o > $o).
% 206.94/30.98 thf(func_def_1781, type, sP1470: $o > $o).
% 206.94/30.98 thf(func_def_1782, type, sP1471: $o > $o).
% 206.94/30.98 thf(func_def_1783, type, sP1472: $o > $o).
% 206.94/30.98 thf(func_def_1784, type, sP1473: $o > $o).
% 206.94/30.98 thf(func_def_1785, type, sP1474: $o > $o).
% 206.94/30.98 thf(func_def_1786, type, sP1475: $o > $o).
% 206.94/30.98 thf(func_def_1787, type, sP1476: $o > $o).
% 206.94/30.98 thf(func_def_1788, type, sP1477: $o > $o).
% 206.94/30.98 thf(func_def_1789, type, sP1478: $o > $o).
% 206.94/30.98 thf(func_def_1790, type, sP1479: $o > $o).
% 206.94/30.98 thf(func_def_1791, type, sP1480: $o > $o).
% 206.94/30.98 thf(func_def_1792, type, sP1481: $o > $o).
% 206.94/30.98 thf(func_def_1793, type, sP1482: $o > $o).
% 206.94/30.98 thf(func_def_1794, type, sP1483: $o > $o).
% 206.94/30.98 thf(func_def_1795, type, sP1484: $i > $o).
% 206.94/30.98 thf(func_def_1796, type, sP1485: $o > $o).
% 206.94/30.98 thf(func_def_1797, type, sP1486: $o > $o).
% 206.94/30.98 thf(func_def_1798, type, sP1487: $o > $o).
% 206.94/30.98 thf(func_def_1799, type, sP1488: $o > $o).
% 206.94/30.98 thf(func_def_1800, type, sP1489: $o > $o).
% 206.94/30.98 thf(func_def_1801, type, sP1490: $o > $o).
% 206.94/30.98 thf(func_def_1802, type, sP1491: $o > $o).
% 206.94/30.98 thf(func_def_1803, type, sP1492: $i > $o).
% 206.94/30.98 thf(func_def_1804, type, sP1493: $o > $o).
% 206.94/30.98 thf(func_def_1805, type, sP1494: $o > $o).
% 206.94/30.98 thf(func_def_1806, type, sP1495: $o > $o).
% 206.94/30.98 thf(func_def_1807, type, sP1496: $o > $o).
% 206.94/30.98 thf(func_def_1808, type, sP1497: $o > $o).
% 206.94/30.98 thf(func_def_1809, type, sP1498: $o > $o).
% 206.94/30.98 thf(func_def_1810, type, sP1499: $o > $o).
% 206.94/30.98 thf(func_def_1811, type, sP1500: $o > $o).
% 206.94/30.98 thf(func_def_1812, type, sP1501: $o > $o).
% 206.94/30.98 thf(func_def_1813, type, sP1502: $o > $o).
% 206.94/30.98 thf(func_def_1814, type, sP1503: $o > $o).
% 206.94/30.98 thf(func_def_1815, type, sP1504: $o > $o).
% 206.94/30.98 thf(func_def_1816, type, sP1505: $o > $o).
% 206.94/30.98 thf(func_def_1817, type, sP1506: $i > $o).
% 206.94/30.98 thf(func_def_1818, type, sP1507: $o > $o).
% 206.94/30.98 thf(func_def_1819, type, sP1508: $o > $o).
% 206.94/30.98 thf(func_def_1820, type, sP1509: $o > $o).
% 206.94/30.98 thf(func_def_1821, type, sP1510: $o > $o).
% 206.94/30.98 thf(func_def_1822, type, sP1511: $o > $o).
% 206.94/30.98 thf(func_def_1823, type, sP1512: $o > $o).
% 206.94/30.98 thf(func_def_1824, type, sP1513: $o > $o).
% 206.94/30.98 thf(func_def_1825, type, sP1514: $o > $o).
% 206.94/30.98 thf(func_def_1826, type, sP1515: $o > $o).
% 206.94/30.98 thf(func_def_1827, type, sP1516: $o > $o).
% 206.94/30.98 thf(func_def_1828, type, sP1517: $o > $o).
% 206.94/30.98 thf(func_def_1829, type, sP1518: $o > $o).
% 206.94/30.98 thf(func_def_1830, type, sP1519: $o > $o).
% 206.94/30.98 thf(func_def_1831, type, sP1520: $o > $o).
% 206.94/30.98 thf(func_def_1832, type, sP1521: $o > $o).
% 206.94/30.98 thf(func_def_1833, type, sP1522: $o > $o).
% 206.94/30.98 thf(func_def_1834, type, sP1523: $o > $o).
% 206.94/30.98 thf(func_def_1835, type, sP1524: $o > $o).
% 206.94/30.98 thf(func_def_1836, type, sP1525: $o > $o).
% 206.94/30.98 thf(func_def_1837, type, sP1526: $o > $o).
% 206.94/30.98 thf(func_def_1838, type, sP1527: $o > $o).
% 206.94/30.98 thf(func_def_1839, type, sP1528: $o > $o).
% 206.94/30.98 thf(func_def_1840, type, sP1529: $o > $o).
% 206.94/30.98 thf(func_def_1841, type, sP1530: $o > $o).
% 206.94/30.98 thf(func_def_1842, type, sP1531: $o > $o).
% 206.94/30.98 thf(func_def_1843, type, sP1532: $o > $o).
% 206.94/30.98 thf(func_def_1844, type, sP1533: $o > $o).
% 206.94/30.98 thf(func_def_1845, type, sP1534: $o > $o).
% 206.94/30.98 thf(func_def_1846, type, sP1535: $i > $o).
% 206.94/30.98 thf(func_def_1847, type, sP1536: $o > $o).
% 206.94/30.98 thf(func_def_1848, type, sP1537: $o > $o).
% 206.94/30.98 thf(func_def_1849, type, sP1538: $o > $o).
% 206.94/30.98 thf(func_def_1850, type, sP1539: $o > $o).
% 206.94/30.98 thf(func_def_1851, type, sP1540: $o > $o).
% 206.94/30.98 thf(func_def_1852, type, sP1541: $o > $o).
% 206.94/30.98 thf(func_def_1853, type, sP1542: $o > $o).
% 206.94/30.98 thf(func_def_1854, type, sP1543: $o > $o).
% 206.94/30.98 thf(func_def_1855, type, sP1544: $o > $o).
% 206.94/30.98 thf(func_def_1856, type, sP1545: $o > $o).
% 206.94/30.98 thf(func_def_1857, type, sP1546: $o > $o).
% 206.94/30.98 thf(func_def_1858, type, sP1547: $o > $o).
% 206.94/30.98 thf(func_def_1859, type, sP1548: $o > $o).
% 206.94/30.98 thf(func_def_1860, type, sP1549: $o > $o).
% 206.94/30.98 thf(func_def_1861, type, sP1550: $o > $o).
% 206.94/30.98 thf(func_def_1862, type, sP1551: $o > $o).
% 206.94/30.98 thf(func_def_1863, type, sP1552: $o > $o).
% 206.94/30.98 thf(func_def_1864, type, sP1553: $o > $o).
% 206.94/30.98 thf(func_def_1865, type, sP1554: $o > $o).
% 206.94/30.98 thf(func_def_1866, type, sP1555: $o > $o).
% 206.94/30.98 thf(func_def_1867, type, sP1556: $o > $o).
% 206.94/30.98 thf(func_def_1868, type, sP1557: $o > $o).
% 206.94/30.98 thf(func_def_1869, type, sP1558: $o > $o).
% 206.94/30.98 thf(func_def_1870, type, sP1559: $o > $o).
% 206.94/30.98 thf(func_def_1871, type, sP1560: $o > $o).
% 206.94/30.98 thf(func_def_1872, type, sP1561: $i > $o).
% 206.94/30.98 thf(func_def_1873, type, sP1562: $o > $o).
% 206.94/30.98 thf(func_def_1874, type, sP1563: $o > $o).
% 206.94/30.98 thf(func_def_1875, type, sP1564: $o > $o).
% 206.94/30.98 thf(func_def_1876, type, sP1565: $o > $o).
% 206.94/30.98 thf(func_def_1877, type, sP1566: $o > $o).
% 206.94/30.98 thf(func_def_1878, type, sP1567: $o > $o).
% 206.94/30.98 thf(func_def_1879, type, sP1568: $o > $o).
% 206.94/30.98 thf(func_def_1880, type, sP1569: $o > $o).
% 206.94/30.98 thf(func_def_1881, type, sP1570: $o > $o).
% 206.94/30.98 thf(func_def_1882, type, sP1571: $o > $o).
% 206.94/30.98 thf(func_def_1883, type, sP1572: $o > $o).
% 206.94/30.98 thf(func_def_1884, type, sP1573: $o > $o).
% 206.94/30.98 thf(func_def_1885, type, sP1574: $o > $o).
% 206.94/30.98 thf(func_def_1886, type, sP1575: $o > $o).
% 206.94/30.98 thf(func_def_1887, type, sP1576: $o > $o).
% 206.94/30.98 thf(func_def_1888, type, sP1577: $o > $o).
% 206.94/30.98 thf(func_def_1889, type, sP1578: $o > $o).
% 206.94/30.98 thf(func_def_1890, type, sP1579: $i > $o).
% 206.94/30.98 thf(func_def_1891, type, sP1580: $o > $o).
% 206.94/30.98 thf(func_def_1892, type, sP1581: $o > $o).
% 206.94/30.98 thf(func_def_1893, type, sP1582: $o > $o).
% 206.94/30.98 thf(func_def_1894, type, sP1583: $o > $o).
% 206.94/30.98 thf(func_def_1895, type, sP1584: $o > $o).
% 206.94/30.98 thf(func_def_1896, type, sP1585: $o > $o).
% 206.94/30.98 thf(func_def_1897, type, sP1586: $o > $o).
% 206.94/30.98 thf(func_def_1898, type, sP1587: $o > $o).
% 206.94/30.98 thf(func_def_1899, type, sP1588: $o > $o).
% 206.94/30.98 thf(func_def_1900, type, sP1589: $o > $o).
% 206.94/30.98 thf(func_def_1901, type, sP1590: $o > $o).
% 206.94/30.98 thf(func_def_1902, type, sP1591: $o > $o).
% 206.94/30.98 thf(func_def_1903, type, sP1592: $o > $o).
% 206.94/30.98 thf(func_def_1904, type, sP1593: $i > $o).
% 206.94/30.98 thf(func_def_1905, type, sP1594: $o > $o).
% 206.94/30.98 thf(func_def_1906, type, sP1595: $o > $o).
% 206.94/30.98 thf(func_def_1907, type, sP1596: $o > $o).
% 206.94/30.98 thf(func_def_1908, type, sP1597: $i > $o).
% 206.94/30.98 thf(func_def_1909, type, sP1598: $o > $o).
% 206.94/30.98 thf(func_def_1910, type, sP1599: $o > $o).
% 206.94/30.98 thf(func_def_1911, type, sP1600: $o > $o).
% 206.94/30.98 thf(func_def_1912, type, sP1601: $o > $o).
% 206.94/30.98 thf(func_def_1913, type, sP1602: $o > $o).
% 206.94/30.98 thf(func_def_1914, type, sP1603: $o > $o).
% 206.94/30.98 thf(func_def_1915, type, sP1604: $o > $o).
% 206.94/30.98 thf(func_def_1916, type, sP1605: $o > $o).
% 206.94/30.98 thf(func_def_1917, type, sP1606: $o > $o).
% 206.94/30.98 thf(func_def_1918, type, sP1607: $o > $o).
% 206.94/30.98 thf(func_def_1919, type, sP1608: $o > $o).
% 206.94/30.98 thf(func_def_1920, type, sP1609: $o > $o).
% 206.94/30.98 thf(func_def_1921, type, sP1610: $o > $o).
% 206.94/30.98 thf(func_def_1922, type, sP1611: $o > $o).
% 206.94/30.98 thf(func_def_1923, type, sP1612: $o > $o).
% 206.94/30.98 thf(func_def_1924, type, sP1613: $o > $o).
% 206.94/30.98 thf(func_def_1925, type, sP1614: $o > $o).
% 206.94/30.98 thf(func_def_1926, type, sP1615: $o > $o).
% 206.94/30.98 thf(func_def_1927, type, sP1616: $o > $o).
% 206.94/30.98 thf(func_def_1928, type, sP1617: $o > $o).
% 206.94/30.98 thf(func_def_1929, type, sP1618: $o > $o).
% 206.94/30.98 thf(func_def_1930, type, sP1619: $o > $o).
% 206.94/30.98 thf(func_def_1931, type, sP1620: $o > $o).
% 206.94/30.98 thf(func_def_1932, type, sP1621: $o > $o).
% 206.94/30.98 thf(func_def_1933, type, sP1622: $o > $o).
% 206.94/30.98 thf(func_def_1934, type, sP1623: $o > $o).
% 206.94/30.98 thf(func_def_1935, type, sP1624: $o > $o).
% 206.94/30.98 thf(func_def_1936, type, sP1625: $o > $o).
% 206.94/30.98 thf(func_def_1937, type, sP1626: $i > $o).
% 206.94/30.98 thf(func_def_1938, type, sP1627: $o > $o).
% 206.94/30.98 thf(func_def_1939, type, sP1628: $o > $o).
% 206.94/30.98 thf(func_def_1940, type, sP1629: $o > $o).
% 206.94/30.98 thf(func_def_1941, type, sP1630: $o > $o).
% 206.94/30.98 thf(func_def_1942, type, sP1631: $o > $o).
% 206.94/30.98 thf(func_def_1943, type, sP1632: $o > $o).
% 206.94/30.98 thf(func_def_1944, type, sP1633: $i > $o).
% 206.94/30.98 thf(func_def_1945, type, sP1634: $i > $o).
% 206.94/30.98 thf(func_def_1946, type, sP1635: $o > $o).
% 206.94/30.98 thf(func_def_1947, type, sP1636: $o > $o).
% 206.94/30.98 thf(func_def_1948, type, sP1637: $o > $o).
% 206.94/30.98 thf(func_def_1949, type, sP1638: $o > $o).
% 206.94/30.98 thf(func_def_1950, type, sP1639: $o > $o).
% 206.94/30.98 thf(func_def_1951, type, sP1640: $o > $o).
% 206.94/30.98 thf(func_def_1952, type, sP1641: $o > $o).
% 206.94/30.98 thf(func_def_1953, type, sP1642: $o > $o).
% 206.94/30.98 thf(func_def_1954, type, sP1643: $o > $o).
% 206.94/30.98 thf(func_def_1955, type, sP1644: $o > $o).
% 206.94/30.98 thf(func_def_1956, type, sP1645: $o > $o).
% 206.94/30.98 thf(func_def_1957, type, sP1646: $o > $o).
% 206.94/30.98 thf(func_def_1958, type, sP1647: $o > $o).
% 206.94/30.98 thf(func_def_1959, type, sP1648: $o > $o).
% 206.94/30.98 thf(func_def_1960, type, sP1649: $o > $o).
% 206.94/30.98 thf(func_def_1961, type, sP1650: $o > $o).
% 206.94/30.98 thf(func_def_1962, type, sP1651: $o > $o).
% 206.94/30.98 thf(func_def_1963, type, sP1652: $o > $o).
% 206.94/30.98 thf(func_def_1964, type, sP1653: $o > $o).
% 206.94/30.98 thf(func_def_1965, type, sP1654: $o > $o).
% 206.94/30.98 thf(func_def_1966, type, sP1655: $o > $o).
% 206.94/30.98 thf(func_def_1967, type, sP1656: $o > $o).
% 206.94/30.98 thf(func_def_1968, type, sP1657: $o > $o).
% 206.94/30.98 thf(func_def_1969, type, sP1658: $o > $o).
% 206.94/30.98 thf(func_def_1970, type, sP1659: $o > $o).
% 206.94/30.98 thf(func_def_1971, type, sP1660: $o > $o).
% 206.94/30.98 thf(func_def_1972, type, sP1661: $o > $o).
% 206.94/30.98 thf(func_def_1973, type, sP1662: $o > $o).
% 206.94/30.98 thf(func_def_1974, type, sP1663: $o > $o).
% 206.94/30.98 thf(func_def_1975, type, sP1664: $o > $o).
% 206.94/30.98 thf(func_def_1976, type, sP1665: $o > $o).
% 206.94/30.98 thf(func_def_1977, type, sP1666: $o > $o).
% 206.94/30.98 thf(func_def_1978, type, sP1667: $o > $o).
% 206.94/30.98 thf(func_def_1979, type, sP1668: $o > $o).
% 206.94/30.98 thf(func_def_1980, type, sP1669: $o > $o).
% 206.94/30.98 thf(func_def_1981, type, sP1670: $o > $o).
% 206.94/30.98 thf(func_def_1982, type, sP1671: $o > $o).
% 206.94/30.98 thf(func_def_1983, type, sP1672: $o > $o).
% 206.94/30.98 thf(func_def_1984, type, sP1673: $o > $o).
% 206.94/30.98 thf(func_def_1985, type, sP1674: $o > $o).
% 206.94/30.98 thf(func_def_1986, type, sP1675: $o > $o).
% 206.94/30.98 thf(func_def_1987, type, sP1676: $o > $o).
% 206.94/30.98 thf(func_def_1988, type, sP1677: $o > $o).
% 206.94/30.98 thf(func_def_1989, type, sP1678: $o > $o).
% 206.94/30.98 thf(func_def_1990, type, sP1679: $o > $o).
% 206.94/30.98 thf(func_def_1991, type, sP1680: $o > $o).
% 206.94/30.98 thf(func_def_1992, type, sP1681: $o > $o).
% 206.94/30.98 thf(func_def_1993, type, sP1682: $o > $o).
% 206.94/30.98 thf(func_def_1994, type, sP1683: $o > $o).
% 206.94/30.98 thf(func_def_1995, type, sP1684: $o > $o).
% 206.94/30.98 thf(func_def_1996, type, sP1685: $o > $o).
% 206.94/30.98 thf(func_def_1997, type, sP1686: $o > $o).
% 206.94/30.98 thf(func_def_1998, type, sP1687: $o > $o).
% 206.94/30.98 thf(func_def_1999, type, sP1688: $o > $o).
% 206.94/30.98 thf(func_def_2000, type, sP1689: $o > $o).
% 206.94/30.98 thf(func_def_2001, type, sP1690: $o > $o).
% 206.94/30.98 thf(func_def_2002, type, sP1691: $o > $o).
% 206.94/30.98 thf(func_def_2003, type, sP1692: $o > $o).
