%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU775^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:37:05 AM UTC 2026
% Result : Theorem 13.03s 3.04s
% Output : Refutation 13.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 4545 (1212 equ; 0 cnn)
% Maximal formula atoms : 293 ( 142 avg)
% Number of connectives : 2321 ( 21 ~; 8 |; 881 &; 240 @)
% ( 1 <=>;1170 =>; 0 <=; 0 <~>)
% Maximal formula depth : 299 ( 67 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 597 ( 594 usr; 297 con; 0-4 aty)
% Number of variables : 113 ( 60 ^; 38 !; 15 ?; 113 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_184,type,
atmost1p: $i > $o ).
thf(func_def_185,type,
atleast2p: $i > $o ).
thf(func_def_186,type,
atmost2p: $i > $o ).
thf(func_def_187,type,
upairsetp: $i > $o ).
thf(func_def_191,type,
kfst: $i > $i ).
thf(func_def_203,type,
ksnd: $i > $i ).
thf(func_def_213,type,
breln: $i > $i > $i > $o ).
thf(func_def_214,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_222,type,
func: $i > $i > $i > $o ).
thf(func_def_223,type,
funcSet: $i > $i > $i ).
thf(func_def_226,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_232,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_259,type,
if: $i > $o > $i > $i > $i ).
thf(func_def_323,type,
breln1: $i > $i > $o ).
thf(func_def_325,type,
breln1Set: $i > $i ).
thf(func_def_327,type,
transitive: $i > $i > $o ).
thf(func_def_328,type,
antisymmetric: $i > $i > $o ).
thf(func_def_329,type,
reflexive: $i > $i > $o ).
thf(func_def_330,type,
refltransitive: $i > $i > $o ).
thf(func_def_331,type,
refllinearorder: $i > $i > $o ).
thf(func_def_332,type,
reflwellordering: $i > $i > $o ).
thf(func_def_338,type,
breln1invset: $i > $i > $i ).
thf(func_def_352,type,
sP0: $i > $i > $i > $o ).
thf(func_def_353,type,
sP1: $i > $i > $o ).
thf(func_def_354,type,
sP2: $i > $i > $o ).
thf(func_def_355,type,
sP3: $i > $i > $o ).
thf(func_def_356,type,
sP4: $i > $i > $o ).
thf(func_def_357,type,
sP5: $i > $o ).
thf(func_def_359,type,
sP7: $i > $i > $i > $o > $o ).
thf(func_def_360,type,
sP8: $o > $i > $i > $i > $o ).
thf(func_def_363,type,
sP11: $i > $i > $i > $i > $o ).
thf(func_def_364,type,
sP12: $i > $i > $i > $i > $o ).
thf(func_def_365,type,
sP13: $o > $i > $i > $o ).
thf(func_def_366,type,
sP14: $i > $i > $i > $o ).
thf(func_def_367,type,
sP15: $i > $i > $i > $o ).
thf(func_def_370,type,
sP18: $i > $i > $o ).
thf(func_def_372,type,
sP20: ( $i > $o ) > $i > $o ).
thf(func_def_373,type,
sP21: ( $i > $o ) > $i > $i > $o ).
thf(func_def_375,type,
sP23: $i > $i > $i > $i > $o ).
thf(func_def_376,type,
sP24: $i > $o > $i > $o ).
thf(func_def_377,type,
sP25: $i > $i > $i > $o ).
thf(func_def_378,type,
sP26: $i > ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_379,type,
sP27: ( $i > $o ) > $i > $o ).
thf(func_def_381,type,
sP29: $i > ( $i > $o ) > $o ).
thf(func_def_382,type,
sP30: $i > ( $i > $o ) > $i > $o ).
thf(func_def_383,type,
sP31: $i > ( $i > $o ) > $o ).
thf(func_def_385,type,
sP33: ( $i > $o ) > $i > $o ).
thf(func_def_386,type,
sP34: $i > $i > ( $i > $o ) > $i > $o ).
thf(func_def_389,type,
sP37: $i > $i > $i > $o ).
thf(func_def_390,type,
sP38: $i > ( $i > $i > $o ) > $i > $o ).
thf(func_def_391,type,
sP39: $i > ( $i > $i > $o ) > $o ).
thf(func_def_393,type,
sP41: ( $i > $o ) > $o ).
thf(func_def_394,type,
sP42: $i > ( $i > $o ) > $o ).
thf(func_def_396,type,
sP44: $i > $i > $i > $o ).
thf(func_def_397,type,
sP45: $i > $i > $o > $o ).
thf(func_def_399,type,
sP47: $i > ( $i > $o ) > $o ).
thf(func_def_400,type,
sP48: ( $i > $o ) > $i > $o ).
thf(func_def_401,type,
sP49: $i > $i > $i > $o ).
thf(func_def_402,type,
sP50: $i > $i > $i > $o ).
thf(func_def_404,type,
sP52: $i > ( $i > $o ) > $o ).
thf(func_def_406,type,
sP54: ( $i > $o ) > $o ).
thf(func_def_407,type,
sP55: $i > ( $i > $o ) > $o ).
thf(func_def_408,type,
sP56: $i > ( $i > $o ) > $o ).
thf(func_def_409,type,
sP57: ( $i > $o ) > $i > $o ).
thf(func_def_411,type,
sP59: ( $i > $o ) > $o ).
thf(func_def_412,type,
sP60: $i > $i > $i > $o ).
thf(func_def_414,type,
sP62: $i > $i > $i > $i > $o ).
thf(func_def_415,type,
sP63: $i > $i > $i > $o ).
thf(func_def_416,type,
sP64: $i > $i > $o ).
thf(func_def_418,type,
sP66: ( $i > $o ) > $i > $o ).
thf(func_def_419,type,
sP67: $i > $i > ( $i > $o ) > $i > $o ).
thf(func_def_420,type,
sP68: $i > ( $i > $i ) > $i > $o ).
thf(func_def_423,type,
sP71: ( $i > $o ) > $o ).
thf(func_def_424,type,
sP72: $i > ( $i > $o ) > $i > $o ).
thf(func_def_425,type,
sP73: $i > ( $i > $o ) > $o ).
thf(func_def_428,type,
sP76: $i > $i > $o ).
thf(func_def_430,type,
sP78: $i > $i > ( $i > $i ) > $o ).
thf(func_def_433,type,
sP81: $i > $o ).
thf(func_def_434,type,
sP82: $i > $o ).
thf(func_def_435,type,
sP83: $i > $i > $i > $o ).
thf(func_def_436,type,
sP84: $i > ( $i > $i > $o ) > $i > $o ).
thf(func_def_437,type,
sP85: $i > $i > ( $i > $i > $o ) > $o ).
thf(func_def_438,type,
sP86: $i > $o ).
thf(func_def_439,type,
sP87: $i > $i > $i > $o ).
thf(func_def_440,type,
sP88: $o > $i > $i > $o ).
thf(func_def_441,type,
sP89: $i > $i > $i > $o ).
thf(func_def_442,type,
sP90: ( $i > $o ) > $o ).
thf(func_def_443,type,
sP91: $i > $i > $i > $o ).
thf(func_def_444,type,
sP92: $i > $i > $i > $o ).
thf(func_def_456,type,
sK104: $i > $i ).
thf(func_def_457,type,
sK105: $i > $i ).
thf(func_def_458,type,
sK106: $i > $i ).
thf(func_def_459,type,
sK107: $i > $i ).
thf(func_def_460,type,
sK108: $i > $i > $i ).
thf(func_def_461,type,
sK109: $i > $i > $i ).
thf(func_def_462,type,
sK110: $i > $i > $i > $i ).
thf(func_def_463,type,
sK111: $i > $i > $i ).
thf(func_def_464,type,
sK112: $i > $i > $i ).
thf(func_def_465,type,
sK113: $i > $i > $i ).
thf(func_def_466,type,
sK114: $i > $i > $i ).
thf(func_def_467,type,
sK115: $i > $i > $i ).
thf(func_def_468,type,
sK116: $i > $i > $i ).
thf(func_def_469,type,
sK117: $i > $i > $i ).
thf(func_def_470,type,
sK118: $i > $i > $i ).
thf(func_def_471,type,
sK119: $i > $i > $i > $i ).
thf(func_def_472,type,
sK120: $i > $i > $i > $i ).
thf(func_def_474,type,
sK122: $i > $i ).
thf(func_def_481,type,
sK129: $i > $o ).
thf(func_def_482,type,
sK130: $i > $o ).
thf(func_def_483,type,
sK131: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_484,type,
sK132: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_502,type,
sK150: $i > $i ).
thf(func_def_525,type,
sK173: $i > $i > $i ).
thf(func_def_548,type,
sK196: $i > $i > $o ).
thf(func_def_562,type,
sK210: $i > $i > $i ).
thf(func_def_579,type,
sK227: $i > $i > $o ).
thf(func_def_584,type,
sK232: $i > $i > $i > $i > $i ).
thf(func_def_585,type,
sK233: $i > $i > $i > $i > $i ).
thf(func_def_586,type,
sK234: $i > $i > $i > $i > $i ).
thf(func_def_587,type,
sK235: $i > $i > $i > $i > $i ).
thf(func_def_605,type,
sK253: $i > $i > $i > $o ).
thf(func_def_609,type,
sK257: $i > $i > $i > $i ).
thf(func_def_610,type,
sK258: $i > $i > $i > $i ).
thf(func_def_614,type,
sK262: $i > $i > $o ).
thf(func_def_621,type,
sK269: $i > $i ).
thf(func_def_622,type,
sK270: ( $i > $i ) > $i > $i > $i ).
thf(func_def_643,type,
sK291: $i > $i > $o ).
thf(func_def_656,type,
sK304: $i > $i ).
thf(func_def_657,type,
sK305: ( $i > $i ) > $i > $i > $i ).
thf(func_def_659,type,
sK307: $i > $i > $o ).
thf(func_def_675,type,
sK323: $i > $o ).
thf(func_def_681,type,
sK329: $i > $o ).
thf(func_def_693,type,
sK341: $i > $i > $i ).
thf(func_def_694,type,
sK342: $i > $i > $i ).
thf(func_def_699,type,
sK347: ( $i > $o ) > $i > $i > $i ).
thf(func_def_700,type,
sK348: ( $i > $o ) > $i > $i > $i ).
thf(func_def_701,type,
sK349: ( $i > $o ) > $i > $i ).
thf(func_def_704,type,
sK352: $i > $o ).
thf(func_def_707,type,
sK355: $i > $i > $i ).
thf(func_def_722,type,
sK370: $i > $i > $i > $i > $i ).
thf(func_def_723,type,
sK371: $i > $i > $i > $i > $i ).
thf(func_def_728,type,
sK376: $i > $o > $i > $i ).
thf(func_def_741,type,
sK389: $i > $i > $i > $i ).
thf(func_def_742,type,
sK390: $i > $i > $i > $i > $i ).
thf(func_def_746,type,
sK394: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(func_def_747,type,
sK395: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(func_def_750,type,
sK398: $i > $o ).
thf(func_def_751,type,
sK399: $i > $o ).
thf(func_def_755,type,
sK403: $i > $i > $o ).
thf(func_def_771,type,
sK419: $i > $o ).
thf(func_def_772,type,
sK420: ( $i > $o ) > $i > $i ).
thf(func_def_773,type,
sK421: ( $i > $o ) > $i > $i ).
thf(func_def_776,type,
sK424: $i > $i > $o ).
thf(func_def_789,type,
sK437: $i > ( $i > $o ) > $i > $i ).
thf(func_def_790,type,
sK438: $i > ( $i > $o ) > $i > $i ).
thf(func_def_791,type,
sK439: $i > ( $i > $o ) > $i ).
thf(func_def_794,type,
sK442: $i > $o ).
thf(func_def_799,type,
sK447: $i > $o ).
thf(func_def_801,type,
sK449: $i > ( $i > $o ) > $i ).
thf(func_def_802,type,
sK450: $i > ( $i > $o ) > $i ).
thf(func_def_823,type,
sK471: $i > $i ).
thf(func_def_827,type,
sK475: $i > $o ).
thf(func_def_828,type,
sK476: $i > $i > ( $i > $o ) > $i > $i ).
thf(func_def_829,type,
sK477: $i > $i > ( $i > $o ) > $i > $i ).
thf(func_def_830,type,
sK478: ( $i > $o ) > $i > $i ).
thf(func_def_834,type,
sK482: $i > $o ).
thf(func_def_853,type,
sK501: $i > $i ).
thf(func_def_854,type,
sK502: ( $i > $i ) > $i > $i > $i ).
thf(func_def_857,type,
sK505: $i > $o ).
thf(func_def_859,type,
sK507: $i > ( $i > $o ) > $i ).
thf(func_def_866,type,
sK514: $i > $o ).
thf(func_def_867,type,
sK515: $i > $i > $i > $i ).
thf(func_def_868,type,
sK516: $i > $i > $i > $i > $i ).
thf(func_def_888,type,
sK536: $i > $i ).
thf(func_def_893,type,
sK541: $i > $o ).
thf(func_def_900,type,
sK548: $i > $o ).
thf(func_def_926,type,
sK574: $i > $i > $o ).
thf(func_def_927,type,
sK575: ( $i > $i > $o ) > $i > $i ).
thf(func_def_928,type,
sK576: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_929,type,
sK577: $i > ( $i > $i > $o ) > $i ).
thf(func_def_930,type,
sK578: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_932,type,
sK580: $i > $o ).
thf(func_def_937,type,
sK585: $i > $i ).
thf(func_def_954,type,
sK602: $i > $o ).
thf(func_def_964,type,
sK612: $i > $o ).
thf(func_def_971,type,
sK619: ( $i > $o ) > $i ).
thf(func_def_972,type,
sK620: ( $i > $o ) > $i ).
thf(func_def_973,type,
sK621: $i > $o ).
thf(func_def_978,type,
sK626: $i > $i > $o ).
thf(func_def_981,type,
sK629: $i > $o ).
thf(func_def_1005,type,
sK653: $i > $o ).
thf(func_def_1006,type,
sK654: ( $i > $o ) > $i > $i ).
thf(func_def_1007,type,
sK655: $i > ( $i > $o ) > $i ).
thf(func_def_1008,type,
sK656: $i > $i > $i > $i ).
thf(func_def_1020,type,
sK668: ( $i > $o ) > $i > $i ).
thf(func_def_1021,type,
sK669: ( $i > $o ) > $i > $i ).
thf(func_def_1022,type,
sK670: $i > ( $i > $o ) > $i ).
thf(func_def_1024,type,
sK672: $i > $o ).
thf(func_def_1039,type,
sK687: $i > $i > $i > $i ).
thf(func_def_1040,type,
sK688: $i > $i > $i > $i ).
thf(func_def_1057,type,
sK705: $i > $i > $i ).
thf(func_def_1058,type,
sK706: $i > $o ).
thf(func_def_1060,type,
sK708: $i > ( $i > $o ) > $i ).
thf(func_def_1061,type,
sK709: $i > ( $i > $o ) > $i ).
thf(func_def_1067,type,
sK715: ( $i > $o ) > $i ).
thf(func_def_1068,type,
sK716: $i > ( $i > $o ) > $i ).
thf(func_def_1069,type,
sK717: $i > $o ).
thf(func_def_1079,type,
sK727: $i > ( $i > $o ) > $i ).
thf(func_def_1080,type,
sK728: $i > ( $i > $o ) > $i ).
thf(func_def_1081,type,
sK729: $i > ( $i > $o ) > $i ).
thf(func_def_1082,type,
sK730: $i > $o ).
thf(func_def_1085,type,
sK733: $i > $o ).
thf(func_def_1086,type,
sK734: ( $i > $o ) > $i > $i ).
thf(func_def_1087,type,
sK735: ( $i > $o ) > $i > $i ).
thf(func_def_1090,type,
sK738: $i > $o ).
thf(func_def_1091,type,
sK739: ( $i > $o ) > $i ).
thf(func_def_1101,type,
sK749: $i > ( $i > $o ) > $i ).
thf(func_def_1102,type,
sK750: ( $i > $o ) > $i ).
thf(func_def_1103,type,
sK751: $i > $o ).
thf(func_def_1126,type,
sK774: $i > $i > $i > $i ).
thf(func_def_1127,type,
sK775: $i > $i > $i > $i > $i ).
thf(func_def_1128,type,
sK776: $i > $i > $i > $i > $i ).
thf(func_def_1129,type,
sK777: $i > $i > $i > $i > $i ).
thf(func_def_1135,type,
sK783: $i > $i > $i ).
thf(func_def_1141,type,
sK789: $i > $i > $i ).
thf(func_def_1147,type,
sK795: $i > $i > ( $i > $o ) > $i > $i ).
thf(func_def_1148,type,
sK796: $i > $i > ( $i > $o ) > $i > $i ).
thf(func_def_1149,type,
sK797: ( $i > $o ) > $i > $i ).
thf(func_def_1153,type,
sK801: $i > $o ).
thf(func_def_1174,type,
sK822: $i > $i ).
thf(func_def_1176,type,
sK824: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1177,type,
sK825: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1206,type,
sK854: $i > $i > $i ).
thf(func_def_1212,type,
sK860: ( $i > $o ) > $i ).
thf(func_def_1213,type,
sK861: $i > ( $i > $o ) > $i ).
thf(func_def_1214,type,
sK862: $i > $o ).
thf(func_def_1220,type,
sK868: $i > ( $i > $o ) > $i > $i ).
thf(func_def_1222,type,
sK870: $i > $o ).
thf(func_def_1226,type,
sK874: $i > $o ).
thf(func_def_1228,type,
sK876: $i > ( $i > $o ) > $i ).
thf(func_def_1229,type,
sK877: $i > ( $i > $o ) > $i ).
thf(func_def_1236,type,
sK884: $i > $o ).
thf(func_def_1237,type,
sK885: $i > $i ).
thf(func_def_1240,type,
sK888: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1243,type,
sK891: $i > $i > $i ).
thf(func_def_1266,type,
sK914: $i > $i ).
thf(func_def_1268,type,
sK916: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1269,type,
sK917: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1293,type,
sK941: $i > $o ).
thf(func_def_1294,type,
sK942: $i > $o ).
thf(func_def_1295,type,
sK943: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1296,type,
sK944: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1297,type,
sK945: $i > $o ).
thf(func_def_1302,type,
sK950: $i > $i ).
thf(func_def_1303,type,
sK951: $i > $i ).
thf(func_def_1309,type,
sK957: $i > $i > $i > $i ).
thf(func_def_1322,type,
sK970: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_1323,type,
sK971: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_1324,type,
sK972: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_1325,type,
sK973: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_1328,type,
sK976: $i > $i > $o ).
thf(func_def_1339,type,
sK987: $i > $i > $i ).
thf(func_def_1340,type,
sK988: $i > $i ).
thf(func_def_1349,type,
sK997: $i > $i > $i > $i ).
thf(func_def_1350,type,
sK998: $i > $i > $i > $i ).
thf(func_def_1362,type,
sK1010: $i > $i > $i > $o ).
thf(func_def_1363,type,
sK1011: $i > $i > $i > $i ).
thf(func_def_1367,type,
sK1015: $i > ( $i > $o ) > $i ).
thf(func_def_1368,type,
sK1016: ( $i > $o ) > $i ).
thf(func_def_1369,type,
sK1017: $i > $o ).
thf(func_def_1370,type,
sK1018: $i > $i > $i > $i ).
thf(func_def_1371,type,
sK1019: $i > $i > $i > $i ).
thf(func_def_1372,type,
sK1020: $i > $i > $i > $i ).
thf(func_def_1373,type,
sK1021: $i > $i > $i > $i ).
thf(func_def_1387,type,
sK1035: $i > $o ).
thf(func_def_1390,type,
ph1038:
!>[X0: $tType] : X0 ).
thf(f11829,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f6264,f5973]) ).
thf(f5973,plain,
! [X2: $i,X0: $i > $i > $o,X1: $i] :
( $true
= ( breln @ X1 @ X2 @ ( dpsetconstr @ X1 @ X2 @ X0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f5972]) ).
thf(f5972,plain,
! [X2: $i,X0: $i > $i > $o,X1: $i] :
( $true
= ( breln @ X1 @ X2
@ ( dpsetconstr @ X1 @ X2
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f5183]) ).
thf(f5183,plain,
! [X2: $i,X0: $i > $i > $o,X1: $i] :
( ( $true
= ( breln @ X1 @ X2
@ ( dpsetconstr @ X1 @ X2
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f3585,f4420]) ).
thf(f4420,plain,
setOfPairsIsBReln = $true,
inference(cnf_transformation,[status(thm)],[f2811]) ).
thf(f2811,plain,
( ( iftrueorfalse = $true )
& ( powersetI = $true )
& ( demorgan2a = $true )
& ( ksndpairEq = $true )
& ( subset2powerset = $true )
& ( kpairp = $true )
& ( complementTI1 = $true )
& ( setminusSubset2 = $true )
& ( binunionTILcontra = $true )
& ( demorgan2a2 = $true )
& ( binintersectER = $true )
& ( powersetTI1 = $true )
& ( setbeta = $true )
& ( symdiffIneg1 = $true )
& ( notequalI1 = $true )
& ( upairsetE = $true )
& ( setadjoinSub2 = $true )
& ( funcext = $true )
& ( demorgan1b = $true )
& ( omegaIndAx = $true )
& ( setunionAx = $true )
& ( iftrue = $true )
& ( subbreln = $true )
& ( cartprodsndin = $true )
& ( woz1_5 = $true )
& ( doubleComplementE1 = $true )
& ( setunionI = $true )
& ( woz13rule2 = $true )
& ( foundationAx = $true )
& ( complementT_lem = $true )
& ( in__Cong = $true )
& ( woz1_2 = $true )
& ( notsubsetI = $true )
& ( nonemptyImpWitness = $true )
& ( eqinunit = $true )
& ( setOfPairsIsBReln1 = $true )
& ( subsetE2 = $true )
& ( complementTE1 = $true )
& ( binunionIR = $true )
& ( inIntersectImpInUnion = $true )
& ( complementSubsetComplementIntersect = $true )
& ( notequalI2 = $true )
& ( app = $true )
& ( complementImpComplementIntersect = $true )
& ( cartprodsndpairEq = $true )
& ( eqbreln1 = $true )
& ( cartprodfstpairEq = $true )
& ( complementUnionInPowersetComplement = $true )
& ( exuE3u = $true )
& ( noeltsimpempty = $true )
& ( binunionTEcontra = $true )
& ( secondinupair = $true )
& ( powersetAx = $true )
& ( binunionIL = $true )
& ( setminusER = $true )
& ( wellorderingAx = $true )
& ( dpsetconstrER = $true )
& ( powersetE = $true )
& ( binintersectTELcontra = $true )
& ( demorgan1 = $true )
& ( beta1 = $true )
& ( sepSubset = $true )
& ( setadjoinOr = $true )
& ( setukpairinjR = $true )
& ( setextAx = $true )
& ( eta2 = $true )
& ( choice2fnsingleton = $true )
& ( breln1all2 = $true )
& ( exuE2 = $true )
& ( setukpairinjL2 = $true )
& ( eqimpsubset2 = $true )
& ( vacuousDall = $true )
& ( setadjoin__Cong = $true )
& ( exuI3 = $true )
& ( setukpairinjR11 = $true )
& ( demorgan1a = $true )
& ( iffalseProp1 = $true )
& ( iftrueProp2 = $true )
& ( cartprodpairin = $true )
& ( singletonprop = $true )
& ( setadjoinE = $true )
& ( cartprodfstin = $true )
& ( binunionE = $true )
& ( prop2set2propI = $true )
& ( woz13rule3 = $true )
& ( binintersectLsub = $true )
& ( funcGraphProp1 = $true )
& ( nonemptyE1 = $true )
& ( kfstsingleton = $true )
& ( replAx = $true )
& ( upairinpowunion = $true )
& ( ubforcartprodlem1 = $true )
& ( ap2apEq1 = $true )
& ( singletonsubset = $true )
& ( descr__Cong = $true )
& ( binintersectSubset2 = $true )
& ( contrasubsetT1 = $true )
& ( nonemptyI1 = $true )
& ( disjointsetsI1 = $true )
& ( theeq = $true )
& ( notinemptyset = $true )
& ( inIntersectImpInUnion2 = $true )
& ( exuE3e = $true )
& ( doubleComplementSub1 = $true )
& ( binintersectEL = $true )
& ( brelnall1 = $true )
& ( iffalse = $true )
& ( funcImageSingleton = $true )
& ( ubforcartprodlem3 = $true )
& ( omega__Cong = $true )
& ( ap2p = $true )
& ( cartprodmempaircEq = $true )
& ( complementTcontraSubset = $true )
& ( dsetconstrEL = $true )
& ( emptysetimpfalse = $true )
& ( lamp = $true )
& ( ap2apEq2 = $true )
& ( prop2setI = $true )
& ( subsetTI = $true )
& ( setadjoinIR = $true )
& ( setukpairIR = $true )
& ( emptyinunitempty = $true )
& ( binintersectRsub = $true )
& ( binintersectTERcontra = $true )
& ( setadjoinAx = $true )
& ( singletoninpowunion = $true )
& ( funcinfuncset = $true )
& ( symdiffI2 = $true )
& ( complementTnotintersectT = $true )
& ( dsetconstrI = $true )
& ( binunionTIRcontra = $true )
& ( binintersectSubset3 = $true )
& ( powerset__Cong = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( kfstpairEq = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodpairmemER = $true )
& ( notdallE = $true )
& ( ex1E2 = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( binintersectSubset5 = $true )
& ( subsetTrans = $true )
& ( breln1SetBreln1 = $true )
& ( setunionsingleton2 = $true )
& ( subsetRefl = $true )
& ( demorgan2 = $true )
& ( ubforcartprodlem2 = $true )
& ( setminusT_lem = $true )
& ( descrp = $true )
& ( demorgan2a1 = $true )
& ( setextT = $true )
& ( dpsetconstrEL1 = $true )
& ( demorgan2b2 = $true )
& ( setOfPairsIsBReln = $true )
& ( quantDeMorgan3 = $true )
& ( lam2p = $true )
& ( singletonsuniq = $true )
& ( symdiffE = $true )
& ( powersetT_lem = $true )
& ( emptysetE = $true )
& ( binintersectT_lem = $true )
& ( exuEu = $true )
& ( setunionsingleton = $true )
& ( cartprodpairsurjEq = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( ex1E1 = $true )
& ( dsetconstr__Cong = $true )
& ( subsetemptysetimpeq = $true )
& ( setminusLsub = $true )
& ( subsetI2 = $true )
& ( emptyI = $true )
& ( emptyset__Cong = $true )
& ( setminusELneg = $true )
& ( theprop = $true )
& ( setukpairinjL1 = $true )
& ( exu__Cong = $true )
& ( contrasubsetT3 = $true )
& ( symdiffIneg2 = $true )
& ( upairequniteq = $true )
& ( powersetI1 = $true )
& ( upairset2IR = $true )
& ( doubleComplementI1 = $true )
& ( binunionTE = $true )
& ( demorgan2b = $true )
& ( symdiffI1 = $true )
& ( dpsetconstrI = $true )
& ( powersetsubset = $true )
& ( contraSubsetComplement = $true )
& ( setminusILneg = $true )
& ( omegaSAx = $true )
& ( exuI2 = $true )
& ( doubleComplementEq = $true )
& ( funcGraphProp3 = $true )
& ( ( breln1 @ sK880 @ ( breln1invset @ sK880 @ sK881 ) )
!= $true )
& ( $true
= ( breln1 @ sK880 @ sK881 ) )
& ( setextsub = $true )
& ( subsetE = $true )
& ( setunion__Cong = $true )
& ( setukpairinjL = $true )
& ( upairsetIR = $true )
& ( woz13rule0 = $true )
& ( emptyInPowerset = $true )
& ( iftrueProp1 = $true )
& ( setukpairinjR1 = $true )
& ( setukpairIL = $true )
& ( infuncsetfunc = $true )
& ( dpsetconstrERa = $true )
& ( setukpairinjR2 = $true )
& ( exuE1 = $true )
& ( binunionT_lem = $true )
& ( woz13rule4 = $true )
& ( setminusERneg = $true )
& ( funcextLem = $true )
& ( ex1I2 = $true )
& ( emptyinPowerset = $true )
& ( setoftrueEq = $true )
& ( contrasubsetT2 = $true )
& ( lam2lamEq = $true )
& ( prop2setE = $true )
& ( woz1_4 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( eta1 = $true )
& ( quantDeMorgan4 = $true )
& ( emptysetsubset = $true )
& ( breln1all1 = $true )
& ( setminusI = $true )
& ( setunionsingleton1 = $true )
& ( emptysetAx = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( setunionE2 = $true )
& ( dsetconstrER = $true )
& ( upairsubunion = $true )
& ( beta2 = $true )
& ( binintersectSubset4 = $true )
& ( setukpairinjR12 = $true )
& ( binunionEcases = $true )
& ( woz1_3 = $true )
& ( inPowerset = $true )
& ( eqimpsubset1 = $true )
& ( woz1_1 = $true )
& ( brelnall2 = $true )
& ( ex1I = $true )
& ( setminusEL = $true )
& ( upairsetIL = $true )
& ( setadjoinIL = $true )
& ( bs114d = $true )
& ( notdexE = $true )
& ( binintersectSubset1 = $true )
& ( cartprodmempair1 = $true )
& ( iffalseProp2 = $true )
& ( funcGraphProp4 = $true )
& ( ksndsingleton = $true )
& ( subbreln1 = $true )
& ( upairset2E = $true )
& ( dpsetconstrEL2 = $true )
& ( singletonsswitch = $true )
& ( notinsingleton = $true )
& ( nonemptyI = $true )
& ( subsetI1 = $true )
& ( quantDeMorgan2 = $true )
& ( subPowSU = $true )
& ( singletoninpowerset = $true )
& ( powersetE1 = $true )
& ( binunionRsub = $true )
& ( omega0Ax = $true )
& ( setunionE = $true )
& ( contrasubsetT = $true )
& ( kpairsurjEq = $true )
& ( setminusIRneg = $true )
& ( funcext2 = $true )
& ( lamProp = $true )
& ( powersetTE1 = $true )
& ( inCongP = $true )
& ( setext = $true )
& ( setminusSubset1 = $true )
& ( dpsetconstrSub = $true )
& ( doubleComplementSub2 = $true )
& ( eqbreln = $true )
& ( uniqinunit = $true )
& ( ifSingleton = $true )
& ( quantDeMorgan1 = $true )
& ( woz13rule1 = $true )
& ( binintersectI = $true )
& ( binunionLsub = $true )
& ( exuI1 = $true )
& ( apProp = $true )
& ( funcGraphProp2 = $true )
& ( sepInPowerset = $true )
& ( ifp = $true )
& ( setadjoinSub = $true )
& ( kpairiskpair = $true )
& ( cartprodmempair = $true )
& ( emptyE1 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK880,sK881])],[f989,f2810]) ).
thf(f2810,plain,
( ? [X0: $i,X1: $i] :
( ( $true
!= ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
& ( $true
= ( breln1 @ X0 @ X1 ) ) )
=> ( ( ( breln1 @ sK880 @ ( breln1invset @ sK880 @ sK881 ) )
!= $true )
& ( $true
= ( breln1 @ sK880 @ sK881 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f989,plain,
( ( iftrueorfalse = $true )
& ( powersetI = $true )
& ( demorgan2a = $true )
& ( ksndpairEq = $true )
& ( subset2powerset = $true )
& ( kpairp = $true )
& ( complementTI1 = $true )
& ( setminusSubset2 = $true )
& ( binunionTILcontra = $true )
& ( demorgan2a2 = $true )
& ( binintersectER = $true )
& ( powersetTI1 = $true )
& ( setbeta = $true )
& ( symdiffIneg1 = $true )
& ( notequalI1 = $true )
& ( upairsetE = $true )
& ( setadjoinSub2 = $true )
& ( funcext = $true )
& ( demorgan1b = $true )
& ( omegaIndAx = $true )
& ( setunionAx = $true )
& ( iftrue = $true )
& ( subbreln = $true )
& ( cartprodsndin = $true )
& ( woz1_5 = $true )
& ( doubleComplementE1 = $true )
& ( setunionI = $true )
& ( woz13rule2 = $true )
& ( foundationAx = $true )
& ( complementT_lem = $true )
& ( in__Cong = $true )
& ( woz1_2 = $true )
& ( notsubsetI = $true )
& ( nonemptyImpWitness = $true )
& ( eqinunit = $true )
& ( setOfPairsIsBReln1 = $true )
& ( subsetE2 = $true )
& ( complementTE1 = $true )
& ( binunionIR = $true )
& ( inIntersectImpInUnion = $true )
& ( complementSubsetComplementIntersect = $true )
& ( notequalI2 = $true )
& ( app = $true )
& ( complementImpComplementIntersect = $true )
& ( cartprodsndpairEq = $true )
& ( eqbreln1 = $true )
& ( cartprodfstpairEq = $true )
& ( complementUnionInPowersetComplement = $true )
& ( exuE3u = $true )
& ( noeltsimpempty = $true )
& ( binunionTEcontra = $true )
& ( secondinupair = $true )
& ( powersetAx = $true )
& ( binunionIL = $true )
& ( setminusER = $true )
& ( wellorderingAx = $true )
& ( dpsetconstrER = $true )
& ( powersetE = $true )
& ( binintersectTELcontra = $true )
& ( demorgan1 = $true )
& ( beta1 = $true )
& ( sepSubset = $true )
& ( setadjoinOr = $true )
& ( setukpairinjR = $true )
& ( setextAx = $true )
& ( eta2 = $true )
& ( choice2fnsingleton = $true )
& ( breln1all2 = $true )
& ( exuE2 = $true )
& ( setukpairinjL2 = $true )
& ( eqimpsubset2 = $true )
& ( vacuousDall = $true )
& ( setadjoin__Cong = $true )
& ( exuI3 = $true )
& ( setukpairinjR11 = $true )
& ( demorgan1a = $true )
& ( iffalseProp1 = $true )
& ( iftrueProp2 = $true )
& ( cartprodpairin = $true )
& ( singletonprop = $true )
& ( setadjoinE = $true )
& ( cartprodfstin = $true )
& ( binunionE = $true )
& ( prop2set2propI = $true )
& ( woz13rule3 = $true )
& ( binintersectLsub = $true )
& ( funcGraphProp1 = $true )
& ( nonemptyE1 = $true )
& ( kfstsingleton = $true )
& ( replAx = $true )
& ( upairinpowunion = $true )
& ( ubforcartprodlem1 = $true )
& ( ap2apEq1 = $true )
& ( singletonsubset = $true )
& ( descr__Cong = $true )
& ( binintersectSubset2 = $true )
& ( contrasubsetT1 = $true )
& ( nonemptyI1 = $true )
& ( disjointsetsI1 = $true )
& ( theeq = $true )
& ( notinemptyset = $true )
& ( inIntersectImpInUnion2 = $true )
& ( exuE3e = $true )
& ( doubleComplementSub1 = $true )
& ( binintersectEL = $true )
& ( brelnall1 = $true )
& ( iffalse = $true )
& ( funcImageSingleton = $true )
& ( ubforcartprodlem3 = $true )
& ( omega__Cong = $true )
& ( ap2p = $true )
& ( cartprodmempaircEq = $true )
& ( complementTcontraSubset = $true )
& ( dsetconstrEL = $true )
& ( emptysetimpfalse = $true )
& ( lamp = $true )
& ( ap2apEq2 = $true )
& ( prop2setI = $true )
& ( subsetTI = $true )
& ( setadjoinIR = $true )
& ( setukpairIR = $true )
& ( emptyinunitempty = $true )
& ( binintersectRsub = $true )
& ( binintersectTERcontra = $true )
& ( setadjoinAx = $true )
& ( singletoninpowunion = $true )
& ( funcinfuncset = $true )
& ( symdiffI2 = $true )
& ( complementTnotintersectT = $true )
& ( dsetconstrI = $true )
& ( binunionTIRcontra = $true )
& ( binintersectSubset3 = $true )
& ( powerset__Cong = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( kfstpairEq = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodpairmemER = $true )
& ( notdallE = $true )
& ( ex1E2 = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( binintersectSubset5 = $true )
& ( subsetTrans = $true )
& ( breln1SetBreln1 = $true )
& ( setunionsingleton2 = $true )
& ( subsetRefl = $true )
& ( demorgan2 = $true )
& ( ubforcartprodlem2 = $true )
& ( setminusT_lem = $true )
& ( descrp = $true )
& ( demorgan2a1 = $true )
& ( setextT = $true )
& ( dpsetconstrEL1 = $true )
& ( demorgan2b2 = $true )
& ( setOfPairsIsBReln = $true )
& ( quantDeMorgan3 = $true )
& ( lam2p = $true )
& ( singletonsuniq = $true )
& ( symdiffE = $true )
& ( powersetT_lem = $true )
& ( emptysetE = $true )
& ( binintersectT_lem = $true )
& ( exuEu = $true )
& ( setunionsingleton = $true )
& ( cartprodpairsurjEq = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( ex1E1 = $true )
& ( dsetconstr__Cong = $true )
& ( subsetemptysetimpeq = $true )
& ( setminusLsub = $true )
& ( subsetI2 = $true )
& ( emptyI = $true )
& ( emptyset__Cong = $true )
& ( setminusELneg = $true )
& ( theprop = $true )
& ( setukpairinjL1 = $true )
& ( exu__Cong = $true )
& ( contrasubsetT3 = $true )
& ( symdiffIneg2 = $true )
& ( upairequniteq = $true )
& ( powersetI1 = $true )
& ( upairset2IR = $true )
& ( doubleComplementI1 = $true )
& ( binunionTE = $true )
& ( demorgan2b = $true )
& ( symdiffI1 = $true )
& ( dpsetconstrI = $true )
& ( powersetsubset = $true )
& ( contraSubsetComplement = $true )
& ( setminusILneg = $true )
& ( omegaSAx = $true )
& ( exuI2 = $true )
& ( doubleComplementEq = $true )
& ( funcGraphProp3 = $true )
& ? [X0: $i,X1: $i] :
( ( $true
!= ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
& ( $true
= ( breln1 @ X0 @ X1 ) ) )
& ( setextsub = $true )
& ( subsetE = $true )
& ( setunion__Cong = $true )
& ( setukpairinjL = $true )
& ( upairsetIR = $true )
& ( woz13rule0 = $true )
& ( emptyInPowerset = $true )
& ( iftrueProp1 = $true )
& ( setukpairinjR1 = $true )
& ( setukpairIL = $true )
& ( infuncsetfunc = $true )
& ( dpsetconstrERa = $true )
& ( setukpairinjR2 = $true )
& ( exuE1 = $true )
& ( binunionT_lem = $true )
& ( woz13rule4 = $true )
& ( setminusERneg = $true )
& ( funcextLem = $true )
& ( ex1I2 = $true )
& ( emptyinPowerset = $true )
& ( setoftrueEq = $true )
& ( contrasubsetT2 = $true )
& ( lam2lamEq = $true )
& ( prop2setE = $true )
& ( woz1_4 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( eta1 = $true )
& ( quantDeMorgan4 = $true )
& ( emptysetsubset = $true )
& ( breln1all1 = $true )
& ( setminusI = $true )
& ( setunionsingleton1 = $true )
& ( emptysetAx = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( setunionE2 = $true )
& ( dsetconstrER = $true )
& ( upairsubunion = $true )
& ( beta2 = $true )
& ( binintersectSubset4 = $true )
& ( setukpairinjR12 = $true )
& ( binunionEcases = $true )
& ( woz1_3 = $true )
& ( inPowerset = $true )
& ( eqimpsubset1 = $true )
& ( woz1_1 = $true )
& ( brelnall2 = $true )
& ( ex1I = $true )
& ( setminusEL = $true )
& ( upairsetIL = $true )
& ( setadjoinIL = $true )
& ( bs114d = $true )
& ( notdexE = $true )
& ( binintersectSubset1 = $true )
& ( cartprodmempair1 = $true )
& ( iffalseProp2 = $true )
& ( funcGraphProp4 = $true )
& ( ksndsingleton = $true )
& ( subbreln1 = $true )
& ( upairset2E = $true )
& ( dpsetconstrEL2 = $true )
& ( singletonsswitch = $true )
& ( notinsingleton = $true )
& ( nonemptyI = $true )
& ( subsetI1 = $true )
& ( quantDeMorgan2 = $true )
& ( subPowSU = $true )
& ( singletoninpowerset = $true )
& ( powersetE1 = $true )
& ( binunionRsub = $true )
& ( omega0Ax = $true )
& ( setunionE = $true )
& ( contrasubsetT = $true )
& ( kpairsurjEq = $true )
& ( setminusIRneg = $true )
& ( funcext2 = $true )
& ( lamProp = $true )
& ( powersetTE1 = $true )
& ( inCongP = $true )
& ( setext = $true )
& ( setminusSubset1 = $true )
& ( dpsetconstrSub = $true )
& ( doubleComplementSub2 = $true )
& ( eqbreln = $true )
& ( uniqinunit = $true )
& ( ifSingleton = $true )
& ( quantDeMorgan1 = $true )
& ( woz13rule1 = $true )
& ( binintersectI = $true )
& ( binunionLsub = $true )
& ( exuI1 = $true )
& ( apProp = $true )
& ( funcGraphProp2 = $true )
& ( sepInPowerset = $true )
& ( ifp = $true )
& ( setadjoinSub = $true )
& ( kpairiskpair = $true )
& ( cartprodmempair = $true )
& ( emptyE1 = $true ) ),
inference(flattening,[status(thm)],[f988]) ).
thf(f988,plain,
( ? [X0: $i,X1: $i] :
( ( $true
!= ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
& ( $true
= ( breln1 @ X0 @ X1 ) ) )
& ( eqbreln1 = $true )
& ( subbreln1 = $true )
& ( breln1all1 = $true )
& ( setOfPairsIsBReln1 = $true )
& ( choice2fnsingleton = $true )
& ( breln1SetBreln1 = $true )
& ( breln1all2 = $true )
& ( woz1_5 = $true )
& ( woz1_4 = $true )
& ( woz1_3 = $true )
& ( woz1_2 = $true )
& ( woz1_1 = $true )
& ( woz13rule4 = $true )
& ( woz13rule3 = $true )
& ( woz13rule2 = $true )
& ( woz13rule1 = $true )
& ( woz13rule0 = $true )
& ( demorgan2 = $true )
& ( demorgan2b = $true )
& ( demorgan2b2 = $true )
& ( demorgan2a = $true )
& ( demorgan1 = $true )
& ( demorgan1b = $true )
& ( demorgan1a = $true )
& ( demorgan2a2 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( demorgan2a1 = $true )
& ( binunionTEcontra = $true )
& ( binunionTE = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( inIntersectImpInUnion2 = $true )
& ( inIntersectImpInUnion = $true )
& ( binunionTIRcontra = $true )
& ( binunionTILcontra = $true )
& ( complementTcontraSubset = $true )
& ( contraSubsetComplement = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( complementSubsetComplementIntersect = $true )
& ( complementImpComplementIntersect = $true )
& ( complementTnotintersectT = $true )
& ( doubleComplementEq = $true )
& ( doubleComplementSub2 = $true )
& ( doubleComplementSub1 = $true )
& ( doubleComplementE1 = $true )
& ( doubleComplementI1 = $true )
& ( contrasubsetT3 = $true )
& ( contrasubsetT2 = $true )
& ( contrasubsetT1 = $true )
& ( contrasubsetT = $true )
& ( binintersectTERcontra = $true )
& ( binintersectTELcontra = $true )
& ( complementTE1 = $true )
& ( complementTI1 = $true )
& ( powersetTE1 = $true )
& ( powersetTI1 = $true )
& ( subsetTI = $true )
& ( setextT = $true )
& ( complementT_lem = $true )
& ( setminusT_lem = $true )
& ( powersetT_lem = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true )
& ( iftrueorfalse = $true )
& ( iffalse = $true )
& ( iftrue = $true )
& ( theeq = $true )
& ( ifp = $true )
& ( ifSingleton = $true )
& ( iftrueProp2 = $true )
& ( iftrueProp1 = $true )
& ( iffalseProp2 = $true )
& ( iffalseProp1 = $true )
& ( eta2 = $true )
& ( beta2 = $true )
& ( lam2lamEq = $true )
& ( eta1 = $true )
& ( beta1 = $true )
& ( ap2apEq2 = $true )
& ( ap2apEq1 = $true )
& ( funcext2 = $true )
& ( funcext = $true )
& ( eqbreln = $true )
& ( subbreln = $true )
& ( funcGraphProp4 = $true )
& ( funcextLem = $true )
& ( funcGraphProp2 = $true )
& ( funcGraphProp3 = $true )
& ( funcGraphProp1 = $true )
& ( ex1E2 = $true )
& ( brelnall2 = $true )
& ( brelnall1 = $true )
& ( lam2p = $true )
& ( lamp = $true )
& ( lamProp = $true )
& ( funcinfuncset = $true )
& ( ap2p = $true )
& ( infuncsetfunc = $true )
& ( app = $true )
& ( apProp = $true )
& ( funcImageSingleton = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrEL2 = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrERa = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrI = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodsndin = $true )
& ( kpairsurjEq = $true )
& ( ksndpairEq = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( setukpairinjR2 = $true )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f444]) ).
thf(f444,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ( ( ap2p = $true )
=> ( ( funcinfuncset = $true )
=> ( ( lamProp = $true )
=> ( ( lamp = $true )
=> ( ( lam2p = $true )
=> ( ( brelnall1 = $true )
=> ( ( brelnall2 = $true )
=> ( ( ex1E2 = $true )
=> ( ( funcGraphProp1 = $true )
=> ( ( funcGraphProp3 = $true )
=> ( ( funcGraphProp2 = $true )
=> ( ( funcextLem = $true )
=> ( ( funcGraphProp4 = $true )
=> ( ( subbreln = $true )
=> ( ( eqbreln = $true )
=> ( ( funcext = $true )
=> ( ( funcext2 = $true )
=> ( ( ap2apEq1 = $true )
=> ( ( ap2apEq2 = $true )
=> ( ( beta1 = $true )
=> ( ( eta1 = $true )
=> ( ( lam2lamEq = $true )
=> ( ( beta2 = $true )
=> ( ( eta2 = $true )
=> ( ( iffalseProp1 = $true )
=> ( ( iffalseProp2 = $true )
=> ( ( iftrueProp1 = $true )
=> ( ( iftrueProp2 = $true )
=> ( ( ifSingleton = $true )
=> ( ( ifp = $true )
=> ( ( theeq = $true )
=> ( ( iftrue = $true )
=> ( ( iffalse = $true )
=> ( ( iftrueorfalse = $true )
=> ( ( binintersectT_lem = $true )
=> ( ( binunionT_lem = $true )
=> ( ( powersetT_lem = $true )
=> ( ( setminusT_lem = $true )
=> ( ( complementT_lem = $true )
=> ( ( setextT = $true )
=> ( ( subsetTI = $true )
=> ( ( powersetTI1 = $true )
=> ( ( powersetTE1 = $true )
=> ( ( complementTI1 = $true )
=> ( ( complementTE1 = $true )
=> ( ( binintersectTELcontra = $true )
=> ( ( binintersectTERcontra = $true )
=> ( ( contrasubsetT = $true )
=> ( ( contrasubsetT1 = $true )
=> ( ( contrasubsetT2 = $true )
=> ( ( contrasubsetT3 = $true )
=> ( ( doubleComplementI1 = $true )
=> ( ( doubleComplementE1 = $true )
=> ( ( doubleComplementSub1 = $true )
=> ( ( doubleComplementSub2 = $true )
=> ( ( doubleComplementEq = $true )
=> ( ( complementTnotintersectT = $true )
=> ( ( complementImpComplementIntersect = $true )
=> ( ( complementSubsetComplementIntersect = $true )
=> ( ( complementInPowersetComplementIntersect = $true )
=> ( ( contraSubsetComplement = $true )
=> ( ( complementTcontraSubset = $true )
=> ( ( binunionTILcontra = $true )
=> ( ( binunionTIRcontra = $true )
=> ( ( inIntersectImpInUnion = $true )
=> ( ( inIntersectImpInUnion2 = $true )
=> ( ( inIntersectImpInIntersectUnions = $true )
=> ( ( intersectInPowersetIntersectUnions = $true )
=> ( ( inComplementUnionImpNotIn1 = $true )
=> ( ( inComplementUnionImpInComplement1 = $true )
=> ( ( binunionTE = $true )
=> ( ( binunionTEcontra = $true )
=> ( ( demorgan2a1 = $true )
=> ( ( complementUnionInPowersetComplement = $true )
=> ( ( demorgan2a2 = $true )
=> ( ( demorgan1a = $true )
=> ( ( demorgan1b = $true )
=> ( ( demorgan1 = $true )
=> ( ( demorgan2a = $true )
=> ( ( demorgan2b2 = $true )
=> ( ( demorgan2b = $true )
=> ( ( demorgan2 = $true )
=> ( ( woz13rule0 = $true )
=> ( ( woz13rule1 = $true )
=> ( ( woz13rule2 = $true )
=> ( ( woz13rule3 = $true )
=> ( ( woz13rule4 = $true )
=> ( ( woz1_1 = $true )
=> ( ( woz1_2 = $true )
=> ( ( woz1_3 = $true )
=> ( ( woz1_4 = $true )
=> ( ( woz1_5 = $true )
=> ( ( breln1all2 = $true )
=> ( ( breln1SetBreln1 = $true )
=> ( ( choice2fnsingleton = $true )
=> ( ( setOfPairsIsBReln1 = $true )
=> ( ( breln1all1 = $true )
=> ( ( subbreln1 = $true )
=> ( ( eqbreln1 = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
=> ( $true
= ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f443]) ).
thf(f443,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f298]) ).
thf(f298,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ! [X3: $i,X13: $i] :
( ( breln1 @ X3 @ X13 )
=> ( breln1 @ X3 @ ( breln1invset @ X3 @ X13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f297]) ).
thf(f297,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ! [X3: $i,X13: $i] :
( ( breln1 @ X3 @ X13 )
=> ( breln1 @ X3 @ ( breln1invset @ X3 @ X13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VPOVQ5G1w9/DTF2THF_2668.p',breln1invprop) ).
thf(f3585,plain,
! [X2: $i,X0: $i > $i > $o,X1: $i] :
( ( $true
= ( breln @ X1 @ X2
@ ( dpsetconstr @ X1 @ X2
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) ) )
| ( setOfPairsIsBReln != $true ) ),
inference(cnf_transformation,[status(thm)],[f2006]) ).
thf(f2006,plain,
( ( ! [X0: $i > $i > $o,X1: $i,X2: $i] :
( $true
= ( breln @ X1 @ X2
@ ( dpsetconstr @ X1 @ X2
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) ) )
| ( setOfPairsIsBReln != $true ) )
& ( ( setOfPairsIsBReln = $true )
| ( $true
!= ( breln @ sK425 @ sK426
@ ( dpsetconstr @ sK425 @ sK426
@ ^ [Y0: $i,Y1: $i] : ( sK424 @ Y0 @ Y1 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK424,sK425,sK426])],[f2004,f2005]) ).
thf(f2005,plain,
( ? [X3: $i > $i > $o,X4: $i,X5: $i] :
( $true
!= ( breln @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [Y0: $i,Y1: $i] : ( X3 @ Y0 @ Y1 ) ) ) )
=> ( $true
!= ( breln @ sK425 @ sK426
@ ( dpsetconstr @ sK425 @ sK426
@ ^ [Y0: $i,Y1: $i] : ( sK424 @ Y0 @ Y1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2004,plain,
( ( ! [X0: $i > $i > $o,X1: $i,X2: $i] :
( $true
= ( breln @ X1 @ X2
@ ( dpsetconstr @ X1 @ X2
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) ) )
| ( setOfPairsIsBReln != $true ) )
& ( ( setOfPairsIsBReln = $true )
| ? [X3: $i > $i > $o,X4: $i,X5: $i] :
( $true
!= ( breln @ X4 @ X5
@ ( dpsetconstr @ X4 @ X5
@ ^ [Y0: $i,Y1: $i] : ( X3 @ Y0 @ Y1 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2003]) ).
thf(f2003,plain,
( ( ! [X0: $i > $i > $o,X1: $i,X2: $i] :
( $true
= ( breln @ X1 @ X2
@ ( dpsetconstr @ X1 @ X2
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) ) )
| ( setOfPairsIsBReln != $true ) )
& ( ( setOfPairsIsBReln = $true )
| ? [X0: $i > $i > $o,X1: $i,X2: $i] :
( $true
!= ( breln @ X1 @ X2
@ ( dpsetconstr @ X1 @ X2
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f522]) ).
thf(f522,plain,
( ! [X0: $i > $i > $o,X1: $i,X2: $i] :
( $true
= ( breln @ X1 @ X2
@ ( dpsetconstr @ X1 @ X2
@ ^ [Y0: $i,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) ) )
<=> ( setOfPairsIsBReln = $true ) ),
inference(fool_elimination,[status(thm)],[f521]) ).
thf(f521,plain,
! [X0: $i > $i > $o,X1: $i,X2: $i] :
( ( breln @ X1 @ X2
@ ( dpsetconstr @ X1 @ X2
@ ^ [X3: $i,X4: $i] : ( X0 @ X3 @ X4 ) ) )
= setOfPairsIsBReln ),
inference(rectify,[status(thm)],[f187]) ).
thf(f187,axiom,
! [X0: $i > $i > $o,X3: $i,X4: $i] :
( ( breln @ X3 @ X4
@ ( dpsetconstr @ X3 @ X4
@ ^ [X1: $i,X2: $i] : ( X0 @ X1 @ X2 ) ) )
= setOfPairsIsBReln ),
file('/export/starexec/sandbox2/tmp/tmp.VPOVQ5G1w9/DTF2THF_2668.p',setOfPairsIsBReln) ).
thf(f6264,plain,
( $true
!= ( breln @ sK880 @ sK880
@ ( dpsetconstr @ sK880 @ sK880
@ ^ [Y0: $i,Y1: $i] : ( in @ ( kpair @ Y1 @ Y0 ) @ sK881 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f5698]) ).
thf(f5698,plain,
( $true
!= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 )
@ sK880
@ ( ^ [Y0: $i,Y1: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y2: $i,Y3: $i] : ( in @ ( kpair @ Y3 @ Y2 ) @ Y1 ) )
@ sK880
@ sK881 ) ) ),
inference(definition_unfolding,[status(thm)],[f4380,f3514,f3332]) ).
thf(f3332,plain,
( breln1invset
= ( ^ [Y0: $i,Y1: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y2: $i,Y3: $i] : ( in @ ( kpair @ Y3 @ Y2 ) @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f747]) ).
thf(f747,plain,
( breln1invset
= ( ^ [Y0: $i,Y1: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y2: $i,Y3: $i] : ( in @ ( kpair @ Y3 @ Y2 ) @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f746]) ).
thf(f746,plain,
( breln1invset
= ( ^ [X0: $i,X1: $i] :
( dpsetconstr @ X0 @ X0
@ ^ [X2: $i,X3: $i] : ( in @ ( kpair @ X3 @ X2 ) @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f296]) ).
thf(f296,axiom,
( breln1invset
= ( ^ [X3: $i,X13: $i] :
( dpsetconstr @ X3 @ X3
@ ^ [X1: $i,X2: $i] : ( in @ ( kpair @ X2 @ X1 ) @ X13 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VPOVQ5G1w9/DTF2THF_2668.p',breln1invset) ).
thf(f3514,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f751]) ).
thf(f751,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f750]) ).
thf(f750,plain,
( breln1
= ( ^ [X0: $i,X1: $i] : ( breln @ X0 @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f288]) ).
thf(f288,axiom,
( breln1
= ( ^ [X3: $i,X13: $i] : ( breln @ X3 @ X3 @ X13 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VPOVQ5G1w9/DTF2THF_2668.p',breln1) ).
thf(f4380,plain,
( ( breln1 @ sK880 @ ( breln1invset @ sK880 @ sK881 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f2811]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU775^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n031.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:34:33 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.46 ---- Original DTF file ---
% 0.27/0.46 thf(spec,logic,$$dhol).
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 % File : SEU775^1 : TPTP v9.2.1. Released v3.7.0.
% 0.27/0.46 % Domain : Set Theory
% 0.27/0.46 % Problem : Binary Relations on a Set
% 0.27/0.46 % Version : Especial.
% 0.27/0.46 % English : (! A:i.! R:i.breln1 A R -> breln1 A (breln1invset A R))
% 0.27/0.46
% 0.27/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.27/0.46 % Source : [Bro08]
% 0.27/0.46 % Names : ZFC277g [Bro08]
% 0.27/0.46
% 0.27/0.46 % Status : Theorem
% 0.27/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.54 v8.1.0, 0.45 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0, 0.80 v4.1.0, 1.00 v3.7.0
% 0.27/0.46 % Syntax : Number of formulae : 635 ( 296 unt; 338 typ; 296 def)
% 0.27/0.46 % Number of atoms : 1785 ( 426 equ; 0 cnn)
% 0.27/0.46 % Maximal formula atoms : 293 ( 6 avg)
% 0.27/0.46 % Number of connectives : 3850 ( 73 ~; 12 |; 46 &;2791 @)
% 0.27/0.46 % ( 14 <=>; 914 =>; 0 <=; 0 <~>)
% 0.27/0.46 % Maximal formula depth : 298 ( 2 avg)
% 0.27/0.46 % Number of types : 2 ( 0 usr)
% 0.27/0.46 % Number of type conns : 154 ( 154 >; 0 *; 0 +; 0 <<)
% 0.27/0.46 % Number of symbols : 341 ( 338 usr; 295 con; 0-4 aty)
% 0.27/0.46 % Number of variables : 1027 ( 80 ^; 911 !; 36 ?;1027 :)
% 0.27/0.46 % SPC : TH0_THM_EQU_NAR
% 0.27/0.46
% 0.27/0.46 % Comments : http://mathgate.info/detsetitem.php?id=335
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 thf(in_type,type,
% 0.27/0.46 in: $i > $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(exu_type,type,
% 0.27/0.46 exu: ( $i > $o ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(exu,definition,
% 0.27/0.46 ( exu
% 0.27/0.46 = ( ^ [Xphi: $i > $o] :
% 0.27/0.46 ? [Xx: $i] :
% 0.27/0.46 ( ( Xphi @ Xx )
% 0.27/0.46 & ! [Xy: $i] :
% 0.27/0.46 ( ( Xphi @ Xy )
% 0.27/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(setextAx_type,type,
% 0.27/0.46 setextAx: $o ).
% 0.27/0.46
% 0.27/0.46 thf(setextAx,definition,
% 0.27/0.46 ( setextAx
% 0.27/0.46 = ( ! [A: $i,B: $i] :
% 0.27/0.46 ( ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 <=> ( in @ Xx @ B ) )
% 0.27/0.46 => ( A = B ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(emptyset_type,type,
% 0.27/0.46 emptyset: $i ).
% 0.27/0.46
% 0.27/0.46 thf(emptysetAx_type,type,
% 0.27/0.46 emptysetAx: $o ).
% 0.27/0.46
% 0.27/0.46 thf(emptysetAx,definition,
% 0.27/0.46 ( emptysetAx
% 0.27/0.46 = ( ! [Xx: $i] :
% 0.27/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(setadjoin_type,type,
% 0.27/0.46 setadjoin: $i > $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(setadjoinAx_type,type,
% 0.27/0.46 setadjoinAx: $o ).
% 0.27/0.46
% 0.27/0.46 thf(setadjoinAx,definition,
% 0.27/0.46 ( setadjoinAx
% 0.27/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.27/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.27/0.46 <=> ( ( Xy = Xx )
% 0.27/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(powerset_type,type,
% 0.27/0.46 powerset: $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(powersetAx_type,type,
% 0.27/0.46 powersetAx: $o ).
% 0.27/0.46
% 0.27/0.46 thf(powersetAx,definition,
% 0.27/0.46 ( powersetAx
% 0.27/0.46 = ( ! [A: $i,B: $i] :
% 0.27/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.27/0.46 <=> ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ B )
% 0.27/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(setunion_type,type,
% 0.27/0.46 setunion: $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(setunionAx_type,type,
% 0.27/0.46 setunionAx: $o ).
% 0.27/0.46
% 0.27/0.46 thf(setunionAx,definition,
% 0.27/0.46 ( setunionAx
% 0.27/0.46 = ( ! [A: $i,Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.27/0.46 <=> ? [B: $i] :
% 0.27/0.46 ( ( in @ Xx @ B )
% 0.27/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(omega_type,type,
% 0.27/0.46 omega: $i ).
% 0.27/0.46
% 0.27/0.46 thf(omega0Ax_type,type,
% 0.27/0.46 omega0Ax: $o ).
% 0.27/0.46
% 0.27/0.46 thf(omega0Ax,definition,
% 0.27/0.46 ( omega0Ax
% 0.27/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(omegaSAx_type,type,
% 0.27/0.46 omegaSAx: $o ).
% 0.27/0.46
% 0.27/0.46 thf(omegaSAx,definition,
% 0.27/0.46 ( omegaSAx
% 0.27/0.46 = ( ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ omega )
% 0.27/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(omegaIndAx_type,type,
% 0.27/0.46 omegaIndAx: $o ).
% 0.27/0.46
% 0.27/0.46 thf(omegaIndAx,definition,
% 0.27/0.46 ( omegaIndAx
% 0.27/0.46 = ( ! [A: $i] :
% 0.27/0.46 ( ( ( in @ emptyset @ A )
% 0.27/0.46 & ! [Xx: $i] :
% 0.27/0.46 ( ( ( in @ Xx @ omega )
% 0.27/0.46 & ( in @ Xx @ A ) )
% 0.27/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.27/0.46 => ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ omega )
% 0.27/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(replAx_type,type,
% 0.27/0.46 replAx: $o ).
% 0.27/0.46
% 0.27/0.46 thf(replAx,definition,
% 0.27/0.46 ( replAx
% 0.27/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.27/0.46 ( ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ( exu
% 0.27/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.27/0.46 => ? [B: $i] :
% 0.27/0.46 ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ B )
% 0.27/0.46 <=> ? [Xy: $i] :
% 0.27/0.46 ( ( in @ Xy @ A )
% 0.27/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(foundationAx_type,type,
% 0.27/0.46 foundationAx: $o ).
% 0.27/0.46
% 0.27/0.46 thf(foundationAx,definition,
% 0.27/0.46 ( foundationAx
% 0.27/0.46 = ( ! [A: $i] :
% 0.27/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.27/0.46 => ? [B: $i] :
% 0.27/0.46 ( ( in @ B @ A )
% 0.27/0.46 & ~ ? [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ B )
% 0.27/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(wellorderingAx_type,type,
% 0.27/0.46 wellorderingAx: $o ).
% 0.27/0.46
% 0.27/0.46 thf(wellorderingAx,definition,
% 0.27/0.46 ( wellorderingAx
% 0.27/0.46 = ( ! [A: $i] :
% 0.27/0.46 ? [B: $i] :
% 0.27/0.46 ( ! [C: $i] :
% 0.27/0.46 ( ( in @ C @ B )
% 0.27/0.46 => ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ C )
% 0.27/0.46 => ( in @ Xx @ A ) ) )
% 0.27/0.46 & ! [Xx: $i,Xy: $i] :
% 0.27/0.46 ( ( ( in @ Xx @ A )
% 0.27/0.46 & ( in @ Xy @ A ) )
% 0.27/0.46 => ( ! [C: $i] :
% 0.27/0.46 ( ( in @ C @ B )
% 0.27/0.46 => ( ( in @ Xx @ C )
% 0.27/0.46 <=> ( in @ Xy @ C ) ) )
% 0.27/0.46 => ( Xx = Xy ) ) )
% 0.27/0.46 & ! [C: $i,D: $i] :
% 0.27/0.46 ( ( ( in @ C @ B )
% 0.27/0.46 & ( in @ D @ B ) )
% 0.27/0.46 => ( ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ C )
% 0.27/0.46 => ( in @ Xx @ D ) )
% 0.27/0.46 | ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ D )
% 0.27/0.46 => ( in @ Xx @ C ) ) ) )
% 0.27/0.46 & ! [C: $i] :
% 0.27/0.46 ( ( ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ C )
% 0.27/0.46 => ( in @ Xx @ A ) )
% 0.27/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.27/0.46 => ? [D: $i,Xx: $i] :
% 0.27/0.46 ( ( in @ D @ B )
% 0.27/0.46 & ( in @ Xx @ C )
% 0.27/0.46 & ~ ? [Xy: $i] :
% 0.27/0.46 ( ( in @ Xy @ D )
% 0.27/0.46 & ( in @ Xy @ C ) )
% 0.27/0.46 & ! [E: $i] :
% 0.27/0.46 ( ( in @ E @ B )
% 0.27/0.46 => ( ! [Xy: $i] :
% 0.27/0.46 ( ( in @ Xy @ E )
% 0.27/0.46 => ( in @ Xy @ D ) )
% 0.27/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(descr_type,type,
% 0.27/0.46 descr: ( $i > $o ) > $i ).
% 0.27/0.46
% 0.27/0.46 thf(descrp_type,type,
% 0.27/0.46 descrp: $o ).
% 0.27/0.46
% 0.27/0.46 thf(descrp,definition,
% 0.27/0.46 ( descrp
% 0.27/0.46 = ( ! [Xphi: $i > $o] :
% 0.27/0.46 ( ( exu
% 0.27/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.46 => ( Xphi
% 0.27/0.46 @ ( descr
% 0.27/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(dsetconstr_type,type,
% 0.27/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.27/0.46
% 0.27/0.46 thf(dsetconstrI_type,type,
% 0.27/0.46 dsetconstrI: $o ).
% 0.27/0.46
% 0.27/0.46 thf(dsetconstrI,definition,
% 0.27/0.46 ( dsetconstrI
% 0.27/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ( ( Xphi @ Xx )
% 0.27/0.46 => ( in @ Xx
% 0.27/0.46 @ ( dsetconstr @ A
% 0.27/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(dsetconstrEL_type,type,
% 0.27/0.46 dsetconstrEL: $o ).
% 0.27/0.46
% 0.27/0.46 thf(dsetconstrEL,definition,
% 0.27/0.46 ( dsetconstrEL
% 0.27/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.46 ( ( in @ Xx
% 0.27/0.46 @ ( dsetconstr @ A
% 0.27/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.27/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(dsetconstrER_type,type,
% 0.27/0.46 dsetconstrER: $o ).
% 0.27/0.46
% 0.27/0.46 thf(dsetconstrER,definition,
% 0.27/0.46 ( dsetconstrER
% 0.27/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.46 ( ( in @ Xx
% 0.27/0.46 @ ( dsetconstr @ A
% 0.27/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.27/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(exuE1_type,type,
% 0.27/0.46 exuE1: $o ).
% 0.27/0.46
% 0.27/0.46 thf(exuE1,definition,
% 0.27/0.46 ( exuE1
% 0.27/0.46 = ( ! [Xphi: $i > $o] :
% 0.27/0.46 ( ( exu
% 0.27/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.46 => ? [Xx: $i] :
% 0.27/0.46 ( ( Xphi @ Xx )
% 0.27/0.46 & ! [Xy: $i] :
% 0.27/0.46 ( ( Xphi @ Xy )
% 0.27/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(prop2set_type,type,
% 0.27/0.46 prop2set: $o > $i ).