% 206.94/30.98 thf(func_def_2004, type, sP1693: $o > $o).
% 206.94/30.98 thf(func_def_2005, type, sP1694: $o > $o).
% 206.94/30.98 thf(func_def_2006, type, sP1695: $o > $o).
% 206.94/30.98 thf(func_def_2007, type, sP1696: $o > $o).
% 206.94/30.98 thf(func_def_2008, type, sP1697: $o > $o).
% 206.94/30.98 thf(func_def_2009, type, sP1698: $o > $o).
% 206.94/30.98 thf(func_def_2010, type, sP1699: $o > $o).
% 206.94/30.98 thf(func_def_2011, type, sP1700: $o > $o).
% 206.94/30.98 thf(func_def_2012, type, sP1701: $o > $o).
% 206.94/30.98 thf(func_def_2013, type, sP1702: $o > $o).
% 206.94/30.98 thf(func_def_2014, type, sP1703: $o > $o).
% 206.94/30.98 thf(func_def_2015, type, sP1704: $o > $o).
% 206.94/30.98 thf(func_def_2016, type, sP1705: $o > $o).
% 206.94/30.98 thf(func_def_2017, type, sP1706: $o > $o).
% 206.94/30.98 thf(func_def_2018, type, sP1707: $o > $o).
% 206.94/30.98 thf(func_def_2019, type, sP1708: $o > $o).
% 206.94/30.98 thf(func_def_2020, type, sP1709: $o > $o).
% 206.94/30.98 thf(func_def_2021, type, sP1710: $o > $o).
% 206.94/30.98 thf(func_def_2022, type, sP1711: $i > $o).
% 206.94/30.98 thf(func_def_2023, type, sP1712: $o > $o).
% 206.94/30.98 thf(func_def_2024, type, sP1713: $o > $o).
% 206.94/30.98 thf(func_def_2025, type, sP1714: $o > $o).
% 206.94/30.98 thf(func_def_2026, type, sP1715: $o > $o).
% 206.94/30.98 thf(func_def_2027, type, sP1716: $o > $o).
% 206.94/30.98 thf(func_def_2028, type, sP1717: $o > $o).
% 206.94/30.98 thf(func_def_2029, type, sP1718: $o > $o).
% 206.94/30.98 thf(func_def_2030, type, sP1719: $o > $o).
% 206.94/30.98 thf(func_def_2031, type, sP1720: $o > $o).
% 206.94/30.98 thf(func_def_2032, type, sP1721: $o > $o).
% 206.94/30.98 thf(func_def_2033, type, sP1722: $o > $o).
% 206.94/30.98 thf(func_def_2034, type, sP1723: $o > $o).
% 206.94/30.98 thf(func_def_2035, type, sP1724: $o > $o).
% 206.94/30.98 thf(func_def_2036, type, sP1725: $o > $o).
% 206.94/30.98 thf(func_def_2037, type, sP1726: $o > $o).
% 206.94/30.98 thf(func_def_2038, type, sP1727: $o > $o).
% 206.94/30.98 thf(func_def_2039, type, sP1728: $o > $o).
% 206.94/30.98 thf(func_def_2040, type, sP1729: $o > $o).
% 206.94/30.98 thf(func_def_2041, type, sP1730: $o > $o).
% 206.94/30.98 thf(func_def_2042, type, sP1731: $o > $o).
% 206.94/30.98 thf(func_def_2043, type, sP1732: $o > $o).
% 206.94/30.98 thf(func_def_2044, type, sP1733: $i > $o).
% 206.94/30.98 thf(func_def_2045, type, sP1734: $o > $o).
% 206.94/30.98 thf(func_def_2046, type, sP1735: $o > $o).
% 206.94/30.98 thf(func_def_2047, type, sP1736: $o > $o).
% 206.94/30.98 thf(func_def_2048, type, sP1737: $o > $o).
% 206.94/30.98 thf(func_def_2049, type, sP1738: $o > $o).
% 206.94/30.98 thf(func_def_2050, type, sP1739: $o > $o).
% 206.94/30.98 thf(func_def_2051, type, sP1740: $o > $o).
% 206.94/30.98 thf(func_def_2052, type, sP1741: $o > $o).
% 206.94/30.98 thf(func_def_2053, type, sP1742: $i > $o).
% 206.94/30.98 thf(func_def_2054, type, sP1743: $o > $o).
% 206.94/30.98 thf(func_def_2055, type, sP1744: $o > $o).
% 206.94/30.98 thf(func_def_2056, type, sP1745: $o > $o).
% 206.94/30.98 thf(func_def_2057, type, sP1746: $o > $o).
% 206.94/30.98 thf(func_def_2058, type, sP1747: $o > $o).
% 206.94/30.98 thf(func_def_2059, type, sP1748: $o > $o).
% 206.94/30.98 thf(func_def_2060, type, sP1749: $o > $o).
% 206.94/30.98 thf(func_def_2061, type, sP1750: $o > $o).
% 206.94/30.98 thf(func_def_2062, type, sP1751: $i > $o).
% 206.94/30.98 thf(func_def_2063, type, sP1752: $o > $o).
% 206.94/30.98 thf(func_def_2064, type, sP1753: $o > $o).
% 206.94/30.98 thf(func_def_2065, type, sP1754: $o > $o).
% 206.94/30.98 thf(func_def_2066, type, sP1755: $o > $o).
% 206.94/30.98 thf(func_def_2067, type, sP1756: $o > $o).
% 206.94/30.98 thf(func_def_2068, type, sP1757: $o > $o).
% 206.94/30.98 thf(func_def_2069, type, sP1758: $o > $o).
% 206.94/30.98 thf(func_def_2070, type, sP1759: $o > $o).
% 206.94/30.98 thf(func_def_2071, type, sP1760: $o > $o).
% 206.94/30.98 thf(func_def_2072, type, sP1761: $o > $o).
% 206.94/30.98 thf(func_def_2073, type, sP1762: $o > $o).
% 206.94/30.98 thf(func_def_2074, type, sP1763: $o > $o).
% 206.94/30.98 thf(func_def_2075, type, sP1764: $o > $o).
% 206.94/30.98 thf(func_def_2076, type, sP1765: $i > $o).
% 206.94/30.98 thf(func_def_2077, type, sP1766: $i > $o).
% 206.94/30.98 thf(func_def_2078, type, sP1767: $o > $o).
% 206.94/30.98 thf(func_def_2079, type, sP1768: $o > $o).
% 206.94/30.98 thf(func_def_2080, type, sP1769: $o > $o).
% 206.94/30.98 thf(func_def_2081, type, sP1770: $o > $o).
% 206.94/30.98 thf(func_def_2082, type, sP1771: $o > $o).
% 206.94/30.98 thf(func_def_2083, type, sP1772: $o > $o).
% 206.94/30.98 thf(func_def_2084, type, sP1773: $o > $o).
% 206.94/30.98 thf(func_def_2085, type, sP1774: $o > $o).
% 206.94/30.98 thf(func_def_2086, type, sP1775: $o > $o).
% 206.94/30.98 thf(func_def_2087, type, sP1776: $o > $o).
% 206.94/30.98 thf(func_def_2088, type, sP1777: $o > $o).
% 206.94/30.98 thf(func_def_2089, type, sP1778: $o > $o).
% 206.94/30.98 thf(func_def_2090, type, sP1779: $o > $o).
% 206.94/30.98 thf(func_def_2091, type, sP1780: $i > $o).
% 206.94/30.98 thf(func_def_2092, type, sP1781: $o > $o).
% 206.94/30.98 thf(func_def_2093, type, sP1782: $o > $o).
% 206.94/30.98 thf(func_def_2094, type, sP1783: $o > $o).
% 206.94/30.98 thf(func_def_2095, type, sP1784: $i > $o).
% 206.94/30.98 thf(func_def_2096, type, sP1785: $o > $o).
% 206.94/30.98 thf(func_def_2097, type, sP1786: $o > $o).
% 206.94/30.98 thf(func_def_2098, type, sP1787: $o > $o).
% 206.94/30.98 thf(func_def_2099, type, sP1788: $o > $o).
% 206.94/30.98 thf(func_def_2100, type, sP1789: $o > $o).
% 206.94/30.98 thf(func_def_2101, type, sP1790: $o > $o).
% 206.94/30.98 thf(func_def_2102, type, sP1791: $o > $o).
% 206.94/30.98 thf(func_def_2103, type, sP1792: $o > $o).
% 206.94/30.98 thf(func_def_2104, type, sP1793: $o > $o).
% 206.94/30.98 thf(func_def_2105, type, sP1794: $o > $o).
% 206.94/30.98 thf(func_def_2106, type, sP1795: $o > $o).
% 206.94/30.98 thf(func_def_2107, type, sP1796: $o > $o).
% 206.94/30.98 thf(func_def_2108, type, sP1797: $o > $o).
% 206.94/30.98 thf(func_def_2109, type, sP1798: $o > $o).
% 206.94/30.98 thf(func_def_2110, type, sP1799: $o > $o).
% 206.94/30.98 thf(func_def_2111, type, sP1800: $i > $o).
% 206.94/30.98 thf(func_def_2112, type, sP1801: $o > $o).
% 206.94/30.98 thf(func_def_2113, type, sP1802: $o > $o).
% 206.94/30.98 thf(func_def_2114, type, sP1803: $o > $o).
% 206.94/30.98 thf(func_def_2115, type, sP1804: $o > $o).
% 206.94/30.98 thf(func_def_2116, type, sP1805: $o > $o).
% 206.94/30.98 thf(func_def_2117, type, sP1806: $i > $o).
% 206.94/30.98 thf(func_def_2118, type, sP1807: $o > $o).
% 206.94/30.98 thf(func_def_2119, type, sP1808: $o > $o).
% 206.94/30.98 thf(func_def_2120, type, sP1809: $o > $o).
% 206.94/30.98 thf(func_def_2121, type, sP1810: $o > $o).
% 206.94/30.98 thf(func_def_2122, type, sP1811: $o > $o).
% 206.94/30.98 thf(func_def_2123, type, sP1812: $i > $o).
% 206.94/30.98 thf(func_def_2124, type, sP1813: $o > $o).
% 206.94/30.98 thf(func_def_2125, type, sP1814: $o > $o).
% 206.94/30.98 thf(func_def_2126, type, sP1815: $o > $o).
% 206.94/30.98 thf(func_def_2127, type, sP1816: $o > $o).
% 206.94/30.98 thf(func_def_2128, type, sP1817: $o > $o).
% 206.94/30.98 thf(func_def_2129, type, sP1818: $o > $o).
% 206.94/30.98 thf(func_def_2130, type, sP1819: $o > $o).
% 206.94/30.98 thf(func_def_2131, type, sP1820: $i > $o).
% 206.94/30.98 thf(func_def_2132, type, sP1821: $o > $o).
% 206.94/30.98 thf(func_def_2133, type, sP1822: $o > $o).
% 206.94/30.98 thf(func_def_2134, type, sP1823: $o > $o).
% 206.94/30.98 thf(func_def_2135, type, sP1824: $i > $o).
% 206.94/30.98 thf(func_def_2136, type, sP1825: $o > $o).
% 206.94/30.98 thf(func_def_2137, type, sP1826: $o > $o).
% 206.94/30.98 thf(func_def_2138, type, sP1827: $o > $o).
% 206.94/30.98 thf(func_def_2139, type, sP1828: $o > $o).
% 206.94/30.98 thf(func_def_2140, type, sP1829: $o > $o).
% 206.94/30.98 thf(func_def_2141, type, sP1830: $o > $o).
% 206.94/30.98 thf(func_def_2142, type, sP1831: $o > $o).
% 206.94/30.98 thf(func_def_2143, type, sP1832: $o > $o).
% 206.94/30.98 thf(func_def_2144, type, sP1833: $o > $o).
% 206.94/30.98 thf(func_def_2145, type, sP1834: $o > $o).
% 206.94/30.98 thf(func_def_2146, type, sP1835: $o > $o).
% 206.94/30.98 thf(func_def_2147, type, sP1836: $o > $o).
% 206.94/30.98 thf(func_def_2148, type, sP1837: $o > $o).
% 206.94/30.98 thf(func_def_2149, type, sP1838: $o > $o).
% 206.94/30.98 thf(func_def_2150, type, sP1839: $o > $o).
% 206.94/30.98 thf(func_def_2151, type, sP1840: $o > $o).
% 206.94/30.98 thf(func_def_2152, type, sP1841: $o > $o).
% 206.94/30.98 thf(func_def_2153, type, sP1842: $o > $o).
% 206.94/30.98 thf(func_def_2154, type, sP1843: $o > $o).
% 206.94/30.98 thf(func_def_2155, type, sP1844: $o > $o).
% 206.94/30.98 thf(func_def_2156, type, sP1845: $o > $o).
% 206.94/30.98 thf(func_def_2157, type, sP1846: $o > $o).
% 206.94/30.98 thf(func_def_2158, type, sP1847: $i > $o).
% 206.94/30.98 thf(func_def_2159, type, sP1848: $o > $o).
% 206.94/30.98 thf(func_def_2160, type, sP1849: $o > $o).
% 206.94/30.98 thf(func_def_2161, type, sP1850: $i > $o).
% 206.94/30.98 thf(func_def_2162, type, sP1851: $o > $o).
% 206.94/30.98 thf(func_def_2163, type, sP1852: $o > $o).
% 206.94/30.98 thf(func_def_2164, type, sP1853: $o > $o).
% 206.94/30.98 thf(func_def_2165, type, sP1854: $o > $o).
% 206.94/30.98 thf(func_def_2166, type, sP1855: $o > $o).
% 206.94/30.98 thf(func_def_2167, type, sP1856: $o > $o).
% 206.94/30.98 thf(func_def_2168, type, sP1857: $o > $o).
% 206.94/30.98 thf(func_def_2169, type, sP1858: $o > $o).
% 206.94/30.98 thf(func_def_2170, type, sP1859: $o > $o).
% 206.94/30.98 thf(func_def_2171, type, sP1860: $o > $o).
% 206.94/30.98 thf(func_def_2172, type, sP1861: $o > $o).
% 206.94/30.98 thf(func_def_2173, type, sP1862: $o > $o).
% 206.94/30.98 thf(func_def_2174, type, sP1863: $o > $o).
% 206.94/30.98 thf(func_def_2175, type, sP1864: $o > $o).
% 206.94/30.98 thf(func_def_2176, type, sP1865: $o > $o).
% 206.94/30.98 thf(func_def_2177, type, sP1866: $o > $o).
% 206.94/30.98 thf(func_def_2178, type, sP1867: $o > $o).
% 206.94/30.98 thf(func_def_2179, type, sP1868: $o > $o).
% 206.94/30.98 thf(func_def_2180, type, sP1869: $o > $o).
% 206.94/30.98 thf(func_def_2181, type, sP1870: $o > $o).
% 206.94/30.98 thf(func_def_2182, type, sP1871: $o > $o).
% 206.94/30.98 thf(func_def_2183, type, sP1872: $o > $o).
% 206.94/30.98 thf(func_def_2184, type, sP1873: $o > $o).
% 206.94/30.98 thf(func_def_2185, type, sP1874: $o > $o).
% 206.94/30.98 thf(func_def_2186, type, sP1875: $o > $o).
% 206.94/30.98 thf(func_def_2187, type, sP1876: $o > $o).
% 206.94/30.98 thf(func_def_2188, type, sP1877: $o > $o).
% 206.94/30.98 thf(func_def_2189, type, sP1878: $o > $o).
% 206.94/30.98 thf(func_def_2190, type, sP1879: $i > $o).
% 206.94/30.98 thf(func_def_2191, type, sP1880: $o > $o).
% 206.94/30.98 thf(func_def_2192, type, sP1881: $o > $o).
% 206.94/30.98 thf(func_def_2193, type, sP1882: $o > $o).
% 206.94/30.98 thf(func_def_2194, type, sP1883: $o > $o).
% 206.94/30.98 thf(func_def_2195, type, sP1884: $o > $o).
% 206.94/30.98 thf(func_def_2196, type, sP1885: $o > $o).
% 206.94/30.98 thf(func_def_2197, type, sP1886: $o > $o).
% 206.94/30.98 thf(func_def_2198, type, sP1887: $o > $o).
% 206.94/30.98 thf(func_def_2199, type, sP1888: $o > $o).
% 206.94/30.98 thf(func_def_2200, type, sP1889: $o > $o).
% 206.94/30.98 thf(func_def_2201, type, sP1890: $o > $o).
% 206.94/30.98 thf(func_def_2202, type, sP1891: $o > $o).
% 206.94/30.98 thf(func_def_2203, type, sP1892: $o > $o).
% 206.94/30.98 thf(func_def_2204, type, sP1893: $o > $o).
% 206.94/30.98 thf(func_def_2205, type, sP1894: $o > $o).
% 206.94/30.98 thf(func_def_2206, type, sP1895: $o > $o).
% 206.94/30.98 thf(func_def_2207, type, sP1896: $o > $o).
% 206.94/30.98 thf(func_def_2208, type, sP1897: $o > $o).
% 206.94/30.98 thf(func_def_2209, type, sP1898: $o > $o).
% 206.94/30.98 thf(func_def_2210, type, sP1899: $o > $o).
% 206.94/30.98 thf(func_def_2211, type, sP1900: $o > $o).
% 206.94/30.98 thf(func_def_2212, type, sP1901: $o > $o).
% 206.94/30.98 thf(func_def_2213, type, sP1902: $o > $o).
% 206.94/30.98 thf(func_def_2214, type, sP1903: $o > $o).
% 206.94/30.98 thf(func_def_2215, type, sP1904: $o > $o).
% 206.94/30.98 thf(func_def_2216, type, sP1905: $o > $o).
% 206.94/30.98 thf(func_def_2217, type, sP1906: $o > $o).
% 206.94/30.98 thf(func_def_2218, type, sP1907: $o > $o).
% 206.94/30.98 thf(func_def_2219, type, sP1908: $o > $o).
% 206.94/30.98 thf(func_def_2220, type, sP1909: $o > $o).
% 206.94/30.98 thf(func_def_2221, type, sP1910: $o > $o).
% 206.94/30.98 thf(func_def_2222, type, sP1911: $o > $o).
% 206.94/30.98 thf(func_def_2223, type, sP1912: $o > $o).
% 206.94/30.98 thf(func_def_2224, type, sP1913: $o > $o).
% 206.94/30.98 thf(func_def_2225, type, sP1914: $o > $o).
% 206.94/30.98 thf(func_def_2226, type, sP1915: $i > $o).
% 206.94/30.98 thf(func_def_2227, type, sP1916: $o > $o).
% 206.94/30.98 thf(func_def_2228, type, sP1917: $o > $o).
% 206.94/30.98 thf(func_def_2229, type, sP1918: $o > $o).
% 206.94/30.98 thf(func_def_2230, type, sP1919: $o > $o).
% 206.94/30.98 thf(func_def_2231, type, sP1920: $o > $o).
% 206.94/30.98 thf(func_def_2232, type, sP1921: $o > $o).
% 206.94/30.98 thf(func_def_2233, type, sP1922: $o > $o).
% 206.94/30.98 thf(func_def_2234, type, sP1923: $o > $o).
% 206.94/30.98 thf(func_def_2235, type, sP1924: $o > $o).
% 206.94/30.98 thf(func_def_2236, type, sP1925: $o > $o).
% 206.94/30.98 thf(func_def_2237, type, sP1926: $o > $o).
% 206.94/30.98 thf(func_def_2238, type, sP1927: $o > $o).
% 206.94/30.98 thf(func_def_2239, type, sP1928: $o > $o).
% 206.94/30.98 thf(func_def_2240, type, sP1929: $o > $o).
% 206.94/30.98 thf(func_def_2241, type, sP1930: $o > $o).
% 206.94/30.98 thf(func_def_2242, type, sP1931: $o > $o).
% 206.94/30.98 thf(func_def_2243, type, sP1932: $o > $o).
% 206.94/30.98 thf(func_def_2244, type, sP1933: $o > $o).
% 206.94/30.98 thf(func_def_2245, type, sP1934: $o > $o).
% 206.94/30.98 thf(func_def_2246, type, sP1935: $o > $o).
% 206.94/30.98 thf(func_def_2247, type, sP1936: $o > $o).
% 206.94/30.98 thf(func_def_2248, type, sP1937: $o > $o).
% 206.94/30.98 thf(func_def_2249, type, sP1938: $o > $o).
% 206.94/30.98 thf(func_def_2250, type, sP1939: $o > $o).
% 206.94/30.98 thf(func_def_2251, type, sP1940: $o > $o).
% 206.94/30.98 thf(func_def_2252, type, sP1941: $o > $o).
% 206.94/30.98 thf(func_def_2253, type, sP1942: $o > $o).
% 206.94/30.98 thf(func_def_2254, type, sP1943: $o > $o).
% 206.94/30.98 thf(func_def_2255, type, sP1944: $o > $o).
% 206.94/30.98 thf(func_def_2256, type, sP1945: $o > $o).
% 206.94/30.98 thf(func_def_2257, type, sP1946: $o > $o).
% 206.94/30.98 thf(func_def_2258, type, sP1947: $o > $o).
% 206.94/30.98 thf(func_def_2259, type, sP1948: $o > $o).
% 206.94/30.98 thf(func_def_2260, type, sP1949: $o > $o).
% 206.94/30.98 thf(func_def_2261, type, sP1950: $o > $o).
% 206.94/30.98 thf(func_def_2262, type, sP1951: $o > $o).
% 206.94/30.98 thf(func_def_2263, type, sP1952: $o > $o).
% 206.94/30.98 thf(func_def_2264, type, sP1953: $o > $o).
% 206.94/30.98 thf(func_def_2265, type, sP1954: $o > $o).
% 206.94/30.98 thf(func_def_2266, type, sP1955: $o > $o).
% 206.94/30.98 thf(func_def_2267, type, sP1956: $o > $o).
% 206.94/30.98 thf(func_def_2268, type, sP1957: $o > $o).
% 206.94/30.98 thf(func_def_2269, type, sP1958: $o > $o).
% 206.94/30.98 thf(func_def_2270, type, sP1959: $o > $o).
% 206.94/30.98 thf(func_def_2271, type, sP1960: $o > $o).
% 206.94/30.98 thf(func_def_2272, type, sP1961: $o > $o).
% 206.94/30.98 thf(func_def_2273, type, sP1962: $o > $o).
% 206.94/30.98 thf(func_def_2274, type, sP1963: $o > $o).
% 206.94/30.98 thf(func_def_2275, type, sP1964: $o > $o).
% 206.94/30.98 thf(func_def_2276, type, sP1965: $o > $o).
% 206.94/30.98 thf(func_def_2277, type, sP1966: $o > $o).
% 206.94/30.98 thf(func_def_2278, type, sP1967: $o > $o).
% 206.94/30.98 thf(func_def_2279, type, sP1968: $i > $o).
% 206.94/30.98 thf(func_def_2280, type, sP1969: $o > $o).
% 206.94/30.98 thf(func_def_2281, type, sP1970: $o > $o).
% 206.94/30.98 thf(func_def_2282, type, sP1971: $o > $o).
% 206.94/30.98 thf(func_def_2283, type, sP1972: $o > $o).
% 206.94/30.98 thf(func_def_2284, type, sP1973: $o > $o).
% 206.94/30.98 thf(func_def_2285, type, sP1974: $o > $o).
% 206.94/30.98 thf(func_def_2286, type, sP1975: $i > $o).
% 206.94/30.98 thf(func_def_2287, type, sP1976: $o > $o).
% 206.94/30.98 thf(func_def_2288, type, sP1977: $o > $o).
% 206.94/30.98 thf(func_def_2289, type, sP1978: $o > $o).
% 206.94/30.98 thf(func_def_2290, type, sP1979: $o > $o).
% 206.94/30.98 thf(func_def_2291, type, sP1980: $o > $o).
% 206.94/30.98 thf(func_def_2292, type, sP1981: $o > $o).
% 206.94/30.98 thf(func_def_2293, type, sP1982: $o > $o).
% 206.94/30.98 thf(func_def_2294, type, sP1983: $o > $o).
% 206.94/30.98 thf(func_def_2295, type, sP1984: $o > $o).
% 206.94/30.98 thf(func_def_2296, type, sP1985: $o > $o).
% 206.94/30.98 thf(func_def_2297, type, sP1986: $i > $o).
% 206.94/30.98 thf(func_def_2298, type, sP1987: $i > $o).
% 206.94/30.98 thf(func_def_2299, type, sP1988: $o > $o).
% 206.94/30.98 thf(func_def_2300, type, sP1989: $o > $o).
% 206.94/30.98 thf(func_def_2301, type, sP1990: $o > $o).
% 206.94/30.98 thf(func_def_2302, type, sP1991: $o > $o).
% 206.94/30.98 thf(func_def_2303, type, sP1992: $i > $o).
% 206.94/30.98 thf(func_def_2304, type, sP1993: $o > $o).
% 206.94/30.98 thf(func_def_2305, type, sP1994: $o > $o).
% 206.94/30.98 thf(func_def_2306, type, sP1995: $i > $o).
% 206.94/30.98 thf(func_def_2307, type, sP1996: $o > $o).
% 206.94/30.98 thf(func_def_2308, type, sP1997: $o > $o).
% 206.94/30.98 thf(func_def_2309, type, sP1998: $o > $o).
% 206.94/30.98 thf(func_def_2310, type, sP1999: $o > $o).
% 206.94/30.98 thf(func_def_2311, type, sP2000: $o > $o).
% 206.94/30.98 thf(func_def_2312, type, sP2001: $o > $o).
% 206.94/30.98 thf(func_def_2313, type, sP2002: $i > $o).
% 206.94/30.98 thf(func_def_2314, type, sP2003: $o > $o).
% 206.94/30.98 thf(func_def_2315, type, sP2004: $o > $o).
% 206.94/30.98 thf(func_def_2316, type, sP2005: $i > $o).
% 206.94/30.98 thf(func_def_2317, type, sP2006: $o > $o).
% 206.94/30.98 thf(func_def_2318, type, sP2007: $o > $o).
% 206.94/30.98 thf(func_def_2319, type, sP2008: $o > $o).
% 206.94/30.98 thf(func_def_2320, type, sP2009: $o > $o).
% 206.94/30.98 thf(func_def_2321, type, sP2010: $o > $o).
% 206.94/30.98 thf(func_def_2322, type, sP2011: $o > $o).
% 206.94/30.98 thf(func_def_2323, type, sP2012: $o > $o).
% 206.94/30.98 thf(func_def_2324, type, sP2013: $o > $o).
% 206.94/30.98 thf(func_def_2325, type, sP2014: $o > $o).
% 206.94/30.98 thf(func_def_2326, type, sP2015: $o > $o).
% 206.94/30.98 thf(func_def_2327, type, sP2016: $o > $o).
% 206.94/30.98 thf(func_def_2328, type, sP2017: $i > $o).
% 206.94/30.98 thf(func_def_2329, type, sP2018: $o > $o).
% 206.94/30.98 thf(func_def_2330, type, sP2019: $o > $o).
% 206.94/30.98 thf(func_def_2331, type, sP2020: $o > $o).
% 206.94/30.98 thf(func_def_2332, type, sP2021: $o > $o).
% 206.94/30.98 thf(func_def_2333, type, sP2022: $i > $o).
% 206.94/30.98 thf(func_def_2334, type, sP2023: $o > $o).
% 206.94/30.98 thf(func_def_2335, type, sP2024: $o > $o).
% 206.94/30.98 thf(func_def_2336, type, sP2025: $o > $o).
% 206.94/30.98 thf(func_def_2337, type, sP2026: $o > $o).
% 206.94/30.98 thf(func_def_2338, type, sP2027: $o > $o).
% 206.94/30.98 thf(func_def_2339, type, sP2028: $o > $o).
% 206.94/30.98 thf(func_def_2340, type, sP2029: $o > $o).
% 206.94/30.98 thf(func_def_2341, type, sP2030: $o > $o).
% 206.94/30.98 thf(func_def_2342, type, sP2031: $o > $o).
% 206.94/30.98 thf(func_def_2343, type, sP2032: $o > $o).
% 206.94/30.98 thf(func_def_2344, type, sP2033: $o > $o).
% 206.94/30.98 thf(func_def_2345, type, sP2034: $o > $o).
% 206.94/30.98 thf(func_def_2346, type, sP2035: $o > $o).
% 206.94/30.98 thf(func_def_2347, type, sP2036: $o > $o).
% 206.94/30.98 thf(func_def_2348, type, sP2037: $o > $o).
% 206.94/30.98 thf(func_def_2349, type, sP2038: $o > $o).
% 206.94/30.98 thf(func_def_2350, type, sP2039: $o > $o).
% 206.94/30.98 thf(func_def_2351, type, sP2040: $o > $o).
% 206.94/30.98 thf(func_def_2352, type, sP2041: $o > $o).
% 206.94/30.98 thf(func_def_2353, type, sP2042: $o > $o).
% 206.94/30.98 thf(func_def_2354, type, sP2043: $o > $o).
% 206.94/30.98 thf(func_def_2355, type, sP2044: $o > $o).
% 206.94/30.98 thf(func_def_2356, type, sP2045: $o > $o).
% 206.94/30.98 thf(func_def_2357, type, sP2046: $o > $o).
% 206.94/30.98 thf(func_def_2358, type, sP2047: $o > $o).
% 206.94/30.98 thf(func_def_2359, type, sP2048: $o > $o).
% 206.94/30.98 thf(func_def_2360, type, sP2049: $o > $o).
% 206.94/30.98 thf(func_def_2361, type, sP2050: $o > $o).
% 206.94/30.98 thf(func_def_2362, type, sP2051: $o > $o).
% 206.94/30.98 thf(func_def_2363, type, sP2052: $o > $o).
% 206.94/30.98 thf(func_def_2364, type, sP2053: $o > $o).
% 206.94/30.98 thf(func_def_2365, type, sP2054: $o > $o).
% 206.94/30.98 thf(func_def_2366, type, sP2055: $o > $o).
% 206.94/30.98 thf(func_def_2367, type, sP2056: $o > $o).
% 206.94/30.98 thf(func_def_2368, type, sP2057: $o > $o).
% 206.94/30.98 thf(func_def_2369, type, sP2058: $o > $o).
% 206.94/30.98 thf(func_def_2370, type, sP2059: $o > $o).
% 206.94/30.98 thf(func_def_2371, type, sP2060: $o > $o).
% 206.94/30.98 thf(func_def_2372, type, sP2061: $o > $o).
% 206.94/30.98 thf(func_def_2373, type, sP2062: $o > $o).
% 206.94/30.98 thf(func_def_2374, type, sP2063: $o > $o).
% 206.94/30.98 thf(func_def_2375, type, sP2064: $o > $o).
% 206.94/30.98 thf(func_def_2376, type, sP2065: $o > $o).
% 206.94/30.98 thf(func_def_2377, type, sP2066: $o > $o).
% 206.94/30.98 thf(func_def_2378, type, sP2067: $o > $o).
% 206.94/30.98 thf(func_def_2379, type, sP2068: $o > $o).
% 206.94/30.98 thf(func_def_2380, type, sP2069: $o > $o).
% 206.94/30.98 thf(func_def_2381, type, sP2070: $o > $o).
% 206.94/30.98 thf(func_def_2382, type, sP2071: $o > $o).
% 206.94/30.98 thf(func_def_2383, type, sP2072: $o > $o).
% 206.94/30.98 thf(func_def_2384, type, sP2073: $o > $o).
% 206.94/30.98 thf(func_def_2385, type, sP2074: $o > $o).
% 206.94/30.98 thf(func_def_2386, type, sP2075: $o > $o).
% 206.94/30.98 thf(func_def_2387, type, sP2076: $o > $o).
% 206.94/30.98 thf(func_def_2388, type, sP2077: $o > $o).
% 206.94/30.98 thf(func_def_2389, type, sP2078: $o > $o).
% 206.94/30.98 thf(func_def_2390, type, sP2079: $o > $o).
% 206.94/30.98 thf(func_def_2391, type, sP2080: $o > $o).
% 206.94/30.98 thf(func_def_2392, type, sP2081: $o > $o).
% 206.94/30.98 thf(func_def_2393, type, sP2082: $o > $o).
% 206.94/30.98 thf(func_def_2394, type, sP2083: $o > $o).
% 206.94/30.98 thf(func_def_2395, type, sP2084: $o > $o).
% 206.94/30.98 thf(func_def_2396, type, sP2085: $o > $o).
% 206.94/30.98 thf(func_def_2397, type, sP2086: $o > $o).
% 206.94/30.98 thf(func_def_2398, type, sP2087: $o > $o).
% 206.94/30.98 thf(func_def_2399, type, sP2088: $o > $o).
% 206.94/30.98 thf(func_def_2400, type, sP2089: $i > $o).
% 206.94/30.98 thf(func_def_2401, type, sP2090: $o > $o).
% 206.94/30.98 thf(func_def_2402, type, sP2091: $o > $o).
% 206.94/30.98 thf(func_def_2403, type, sP2092: $o > $o).
% 206.94/30.98 thf(func_def_2404, type, sP2093: $o > $o).
% 206.94/30.98 thf(func_def_2405, type, sP2094: $o > $o).
% 206.94/30.98 thf(func_def_2406, type, sP2095: $o > $o).
% 206.94/30.98 thf(func_def_2407, type, sP2096: $o > $o).
% 206.94/30.98 thf(func_def_2408, type, sP2097: $o > $o).
% 206.94/30.98 thf(func_def_2409, type, sP2098: $o > $o).
% 206.94/30.98 thf(func_def_2410, type, sP2099: $o > $o).
% 206.94/30.98 thf(func_def_2411, type, sP2100: $o > $o).
% 206.94/30.98 thf(func_def_2412, type, sP2101: $o > $o).
% 206.94/30.98 thf(func_def_2413, type, sP2102: $o > $o).
% 206.94/30.98 thf(func_def_2414, type, sP2103: $i > $o).
% 206.94/30.98 thf(func_def_2415, type, sP2104: $o > $o).
% 206.94/30.98 thf(func_def_2416, type, sP2105: $o > $o).
% 206.94/30.98 thf(func_def_2417, type, sP2106: $o > $o).
% 206.94/30.98 thf(func_def_2418, type, sP2107: $o > $o).
% 206.94/30.98 thf(func_def_2419, type, sP2108: $o > $o).
% 206.94/30.98 thf(func_def_2420, type, sP2109: $o > $o).
% 206.94/30.98 thf(func_def_2421, type, sP2110: $i > $o).
% 206.94/30.98 thf(func_def_2422, type, sP2111: $o > $o).
% 206.94/30.98 thf(func_def_2423, type, sP2112: $o > $o).
% 206.94/30.98 thf(func_def_2424, type, sP2113: $i > $o).
% 206.94/30.98 thf(func_def_2425, type, sP2114: $o > $o).
% 206.94/30.98 thf(func_def_2426, type, sP2115: $o > $o).
% 206.94/30.98 thf(func_def_2427, type, sP2116: $o > $o).
% 206.94/30.98 thf(func_def_2428, type, sP2117: $o > $o).
% 206.94/30.98 thf(func_def_2429, type, sP2118: $o > $o).
% 206.94/30.98 thf(func_def_2431, type, sK2120: ($i > $o) > $i).
% 206.94/30.98 thf(func_def_2432, type, sK2121: ($i > $o) > $i).
% 206.94/30.98 thf(func_def_2433, type, sK2122: ($i > $o) > $i).
% 206.94/30.98 thf(func_def_2434, type, sK2123: ($i > $o) > $i).
% 206.94/30.98 thf(func_def_2435, type, sK2124: ($i > $o) > $i).
% 206.94/30.98 thf(func_def_2436, type, sK2125: ($i > $o) > $i).
% 206.94/30.98 thf(func_def_2437, type, sK2126: ($i > $o) > $i).
% 206.94/30.98 thf(func_def_2438, type, sK2127: ($i > $o) > $i > $i).
% 206.94/30.98 thf(func_def_2439, type, sK2128: ($i > $o) > $i > $i).
% 206.94/30.98 thf(func_def_2440, type, sK2129: ($i > $o) > $i > $i).
% 206.94/30.98 thf(func_def_2441, type, sK2130: ($i > $o) > $i).
% 206.94/30.98 thf(func_def_2442, type, sK2131: ($i > $o) > $i).
% 206.94/30.98 thf(func_def_2443, type, sK2132: ($i > $o) > $i > $i).
% 206.94/30.98 thf(func_def_2444, type, sK2133: ($i > $o) > $i).
% 206.94/30.98 thf(func_def_2445, type, sK2134: $i > $i).
% 206.94/30.98 thf(func_def_2446, type, sK2135: ($i > $o) > $i).
% 206.94/30.98 thf(func_def_2447, type, sK2136: ($i > $o) > $i > $i).
% 206.94/30.98 thf(func_def_2448, type, sK2137: ($i > $o) > $i > $i).