% 0.27/0.46
% 0.27/0.46 thf(prop2setE_type,type,
% 0.27/0.46 prop2setE: $o ).
% 0.27/0.46
% 0.27/0.46 thf(prop2setE,definition,
% 0.27/0.46 ( prop2setE
% 0.27/0.46 = ( ! [Xphi: $o,Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.27/0.46 => Xphi ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(emptysetE_type,type,
% 0.27/0.46 emptysetE: $o ).
% 0.27/0.46
% 0.27/0.46 thf(emptysetE,definition,
% 0.27/0.46 ( emptysetE
% 0.27/0.46 = ( ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ emptyset )
% 0.27/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(emptysetimpfalse_type,type,
% 0.27/0.46 emptysetimpfalse: $o ).
% 0.27/0.46
% 0.27/0.46 thf(emptysetimpfalse,definition,
% 0.27/0.46 ( emptysetimpfalse
% 0.27/0.46 = ( ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ emptyset )
% 0.27/0.46 => $false ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(notinemptyset_type,type,
% 0.27/0.46 notinemptyset: $o ).
% 0.27/0.46
% 0.27/0.46 thf(notinemptyset,definition,
% 0.27/0.46 ( notinemptyset
% 0.27/0.46 = ( ! [Xx: $i] :
% 0.27/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(exuE3e_type,type,
% 0.27/0.46 exuE3e: $o ).
% 0.27/0.46
% 0.27/0.46 thf(exuE3e,definition,
% 0.27/0.46 ( exuE3e
% 0.27/0.46 = ( ! [Xphi: $i > $o] :
% 0.27/0.46 ( ( exu
% 0.27/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(setext_type,type,
% 0.27/0.46 setext: $o ).
% 0.27/0.46
% 0.27/0.46 thf(setext,definition,
% 0.27/0.46 ( setext
% 0.27/0.46 = ( ! [A: $i,B: $i] :
% 0.27/0.46 ( ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ( in @ Xx @ B ) )
% 0.27/0.46 => ( ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ B )
% 0.27/0.46 => ( in @ Xx @ A ) )
% 0.27/0.46 => ( A = B ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(emptyI_type,type,
% 0.27/0.46 emptyI: $o ).
% 0.27/0.46
% 0.27/0.46 thf(emptyI,definition,
% 0.27/0.46 ( emptyI
% 0.27/0.46 = ( ! [A: $i] :
% 0.27/0.46 ( ! [Xx: $i] :
% 0.27/0.46 ~ ( in @ Xx @ A )
% 0.27/0.46 => ( A = emptyset ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(noeltsimpempty_type,type,
% 0.27/0.46 noeltsimpempty: $o ).
% 0.27/0.46
% 0.27/0.46 thf(noeltsimpempty,definition,
% 0.27/0.46 ( noeltsimpempty
% 0.27/0.46 = ( ! [A: $i] :
% 0.27/0.46 ( ! [Xx: $i] :
% 0.27/0.46 ~ ( in @ Xx @ A )
% 0.27/0.46 => ( A = emptyset ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(setbeta_type,type,
% 0.27/0.46 setbeta: $o ).
% 0.27/0.46
% 0.27/0.46 thf(setbeta,definition,
% 0.27/0.46 ( setbeta
% 0.27/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ( ( in @ Xx
% 0.27/0.46 @ ( dsetconstr @ A
% 0.27/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.27/0.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(nonempty_type,type,
% 0.27/0.46 nonempty: $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(nonempty,definition,
% 0.27/0.46 ( nonempty
% 0.27/0.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(nonemptyE1_type,type,
% 0.27/0.46 nonemptyE1: $o ).
% 0.27/0.46
% 0.27/0.46 thf(nonemptyE1,definition,
% 0.27/0.46 ( nonemptyE1
% 0.27/0.46 = ( ! [A: $i] :
% 0.27/0.46 ( ( nonempty @ A )
% 0.27/0.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(nonemptyI_type,type,
% 0.27/0.46 nonemptyI: $o ).
% 0.27/0.46
% 0.27/0.46 thf(nonemptyI,definition,
% 0.27/0.46 ( nonemptyI
% 0.27/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ( ( Xphi @ Xx )
% 0.27/0.46 => ( nonempty
% 0.27/0.46 @ ( dsetconstr @ A
% 0.27/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(nonemptyI1_type,type,
% 0.27/0.46 nonemptyI1: $o ).
% 0.27/0.46
% 0.27/0.46 thf(nonemptyI1,definition,
% 0.27/0.46 ( nonemptyI1
% 0.27/0.46 = ( ! [A: $i] :
% 0.27/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.27/0.46 => ( nonempty @ A ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(setadjoinIL_type,type,
% 0.27/0.46 setadjoinIL: $o ).
% 0.27/0.46
% 0.27/0.46 thf(setadjoinIL,definition,
% 0.27/0.46 ( setadjoinIL
% 0.27/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(emptyinunitempty_type,type,
% 0.27/0.46 emptyinunitempty: $o ).
% 0.27/0.46
% 0.27/0.46 thf(emptyinunitempty,definition,
% 0.27/0.46 ( emptyinunitempty
% 0.27/0.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(setadjoinIR_type,type,
% 0.27/0.46 setadjoinIR: $o ).
% 0.27/0.46
% 0.27/0.46 thf(setadjoinIR,definition,
% 0.27/0.46 ( setadjoinIR
% 0.27/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.27/0.46 ( ( in @ Xy @ A )
% 0.27/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(setadjoinE_type,type,
% 0.27/0.46 setadjoinE: $o ).
% 0.27/0.46
% 0.27/0.46 thf(setadjoinE,definition,
% 0.27/0.46 ( setadjoinE
% 0.27/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.27/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.27/0.46 => ! [Xphi: $o] :
% 0.27/0.46 ( ( ( Xy = Xx )
% 0.27/0.46 => Xphi )
% 0.27/0.46 => ( ( ( in @ Xy @ A )
% 0.27/0.46 => Xphi )
% 0.27/0.46 => Xphi ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(setadjoinOr_type,type,
% 0.27/0.46 setadjoinOr: $o ).
% 0.27/0.46
% 0.27/0.46 thf(setadjoinOr,definition,
% 0.27/0.46 ( setadjoinOr
% 0.27/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.27/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.27/0.46 => ( ( Xy = Xx )
% 0.27/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(setoftrueEq_type,type,
% 0.27/0.46 setoftrueEq: $o ).
% 0.27/0.46
% 0.27/0.46 thf(setoftrueEq,definition,
% 0.27/0.46 ( setoftrueEq
% 0.27/0.46 = ( ! [A: $i] :
% 0.27/0.46 ( ( dsetconstr @ A
% 0.27/0.46 @ ^ [Xx: $i] : $true )
% 0.27/0.46 = A ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(powersetI_type,type,
% 0.27/0.46 powersetI: $o ).
% 0.27/0.46
% 0.27/0.46 thf(powersetI,definition,
% 0.27/0.46 ( powersetI
% 0.27/0.46 = ( ! [A: $i,B: $i] :
% 0.27/0.46 ( ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ B )
% 0.27/0.46 => ( in @ Xx @ A ) )
% 0.27/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(emptyinPowerset_type,type,
% 0.27/0.46 emptyinPowerset: $o ).
% 0.27/0.46
% 0.27/0.46 thf(emptyinPowerset,definition,
% 0.27/0.46 ( emptyinPowerset
% 0.27/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(emptyInPowerset_type,type,
% 0.27/0.46 emptyInPowerset: $o ).
% 0.27/0.46
% 0.27/0.46 thf(emptyInPowerset,definition,
% 0.27/0.46 ( emptyInPowerset
% 0.27/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(powersetE_type,type,
% 0.27/0.46 powersetE: $o ).
% 0.27/0.46
% 0.27/0.46 thf(powersetE,definition,
% 0.27/0.46 ( powersetE
% 0.27/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.27/0.46 => ( ( in @ Xx @ B )
% 0.27/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(setunionI_type,type,
% 0.27/0.46 setunionI: $o ).
% 0.27/0.46
% 0.27/0.46 thf(setunionI,definition,
% 0.27/0.46 ( setunionI
% 0.27/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.27/0.46 ( ( in @ Xx @ B )
% 0.27/0.46 => ( ( in @ B @ A )
% 0.27/0.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(setunionE_type,type,
% 0.27/0.46 setunionE: $o ).
% 0.27/0.46
% 0.27/0.46 thf(setunionE,definition,
% 0.27/0.46 ( setunionE
% 0.27/0.46 = ( ! [A: $i,Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.27/0.46 => ! [Xphi: $o] :
% 0.27/0.46 ( ! [B: $i] :
% 0.27/0.46 ( ( in @ Xx @ B )
% 0.27/0.46 => ( ( in @ B @ A )
% 0.27/0.46 => Xphi ) )
% 0.27/0.46 => Xphi ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(subPowSU_type,type,
% 0.27/0.46 subPowSU: $o ).
% 0.27/0.46
% 0.27/0.46 thf(subPowSU,definition,
% 0.27/0.46 ( subPowSU
% 0.27/0.46 = ( ! [A: $i,Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(exuE2_type,type,
% 0.27/0.46 exuE2: $o ).
% 0.27/0.46
% 0.27/0.46 thf(exuE2,definition,
% 0.27/0.46 ( exuE2
% 0.27/0.46 = ( ! [Xphi: $i > $o] :
% 0.27/0.46 ( ( exu
% 0.27/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.46 => ? [Xx: $i] :
% 0.27/0.46 ! [Xy: $i] :
% 0.27/0.46 ( ( Xphi @ Xy )
% 0.27/0.46 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(nonemptyImpWitness_type,type,
% 0.27/0.46 nonemptyImpWitness: $o ).
% 0.27/0.46
% 0.27/0.46 thf(nonemptyImpWitness,definition,
% 0.27/0.46 ( nonemptyImpWitness
% 0.27/0.46 = ( ! [A: $i] :
% 0.27/0.46 ( ( nonempty @ A )
% 0.27/0.46 => ? [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 & $true ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(uniqinunit_type,type,
% 0.27/0.46 uniqinunit: $o ).
% 0.27/0.46
% 0.27/0.46 thf(uniqinunit,definition,
% 0.27/0.46 ( uniqinunit
% 0.27/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.27/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(notinsingleton_type,type,
% 0.27/0.46 notinsingleton: $o ).
% 0.27/0.46
% 0.27/0.46 thf(notinsingleton,definition,
% 0.27/0.46 ( notinsingleton
% 0.27/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.46 ( ( Xx != Xy )
% 0.27/0.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(eqinunit_type,type,
% 0.27/0.46 eqinunit: $o ).
% 0.27/0.46
% 0.27/0.46 thf(eqinunit,definition,
% 0.27/0.46 ( eqinunit
% 0.27/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.46 ( ( Xx = Xy )
% 0.27/0.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(singletonsswitch_type,type,
% 0.27/0.46 singletonsswitch: $o ).
% 0.27/0.46
% 0.27/0.46 thf(singletonsswitch,definition,
% 0.27/0.46 ( singletonsswitch
% 0.27/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.27/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(upairsetE_type,type,
% 0.27/0.46 upairsetE: $o ).
% 0.27/0.46
% 0.27/0.46 thf(upairsetE,definition,
% 0.27/0.46 ( upairsetE
% 0.27/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.27/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.27/0.46 => ( ( Xz = Xx )
% 0.27/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(upairsetIL_type,type,
% 0.27/0.46 upairsetIL: $o ).
% 0.27/0.46
% 0.27/0.46 thf(upairsetIL,definition,
% 0.27/0.46 ( upairsetIL
% 0.27/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(upairsetIR_type,type,
% 0.27/0.46 upairsetIR: $o ).
% 0.27/0.46
% 0.27/0.46 thf(upairsetIR,definition,
% 0.27/0.46 ( upairsetIR
% 0.27/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(emptyE1_type,type,
% 0.27/0.46 emptyE1: $o ).
% 0.27/0.46
% 0.27/0.46 thf(emptyE1,definition,
% 0.27/0.46 ( emptyE1
% 0.27/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.46 ( ? [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 & ( Xphi @ Xx ) )
% 0.27/0.46 => ( ( ( dsetconstr @ A
% 0.27/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.46 = emptyset )
% 0.27/0.46 => $false ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(vacuousDall_type,type,
% 0.27/0.46 vacuousDall: $o ).
% 0.27/0.46
% 0.27/0.46 thf(vacuousDall,definition,
% 0.27/0.46 ( vacuousDall
% 0.27/0.46 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ emptyset )
% 0.27/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(quantDeMorgan1_type,type,
% 0.27/0.46 quantDeMorgan1: $o ).
% 0.27/0.46
% 0.27/0.46 thf(quantDeMorgan1,definition,
% 0.27/0.46 ( quantDeMorgan1
% 0.27/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.46 ( ~ ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ( Xphi @ Xx ) )
% 0.27/0.46 => ? [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(quantDeMorgan2_type,type,
% 0.27/0.46 quantDeMorgan2: $o ).
% 0.27/0.46
% 0.27/0.46 thf(quantDeMorgan2,definition,
% 0.27/0.46 ( quantDeMorgan2
% 0.27/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.46 ( ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ~ ( Xphi @ Xx ) )
% 0.27/0.46 => ~ ? [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(quantDeMorgan3_type,type,
% 0.27/0.46 quantDeMorgan3: $o ).
% 0.27/0.46
% 0.27/0.46 thf(quantDeMorgan3,definition,
% 0.27/0.46 ( quantDeMorgan3
% 0.27/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.46 ( ~ ? [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 & ( Xphi @ Xx ) )
% 0.27/0.46 => ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(quantDeMorgan4_type,type,
% 0.27/0.46 quantDeMorgan4: $o ).
% 0.27/0.46
% 0.27/0.46 thf(quantDeMorgan4,definition,
% 0.27/0.46 ( quantDeMorgan4
% 0.27/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.46 ( ? [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 & ~ ( Xphi @ Xx ) )
% 0.27/0.46 => ~ ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(prop2setI_type,type,
% 0.27/0.46 prop2setI: $o ).
% 0.27/0.46
% 0.27/0.46 thf(prop2setI,definition,
% 0.27/0.46 ( prop2setI
% 0.27/0.46 = ( ! [Xphi: $o] :
% 0.27/0.46 ( Xphi
% 0.27/0.46 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(set2prop_type,type,
% 0.27/0.46 set2prop: $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(prop2set2propI_type,type,
% 0.27/0.46 prop2set2propI: $o ).
% 0.27/0.46
% 0.27/0.46 thf(prop2set2propI,definition,
% 0.27/0.46 ( prop2set2propI
% 0.27/0.46 = ( ! [Xphi: $o] :
% 0.27/0.46 ( Xphi
% 0.27/0.46 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(notdexE_type,type,
% 0.27/0.46 notdexE: $o ).
% 0.27/0.46
% 0.27/0.46 thf(notdexE,definition,
% 0.27/0.46 ( notdexE
% 0.27/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.46 ( ~ ? [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 & ( Xphi @ Xx ) )
% 0.27/0.46 => ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(notdallE_type,type,
% 0.27/0.46 notdallE: $o ).
% 0.27/0.46
% 0.27/0.46 thf(notdallE,definition,
% 0.27/0.46 ( notdallE
% 0.27/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.46 ( ~ ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ( Xphi @ Xx ) )
% 0.27/0.46 => ? [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(exuI1_type,type,
% 0.27/0.46 exuI1: $o ).
% 0.27/0.46
% 0.27/0.46 thf(exuI1,definition,
% 0.27/0.46 ( exuI1
% 0.27/0.46 = ( ! [Xphi: $i > $o] :
% 0.27/0.46 ( ? [Xx: $i] :
% 0.27/0.46 ( ( Xphi @ Xx )
% 0.27/0.46 & ! [Xy: $i] :
% 0.27/0.46 ( ( Xphi @ Xy )
% 0.27/0.46 => ( Xx = Xy ) ) )
% 0.27/0.46 => ( exu
% 0.27/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(exuI3_type,type,
% 0.27/0.46 exuI3: $o ).
% 0.27/0.46
% 0.27/0.46 thf(exuI3,definition,
% 0.27/0.46 ( exuI3
% 0.27/0.46 = ( ! [Xphi: $i > $o] :
% 0.27/0.46 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.27/0.46 => ( ! [Xx: $i,Xy: $i] :
% 0.27/0.46 ( ( Xphi @ Xx )
% 0.27/0.46 => ( ( Xphi @ Xy )
% 0.27/0.46 => ( Xx = Xy ) ) )
% 0.27/0.46 => ( exu
% 0.27/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(exuI2_type,type,
% 0.27/0.46 exuI2: $o ).
% 0.27/0.46
% 0.27/0.46 thf(exuI2,definition,
% 0.27/0.46 ( exuI2
% 0.27/0.46 = ( ! [Xphi: $i > $o] :
% 0.27/0.46 ( ? [Xx: $i] :
% 0.27/0.46 ! [Xy: $i] :
% 0.27/0.46 ( ( Xphi @ Xy )
% 0.27/0.46 <=> ( Xy = Xx ) )
% 0.27/0.46 => ( exu
% 0.27/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(inCongP_type,type,
% 0.27/0.46 inCongP: $o ).
% 0.27/0.46
% 0.27/0.46 thf(inCongP,definition,
% 0.27/0.46 ( inCongP
% 0.27/0.46 = ( ! [A: $i,B: $i] :
% 0.27/0.46 ( ( A = B )
% 0.27/0.46 => ! [Xx: $i,Xy: $i] :
% 0.27/0.46 ( ( Xx = Xy )
% 0.27/0.46 => ( ( in @ Xx @ A )
% 0.27/0.46 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(in__Cong_type,type,
% 0.27/0.46 in__Cong: $o ).
% 0.27/0.46
% 0.27/0.46 thf(in__Cong,definition,
% 0.27/0.46 ( in__Cong
% 0.27/0.46 = ( ! [A: $i,B: $i] :
% 0.27/0.46 ( ( A = B )
% 0.27/0.46 => ! [Xx: $i,Xy: $i] :
% 0.27/0.46 ( ( Xx = Xy )
% 0.27/0.46 => ( ( in @ Xx @ A )
% 0.27/0.46 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(exuE3u_type,type,
% 0.27/0.46 exuE3u: $o ).
% 0.27/0.46
% 0.27/0.46 thf(exuE3u,definition,
% 0.27/0.46 ( exuE3u
% 0.27/0.46 = ( ! [Xphi: $i > $o] :
% 0.27/0.46 ( ( exu
% 0.27/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.46 => ! [Xx: $i,Xy: $i] :
% 0.27/0.46 ( ( Xphi @ Xx )
% 0.27/0.46 => ( ( Xphi @ Xy )
% 0.27/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(exu__Cong_type,type,
% 0.27/0.46 exu__Cong: $o ).
% 0.27/0.46
% 0.27/0.46 thf(exu__Cong,definition,
% 0.27/0.46 ( exu__Cong
% 0.27/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.27/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.27/0.46 ( ( Xx = Xy )
% 0.27/0.46 => ( ( Xphi @ Xx )
% 0.27/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.27/0.46 => ( ( exu
% 0.27/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.46 <=> ( exu
% 0.27/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(emptyset__Cong_type,type,
% 0.27/0.46 emptyset__Cong: $o ).
% 0.27/0.46
% 0.27/0.46 thf(emptyset__Cong,definition,
% 0.27/0.46 ( emptyset__Cong
% 0.27/0.46 = ( emptyset = emptyset ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(setadjoin__Cong_type,type,
% 0.27/0.46 setadjoin__Cong: $o ).
% 0.27/0.46
% 0.27/0.46 thf(setadjoin__Cong,definition,
% 0.27/0.46 ( setadjoin__Cong
% 0.27/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.46 ( ( Xx = Xy )
% 0.27/0.46 => ! [Xz: $i,Xu: $i] :
% 0.27/0.46 ( ( Xz = Xu )
% 0.27/0.46 => ( ( setadjoin @ Xx @ Xz )
% 0.27/0.46 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(powerset__Cong_type,type,
% 0.27/0.46 powerset__Cong: $o ).
% 0.27/0.46
% 0.27/0.46 thf(powerset__Cong,definition,
% 0.27/0.46 ( powerset__Cong
% 0.27/0.46 = ( ! [A: $i,B: $i] :
% 0.27/0.46 ( ( A = B )
% 0.27/0.46 => ( ( powerset @ A )
% 0.27/0.46 = ( powerset @ B ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(setunion__Cong_type,type,
% 0.27/0.46 setunion__Cong: $o ).
% 0.27/0.46
% 0.27/0.46 thf(setunion__Cong,definition,
% 0.27/0.46 ( setunion__Cong
% 0.27/0.46 = ( ! [A: $i,B: $i] :
% 0.27/0.46 ( ( A = B )
% 0.27/0.46 => ( ( setunion @ A )
% 0.27/0.46 = ( setunion @ B ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(omega__Cong_type,type,
% 0.27/0.46 omega__Cong: $o ).
% 0.27/0.46
% 0.27/0.46 thf(omega__Cong,definition,
% 0.27/0.46 ( omega__Cong
% 0.27/0.46 = ( omega = omega ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(exuEu_type,type,
% 0.27/0.46 exuEu: $o ).
% 0.27/0.46
% 0.27/0.46 thf(exuEu,definition,
% 0.27/0.46 ( exuEu
% 0.27/0.46 = ( ! [Xphi: $i > $o] :
% 0.27/0.46 ( ( exu
% 0.27/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.46 => ! [Xx: $i,Xy: $i] :
% 0.27/0.46 ( ( Xphi @ Xx )
% 0.27/0.46 => ( ( Xphi @ Xy )
% 0.27/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(descr__Cong_type,type,
% 0.27/0.46 descr__Cong: $o ).
% 0.27/0.46
% 0.27/0.46 thf(descr__Cong,definition,
% 0.27/0.46 ( descr__Cong
% 0.27/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.27/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.27/0.46 ( ( Xx = Xy )
% 0.27/0.46 => ( ( Xphi @ Xx )
% 0.27/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.27/0.46 => ( ( exu
% 0.27/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.46 => ( ( exu
% 0.27/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.27/0.46 => ( ( descr
% 0.27/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.46 = ( descr
% 0.27/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(dsetconstr__Cong_type,type,
% 0.27/0.46 dsetconstr__Cong: $o ).
% 0.27/0.46
% 0.27/0.46 thf(dsetconstr__Cong,definition,
% 0.27/0.46 ( dsetconstr__Cong
% 0.27/0.46 = ( ! [A: $i,B: $i] :
% 0.27/0.46 ( ( A = B )
% 0.27/0.46 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.27/0.46 ( ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ! [Xy: $i] :
% 0.27/0.46 ( ( in @ Xy @ B )
% 0.27/0.46 => ( ( Xx = Xy )
% 0.27/0.46 => ( ( Xphi @ Xx )
% 0.27/0.46 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.27/0.46 => ( ( dsetconstr @ A
% 0.27/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.46 = ( dsetconstr @ B
% 0.27/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(subset_type,type,
% 0.27/0.46 subset: $i > $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(disjoint_type,type,
% 0.27/0.46 disjoint: $i > $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(setsmeet_type,type,
% 0.27/0.46 setsmeet: $i > $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(subsetI1_type,type,
% 0.27/0.46 subsetI1: $o ).
% 0.27/0.46
% 0.27/0.46 thf(subsetI1,definition,
% 0.27/0.46 ( subsetI1
% 0.27/0.46 = ( ! [A: $i,B: $i] :
% 0.27/0.46 ( ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ( in @ Xx @ B ) )
% 0.27/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(eqimpsubset2_type,type,
% 0.27/0.46 eqimpsubset2: $o ).
% 0.27/0.46
% 0.27/0.46 thf(eqimpsubset2,definition,
% 0.27/0.46 ( eqimpsubset2
% 0.27/0.46 = ( ! [A: $i,B: $i] :
% 0.27/0.46 ( ( A = B )
% 0.27/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(eqimpsubset1_type,type,
% 0.27/0.46 eqimpsubset1: $o ).
% 0.27/0.46
% 0.27/0.46 thf(eqimpsubset1,definition,
% 0.27/0.46 ( eqimpsubset1
% 0.27/0.46 = ( ! [A: $i,B: $i] :
% 0.27/0.46 ( ( A = B )
% 0.27/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(subsetI2_type,type,
% 0.27/0.46 subsetI2: $o ).
% 0.27/0.46
% 0.27/0.46 thf(subsetI2,definition,
% 0.27/0.46 ( subsetI2
% 0.27/0.46 = ( ! [A: $i,B: $i] :
% 0.27/0.46 ( ! [Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ( in @ Xx @ B ) )
% 0.27/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(emptysetsubset_type,type,
% 0.27/0.46 emptysetsubset: $o ).
% 0.27/0.46
% 0.27/0.46 thf(emptysetsubset,definition,
% 0.27/0.46 ( emptysetsubset
% 0.27/0.46 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(subsetE_type,type,
% 0.27/0.46 subsetE: $o ).
% 0.27/0.46
% 0.27/0.46 thf(subsetE,definition,
% 0.27/0.46 ( subsetE
% 0.27/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.46 ( ( subset @ A @ B )
% 0.27/0.46 => ( ( in @ Xx @ A )
% 0.27/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(subsetE2_type,type,
% 0.27/0.46 subsetE2: $o ).
% 0.27/0.46
% 0.27/0.46 thf(subsetE2,definition,
% 0.27/0.46 ( subsetE2
% 0.27/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.46 ( ( subset @ A @ B )
% 0.27/0.46 => ( ~ ( in @ Xx @ B )
% 0.27/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(notsubsetI_type,type,
% 0.27/0.46 notsubsetI: $o ).
% 0.27/0.46
% 0.27/0.46 thf(notsubsetI,definition,
% 0.27/0.46 ( notsubsetI
% 0.27/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ( ~ ( in @ Xx @ B )
% 0.27/0.46 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(notequalI1_type,type,
% 0.27/0.46 notequalI1: $o ).
% 0.27/0.46
% 0.27/0.46 thf(notequalI1,definition,
% 0.27/0.46 ( notequalI1
% 0.27/0.46 = ( ! [A: $i,B: $i] :
% 0.27/0.46 ( ~ ( subset @ A @ B )
% 0.27/0.46 => ( A != B ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(notequalI2_type,type,
% 0.27/0.46 notequalI2: $o ).
% 0.27/0.46
% 0.27/0.46 thf(notequalI2,definition,
% 0.27/0.46 ( notequalI2
% 0.27/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.46 ( ( in @ Xx @ A )
% 0.27/0.46 => ( ~ ( in @ Xx @ B )
% 0.27/0.46 => ( A != B ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(subsetRefl_type,type,
% 0.27/0.46 subsetRefl: $o ).
% 0.27/0.46
% 0.27/0.46 thf(subsetRefl,definition,
% 0.27/0.46 ( subsetRefl
% 0.27/0.46 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(subsetTrans_type,type,
% 0.27/0.46 subsetTrans: $o ).
% 0.27/0.46
% 0.27/0.46 thf(subsetTrans,definition,
% 0.27/0.46 ( subsetTrans
% 0.27/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.27/0.46 ( ( subset @ A @ B )
% 0.27/0.46 => ( ( subset @ B @ C )
% 0.27/0.46 => ( subset @ A @ C ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(setadjoinSub_type,type,
% 0.27/0.46 setadjoinSub: $o ).
% 0.27/0.46
% 0.27/0.46 thf(setadjoinSub,definition,
% 0.27/0.46 ( setadjoinSub
% 0.27/0.46 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(setadjoinSub2_type,type,
% 0.27/0.46 setadjoinSub2: $o ).
% 0.27/0.46
% 0.27/0.46 thf(setadjoinSub2,definition,
% 0.27/0.47 ( setadjoinSub2
% 0.27/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.27/0.47 ( ( subset @ A @ B )
% 0.27/0.47 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(subset2powerset_type,type,
% 0.27/0.47 subset2powerset: $o ).
% 0.27/0.47
% 0.27/0.47 thf(subset2powerset,definition,
% 0.27/0.47 ( subset2powerset
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( subset @ A @ B )
% 0.27/0.47 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setextsub_type,type,
% 0.27/0.47 setextsub: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setextsub,definition,
% 0.27/0.47 ( setextsub
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( subset @ A @ B )
% 0.27/0.47 => ( ( subset @ B @ A )
% 0.27/0.47 => ( A = B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(subsetemptysetimpeq_type,type,
% 0.27/0.47 subsetemptysetimpeq: $o ).
% 0.27/0.47
% 0.27/0.47 thf(subsetemptysetimpeq,definition,
% 0.27/0.47 ( subsetemptysetimpeq
% 0.27/0.47 = ( ! [A: $i] :
% 0.27/0.47 ( ( subset @ A @ emptyset )
% 0.27/0.47 => ( A = emptyset ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(powersetI1_type,type,
% 0.27/0.47 powersetI1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(powersetI1,definition,
% 0.27/0.47 ( powersetI1
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( subset @ B @ A )
% 0.27/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(powersetE1_type,type,
% 0.27/0.47 powersetE1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(powersetE1,definition,
% 0.27/0.47 ( powersetE1
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.27/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(inPowerset_type,type,
% 0.27/0.47 inPowerset: $o ).
% 0.27/0.47
% 0.27/0.47 thf(inPowerset,definition,
% 0.27/0.47 ( inPowerset
% 0.27/0.47 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(powersetsubset_type,type,
% 0.27/0.47 powersetsubset: $o ).
% 0.27/0.47
% 0.27/0.47 thf(powersetsubset,definition,
% 0.27/0.47 ( powersetsubset
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( subset @ A @ B )
% 0.27/0.47 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(sepInPowerset_type,type,
% 0.27/0.47 sepInPowerset: $o ).
% 0.27/0.47
% 0.27/0.47 thf(sepInPowerset,definition,
% 0.27/0.47 ( sepInPowerset
% 0.27/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.47 ( in
% 0.27/0.47 @ ( dsetconstr @ A
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.47 @ ( powerset @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(sepSubset_type,type,
% 0.27/0.47 sepSubset: $o ).
% 0.27/0.47
% 0.27/0.47 thf(sepSubset,definition,
% 0.27/0.47 ( sepSubset
% 0.27/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.47 ( subset
% 0.27/0.47 @ ( dsetconstr @ A
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.47 @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binunion_type,type,
% 0.27/0.47 binunion: $i > $i > $i ).
% 0.27/0.47
% 0.27/0.47 thf(binunionIL_type,type,
% 0.27/0.47 binunionIL: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binunionIL,definition,
% 0.27/0.47 ( binunionIL
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(upairset2IR_type,type,
% 0.27/0.47 upairset2IR: $o ).
% 0.27/0.47
% 0.27/0.47 thf(upairset2IR,definition,
% 0.27/0.47 ( upairset2IR
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binunionIR_type,type,
% 0.27/0.47 binunionIR: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binunionIR,definition,
% 0.27/0.47 ( binunionIR
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ B )
% 0.27/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binunionEcases_type,type,
% 0.27/0.47 binunionEcases: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binunionEcases,definition,
% 0.27/0.47 ( binunionEcases
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.27/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.27/0.47 => ( ( ( in @ Xx @ A )
% 0.27/0.47 => Xphi )
% 0.27/0.47 => ( ( ( in @ Xx @ B )
% 0.27/0.47 => Xphi )
% 0.27/0.47 => Xphi ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binunionE_type,type,
% 0.27/0.47 binunionE: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binunionE,definition,
% 0.27/0.47 ( binunionE
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.27/0.47 => ( ( in @ Xx @ A )
% 0.27/0.47 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binunionLsub_type,type,
% 0.27/0.47 binunionLsub: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binunionLsub,definition,
% 0.27/0.47 ( binunionLsub
% 0.27/0.47 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binunionRsub_type,type,
% 0.27/0.47 binunionRsub: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binunionRsub,definition,
% 0.27/0.47 ( binunionRsub
% 0.27/0.47 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binintersect_type,type,
% 0.27/0.47 binintersect: $i > $i > $i ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectI_type,type,
% 0.27/0.47 binintersectI: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectI,definition,
% 0.27/0.47 ( binintersectI
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ B )
% 0.27/0.47 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectSubset5_type,type,
% 0.27/0.47 binintersectSubset5: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectSubset5,definition,
% 0.27/0.47 ( binintersectSubset5
% 0.27/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.27/0.47 ( ( subset @ C @ A )
% 0.27/0.47 => ( ( subset @ C @ B )
% 0.27/0.47 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectEL_type,type,
% 0.27/0.47 binintersectEL: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectEL,definition,
% 0.27/0.47 ( binintersectEL
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.27/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectLsub_type,type,
% 0.27/0.47 binintersectLsub: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectLsub,definition,
% 0.27/0.47 ( binintersectLsub
% 0.27/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectSubset2_type,type,
% 0.27/0.47 binintersectSubset2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectSubset2,definition,
% 0.27/0.47 ( binintersectSubset2
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( subset @ A @ B )
% 0.27/0.47 => ( ( binintersect @ A @ B )
% 0.27/0.47 = A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectSubset3_type,type,
% 0.27/0.47 binintersectSubset3: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectSubset3,definition,
% 0.27/0.47 ( binintersectSubset3
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( ( binintersect @ A @ B )
% 0.27/0.47 = B )
% 0.27/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectER_type,type,
% 0.27/0.47 binintersectER: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectER,definition,
% 0.27/0.47 ( binintersectER
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.27/0.47 => ( in @ Xx @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(disjointsetsI1_type,type,
% 0.27/0.47 disjointsetsI1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(disjointsetsI1,definition,
% 0.27/0.47 ( disjointsetsI1
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ~ ? [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 & ( in @ Xx @ B ) )
% 0.27/0.47 => ( ( binintersect @ A @ B )
% 0.27/0.47 = emptyset ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectRsub_type,type,
% 0.27/0.47 binintersectRsub: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectRsub,definition,
% 0.27/0.47 ( binintersectRsub
% 0.27/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectSubset4_type,type,
% 0.27/0.47 binintersectSubset4: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectSubset4,definition,
% 0.27/0.47 ( binintersectSubset4
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( subset @ B @ A )
% 0.27/0.47 => ( ( binintersect @ A @ B )
% 0.27/0.47 = B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectSubset1_type,type,
% 0.27/0.47 binintersectSubset1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectSubset1,definition,
% 0.27/0.47 ( binintersectSubset1
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( ( binintersect @ A @ B )
% 0.27/0.47 = A )
% 0.27/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(bs114d_type,type,
% 0.27/0.47 bs114d: $o ).