% 206.94/30.98 thf(func_def_2449, type, sK2138: ($i > $o) > $i).
% 206.94/30.98 thf(func_def_2450, type, sK2139: ($i > $o) > $i > $i).
% 206.94/30.98 thf(func_def_2451, type, ph2140: !>[X0: $tType]:(X0)).
% 206.94/30.98 thf(f47809,plain,(
% 206.94/30.98 $false),
% 206.94/30.98 inference(avatar_sat_refutation,[status(thm)],[f7421,f8431,f9194,f9546,f47531])).
% 206.94/30.98 thf(f47531,plain,(
% 206.94/30.98 ~spl2119_70 | ~spl2119_299),
% 206.94/30.98 inference(avatar_contradiction_clause,[status(thm)],[f47530])).
% 206.94/30.98 thf(f47530,plain,(
% 206.94/30.98 $false | (~spl2119_70 | ~spl2119_299)),
% 206.94/30.98 inference(subsumption_resolution,[status(thm)],[f47529,f46109])).
% 206.94/30.98 thf(f46109,plain,(
% 206.94/30.98 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = (binintersect @ (binintersect @ X0 @ X1) @ (binunion @ X3 @ (binintersect @ X1 @ (binunion @ X0 @ X2)))))) )),
% 206.94/30.98 inference(backward_demodulation,[status(thm)],[f41202,f46085])).
% 206.94/30.98 thf(f46085,plain,(
% 206.94/30.98 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((binintersect @ X0 @ (binunion @ X2 @ X1)) = (binintersect @ X0 @ (binunion @ (binintersect @ X2 @ X0) @ X1)))) )),
% 206.94/30.98 inference(backward_demodulation,[status(thm)],[f46071,f46084])).
% 206.94/30.98 thf(f46084,plain,(
% 206.94/30.98 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((binunion @ (binintersect @ X1 @ X0) @ (binintersect @ X2 @ X0)) = (binintersect @ X0 @ (binunion @ X1 @ X2)))) )),
% 206.94/30.98 inference(forward_demodulation,[status(thm)],[f45753,f45886])).
% 206.94/30.98 thf(f45886,plain,(
% 206.94/30.98 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((binintersect @ X0 @ (binunion @ X2 @ X1)) = (binintersect @ X0 @ (binunion @ X2 @ (binintersect @ X1 @ X0))))) )),
% 206.94/30.98 inference(superposition,[status(thm)],[f31098,f41548])).
% 206.94/30.98 thf(f41548,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((binintersect @ X1 @ X0) = (binintersect @ X0 @ X1))) )),
% 206.94/30.98 inference(forward_demodulation,[status(thm)],[f41547,f29976])).
% 206.94/30.98 thf(f29976,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((binunion @ (binintersect @ X0 @ X1) @ X0) = X0)) )),
% 206.94/30.98 inference(forward_demodulation,[status(thm)],[f29947,f29004])).
% 206.94/30.98 thf(f29004,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ (binunion @ X1 @ X0)) = X0)) )),
% 206.94/30.98 inference(trivial_inequality_removal,[status(thm)],[f29003])).
% 206.94/30.98 thf(f29003,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ (binunion @ X1 @ X0)) = X0) | ($false = $true)) )),
% 206.94/30.98 inference(forward_demodulation,[status(thm)],[f28998,f5926])).
% 206.94/30.98 thf(f5926,plain,(
% 206.94/30.98 ($false = (sP1559 @ $true))),
% 206.94/30.98 introduced(definition,[new_symbols(naming,[sP1559])],[inequality_splitting_name_introduction])).
% 206.94/30.98 thf(f28998,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (($true = (sP1559 @ $true)) | ((binintersect @ X0 @ (binunion @ X1 @ X0)) = X0)) )),
% 206.94/30.98 inference(superposition,[status(thm)],[f7865,f8122])).
% 206.94/30.98 thf(f8122,plain,(
% 206.94/30.98 ( ! [X2 : $i,X3 : $i] : (((subset @ X3 @ (binunion @ X2 @ X3)) = $true)) )),
% 206.94/30.98 inference(trivial_inequality_removal,[status(thm)],[f8121])).
% 206.94/30.98 thf(f8121,plain,(
% 206.94/30.98 ( ! [X2 : $i,X3 : $i] : (((subset @ X3 @ (binunion @ X2 @ X3)) = $true) | ($false = $true)) )),
% 206.94/30.98 inference(forward_demodulation,[status(thm)],[f6779,f6778])).
% 206.94/30.98 thf(f6778,plain,(
% 206.94/30.98 ($false = (sP2108 @ $true))),
% 206.94/30.98 introduced(definition,[new_symbols(naming,[sP2108])],[inequality_splitting_name_introduction])).
% 206.94/30.98 thf(f6779,plain,(
% 206.94/30.98 ( ! [X2 : $i,X3 : $i] : (($true = (sP2108 @ $true)) | ((subset @ X3 @ (binunion @ X2 @ X3)) = $true)) )),
% 206.94/30.98 inference(inequality_splitting,[status(thm)],[f4787,f6778])).
% 206.94/30.98 thf(f4787,plain,(
% 206.94/30.98 ( ! [X2 : $i,X3 : $i] : (((subset @ X3 @ (binunion @ X2 @ X3)) = $true) | ($true != $true)) )),
% 206.94/30.98 inference(definition_unfolding,[status(thm)],[f3768,f2651])).
% 206.94/30.98 thf(f2651,plain,(
% 206.94/30.98 (binunionRsub = $true)),
% 206.94/30.98 inference(cnf_transformation,[status(thm)],[f1190])).
% 206.94/30.98 thf(f1190,plain,(
% 206.94/30.98 (setunion__Cong = $true) & (doubleComplementI1 = $true) & (ksndsingleton = $true) & (iftrueorfalse = $true) & (eta1 = $true) & (subset2powerset = $true) & (binunionE = $true) & (iffalse = $true) & (uniqinunit = $true) & (prop2setI = $true) & (apProp = $true) & (lamp = $true) & (iftrueProp1 = $true) & (upairsetIR = $true) & (notsubsetI = $true) & (inCongP = $true) & (contraSubsetComplement = $true) & (binunionIL = $true) & (descrp = $true) & (dpsetconstrI = $true) & (kpairiskpair = $true) & (cartprodsndin = $true) & (doubleComplementSub1 = $true) & (ifp = $true) & (symdiffIneg1 = $true) & (emptyE1 = $true) & (funcextLem = $true) & (setminusIRneg = $true) & (binunionTIRcontra = $true) & (theprop = $true) & (powersetE = $true) & (dsetconstrI = $true) & (funcinfuncset = $true) & (ubforcartprodlem3 = $true) & (iftrue = $true) & (complementTI1 = $true) & (subsetI2 = $true) & (inIntersectImpInUnion = $true) & (binunionLsub = $true) & (inIntersectImpInUnion2 = $true) & (dpsetconstrER = $true) & (setminusSubset2 = $true) & (funcext = $true) & (setadjoinIR = $true) & (funcImageSingleton = $true) & (setukpairIL = $true) & (complementTnotintersectT = $true) & (exuI2 = $true) & (emptyInPowerset = $true) & (binunionTILcontra = $true) & (cartprodfstin = $true) & (binintersectSubset2 = $true) & (binunionRsub = $true) & (funcGraphProp1 = $true) & (powersetsubset = $true) & (setminusSubset1 = $true) & (binintersectRsub = $true) & (contrasubsetT = $true) & (binunionEcases = $true) & (setunionsingleton2 = $true) & (binintersectSubset3 = $true) & (dpsetconstrSub = $true) & (eqimpsubset2 = $true) & (dsetconstrER = $true) & (setadjoinSub = $true) & (binintersectTERcontra = $true) & (foundationAx = $true) & (singletoninpowerset = $true) & (funcGraphProp3 = $true) & (setukpairinjR = $true) & (emptyI = $true) & (exu__Cong = $true) & (in__Cong = $true) & (setOfPairsIsBReln = $true) & (ubforcartprodlem2 = $true) & (powerset__Cong = $true) & (nonemptyE1 = $true) & (app = $true) & (complementTE1 = $true) & (contrasubsetT1 = $true) & (subsetTrans = $true) & (singletonsswitch = $true) & (lam2lamEq = $true) & (setunionE2 = $true) & (ksndpairEq = $true) & (cartprodfstpairEq = $true) & (exuEu = $true) & (quantDeMorgan1 = $true) & (infuncsetfunc = $true) & (upairset2E = $true) & (powersetTI1 = $true) & (setunionsingleton1 = $true) & (ex1I2 = $true) & (subsetE2 = $true) & (setadjoinIL = $true) & (lam2p = $true) & (symdiffIneg2 = $true) & (inIntersectImpInIntersectUnions = $true) & (binintersectLsub = $true) & (exuI1 = $true) & (setadjoinE = $true) & (setadjoinAx = $true) & (setunionE = $true) & (brelnall1 = $true) & (upairsetIL = $true) & (binintersectSubset1 = $true) & (subsetE = $true) & (replAx = $true) & (emptysetAx = $true) & (emptyinunitempty = $true) & (contrasubsetT2 = $true) & (setukpairinjL = $true) & (setminusERneg = $true) & (setminusT_lem = $true) & (powersetI1 = $true) & (kfstsingleton = $true) & (setminusILneg = $true) & (iffalseProp1 = $true) & (wellorderingAx = $true) & (ap2p = $true) & (exuE1 = $true) & (doubleComplementSub2 = $true) & (notinemptyset = $true) & (upairsetE = $true) & (powersetE1 = $true) & (ap2apEq2 = $true) & (singletonsubset = $true) & (subsetI1 = $true) & (complementT_lem = $true) & (inPowerset = $true) & (contrasubsetT3 = $true) & (exuE2 = $true) & (prop2set2propI = $true) & (brelnall2 = $true) & (omegaSAx = $true) & (nonemptyImpWitness = $true) & (binintersectSubset5 = $true) & (symdiffI2 = $true) & (ubforcartprodlem1 = $true) & (notequalI2 = $true) & (quantDeMorgan4 = $true) & (symdiffE = $true) & (kpairp = $true) & (ex1I = $true) & (cartprodsndpairEq = $true) & (secondinupair = $true) & (nonemptyI1 = $true) & (quantDeMorgan3 = $true) & (powersetT_lem = $true) & (setbeta = $true) & (iftrueProp2 = $true) & (setoftrueEq = $true) & (symdiffI1 = $true) & (powersetAx = $true) & (sepInPowerset = $true) & (binintersectSubset4 = $true) & (cartprodmempair = $true) & (binintersectT_lem = $true) & (subsetTI = $true) & (emptyset__Cong = $true) & (setukpairinjR1 = $true) & (funcGraphProp2 = $true) & (setextAx = $true) & (setminusEL = $true) & (disjointsetsI1 = $true) & (dpsetconstrEL1 = $true) & (subPowSU = $true) & (notdallE = $true) & (singletonprop = $true) & (binunionT_lem = $true) & (dsetconstr__Cong = $true) & (setminusER = $true) & (kpairsurjEq = $true) & (iffalseProp2 = $true) & (powersetI = $true) & (exuI3 = $true) & (complementTcontraSubset = $true) & (singletonsuniq = $true) & (setminusLsub = $true) & (ex1E1 = $true) & (prop2setE = $true) & (omegaIndAx = $true) & (dsetconstrEL = $true) & (emptysetE = $true) & (setadjoin__Cong = $true) & (binintersectTELcontra = $true) & (eqbreln = $true) & (exuE3e = $true) & (doubleComplementE1 = $true) & (setunionsingleton = $true) & (setext = $true) & (lamProp = $true) & (ap2apEq1 = $true) & (eqimpsubset1 = $true) & (subsetRefl = $true) & (upairsubunion = $true) & (upairinpowunion = $true) & (emptyinPowerset = $true) & (upairset2IR = $true) & (nonemptyI = $true) & (beta1 = $true) & (vacuousDall = $true) & (theeq = $true) & (notdexE = $true) & (quantDeMorgan2 = $true) & (singletoninpowunion = $true) & (setukpairinjR2 = $true) & (emptysetsubset = $true) & (setunionI = $true) & (upairequniteq = $true) & (dpsetconstrERa = $true) & (kfstpairEq = $true) & (descr__Cong = $true) & (subbreln = $true) & (omega0Ax = $true) & (bs114d = $true) & (setextsub = $true) & (setadjoinSub2 = $true) & (setukpairinjL1 = $true) & (cartprodpairin = $true) & (notequalI1 = $true) & (dpsetconstrEL2 = $true) & (((($true = (in @ sK30 @ (powerset @ sK27))) & ($true != (in @ (binintersect @ sK28 @ sK29) @ (powerset @ (binintersect @ (binunion @ sK28 @ sK30) @ (binunion @ sK29 @ sK30)))))) & ($true = (in @ sK29 @ (powerset @ sK27)))) & ($true = (in @ sK28 @ (powerset @ sK27)))) & (binintersectI = $true) & (powersetTE1 = $true) & (complementSubsetComplementIntersect = $true) & (setukpairinjR11 = $true) & (omega__Cong = $true) & (exuE3u = $true) & (cartprodpairmemEL = $true) & (eqinunit = $true) & (setminusI = $true) & (binunionIR = $true) & (setunionAx = $true) & (setukpairinjL2 = $true) & (sepSubset = $true) & (setminusELneg = $true) & (complementInPowersetComplementIntersect = $true) & (funcGraphProp4 = $true) & (ex1E2 = $true) & (noeltsimpempty = $true) & (setukpairIR = $true) & (subsetemptysetimpeq = $true) & (beta2 = $true) & (setextT = $true) & (notinsingleton = $true) & (cartprodmempaircEq = $true) & (cartprodpairmemER = $true) & (eta2 = $true) & (binintersectER = $true) & (funcext2 = $true) & (cartprodpairsurjEq = $true) & (doubleComplementEq = $true) & (binintersectEL = $true) & (setukpairinjR12 = $true) & (setadjoinOr = $true) & (cartprodmempair1 = $true) & (ifSingleton = $true) & (emptysetimpfalse = $true) & (complementImpComplementIntersect = $true)),
% 206.94/30.98 inference(skolemisation,[status(esa),new_symbols(skolem,[sK27,sK28,sK29,sK30])],[f1025,f1189,f1188,f1187])).
% 206.94/30.98 thf(f1187,plain,(
% 206.94/30.98 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ (powerset @ X0)) = $true) & ((in @ (binintersect @ X1 @ X2) @ (powerset @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3)))) != $true)) & ((in @ X2 @ (powerset @ X0)) = $true)) & ($true = (in @ X1 @ (powerset @ X0)))) => (? [X2 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ (powerset @ sK27))) & ($true != (in @ (binintersect @ sK28 @ X2) @ (powerset @ (binintersect @ (binunion @ sK28 @ X3) @ (binunion @ X2 @ X3)))))) & ($true = (in @ X2 @ (powerset @ sK27)))) & ($true = (in @ sK28 @ (powerset @ sK27))))),
% 206.94/30.98 introduced(definition,[],[choice_axiom])).
% 206.94/30.98 thf(f1188,plain,(
% 206.94/30.98 ? [X2 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ (powerset @ sK27))) & ($true != (in @ (binintersect @ sK28 @ X2) @ (powerset @ (binintersect @ (binunion @ sK28 @ X3) @ (binunion @ X2 @ X3)))))) & ($true = (in @ X2 @ (powerset @ sK27)))) => (? [X3 : $i] : (($true = (in @ X3 @ (powerset @ sK27))) & ((in @ (binintersect @ sK28 @ sK29) @ (powerset @ (binintersect @ (binunion @ sK28 @ X3) @ (binunion @ sK29 @ X3)))) != $true)) & ($true = (in @ sK29 @ (powerset @ sK27))))),
% 206.94/30.98 introduced(definition,[],[choice_axiom])).
% 206.94/30.98 thf(f1189,plain,(
% 206.94/30.98 ? [X3 : $i] : (($true = (in @ X3 @ (powerset @ sK27))) & ((in @ (binintersect @ sK28 @ sK29) @ (powerset @ (binintersect @ (binunion @ sK28 @ X3) @ (binunion @ sK29 @ X3)))) != $true)) => (($true = (in @ sK30 @ (powerset @ sK27))) & ($true != (in @ (binintersect @ sK28 @ sK29) @ (powerset @ (binintersect @ (binunion @ sK28 @ sK30) @ (binunion @ sK29 @ sK30))))))),
% 206.94/30.98 introduced(definition,[],[choice_axiom])).
% 206.94/30.98 thf(f1025,plain,(
% 206.94/30.98 (setunion__Cong = $true) & (doubleComplementI1 = $true) & (ksndsingleton = $true) & (iftrueorfalse = $true) & (eta1 = $true) & (subset2powerset = $true) & (binunionE = $true) & (iffalse = $true) & (uniqinunit = $true) & (prop2setI = $true) & (apProp = $true) & (lamp = $true) & (iftrueProp1 = $true) & (upairsetIR = $true) & (notsubsetI = $true) & (inCongP = $true) & (contraSubsetComplement = $true) & (binunionIL = $true) & (descrp = $true) & (dpsetconstrI = $true) & (kpairiskpair = $true) & (cartprodsndin = $true) & (doubleComplementSub1 = $true) & (ifp = $true) & (symdiffIneg1 = $true) & (emptyE1 = $true) & (funcextLem = $true) & (setminusIRneg = $true) & (binunionTIRcontra = $true) & (theprop = $true) & (powersetE = $true) & (dsetconstrI = $true) & (funcinfuncset = $true) & (ubforcartprodlem3 = $true) & (iftrue = $true) & (complementTI1 = $true) & (subsetI2 = $true) & (inIntersectImpInUnion = $true) & (binunionLsub = $true) & (inIntersectImpInUnion2 = $true) & (dpsetconstrER = $true) & (setminusSubset2 = $true) & (funcext = $true) & (setadjoinIR = $true) & (funcImageSingleton = $true) & (setukpairIL = $true) & (complementTnotintersectT = $true) & (exuI2 = $true) & (emptyInPowerset = $true) & (binunionTILcontra = $true) & (cartprodfstin = $true) & (binintersectSubset2 = $true) & (binunionRsub = $true) & (funcGraphProp1 = $true) & (powersetsubset = $true) & (setminusSubset1 = $true) & (binintersectRsub = $true) & (contrasubsetT = $true) & (binunionEcases = $true) & (setunionsingleton2 = $true) & (binintersectSubset3 = $true) & (dpsetconstrSub = $true) & (eqimpsubset2 = $true) & (dsetconstrER = $true) & (setadjoinSub = $true) & (binintersectTERcontra = $true) & (foundationAx = $true) & (singletoninpowerset = $true) & (funcGraphProp3 = $true) & (setukpairinjR = $true) & (emptyI = $true) & (exu__Cong = $true) & (in__Cong = $true) & (setOfPairsIsBReln = $true) & (ubforcartprodlem2 = $true) & (powerset__Cong = $true) & (nonemptyE1 = $true) & (app = $true) & (complementTE1 = $true) & (contrasubsetT1 = $true) & (subsetTrans = $true) & (singletonsswitch = $true) & (lam2lamEq = $true) & (setunionE2 = $true) & (ksndpairEq = $true) & (cartprodfstpairEq = $true) & (exuEu = $true) & (quantDeMorgan1 = $true) & (infuncsetfunc = $true) & (upairset2E = $true) & (powersetTI1 = $true) & (setunionsingleton1 = $true) & (ex1I2 = $true) & (subsetE2 = $true) & (setadjoinIL = $true) & (lam2p = $true) & (symdiffIneg2 = $true) & (inIntersectImpInIntersectUnions = $true) & (binintersectLsub = $true) & (exuI1 = $true) & (setadjoinE = $true) & (setadjoinAx = $true) & (setunionE = $true) & (brelnall1 = $true) & (upairsetIL = $true) & (binintersectSubset1 = $true) & (subsetE = $true) & (replAx = $true) & (emptysetAx = $true) & (emptyinunitempty = $true) & (contrasubsetT2 = $true) & (setukpairinjL = $true) & (setminusERneg = $true) & (setminusT_lem = $true) & (powersetI1 = $true) & (kfstsingleton = $true) & (setminusILneg = $true) & (iffalseProp1 = $true) & (wellorderingAx = $true) & (ap2p = $true) & (exuE1 = $true) & (doubleComplementSub2 = $true) & (notinemptyset = $true) & (upairsetE = $true) & (powersetE1 = $true) & (ap2apEq2 = $true) & (singletonsubset = $true) & (subsetI1 = $true) & (complementT_lem = $true) & (inPowerset = $true) & (contrasubsetT3 = $true) & (exuE2 = $true) & (prop2set2propI = $true) & (brelnall2 = $true) & (omegaSAx = $true) & (nonemptyImpWitness = $true) & (binintersectSubset5 = $true) & (symdiffI2 = $true) & (ubforcartprodlem1 = $true) & (notequalI2 = $true) & (quantDeMorgan4 = $true) & (symdiffE = $true) & (kpairp = $true) & (ex1I = $true) & (cartprodsndpairEq = $true) & (secondinupair = $true) & (nonemptyI1 = $true) & (quantDeMorgan3 = $true) & (powersetT_lem = $true) & (setbeta = $true) & (iftrueProp2 = $true) & (setoftrueEq = $true) & (symdiffI1 = $true) & (powersetAx = $true) & (sepInPowerset = $true) & (binintersectSubset4 = $true) & (cartprodmempair = $true) & (binintersectT_lem = $true) & (subsetTI = $true) & (emptyset__Cong = $true) & (setukpairinjR1 = $true) & (funcGraphProp2 = $true) & (setextAx = $true) & (setminusEL = $true) & (disjointsetsI1 = $true) & (dpsetconstrEL1 = $true) & (subPowSU = $true) & (notdallE = $true) & (singletonprop = $true) & (binunionT_lem = $true) & (dsetconstr__Cong = $true) & (setminusER = $true) & (kpairsurjEq = $true) & (iffalseProp2 = $true) & (powersetI = $true) & (exuI3 = $true) & (complementTcontraSubset = $true) & (singletonsuniq = $true) & (setminusLsub = $true) & (ex1E1 = $true) & (prop2setE = $true) & (omegaIndAx = $true) & (dsetconstrEL = $true) & (emptysetE = $true) & (setadjoin__Cong = $true) & (binintersectTELcontra = $true) & (eqbreln = $true) & (exuE3e = $true) & (doubleComplementE1 = $true) & (setunionsingleton = $true) & (setext = $true) & (lamProp = $true) & (ap2apEq1 = $true) & (eqimpsubset1 = $true) & (subsetRefl = $true) & (upairsubunion = $true) & (upairinpowunion = $true) & (emptyinPowerset = $true) & (upairset2IR = $true) & (nonemptyI = $true) & (beta1 = $true) & (vacuousDall = $true) & (theeq = $true) & (notdexE = $true) & (quantDeMorgan2 = $true) & (singletoninpowunion = $true) & (setukpairinjR2 = $true) & (emptysetsubset = $true) & (setunionI = $true) & (upairequniteq = $true) & (dpsetconstrERa = $true) & (kfstpairEq = $true) & (descr__Cong = $true) & (subbreln = $true) & (omega0Ax = $true) & (bs114d = $true) & (setextsub = $true) & (setadjoinSub2 = $true) & (setukpairinjL1 = $true) & (cartprodpairin = $true) & (notequalI1 = $true) & (dpsetconstrEL2 = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ (powerset @ X0)) = $true) & ((in @ (binintersect @ X1 @ X2) @ (powerset @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3)))) != $true)) & ((in @ X2 @ (powerset @ X0)) = $true)) & ($true = (in @ X1 @ (powerset @ X0)))) & (binintersectI = $true) & (powersetTE1 = $true) & (complementSubsetComplementIntersect = $true) & (setukpairinjR11 = $true) & (omega__Cong = $true) & (exuE3u = $true) & (cartprodpairmemEL = $true) & (eqinunit = $true) & (setminusI = $true) & (binunionIR = $true) & (setunionAx = $true) & (setukpairinjL2 = $true) & (sepSubset = $true) & (setminusELneg = $true) & (complementInPowersetComplementIntersect = $true) & (funcGraphProp4 = $true) & (ex1E2 = $true) & (noeltsimpempty = $true) & (setukpairIR = $true) & (subsetemptysetimpeq = $true) & (beta2 = $true) & (setextT = $true) & (notinsingleton = $true) & (cartprodmempaircEq = $true) & (cartprodpairmemER = $true) & (eta2 = $true) & (binintersectER = $true) & (funcext2 = $true) & (cartprodpairsurjEq = $true) & (doubleComplementEq = $true) & (binintersectEL = $true) & (setukpairinjR12 = $true) & (setadjoinOr = $true) & (cartprodmempair1 = $true) & (ifSingleton = $true) & (emptysetimpfalse = $true) & (complementImpComplementIntersect = $true)),
% 206.94/30.98 inference(flattening,[status(thm)],[f1024])).
% 206.94/30.98 thf(f1024,plain,(
% 206.94/30.98 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ (powerset @ X0)) = $true) & ((in @ (binintersect @ X1 @ X2) @ (powerset @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3)))) != $true)) & ((in @ X2 @ (powerset @ X0)) = $true)) & ($true = (in @ X1 @ (powerset @ X0)))) & (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)),
% 206.94/30.98 inference(ennf_transformation,[status(thm)],[f557])).
% 206.94/30.98 thf(f557,plain,(
% 206.94/30.98 ~((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) => ! [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (powerset @ X0))) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3 : $i] : (((in @ X3 @ (powerset @ X0)) = $true) => ((in @ (binintersect @ X1 @ X2) @ (powerset @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3)))) = $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 206.94/30.98 inference(fool_elimination,[status(thm)],[f556])).
% 206.94/30.98 thf(f556,plain,(
% 206.94/30.98 ~(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 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 206.94/30.98 inference(rectify,[status(thm)],[f265])).
% 206.94/30.98 thf(f265,negated_conjecture,(
% 206.94/30.98 ~(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 => ! [X3 : $i,X11 : $i] : ((in @ X11 @ (powerset @ X3)) => ! [X16 : $i] : ((in @ X16 @ (powerset @ X3)) => ! [X17 : $i] : ((in @ X17 @ (powerset @ X3)) => (in @ (binintersect @ X11 @ X16) @ (powerset @ (binintersect @ (binunion @ X11 @ X17) @ (binunion @ X16 @ X17))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 206.94/30.98 inference(negated_conjecture,[status(cth)],[f264])).
% 206.94/30.98 thf(f264,conjecture,(
% 206.94/30.98 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 => ! [X3 : $i,X11 : $i] : ((in @ X11 @ (powerset @ X3)) => ! [X16 : $i] : ((in @ X16 @ (powerset @ X3)) => ! [X17 : $i] : ((in @ X17 @ (powerset @ X3)) => (in @ (binintersect @ X11 @ X16) @ (powerset @ (binintersect @ (binunion @ X11 @ X17) @ (binunion @ X16 @ X17)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 206.94/30.98 file('/export/starexec/sandbox/tmp/tmp.XapuwXWeE6/DTF2THF_1199.p',intersectInPowersetIntersectUnions)).
% 206.94/30.98 thf(f3768,plain,(
% 206.94/30.98 ( ! [X2 : $i,X3 : $i] : (((subset @ X3 @ (binunion @ X2 @ X3)) = $true) | (binunionRsub != $true)) )),
% 206.94/30.98 inference(cnf_transformation,[status(thm)],[f2408])).
% 206.94/30.98 thf(f2408,plain,(
% 206.94/30.98 ((binunionRsub = $true) | ((subset @ sK822 @ (binunion @ sK821 @ sK822)) != $true)) & (! [X2 : $i,X3 : $i] : ((subset @ X3 @ (binunion @ X2 @ X3)) = $true) | (binunionRsub != $true))),
% 206.94/30.98 inference(skolemisation,[status(esa),new_symbols(skolem,[sK821,sK822])],[f2406,f2407])).
% 206.94/30.98 thf(f2407,plain,(
% 206.94/30.98 ? [X0 : $i,X1 : $i] : ($true != (subset @ X1 @ (binunion @ X0 @ X1))) => ((subset @ sK822 @ (binunion @ sK821 @ sK822)) != $true)),
% 206.94/30.98 introduced(definition,[],[choice_axiom])).
% 206.94/30.98 thf(f2406,plain,(
% 206.94/30.98 ((binunionRsub = $true) | ? [X0 : $i,X1 : $i] : ($true != (subset @ X1 @ (binunion @ X0 @ X1)))) & (! [X2 : $i,X3 : $i] : ((subset @ X3 @ (binunion @ X2 @ X3)) = $true) | (binunionRsub != $true))),
% 206.94/30.98 inference(rectify,[status(thm)],[f2405])).
% 206.94/30.98 thf(f2405,plain,(
% 206.94/30.98 ((binunionRsub = $true) | ? [X0 : $i,X1 : $i] : ($true != (subset @ X1 @ (binunion @ X0 @ X1)))) & (! [X0 : $i,X1 : $i] : ($true = (subset @ X1 @ (binunion @ X0 @ X1))) | (binunionRsub != $true))),
% 206.94/30.98 inference(nnf_transformation,[status(thm)],[f736])).
% 206.94/30.98 thf(f736,plain,(
% 206.94/30.98 (binunionRsub = $true) <=> ! [X0 : $i,X1 : $i] : ($true = (subset @ X1 @ (binunion @ X0 @ X1)))),
% 206.94/30.98 inference(fool_elimination,[status(thm)],[f735])).
% 206.94/30.98 thf(f735,plain,(
% 206.94/30.98 (! [X0 : $i,X1 : $i] : (subset @ X1 @ (binunion @ X0 @ X1)) = binunionRsub)),
% 206.94/30.98 inference(rectify,[status(thm)],[f107])).
% 206.94/30.98 thf(f107,axiom,(
% 206.94/30.98 (! [X3 : $i,X4 : $i] : (subset @ X4 @ (binunion @ X3 @ X4)) = binunionRsub)),
% 206.94/30.98 file('/export/starexec/sandbox/tmp/tmp.XapuwXWeE6/DTF2THF_1199.p',binunionRsub)).
% 206.94/30.98 thf(f7865,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((sP1559 @ (subset @ X0 @ X1)) = $true) | ((binintersect @ X0 @ X1) = X0)) )),
% 206.94/30.98 inference(trivial_inequality_removal,[status(thm)],[f7864])).
% 206.94/30.98 thf(f7864,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((sP1559 @ (subset @ X0 @ X1)) = $true) | ($false = $true) | ((binintersect @ X0 @ X1) = X0)) )),
% 206.94/30.98 inference(forward_demodulation,[status(thm)],[f5928,f5927])).
% 206.94/30.98 thf(f5927,plain,(
% 206.94/30.98 ($false = (sP1560 @ $true))),
% 206.94/30.98 introduced(definition,[new_symbols(naming,[sP1560])],[inequality_splitting_name_introduction])).
% 206.94/30.98 thf(f5928,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X0) | ($true = (sP1560 @ $true)) | ((sP1559 @ (subset @ X0 @ X1)) = $true)) )),
% 206.94/30.98 inference(inequality_splitting,[status(thm)],[f4331,f5927,f5926])).
% 206.94/30.98 thf(f4331,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X0) | ((subset @ X0 @ X1) != $true) | ($true != $true)) )),
% 206.94/30.98 inference(definition_unfolding,[status(thm)],[f3292,f2652])).
% 206.94/30.98 thf(f2652,plain,(
% 206.94/30.98 (binintersectSubset2 = $true)),
% 206.94/30.98 inference(cnf_transformation,[status(thm)],[f1190])).
% 206.94/30.98 thf(f3292,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X0) | ((subset @ X0 @ X1) != $true) | (binintersectSubset2 != $true)) )),
% 206.94/30.98 inference(cnf_transformation,[status(thm)],[f1863])).
% 206.94/30.98 thf(f1863,plain,(
% 206.94/30.98 (! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X0) | ((subset @ X0 @ X1) != $true)) | (binintersectSubset2 != $true)) & ((binintersectSubset2 = $true) | ((sK459 != (binintersect @ sK459 @ sK460)) & ((subset @ sK459 @ sK460) = $true)))),
% 206.94/30.98 inference(skolemisation,[status(esa),new_symbols(skolem,[sK459,sK460])],[f1861,f1862])).
% 206.94/30.98 thf(f1862,plain,(
% 206.94/30.98 ? [X2 : $i,X3 : $i] : (((binintersect @ X2 @ X3) != X2) & ($true = (subset @ X2 @ X3))) => ((sK459 != (binintersect @ sK459 @ sK460)) & ((subset @ sK459 @ sK460) = $true))),
% 206.94/30.98 introduced(definition,[],[choice_axiom])).
% 206.94/30.98 thf(f1861,plain,(
% 206.94/30.98 (! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X0) | ((subset @ X0 @ X1) != $true)) | (binintersectSubset2 != $true)) & ((binintersectSubset2 = $true) | ? [X2 : $i,X3 : $i] : (((binintersect @ X2 @ X3) != X2) & ($true = (subset @ X2 @ X3))))),
% 206.94/30.98 inference(rectify,[status(thm)],[f1860])).
% 206.94/30.98 thf(f1860,plain,(
% 206.94/30.98 (! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X0) | ((subset @ X0 @ X1) != $true)) | (binintersectSubset2 != $true)) & ((binintersectSubset2 = $true) | ? [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) != X0) & ((subset @ X0 @ X1) = $true)))),
% 206.94/30.98 inference(nnf_transformation,[status(thm)],[f969])).
% 206.94/30.98 thf(f969,plain,(
% 206.94/30.98 ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X0) | ((subset @ X0 @ X1) != $true)) <=> (binintersectSubset2 = $true)),
% 206.94/30.98 inference(ennf_transformation,[status(thm)],[f447])).
% 206.94/30.98 thf(f447,plain,(
% 206.94/30.98 ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) => ((binintersect @ X0 @ X1) = X0)) <=> (binintersectSubset2 = $true)),
% 206.94/30.98 inference(fool_elimination,[status(thm)],[f446])).
% 206.94/30.98 thf(f446,plain,(
% 206.94/30.98 (! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((binintersect @ X0 @ X1) = X0)) = binintersectSubset2)),
% 206.94/30.98 inference(rectify,[status(thm)],[f112])).
% 206.94/30.98 thf(f112,axiom,(
% 206.94/30.98 (! [X3 : $i,X4 : $i] : ((subset @ X3 @ X4) => ((binintersect @ X3 @ X4) = X3)) = binintersectSubset2)),
% 206.94/30.98 file('/export/starexec/sandbox/tmp/tmp.XapuwXWeE6/DTF2THF_1199.p',binintersectSubset2)).
% 206.94/30.98 thf(f29947,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ (binunion @ X1 @ X0)) = (binunion @ (binintersect @ X0 @ X1) @ X0))) )),
% 206.94/30.98 inference(superposition,[status(thm)],[f9106,f28233])).
% 206.94/30.98 thf(f28233,plain,(
% 206.94/30.98 ( ! [X0 : $i] : (((binintersect @ X0 @ X0) = X0)) )),
% 206.94/30.98 inference(trivial_inequality_removal,[status(thm)],[f28232])).
% 206.94/30.98 thf(f28232,plain,(
% 206.94/30.98 ( ! [X0 : $i] : (((binintersect @ X0 @ X0) = X0) | ($false = $true)) )),
% 206.94/30.98 inference(forward_demodulation,[status(thm)],[f28229,f5812])).
% 206.94/30.98 thf(f5812,plain,(
% 206.94/30.98 ($false = (sP1490 @ $true))),
% 206.94/30.98 introduced(definition,[new_symbols(naming,[sP1490])],[inequality_splitting_name_introduction])).
% 206.94/30.98 thf(f28229,plain,(
% 206.94/30.98 ( ! [X0 : $i] : (((sP1490 @ $true) = $true) | ((binintersect @ X0 @ X0) = X0)) )),
% 206.94/30.98 inference(superposition,[status(thm)],[f9027,f8209])).
% 206.94/30.98 thf(f8209,plain,(
% 206.94/30.98 ( ! [X3 : $i] : (((subset @ X3 @ X3) = $true)) )),
% 206.94/30.98 inference(trivial_inequality_removal,[status(thm)],[f8208])).
% 206.94/30.98 thf(f8208,plain,(
% 206.94/30.98 ( ! [X3 : $i] : (((subset @ X3 @ X3) = $true) | ($false = $true)) )),
% 206.94/30.98 inference(forward_demodulation,[status(thm)],[f6805,f5207])).
% 206.94/30.98 thf(f5207,plain,(
% 206.94/30.98 ($false = (sP1092 @ $true))),
% 206.94/30.98 introduced(definition,[new_symbols(naming,[sP1092])],[inequality_splitting_name_introduction])).