% 0.27/0.47
% 0.27/0.47 thf(bs114d,definition,
% 0.27/0.47 ( bs114d
% 0.27/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.27/0.47 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.27/0.47 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(regular_type,type,
% 0.27/0.47 regular: $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(setminus_type,type,
% 0.27/0.47 setminus: $i > $i > $i ).
% 0.27/0.47
% 0.27/0.47 thf(setminusI_type,type,
% 0.27/0.47 setminusI: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setminusI,definition,
% 0.27/0.47 ( setminusI
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ~ ( in @ Xx @ B )
% 0.27/0.47 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setminusEL_type,type,
% 0.27/0.47 setminusEL: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setminusEL,definition,
% 0.27/0.47 ( setminusEL
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.27/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setminusER_type,type,
% 0.27/0.47 setminusER: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setminusER,definition,
% 0.27/0.47 ( setminusER
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.27/0.47 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setminusSubset2_type,type,
% 0.27/0.47 setminusSubset2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setminusSubset2,definition,
% 0.27/0.47 ( setminusSubset2
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( subset @ A @ B )
% 0.27/0.47 => ( ( setminus @ A @ B )
% 0.27/0.47 = emptyset ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setminusERneg_type,type,
% 0.27/0.47 setminusERneg: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setminusERneg,definition,
% 0.27/0.47 ( setminusERneg
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.27/0.47 => ( ( in @ Xx @ A )
% 0.27/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setminusELneg_type,type,
% 0.27/0.47 setminusELneg: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setminusELneg,definition,
% 0.27/0.47 ( setminusELneg
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.27/0.47 => ( ~ ( in @ Xx @ B )
% 0.27/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setminusILneg_type,type,
% 0.27/0.47 setminusILneg: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setminusILneg,definition,
% 0.27/0.47 ( setminusILneg
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ~ ( in @ Xx @ A )
% 0.27/0.47 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setminusIRneg_type,type,
% 0.27/0.47 setminusIRneg: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setminusIRneg,definition,
% 0.27/0.47 ( setminusIRneg
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ B )
% 0.27/0.47 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setminusLsub_type,type,
% 0.27/0.47 setminusLsub: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setminusLsub,definition,
% 0.27/0.47 ( setminusLsub
% 0.27/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setminusSubset1_type,type,
% 0.27/0.47 setminusSubset1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setminusSubset1,definition,
% 0.27/0.47 ( setminusSubset1
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( ( setminus @ A @ B )
% 0.27/0.47 = emptyset )
% 0.27/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(symdiff_type,type,
% 0.27/0.47 symdiff: $i > $i > $i ).
% 0.27/0.47
% 0.27/0.47 thf(symdiffE_type,type,
% 0.27/0.47 symdiffE: $o ).
% 0.27/0.47
% 0.27/0.47 thf(symdiffE,definition,
% 0.27/0.47 ( symdiffE
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.27/0.47 => ! [Xphi: $o] :
% 0.27/0.47 ( ( ( in @ Xx @ A )
% 0.27/0.47 => ( ~ ( in @ Xx @ B )
% 0.27/0.47 => Xphi ) )
% 0.27/0.47 => ( ( ~ ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ B )
% 0.27/0.47 => Xphi ) )
% 0.27/0.47 => Xphi ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(symdiffI1_type,type,
% 0.27/0.47 symdiffI1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(symdiffI1,definition,
% 0.27/0.47 ( symdiffI1
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ~ ( in @ Xx @ B )
% 0.27/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(symdiffI2_type,type,
% 0.27/0.47 symdiffI2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(symdiffI2,definition,
% 0.27/0.47 ( symdiffI2
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ~ ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ B )
% 0.27/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(symdiffIneg1_type,type,
% 0.27/0.47 symdiffIneg1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(symdiffIneg1,definition,
% 0.27/0.47 ( symdiffIneg1
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ B )
% 0.27/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(symdiffIneg2_type,type,
% 0.27/0.47 symdiffIneg2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(symdiffIneg2,definition,
% 0.27/0.47 ( symdiffIneg2
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ~ ( in @ Xx @ A )
% 0.27/0.47 => ( ~ ( in @ Xx @ B )
% 0.27/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(iskpair_type,type,
% 0.27/0.47 iskpair: $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(secondinupair_type,type,
% 0.27/0.47 secondinupair: $o ).
% 0.27/0.47
% 0.27/0.47 thf(secondinupair,definition,
% 0.27/0.47 ( secondinupair
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setukpairIL_type,type,
% 0.27/0.47 setukpairIL: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setukpairIL,definition,
% 0.27/0.47 ( setukpairIL
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setukpairIR_type,type,
% 0.27/0.47 setukpairIR: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setukpairIR,definition,
% 0.27/0.47 ( setukpairIR
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(kpairiskpair_type,type,
% 0.27/0.47 kpairiskpair: $o ).
% 0.27/0.47
% 0.27/0.47 thf(kpairiskpair,definition,
% 0.27/0.47 ( kpairiskpair
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(kpair_type,type,
% 0.27/0.47 kpair: $i > $i > $i ).
% 0.27/0.47
% 0.27/0.47 thf(kpairp_type,type,
% 0.27/0.47 kpairp: $o ).
% 0.27/0.47
% 0.27/0.47 thf(kpairp,definition,
% 0.27/0.47 ( kpairp
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(cartprod_type,type,
% 0.27/0.47 cartprod: $i > $i > $i ).
% 0.27/0.47
% 0.27/0.47 thf(singletonsubset_type,type,
% 0.27/0.47 singletonsubset: $o ).
% 0.27/0.47
% 0.27/0.47 thf(singletonsubset,definition,
% 0.27/0.47 ( singletonsubset
% 0.27/0.47 = ( ! [A: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(singletoninpowerset_type,type,
% 0.27/0.47 singletoninpowerset: $o ).
% 0.27/0.47
% 0.27/0.47 thf(singletoninpowerset,definition,
% 0.27/0.47 ( singletoninpowerset
% 0.27/0.47 = ( ! [A: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(singletoninpowunion_type,type,
% 0.27/0.47 singletoninpowunion: $o ).
% 0.27/0.47
% 0.27/0.47 thf(singletoninpowunion,definition,
% 0.27/0.47 ( singletoninpowunion
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(upairset2E_type,type,
% 0.27/0.47 upairset2E: $o ).
% 0.27/0.47
% 0.27/0.47 thf(upairset2E,definition,
% 0.27/0.47 ( upairset2E
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.27/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.27/0.47 => ( ( Xz = Xx )
% 0.27/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(upairsubunion_type,type,
% 0.27/0.47 upairsubunion: $o ).
% 0.27/0.47
% 0.27/0.47 thf(upairsubunion,definition,
% 0.27/0.47 ( upairsubunion
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(upairinpowunion_type,type,
% 0.27/0.47 upairinpowunion: $o ).
% 0.27/0.47
% 0.27/0.47 thf(upairinpowunion,definition,
% 0.27/0.47 ( upairinpowunion
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(ubforcartprodlem1_type,type,
% 0.27/0.47 ubforcartprodlem1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(ubforcartprodlem1,definition,
% 0.27/0.47 ( ubforcartprodlem1
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(ubforcartprodlem2_type,type,
% 0.27/0.47 ubforcartprodlem2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(ubforcartprodlem2,definition,
% 0.27/0.47 ( ubforcartprodlem2
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(ubforcartprodlem3_type,type,
% 0.27/0.47 ubforcartprodlem3: $o ).
% 0.27/0.47
% 0.27/0.47 thf(ubforcartprodlem3,definition,
% 0.27/0.47 ( ubforcartprodlem3
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(cartprodpairin_type,type,
% 0.27/0.47 cartprodpairin: $o ).
% 0.27/0.47
% 0.27/0.47 thf(cartprodpairin,definition,
% 0.27/0.47 ( cartprodpairin
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(cartprodmempair1_type,type,
% 0.27/0.47 cartprodmempair1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(cartprodmempair1,definition,
% 0.27/0.47 ( cartprodmempair1
% 0.27/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.27/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.27/0.47 => ? [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 & ? [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 & ( Xu
% 0.27/0.47 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(cartprodmempair_type,type,
% 0.27/0.47 cartprodmempair: $o ).
% 0.27/0.47
% 0.27/0.47 thf(cartprodmempair,definition,
% 0.27/0.47 ( cartprodmempair
% 0.27/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.27/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.27/0.47 => ( iskpair @ Xu ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setunionE2_type,type,
% 0.27/0.47 setunionE2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setunionE2,definition,
% 0.27/0.47 ( setunionE2
% 0.27/0.47 = ( ! [A: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.27/0.47 => ? [X: $i] :
% 0.27/0.47 ( ( in @ X @ A )
% 0.27/0.47 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setunionsingleton1_type,type,
% 0.27/0.47 setunionsingleton1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setunionsingleton1,definition,
% 0.27/0.47 ( setunionsingleton1
% 0.27/0.47 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setunionsingleton2_type,type,
% 0.27/0.47 setunionsingleton2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setunionsingleton2,definition,
% 0.27/0.47 ( setunionsingleton2
% 0.27/0.47 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setunionsingleton_type,type,
% 0.27/0.47 setunionsingleton: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setunionsingleton,definition,
% 0.27/0.47 ( setunionsingleton
% 0.27/0.47 = ( ! [Xx: $i] :
% 0.27/0.47 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.27/0.47 = Xx ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(singleton_type,type,
% 0.27/0.47 singleton: $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(singletonprop_type,type,
% 0.27/0.47 singletonprop: $o ).
% 0.27/0.47
% 0.27/0.47 thf(singletonprop,definition,
% 0.27/0.47 ( singletonprop
% 0.27/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.47 ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ A )
% 0.27/0.47 => ( ( Xphi @ Xx )
% 0.27/0.47 => ( ( Xphi @ Xy )
% 0.27/0.47 => ( Xx = Xy ) ) ) ) )
% 0.27/0.47 => ( ? [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 & ( Xphi @ Xx ) )
% 0.27/0.47 => ( singleton
% 0.27/0.47 @ ( dsetconstr @ A
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(ex1_type,type,
% 0.27/0.47 ex1: $i > ( $i > $o ) > $o ).
% 0.27/0.47
% 0.27/0.47 thf(ex1E1_type,type,
% 0.27/0.47 ex1E1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(ex1E1,definition,
% 0.27/0.47 ( ex1E1
% 0.27/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.47 ( ( ex1 @ A
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.47 => ? [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(ex1I_type,type,
% 0.27/0.47 ex1I: $o ).
% 0.27/0.47
% 0.27/0.47 thf(ex1I,definition,
% 0.27/0.47 ( ex1I
% 0.27/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( Xphi @ Xx )
% 0.27/0.47 => ( ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ A )
% 0.27/0.47 => ( ( Xphi @ Xy )
% 0.27/0.47 => ( Xy = Xx ) ) )
% 0.27/0.47 => ( ex1 @ A
% 0.27/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(ex1I2_type,type,
% 0.27/0.47 ex1I2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(ex1I2,definition,
% 0.27/0.47 ( ex1I2
% 0.27/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.47 ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ A )
% 0.27/0.47 => ( ( Xphi @ Xx )
% 0.27/0.47 => ( ( Xphi @ Xy )
% 0.27/0.47 => ( Xx = Xy ) ) ) ) )
% 0.27/0.47 => ( ? [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 & ( Xphi @ Xx ) )
% 0.27/0.47 => ( ex1 @ A
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(singletonsuniq_type,type,
% 0.27/0.47 singletonsuniq: $o ).
% 0.27/0.47
% 0.27/0.47 thf(singletonsuniq,definition,
% 0.27/0.47 ( singletonsuniq
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( ( setadjoin @ Xx @ emptyset )
% 0.27/0.47 = ( setadjoin @ Xy @ emptyset ) )
% 0.27/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(atmost1p_type,type,
% 0.27/0.47 atmost1p: $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(atleast2p_type,type,
% 0.27/0.47 atleast2p: $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(atmost2p_type,type,
% 0.27/0.47 atmost2p: $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(upairsetp_type,type,
% 0.27/0.47 upairsetp: $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(setukpairinjL1_type,type,
% 0.27/0.47 setukpairinjL1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setukpairinjL1,definition,
% 0.27/0.47 ( setukpairinjL1
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.27/0.47 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.27/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(kfstsingleton_type,type,
% 0.27/0.47 kfstsingleton: $o ).
% 0.27/0.47
% 0.27/0.47 thf(kfstsingleton,definition,
% 0.27/0.47 ( kfstsingleton
% 0.27/0.47 = ( ! [Xu: $i] :
% 0.27/0.47 ( ( iskpair @ Xu )
% 0.27/0.47 => ( singleton
% 0.27/0.47 @ ( dsetconstr @ ( setunion @ Xu )
% 0.27/0.47 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(theprop_type,type,
% 0.27/0.47 theprop: $o ).
% 0.27/0.47
% 0.27/0.47 thf(theprop,definition,
% 0.27/0.47 ( theprop
% 0.27/0.47 = ( ! [X: $i] :
% 0.27/0.47 ( ( singleton @ X )
% 0.27/0.47 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(kfst_type,type,
% 0.27/0.47 kfst: $i > $i ).
% 0.27/0.47
% 0.27/0.47 thf(kfstpairEq_type,type,
% 0.27/0.47 kfstpairEq: $o ).
% 0.27/0.47
% 0.27/0.47 thf(kfstpairEq,definition,
% 0.27/0.47 ( kfstpairEq
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.27/0.47 = Xx ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(cartprodfstin_type,type,
% 0.27/0.47 cartprodfstin: $o ).
% 0.27/0.47
% 0.27/0.47 thf(cartprodfstin,definition,
% 0.27/0.47 ( cartprodfstin
% 0.27/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.27/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.27/0.47 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setukpairinjL2_type,type,
% 0.27/0.47 setukpairinjL2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setukpairinjL2,definition,
% 0.27/0.47 ( setukpairinjL2
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.27/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.27/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.27/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setukpairinjL_type,type,
% 0.27/0.47 setukpairinjL: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setukpairinjL,definition,
% 0.27/0.47 ( setukpairinjL
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.27/0.47 ( ( ( kpair @ Xx @ Xy )
% 0.27/0.47 = ( kpair @ Xz @ Xu ) )
% 0.27/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setukpairinjR11_type,type,
% 0.27/0.47 setukpairinjR11: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setukpairinjR11,definition,
% 0.27/0.47 ( setukpairinjR11
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( Xx = Xy )
% 0.27/0.47 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.27/0.47 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setukpairinjR12_type,type,
% 0.27/0.47 setukpairinjR12: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setukpairinjR12,definition,
% 0.27/0.47 ( setukpairinjR12
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( Xx = Xy )
% 0.27/0.47 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.27/0.47 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setukpairinjR1_type,type,
% 0.27/0.47 setukpairinjR1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setukpairinjR1,definition,
% 0.27/0.47 ( setukpairinjR1
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.27/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.27/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.27/0.47 => ( ( Xz = Xu )
% 0.27/0.47 => ( Xy = Xu ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(upairequniteq_type,type,
% 0.27/0.47 upairequniteq: $o ).
% 0.27/0.47
% 0.27/0.47 thf(upairequniteq,definition,
% 0.27/0.47 ( upairequniteq
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.27/0.47 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.27/0.47 = ( setadjoin @ Xz @ emptyset ) )
% 0.27/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setukpairinjR2_type,type,
% 0.27/0.47 setukpairinjR2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setukpairinjR2,definition,
% 0.27/0.47 ( setukpairinjR2
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.27/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.27/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.27/0.47 => ( Xy = Xu ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setukpairinjR_type,type,
% 0.27/0.47 setukpairinjR: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setukpairinjR,definition,
% 0.27/0.47 ( setukpairinjR
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.27/0.47 ( ( ( kpair @ Xx @ Xy )
% 0.27/0.47 = ( kpair @ Xz @ Xu ) )
% 0.27/0.47 => ( Xy = Xu ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(ksndsingleton_type,type,
% 0.27/0.47 ksndsingleton: $o ).
% 0.27/0.47
% 0.27/0.47 thf(ksndsingleton,definition,
% 0.27/0.47 ( ksndsingleton
% 0.27/0.47 = ( ! [Xu: $i] :
% 0.27/0.47 ( ( iskpair @ Xu )
% 0.27/0.47 => ( singleton
% 0.27/0.47 @ ( dsetconstr @ ( setunion @ Xu )
% 0.27/0.47 @ ^ [Xx: $i] :
% 0.27/0.47 ( Xu
% 0.27/0.47 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(ksnd_type,type,
% 0.27/0.47 ksnd: $i > $i ).
% 0.27/0.47
% 0.27/0.47 thf(ksndpairEq_type,type,
% 0.27/0.47 ksndpairEq: $o ).
% 0.27/0.47
% 0.27/0.47 thf(ksndpairEq,definition,
% 0.27/0.47 ( ksndpairEq
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.27/0.47 = Xy ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(kpairsurjEq_type,type,
% 0.27/0.47 kpairsurjEq: $o ).
% 0.27/0.47
% 0.27/0.47 thf(kpairsurjEq,definition,
% 0.27/0.47 ( kpairsurjEq
% 0.27/0.47 = ( ! [Xu: $i] :
% 0.27/0.47 ( ( iskpair @ Xu )
% 0.27/0.47 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.27/0.47 = Xu ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(cartprodsndin_type,type,
% 0.27/0.47 cartprodsndin: $o ).
% 0.27/0.47
% 0.27/0.47 thf(cartprodsndin,definition,
% 0.27/0.47 ( cartprodsndin
% 0.27/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.27/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.27/0.47 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(cartprodpairmemEL_type,type,
% 0.27/0.47 cartprodpairmemEL: $o ).
% 0.27/0.47
% 0.27/0.47 thf(cartprodpairmemEL,definition,
% 0.27/0.47 ( cartprodpairmemEL
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.27/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(cartprodpairmemER_type,type,
% 0.27/0.47 cartprodpairmemER: $o ).
% 0.27/0.47
% 0.27/0.47 thf(cartprodpairmemER,definition,
% 0.27/0.47 ( cartprodpairmemER
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.27/0.47 => ( in @ Xy @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(cartprodmempaircEq_type,type,
% 0.27/0.47 cartprodmempaircEq: $o ).
% 0.27/0.47
% 0.27/0.47 thf(cartprodmempaircEq,definition,
% 0.27/0.47 ( cartprodmempaircEq
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( ( kpair @ Xx @ Xy )
% 0.27/0.47 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(cartprodfstpairEq_type,type,
% 0.27/0.47 cartprodfstpairEq: $o ).
% 0.27/0.47
% 0.27/0.47 thf(cartprodfstpairEq,definition,
% 0.27/0.47 ( cartprodfstpairEq
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.27/0.47 = Xx ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(cartprodsndpairEq_type,type,
% 0.27/0.47 cartprodsndpairEq: $o ).
% 0.27/0.47
% 0.27/0.47 thf(cartprodsndpairEq,definition,
% 0.27/0.47 ( cartprodsndpairEq
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.27/0.47 = Xy ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(cartprodpairsurjEq_type,type,
% 0.27/0.47 cartprodpairsurjEq: $o ).
% 0.27/0.47
% 0.27/0.47 thf(cartprodpairsurjEq,definition,
% 0.27/0.47 ( cartprodpairsurjEq
% 0.27/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.27/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.27/0.47 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.27/0.47 = Xu ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(breln_type,type,
% 0.27/0.47 breln: $i > $i > $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(breln,definition,
% 0.27/0.47 ( breln
% 0.27/0.47 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(dpsetconstr_type,type,
% 0.27/0.47 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.27/0.47
% 0.27/0.47 thf(dpsetconstrI_type,type,
% 0.27/0.47 dpsetconstrI: $o ).
% 0.27/0.47
% 0.27/0.47 thf(dpsetconstrI,definition,
% 0.27/0.47 ( dpsetconstrI
% 0.27/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( ( Xphi @ Xx @ Xy )
% 0.27/0.47 => ( in @ ( kpair @ Xx @ Xy )
% 0.27/0.47 @ ( dpsetconstr @ A @ B
% 0.27/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(dpsetconstrSub_type,type,
% 0.27/0.47 dpsetconstrSub: $o ).
% 0.27/0.47
% 0.27/0.47 thf(dpsetconstrSub,definition,
% 0.27/0.47 ( dpsetconstrSub
% 0.27/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.27/0.47 ( subset
% 0.27/0.47 @ ( dpsetconstr @ A @ B
% 0.27/0.47 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.27/0.47 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setOfPairsIsBReln_type,type,
% 0.27/0.47 setOfPairsIsBReln: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setOfPairsIsBReln,definition,
% 0.27/0.47 ( setOfPairsIsBReln
% 0.27/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.27/0.47 ( breln @ A @ B
% 0.27/0.47 @ ( dpsetconstr @ A @ B
% 0.27/0.47 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(dpsetconstrERa_type,type,
% 0.27/0.47 dpsetconstrERa: $o ).
% 0.27/0.47
% 0.27/0.47 thf(dpsetconstrERa,definition,
% 0.27/0.47 ( dpsetconstrERa
% 0.27/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.27/0.47 @ ( dpsetconstr @ A @ B
% 0.27/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.27/0.47 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(dpsetconstrEL1_type,type,
% 0.27/0.47 dpsetconstrEL1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(dpsetconstrEL1,definition,
% 0.27/0.47 ( dpsetconstrEL1
% 0.27/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.27/0.47 @ ( dpsetconstr @ A @ B
% 0.27/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.27/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(dpsetconstrEL2_type,type,
% 0.27/0.47 dpsetconstrEL2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(dpsetconstrEL2,definition,
% 0.27/0.47 ( dpsetconstrEL2
% 0.27/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.27/0.47 @ ( dpsetconstr @ A @ B
% 0.27/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.27/0.47 => ( in @ Xy @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(dpsetconstrER_type,type,
% 0.27/0.47 dpsetconstrER: $o ).
% 0.27/0.47
% 0.27/0.47 thf(dpsetconstrER,definition,
% 0.27/0.47 ( dpsetconstrER
% 0.27/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.27/0.47 @ ( dpsetconstr @ A @ B
% 0.27/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.27/0.47 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(func_type,type,
% 0.27/0.47 func: $i > $i > $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(funcSet_type,type,
% 0.27/0.47 funcSet: $i > $i > $i ).
% 0.27/0.47
% 0.27/0.47 thf(funcImageSingleton_type,type,
% 0.27/0.47 funcImageSingleton: $o ).
% 0.27/0.47
% 0.27/0.47 thf(funcImageSingleton,definition,
% 0.27/0.47 ( funcImageSingleton
% 0.27/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.27/0.47 ( ( func @ A @ B @ Xf )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( singleton
% 0.27/0.47 @ ( dsetconstr @ B
% 0.27/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(apProp_type,type,
% 0.27/0.47 apProp: $o ).
% 0.27/0.47
% 0.27/0.47 thf(apProp,definition,
% 0.27/0.47 ( apProp
% 0.27/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.27/0.47 ( ( func @ A @ B @ Xf )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( in
% 0.27/0.47 @ ( setunion
% 0.27/0.47 @ ( dsetconstr @ B
% 0.27/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.27/0.47 @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(ap_type,type,
% 0.27/0.47 ap: $i > $i > $i > $i > $i ).
% 0.27/0.47
% 0.27/0.47 thf(app_type,type,
% 0.27/0.47 app: $o ).
% 0.27/0.47
% 0.27/0.47 thf(app,definition,
% 0.27/0.47 ( app
% 0.27/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.27/0.47 ( ( func @ A @ B @ Xf )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(infuncsetfunc_type,type,
% 0.27/0.47 infuncsetfunc: $o ).
% 0.27/0.47
% 0.27/0.47 thf(infuncsetfunc,definition,
% 0.27/0.47 ( infuncsetfunc
% 0.27/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.27/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.27/0.47 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(ap2p_type,type,
% 0.27/0.47 ap2p: $o ).
% 0.27/0.47
% 0.27/0.47 thf(ap2p,definition,
% 0.27/0.47 ( ap2p
% 0.27/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.27/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(funcinfuncset_type,type,
% 0.27/0.47 funcinfuncset: $o ).
% 0.27/0.47
% 0.27/0.47 thf(funcinfuncset,definition,
% 0.27/0.47 ( funcinfuncset
% 0.27/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.27/0.47 ( ( func @ A @ B @ Xf )
% 0.27/0.47 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(lamProp_type,type,
% 0.27/0.47 lamProp: $o ).
% 0.27/0.47
% 0.27/0.47 thf(lamProp,definition,
% 0.27/0.47 ( lamProp
% 0.27/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.27/0.47 ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.27/0.47 => ( func @ A @ B
% 0.27/0.47 @ ( dpsetconstr @ A @ B
% 0.27/0.47 @ ^ [Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( Xf @ Xx )
% 0.27/0.47 = Xy ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(lam_type,type,
% 0.27/0.47 lam: $i > $i > ( $i > $i ) > $i ).
% 0.27/0.47
% 0.27/0.47 thf(lamp_type,type,
% 0.27/0.47 lamp: $o ).
% 0.27/0.47
% 0.27/0.47 thf(lamp,definition,
% 0.27/0.47 ( lamp
% 0.27/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.27/0.47 ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.27/0.47 => ( func @ A @ B
% 0.27/0.47 @ ( lam @ A @ B
% 0.27/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(lam2p_type,type,
% 0.27/0.47 lam2p: $o ).
% 0.27/0.47
% 0.27/0.47 thf(lam2p,definition,
% 0.27/0.47 ( lam2p
% 0.27/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.27/0.47 ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.27/0.47 => ( in
% 0.27/0.47 @ ( lam @ A @ B
% 0.27/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.27/0.47 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(brelnall1_type,type,
% 0.27/0.47 brelnall1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(brelnall1,definition,
% 0.27/0.47 ( brelnall1
% 0.27/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.27/0.47 ( ( breln @ A @ B @ R )
% 0.27/0.47 => ! [Xphi: $i > $o] :
% 0.27/0.47 ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.27/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ R )
% 0.27/0.47 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(brelnall2_type,type,
% 0.27/0.47 brelnall2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(brelnall2,definition,
% 0.27/0.47 ( brelnall2
% 0.27/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.27/0.47 ( ( breln @ A @ B @ R )
% 0.27/0.47 => ! [Xphi: $i > $o] :
% 0.27/0.47 ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.27/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ R )
% 0.27/0.47 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(ex1E2_type,type,
% 0.27/0.47 ex1E2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(ex1E2,definition,
% 0.27/0.47 ( ex1E2
% 0.27/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.47 ( ( ex1 @ A
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ A )
% 0.27/0.47 => ( ( Xphi @ Xx )
% 0.27/0.47 => ( ( Xphi @ Xy )
% 0.27/0.47 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(funcGraphProp1_type,type,
% 0.27/0.47 funcGraphProp1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(funcGraphProp1,definition,
% 0.27/0.47 ( funcGraphProp1
% 0.27/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.27/0.47 ( ( func @ A @ B @ Xf )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(funcGraphProp3_type,type,
% 0.27/0.47 funcGraphProp3: $o ).
% 0.27/0.47
% 0.27/0.47 thf(funcGraphProp3,definition,
% 0.27/0.47 ( funcGraphProp3
% 0.27/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.27/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(funcGraphProp2_type,type,
% 0.27/0.47 funcGraphProp2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(funcGraphProp2,definition,
% 0.27/0.47 ( funcGraphProp2
% 0.27/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.27/0.47 ( ( func @ A @ B @ Xf )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.27/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.27/0.47 = Xy ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(funcextLem_type,type,
% 0.27/0.47 funcextLem: $o ).
% 0.27/0.47
% 0.27/0.47 thf(funcextLem,definition,
% 0.27/0.47 ( funcextLem
% 0.27/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.27/0.47 ( ( func @ A @ B @ Xf )
% 0.27/0.47 => ! [Xg: $i] :
% 0.27/0.47 ( ( func @ A @ B @ Xg )
% 0.27/0.47 => ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.27/0.47 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 0.27/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(funcGraphProp4_type,type,
% 0.27/0.47 funcGraphProp4: $o ).
% 0.27/0.47
% 0.27/0.47 thf(funcGraphProp4,definition,
% 0.27/0.47 ( funcGraphProp4
% 0.27/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.27/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.27/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.27/0.47 = Xy ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(subbreln_type,type,
% 0.27/0.47 subbreln: $o ).
% 0.27/0.47
% 0.27/0.47 thf(subbreln,definition,
% 0.27/0.47 ( subbreln
% 0.27/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.27/0.47 ( ( breln @ A @ B @ R )
% 0.27/0.47 => ! [S: $i] :
% 0.27/0.47 ( ( breln @ A @ B @ S )
% 0.27/0.47 => ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.27/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.27/0.47 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(eqbreln_type,type,
% 0.27/0.47 eqbreln: $o ).
% 0.27/0.47
% 0.27/0.47 thf(eqbreln,definition,
% 0.27/0.47 ( eqbreln
% 0.27/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.27/0.47 ( ( breln @ A @ B @ R )
% 0.27/0.47 => ! [S: $i] :
% 0.27/0.47 ( ( breln @ A @ B @ S )
% 0.27/0.47 => ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.27/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.27/0.47 => ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.27/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.27/0.47 => ( R = S ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(funcext_type,type,
% 0.27/0.47 funcext: $o ).
% 0.27/0.47
% 0.27/0.47 thf(funcext,definition,
% 0.27/0.47 ( funcext
% 0.27/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.27/0.47 ( ( func @ A @ B @ Xf )
% 0.27/0.47 => ! [Xg: $i] :
% 0.27/0.47 ( ( func @ A @ B @ Xg )
% 0.27/0.47 => ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.27/0.47 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.27/0.47 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(funcext2_type,type,
% 0.27/0.47 funcext2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(funcext2,definition,
% 0.27/0.47 ( funcext2
% 0.27/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.27/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.27/0.47 => ! [Xg: $i] :
% 0.27/0.47 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 0.27/0.47 => ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.27/0.47 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.27/0.47 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(ap2apEq1_type,type,
% 0.27/0.47 ap2apEq1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(ap2apEq1,definition,
% 0.27/0.47 ( ap2apEq1
% 0.27/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.27/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.27/0.47 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(ap2apEq2_type,type,
% 0.27/0.47 ap2apEq2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(ap2apEq2,definition,
% 0.27/0.47 ( ap2apEq2
% 0.27/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.27/0.47 ( ( func @ A @ B @ Xf )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.27/0.47 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(beta1_type,type,
% 0.27/0.47 beta1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(beta1,definition,
% 0.27/0.47 ( beta1
% 0.27/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.27/0.47 ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( ap @ A @ B
% 0.27/0.47 @ ( lam @ A @ B
% 0.27/0.47 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.27/0.47 @ Xx )
% 0.27/0.47 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(eta1_type,type,
% 0.27/0.47 eta1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(eta1,definition,
% 0.27/0.47 ( eta1
% 0.27/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.27/0.47 ( ( func @ A @ B @ Xf )
% 0.27/0.47 => ( ( lam @ A @ B
% 0.27/0.47 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.27/0.47 = Xf ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(lam2lamEq_type,type,
% 0.27/0.47 lam2lamEq: $o ).
% 0.27/0.47
% 0.27/0.47 thf(lam2lamEq,definition,
% 0.27/0.47 ( lam2lamEq
% 0.27/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.27/0.47 ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.27/0.47 => ( ( lam @ A @ B
% 0.27/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.27/0.47 = ( lam @ A @ B
% 0.27/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(beta2_type,type,
% 0.27/0.47 beta2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(beta2,definition,
% 0.27/0.47 ( beta2
% 0.27/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.27/0.47 ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( ap @ A @ B
% 0.27/0.47 @ ( lam @ A @ B
% 0.27/0.47 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.27/0.47 @ Xx )
% 0.27/0.47 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(eta2_type,type,
% 0.27/0.47 eta2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(eta2,definition,
% 0.27/0.47 ( eta2
% 0.27/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.27/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.27/0.47 => ( ( lam @ A @ B
% 0.27/0.47 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.27/0.47 = Xf ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(iffalseProp1_type,type,
% 0.27/0.47 iffalseProp1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(iffalseProp1,definition,
% 0.27/0.47 ( iffalseProp1
% 0.27/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ A )
% 0.27/0.47 => ( ~ Xphi
% 0.27/0.47 => ( in @ Xy
% 0.27/0.47 @ ( dsetconstr @ A
% 0.27/0.47 @ ^ [Xz: $i] :
% 0.27/0.47 ( ( Xphi
% 0.27/0.47 & ( Xz = Xx ) )
% 0.27/0.47 | ( ~ Xphi
% 0.27/0.47 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(iffalseProp2_type,type,
% 0.27/0.47 iffalseProp2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(iffalseProp2,definition,
% 0.27/0.47 ( iffalseProp2
% 0.27/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ A )
% 0.27/0.47 => ( ~ Xphi
% 0.27/0.47 => ( ( dsetconstr @ A
% 0.27/0.47 @ ^ [Xz: $i] :
% 0.27/0.47 ( ( Xphi
% 0.27/0.47 & ( Xz = Xx ) )
% 0.27/0.47 | ( ~ Xphi
% 0.27/0.47 & ( Xz = Xy ) ) ) )
% 0.27/0.47 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(iftrueProp1_type,type,
% 0.27/0.47 iftrueProp1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(iftrueProp1,definition,
% 0.27/0.47 ( iftrueProp1
% 0.27/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ A )
% 0.27/0.47 => ( Xphi
% 0.27/0.47 => ( in @ Xx
% 0.27/0.47 @ ( dsetconstr @ A
% 0.27/0.47 @ ^ [Xz: $i] :
% 0.27/0.47 ( ( Xphi
% 0.27/0.47 & ( Xz = Xx ) )
% 0.27/0.47 | ( ~ Xphi
% 0.27/0.47 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(iftrueProp2_type,type,
% 0.27/0.47 iftrueProp2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(iftrueProp2,definition,
% 0.27/0.47 ( iftrueProp2
% 0.27/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ A )
% 0.27/0.47 => ( Xphi
% 0.27/0.47 => ( ( dsetconstr @ A
% 0.27/0.47 @ ^ [Xz: $i] :
% 0.27/0.47 ( ( Xphi
% 0.27/0.47 & ( Xz = Xx ) )
% 0.27/0.47 | ( ~ Xphi
% 0.27/0.47 & ( Xz = Xy ) ) ) )
% 0.27/0.47 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(ifSingleton_type,type,
% 0.27/0.47 ifSingleton: $o ).