% 206.94/30.98 thf(f6805,plain,(
% 206.94/30.98 ( ! [X3 : $i] : (((subset @ X3 @ X3) = $true) | ($true = (sP1092 @ $true))) )),
% 206.94/30.98 inference(equality_resolution,[status(thm)],[f5208])).
% 206.94/30.98 thf(f5208,plain,(
% 206.94/30.98 ( ! [X2 : $i,X3 : $i] : (($true = (subset @ X2 @ X3)) | (X2 != X3) | ($true = (sP1092 @ $true))) )),
% 206.94/30.98 inference(inequality_splitting,[status(thm)],[f3962,f5207])).
% 206.94/30.98 thf(f3962,plain,(
% 206.94/30.98 ( ! [X2 : $i,X3 : $i] : (($true = (subset @ X2 @ X3)) | (X2 != X3) | ($true != $true)) )),
% 206.94/30.98 inference(definition_unfolding,[status(thm)],[f2895,f2510])).
% 206.94/30.98 thf(f2510,plain,(
% 206.94/30.98 (eqimpsubset1 = $true)),
% 206.94/30.98 inference(cnf_transformation,[status(thm)],[f1190])).
% 206.94/30.98 thf(f2895,plain,(
% 206.94/30.98 ( ! [X2 : $i,X3 : $i] : (($true = (subset @ X2 @ X3)) | (X2 != X3) | (eqimpsubset1 != $true)) )),
% 206.94/30.98 inference(cnf_transformation,[status(thm)],[f1408])).
% 206.94/30.98 thf(f1408,plain,(
% 206.94/30.98 ((eqimpsubset1 = $true) | (($true != (subset @ sK170 @ sK171)) & (sK171 = sK170))) & (! [X2 : $i,X3 : $i] : (($true = (subset @ X2 @ X3)) | (X2 != X3)) | (eqimpsubset1 != $true))),
% 206.94/30.98 inference(skolemisation,[status(esa),new_symbols(skolem,[sK170,sK171])],[f1406,f1407])).
% 206.94/30.98 thf(f1407,plain,(
% 206.94/30.98 ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) & (X0 = X1)) => (($true != (subset @ sK170 @ sK171)) & (sK171 = sK170))),
% 206.94/30.98 introduced(definition,[],[choice_axiom])).
% 206.94/30.98 thf(f1406,plain,(
% 206.94/30.98 ((eqimpsubset1 = $true) | ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) & (X0 = X1))) & (! [X2 : $i,X3 : $i] : (($true = (subset @ X2 @ X3)) | (X2 != X3)) | (eqimpsubset1 != $true))),
% 206.94/30.98 inference(rectify,[status(thm)],[f1405])).
% 206.94/30.98 thf(f1405,plain,(
% 206.94/30.98 ((eqimpsubset1 = $true) | ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) & (X0 = X1))) & (! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | (X0 != X1)) | (eqimpsubset1 != $true))),
% 206.94/30.98 inference(nnf_transformation,[status(thm)],[f1120])).
% 206.94/30.98 thf(f1120,plain,(
% 206.94/30.98 (eqimpsubset1 = $true) <=> ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | (X0 != X1))),
% 206.94/30.98 inference(ennf_transformation,[status(thm)],[f607])).
% 206.94/30.98 thf(f607,plain,(
% 206.94/30.98 (eqimpsubset1 = $true) <=> ! [X0 : $i,X1 : $i] : ((X0 = X1) => ((subset @ X0 @ X1) = $true))),
% 206.94/30.98 inference(fool_elimination,[status(thm)],[f606])).
% 206.94/30.98 thf(f606,plain,(
% 206.94/30.98 (eqimpsubset1 = ! [X0 : $i,X1 : $i] : ((X0 = X1) => (subset @ X0 @ X1)))),
% 206.94/30.98 inference(rectify,[status(thm)],[f80])).
% 206.94/30.98 thf(f80,axiom,(
% 206.94/30.98 (eqimpsubset1 = ! [X3 : $i,X4 : $i] : ((X3 = X4) => (subset @ X3 @ X4)))),
% 206.94/30.98 file('/export/starexec/sandbox/tmp/tmp.XapuwXWeE6/DTF2THF_1199.p',eqimpsubset1)).
% 206.94/30.98 thf(f9027,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (($true = (sP1490 @ (subset @ X0 @ X1))) | ((binintersect @ X1 @ X0) = X0)) )),
% 206.94/30.98 inference(trivial_inequality_removal,[status(thm)],[f9026])).
% 206.94/30.98 thf(f9026,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((binintersect @ X1 @ X0) = X0) | ($true = (sP1490 @ (subset @ X0 @ X1))) | ($false = $true)) )),
% 206.94/30.98 inference(forward_demodulation,[status(thm)],[f5814,f5813])).
% 206.94/30.98 thf(f5813,plain,(
% 206.94/30.98 ($false = (sP1491 @ $true))),
% 206.94/30.98 introduced(definition,[new_symbols(naming,[sP1491])],[inequality_splitting_name_introduction])).
% 206.94/30.98 thf(f5814,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (($true = (sP1491 @ $true)) | ($true = (sP1490 @ (subset @ X0 @ X1))) | ((binintersect @ X1 @ X0) = X0)) )),
% 206.94/30.98 inference(inequality_splitting,[status(thm)],[f4267,f5813,f5812])).
% 206.94/30.98 thf(f4267,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((binintersect @ X1 @ X0) = X0) | ((subset @ X0 @ X1) != $true) | ($true != $true)) )),
% 206.94/30.98 inference(definition_unfolding,[status(thm)],[f3228,f2548])).
% 206.94/30.98 thf(f2548,plain,(
% 206.94/30.98 (binintersectSubset4 = $true)),
% 206.94/30.98 inference(cnf_transformation,[status(thm)],[f1190])).
% 206.94/30.98 thf(f3228,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((binintersect @ X1 @ X0) = X0) | ((subset @ X0 @ X1) != $true) | (binintersectSubset4 != $true)) )),
% 206.94/30.98 inference(cnf_transformation,[status(thm)],[f1776])).
% 206.94/30.98 thf(f1776,plain,(
% 206.94/30.98 (! [X0 : $i,X1 : $i] : (((binintersect @ X1 @ X0) = X0) | ((subset @ X0 @ X1) != $true)) | (binintersectSubset4 != $true)) & ((binintersectSubset4 = $true) | (((binintersect @ sK411 @ sK410) != sK410) & ($true = (subset @ sK410 @ sK411))))),
% 206.94/30.98 inference(skolemisation,[status(esa),new_symbols(skolem,[sK410,sK411])],[f1774,f1775])).
% 206.94/30.98 thf(f1775,plain,(
% 206.94/30.98 ? [X2 : $i,X3 : $i] : (((binintersect @ X3 @ X2) != X2) & ($true = (subset @ X2 @ X3))) => (((binintersect @ sK411 @ sK410) != sK410) & ($true = (subset @ sK410 @ sK411)))),
% 206.94/30.98 introduced(definition,[],[choice_axiom])).
% 206.94/30.98 thf(f1774,plain,(
% 206.94/30.98 (! [X0 : $i,X1 : $i] : (((binintersect @ X1 @ X0) = X0) | ((subset @ X0 @ X1) != $true)) | (binintersectSubset4 != $true)) & ((binintersectSubset4 = $true) | ? [X2 : $i,X3 : $i] : (((binintersect @ X3 @ X2) != X2) & ($true = (subset @ X2 @ X3))))),
% 206.94/30.98 inference(rectify,[status(thm)],[f1773])).
% 206.94/30.98 thf(f1773,plain,(
% 206.94/30.98 (! [X0 : $i,X1 : $i] : (((binintersect @ X1 @ X0) = X0) | ((subset @ X0 @ X1) != $true)) | (binintersectSubset4 != $true)) & ((binintersectSubset4 = $true) | ? [X0 : $i,X1 : $i] : (((binintersect @ X1 @ X0) != X0) & ((subset @ X0 @ X1) = $true)))),
% 206.94/30.98 inference(nnf_transformation,[status(thm)],[f902])).
% 206.94/30.98 thf(f902,plain,(
% 206.94/30.98 ! [X0 : $i,X1 : $i] : (((binintersect @ X1 @ X0) = X0) | ((subset @ X0 @ X1) != $true)) <=> (binintersectSubset4 = $true)),
% 206.94/30.98 inference(ennf_transformation,[status(thm)],[f366])).
% 206.94/30.98 thf(f366,plain,(
% 206.94/30.98 ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) => ((binintersect @ X1 @ X0) = X0)) <=> (binintersectSubset4 = $true)),
% 206.94/30.98 inference(fool_elimination,[status(thm)],[f365])).
% 206.94/30.98 thf(f365,plain,(
% 206.94/30.98 (! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((binintersect @ X1 @ X0) = X0)) = binintersectSubset4)),
% 206.94/30.98 inference(rectify,[status(thm)],[f117])).
% 206.94/30.98 thf(f117,axiom,(
% 206.94/30.98 (! [X4 : $i,X3 : $i] : ((subset @ X4 @ X3) => ((binintersect @ X3 @ X4) = X4)) = binintersectSubset4)),
% 206.94/30.98 file('/export/starexec/sandbox/tmp/tmp.XapuwXWeE6/DTF2THF_1199.p',binintersectSubset4)).
% 206.94/30.98 thf(f9106,plain,(
% 206.94/30.98 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((binintersect @ X0 @ (binunion @ X1 @ X2)) = (binunion @ (binintersect @ X0 @ X1) @ (binintersect @ X0 @ X2)))) )),
% 206.94/30.98 inference(trivial_inequality_removal,[status(thm)],[f9105])).
% 206.94/30.98 thf(f9105,plain,(
% 206.94/30.98 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((binintersect @ X0 @ (binunion @ X1 @ X2)) = (binunion @ (binintersect @ X0 @ X1) @ (binintersect @ X0 @ X2))) | ($false = $true)) )),
% 206.94/30.98 inference(forward_demodulation,[status(thm)],[f6595,f6594])).
% 206.94/30.98 thf(f6594,plain,(
% 206.94/30.98 ($false = (sP1994 @ $true))),
% 206.94/30.98 introduced(definition,[new_symbols(naming,[sP1994])],[inequality_splitting_name_introduction])).
% 206.94/30.98 thf(f6595,plain,(
% 206.94/30.98 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((sP1994 @ $true) = $true) | ((binintersect @ X0 @ (binunion @ X1 @ X2)) = (binunion @ (binintersect @ X0 @ X1) @ (binintersect @ X0 @ X2)))) )),
% 206.94/30.98 inference(inequality_splitting,[status(thm)],[f4681,f6594])).
% 206.94/30.98 thf(f4681,plain,(
% 206.94/30.98 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((binintersect @ X0 @ (binunion @ X1 @ X2)) = (binunion @ (binintersect @ X0 @ X1) @ (binintersect @ X0 @ X2))) | ($true != $true)) )),
% 206.94/30.98 inference(definition_unfolding,[status(thm)],[f3659,f2488])).
% 206.94/30.98 thf(f2488,plain,(
% 206.94/30.98 (bs114d = $true)),
% 206.94/30.98 inference(cnf_transformation,[status(thm)],[f1190])).
% 206.94/30.98 thf(f3659,plain,(
% 206.94/30.98 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((binintersect @ X0 @ (binunion @ X1 @ X2)) = (binunion @ (binintersect @ X0 @ X1) @ (binintersect @ X0 @ X2))) | (bs114d != $true)) )),
% 206.94/30.98 inference(cnf_transformation,[status(thm)],[f2279])).
% 206.94/30.98 thf(f2279,plain,(
% 206.94/30.98 (! [X0 : $i,X1 : $i,X2 : $i] : ((binintersect @ X0 @ (binunion @ X1 @ X2)) = (binunion @ (binintersect @ X0 @ X1) @ (binintersect @ X0 @ X2))) | (bs114d != $true)) & ((bs114d = $true) | ((binintersect @ sK744 @ (binunion @ sK745 @ sK746)) != (binunion @ (binintersect @ sK744 @ sK745) @ (binintersect @ sK744 @ sK746))))),
% 206.94/30.98 inference(skolemisation,[status(esa),new_symbols(skolem,[sK744,sK745,sK746])],[f2277,f2278])).
% 206.94/30.98 thf(f2278,plain,(
% 206.94/30.98 ? [X3 : $i,X4 : $i,X5 : $i] : ((binintersect @ X3 @ (binunion @ X4 @ X5)) != (binunion @ (binintersect @ X3 @ X4) @ (binintersect @ X3 @ X5))) => ((binintersect @ sK744 @ (binunion @ sK745 @ sK746)) != (binunion @ (binintersect @ sK744 @ sK745) @ (binintersect @ sK744 @ sK746)))),
% 206.94/30.98 introduced(definition,[],[choice_axiom])).
% 206.94/30.98 thf(f2277,plain,(
% 206.94/30.98 (! [X0 : $i,X1 : $i,X2 : $i] : ((binintersect @ X0 @ (binunion @ X1 @ X2)) = (binunion @ (binintersect @ X0 @ X1) @ (binintersect @ X0 @ X2))) | (bs114d != $true)) & ((bs114d = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : ((binintersect @ X3 @ (binunion @ X4 @ X5)) != (binunion @ (binintersect @ X3 @ X4) @ (binintersect @ X3 @ X5))))),
% 206.94/30.98 inference(rectify,[status(thm)],[f2276])).
% 206.94/30.98 thf(f2276,plain,(
% 206.94/30.98 (! [X0 : $i,X1 : $i,X2 : $i] : ((binintersect @ X0 @ (binunion @ X1 @ X2)) = (binunion @ (binintersect @ X0 @ X1) @ (binintersect @ X0 @ X2))) | (bs114d != $true)) & ((bs114d = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((binintersect @ X0 @ (binunion @ X1 @ X2)) != (binunion @ (binintersect @ X0 @ X1) @ (binintersect @ X0 @ X2))))),
% 206.94/30.98 inference(nnf_transformation,[status(thm)],[f358])).
% 206.94/30.98 thf(f358,plain,(
% 206.94/30.98 ! [X0 : $i,X1 : $i,X2 : $i] : ((binintersect @ X0 @ (binunion @ X1 @ X2)) = (binunion @ (binintersect @ X0 @ X1) @ (binintersect @ X0 @ X2))) <=> (bs114d = $true)),
% 206.94/30.98 inference(fool_elimination,[status(thm)],[f357])).
% 206.94/30.98 thf(f357,plain,(
% 206.94/30.98 (! [X0 : $i,X1 : $i,X2 : $i] : ((binintersect @ X0 @ (binunion @ X1 @ X2)) = (binunion @ (binintersect @ X0 @ X1) @ (binintersect @ X0 @ X2))) = bs114d)),
% 206.94/30.98 inference(rectify,[status(thm)],[f119])).
% 206.94/30.98 thf(f119,axiom,(
% 206.94/30.98 (! [X3 : $i,X4 : $i,X5 : $i] : ((binintersect @ X3 @ (binunion @ X4 @ X5)) = (binunion @ (binintersect @ X3 @ X4) @ (binintersect @ X3 @ X5))) = bs114d)),
% 206.94/30.98 file('/export/starexec/sandbox/tmp/tmp.XapuwXWeE6/DTF2THF_1199.p',bs114d)).
% 206.94/30.98 thf(f41547,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = (binintersect @ X1 @ (binunion @ (binintersect @ X0 @ X1) @ X0)))) )),
% 206.94/30.98 inference(forward_demodulation,[status(thm)],[f41474,f29974])).
% 206.94/30.98 thf(f29974,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((binunion @ X0 @ (binintersect @ X0 @ X1)) = X0)) )),
% 206.94/30.98 inference(forward_demodulation,[status(thm)],[f29956,f29029])).
% 206.94/30.98 thf(f29029,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ (binunion @ X0 @ X1)) = X0)) )),
% 206.94/30.98 inference(trivial_inequality_removal,[status(thm)],[f29028])).
% 206.94/30.98 thf(f29028,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (($false = $true) | ((binintersect @ X0 @ (binunion @ X0 @ X1)) = X0)) )),
% 206.94/30.98 inference(forward_demodulation,[status(thm)],[f29025,f5926])).
% 206.94/30.98 thf(f29025,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (($true = (sP1559 @ $true)) | ((binintersect @ X0 @ (binunion @ X0 @ X1)) = X0)) )),
% 206.94/30.98 inference(superposition,[status(thm)],[f7865,f8573])).
% 206.94/30.98 thf(f8573,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ (binunion @ X1 @ X0)))) )),
% 206.94/30.98 inference(trivial_inequality_removal,[status(thm)],[f8572])).
% 206.94/30.98 thf(f8572,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (($false = $true) | ($true = (subset @ X1 @ (binunion @ X1 @ X0)))) )),
% 206.94/30.98 inference(forward_demodulation,[status(thm)],[f5251,f5250])).
% 206.94/30.98 thf(f5250,plain,(
% 206.94/30.98 ($false = (sP1119 @ $true))),
% 206.94/30.98 introduced(definition,[new_symbols(naming,[sP1119])],[inequality_splitting_name_introduction])).
% 206.94/30.98 thf(f5251,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ (binunion @ X1 @ X0))) | ($true = (sP1119 @ $true))) )),
% 206.94/30.98 inference(inequality_splitting,[status(thm)],[f3987,f5250])).
% 206.94/30.98 thf(f3987,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ (binunion @ X1 @ X0))) | ($true != $true)) )),
% 206.94/30.98 inference(definition_unfolding,[status(thm)],[f2923,f2665])).
% 206.94/30.98 thf(f2665,plain,(
% 206.94/30.98 (binunionLsub = $true)),
% 206.94/30.98 inference(cnf_transformation,[status(thm)],[f1190])).
% 206.94/30.98 thf(f2923,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ (binunion @ X1 @ X0))) | (binunionLsub != $true)) )),
% 206.94/30.98 inference(cnf_transformation,[status(thm)],[f1439])).
% 206.94/30.98 thf(f1439,plain,(
% 206.94/30.98 (! [X0 : $i,X1 : $i] : ($true = (subset @ X1 @ (binunion @ X1 @ X0))) | (binunionLsub != $true)) & ((binunionLsub = $true) | ($true != (subset @ sK192 @ (binunion @ sK192 @ sK191))))),
% 206.94/30.98 inference(skolemisation,[status(esa),new_symbols(skolem,[sK191,sK192])],[f1437,f1438])).
% 206.94/30.98 thf(f1438,plain,(
% 206.94/30.98 ? [X2 : $i,X3 : $i] : ($true != (subset @ X3 @ (binunion @ X3 @ X2))) => ($true != (subset @ sK192 @ (binunion @ sK192 @ sK191)))),
% 206.94/30.98 introduced(definition,[],[choice_axiom])).