% 0.27/0.47
% 0.27/0.47 thf(ifSingleton,definition,
% 0.27/0.47 ( ifSingleton
% 0.27/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ A )
% 0.27/0.47 => ( singleton
% 0.27/0.47 @ ( dsetconstr @ A
% 0.27/0.47 @ ^ [Xz: $i] :
% 0.27/0.47 ( ( Xphi
% 0.27/0.47 & ( Xz = Xx ) )
% 0.27/0.47 | ( ~ Xphi
% 0.27/0.47 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(if_type,type,
% 0.27/0.47 if: $i > $o > $i > $i > $i ).
% 0.27/0.47
% 0.27/0.47 thf(ifp_type,type,
% 0.27/0.47 ifp: $o ).
% 0.27/0.47
% 0.27/0.47 thf(ifp,definition,
% 0.27/0.47 ( ifp
% 0.27/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ A )
% 0.27/0.47 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(theeq_type,type,
% 0.27/0.47 theeq: $o ).
% 0.27/0.47
% 0.27/0.47 thf(theeq,definition,
% 0.27/0.47 ( theeq
% 0.27/0.47 = ( ! [X: $i] :
% 0.27/0.47 ( ( singleton @ X )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ X )
% 0.27/0.47 => ( ( setunion @ X )
% 0.27/0.47 = Xx ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(iftrue_type,type,
% 0.27/0.47 iftrue: $o ).
% 0.27/0.47
% 0.27/0.47 thf(iftrue,definition,
% 0.27/0.47 ( iftrue
% 0.27/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ A )
% 0.27/0.47 => ( Xphi
% 0.27/0.47 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.27/0.47 = Xx ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(iffalse_type,type,
% 0.27/0.47 iffalse: $o ).
% 0.27/0.47
% 0.27/0.47 thf(iffalse,definition,
% 0.27/0.47 ( iffalse
% 0.27/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ A )
% 0.27/0.47 => ( ~ Xphi
% 0.27/0.47 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.27/0.47 = Xy ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(iftrueorfalse_type,type,
% 0.27/0.47 iftrueorfalse: $o ).
% 0.27/0.47
% 0.27/0.47 thf(iftrueorfalse,definition,
% 0.27/0.47 ( iftrueorfalse
% 0.27/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ A )
% 0.27/0.47 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectT_lem_type,type,
% 0.27/0.47 binintersectT_lem: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectT_lem,definition,
% 0.27/0.47 ( binintersectT_lem
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binunionT_lem_type,type,
% 0.27/0.47 binunionT_lem: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binunionT_lem,definition,
% 0.27/0.47 ( binunionT_lem
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(powersetT_lem_type,type,
% 0.27/0.47 powersetT_lem: $o ).
% 0.27/0.47
% 0.27/0.47 thf(powersetT_lem,definition,
% 0.27/0.47 ( powersetT_lem
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setminusT_lem_type,type,
% 0.27/0.47 setminusT_lem: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setminusT_lem,definition,
% 0.27/0.47 ( setminusT_lem
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(complementT_lem_type,type,
% 0.27/0.47 complementT_lem: $o ).
% 0.27/0.47
% 0.27/0.47 thf(complementT_lem,definition,
% 0.27/0.47 ( complementT_lem
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setextT_type,type,
% 0.27/0.47 setextT: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setextT,definition,
% 0.27/0.47 ( setextT
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ X )
% 0.27/0.47 => ( in @ Xx @ Y ) ) )
% 0.27/0.47 => ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ Y )
% 0.27/0.47 => ( in @ Xx @ X ) ) )
% 0.27/0.47 => ( X = Y ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(subsetTI_type,type,
% 0.27/0.47 subsetTI: $o ).
% 0.27/0.47
% 0.27/0.47 thf(subsetTI,definition,
% 0.27/0.47 ( subsetTI
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ X )
% 0.27/0.47 => ( in @ Xx @ Y ) ) )
% 0.27/0.47 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(powersetTI1_type,type,
% 0.27/0.47 powersetTI1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(powersetTI1,definition,
% 0.27/0.47 ( powersetTI1
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ X )
% 0.27/0.47 => ( in @ Xx @ Y ) ) )
% 0.27/0.47 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(powersetTE1_type,type,
% 0.27/0.47 powersetTE1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(powersetTE1,definition,
% 0.27/0.47 ( powersetTE1
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ X @ ( powerset @ Y ) )
% 0.27/0.47 => ( ( in @ Xx @ X )
% 0.27/0.47 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(complementTI1_type,type,
% 0.27/0.47 complementTI1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(complementTI1,definition,
% 0.27/0.47 ( complementTI1
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ X )
% 0.27/0.47 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(complementTE1_type,type,
% 0.27/0.47 complementTE1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(complementTE1,definition,
% 0.27/0.47 ( complementTE1
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 0.27/0.47 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectTELcontra_type,type,
% 0.27/0.47 binintersectTELcontra: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectTELcontra,definition,
% 0.27/0.47 ( binintersectTELcontra
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ~ ( in @ Xx @ X )
% 0.27/0.47 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectTERcontra_type,type,
% 0.27/0.47 binintersectTERcontra: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectTERcontra,definition,
% 0.27/0.47 ( binintersectTERcontra
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ~ ( in @ Xx @ Y )
% 0.27/0.47 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(contrasubsetT_type,type,
% 0.27/0.47 contrasubsetT: $o ).
% 0.27/0.47
% 0.27/0.47 thf(contrasubsetT,definition,
% 0.27/0.47 ( contrasubsetT
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.27/0.47 => ( ( in @ Xx @ Y )
% 0.27/0.47 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(contrasubsetT1_type,type,
% 0.27/0.47 contrasubsetT1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(contrasubsetT1,definition,
% 0.27/0.47 ( contrasubsetT1
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( subset @ X @ Y )
% 0.27/0.47 => ( ~ ( in @ Xx @ Y )
% 0.27/0.47 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(contrasubsetT2_type,type,
% 0.27/0.47 contrasubsetT2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(contrasubsetT2,definition,
% 0.27/0.47 ( contrasubsetT2
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ( ( subset @ X @ Y )
% 0.27/0.47 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(contrasubsetT3_type,type,
% 0.27/0.47 contrasubsetT3: $o ).
% 0.27/0.47
% 0.27/0.47 thf(contrasubsetT3,definition,
% 0.27/0.47 ( contrasubsetT3
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 0.27/0.47 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(doubleComplementI1_type,type,
% 0.27/0.47 doubleComplementI1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(doubleComplementI1,definition,
% 0.27/0.47 ( doubleComplementI1
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ X )
% 0.27/0.47 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(doubleComplementE1_type,type,
% 0.27/0.47 doubleComplementE1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(doubleComplementE1,definition,
% 0.27/0.47 ( doubleComplementE1
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 0.27/0.47 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(doubleComplementSub1_type,type,
% 0.27/0.47 doubleComplementSub1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(doubleComplementSub1,definition,
% 0.27/0.47 ( doubleComplementSub1
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(doubleComplementSub2_type,type,
% 0.27/0.47 doubleComplementSub2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(doubleComplementSub2,definition,
% 0.27/0.47 ( doubleComplementSub2
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(doubleComplementEq_type,type,
% 0.27/0.47 doubleComplementEq: $o ).
% 0.27/0.47
% 0.27/0.47 thf(doubleComplementEq,definition,
% 0.27/0.47 ( doubleComplementEq
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ( X
% 0.27/0.47 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(complementTnotintersectT_type,type,
% 0.27/0.47 complementTnotintersectT: $o ).
% 0.27/0.47
% 0.27/0.47 thf(complementTnotintersectT,definition,
% 0.27/0.47 ( complementTnotintersectT
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.27/0.47 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(complementImpComplementIntersect_type,type,
% 0.27/0.47 complementImpComplementIntersect: $o ).
% 0.27/0.47
% 0.27/0.47 thf(complementImpComplementIntersect,definition,
% 0.27/0.47 ( complementImpComplementIntersect
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.27/0.47 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(complementSubsetComplementIntersect_type,type,
% 0.27/0.47 complementSubsetComplementIntersect: $o ).
% 0.27/0.47
% 0.27/0.47 thf(complementSubsetComplementIntersect,definition,
% 0.27/0.47 ( complementSubsetComplementIntersect
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(complementInPowersetComplementIntersect_type,type,
% 0.27/0.47 complementInPowersetComplementIntersect: $o ).
% 0.27/0.47
% 0.27/0.47 thf(complementInPowersetComplementIntersect,definition,
% 0.27/0.47 ( complementInPowersetComplementIntersect
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(contraSubsetComplement_type,type,
% 0.27/0.47 contraSubsetComplement: $o ).
% 0.27/0.47
% 0.27/0.47 thf(contraSubsetComplement,definition,
% 0.27/0.47 ( contraSubsetComplement
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ Y )
% 0.27/0.47 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(complementTcontraSubset_type,type,
% 0.27/0.47 complementTcontraSubset: $o ).
% 0.27/0.47
% 0.27/0.47 thf(complementTcontraSubset,definition,
% 0.27/0.47 ( complementTcontraSubset
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.27/0.47 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binunionTILcontra_type,type,
% 0.27/0.47 binunionTILcontra: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binunionTILcontra,definition,
% 0.27/0.47 ( binunionTILcontra
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.27/0.47 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binunionTIRcontra_type,type,
% 0.27/0.47 binunionTIRcontra: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binunionTIRcontra,definition,
% 0.27/0.47 ( binunionTIRcontra
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.27/0.47 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(inIntersectImpInUnion_type,type,
% 0.27/0.47 inIntersectImpInUnion: $o ).
% 0.27/0.47
% 0.27/0.47 thf(inIntersectImpInUnion,definition,
% 0.27/0.47 ( inIntersectImpInUnion
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Z: $i] :
% 0.27/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.27/0.47 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(inIntersectImpInUnion2_type,type,
% 0.27/0.47 inIntersectImpInUnion2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(inIntersectImpInUnion2,definition,
% 0.27/0.47 ( inIntersectImpInUnion2
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Z: $i] :
% 0.27/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.27/0.47 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(inIntersectImpInIntersectUnions_type,type,
% 0.27/0.47 inIntersectImpInIntersectUnions: $o ).
% 0.27/0.47
% 0.27/0.47 thf(inIntersectImpInIntersectUnions,definition,
% 0.27/0.47 ( inIntersectImpInIntersectUnions
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Z: $i] :
% 0.27/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.27/0.47 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(intersectInPowersetIntersectUnions_type,type,
% 0.27/0.47 intersectInPowersetIntersectUnions: $o ).
% 0.27/0.47
% 0.27/0.47 thf(intersectInPowersetIntersectUnions,definition,
% 0.27/0.47 ( intersectInPowersetIntersectUnions
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Z: $i] :
% 0.27/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.27/0.47 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(inComplementUnionImpNotIn1_type,type,
% 0.27/0.47 inComplementUnionImpNotIn1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(inComplementUnionImpNotIn1,definition,
% 0.27/0.47 ( inComplementUnionImpNotIn1
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.27/0.47 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(inComplementUnionImpInComplement1_type,type,
% 0.27/0.47 inComplementUnionImpInComplement1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(inComplementUnionImpInComplement1,definition,
% 0.27/0.47 ( inComplementUnionImpInComplement1
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.27/0.47 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binunionTE_type,type,
% 0.27/0.47 binunionTE: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binunionTE,definition,
% 0.27/0.47 ( binunionTE
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Xphi: $o,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.27/0.47 => ( ( ( in @ Xx @ X )
% 0.27/0.47 => Xphi )
% 0.27/0.47 => ( ( ( in @ Xx @ Y )
% 0.27/0.47 => Xphi )
% 0.27/0.47 => Xphi ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binunionTEcontra_type,type,
% 0.27/0.47 binunionTEcontra: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binunionTEcontra,definition,
% 0.27/0.47 ( binunionTEcontra
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ~ ( in @ Xx @ X )
% 0.27/0.47 => ( ~ ( in @ Xx @ Y )
% 0.27/0.47 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(demorgan2a1_type,type,
% 0.27/0.47 demorgan2a1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(demorgan2a1,definition,
% 0.27/0.47 ( demorgan2a1
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.27/0.47 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(complementUnionInPowersetComplement_type,type,
% 0.27/0.47 complementUnionInPowersetComplement: $o ).
% 0.27/0.47
% 0.27/0.47 thf(complementUnionInPowersetComplement,definition,
% 0.27/0.47 ( complementUnionInPowersetComplement
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(demorgan2a2_type,type,
% 0.27/0.47 demorgan2a2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(demorgan2a2,definition,
% 0.27/0.47 ( demorgan2a2
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.27/0.47 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(demorgan1a_type,type,
% 0.27/0.47 demorgan1a: $o ).
% 0.27/0.47
% 0.27/0.47 thf(demorgan1a,definition,
% 0.27/0.47 ( demorgan1a
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 0.27/0.47 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(demorgan1b_type,type,
% 0.27/0.47 demorgan1b: $o ).
% 0.27/0.47
% 0.27/0.47 thf(demorgan1b,definition,
% 0.27/0.47 ( demorgan1b
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.27/0.47 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(demorgan1_type,type,
% 0.27/0.47 demorgan1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(demorgan1,definition,
% 0.27/0.47 ( demorgan1
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 0.27/0.47 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(demorgan2a_type,type,
% 0.27/0.47 demorgan2a: $o ).
% 0.27/0.47
% 0.27/0.47 thf(demorgan2a,definition,
% 0.27/0.47 ( demorgan2a
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.27/0.47 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(demorgan2b2_type,type,
% 0.27/0.47 demorgan2b2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(demorgan2b2,definition,
% 0.27/0.47 ( demorgan2b2
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.27/0.47 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 0.27/0.47 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(demorgan2b_type,type,
% 0.27/0.47 demorgan2b: $o ).
% 0.27/0.47
% 0.27/0.47 thf(demorgan2b,definition,
% 0.27/0.47 ( demorgan2b
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.27/0.47 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(demorgan2_type,type,
% 0.27/0.47 demorgan2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(demorgan2,definition,
% 0.27/0.47 ( demorgan2
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 0.27/0.47 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(woz13rule0_type,type,
% 0.27/0.47 woz13rule0: $o ).
% 0.27/0.47
% 0.27/0.47 thf(woz13rule0,definition,
% 0.27/0.47 ( woz13rule0
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.27/0.47 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(woz13rule1_type,type,
% 0.27/0.47 woz13rule1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(woz13rule1,definition,
% 0.27/0.47 ( woz13rule1
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Z: $i] :
% 0.27/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.27/0.47 => ( ( subset @ X @ Z )
% 0.27/0.47 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(woz13rule2_type,type,
% 0.27/0.47 woz13rule2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(woz13rule2,definition,
% 0.27/0.47 ( woz13rule2
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Z: $i] :
% 0.27/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.27/0.47 => ( ( subset @ Y @ Z )
% 0.27/0.47 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(woz13rule3_type,type,
% 0.27/0.47 woz13rule3: $o ).
% 0.27/0.47
% 0.27/0.47 thf(woz13rule3,definition,
% 0.27/0.47 ( woz13rule3
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Z: $i] :
% 0.27/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.27/0.47 => ( ( subset @ X @ Y )
% 0.27/0.47 => ( ( subset @ X @ Z )
% 0.27/0.47 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(woz13rule4_type,type,
% 0.27/0.47 woz13rule4: $o ).
% 0.27/0.47
% 0.27/0.47 thf(woz13rule4,definition,
% 0.27/0.47 ( woz13rule4
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Z: $i] :
% 0.27/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.27/0.47 => ! [W: $i] :
% 0.27/0.47 ( ( in @ W @ ( powerset @ A ) )
% 0.27/0.47 => ( ( subset @ X @ Z )
% 0.27/0.47 => ( ( subset @ Y @ W )
% 0.27/0.47 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(woz1_1_type,type,
% 0.27/0.47 woz1_1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(woz1_1,definition,
% 0.27/0.47 ( woz1_1
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(woz1_2_type,type,
% 0.27/0.47 woz1_2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(woz1_2,definition,
% 0.27/0.47 ( woz1_2
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Z: $i] :
% 0.27/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.27/0.47 => ! [W: $i] :
% 0.27/0.47 ( ( in @ W @ ( powerset @ A ) )
% 0.27/0.47 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 0.27/0.47 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(woz1_3_type,type,
% 0.27/0.47 woz1_3: $o ).
% 0.27/0.47
% 0.27/0.47 thf(woz1_3,definition,
% 0.27/0.47 ( woz1_3
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ! [Z: $i] :
% 0.27/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.27/0.47 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(woz1_4_type,type,
% 0.27/0.47 woz1_4: $o ).
% 0.27/0.47
% 0.27/0.47 thf(woz1_4,definition,
% 0.27/0.47 ( woz1_4
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.27/0.47 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(woz1_5_type,type,
% 0.27/0.47 woz1_5: $o ).
% 0.27/0.47
% 0.27/0.47 thf(woz1_5,definition,
% 0.27/0.47 ( woz1_5
% 0.27/0.47 = ( ! [A: $i,X: $i] :
% 0.27/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.27/0.47 => ! [Y: $i] :
% 0.27/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.27/0.47 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(breln1_type,type,
% 0.27/0.47 breln1: $i > $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(breln1,definition,
% 0.27/0.47 ( breln1
% 0.27/0.47 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(breln1all2_type,type,
% 0.27/0.47 breln1all2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(breln1all2,definition,
% 0.27/0.47 ( breln1all2
% 0.27/0.47 = ( ! [A: $i,R: $i] :
% 0.27/0.47 ( ( breln1 @ A @ R )
% 0.27/0.47 => ! [Xphi: $i > $o] :
% 0.27/0.47 ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ A )
% 0.27/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.27/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ R )
% 0.27/0.47 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(breln1Set_type,type,
% 0.27/0.47 breln1Set: $i > $i ).
% 0.27/0.47
% 0.27/0.47 thf(breln1SetBreln1_type,type,
% 0.27/0.47 breln1SetBreln1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(breln1SetBreln1,definition,
% 0.27/0.47 ( breln1SetBreln1
% 0.27/0.47 = ( ! [A: $i,R: $i] :
% 0.27/0.47 ( ( in @ R @ ( breln1Set @ A ) )
% 0.27/0.47 => ( breln1 @ A @ R ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(transitive_type,type,
% 0.27/0.47 transitive: $i > $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(antisymmetric_type,type,
% 0.27/0.47 antisymmetric: $i > $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(reflexive_type,type,
% 0.27/0.47 reflexive: $i > $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(refltransitive_type,type,
% 0.27/0.47 refltransitive: $i > $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(refllinearorder_type,type,
% 0.27/0.47 refllinearorder: $i > $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(reflwellordering_type,type,
% 0.27/0.47 reflwellordering: $i > $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(choice2fnsingleton_type,type,
% 0.27/0.47 choice2fnsingleton: $o ).
% 0.27/0.47
% 0.27/0.47 thf(choice2fnsingleton,definition,
% 0.27/0.47 ( choice2fnsingleton
% 0.27/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.27/0.47 ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ? [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 & ( Xphi @ Xx @ Xy ) ) )
% 0.27/0.47 => ! [R: $i] :
% 0.27/0.47 ( ( in @ R @ ( breln1Set @ B ) )
% 0.27/0.47 => ( ( reflwellordering @ B @ R )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( singleton
% 0.27/0.47 @ ( dsetconstr @ B
% 0.27/0.47 @ ^ [Xy: $i] :
% 0.27/0.47 ( ( Xphi @ Xx @ Xy )
% 0.27/0.47 & ! [Xz: $i] :
% 0.27/0.47 ( ( in @ Xz @ B )
% 0.27/0.47 => ( ( Xphi @ Xx @ Xz )
% 0.27/0.47 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setOfPairsIsBReln1_type,type,
% 0.27/0.47 setOfPairsIsBReln1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setOfPairsIsBReln1,definition,
% 0.27/0.47 ( setOfPairsIsBReln1
% 0.27/0.47 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 0.27/0.47 ( breln1 @ A
% 0.27/0.47 @ ( dpsetconstr @ A @ A
% 0.27/0.47 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(breln1all1_type,type,
% 0.27/0.47 breln1all1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(breln1all1,definition,
% 0.27/0.47 ( breln1all1
% 0.27/0.47 = ( ! [A: $i,R: $i] :
% 0.27/0.47 ( ( breln1 @ A @ R )
% 0.27/0.47 => ! [Xphi: $i > $o] :
% 0.27/0.47 ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ A )
% 0.27/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.27/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ R )
% 0.27/0.47 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(subbreln1_type,type,
% 0.27/0.47 subbreln1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(subbreln1,definition,
% 0.27/0.47 ( subbreln1
% 0.27/0.47 = ( ! [A: $i,R: $i] :
% 0.27/0.47 ( ( breln1 @ A @ R )
% 0.27/0.47 => ! [S: $i] :
% 0.27/0.47 ( ( breln1 @ A @ S )
% 0.27/0.47 => ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ A )
% 0.27/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.27/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.27/0.47 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(eqbreln1_type,type,
% 0.27/0.47 eqbreln1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(eqbreln1,definition,
% 0.27/0.47 ( eqbreln1
% 0.27/0.47 = ( ! [A: $i,R: $i] :
% 0.27/0.47 ( ( breln1 @ A @ R )
% 0.27/0.47 => ! [S: $i] :
% 0.27/0.47 ( ( breln1 @ A @ S )
% 0.27/0.47 => ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ A )
% 0.27/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.27/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.27/0.47 => ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ A )
% 0.27/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.27/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.27/0.47 => ( R = S ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(breln1invset_type,type,
% 0.27/0.47 breln1invset: $i > $i > $i ).
% 0.27/0.47
% 0.27/0.47 thf(breln1invset,definition,
% 0.27/0.47 ( breln1invset
% 0.27/0.47 = ( ^ [A: $i,R: $i] :
% 0.27/0.47 ( dpsetconstr @ A @ A
% 0.27/0.47 @ ^ [Xx: $i,Xy: $i] : ( in @ ( kpair @ Xy @ Xx ) @ R ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(breln1invprop,conjecture,
% 0.27/0.47 ( setextAx
% 0.27/0.47 => ( emptysetAx
% 0.27/0.47 => ( setadjoinAx
% 0.27/0.47 => ( powersetAx
% 0.27/0.47 => ( setunionAx
% 0.27/0.47 => ( omega0Ax
% 0.27/0.47 => ( omegaSAx
% 0.27/0.47 => ( omegaIndAx
% 0.27/0.47 => ( replAx
% 0.27/0.47 => ( foundationAx
% 0.27/0.47 => ( wellorderingAx
% 0.27/0.47 => ( descrp
% 0.27/0.47 => ( dsetconstrI
% 0.27/0.47 => ( dsetconstrEL
% 0.27/0.47 => ( dsetconstrER
% 0.27/0.47 => ( exuE1
% 0.27/0.47 => ( prop2setE
% 0.27/0.47 => ( emptysetE
% 0.27/0.47 => ( emptysetimpfalse
% 0.27/0.47 => ( notinemptyset
% 0.27/0.47 => ( exuE3e
% 0.27/0.47 => ( setext
% 0.27/0.47 => ( emptyI
% 0.27/0.47 => ( noeltsimpempty
% 0.27/0.47 => ( setbeta
% 0.27/0.47 => ( nonemptyE1
% 0.27/0.47 => ( nonemptyI
% 0.27/0.47 => ( nonemptyI1
% 0.27/0.47 => ( setadjoinIL
% 0.27/0.47 => ( emptyinunitempty
% 0.27/0.47 => ( setadjoinIR
% 0.27/0.47 => ( setadjoinE
% 0.27/0.47 => ( setadjoinOr
% 0.27/0.47 => ( setoftrueEq
% 0.27/0.47 => ( powersetI
% 0.27/0.47 => ( emptyinPowerset
% 0.27/0.47 => ( emptyInPowerset
% 0.27/0.47 => ( powersetE
% 0.27/0.47 => ( setunionI
% 0.27/0.47 => ( setunionE
% 0.27/0.47 => ( subPowSU
% 0.27/0.47 => ( exuE2
% 0.27/0.47 => ( nonemptyImpWitness
% 0.27/0.47 => ( uniqinunit
% 0.27/0.47 => ( notinsingleton
% 0.27/0.47 => ( eqinunit
% 0.27/0.47 => ( singletonsswitch
% 0.27/0.47 => ( upairsetE
% 0.27/0.47 => ( upairsetIL
% 0.27/0.47 => ( upairsetIR
% 0.27/0.47 => ( emptyE1
% 0.27/0.47 => ( vacuousDall
% 0.27/0.47 => ( quantDeMorgan1
% 0.27/0.47 => ( quantDeMorgan2
% 0.27/0.47 => ( quantDeMorgan3
% 0.27/0.47 => ( quantDeMorgan4
% 0.27/0.47 => ( prop2setI
% 0.27/0.47 => ( prop2set2propI
% 0.27/0.47 => ( notdexE
% 0.27/0.47 => ( notdallE
% 0.27/0.47 => ( exuI1
% 0.27/0.47 => ( exuI3
% 0.27/0.47 => ( exuI2
% 0.27/0.47 => ( inCongP
% 0.27/0.47 => ( in__Cong
% 0.27/0.47 => ( exuE3u
% 0.27/0.47 => ( exu__Cong
% 0.27/0.47 => ( emptyset__Cong
% 0.27/0.47 => ( setadjoin__Cong
% 0.27/0.47 => ( powerset__Cong
% 0.27/0.47 => ( setunion__Cong
% 0.27/0.47 => ( omega__Cong
% 0.27/0.47 => ( exuEu
% 0.27/0.47 => ( descr__Cong
% 0.27/0.47 => ( dsetconstr__Cong
% 0.27/0.47 => ( subsetI1
% 0.27/0.47 => ( eqimpsubset2
% 0.27/0.47 => ( eqimpsubset1
% 0.27/0.47 => ( subsetI2
% 0.27/0.47 => ( emptysetsubset
% 0.27/0.47 => ( subsetE
% 0.27/0.47 => ( subsetE2
% 0.27/0.47 => ( notsubsetI
% 0.27/0.47 => ( notequalI1
% 0.27/0.47 => ( notequalI2
% 0.27/0.47 => ( subsetRefl
% 0.27/0.47 => ( subsetTrans
% 0.27/0.47 => ( setadjoinSub
% 0.27/0.47 => ( setadjoinSub2
% 0.27/0.47 => ( subset2powerset
% 0.27/0.47 => ( setextsub
% 0.27/0.47 => ( subsetemptysetimpeq
% 0.27/0.47 => ( powersetI1
% 0.27/0.47 => ( powersetE1
% 0.27/0.47 => ( inPowerset
% 0.27/0.47 => ( powersetsubset
% 0.27/0.47 => ( sepInPowerset
% 0.27/0.47 => ( sepSubset
% 0.27/0.47 => ( binunionIL
% 0.27/0.47 => ( upairset2IR
% 0.27/0.47 => ( binunionIR
% 0.27/0.47 => ( binunionEcases
% 0.27/0.47 => ( binunionE
% 0.27/0.47 => ( binunionLsub
% 0.27/0.47 => ( binunionRsub
% 0.27/0.47 => ( binintersectI
% 0.27/0.47 => ( binintersectSubset5
% 0.27/0.47 => ( binintersectEL
% 0.27/0.47 => ( binintersectLsub
% 0.27/0.47 => ( binintersectSubset2
% 0.27/0.47 => ( binintersectSubset3
% 0.27/0.47 => ( binintersectER
% 0.27/0.47 => ( disjointsetsI1
% 0.27/0.47 => ( binintersectRsub
% 0.27/0.47 => ( binintersectSubset4
% 0.27/0.47 => ( binintersectSubset1
% 0.27/0.47 => ( bs114d
% 0.27/0.47 => ( setminusI
% 0.27/0.47 => ( setminusEL
% 0.27/0.47 => ( setminusER
% 0.27/0.47 => ( setminusSubset2
% 0.27/0.47 => ( setminusERneg
% 0.27/0.47 => ( setminusELneg
% 0.27/0.47 => ( setminusILneg
% 0.27/0.47 => ( setminusIRneg
% 0.27/0.47 => ( setminusLsub
% 0.27/0.47 => ( setminusSubset1
% 0.27/0.47 => ( symdiffE
% 0.27/0.47 => ( symdiffI1
% 0.27/0.47 => ( symdiffI2
% 0.27/0.47 => ( symdiffIneg1
% 0.27/0.47 => ( symdiffIneg2
% 0.27/0.47 => ( secondinupair
% 0.27/0.47 => ( setukpairIL
% 0.27/0.47 => ( setukpairIR
% 0.27/0.47 => ( kpairiskpair
% 0.27/0.47 => ( kpairp
% 0.27/0.47 => ( singletonsubset
% 0.27/0.47 => ( singletoninpowerset
% 0.27/0.47 => ( singletoninpowunion
% 0.27/0.47 => ( upairset2E
% 0.27/0.47 => ( upairsubunion
% 0.27/0.47 => ( upairinpowunion
% 0.27/0.47 => ( ubforcartprodlem1
% 0.27/0.47 => ( ubforcartprodlem2
% 0.27/0.47 => ( ubforcartprodlem3
% 0.27/0.47 => ( cartprodpairin
% 0.27/0.47 => ( cartprodmempair1
% 0.27/0.47 => ( cartprodmempair
% 0.27/0.47 => ( setunionE2
% 0.27/0.47 => ( setunionsingleton1
% 0.27/0.47 => ( setunionsingleton2
% 0.27/0.47 => ( setunionsingleton
% 0.27/0.47 => ( singletonprop
% 0.27/0.47 => ( ex1E1
% 0.27/0.47 => ( ex1I
% 0.27/0.47 => ( ex1I2
% 0.27/0.47 => ( singletonsuniq
% 0.27/0.47 => ( setukpairinjL1
% 0.27/0.47 => ( kfstsingleton
% 0.27/0.47 => ( theprop
% 0.27/0.47 => ( kfstpairEq
% 0.27/0.47 => ( cartprodfstin
% 0.27/0.47 => ( setukpairinjL2
% 0.27/0.47 => ( setukpairinjL
% 0.27/0.47 => ( setukpairinjR11
% 0.27/0.47 => ( setukpairinjR12
% 0.27/0.47 => ( setukpairinjR1
% 0.27/0.47 => ( upairequniteq
% 0.27/0.47 => ( setukpairinjR2
% 0.27/0.47 => ( setukpairinjR
% 0.27/0.47 => ( ksndsingleton
% 0.27/0.47 => ( ksndpairEq
% 0.27/0.47 => ( kpairsurjEq
% 0.27/0.47 => ( cartprodsndin
% 0.27/0.47 => ( cartprodpairmemEL
% 0.27/0.47 => ( cartprodpairmemER
% 0.27/0.47 => ( cartprodmempaircEq
% 0.27/0.47 => ( cartprodfstpairEq
% 0.27/0.47 => ( cartprodsndpairEq
% 0.27/0.47 => ( cartprodpairsurjEq
% 0.27/0.47 => ( dpsetconstrI
% 0.27/0.47 => ( dpsetconstrSub
% 0.27/0.47 => ( setOfPairsIsBReln
% 0.27/0.47 => ( dpsetconstrERa
% 0.27/0.47 => ( dpsetconstrEL1
% 0.27/0.47 => ( dpsetconstrEL2
% 0.27/0.47 => ( dpsetconstrER
% 0.27/0.47 => ( funcImageSingleton
% 0.27/0.47 => ( apProp
% 0.27/0.47 => ( app
% 0.27/0.47 => ( infuncsetfunc
% 0.27/0.47 => ( ap2p
% 0.27/0.47 => ( funcinfuncset
% 0.27/0.47 => ( lamProp
% 0.27/0.47 => ( lamp
% 0.27/0.47 => ( lam2p
% 0.27/0.47 => ( brelnall1
% 0.27/0.47 => ( brelnall2
% 0.27/0.47 => ( ex1E2
% 0.27/0.47 => ( funcGraphProp1
% 0.27/0.47 => ( funcGraphProp3
% 0.27/0.47 => ( funcGraphProp2
% 0.27/0.47 => ( funcextLem
% 0.27/0.47 => ( funcGraphProp4
% 0.27/0.47 => ( subbreln
% 0.27/0.47 => ( eqbreln
% 0.27/0.47 => ( funcext
% 0.27/0.47 => ( funcext2
% 0.27/0.47 => ( ap2apEq1
% 0.27/0.47 => ( ap2apEq2
% 0.27/0.47 => ( beta1
% 0.27/0.47 => ( eta1
% 0.27/0.47 => ( lam2lamEq
% 0.27/0.47 => ( beta2
% 0.27/0.47 => ( eta2
% 0.27/0.47 => ( iffalseProp1
% 0.27/0.47 => ( iffalseProp2
% 0.27/0.47 => ( iftrueProp1
% 0.27/0.47 => ( iftrueProp2
% 0.27/0.47 => ( ifSingleton
% 0.27/0.47 => ( ifp
% 0.27/0.47 => ( theeq
% 0.27/0.47 => ( iftrue
% 0.27/0.47 => ( iffalse
% 0.27/0.47 => ( iftrueorfalse
% 0.27/0.47 => ( binintersectT_lem
% 0.27/0.47 => ( binunionT_lem
% 0.27/0.47 => ( powersetT_lem
% 0.27/0.47 => ( setminusT_lem
% 0.27/0.47 => ( complementT_lem
% 0.27/0.47 => ( setextT
% 0.27/0.47 => ( subsetTI
% 0.27/0.47 => ( powersetTI1
% 0.27/0.47 => ( powersetTE1
% 0.27/0.47 => ( complementTI1
% 0.27/0.47 => ( complementTE1
% 0.27/0.47 => ( binintersectTELcontra
% 0.27/0.47 => ( binintersectTERcontra
% 0.27/0.47 => ( contrasubsetT
% 0.27/0.47 => ( contrasubsetT1
% 0.27/0.47 => ( contrasubsetT2
% 0.27/0.47 => ( contrasubsetT3
% 0.27/0.47 => ( doubleComplementI1
% 0.27/0.47 => ( doubleComplementE1
% 0.27/0.47 => ( doubleComplementSub1
% 0.27/0.47 => ( doubleComplementSub2
% 0.27/0.47 => ( doubleComplementEq
% 0.27/0.47 => ( complementTnotintersectT
% 0.27/0.47 => ( complementImpComplementIntersect
% 0.27/0.47 => ( complementSubsetComplementIntersect
% 0.27/0.47 => ( complementInPowersetComplementIntersect
% 0.27/0.47 => ( contraSubsetComplement
% 0.27/0.47 => ( complementTcontraSubset
% 0.27/0.47 => ( binunionTILcontra
% 0.27/0.47 => ( binunionTIRcontra
% 0.27/0.47 => ( inIntersectImpInUnion
% 0.27/0.47 => ( inIntersectImpInUnion2
% 0.27/0.47 => ( inIntersectImpInIntersectUnions
% 0.27/0.47 => ( intersectInPowersetIntersectUnions
% 0.27/0.47 => ( inComplementUnionImpNotIn1
% 0.27/0.47 => ( inComplementUnionImpInComplement1
% 0.27/0.47 => ( binunionTE
% 0.27/0.47 => ( binunionTEcontra
% 0.27/0.47 => ( demorgan2a1
% 0.27/0.47 => ( complementUnionInPowersetComplement
% 0.27/0.47 => ( demorgan2a2
% 0.27/0.47 => ( demorgan1a
% 0.27/0.47 => ( demorgan1b
% 0.27/0.47 => ( demorgan1
% 0.27/0.47 => ( demorgan2a
% 0.27/0.47 => ( demorgan2b2
% 0.27/0.47 => ( demorgan2b
% 0.27/0.47 => ( demorgan2
% 0.27/0.47 => ( woz13rule0
% 0.27/0.47 => ( woz13rule1
% 0.27/0.47 => ( woz13rule2
% 0.27/0.47 => ( woz13rule3
% 0.27/0.47 => ( woz13rule4
% 0.27/0.47 => ( woz1_1
% 0.27/0.47 => ( woz1_2
% 0.27/0.47 => ( woz1_3
% 0.27/0.47 => ( woz1_4
% 0.27/0.47 => ( woz1_5
% 0.27/0.47 => ( breln1all2
% 0.27/0.47 => ( breln1SetBreln1
% 0.27/0.47 => ( choice2fnsingleton
% 0.27/0.47 => ( setOfPairsIsBReln1
% 0.27/0.47 => ( breln1all1
% 0.27/0.47 => ( subbreln1
% 0.27/0.47 => ( eqbreln1
% 0.27/0.47 => ! [A: $i,R: $i] :
% 0.27/0.47 ( ( breln1 @ A @ R )
% 0.27/0.47 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 ------------------------
% 2.98/1.53 ---- Embedded in THF ---
% 2.98/1.54 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.98/1.54 %%% Generated on Tue Feb 24 12:34:34 EST 2026
% 2.98/1.54 %%% using '$$dhol' embedding, version 1.3.0.