% 206.94/30.98 thf(f1437,plain,(
% 206.94/30.98 (! [X0 : $i,X1 : $i] : ($true = (subset @ X1 @ (binunion @ X1 @ X0))) | (binunionLsub != $true)) & ((binunionLsub = $true) | ? [X2 : $i,X3 : $i] : ($true != (subset @ X3 @ (binunion @ X3 @ X2))))),
% 206.94/30.98 inference(rectify,[status(thm)],[f1436])).
% 206.94/30.98 thf(f1436,plain,(
% 206.94/30.98 (! [X0 : $i,X1 : $i] : ($true = (subset @ X1 @ (binunion @ X1 @ X0))) | (binunionLsub != $true)) & ((binunionLsub = $true) | ? [X0 : $i,X1 : $i] : ($true != (subset @ X1 @ (binunion @ X1 @ X0))))),
% 206.94/30.98 inference(nnf_transformation,[status(thm)],[f292])).
% 206.94/30.98 thf(f292,plain,(
% 206.94/30.98 ! [X0 : $i,X1 : $i] : ($true = (subset @ X1 @ (binunion @ X1 @ X0))) <=> (binunionLsub = $true)),
% 206.94/30.98 inference(fool_elimination,[status(thm)],[f291])).
% 206.94/30.98 thf(f291,plain,(
% 206.94/30.98 (binunionLsub = ! [X0 : $i,X1 : $i] : (subset @ X1 @ (binunion @ X1 @ X0)))),
% 206.94/30.98 inference(rectify,[status(thm)],[f106])).
% 206.94/30.98 thf(f106,axiom,(
% 206.94/30.98 (binunionLsub = ! [X4 : $i,X3 : $i] : (subset @ X3 @ (binunion @ X3 @ X4)))),
% 206.94/30.98 file('/export/starexec/sandbox/tmp/tmp.XapuwXWeE6/DTF2THF_1199.p',binunionLsub)).
% 206.94/30.98 thf(f29956,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ (binunion @ X0 @ X1)) = (binunion @ X0 @ (binintersect @ X0 @ X1)))) )),
% 206.94/30.98 inference(superposition,[status(thm)],[f9106,f28233])).
% 206.94/30.98 thf(f41474,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((binintersect @ X1 @ (binunion @ (binintersect @ X0 @ X1) @ X0)) = (binintersect @ X0 @ (binunion @ X1 @ (binintersect @ X1 @ X0))))) )),
% 206.94/30.98 inference(superposition,[status(thm)],[f31203,f31204])).
% 206.94/30.98 thf(f31204,plain,(
% 206.94/30.98 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((binintersect @ X0 @ (binunion @ X2 @ (binintersect @ X1 @ X0))) = (binunion @ (binintersect @ X0 @ X2) @ (binintersect @ X1 @ X0)))) )),
% 206.94/30.98 inference(superposition,[status(thm)],[f9106,f29062])).
% 206.94/30.98 thf(f29062,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((binintersect @ X1 @ (binintersect @ X0 @ X1)) = (binintersect @ X0 @ X1))) )),
% 206.94/30.98 inference(trivial_inequality_removal,[status(thm)],[f29061])).
% 206.94/30.98 thf(f29061,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((binintersect @ X1 @ (binintersect @ X0 @ X1)) = (binintersect @ X0 @ X1)) | ($false = $true)) )),
% 206.94/30.98 inference(forward_demodulation,[status(thm)],[f29052,f5812])).
% 206.94/30.98 thf(f29052,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((sP1490 @ $true) = $true) | ((binintersect @ X1 @ (binintersect @ X0 @ X1)) = (binintersect @ X0 @ X1))) )),
% 206.94/30.98 inference(superposition,[status(thm)],[f9027,f8991])).
% 206.94/30.98 thf(f8991,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ (binintersect @ X0 @ X1) @ X1))) )),
% 206.94/30.98 inference(trivial_inequality_removal,[status(thm)],[f8990])).
% 206.94/30.98 thf(f8990,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ (binintersect @ X0 @ X1) @ X1)) | ($false = $true)) )),
% 206.94/30.98 inference(forward_demodulation,[status(thm)],[f6247,f6246])).
% 206.94/30.98 thf(f6246,plain,(
% 206.94/30.98 ($false = (sP1769 @ $true))),
% 206.94/30.98 introduced(definition,[new_symbols(naming,[sP1769])],[inequality_splitting_name_introduction])).
% 206.94/30.98 thf(f6247,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ (binintersect @ X0 @ X1) @ X1)) | ($true = (sP1769 @ $true))) )),
% 206.94/30.98 inference(inequality_splitting,[status(thm)],[f4509,f6246])).
% 206.94/30.98 thf(f4509,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ (binintersect @ X0 @ X1) @ X1)) | ($true != $true)) )),
% 206.94/30.98 inference(definition_unfolding,[status(thm)],[f3479,f2647])).
% 206.94/30.98 thf(f2647,plain,(
% 206.94/30.98 (binintersectRsub = $true)),
% 206.94/30.98 inference(cnf_transformation,[status(thm)],[f1190])).
% 206.94/30.98 thf(f3479,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ (binintersect @ X0 @ X1) @ X1)) | (binintersectRsub != $true)) )),
% 206.94/30.98 inference(cnf_transformation,[status(thm)],[f2076])).
% 206.94/30.98 thf(f2076,plain,(
% 206.94/30.98 (! [X0 : $i,X1 : $i] : ($true = (subset @ (binintersect @ X0 @ X1) @ X1)) | (binintersectRsub != $true)) & ((binintersectRsub = $true) | ($true != (subset @ (binintersect @ sK606 @ sK607) @ sK607)))),
% 206.94/30.98 inference(skolemisation,[status(esa),new_symbols(skolem,[sK606,sK607])],[f2074,f2075])).
% 206.94/30.98 thf(f2075,plain,(
% 206.94/30.98 ? [X2 : $i,X3 : $i] : ($true != (subset @ (binintersect @ X2 @ X3) @ X3)) => ($true != (subset @ (binintersect @ sK606 @ sK607) @ sK607))),
% 206.94/30.98 introduced(definition,[],[choice_axiom])).
% 206.94/30.98 thf(f2074,plain,(
% 206.94/30.98 (! [X0 : $i,X1 : $i] : ($true = (subset @ (binintersect @ X0 @ X1) @ X1)) | (binintersectRsub != $true)) & ((binintersectRsub = $true) | ? [X2 : $i,X3 : $i] : ($true != (subset @ (binintersect @ X2 @ X3) @ X3)))),
% 206.94/30.98 inference(rectify,[status(thm)],[f2073])).
% 206.94/30.98 thf(f2073,plain,(
% 206.94/30.98 (! [X0 : $i,X1 : $i] : ($true = (subset @ (binintersect @ X0 @ X1) @ X1)) | (binintersectRsub != $true)) & ((binintersectRsub = $true) | ? [X0 : $i,X1 : $i] : ($true != (subset @ (binintersect @ X0 @ X1) @ X1)))),
% 206.94/30.98 inference(nnf_transformation,[status(thm)],[f436])).
% 206.94/30.98 thf(f436,plain,(
% 206.94/30.98 ! [X0 : $i,X1 : $i] : ($true = (subset @ (binintersect @ X0 @ X1) @ X1)) <=> (binintersectRsub = $true)),
% 206.94/30.98 inference(fool_elimination,[status(thm)],[f435])).
% 206.94/30.98 thf(f435,plain,(
% 206.94/30.98 (! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X0 @ X1) @ X1) = binintersectRsub)),
% 206.94/30.98 inference(rectify,[status(thm)],[f116])).
% 206.94/30.98 thf(f116,axiom,(
% 206.94/30.98 (! [X3 : $i,X4 : $i] : (subset @ (binintersect @ X3 @ X4) @ X4) = binintersectRsub)),
% 206.94/30.98 file('/export/starexec/sandbox/tmp/tmp.XapuwXWeE6/DTF2THF_1199.p',binintersectRsub)).
% 206.94/30.98 thf(f31203,plain,(
% 206.94/30.98 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((binintersect @ X0 @ (binunion @ (binintersect @ X1 @ X0) @ X2)) = (binunion @ (binintersect @ X1 @ X0) @ (binintersect @ X0 @ X2)))) )),
% 206.94/30.98 inference(superposition,[status(thm)],[f9106,f29062])).
% 206.94/30.98 thf(f31098,plain,(
% 206.94/30.98 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((binintersect @ X0 @ (binunion @ X2 @ (binintersect @ X0 @ X1))) = (binintersect @ X0 @ (binunion @ X2 @ X1)))) )),
% 206.94/30.98 inference(forward_demodulation,[status(thm)],[f31082,f9106])).
% 206.94/30.98 thf(f31082,plain,(
% 206.94/30.98 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((binintersect @ X0 @ (binunion @ X2 @ (binintersect @ X0 @ X1))) = (binunion @ (binintersect @ X0 @ X2) @ (binintersect @ X0 @ X1)))) )),
% 206.94/30.98 inference(superposition,[status(thm)],[f9106,f29045])).
% 206.94/30.98 thf(f29045,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = (binintersect @ X0 @ (binintersect @ X0 @ X1)))) )),
% 206.94/30.98 inference(trivial_inequality_removal,[status(thm)],[f29044])).
% 206.94/30.98 thf(f29044,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (($false = $true) | ((binintersect @ X0 @ X1) = (binintersect @ X0 @ (binintersect @ X0 @ X1)))) )),
% 206.94/30.98 inference(forward_demodulation,[status(thm)],[f29037,f5812])).
% 206.94/30.98 thf(f29037,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((sP1490 @ $true) = $true) | ((binintersect @ X0 @ X1) = (binintersect @ X0 @ (binintersect @ X0 @ X1)))) )),
% 206.94/30.98 inference(superposition,[status(thm)],[f9027,f8886])).
% 206.94/30.98 thf(f8886,plain,(
% 206.94/30.98 ( ! [X2 : $i,X3 : $i] : (($true = (subset @ (binintersect @ X3 @ X2) @ X3))) )),
% 206.94/30.98 inference(trivial_inequality_removal,[status(thm)],[f8885])).
% 206.94/30.98 thf(f8885,plain,(
% 206.94/30.98 ( ! [X2 : $i,X3 : $i] : (($true = (subset @ (binintersect @ X3 @ X2) @ X3)) | ($false = $true)) )),
% 206.94/30.98 inference(forward_demodulation,[status(thm)],[f6196,f6195])).
% 206.94/30.98 thf(f6195,plain,(
% 206.94/30.98 ($false = (sP1739 @ $true))),
% 206.94/30.98 introduced(definition,[new_symbols(naming,[sP1739])],[inequality_splitting_name_introduction])).
% 206.94/30.98 thf(f6196,plain,(
% 206.94/30.98 ( ! [X2 : $i,X3 : $i] : (($true = (subset @ (binintersect @ X3 @ X2) @ X3)) | ($true = (sP1739 @ $true))) )),
% 206.94/30.98 inference(inequality_splitting,[status(thm)],[f4478,f6195])).
% 206.94/30.98 thf(f4478,plain,(
% 206.94/30.98 ( ! [X2 : $i,X3 : $i] : (($true = (subset @ (binintersect @ X3 @ X2) @ X3)) | ($true != $true)) )),
% 206.94/30.98 inference(definition_unfolding,[status(thm)],[f3445,f2605])).
% 206.94/30.98 thf(f2605,plain,(
% 206.94/30.98 (binintersectLsub = $true)),
% 206.94/30.98 inference(cnf_transformation,[status(thm)],[f1190])).
% 206.94/30.98 thf(f3445,plain,(
% 206.94/30.98 ( ! [X2 : $i,X3 : $i] : (($true = (subset @ (binintersect @ X3 @ X2) @ X3)) | (binintersectLsub != $true)) )),
% 206.94/30.98 inference(cnf_transformation,[status(thm)],[f2035])).
% 206.94/30.98 thf(f2035,plain,(
% 206.94/30.98 ((binintersectLsub = $true) | ($true != (subset @ (binintersect @ sK581 @ sK580) @ sK581))) & (! [X2 : $i,X3 : $i] : ($true = (subset @ (binintersect @ X3 @ X2) @ X3)) | (binintersectLsub != $true))),
% 206.94/30.98 inference(skolemisation,[status(esa),new_symbols(skolem,[sK580,sK581])],[f2033,f2034])).
% 206.94/30.98 thf(f2034,plain,(
% 206.94/30.98 ? [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X1 @ X0) @ X1) != $true) => ($true != (subset @ (binintersect @ sK581 @ sK580) @ sK581))),
% 206.94/30.98 introduced(definition,[],[choice_axiom])).
% 206.94/30.98 thf(f2033,plain,(
% 206.94/30.98 ((binintersectLsub = $true) | ? [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X1 @ X0) @ X1) != $true)) & (! [X2 : $i,X3 : $i] : ($true = (subset @ (binintersect @ X3 @ X2) @ X3)) | (binintersectLsub != $true))),
% 206.94/30.98 inference(rectify,[status(thm)],[f2032])).
% 206.94/30.98 thf(f2032,plain,(
% 206.94/30.98 ((binintersectLsub = $true) | ? [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X1 @ X0) @ X1) != $true)) & (! [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X1 @ X0) @ X1) = $true) | (binintersectLsub != $true))),
% 206.94/30.98 inference(nnf_transformation,[status(thm)],[f330])).
% 206.94/30.98 thf(f330,plain,(
% 206.94/30.98 (binintersectLsub = $true) <=> ! [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X1 @ X0) @ X1) = $true)),
% 206.94/30.98 inference(fool_elimination,[status(thm)],[f329])).
% 206.94/30.98 thf(f329,plain,(
% 206.94/30.98 (! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X1 @ X0) @ X1) = binintersectLsub)),
% 206.94/30.98 inference(rectify,[status(thm)],[f111])).
% 206.94/30.98 thf(f111,axiom,(
% 206.94/30.98 (! [X4 : $i,X3 : $i] : (subset @ (binintersect @ X3 @ X4) @ X3) = binintersectLsub)),
% 206.94/30.98 file('/export/starexec/sandbox/tmp/tmp.XapuwXWeE6/DTF2THF_1199.p',binintersectLsub)).
% 206.94/30.98 thf(f45753,plain,(
% 206.94/30.98 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((binintersect @ X0 @ (binunion @ X1 @ (binintersect @ X2 @ X0))) = (binunion @ (binintersect @ X1 @ X0) @ (binintersect @ X2 @ X0)))) )),
% 206.94/30.98 inference(superposition,[status(thm)],[f31204,f41548])).
% 206.94/30.98 thf(f46071,plain,(
% 206.94/30.98 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((binunion @ (binintersect @ X2 @ X0) @ (binintersect @ X1 @ X0)) = (binintersect @ X0 @ (binunion @ (binintersect @ X2 @ X0) @ X1)))) )),
% 206.94/30.98 inference(backward_demodulation,[status(thm)],[f41047,f45886])).
% 206.94/30.98 thf(f41047,plain,(
% 206.94/30.98 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((binintersect @ X0 @ (binunion @ (binintersect @ X2 @ X0) @ (binintersect @ X1 @ X0))) = (binunion @ (binintersect @ X2 @ X0) @ (binintersect @ X1 @ X0)))) )),
% 206.94/30.98 inference(superposition,[status(thm)],[f31203,f29062])).
% 206.94/30.98 thf(f41202,plain,(
% 206.94/30.98 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((binintersect @ (binintersect @ X0 @ X1) @ (binunion @ X3 @ (binintersect @ X1 @ (binunion @ (binintersect @ X0 @ X1) @ X2)))) = (binintersect @ X0 @ X1))) )),
% 206.94/30.98 inference(superposition,[status(thm)],[f29982,f31203])).
% 206.94/30.98 thf(f29982,plain,(
% 206.94/30.98 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((binintersect @ X0 @ (binunion @ X2 @ (binunion @ X0 @ X1))) = X0)) )),
% 206.94/30.98 inference(forward_demodulation,[status(thm)],[f29953,f29976])).
% 206.94/30.98 thf(f29953,plain,(
% 206.94/30.98 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((binunion @ (binintersect @ X0 @ X2) @ X0) = (binintersect @ X0 @ (binunion @ X2 @ (binunion @ X0 @ X1))))) )),
% 206.94/30.98 inference(superposition,[status(thm)],[f9106,f29029])).
% 206.94/30.98 thf(f47529,plain,(
% 206.94/30.98 ((binintersect @ (binintersect @ sK28 @ sK29) @ (binunion @ sK30 @ (binintersect @ sK29 @ (binunion @ sK28 @ sK30)))) != (binintersect @ sK28 @ sK29)) | (~spl2119_70 | ~spl2119_299)),
% 206.94/30.98 inference(forward_demodulation,[status(thm)],[f47521,f41548])).
% 206.94/30.98 thf(f47521,plain,(
% 206.94/30.98 ((binintersect @ sK28 @ sK29) != (binintersect @ (binintersect @ sK28 @ sK29) @ (binunion @ sK30 @ (binintersect @ (binunion @ sK28 @ sK30) @ sK29)))) | (~spl2119_70 | ~spl2119_299)),
% 206.94/30.98 inference(backward_demodulation,[status(thm)],[f30896,f47394])).
% 206.94/30.98 thf(f47394,plain,(
% 206.94/30.98 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((binunion @ X1 @ (binintersect @ (binunion @ X0 @ X1) @ X2)) = (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1)))) )),
% 206.94/30.98 inference(backward_demodulation,[status(thm)],[f29949,f47385])).
% 206.94/30.98 thf(f47385,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((binunion @ X0 @ X1) = (binunion @ X1 @ X0))) )),
% 206.94/30.98 inference(forward_demodulation,[status(thm)],[f47213,f29027])).
% 206.94/30.98 thf(f29027,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((binintersect @ (binunion @ X0 @ X1) @ X0) = X0)) )),
% 206.94/30.98 inference(trivial_inequality_removal,[status(thm)],[f29026])).
% 206.94/30.98 thf(f29026,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (($false = $true) | ((binintersect @ (binunion @ X0 @ X1) @ X0) = X0)) )),
% 206.94/30.98 inference(forward_demodulation,[status(thm)],[f29024,f5812])).
% 206.94/30.98 thf(f29024,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((binintersect @ (binunion @ X0 @ X1) @ X0) = X0) | ((sP1490 @ $true) = $true)) )),
% 206.94/30.98 inference(superposition,[status(thm)],[f9027,f8573])).