% 2.98/1.54 %%% Logic specification used:
% 2.98/1.54 %%% thf(spec, logic, $$dhol).
% 2.98/1.54
% 2.98/1.54 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.VPOVQ5G1w9/DTF2DTF2668.p
% See solution above
% 2.98/1.54 ------------------------
% 2.98/1.57 ---- Cleaned THF ---
% 2.98/1.57 thf(in_type,type,
% 2.98/1.57 in: $i > $i > $o ).
% 2.98/1.57
% 2.98/1.57 thf(exu_type,type,
% 2.98/1.57 exu: ( $i > $o ) > $o ).
% 2.98/1.57
% 2.98/1.57 thf(exu,definition,
% 2.98/1.57 ( exu
% 2.98/1.57 = ( ^ [Xphi: $i > $o] :
% 2.98/1.57 ? [Xx: $i] :
% 2.98/1.57 ( ( Xphi @ Xx )
% 2.98/1.57 & ! [Xy: $i] :
% 2.98/1.57 ( ( Xphi @ Xy )
% 2.98/1.57 => ( Xx = Xy ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setextAx_type,type,
% 2.98/1.57 setextAx: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setextAx,definition,
% 2.98/1.57 ( setextAx
% 2.98/1.57 = ( ! [A: $i,B: $i] :
% 2.98/1.57 ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 <=> ( in @ Xx @ B ) )
% 2.98/1.57 => ( A = B ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(emptyset_type,type,
% 2.98/1.57 emptyset: $i ).
% 2.98/1.57
% 2.98/1.57 thf(emptysetAx_type,type,
% 2.98/1.57 emptysetAx: $o ).
% 2.98/1.57
% 2.98/1.57 thf(emptysetAx,definition,
% 2.98/1.57 ( emptysetAx
% 2.98/1.57 = ( ! [Xx: $i] :
% 2.98/1.57 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setadjoin_type,type,
% 2.98/1.57 setadjoin: $i > $i > $i ).
% 2.98/1.57
% 2.98/1.57 thf(setadjoinAx_type,type,
% 2.98/1.57 setadjoinAx: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setadjoinAx,definition,
% 2.98/1.57 ( setadjoinAx
% 2.98/1.57 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.98/1.57 <=> ( ( Xy = Xx )
% 2.98/1.57 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(powerset_type,type,
% 2.98/1.57 powerset: $i > $i ).
% 2.98/1.57
% 2.98/1.57 thf(powersetAx_type,type,
% 2.98/1.57 powersetAx: $o ).
% 2.98/1.57
% 2.98/1.57 thf(powersetAx,definition,
% 2.98/1.57 ( powersetAx
% 2.98/1.57 = ( ! [A: $i,B: $i] :
% 2.98/1.57 ( ( in @ B @ ( powerset @ A ) )
% 2.98/1.57 <=> ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ B )
% 2.98/1.57 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setunion_type,type,
% 2.98/1.57 setunion: $i > $i ).
% 2.98/1.57
% 2.98/1.57 thf(setunionAx_type,type,
% 2.98/1.57 setunionAx: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setunionAx,definition,
% 2.98/1.57 ( setunionAx
% 2.98/1.57 = ( ! [A: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ ( setunion @ A ) )
% 2.98/1.57 <=> ? [B: $i] :
% 2.98/1.57 ( ( in @ Xx @ B )
% 2.98/1.57 & ( in @ B @ A ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(omega_type,type,
% 2.98/1.57 omega: $i ).
% 2.98/1.57
% 2.98/1.57 thf(omega0Ax_type,type,
% 2.98/1.57 omega0Ax: $o ).
% 2.98/1.57
% 2.98/1.57 thf(omega0Ax,definition,
% 2.98/1.57 ( omega0Ax
% 2.98/1.57 = ( in @ emptyset @ omega ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(omegaSAx_type,type,
% 2.98/1.57 omegaSAx: $o ).
% 2.98/1.57
% 2.98/1.57 thf(omegaSAx,definition,
% 2.98/1.57 ( omegaSAx
% 2.98/1.57 = ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ omega )
% 2.98/1.57 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(omegaIndAx_type,type,
% 2.98/1.57 omegaIndAx: $o ).
% 2.98/1.57
% 2.98/1.57 thf(omegaIndAx,definition,
% 2.98/1.57 ( omegaIndAx
% 2.98/1.57 = ( ! [A: $i] :
% 2.98/1.57 ( ( ( in @ emptyset @ A )
% 2.98/1.57 & ! [Xx: $i] :
% 2.98/1.57 ( ( ( in @ Xx @ omega )
% 2.98/1.57 & ( in @ Xx @ A ) )
% 2.98/1.57 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ omega )
% 2.98/1.57 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(replAx_type,type,
% 2.98/1.57 replAx: $o ).
% 2.98/1.57
% 2.98/1.57 thf(replAx,definition,
% 2.98/1.57 ( replAx
% 2.98/1.57 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.98/1.57 ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( exu
% 2.98/1.57 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.98/1.57 => ? [B: $i] :
% 2.98/1.57 ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ B )
% 2.98/1.57 <=> ? [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ A )
% 2.98/1.57 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(foundationAx_type,type,
% 2.98/1.57 foundationAx: $o ).
% 2.98/1.57
% 2.98/1.57 thf(foundationAx,definition,
% 2.98/1.57 ( foundationAx
% 2.98/1.57 = ( ! [A: $i] :
% 2.98/1.57 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.98/1.57 => ? [B: $i] :
% 2.98/1.57 ( ( in @ B @ A )
% 2.98/1.57 & ~ ? [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ B )
% 2.98/1.57 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(wellorderingAx_type,type,
% 2.98/1.57 wellorderingAx: $o ).
% 2.98/1.57
% 2.98/1.57 thf(wellorderingAx,definition,
% 2.98/1.57 ( wellorderingAx
% 2.98/1.57 = ( ! [A: $i] :
% 2.98/1.57 ? [B: $i] :
% 2.98/1.57 ( ! [C: $i] :
% 2.98/1.57 ( ( in @ C @ B )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ C )
% 2.98/1.57 => ( in @ Xx @ A ) ) )
% 2.98/1.57 & ! [Xx: $i,Xy: $i] :
% 2.98/1.57 ( ( ( in @ Xx @ A )
% 2.98/1.57 & ( in @ Xy @ A ) )
% 2.98/1.57 => ( ! [C: $i] :
% 2.98/1.57 ( ( in @ C @ B )
% 2.98/1.57 => ( ( in @ Xx @ C )
% 2.98/1.57 <=> ( in @ Xy @ C ) ) )
% 2.98/1.57 => ( Xx = Xy ) ) )
% 2.98/1.57 & ! [C: $i,D: $i] :
% 2.98/1.57 ( ( ( in @ C @ B )
% 2.98/1.57 & ( in @ D @ B ) )
% 2.98/1.57 => ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ C )
% 2.98/1.57 => ( in @ Xx @ D ) )
% 2.98/1.57 | ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ D )
% 2.98/1.57 => ( in @ Xx @ C ) ) ) )
% 2.98/1.57 & ! [C: $i] :
% 2.98/1.57 ( ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ C )
% 2.98/1.57 => ( in @ Xx @ A ) )
% 2.98/1.57 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.98/1.57 => ? [D: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ D @ B )
% 2.98/1.57 & ( in @ Xx @ C )
% 2.98/1.57 & ~ ? [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ D )
% 2.98/1.57 & ( in @ Xy @ C ) )
% 2.98/1.57 & ! [E: $i] :
% 2.98/1.57 ( ( in @ E @ B )
% 2.98/1.57 => ( ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ E )
% 2.98/1.57 => ( in @ Xy @ D ) )
% 2.98/1.57 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(descr_type,type,
% 2.98/1.57 descr: ( $i > $o ) > $i ).
% 2.98/1.57
% 2.98/1.57 thf(descrp_type,type,
% 2.98/1.57 descrp: $o ).
% 2.98/1.57
% 2.98/1.57 thf(descrp,definition,
% 2.98/1.57 ( descrp
% 2.98/1.57 = ( ! [Xphi: $i > $o] :
% 2.98/1.57 ( ( exu
% 2.98/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.57 => ( Xphi
% 2.98/1.57 @ ( descr
% 2.98/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(dsetconstr_type,type,
% 2.98/1.57 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.98/1.57
% 2.98/1.57 thf(dsetconstrI_type,type,
% 2.98/1.57 dsetconstrI: $o ).
% 2.98/1.57
% 2.98/1.57 thf(dsetconstrI,definition,
% 2.98/1.57 ( dsetconstrI
% 2.98/1.57 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( Xphi @ Xx )
% 2.98/1.57 => ( in @ Xx
% 2.98/1.57 @ ( dsetconstr @ A
% 2.98/1.57 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(dsetconstrEL_type,type,
% 2.98/1.57 dsetconstrEL: $o ).
% 2.98/1.57
% 2.98/1.57 thf(dsetconstrEL,definition,
% 2.98/1.57 ( dsetconstrEL
% 2.98/1.57 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx
% 2.98/1.57 @ ( dsetconstr @ A
% 2.98/1.57 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.98/1.57 => ( in @ Xx @ A ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(dsetconstrER_type,type,
% 2.98/1.57 dsetconstrER: $o ).
% 2.98/1.57
% 2.98/1.57 thf(dsetconstrER,definition,
% 2.98/1.57 ( dsetconstrER
% 2.98/1.57 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx
% 2.98/1.57 @ ( dsetconstr @ A
% 2.98/1.57 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.98/1.57 => ( Xphi @ Xx ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(exuE1_type,type,
% 2.98/1.57 exuE1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(exuE1,definition,
% 2.98/1.57 ( exuE1
% 2.98/1.57 = ( ! [Xphi: $i > $o] :
% 2.98/1.57 ( ( exu
% 2.98/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.57 => ? [Xx: $i] :
% 2.98/1.57 ( ( Xphi @ Xx )
% 2.98/1.57 & ! [Xy: $i] :
% 2.98/1.57 ( ( Xphi @ Xy )
% 2.98/1.57 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(prop2set_type,type,
% 2.98/1.57 prop2set: $o > $i ).
% 2.98/1.57
% 2.98/1.57 thf(prop2setE_type,type,
% 2.98/1.57 prop2setE: $o ).
% 2.98/1.57
% 2.98/1.57 thf(prop2setE,definition,
% 2.98/1.57 ( prop2setE
% 2.98/1.57 = ( ! [Xphi: $o,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.98/1.57 => Xphi ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(emptysetE_type,type,
% 2.98/1.57 emptysetE: $o ).
% 2.98/1.57
% 2.98/1.57 thf(emptysetE,definition,
% 2.98/1.57 ( emptysetE
% 2.98/1.57 = ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ emptyset )
% 2.98/1.57 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(emptysetimpfalse_type,type,
% 2.98/1.57 emptysetimpfalse: $o ).
% 2.98/1.57
% 2.98/1.57 thf(emptysetimpfalse,definition,
% 2.98/1.57 ( emptysetimpfalse
% 2.98/1.57 = ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ emptyset )
% 2.98/1.57 => $false ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(notinemptyset_type,type,
% 2.98/1.57 notinemptyset: $o ).
% 2.98/1.57
% 2.98/1.57 thf(notinemptyset,definition,
% 2.98/1.57 ( notinemptyset
% 2.98/1.57 = ( ! [Xx: $i] :
% 2.98/1.57 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(exuE3e_type,type,
% 2.98/1.57 exuE3e: $o ).
% 2.98/1.57
% 2.98/1.57 thf(exuE3e,definition,
% 2.98/1.57 ( exuE3e
% 2.98/1.57 = ( ! [Xphi: $i > $o] :
% 2.98/1.57 ( ( exu
% 2.98/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.57 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setext_type,type,
% 2.98/1.57 setext: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setext,definition,
% 2.98/1.57 ( setext
% 2.98/1.57 = ( ! [A: $i,B: $i] :
% 2.98/1.57 ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( in @ Xx @ B ) )
% 2.98/1.57 => ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ B )
% 2.98/1.57 => ( in @ Xx @ A ) )
% 2.98/1.57 => ( A = B ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(emptyI_type,type,
% 2.98/1.57 emptyI: $o ).
% 2.98/1.57
% 2.98/1.57 thf(emptyI,definition,
% 2.98/1.57 ( emptyI
% 2.98/1.57 = ( ! [A: $i] :
% 2.98/1.57 ( ! [Xx: $i] :
% 2.98/1.57 ~ ( in @ Xx @ A )
% 2.98/1.57 => ( A = emptyset ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(noeltsimpempty_type,type,
% 2.98/1.57 noeltsimpempty: $o ).
% 2.98/1.57
% 2.98/1.57 thf(noeltsimpempty,definition,
% 2.98/1.57 ( noeltsimpempty
% 2.98/1.57 = ( ! [A: $i] :
% 2.98/1.57 ( ! [Xx: $i] :
% 2.98/1.57 ~ ( in @ Xx @ A )
% 2.98/1.57 => ( A = emptyset ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setbeta_type,type,
% 2.98/1.57 setbeta: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setbeta,definition,
% 2.98/1.57 ( setbeta
% 2.98/1.57 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( in @ Xx
% 2.98/1.57 @ ( dsetconstr @ A
% 2.98/1.57 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.98/1.57 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(nonempty_type,type,
% 2.98/1.57 nonempty: $i > $o ).
% 2.98/1.57
% 2.98/1.57 thf(nonempty,definition,
% 2.98/1.57 ( nonempty
% 2.98/1.57 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(nonemptyE1_type,type,
% 2.98/1.57 nonemptyE1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(nonemptyE1,definition,
% 2.98/1.57 ( nonemptyE1
% 2.98/1.57 = ( ! [A: $i] :
% 2.98/1.57 ( ( nonempty @ A )
% 2.98/1.57 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(nonemptyI_type,type,
% 2.98/1.57 nonemptyI: $o ).
% 2.98/1.57
% 2.98/1.57 thf(nonemptyI,definition,
% 2.98/1.57 ( nonemptyI
% 2.98/1.57 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( Xphi @ Xx )
% 2.98/1.57 => ( nonempty
% 2.98/1.57 @ ( dsetconstr @ A
% 2.98/1.57 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(nonemptyI1_type,type,
% 2.98/1.57 nonemptyI1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(nonemptyI1,definition,
% 2.98/1.57 ( nonemptyI1
% 2.98/1.57 = ( ! [A: $i] :
% 2.98/1.57 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.98/1.57 => ( nonempty @ A ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setadjoinIL_type,type,
% 2.98/1.57 setadjoinIL: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setadjoinIL,definition,
% 2.98/1.57 ( setadjoinIL
% 2.98/1.57 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(emptyinunitempty_type,type,
% 2.98/1.57 emptyinunitempty: $o ).
% 2.98/1.57
% 2.98/1.57 thf(emptyinunitempty,definition,
% 2.98/1.57 ( emptyinunitempty
% 2.98/1.57 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setadjoinIR_type,type,
% 2.98/1.57 setadjoinIR: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setadjoinIR,definition,
% 2.98/1.57 ( setadjoinIR
% 2.98/1.57 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ A )
% 2.98/1.57 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setadjoinE_type,type,
% 2.98/1.57 setadjoinE: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setadjoinE,definition,
% 2.98/1.57 ( setadjoinE
% 2.98/1.57 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.98/1.57 => ! [Xphi: $o] :
% 2.98/1.57 ( ( ( Xy = Xx )
% 2.98/1.57 => Xphi )
% 2.98/1.57 => ( ( ( in @ Xy @ A )
% 2.98/1.57 => Xphi )
% 2.98/1.57 => Xphi ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setadjoinOr_type,type,
% 2.98/1.57 setadjoinOr: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setadjoinOr,definition,
% 2.98/1.57 ( setadjoinOr
% 2.98/1.57 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.98/1.57 => ( ( Xy = Xx )
% 2.98/1.57 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setoftrueEq_type,type,
% 2.98/1.57 setoftrueEq: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setoftrueEq,definition,
% 2.98/1.57 ( setoftrueEq
% 2.98/1.57 = ( ! [A: $i] :
% 2.98/1.57 ( ( dsetconstr @ A
% 2.98/1.57 @ ^ [Xx: $i] : $true )
% 2.98/1.57 = A ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(powersetI_type,type,
% 2.98/1.57 powersetI: $o ).
% 2.98/1.57
% 2.98/1.57 thf(powersetI,definition,
% 2.98/1.57 ( powersetI
% 2.98/1.57 = ( ! [A: $i,B: $i] :
% 2.98/1.57 ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ B )
% 2.98/1.57 => ( in @ Xx @ A ) )
% 2.98/1.57 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(emptyinPowerset_type,type,
% 2.98/1.57 emptyinPowerset: $o ).
% 2.98/1.57
% 2.98/1.57 thf(emptyinPowerset,definition,
% 2.98/1.57 ( emptyinPowerset
% 2.98/1.57 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(emptyInPowerset_type,type,
% 2.98/1.57 emptyInPowerset: $o ).
% 2.98/1.57
% 2.98/1.57 thf(emptyInPowerset,definition,
% 2.98/1.57 ( emptyInPowerset
% 2.98/1.57 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(powersetE_type,type,
% 2.98/1.57 powersetE: $o ).
% 2.98/1.57
% 2.98/1.57 thf(powersetE,definition,
% 2.98/1.57 ( powersetE
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ B @ ( powerset @ A ) )
% 2.98/1.57 => ( ( in @ Xx @ B )
% 2.98/1.57 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setunionI_type,type,
% 2.98/1.57 setunionI: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setunionI,definition,
% 2.98/1.57 ( setunionI
% 2.98/1.57 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.98/1.57 ( ( in @ Xx @ B )
% 2.98/1.57 => ( ( in @ B @ A )
% 2.98/1.57 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setunionE_type,type,
% 2.98/1.57 setunionE: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setunionE,definition,
% 2.98/1.57 ( setunionE
% 2.98/1.57 = ( ! [A: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ ( setunion @ A ) )
% 2.98/1.57 => ! [Xphi: $o] :
% 2.98/1.57 ( ! [B: $i] :
% 2.98/1.57 ( ( in @ Xx @ B )
% 2.98/1.57 => ( ( in @ B @ A )
% 2.98/1.57 => Xphi ) )
% 2.98/1.57 => Xphi ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(subPowSU_type,type,
% 2.98/1.57 subPowSU: $o ).
% 2.98/1.57
% 2.98/1.57 thf(subPowSU,definition,
% 2.98/1.57 ( subPowSU
% 2.98/1.57 = ( ! [A: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(exuE2_type,type,
% 2.98/1.57 exuE2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(exuE2,definition,
% 2.98/1.57 ( exuE2
% 2.98/1.57 = ( ! [Xphi: $i > $o] :
% 2.98/1.57 ( ( exu
% 2.98/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.57 => ? [Xx: $i] :
% 2.98/1.57 ! [Xy: $i] :
% 2.98/1.57 ( ( Xphi @ Xy )
% 2.98/1.57 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(nonemptyImpWitness_type,type,
% 2.98/1.57 nonemptyImpWitness: $o ).
% 2.98/1.57
% 2.98/1.57 thf(nonemptyImpWitness,definition,
% 2.98/1.57 ( nonemptyImpWitness
% 2.98/1.57 = ( ! [A: $i] :
% 2.98/1.57 ( ( nonempty @ A )
% 2.98/1.57 => ? [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 & $true ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(uniqinunit_type,type,
% 2.98/1.57 uniqinunit: $o ).
% 2.98/1.57
% 2.98/1.57 thf(uniqinunit,definition,
% 2.98/1.57 ( uniqinunit
% 2.98/1.57 = ( ! [Xx: $i,Xy: $i] :
% 2.98/1.57 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.98/1.57 => ( Xx = Xy ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(notinsingleton_type,type,
% 2.98/1.57 notinsingleton: $o ).
% 2.98/1.57
% 2.98/1.57 thf(notinsingleton,definition,
% 2.98/1.57 ( notinsingleton
% 2.98/1.57 = ( ! [Xx: $i,Xy: $i] :
% 2.98/1.57 ( ( Xx != Xy )
% 2.98/1.57 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(eqinunit_type,type,
% 2.98/1.57 eqinunit: $o ).
% 2.98/1.57
% 2.98/1.57 thf(eqinunit,definition,
% 2.98/1.57 ( eqinunit
% 2.98/1.57 = ( ! [Xx: $i,Xy: $i] :
% 2.98/1.57 ( ( Xx = Xy )
% 2.98/1.57 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(singletonsswitch_type,type,
% 2.98/1.57 singletonsswitch: $o ).
% 2.98/1.57
% 2.98/1.57 thf(singletonsswitch,definition,
% 2.98/1.57 ( singletonsswitch
% 2.98/1.57 = ( ! [Xx: $i,Xy: $i] :
% 2.98/1.57 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.98/1.57 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(upairsetE_type,type,
% 2.98/1.57 upairsetE: $o ).
% 2.98/1.57
% 2.98/1.57 thf(upairsetE,definition,
% 2.98/1.57 ( upairsetE
% 2.98/1.57 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.98/1.57 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.98/1.57 => ( ( Xz = Xx )
% 2.98/1.57 | ( Xz = Xy ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(upairsetIL_type,type,
% 2.98/1.57 upairsetIL: $o ).
% 2.98/1.57
% 2.98/1.57 thf(upairsetIL,definition,
% 2.98/1.57 ( upairsetIL
% 2.98/1.57 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(upairsetIR_type,type,
% 2.98/1.57 upairsetIR: $o ).
% 2.98/1.57
% 2.98/1.57 thf(upairsetIR,definition,
% 2.98/1.57 ( upairsetIR
% 2.98/1.57 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(emptyE1_type,type,
% 2.98/1.57 emptyE1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(emptyE1,definition,
% 2.98/1.57 ( emptyE1
% 2.98/1.57 = ( ! [A: $i,Xphi: $i > $o] :
% 2.98/1.57 ( ? [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 & ( Xphi @ Xx ) )
% 2.98/1.57 => ( ( ( dsetconstr @ A
% 2.98/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.57 = emptyset )
% 2.98/1.57 => $false ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(vacuousDall_type,type,
% 2.98/1.57 vacuousDall: $o ).
% 2.98/1.57
% 2.98/1.57 thf(vacuousDall,definition,
% 2.98/1.57 ( vacuousDall
% 2.98/1.57 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ emptyset )
% 2.98/1.57 => ( Xphi @ Xx ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(quantDeMorgan1_type,type,
% 2.98/1.57 quantDeMorgan1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(quantDeMorgan1,definition,
% 2.98/1.57 ( quantDeMorgan1
% 2.98/1.57 = ( ! [A: $i,Xphi: $i > $o] :
% 2.98/1.57 ( ~ ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( Xphi @ Xx ) )
% 2.98/1.57 => ? [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(quantDeMorgan2_type,type,
% 2.98/1.57 quantDeMorgan2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(quantDeMorgan2,definition,
% 2.98/1.57 ( quantDeMorgan2
% 2.98/1.57 = ( ! [A: $i,Xphi: $i > $o] :
% 2.98/1.57 ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ~ ( Xphi @ Xx ) )
% 2.98/1.57 => ~ ? [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(quantDeMorgan3_type,type,
% 2.98/1.57 quantDeMorgan3: $o ).
% 2.98/1.57
% 2.98/1.57 thf(quantDeMorgan3,definition,
% 2.98/1.57 ( quantDeMorgan3
% 2.98/1.57 = ( ! [A: $i,Xphi: $i > $o] :
% 2.98/1.57 ( ~ ? [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 & ( Xphi @ Xx ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(quantDeMorgan4_type,type,
% 2.98/1.57 quantDeMorgan4: $o ).
% 2.98/1.57
% 2.98/1.57 thf(quantDeMorgan4,definition,
% 2.98/1.57 ( quantDeMorgan4
% 2.98/1.57 = ( ! [A: $i,Xphi: $i > $o] :
% 2.98/1.57 ( ? [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 & ~ ( Xphi @ Xx ) )
% 2.98/1.57 => ~ ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(prop2setI_type,type,
% 2.98/1.57 prop2setI: $o ).
% 2.98/1.57
% 2.98/1.57 thf(prop2setI,definition,
% 2.98/1.57 ( prop2setI
% 2.98/1.57 = ( ! [Xphi: $o] :
% 2.98/1.57 ( Xphi
% 2.98/1.57 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(set2prop_type,type,
% 2.98/1.57 set2prop: $i > $o ).
% 2.98/1.57
% 2.98/1.57 thf(prop2set2propI_type,type,
% 2.98/1.57 prop2set2propI: $o ).
% 2.98/1.57
% 2.98/1.57 thf(prop2set2propI,definition,
% 2.98/1.57 ( prop2set2propI
% 2.98/1.57 = ( ! [Xphi: $o] :
% 2.98/1.57 ( Xphi
% 2.98/1.57 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(notdexE_type,type,
% 2.98/1.57 notdexE: $o ).
% 2.98/1.57
% 2.98/1.57 thf(notdexE,definition,
% 2.98/1.57 ( notdexE
% 2.98/1.57 = ( ! [A: $i,Xphi: $i > $o] :
% 2.98/1.57 ( ~ ? [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 & ( Xphi @ Xx ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(notdallE_type,type,
% 2.98/1.57 notdallE: $o ).
% 2.98/1.57
% 2.98/1.57 thf(notdallE,definition,
% 2.98/1.57 ( notdallE
% 2.98/1.57 = ( ! [A: $i,Xphi: $i > $o] :
% 2.98/1.57 ( ~ ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( Xphi @ Xx ) )
% 2.98/1.57 => ? [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(exuI1_type,type,
% 2.98/1.57 exuI1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(exuI1,definition,
% 2.98/1.57 ( exuI1
% 2.98/1.57 = ( ! [Xphi: $i > $o] :
% 2.98/1.57 ( ? [Xx: $i] :
% 2.98/1.57 ( ( Xphi @ Xx )
% 2.98/1.57 & ! [Xy: $i] :
% 2.98/1.57 ( ( Xphi @ Xy )
% 2.98/1.57 => ( Xx = Xy ) ) )
% 2.98/1.57 => ( exu
% 2.98/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(exuI3_type,type,
% 2.98/1.57 exuI3: $o ).
% 2.98/1.57
% 2.98/1.57 thf(exuI3,definition,
% 2.98/1.57 ( exuI3
% 2.98/1.57 = ( ! [Xphi: $i > $o] :
% 2.98/1.57 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.98/1.57 => ( ! [Xx: $i,Xy: $i] :
% 2.98/1.57 ( ( Xphi @ Xx )
% 2.98/1.57 => ( ( Xphi @ Xy )
% 2.98/1.57 => ( Xx = Xy ) ) )
% 2.98/1.57 => ( exu
% 2.98/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(exuI2_type,type,
% 2.98/1.57 exuI2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(exuI2,definition,
% 2.98/1.57 ( exuI2
% 2.98/1.57 = ( ! [Xphi: $i > $o] :
% 2.98/1.57 ( ? [Xx: $i] :
% 2.98/1.57 ! [Xy: $i] :
% 2.98/1.57 ( ( Xphi @ Xy )
% 2.98/1.57 <=> ( Xy = Xx ) )
% 2.98/1.57 => ( exu
% 2.98/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(inCongP_type,type,
% 2.98/1.57 inCongP: $o ).
% 2.98/1.57
% 2.98/1.57 thf(inCongP,definition,
% 2.98/1.57 ( inCongP
% 2.98/1.57 = ( ! [A: $i,B: $i] :
% 2.98/1.57 ( ( A = B )
% 2.98/1.57 => ! [Xx: $i,Xy: $i] :
% 2.98/1.57 ( ( Xx = Xy )
% 2.98/1.57 => ( ( in @ Xx @ A )
% 2.98/1.57 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(in__Cong_type,type,
% 2.98/1.57 in__Cong: $o ).
% 2.98/1.57
% 2.98/1.57 thf(in__Cong,definition,
% 2.98/1.57 ( in__Cong
% 2.98/1.57 = ( ! [A: $i,B: $i] :
% 2.98/1.57 ( ( A = B )
% 2.98/1.57 => ! [Xx: $i,Xy: $i] :
% 2.98/1.57 ( ( Xx = Xy )
% 2.98/1.57 => ( ( in @ Xx @ A )
% 2.98/1.57 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(exuE3u_type,type,
% 2.98/1.57 exuE3u: $o ).
% 2.98/1.57
% 2.98/1.57 thf(exuE3u,definition,
% 2.98/1.57 ( exuE3u
% 2.98/1.57 = ( ! [Xphi: $i > $o] :
% 2.98/1.57 ( ( exu
% 2.98/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.57 => ! [Xx: $i,Xy: $i] :
% 2.98/1.57 ( ( Xphi @ Xx )
% 2.98/1.57 => ( ( Xphi @ Xy )
% 2.98/1.57 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(exu__Cong_type,type,
% 2.98/1.57 exu__Cong: $o ).
% 2.98/1.57
% 2.98/1.57 thf(exu__Cong,definition,
% 2.98/1.57 ( exu__Cong
% 2.98/1.57 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.98/1.57 ( ! [Xx: $i,Xy: $i] :
% 2.98/1.57 ( ( Xx = Xy )
% 2.98/1.57 => ( ( Xphi @ Xx )
% 2.98/1.57 <=> ( Xpsi @ Xy ) ) )
% 2.98/1.57 => ( ( exu
% 2.98/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.57 <=> ( exu
% 2.98/1.57 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(emptyset__Cong_type,type,
% 2.98/1.57 emptyset__Cong: $o ).
% 2.98/1.57
% 2.98/1.57 thf(emptyset__Cong,definition,
% 2.98/1.57 ( emptyset__Cong
% 2.98/1.57 = ( emptyset = emptyset ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setadjoin__Cong_type,type,
% 2.98/1.57 setadjoin__Cong: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setadjoin__Cong,definition,
% 2.98/1.57 ( setadjoin__Cong
% 2.98/1.57 = ( ! [Xx: $i,Xy: $i] :
% 2.98/1.57 ( ( Xx = Xy )
% 2.98/1.57 => ! [Xz: $i,Xu: $i] :
% 2.98/1.57 ( ( Xz = Xu )
% 2.98/1.57 => ( ( setadjoin @ Xx @ Xz )
% 2.98/1.57 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(powerset__Cong_type,type,
% 2.98/1.57 powerset__Cong: $o ).
% 2.98/1.57
% 2.98/1.57 thf(powerset__Cong,definition,
% 2.98/1.57 ( powerset__Cong
% 2.98/1.57 = ( ! [A: $i,B: $i] :
% 2.98/1.57 ( ( A = B )
% 2.98/1.57 => ( ( powerset @ A )
% 2.98/1.57 = ( powerset @ B ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setunion__Cong_type,type,
% 2.98/1.57 setunion__Cong: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setunion__Cong,definition,
% 2.98/1.57 ( setunion__Cong
% 2.98/1.57 = ( ! [A: $i,B: $i] :
% 2.98/1.57 ( ( A = B )
% 2.98/1.57 => ( ( setunion @ A )
% 2.98/1.57 = ( setunion @ B ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(omega__Cong_type,type,
% 2.98/1.57 omega__Cong: $o ).
% 2.98/1.57
% 2.98/1.57 thf(omega__Cong,definition,
% 2.98/1.57 ( omega__Cong
% 2.98/1.57 = ( omega = omega ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(exuEu_type,type,
% 2.98/1.57 exuEu: $o ).
% 2.98/1.57
% 2.98/1.57 thf(exuEu,definition,
% 2.98/1.57 ( exuEu
% 2.98/1.57 = ( ! [Xphi: $i > $o] :
% 2.98/1.57 ( ( exu
% 2.98/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.57 => ! [Xx: $i,Xy: $i] :
% 2.98/1.57 ( ( Xphi @ Xx )
% 2.98/1.57 => ( ( Xphi @ Xy )
% 2.98/1.57 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(descr__Cong_type,type,
% 2.98/1.57 descr__Cong: $o ).
% 2.98/1.57
% 2.98/1.57 thf(descr__Cong,definition,
% 2.98/1.57 ( descr__Cong
% 2.98/1.57 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.98/1.57 ( ! [Xx: $i,Xy: $i] :
% 2.98/1.57 ( ( Xx = Xy )
% 2.98/1.57 => ( ( Xphi @ Xx )
% 2.98/1.57 <=> ( Xpsi @ Xy ) ) )
% 2.98/1.57 => ( ( exu
% 2.98/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.57 => ( ( exu
% 2.98/1.57 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.98/1.57 => ( ( descr
% 2.98/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.57 = ( descr
% 2.98/1.57 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(dsetconstr__Cong_type,type,
% 2.98/1.57 dsetconstr__Cong: $o ).
% 2.98/1.57
% 2.98/1.57 thf(dsetconstr__Cong,definition,
% 2.98/1.57 ( dsetconstr__Cong
% 2.98/1.57 = ( ! [A: $i,B: $i] :
% 2.98/1.57 ( ( A = B )
% 2.98/1.57 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.98/1.57 ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ B )
% 2.98/1.57 => ( ( Xx = Xy )
% 2.98/1.57 => ( ( Xphi @ Xx )
% 2.98/1.57 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.98/1.57 => ( ( dsetconstr @ A
% 2.98/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.57 = ( dsetconstr @ B
% 2.98/1.57 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(subset_type,type,
% 2.98/1.57 subset: $i > $i > $o ).
% 2.98/1.57
% 2.98/1.57 thf(disjoint_type,type,
% 2.98/1.57 disjoint: $i > $i > $o ).
% 2.98/1.57
% 2.98/1.57 thf(setsmeet_type,type,
% 2.98/1.57 setsmeet: $i > $i > $o ).
% 2.98/1.57
% 2.98/1.57 thf(subsetI1_type,type,
% 2.98/1.57 subsetI1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(subsetI1,definition,
% 2.98/1.57 ( subsetI1
% 2.98/1.57 = ( ! [A: $i,B: $i] :
% 2.98/1.57 ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( in @ Xx @ B ) )
% 2.98/1.57 => ( subset @ A @ B ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(eqimpsubset2_type,type,
% 2.98/1.57 eqimpsubset2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(eqimpsubset2,definition,
% 2.98/1.57 ( eqimpsubset2
% 2.98/1.57 = ( ! [A: $i,B: $i] :
% 2.98/1.57 ( ( A = B )
% 2.98/1.57 => ( subset @ B @ A ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(eqimpsubset1_type,type,
% 2.98/1.57 eqimpsubset1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(eqimpsubset1,definition,
% 2.98/1.57 ( eqimpsubset1
% 2.98/1.57 = ( ! [A: $i,B: $i] :
% 2.98/1.57 ( ( A = B )
% 2.98/1.57 => ( subset @ A @ B ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(subsetI2_type,type,
% 2.98/1.57 subsetI2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(subsetI2,definition,
% 2.98/1.57 ( subsetI2
% 2.98/1.57 = ( ! [A: $i,B: $i] :
% 2.98/1.57 ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( in @ Xx @ B ) )
% 2.98/1.57 => ( subset @ A @ B ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(emptysetsubset_type,type,
% 2.98/1.57 emptysetsubset: $o ).
% 2.98/1.57
% 2.98/1.57 thf(emptysetsubset,definition,
% 2.98/1.57 ( emptysetsubset
% 2.98/1.57 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(subsetE_type,type,
% 2.98/1.57 subsetE: $o ).
% 2.98/1.57
% 2.98/1.57 thf(subsetE,definition,
% 2.98/1.57 ( subsetE
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ( subset @ A @ B )
% 2.98/1.57 => ( ( in @ Xx @ A )
% 2.98/1.57 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(subsetE2_type,type,
% 2.98/1.57 subsetE2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(subsetE2,definition,
% 2.98/1.57 ( subsetE2
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ( subset @ A @ B )
% 2.98/1.57 => ( ~ ( in @ Xx @ B )
% 2.98/1.57 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(notsubsetI_type,type,
% 2.98/1.57 notsubsetI: $o ).
% 2.98/1.57
% 2.98/1.57 thf(notsubsetI,definition,
% 2.98/1.57 ( notsubsetI
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ~ ( in @ Xx @ B )
% 2.98/1.57 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(notequalI1_type,type,
% 2.98/1.57 notequalI1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(notequalI1,definition,
% 2.98/1.57 ( notequalI1
% 2.98/1.57 = ( ! [A: $i,B: $i] :
% 2.98/1.57 ( ~ ( subset @ A @ B )
% 2.98/1.57 => ( A != B ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(notequalI2_type,type,
% 2.98/1.57 notequalI2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(notequalI2,definition,
% 2.98/1.57 ( notequalI2
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ~ ( in @ Xx @ B )
% 2.98/1.57 => ( A != B ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(subsetRefl_type,type,
% 2.98/1.57 subsetRefl: $o ).
% 2.98/1.57
% 2.98/1.57 thf(subsetRefl,definition,
% 2.98/1.57 ( subsetRefl
% 2.98/1.57 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(subsetTrans_type,type,
% 2.98/1.57 subsetTrans: $o ).
% 2.98/1.57
% 2.98/1.57 thf(subsetTrans,definition,
% 2.98/1.57 ( subsetTrans
% 2.98/1.57 = ( ! [A: $i,B: $i,C: $i] :
% 2.98/1.57 ( ( subset @ A @ B )
% 2.98/1.57 => ( ( subset @ B @ C )
% 2.98/1.57 => ( subset @ A @ C ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setadjoinSub_type,type,
% 2.98/1.57 setadjoinSub: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setadjoinSub,definition,
% 2.98/1.57 ( setadjoinSub
% 2.98/1.57 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setadjoinSub2_type,type,
% 2.98/1.57 setadjoinSub2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setadjoinSub2,definition,
% 2.98/1.57 ( setadjoinSub2
% 2.98/1.57 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.98/1.57 ( ( subset @ A @ B )
% 2.98/1.57 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(subset2powerset_type,type,
% 2.98/1.57 subset2powerset: $o ).
% 2.98/1.57
% 2.98/1.57 thf(subset2powerset,definition,
% 2.98/1.57 ( subset2powerset
% 2.98/1.57 = ( ! [A: $i,B: $i] :
% 2.98/1.57 ( ( subset @ A @ B )
% 2.98/1.57 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setextsub_type,type,
% 2.98/1.57 setextsub: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setextsub,definition,
% 2.98/1.57 ( setextsub
% 2.98/1.57 = ( ! [A: $i,B: $i] :
% 2.98/1.57 ( ( subset @ A @ B )
% 2.98/1.57 => ( ( subset @ B @ A )
% 2.98/1.57 => ( A = B ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(subsetemptysetimpeq_type,type,
% 2.98/1.57 subsetemptysetimpeq: $o ).
% 2.98/1.57
% 2.98/1.57 thf(subsetemptysetimpeq,definition,
% 2.98/1.57 ( subsetemptysetimpeq
% 2.98/1.57 = ( ! [A: $i] :
% 2.98/1.57 ( ( subset @ A @ emptyset )
% 2.98/1.57 => ( A = emptyset ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(powersetI1_type,type,
% 2.98/1.57 powersetI1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(powersetI1,definition,
% 2.98/1.57 ( powersetI1
% 2.98/1.57 = ( ! [A: $i,B: $i] :
% 2.98/1.57 ( ( subset @ B @ A )
% 2.98/1.57 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(powersetE1_type,type,
% 2.98/1.57 powersetE1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(powersetE1,definition,
% 2.98/1.57 ( powersetE1
% 2.98/1.57 = ( ! [A: $i,B: $i] :
% 2.98/1.57 ( ( in @ B @ ( powerset @ A ) )
% 2.98/1.57 => ( subset @ B @ A ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(inPowerset_type,type,
% 2.98/1.57 inPowerset: $o ).
% 2.98/1.57
% 2.98/1.57 thf(inPowerset,definition,
% 2.98/1.57 ( inPowerset
% 2.98/1.57 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(powersetsubset_type,type,
% 2.98/1.57 powersetsubset: $o ).
% 2.98/1.57
% 2.98/1.57 thf(powersetsubset,definition,
% 2.98/1.57 ( powersetsubset
% 2.98/1.57 = ( ! [A: $i,B: $i] :
% 2.98/1.57 ( ( subset @ A @ B )
% 2.98/1.57 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(sepInPowerset_type,type,
% 2.98/1.57 sepInPowerset: $o ).
% 2.98/1.57
% 2.98/1.57 thf(sepInPowerset,definition,
% 2.98/1.57 ( sepInPowerset
% 2.98/1.57 = ( ! [A: $i,Xphi: $i > $o] :
% 2.98/1.57 ( in
% 2.98/1.57 @ ( dsetconstr @ A
% 2.98/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.57 @ ( powerset @ A ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(sepSubset_type,type,
% 2.98/1.57 sepSubset: $o ).
% 2.98/1.57
% 2.98/1.57 thf(sepSubset,definition,
% 2.98/1.57 ( sepSubset
% 2.98/1.57 = ( ! [A: $i,Xphi: $i > $o] :
% 2.98/1.57 ( subset
% 2.98/1.57 @ ( dsetconstr @ A
% 2.98/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.57 @ A ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(binunion_type,type,
% 2.98/1.57 binunion: $i > $i > $i ).
% 2.98/1.57
% 2.98/1.57 thf(binunionIL_type,type,
% 2.98/1.57 binunionIL: $o ).
% 2.98/1.57
% 2.98/1.57 thf(binunionIL,definition,
% 2.98/1.57 ( binunionIL
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(upairset2IR_type,type,
% 2.98/1.57 upairset2IR: $o ).
% 2.98/1.57
% 2.98/1.57 thf(upairset2IR,definition,
% 2.98/1.57 ( upairset2IR
% 2.98/1.57 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(binunionIR_type,type,
% 2.98/1.57 binunionIR: $o ).
% 2.98/1.57
% 2.98/1.57 thf(binunionIR,definition,
% 2.98/1.57 ( binunionIR
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ B )
% 2.98/1.57 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(binunionEcases_type,type,
% 2.98/1.57 binunionEcases: $o ).
% 2.98/1.57
% 2.98/1.57 thf(binunionEcases,definition,
% 2.98/1.57 ( binunionEcases
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.98/1.57 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.98/1.57 => ( ( ( in @ Xx @ A )
% 2.98/1.57 => Xphi )
% 2.98/1.57 => ( ( ( in @ Xx @ B )
% 2.98/1.57 => Xphi )
% 2.98/1.57 => Xphi ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(binunionE_type,type,
% 2.98/1.57 binunionE: $o ).
% 2.98/1.57
% 2.98/1.57 thf(binunionE,definition,
% 2.98/1.57 ( binunionE
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.98/1.57 => ( ( in @ Xx @ A )
% 2.98/1.57 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(binunionLsub_type,type,
% 2.98/1.57 binunionLsub: $o ).
% 2.98/1.57
% 2.98/1.57 thf(binunionLsub,definition,
% 2.98/1.57 ( binunionLsub
% 2.98/1.57 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(binunionRsub_type,type,
% 2.98/1.57 binunionRsub: $o ).
% 2.98/1.57
% 2.98/1.57 thf(binunionRsub,definition,
% 2.98/1.57 ( binunionRsub
% 2.98/1.57 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(binintersect_type,type,
% 2.98/1.57 binintersect: $i > $i > $i ).
% 2.98/1.57
% 2.98/1.57 thf(binintersectI_type,type,
% 2.98/1.57 binintersectI: $o ).
% 2.98/1.57
% 2.98/1.57 thf(binintersectI,definition,
% 2.98/1.57 ( binintersectI
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( in @ Xx @ B )
% 2.98/1.57 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(binintersectSubset5_type,type,
% 2.98/1.57 binintersectSubset5: $o ).
% 2.98/1.57
% 2.98/1.57 thf(binintersectSubset5,definition,
% 2.98/1.57 ( binintersectSubset5
% 2.98/1.57 = ( ! [A: $i,B: $i,C: $i] :
% 2.98/1.57 ( ( subset @ C @ A )
% 2.98/1.57 => ( ( subset @ C @ B )
% 2.98/1.57 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(binintersectEL_type,type,
% 2.98/1.57 binintersectEL: $o ).
% 2.98/1.57
% 2.98/1.57 thf(binintersectEL,definition,
% 2.98/1.57 ( binintersectEL
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.98/1.57 => ( in @ Xx @ A ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(binintersectLsub_type,type,
% 2.98/1.57 binintersectLsub: $o ).
% 2.98/1.57
% 2.98/1.57 thf(binintersectLsub,definition,
% 2.98/1.57 ( binintersectLsub
% 2.98/1.57 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(binintersectSubset2_type,type,
% 2.98/1.57 binintersectSubset2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(binintersectSubset2,definition,
% 2.98/1.57 ( binintersectSubset2
% 2.98/1.57 = ( ! [A: $i,B: $i] :
% 2.98/1.57 ( ( subset @ A @ B )
% 2.98/1.57 => ( ( binintersect @ A @ B )
% 2.98/1.57 = A ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(binintersectSubset3_type,type,
% 2.98/1.57 binintersectSubset3: $o ).
% 2.98/1.57
% 2.98/1.57 thf(binintersectSubset3,definition,
% 2.98/1.57 ( binintersectSubset3
% 2.98/1.57 = ( ! [A: $i,B: $i] :
% 2.98/1.57 ( ( ( binintersect @ A @ B )
% 2.98/1.57 = B )
% 2.98/1.57 => ( subset @ B @ A ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(binintersectER_type,type,
% 2.98/1.57 binintersectER: $o ).
% 2.98/1.57
% 2.98/1.57 thf(binintersectER,definition,
% 2.98/1.57 ( binintersectER
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.98/1.57 => ( in @ Xx @ B ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(disjointsetsI1_type,type,
% 2.98/1.57 disjointsetsI1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(disjointsetsI1,definition,
% 2.98/1.57 ( disjointsetsI1
% 2.98/1.57 = ( ! [A: $i,B: $i] :
% 2.98/1.57 ( ~ ? [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 & ( in @ Xx @ B ) )
% 2.98/1.57 => ( ( binintersect @ A @ B )
% 2.98/1.57 = emptyset ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(binintersectRsub_type,type,
% 2.98/1.57 binintersectRsub: $o ).
% 2.98/1.57
% 2.98/1.57 thf(binintersectRsub,definition,
% 2.98/1.57 ( binintersectRsub
% 2.98/1.57 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(binintersectSubset4_type,type,
% 2.98/1.57 binintersectSubset4: $o ).
% 2.98/1.57
% 2.98/1.57 thf(binintersectSubset4,definition,
% 2.98/1.57 ( binintersectSubset4
% 2.98/1.57 = ( ! [A: $i,B: $i] :
% 2.98/1.57 ( ( subset @ B @ A )
% 2.98/1.57 => ( ( binintersect @ A @ B )
% 2.98/1.57 = B ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(binintersectSubset1_type,type,
% 2.98/1.57 binintersectSubset1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(binintersectSubset1,definition,
% 2.98/1.57 ( binintersectSubset1
% 2.98/1.57 = ( ! [A: $i,B: $i] :
% 2.98/1.57 ( ( ( binintersect @ A @ B )
% 2.98/1.57 = A )
% 2.98/1.57 => ( subset @ A @ B ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(bs114d_type,type,
% 2.98/1.57 bs114d: $o ).
% 2.98/1.57
% 2.98/1.57 thf(bs114d,definition,
% 2.98/1.57 ( bs114d
% 2.98/1.57 = ( ! [A: $i,B: $i,C: $i] :
% 2.98/1.57 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.98/1.57 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(regular_type,type,
% 2.98/1.57 regular: $i > $o ).
% 2.98/1.57
% 2.98/1.57 thf(setminus_type,type,
% 2.98/1.57 setminus: $i > $i > $i ).
% 2.98/1.57
% 2.98/1.57 thf(setminusI_type,type,
% 2.98/1.57 setminusI: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setminusI,definition,
% 2.98/1.57 ( setminusI
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ~ ( in @ Xx @ B )
% 2.98/1.57 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setminusEL_type,type,
% 2.98/1.57 setminusEL: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setminusEL,definition,
% 2.98/1.57 ( setminusEL
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.98/1.57 => ( in @ Xx @ A ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setminusER_type,type,
% 2.98/1.57 setminusER: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setminusER,definition,
% 2.98/1.57 ( setminusER
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.98/1.57 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setminusSubset2_type,type,
% 2.98/1.57 setminusSubset2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setminusSubset2,definition,
% 2.98/1.57 ( setminusSubset2
% 2.98/1.57 = ( ! [A: $i,B: $i] :
% 2.98/1.57 ( ( subset @ A @ B )
% 2.98/1.57 => ( ( setminus @ A @ B )
% 2.98/1.57 = emptyset ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setminusERneg_type,type,
% 2.98/1.57 setminusERneg: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setminusERneg,definition,
% 2.98/1.57 ( setminusERneg
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.98/1.57 => ( ( in @ Xx @ A )
% 2.98/1.57 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setminusELneg_type,type,
% 2.98/1.57 setminusELneg: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setminusELneg,definition,
% 2.98/1.57 ( setminusELneg
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.98/1.57 => ( ~ ( in @ Xx @ B )
% 2.98/1.57 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setminusILneg_type,type,
% 2.98/1.57 setminusILneg: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setminusILneg,definition,
% 2.98/1.57 ( setminusILneg
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ~ ( in @ Xx @ A )
% 2.98/1.57 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setminusIRneg_type,type,
% 2.98/1.57 setminusIRneg: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setminusIRneg,definition,
% 2.98/1.57 ( setminusIRneg
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ B )
% 2.98/1.57 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setminusLsub_type,type,
% 2.98/1.57 setminusLsub: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setminusLsub,definition,
% 2.98/1.57 ( setminusLsub
% 2.98/1.57 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setminusSubset1_type,type,
% 2.98/1.57 setminusSubset1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setminusSubset1,definition,
% 2.98/1.57 ( setminusSubset1
% 2.98/1.57 = ( ! [A: $i,B: $i] :
% 2.98/1.57 ( ( ( setminus @ A @ B )
% 2.98/1.57 = emptyset )
% 2.98/1.57 => ( subset @ A @ B ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(symdiff_type,type,
% 2.98/1.57 symdiff: $i > $i > $i ).
% 2.98/1.57
% 2.98/1.57 thf(symdiffE_type,type,
% 2.98/1.57 symdiffE: $o ).
% 2.98/1.57
% 2.98/1.57 thf(symdiffE,definition,
% 2.98/1.57 ( symdiffE
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.98/1.57 => ! [Xphi: $o] :
% 2.98/1.57 ( ( ( in @ Xx @ A )
% 2.98/1.57 => ( ~ ( in @ Xx @ B )
% 2.98/1.57 => Xphi ) )
% 2.98/1.57 => ( ( ~ ( in @ Xx @ A )
% 2.98/1.57 => ( ( in @ Xx @ B )
% 2.98/1.57 => Xphi ) )
% 2.98/1.57 => Xphi ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(symdiffI1_type,type,
% 2.98/1.57 symdiffI1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(symdiffI1,definition,
% 2.98/1.57 ( symdiffI1
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ~ ( in @ Xx @ B )
% 2.98/1.57 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(symdiffI2_type,type,
% 2.98/1.57 symdiffI2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(symdiffI2,definition,
% 2.98/1.57 ( symdiffI2
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ~ ( in @ Xx @ A )
% 2.98/1.57 => ( ( in @ Xx @ B )
% 2.98/1.57 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(symdiffIneg1_type,type,
% 2.98/1.57 symdiffIneg1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(symdiffIneg1,definition,
% 2.98/1.57 ( symdiffIneg1
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( in @ Xx @ B )
% 2.98/1.57 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(symdiffIneg2_type,type,
% 2.98/1.57 symdiffIneg2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(symdiffIneg2,definition,
% 2.98/1.57 ( symdiffIneg2
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ~ ( in @ Xx @ A )
% 2.98/1.57 => ( ~ ( in @ Xx @ B )
% 2.98/1.57 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(iskpair_type,type,
% 2.98/1.57 iskpair: $i > $o ).
% 2.98/1.57
% 2.98/1.57 thf(secondinupair_type,type,
% 2.98/1.57 secondinupair: $o ).
% 2.98/1.57
% 2.98/1.57 thf(secondinupair,definition,
% 2.98/1.57 ( secondinupair
% 2.98/1.57 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setukpairIL_type,type,
% 2.98/1.57 setukpairIL: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setukpairIL,definition,
% 2.98/1.57 ( setukpairIL
% 2.98/1.57 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setukpairIR_type,type,
% 2.98/1.57 setukpairIR: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setukpairIR,definition,
% 2.98/1.57 ( setukpairIR
% 2.98/1.57 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(kpairiskpair_type,type,
% 2.98/1.57 kpairiskpair: $o ).
% 2.98/1.57
% 2.98/1.57 thf(kpairiskpair,definition,
% 2.98/1.57 ( kpairiskpair
% 2.98/1.57 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(kpair_type,type,
% 2.98/1.57 kpair: $i > $i > $i ).
% 2.98/1.57
% 2.98/1.57 thf(kpairp_type,type,
% 2.98/1.57 kpairp: $o ).
% 2.98/1.57
% 2.98/1.57 thf(kpairp,definition,
% 2.98/1.57 ( kpairp
% 2.98/1.57 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(cartprod_type,type,
% 2.98/1.57 cartprod: $i > $i > $i ).
% 2.98/1.57
% 2.98/1.57 thf(singletonsubset_type,type,
% 2.98/1.57 singletonsubset: $o ).
% 2.98/1.57
% 2.98/1.57 thf(singletonsubset,definition,
% 2.98/1.57 ( singletonsubset
% 2.98/1.57 = ( ! [A: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(singletoninpowerset_type,type,
% 2.98/1.57 singletoninpowerset: $o ).
% 2.98/1.57
% 2.98/1.57 thf(singletoninpowerset,definition,
% 2.98/1.57 ( singletoninpowerset
% 2.98/1.57 = ( ! [A: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(singletoninpowunion_type,type,
% 2.98/1.57 singletoninpowunion: $o ).
% 2.98/1.57
% 2.98/1.57 thf(singletoninpowunion,definition,
% 2.98/1.57 ( singletoninpowunion
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(upairset2E_type,type,
% 2.98/1.57 upairset2E: $o ).
% 2.98/1.57
% 2.98/1.57 thf(upairset2E,definition,
% 2.98/1.57 ( upairset2E
% 2.98/1.57 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.98/1.57 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.98/1.57 => ( ( Xz = Xx )
% 2.98/1.57 | ( Xz = Xy ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(upairsubunion_type,type,
% 2.98/1.57 upairsubunion: $o ).
% 2.98/1.57
% 2.98/1.57 thf(upairsubunion,definition,
% 2.98/1.57 ( upairsubunion
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ B )
% 2.98/1.57 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(upairinpowunion_type,type,
% 2.98/1.57 upairinpowunion: $o ).
% 2.98/1.57
% 2.98/1.57 thf(upairinpowunion,definition,
% 2.98/1.57 ( upairinpowunion
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ B )
% 2.98/1.57 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(ubforcartprodlem1_type,type,
% 2.98/1.57 ubforcartprodlem1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(ubforcartprodlem1,definition,
% 2.98/1.57 ( ubforcartprodlem1
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ B )
% 2.98/1.57 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(ubforcartprodlem2_type,type,
% 2.98/1.57 ubforcartprodlem2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(ubforcartprodlem2,definition,
% 2.98/1.57 ( ubforcartprodlem2
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ B )
% 2.98/1.57 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(ubforcartprodlem3_type,type,
% 2.98/1.57 ubforcartprodlem3: $o ).
% 2.98/1.57
% 2.98/1.57 thf(ubforcartprodlem3,definition,
% 2.98/1.57 ( ubforcartprodlem3
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ B )
% 2.98/1.57 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(cartprodpairin_type,type,
% 2.98/1.57 cartprodpairin: $o ).
% 2.98/1.57
% 2.98/1.57 thf(cartprodpairin,definition,
% 2.98/1.57 ( cartprodpairin
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ B )
% 2.98/1.57 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(cartprodmempair1_type,type,
% 2.98/1.57 cartprodmempair1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(cartprodmempair1,definition,
% 2.98/1.57 ( cartprodmempair1
% 2.98/1.57 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.98/1.57 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.98/1.57 => ? [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 & ? [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ B )
% 2.98/1.57 & ( Xu
% 2.98/1.57 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(cartprodmempair_type,type,
% 2.98/1.57 cartprodmempair: $o ).
% 2.98/1.57
% 2.98/1.57 thf(cartprodmempair,definition,
% 2.98/1.57 ( cartprodmempair
% 2.98/1.57 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.98/1.57 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.98/1.57 => ( iskpair @ Xu ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setunionE2_type,type,
% 2.98/1.57 setunionE2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setunionE2,definition,
% 2.98/1.57 ( setunionE2
% 2.98/1.57 = ( ! [A: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ ( setunion @ A ) )
% 2.98/1.57 => ? [X: $i] :
% 2.98/1.57 ( ( in @ X @ A )
% 2.98/1.57 & ( in @ Xx @ X ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setunionsingleton1_type,type,
% 2.98/1.57 setunionsingleton1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setunionsingleton1,definition,
% 2.98/1.57 ( setunionsingleton1
% 2.98/1.57 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setunionsingleton2_type,type,
% 2.98/1.57 setunionsingleton2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setunionsingleton2,definition,
% 2.98/1.57 ( setunionsingleton2
% 2.98/1.57 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setunionsingleton_type,type,
% 2.98/1.57 setunionsingleton: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setunionsingleton,definition,
% 2.98/1.57 ( setunionsingleton
% 2.98/1.57 = ( ! [Xx: $i] :
% 2.98/1.57 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 2.98/1.57 = Xx ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(singleton_type,type,
% 2.98/1.57 singleton: $i > $o ).
% 2.98/1.57
% 2.98/1.57 thf(singletonprop_type,type,
% 2.98/1.57 singletonprop: $o ).
% 2.98/1.57
% 2.98/1.57 thf(singletonprop,definition,
% 2.98/1.57 ( singletonprop
% 2.98/1.57 = ( ! [A: $i,Xphi: $i > $o] :
% 2.98/1.57 ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ A )
% 2.98/1.57 => ( ( Xphi @ Xx )
% 2.98/1.57 => ( ( Xphi @ Xy )
% 2.98/1.57 => ( Xx = Xy ) ) ) ) )
% 2.98/1.57 => ( ? [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 & ( Xphi @ Xx ) )
% 2.98/1.57 => ( singleton
% 2.98/1.57 @ ( dsetconstr @ A
% 2.98/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(ex1_type,type,
% 2.98/1.57 ex1: $i > ( $i > $o ) > $o ).
% 2.98/1.57
% 2.98/1.57 thf(ex1E1_type,type,
% 2.98/1.57 ex1E1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(ex1E1,definition,
% 2.98/1.57 ( ex1E1
% 2.98/1.57 = ( ! [A: $i,Xphi: $i > $o] :
% 2.98/1.57 ( ( ex1 @ A
% 2.98/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.57 => ? [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(ex1I_type,type,
% 2.98/1.57 ex1I: $o ).
% 2.98/1.57
% 2.98/1.57 thf(ex1I,definition,
% 2.98/1.57 ( ex1I
% 2.98/1.57 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( Xphi @ Xx )
% 2.98/1.57 => ( ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ A )
% 2.98/1.57 => ( ( Xphi @ Xy )
% 2.98/1.57 => ( Xy = Xx ) ) )
% 2.98/1.57 => ( ex1 @ A
% 2.98/1.57 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(ex1I2_type,type,
% 2.98/1.57 ex1I2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(ex1I2,definition,
% 2.98/1.57 ( ex1I2
% 2.98/1.57 = ( ! [A: $i,Xphi: $i > $o] :
% 2.98/1.57 ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ A )
% 2.98/1.57 => ( ( Xphi @ Xx )
% 2.98/1.57 => ( ( Xphi @ Xy )
% 2.98/1.57 => ( Xx = Xy ) ) ) ) )
% 2.98/1.57 => ( ? [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 & ( Xphi @ Xx ) )
% 2.98/1.57 => ( ex1 @ A
% 2.98/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(singletonsuniq_type,type,
% 2.98/1.57 singletonsuniq: $o ).
% 2.98/1.57
% 2.98/1.57 thf(singletonsuniq,definition,
% 2.98/1.57 ( singletonsuniq
% 2.98/1.57 = ( ! [Xx: $i,Xy: $i] :
% 2.98/1.57 ( ( ( setadjoin @ Xx @ emptyset )
% 2.98/1.57 = ( setadjoin @ Xy @ emptyset ) )
% 2.98/1.57 => ( Xx = Xy ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(atmost1p_type,type,
% 2.98/1.57 atmost1p: $i > $o ).
% 2.98/1.57
% 2.98/1.57 thf(atleast2p_type,type,
% 2.98/1.57 atleast2p: $i > $o ).
% 2.98/1.57
% 2.98/1.57 thf(atmost2p_type,type,
% 2.98/1.57 atmost2p: $i > $o ).
% 2.98/1.57
% 2.98/1.57 thf(upairsetp_type,type,
% 2.98/1.57 upairsetp: $i > $o ).
% 2.98/1.57
% 2.98/1.57 thf(setukpairinjL1_type,type,
% 2.98/1.57 setukpairinjL1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setukpairinjL1,definition,
% 2.98/1.57 ( setukpairinjL1
% 2.98/1.57 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.98/1.57 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 2.98/1.57 => ( Xx = Xz ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(kfstsingleton_type,type,
% 2.98/1.57 kfstsingleton: $o ).
% 2.98/1.57
% 2.98/1.57 thf(kfstsingleton,definition,
% 2.98/1.57 ( kfstsingleton
% 2.98/1.57 = ( ! [Xu: $i] :
% 2.98/1.57 ( ( iskpair @ Xu )
% 2.98/1.57 => ( singleton
% 2.98/1.57 @ ( dsetconstr @ ( setunion @ Xu )
% 2.98/1.57 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(theprop_type,type,
% 2.98/1.57 theprop: $o ).
% 2.98/1.57
% 2.98/1.57 thf(theprop,definition,
% 2.98/1.57 ( theprop
% 2.98/1.57 = ( ! [X: $i] :
% 2.98/1.57 ( ( singleton @ X )
% 2.98/1.57 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(kfst_type,type,
% 2.98/1.57 kfst: $i > $i ).
% 2.98/1.57
% 2.98/1.57 thf(kfstpairEq_type,type,
% 2.98/1.57 kfstpairEq: $o ).
% 2.98/1.57
% 2.98/1.57 thf(kfstpairEq,definition,
% 2.98/1.57 ( kfstpairEq
% 2.98/1.57 = ( ! [Xx: $i,Xy: $i] :
% 2.98/1.57 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.98/1.57 = Xx ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(cartprodfstin_type,type,
% 2.98/1.57 cartprodfstin: $o ).