% 206.94/30.98 thf(f47213,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((binunion @ X0 @ (binintersect @ (binunion @ X1 @ X0) @ X1)) = (binunion @ X1 @ X0))) )),
% 206.94/30.98 inference(superposition,[status(thm)],[f45981,f29002])).
% 206.94/30.98 thf(f29002,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((binintersect @ (binunion @ X1 @ X0) @ X0) = X0)) )),
% 206.94/30.98 inference(trivial_inequality_removal,[status(thm)],[f29001])).
% 206.94/30.98 thf(f29001,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (($false = $true) | ((binintersect @ (binunion @ X1 @ X0) @ X0) = X0)) )),
% 206.94/30.98 inference(forward_demodulation,[status(thm)],[f28997,f5812])).
% 206.94/30.98 thf(f28997,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((binintersect @ (binunion @ X1 @ X0) @ X0) = X0) | ((sP1490 @ $true) = $true)) )),
% 206.94/30.98 inference(superposition,[status(thm)],[f9027,f8122])).
% 206.94/30.98 thf(f45981,plain,(
% 206.94/30.98 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((binunion @ X0 @ (binintersect @ (binunion @ X2 @ X0) @ X1)) = (binunion @ (binintersect @ (binunion @ X0 @ X1) @ X2) @ X0))) )),
% 206.94/30.98 inference(backward_demodulation,[status(thm)],[f29948,f45946])).
% 206.94/30.98 thf(f45946,plain,(
% 206.94/30.98 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((binunion @ X1 @ (binintersect @ (binunion @ X0 @ X1) @ X2)) = (binintersect @ (binunion @ X1 @ X2) @ (binunion @ X0 @ X1)))) )),
% 206.94/30.98 inference(superposition,[status(thm)],[f29958,f41548])).
% 206.94/30.98 thf(f29958,plain,(
% 206.94/30.98 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((binunion @ X1 @ (binintersect @ (binunion @ X0 @ X1) @ X2)) = (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X1 @ X2)))) )),
% 206.94/30.98 inference(superposition,[status(thm)],[f9106,f29002])).
% 206.94/30.98 thf(f29948,plain,(
% 206.94/30.98 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X0)) = (binunion @ (binintersect @ (binunion @ X0 @ X1) @ X2) @ X0))) )),
% 206.94/30.98 inference(superposition,[status(thm)],[f9106,f29027])).
% 206.94/30.98 thf(f29949,plain,(
% 206.94/30.98 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((binunion @ (binintersect @ (binunion @ X0 @ X1) @ X2) @ X1) = (binintersect @ (binunion @ X0 @ X1) @ (binunion @ X2 @ X1)))) )),
% 206.94/30.98 inference(superposition,[status(thm)],[f9106,f29002])).
% 206.94/30.98 thf(f30896,plain,(
% 206.94/30.98 ((binintersect @ sK28 @ sK29) != (binintersect @ (binintersect @ sK28 @ sK29) @ (binintersect @ (binunion @ sK28 @ sK30) @ (binunion @ sK29 @ sK30)))) | (~spl2119_70 | ~spl2119_299)),
% 206.94/30.98 inference(trivial_inequality_removal,[status(thm)],[f30895])).
% 206.94/30.98 thf(f30895,plain,(
% 206.94/30.98 ($false = $true) | ((binintersect @ sK28 @ sK29) != (binintersect @ (binintersect @ sK28 @ sK29) @ (binintersect @ (binunion @ sK28 @ sK30) @ (binunion @ sK29 @ sK30)))) | (~spl2119_70 | ~spl2119_299)),
% 206.94/30.98 inference(forward_demodulation,[status(thm)],[f30886,f4835])).
% 206.94/30.98 thf(f4835,plain,(
% 206.94/30.98 ($false = (sP854 @ $true))),
% 206.94/30.98 introduced(definition,[new_symbols(naming,[sP854])],[inequality_splitting_name_introduction])).
% 206.94/30.98 thf(f30886,plain,(
% 206.94/30.98 ($true = (sP854 @ $true)) | ((binintersect @ sK28 @ sK29) != (binintersect @ (binintersect @ sK28 @ sK29) @ (binintersect @ (binunion @ sK28 @ sK30) @ (binunion @ sK29 @ sK30)))) | (~spl2119_70 | ~spl2119_299)),
% 206.94/30.98 inference(superposition,[status(thm)],[f4836,f30133])).
% 206.94/30.98 thf(f30133,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) | ((binintersect @ X0 @ X1) != X0)) ) | (~spl2119_70 | ~spl2119_299)),
% 206.94/30.98 inference(trivial_inequality_removal,[status(thm)],[f30132])).
% 206.94/30.98 thf(f30132,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) | ((binintersect @ X0 @ X1) != X0) | ($false = $true)) ) | (~spl2119_70 | ~spl2119_299)),
% 206.94/30.98 inference(forward_demodulation,[status(thm)],[f30125,f5951])).
% 206.94/30.98 thf(f5951,plain,(
% 206.94/30.98 ($false = (sP1575 @ $true))),
% 206.94/30.98 introduced(definition,[new_symbols(naming,[sP1575])],[inequality_splitting_name_introduction])).
% 206.94/30.98 thf(f30125,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (($true = (sP1575 @ $true)) | ((binintersect @ X0 @ X1) != X0) | ($true = (in @ X0 @ (powerset @ X1)))) ) | (~spl2119_70 | ~spl2119_299)),
% 206.94/30.98 inference(superposition,[status(thm)],[f7420,f8430])).
% 206.94/30.98 thf(f8430,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ((binintersect @ X0 @ X1) != X0)) ) | ~spl2119_299),
% 206.94/30.98 inference(avatar_component_clause,[status(thm)],[f8429])).
% 206.94/30.98 thf(f8429,definition,(
% 206.94/30.98 spl2119_299 <=> ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ((binintersect @ X0 @ X1) != X0))),
% 206.94/30.98 introduced(definition,[new_symbols(naming,[spl2119_299])],[avatar_definition])).
% 206.94/30.98 thf(f7420,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (($true = (sP1575 @ (subset @ X1 @ X0))) | ($true = (in @ X1 @ (powerset @ X0)))) ) | ~spl2119_70),
% 206.94/30.98 inference(avatar_component_clause,[status(thm)],[f7419])).
% 206.94/30.98 thf(f7419,definition,(
% 206.94/30.98 spl2119_70 <=> ! [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (powerset @ X0))) | ($true = (sP1575 @ (subset @ X1 @ X0))))),
% 206.94/30.98 introduced(definition,[new_symbols(naming,[spl2119_70])],[avatar_definition])).
% 206.94/30.98 thf(f4836,plain,(
% 206.94/30.98 ((sP854 @ (in @ (binintersect @ sK28 @ sK29) @ (powerset @ (binintersect @ (binunion @ sK28 @ sK30) @ (binunion @ sK29 @ sK30))))) = $true)),
% 206.94/30.98 inference(inequality_splitting,[status(thm)],[f2480,f4835])).
% 206.94/30.98 thf(f2480,plain,(
% 206.94/30.98 ($true != (in @ (binintersect @ sK28 @ sK29) @ (powerset @ (binintersect @ (binunion @ sK28 @ sK30) @ (binunion @ sK29 @ sK30)))))),
% 206.94/30.98 inference(cnf_transformation,[status(thm)],[f1190])).
% 206.94/30.98 thf(f9546,plain,(
% 206.94/30.98 ~spl2119_69),
% 206.94/30.98 inference(avatar_contradiction_clause,[status(thm)],[f9545])).
% 206.94/30.98 thf(f9545,plain,(
% 206.94/30.98 $false | ~spl2119_69),
% 206.94/30.98 inference(trivial_inequality_removal,[status(thm)],[f9544])).
% 206.94/30.98 thf(f9544,plain,(
% 206.94/30.98 ($false = $true) | ~spl2119_69),
% 206.94/30.98 inference(forward_demodulation,[status(thm)],[f7417,f5952])).
% 206.94/30.98 thf(f5952,plain,(
% 206.94/30.98 ($false = (sP1576 @ $true))),
% 206.94/30.98 introduced(definition,[new_symbols(naming,[sP1576])],[inequality_splitting_name_introduction])).
% 206.94/30.98 thf(f7417,plain,(
% 206.94/30.98 ($true = (sP1576 @ $true)) | ~spl2119_69),
% 206.94/30.98 inference(avatar_component_clause,[status(thm)],[f7415])).
% 206.94/30.98 thf(f7415,definition,(
% 206.94/30.98 spl2119_69 <=> ($true = (sP1576 @ $true))),
% 206.94/30.98 introduced(definition,[new_symbols(naming,[spl2119_69])],[avatar_definition])).
% 206.94/30.98 thf(f9194,plain,(
% 206.94/30.98 ~spl2119_298),
% 206.94/30.98 inference(avatar_contradiction_clause,[status(thm)],[f9193])).
% 206.94/30.98 thf(f9193,plain,(
% 206.94/30.98 $false | ~spl2119_298),
% 206.94/30.98 inference(trivial_inequality_removal,[status(thm)],[f9192])).
% 206.94/30.98 thf(f9192,plain,(
% 206.94/30.98 ($false = $true) | ~spl2119_298),
% 206.94/30.98 inference(forward_demodulation,[status(thm)],[f8427,f5870])).
% 206.94/30.98 thf(f5870,plain,(
% 206.94/30.98 ($false = (sP1526 @ $true))),
% 206.94/30.98 introduced(definition,[new_symbols(naming,[sP1526])],[inequality_splitting_name_introduction])).
% 206.94/30.98 thf(f8427,plain,(
% 206.94/30.98 ((sP1526 @ $true) = $true) | ~spl2119_298),
% 206.94/30.98 inference(avatar_component_clause,[status(thm)],[f8425])).
% 206.94/30.98 thf(f8425,definition,(
% 206.94/30.98 spl2119_298 <=> ((sP1526 @ $true) = $true)),
% 206.94/30.98 introduced(definition,[new_symbols(naming,[spl2119_298])],[avatar_definition])).
% 206.94/30.98 thf(f8431,plain,(
% 206.94/30.98 spl2119_298 | spl2119_299),
% 206.94/30.98 inference(avatar_split_clause,[status(thm)],[f5871,f8429,f8425])).
% 206.94/30.98 thf(f5871,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ((sP1526 @ $true) = $true) | ((binintersect @ X0 @ X1) != X0)) )),
% 206.94/30.98 inference(inequality_splitting,[status(thm)],[f4301,f5870])).
% 206.94/30.98 thf(f4301,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ((binintersect @ X0 @ X1) != X0) | ($true != $true)) )),
% 206.94/30.98 inference(definition_unfolding,[status(thm)],[f3262,f2598])).
% 206.94/30.98 thf(f2598,plain,(
% 206.94/30.98 (binintersectSubset1 = $true)),
% 206.94/30.98 inference(cnf_transformation,[status(thm)],[f1190])).
% 206.94/30.98 thf(f3262,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ((binintersect @ X0 @ X1) != X0) | (binintersectSubset1 != $true)) )),
% 206.94/30.98 inference(cnf_transformation,[status(thm)],[f1820])).
% 206.94/30.98 thf(f1820,plain,(
% 206.94/30.98 (! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ((binintersect @ X0 @ X1) != X0)) | (binintersectSubset1 != $true)) & ((binintersectSubset1 = $true) | (($true != (subset @ sK434 @ sK435)) & (sK434 = (binintersect @ sK434 @ sK435))))),
% 206.94/30.98 inference(skolemisation,[status(esa),new_symbols(skolem,[sK434,sK435])],[f1818,f1819])).
% 206.94/30.98 thf(f1819,plain,(
% 206.94/30.98 ? [X2 : $i,X3 : $i] : (($true != (subset @ X2 @ X3)) & ((binintersect @ X2 @ X3) = X2)) => (($true != (subset @ sK434 @ sK435)) & (sK434 = (binintersect @ sK434 @ sK435)))),
% 206.94/30.98 introduced(definition,[],[choice_axiom])).
% 206.94/30.98 thf(f1818,plain,(
% 206.94/30.98 (! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ((binintersect @ X0 @ X1) != X0)) | (binintersectSubset1 != $true)) & ((binintersectSubset1 = $true) | ? [X2 : $i,X3 : $i] : (($true != (subset @ X2 @ X3)) & ((binintersect @ X2 @ X3) = X2)))),
% 206.94/30.98 inference(rectify,[status(thm)],[f1817])).
% 206.94/30.98 thf(f1817,plain,(
% 206.94/30.98 (! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ((binintersect @ X0 @ X1) != X0)) | (binintersectSubset1 != $true)) & ((binintersectSubset1 = $true) | ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) & ((binintersect @ X0 @ X1) = X0)))),
% 206.94/30.98 inference(nnf_transformation,[status(thm)],[f1135])).
% 206.94/30.98 thf(f1135,plain,(
% 206.94/30.98 ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ((binintersect @ X0 @ X1) != X0)) <=> (binintersectSubset1 = $true)),
% 206.94/30.98 inference(ennf_transformation,[status(thm)],[f681])).
% 206.94/30.98 thf(f681,plain,(
% 206.94/30.98 ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X0) => ((subset @ X0 @ X1) = $true)) <=> (binintersectSubset1 = $true)),
% 206.94/30.98 inference(fool_elimination,[status(thm)],[f680])).
% 206.94/30.98 thf(f680,plain,(
% 206.94/30.98 (binintersectSubset1 = ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X0) => (subset @ X0 @ X1)))),
% 206.94/30.98 inference(rectify,[status(thm)],[f118])).
% 206.94/30.98 thf(f118,axiom,(
% 206.94/30.98 (binintersectSubset1 = ! [X3 : $i,X4 : $i] : (((binintersect @ X3 @ X4) = X3) => (subset @ X3 @ X4)))),
% 206.94/30.98 file('/export/starexec/sandbox/tmp/tmp.XapuwXWeE6/DTF2THF_1199.p',binintersectSubset1)).
% 206.94/30.98 thf(f7421,plain,(
% 206.94/30.98 spl2119_69 | spl2119_70),
% 206.94/30.98 inference(avatar_split_clause,[status(thm)],[f5953,f7419,f7415])).
% 206.94/30.98 thf(f5953,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (powerset @ X0))) | ($true = (sP1575 @ (subset @ X1 @ X0))) | ($true = (sP1576 @ $true))) )),
% 206.94/30.98 inference(inequality_splitting,[status(thm)],[f4347,f5952,f5951])).
% 206.94/30.98 thf(f4347,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) | ($true = (in @ X1 @ (powerset @ X0))) | ($true != $true)) )),
% 206.94/30.98 inference(definition_unfolding,[status(thm)],[f3308,f2589])).
% 206.94/30.98 thf(f2589,plain,(
% 206.94/30.98 (powersetI1 = $true)),
% 206.94/30.98 inference(cnf_transformation,[status(thm)],[f1190])).
% 206.94/30.98 thf(f3308,plain,(
% 206.94/30.98 ( ! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) | ($true = (in @ X1 @ (powerset @ X0))) | (powersetI1 != $true)) )),
% 206.94/30.98 inference(cnf_transformation,[status(thm)],[f1880])).
% 206.94/30.98 thf(f1880,plain,(
% 206.94/30.98 (! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) | ($true = (in @ X1 @ (powerset @ X0)))) | (powersetI1 != $true)) & ((powersetI1 = $true) | (((subset @ sK471 @ sK470) = $true) & ((in @ sK471 @ (powerset @ sK470)) != $true)))),
% 206.94/30.98 inference(skolemisation,[status(esa),new_symbols(skolem,[sK470,sK471])],[f1878,f1879])).
% 206.94/30.98 thf(f1879,plain,(
% 206.94/30.98 ? [X2 : $i,X3 : $i] : (($true = (subset @ X3 @ X2)) & ((in @ X3 @ (powerset @ X2)) != $true)) => (((subset @ sK471 @ sK470) = $true) & ((in @ sK471 @ (powerset @ sK470)) != $true))),
% 206.94/30.98 introduced(definition,[],[choice_axiom])).
% 206.94/30.98 thf(f1878,plain,(
% 206.94/30.98 (! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) | ($true = (in @ X1 @ (powerset @ X0)))) | (powersetI1 != $true)) & ((powersetI1 = $true) | ? [X2 : $i,X3 : $i] : (($true = (subset @ X3 @ X2)) & ((in @ X3 @ (powerset @ X2)) != $true)))),
% 206.94/30.98 inference(rectify,[status(thm)],[f1877])).
% 206.94/30.98 thf(f1877,plain,(
% 206.94/30.98 (! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) | ($true = (in @ X1 @ (powerset @ X0)))) | (powersetI1 != $true)) & ((powersetI1 = $true) | ? [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) & ($true != (in @ X1 @ (powerset @ X0)))))),
% 206.94/30.98 inference(nnf_transformation,[status(thm)],[f905])).
% 206.94/30.98 thf(f905,plain,(
% 206.94/30.98 ! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) | ($true = (in @ X1 @ (powerset @ X0)))) <=> (powersetI1 = $true)),
% 206.94/30.98 inference(ennf_transformation,[status(thm)],[f338])).
% 206.94/30.98 thf(f338,plain,(
% 206.94/30.98 (powersetI1 = $true) <=> ! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) => ($true = (in @ X1 @ (powerset @ X0))))),
% 206.94/30.98 inference(fool_elimination,[status(thm)],[f337])).
% 206.94/30.98 thf(f337,plain,(
% 206.94/30.98 (powersetI1 = ! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0))))),
% 206.94/30.98 inference(rectify,[status(thm)],[f95])).
% 206.94/30.98 thf(f95,axiom,(
% 206.94/30.98 (powersetI1 = ! [X3 : $i,X4 : $i] : ((subset @ X4 @ X3) => (in @ X4 @ (powerset @ X3))))),
% 206.94/30.98 file('/export/starexec/sandbox/tmp/tmp.XapuwXWeE6/DTF2THF_1199.p',powersetI1)).
% 206.94/30.98 % SZS output end Proof for DTF2THF_1199
% 206.94/30.98 % (1817)------------------------------
% 206.94/30.98 % (1817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 206.94/30.98 % (1817)Termination reason: Refutation
% 206.94/30.98
% 206.94/30.98 % (1817)Memory used [KB]: 35564
% 206.94/30.98 % (1817)Time elapsed: 3.656 s
% 206.94/30.98 % (1817)Instructions burned: 11489 (million)
% 206.94/30.98 % (1817)------------------------------
% 206.94/30.98 % (1817)------------------------------
% 206.94/30.98 % (1298)Success in time 29.162 s
%------------------------------------------------------------------------------