% 2.98/1.57
% 2.98/1.57 thf(cartprodfstin,definition,
% 2.98/1.57 ( cartprodfstin
% 2.98/1.57 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.98/1.57 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.98/1.57 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setukpairinjL2_type,type,
% 2.98/1.57 setukpairinjL2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setukpairinjL2,definition,
% 2.98/1.57 ( setukpairinjL2
% 2.98/1.57 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.98/1.57 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.98/1.57 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.98/1.57 => ( Xx = Xz ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setukpairinjL_type,type,
% 2.98/1.57 setukpairinjL: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setukpairinjL,definition,
% 2.98/1.57 ( setukpairinjL
% 2.98/1.57 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.98/1.57 ( ( ( kpair @ Xx @ Xy )
% 2.98/1.57 = ( kpair @ Xz @ Xu ) )
% 2.98/1.57 => ( Xx = Xz ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setukpairinjR11_type,type,
% 2.98/1.57 setukpairinjR11: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setukpairinjR11,definition,
% 2.98/1.57 ( setukpairinjR11
% 2.98/1.57 = ( ! [Xx: $i,Xy: $i] :
% 2.98/1.57 ( ( Xx = Xy )
% 2.98/1.57 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.98/1.57 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setukpairinjR12_type,type,
% 2.98/1.57 setukpairinjR12: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setukpairinjR12,definition,
% 2.98/1.57 ( setukpairinjR12
% 2.98/1.57 = ( ! [Xx: $i,Xy: $i] :
% 2.98/1.57 ( ( Xx = Xy )
% 2.98/1.57 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.98/1.57 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setukpairinjR1_type,type,
% 2.98/1.57 setukpairinjR1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setukpairinjR1,definition,
% 2.98/1.57 ( setukpairinjR1
% 2.98/1.57 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.98/1.57 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.98/1.57 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.98/1.57 => ( ( Xz = Xu )
% 2.98/1.57 => ( Xy = Xu ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(upairequniteq_type,type,
% 2.98/1.57 upairequniteq: $o ).
% 2.98/1.57
% 2.98/1.57 thf(upairequniteq,definition,
% 2.98/1.57 ( upairequniteq
% 2.98/1.57 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.98/1.57 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.98/1.57 = ( setadjoin @ Xz @ emptyset ) )
% 2.98/1.57 => ( Xx = Xy ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setukpairinjR2_type,type,
% 2.98/1.57 setukpairinjR2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setukpairinjR2,definition,
% 2.98/1.57 ( setukpairinjR2
% 2.98/1.57 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.98/1.57 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.98/1.57 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.98/1.57 => ( Xy = Xu ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setukpairinjR_type,type,
% 2.98/1.57 setukpairinjR: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setukpairinjR,definition,
% 2.98/1.57 ( setukpairinjR
% 2.98/1.57 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.98/1.57 ( ( ( kpair @ Xx @ Xy )
% 2.98/1.57 = ( kpair @ Xz @ Xu ) )
% 2.98/1.57 => ( Xy = Xu ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(ksndsingleton_type,type,
% 2.98/1.57 ksndsingleton: $o ).
% 2.98/1.57
% 2.98/1.57 thf(ksndsingleton,definition,
% 2.98/1.57 ( ksndsingleton
% 2.98/1.57 = ( ! [Xu: $i] :
% 2.98/1.57 ( ( iskpair @ Xu )
% 2.98/1.57 => ( singleton
% 2.98/1.57 @ ( dsetconstr @ ( setunion @ Xu )
% 2.98/1.57 @ ^ [Xx: $i] :
% 2.98/1.57 ( Xu
% 2.98/1.57 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(ksnd_type,type,
% 2.98/1.57 ksnd: $i > $i ).
% 2.98/1.57
% 2.98/1.57 thf(ksndpairEq_type,type,
% 2.98/1.57 ksndpairEq: $o ).
% 2.98/1.57
% 2.98/1.57 thf(ksndpairEq,definition,
% 2.98/1.57 ( ksndpairEq
% 2.98/1.57 = ( ! [Xx: $i,Xy: $i] :
% 2.98/1.57 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.98/1.57 = Xy ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(kpairsurjEq_type,type,
% 2.98/1.57 kpairsurjEq: $o ).
% 2.98/1.57
% 2.98/1.57 thf(kpairsurjEq,definition,
% 2.98/1.57 ( kpairsurjEq
% 2.98/1.57 = ( ! [Xu: $i] :
% 2.98/1.57 ( ( iskpair @ Xu )
% 2.98/1.57 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.98/1.57 = Xu ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(cartprodsndin_type,type,
% 2.98/1.57 cartprodsndin: $o ).
% 2.98/1.57
% 2.98/1.57 thf(cartprodsndin,definition,
% 2.98/1.57 ( cartprodsndin
% 2.98/1.57 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.98/1.57 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.98/1.57 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(cartprodpairmemEL_type,type,
% 2.98/1.57 cartprodpairmemEL: $o ).
% 2.98/1.57
% 2.98/1.57 thf(cartprodpairmemEL,definition,
% 2.98/1.57 ( cartprodpairmemEL
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.98/1.57 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.98/1.57 => ( in @ Xx @ A ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(cartprodpairmemER_type,type,
% 2.98/1.57 cartprodpairmemER: $o ).
% 2.98/1.57
% 2.98/1.57 thf(cartprodpairmemER,definition,
% 2.98/1.57 ( cartprodpairmemER
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.98/1.57 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.98/1.57 => ( in @ Xy @ B ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(cartprodmempaircEq_type,type,
% 2.98/1.57 cartprodmempaircEq: $o ).
% 2.98/1.57
% 2.98/1.57 thf(cartprodmempaircEq,definition,
% 2.98/1.57 ( cartprodmempaircEq
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ B )
% 2.98/1.57 => ( ( kpair @ Xx @ Xy )
% 2.98/1.57 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(cartprodfstpairEq_type,type,
% 2.98/1.57 cartprodfstpairEq: $o ).
% 2.98/1.57
% 2.98/1.57 thf(cartprodfstpairEq,definition,
% 2.98/1.57 ( cartprodfstpairEq
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ B )
% 2.98/1.57 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.98/1.57 = Xx ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(cartprodsndpairEq_type,type,
% 2.98/1.57 cartprodsndpairEq: $o ).
% 2.98/1.57
% 2.98/1.57 thf(cartprodsndpairEq,definition,
% 2.98/1.57 ( cartprodsndpairEq
% 2.98/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ B )
% 2.98/1.57 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.98/1.57 = Xy ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(cartprodpairsurjEq_type,type,
% 2.98/1.57 cartprodpairsurjEq: $o ).
% 2.98/1.57
% 2.98/1.57 thf(cartprodpairsurjEq,definition,
% 2.98/1.57 ( cartprodpairsurjEq
% 2.98/1.57 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.98/1.57 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.98/1.57 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.98/1.57 = Xu ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(breln_type,type,
% 2.98/1.57 breln: $i > $i > $i > $o ).
% 2.98/1.57
% 2.98/1.57 thf(breln,definition,
% 2.98/1.57 ( breln
% 2.98/1.57 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(dpsetconstr_type,type,
% 2.98/1.57 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 2.98/1.57
% 2.98/1.57 thf(dpsetconstrI_type,type,
% 2.98/1.57 dpsetconstrI: $o ).
% 2.98/1.57
% 2.98/1.57 thf(dpsetconstrI,definition,
% 2.98/1.57 ( dpsetconstrI
% 2.98/1.57 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ B )
% 2.98/1.57 => ( ( Xphi @ Xx @ Xy )
% 2.98/1.57 => ( in @ ( kpair @ Xx @ Xy )
% 2.98/1.57 @ ( dpsetconstr @ A @ B
% 2.98/1.57 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(dpsetconstrSub_type,type,
% 2.98/1.57 dpsetconstrSub: $o ).
% 2.98/1.57
% 2.98/1.57 thf(dpsetconstrSub,definition,
% 2.98/1.57 ( dpsetconstrSub
% 2.98/1.57 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.98/1.57 ( subset
% 2.98/1.57 @ ( dpsetconstr @ A @ B
% 2.98/1.57 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 2.98/1.57 @ ( cartprod @ A @ B ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setOfPairsIsBReln_type,type,
% 2.98/1.57 setOfPairsIsBReln: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setOfPairsIsBReln,definition,
% 2.98/1.57 ( setOfPairsIsBReln
% 2.98/1.57 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.98/1.57 ( breln @ A @ B
% 2.98/1.57 @ ( dpsetconstr @ A @ B
% 2.98/1.57 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(dpsetconstrERa_type,type,
% 2.98/1.57 dpsetconstrERa: $o ).
% 2.98/1.57
% 2.98/1.57 thf(dpsetconstrERa,definition,
% 2.98/1.57 ( dpsetconstrERa
% 2.98/1.57 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ B )
% 2.98/1.57 => ( ( in @ ( kpair @ Xx @ Xy )
% 2.98/1.57 @ ( dpsetconstr @ A @ B
% 2.98/1.57 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.98/1.57 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(dpsetconstrEL1_type,type,
% 2.98/1.57 dpsetconstrEL1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(dpsetconstrEL1,definition,
% 2.98/1.57 ( dpsetconstrEL1
% 2.98/1.57 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.98/1.57 ( ( in @ ( kpair @ Xx @ Xy )
% 2.98/1.57 @ ( dpsetconstr @ A @ B
% 2.98/1.57 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.98/1.57 => ( in @ Xx @ A ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(dpsetconstrEL2_type,type,
% 2.98/1.57 dpsetconstrEL2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(dpsetconstrEL2,definition,
% 2.98/1.57 ( dpsetconstrEL2
% 2.98/1.57 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.98/1.57 ( ( in @ ( kpair @ Xx @ Xy )
% 2.98/1.57 @ ( dpsetconstr @ A @ B
% 2.98/1.57 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.98/1.57 => ( in @ Xy @ B ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(dpsetconstrER_type,type,
% 2.98/1.57 dpsetconstrER: $o ).
% 2.98/1.57
% 2.98/1.57 thf(dpsetconstrER,definition,
% 2.98/1.57 ( dpsetconstrER
% 2.98/1.57 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.98/1.57 ( ( in @ ( kpair @ Xx @ Xy )
% 2.98/1.57 @ ( dpsetconstr @ A @ B
% 2.98/1.57 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.98/1.57 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(func_type,type,
% 2.98/1.57 func: $i > $i > $i > $o ).
% 2.98/1.57
% 2.98/1.57 thf(funcSet_type,type,
% 2.98/1.57 funcSet: $i > $i > $i ).
% 2.98/1.57
% 2.98/1.57 thf(funcImageSingleton_type,type,
% 2.98/1.57 funcImageSingleton: $o ).
% 2.98/1.57
% 2.98/1.57 thf(funcImageSingleton,definition,
% 2.98/1.57 ( funcImageSingleton
% 2.98/1.57 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.57 ( ( func @ A @ B @ Xf )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( singleton
% 2.98/1.57 @ ( dsetconstr @ B
% 2.98/1.57 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(apProp_type,type,
% 2.98/1.57 apProp: $o ).
% 2.98/1.57
% 2.98/1.57 thf(apProp,definition,
% 2.98/1.57 ( apProp
% 2.98/1.57 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.57 ( ( func @ A @ B @ Xf )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( in
% 2.98/1.57 @ ( setunion
% 2.98/1.57 @ ( dsetconstr @ B
% 2.98/1.57 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 2.98/1.57 @ B ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(ap_type,type,
% 2.98/1.57 ap: $i > $i > $i > $i > $i ).
% 2.98/1.57
% 2.98/1.57 thf(app_type,type,
% 2.98/1.57 app: $o ).
% 2.98/1.57
% 2.98/1.57 thf(app,definition,
% 2.98/1.57 ( app
% 2.98/1.57 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.57 ( ( func @ A @ B @ Xf )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(infuncsetfunc_type,type,
% 2.98/1.57 infuncsetfunc: $o ).
% 2.98/1.57
% 2.98/1.57 thf(infuncsetfunc,definition,
% 2.98/1.57 ( infuncsetfunc
% 2.98/1.57 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.57 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.98/1.57 => ( func @ A @ B @ Xf ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(ap2p_type,type,
% 2.98/1.57 ap2p: $o ).
% 2.98/1.57
% 2.98/1.57 thf(ap2p,definition,
% 2.98/1.57 ( ap2p
% 2.98/1.57 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.57 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(funcinfuncset_type,type,
% 2.98/1.57 funcinfuncset: $o ).
% 2.98/1.57
% 2.98/1.57 thf(funcinfuncset,definition,
% 2.98/1.57 ( funcinfuncset
% 2.98/1.57 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.57 ( ( func @ A @ B @ Xf )
% 2.98/1.57 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(lamProp_type,type,
% 2.98/1.57 lamProp: $o ).
% 2.98/1.57
% 2.98/1.57 thf(lamProp,definition,
% 2.98/1.57 ( lamProp
% 2.98/1.57 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.98/1.57 ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.98/1.57 => ( func @ A @ B
% 2.98/1.57 @ ( dpsetconstr @ A @ B
% 2.98/1.57 @ ^ [Xx: $i,Xy: $i] :
% 2.98/1.57 ( ( Xf @ Xx )
% 2.98/1.57 = Xy ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(lam_type,type,
% 2.98/1.57 lam: $i > $i > ( $i > $i ) > $i ).
% 2.98/1.57
% 2.98/1.57 thf(lamp_type,type,
% 2.98/1.57 lamp: $o ).
% 2.98/1.57
% 2.98/1.57 thf(lamp,definition,
% 2.98/1.57 ( lamp
% 2.98/1.57 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.98/1.57 ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.98/1.57 => ( func @ A @ B
% 2.98/1.57 @ ( lam @ A @ B
% 2.98/1.57 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(lam2p_type,type,
% 2.98/1.57 lam2p: $o ).
% 2.98/1.57
% 2.98/1.57 thf(lam2p,definition,
% 2.98/1.57 ( lam2p
% 2.98/1.57 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.98/1.57 ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.98/1.57 => ( in
% 2.98/1.57 @ ( lam @ A @ B
% 2.98/1.57 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 2.98/1.57 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(brelnall1_type,type,
% 2.98/1.57 brelnall1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(brelnall1,definition,
% 2.98/1.57 ( brelnall1
% 2.98/1.57 = ( ! [A: $i,B: $i,R: $i] :
% 2.98/1.57 ( ( breln @ A @ B @ R )
% 2.98/1.57 => ! [Xphi: $i > $o] :
% 2.98/1.57 ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ B )
% 2.98/1.57 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.98/1.57 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ R )
% 2.98/1.57 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(brelnall2_type,type,
% 2.98/1.57 brelnall2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(brelnall2,definition,
% 2.98/1.57 ( brelnall2
% 2.98/1.57 = ( ! [A: $i,B: $i,R: $i] :
% 2.98/1.57 ( ( breln @ A @ B @ R )
% 2.98/1.57 => ! [Xphi: $i > $o] :
% 2.98/1.57 ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ B )
% 2.98/1.57 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.98/1.57 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ R )
% 2.98/1.57 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(ex1E2_type,type,
% 2.98/1.57 ex1E2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(ex1E2,definition,
% 2.98/1.57 ( ex1E2
% 2.98/1.57 = ( ! [A: $i,Xphi: $i > $o] :
% 2.98/1.57 ( ( ex1 @ A
% 2.98/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ A )
% 2.98/1.57 => ( ( Xphi @ Xx )
% 2.98/1.57 => ( ( Xphi @ Xy )
% 2.98/1.57 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(funcGraphProp1_type,type,
% 2.98/1.57 funcGraphProp1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(funcGraphProp1,definition,
% 2.98/1.57 ( funcGraphProp1
% 2.98/1.57 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.57 ( ( func @ A @ B @ Xf )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(funcGraphProp3_type,type,
% 2.98/1.57 funcGraphProp3: $o ).
% 2.98/1.57
% 2.98/1.57 thf(funcGraphProp3,definition,
% 2.98/1.57 ( funcGraphProp3
% 2.98/1.57 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.57 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(funcGraphProp2_type,type,
% 2.98/1.57 funcGraphProp2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(funcGraphProp2,definition,
% 2.98/1.57 ( funcGraphProp2
% 2.98/1.57 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.57 ( ( func @ A @ B @ Xf )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ B )
% 2.98/1.57 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 2.98/1.57 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.98/1.57 = Xy ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(funcextLem_type,type,
% 2.98/1.57 funcextLem: $o ).
% 2.98/1.57
% 2.98/1.57 thf(funcextLem,definition,
% 2.98/1.57 ( funcextLem
% 2.98/1.57 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.57 ( ( func @ A @ B @ Xf )
% 2.98/1.57 => ! [Xg: $i] :
% 2.98/1.57 ( ( func @ A @ B @ Xg )
% 2.98/1.57 => ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.98/1.57 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ B )
% 2.98/1.57 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 2.98/1.57 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(funcGraphProp4_type,type,
% 2.98/1.57 funcGraphProp4: $o ).
% 2.98/1.57
% 2.98/1.57 thf(funcGraphProp4,definition,
% 2.98/1.57 ( funcGraphProp4
% 2.98/1.57 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.57 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ B )
% 2.98/1.57 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 2.98/1.57 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.98/1.57 = Xy ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(subbreln_type,type,
% 2.98/1.57 subbreln: $o ).
% 2.98/1.57
% 2.98/1.57 thf(subbreln,definition,
% 2.98/1.57 ( subbreln
% 2.98/1.57 = ( ! [A: $i,B: $i,R: $i] :
% 2.98/1.57 ( ( breln @ A @ B @ R )
% 2.98/1.57 => ! [S: $i] :
% 2.98/1.57 ( ( breln @ A @ B @ S )
% 2.98/1.57 => ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ B )
% 2.98/1.57 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.98/1.57 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.98/1.57 => ( subset @ R @ S ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(eqbreln_type,type,
% 2.98/1.57 eqbreln: $o ).
% 2.98/1.57
% 2.98/1.57 thf(eqbreln,definition,
% 2.98/1.57 ( eqbreln
% 2.98/1.57 = ( ! [A: $i,B: $i,R: $i] :
% 2.98/1.57 ( ( breln @ A @ B @ R )
% 2.98/1.57 => ! [S: $i] :
% 2.98/1.57 ( ( breln @ A @ B @ S )
% 2.98/1.57 => ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ B )
% 2.98/1.57 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.98/1.57 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.98/1.57 => ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ B )
% 2.98/1.57 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 2.98/1.57 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 2.98/1.57 => ( R = S ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(funcext_type,type,
% 2.98/1.57 funcext: $o ).
% 2.98/1.57
% 2.98/1.57 thf(funcext,definition,
% 2.98/1.57 ( funcext
% 2.98/1.57 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.57 ( ( func @ A @ B @ Xf )
% 2.98/1.57 => ! [Xg: $i] :
% 2.98/1.57 ( ( func @ A @ B @ Xg )
% 2.98/1.57 => ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.98/1.57 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.98/1.57 => ( Xf = Xg ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(funcext2_type,type,
% 2.98/1.57 funcext2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(funcext2,definition,
% 2.98/1.57 ( funcext2
% 2.98/1.57 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.57 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.98/1.57 => ! [Xg: $i] :
% 2.98/1.57 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 2.98/1.57 => ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.98/1.57 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.98/1.57 => ( Xf = Xg ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(ap2apEq1_type,type,
% 2.98/1.57 ap2apEq1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(ap2apEq1,definition,
% 2.98/1.57 ( ap2apEq1
% 2.98/1.57 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.57 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.98/1.57 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(ap2apEq2_type,type,
% 2.98/1.57 ap2apEq2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(ap2apEq2,definition,
% 2.98/1.57 ( ap2apEq2
% 2.98/1.57 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.57 ( ( func @ A @ B @ Xf )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.98/1.57 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(beta1_type,type,
% 2.98/1.57 beta1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(beta1,definition,
% 2.98/1.57 ( beta1
% 2.98/1.57 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.98/1.57 ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( ap @ A @ B
% 2.98/1.57 @ ( lam @ A @ B
% 2.98/1.57 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 2.98/1.57 @ Xx )
% 2.98/1.57 = ( Xf @ Xx ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(eta1_type,type,
% 2.98/1.57 eta1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(eta1,definition,
% 2.98/1.57 ( eta1
% 2.98/1.57 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.57 ( ( func @ A @ B @ Xf )
% 2.98/1.57 => ( ( lam @ A @ B
% 2.98/1.57 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 2.98/1.57 = Xf ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(lam2lamEq_type,type,
% 2.98/1.57 lam2lamEq: $o ).
% 2.98/1.57
% 2.98/1.57 thf(lam2lamEq,definition,
% 2.98/1.57 ( lam2lamEq
% 2.98/1.57 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.98/1.57 ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.98/1.57 => ( ( lam @ A @ B
% 2.98/1.57 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 2.98/1.57 = ( lam @ A @ B
% 2.98/1.57 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(beta2_type,type,
% 2.98/1.57 beta2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(beta2,definition,
% 2.98/1.57 ( beta2
% 2.98/1.57 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.98/1.57 ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( ap @ A @ B
% 2.98/1.57 @ ( lam @ A @ B
% 2.98/1.57 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 2.98/1.57 @ Xx )
% 2.98/1.57 = ( Xf @ Xx ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(eta2_type,type,
% 2.98/1.57 eta2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(eta2,definition,
% 2.98/1.57 ( eta2
% 2.98/1.57 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.57 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.98/1.57 => ( ( lam @ A @ B
% 2.98/1.57 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 2.98/1.57 = Xf ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(iffalseProp1_type,type,
% 2.98/1.57 iffalseProp1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(iffalseProp1,definition,
% 2.98/1.57 ( iffalseProp1
% 2.98/1.57 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ A )
% 2.98/1.57 => ( ~ Xphi
% 2.98/1.57 => ( in @ Xy
% 2.98/1.57 @ ( dsetconstr @ A
% 2.98/1.57 @ ^ [Xz: $i] :
% 2.98/1.57 ( ( Xphi
% 2.98/1.57 & ( Xz = Xx ) )
% 2.98/1.57 | ( ~ Xphi
% 2.98/1.57 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(iffalseProp2_type,type,
% 2.98/1.57 iffalseProp2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(iffalseProp2,definition,
% 2.98/1.57 ( iffalseProp2
% 2.98/1.57 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ A )
% 2.98/1.57 => ( ~ Xphi
% 2.98/1.57 => ( ( dsetconstr @ A
% 2.98/1.57 @ ^ [Xz: $i] :
% 2.98/1.57 ( ( Xphi
% 2.98/1.57 & ( Xz = Xx ) )
% 2.98/1.57 | ( ~ Xphi
% 2.98/1.57 & ( Xz = Xy ) ) ) )
% 2.98/1.57 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(iftrueProp1_type,type,
% 2.98/1.57 iftrueProp1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(iftrueProp1,definition,
% 2.98/1.57 ( iftrueProp1
% 2.98/1.57 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ A )
% 2.98/1.57 => ( Xphi
% 2.98/1.57 => ( in @ Xx
% 2.98/1.57 @ ( dsetconstr @ A
% 2.98/1.57 @ ^ [Xz: $i] :
% 2.98/1.57 ( ( Xphi
% 2.98/1.57 & ( Xz = Xx ) )
% 2.98/1.57 | ( ~ Xphi
% 2.98/1.57 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(iftrueProp2_type,type,
% 2.98/1.57 iftrueProp2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(iftrueProp2,definition,
% 2.98/1.57 ( iftrueProp2
% 2.98/1.57 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ A )
% 2.98/1.57 => ( Xphi
% 2.98/1.57 => ( ( dsetconstr @ A
% 2.98/1.57 @ ^ [Xz: $i] :
% 2.98/1.57 ( ( Xphi
% 2.98/1.57 & ( Xz = Xx ) )
% 2.98/1.57 | ( ~ Xphi
% 2.98/1.57 & ( Xz = Xy ) ) ) )
% 2.98/1.57 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(ifSingleton_type,type,
% 2.98/1.57 ifSingleton: $o ).
% 2.98/1.57
% 2.98/1.57 thf(ifSingleton,definition,
% 2.98/1.57 ( ifSingleton
% 2.98/1.57 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ A )
% 2.98/1.57 => ( singleton
% 2.98/1.57 @ ( dsetconstr @ A
% 2.98/1.57 @ ^ [Xz: $i] :
% 2.98/1.57 ( ( Xphi
% 2.98/1.57 & ( Xz = Xx ) )
% 2.98/1.57 | ( ~ Xphi
% 2.98/1.57 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(if_type,type,
% 2.98/1.57 if: $i > $o > $i > $i > $i ).
% 2.98/1.57
% 2.98/1.57 thf(ifp_type,type,
% 2.98/1.57 ifp: $o ).
% 2.98/1.57
% 2.98/1.57 thf(ifp,definition,
% 2.98/1.57 ( ifp
% 2.98/1.57 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ A )
% 2.98/1.57 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(theeq_type,type,
% 2.98/1.57 theeq: $o ).
% 2.98/1.57
% 2.98/1.57 thf(theeq,definition,
% 2.98/1.57 ( theeq
% 2.98/1.57 = ( ! [X: $i] :
% 2.98/1.57 ( ( singleton @ X )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ X )
% 2.98/1.57 => ( ( setunion @ X )
% 2.98/1.57 = Xx ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(iftrue_type,type,
% 2.98/1.57 iftrue: $o ).
% 2.98/1.57
% 2.98/1.57 thf(iftrue,definition,
% 2.98/1.57 ( iftrue
% 2.98/1.57 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ A )
% 2.98/1.57 => ( Xphi
% 2.98/1.57 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 2.98/1.57 = Xx ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(iffalse_type,type,
% 2.98/1.57 iffalse: $o ).
% 2.98/1.57
% 2.98/1.57 thf(iffalse,definition,
% 2.98/1.57 ( iffalse
% 2.98/1.57 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ A )
% 2.98/1.57 => ( ~ Xphi
% 2.98/1.57 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 2.98/1.57 = Xy ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(iftrueorfalse_type,type,
% 2.98/1.57 iftrueorfalse: $o ).
% 2.98/1.57
% 2.98/1.57 thf(iftrueorfalse,definition,
% 2.98/1.57 ( iftrueorfalse
% 2.98/1.57 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ A )
% 2.98/1.57 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(binintersectT_lem_type,type,
% 2.98/1.57 binintersectT_lem: $o ).
% 2.98/1.57
% 2.98/1.57 thf(binintersectT_lem,definition,
% 2.98/1.57 ( binintersectT_lem
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(binunionT_lem_type,type,
% 2.98/1.57 binunionT_lem: $o ).
% 2.98/1.57
% 2.98/1.57 thf(binunionT_lem,definition,
% 2.98/1.57 ( binunionT_lem
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(powersetT_lem_type,type,
% 2.98/1.57 powersetT_lem: $o ).
% 2.98/1.57
% 2.98/1.57 thf(powersetT_lem,definition,
% 2.98/1.57 ( powersetT_lem
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setminusT_lem_type,type,
% 2.98/1.57 setminusT_lem: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setminusT_lem,definition,
% 2.98/1.57 ( setminusT_lem
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(complementT_lem_type,type,
% 2.98/1.57 complementT_lem: $o ).
% 2.98/1.57
% 2.98/1.57 thf(complementT_lem,definition,
% 2.98/1.57 ( complementT_lem
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setextT_type,type,
% 2.98/1.57 setextT: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setextT,definition,
% 2.98/1.57 ( setextT
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( in @ Xx @ X )
% 2.98/1.57 => ( in @ Xx @ Y ) ) )
% 2.98/1.57 => ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( in @ Xx @ Y )
% 2.98/1.57 => ( in @ Xx @ X ) ) )
% 2.98/1.57 => ( X = Y ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(subsetTI_type,type,
% 2.98/1.57 subsetTI: $o ).
% 2.98/1.57
% 2.98/1.57 thf(subsetTI,definition,
% 2.98/1.57 ( subsetTI
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( in @ Xx @ X )
% 2.98/1.57 => ( in @ Xx @ Y ) ) )
% 2.98/1.57 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(powersetTI1_type,type,
% 2.98/1.57 powersetTI1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(powersetTI1,definition,
% 2.98/1.57 ( powersetTI1
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( in @ Xx @ X )
% 2.98/1.57 => ( in @ Xx @ Y ) ) )
% 2.98/1.57 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(powersetTE1_type,type,
% 2.98/1.57 powersetTE1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(powersetTE1,definition,
% 2.98/1.57 ( powersetTE1
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( in @ X @ ( powerset @ Y ) )
% 2.98/1.57 => ( ( in @ Xx @ X )
% 2.98/1.57 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(complementTI1_type,type,
% 2.98/1.57 complementTI1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(complementTI1,definition,
% 2.98/1.57 ( complementTI1
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( in @ Xx @ X )
% 2.98/1.57 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(complementTE1_type,type,
% 2.98/1.57 complementTE1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(complementTE1,definition,
% 2.98/1.57 ( complementTE1
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 2.98/1.57 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(binintersectTELcontra_type,type,
% 2.98/1.57 binintersectTELcontra: $o ).
% 2.98/1.57
% 2.98/1.57 thf(binintersectTELcontra,definition,
% 2.98/1.57 ( binintersectTELcontra
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ~ ( in @ Xx @ X )
% 2.98/1.57 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(binintersectTERcontra_type,type,
% 2.98/1.57 binintersectTERcontra: $o ).
% 2.98/1.57
% 2.98/1.57 thf(binintersectTERcontra,definition,
% 2.98/1.57 ( binintersectTERcontra
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ~ ( in @ Xx @ Y )
% 2.98/1.57 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(contrasubsetT_type,type,
% 2.98/1.57 contrasubsetT: $o ).
% 2.98/1.57
% 2.98/1.57 thf(contrasubsetT,definition,
% 2.98/1.57 ( contrasubsetT
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.98/1.57 => ( ( in @ Xx @ Y )
% 2.98/1.57 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(contrasubsetT1_type,type,
% 2.98/1.57 contrasubsetT1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(contrasubsetT1,definition,
% 2.98/1.57 ( contrasubsetT1
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( subset @ X @ Y )
% 2.98/1.57 => ( ~ ( in @ Xx @ Y )
% 2.98/1.57 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(contrasubsetT2_type,type,
% 2.98/1.57 contrasubsetT2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(contrasubsetT2,definition,
% 2.98/1.57 ( contrasubsetT2
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ( ( subset @ X @ Y )
% 2.98/1.57 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(contrasubsetT3_type,type,
% 2.98/1.57 contrasubsetT3: $o ).
% 2.98/1.57
% 2.98/1.57 thf(contrasubsetT3,definition,
% 2.98/1.57 ( contrasubsetT3
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 2.98/1.57 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(doubleComplementI1_type,type,
% 2.98/1.57 doubleComplementI1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(doubleComplementI1,definition,
% 2.98/1.57 ( doubleComplementI1
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( in @ Xx @ X )
% 2.98/1.57 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(doubleComplementE1_type,type,
% 2.98/1.57 doubleComplementE1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(doubleComplementE1,definition,
% 2.98/1.57 ( doubleComplementE1
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 2.98/1.57 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(doubleComplementSub1_type,type,
% 2.98/1.57 doubleComplementSub1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(doubleComplementSub1,definition,
% 2.98/1.57 ( doubleComplementSub1
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(doubleComplementSub2_type,type,
% 2.98/1.57 doubleComplementSub2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(doubleComplementSub2,definition,
% 2.98/1.57 ( doubleComplementSub2
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(doubleComplementEq_type,type,
% 2.98/1.57 doubleComplementEq: $o ).
% 2.98/1.57
% 2.98/1.57 thf(doubleComplementEq,definition,
% 2.98/1.57 ( doubleComplementEq
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ( X
% 2.98/1.57 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(complementTnotintersectT_type,type,
% 2.98/1.57 complementTnotintersectT: $o ).
% 2.98/1.57
% 2.98/1.57 thf(complementTnotintersectT,definition,
% 2.98/1.57 ( complementTnotintersectT
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 2.98/1.57 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(complementImpComplementIntersect_type,type,
% 2.98/1.57 complementImpComplementIntersect: $o ).
% 2.98/1.57
% 2.98/1.57 thf(complementImpComplementIntersect,definition,
% 2.98/1.57 ( complementImpComplementIntersect
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 2.98/1.57 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(complementSubsetComplementIntersect_type,type,
% 2.98/1.57 complementSubsetComplementIntersect: $o ).
% 2.98/1.57
% 2.98/1.57 thf(complementSubsetComplementIntersect,definition,
% 2.98/1.57 ( complementSubsetComplementIntersect
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(complementInPowersetComplementIntersect_type,type,
% 2.98/1.57 complementInPowersetComplementIntersect: $o ).
% 2.98/1.57
% 2.98/1.57 thf(complementInPowersetComplementIntersect,definition,
% 2.98/1.57 ( complementInPowersetComplementIntersect
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(contraSubsetComplement_type,type,
% 2.98/1.57 contraSubsetComplement: $o ).
% 2.98/1.57
% 2.98/1.57 thf(contraSubsetComplement,definition,
% 2.98/1.57 ( contraSubsetComplement
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( in @ Xx @ Y )
% 2.98/1.57 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(complementTcontraSubset_type,type,
% 2.98/1.57 complementTcontraSubset: $o ).
% 2.98/1.57
% 2.98/1.57 thf(complementTcontraSubset,definition,
% 2.98/1.57 ( complementTcontraSubset
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.98/1.57 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(binunionTILcontra_type,type,
% 2.98/1.57 binunionTILcontra: $o ).
% 2.98/1.57
% 2.98/1.57 thf(binunionTILcontra,definition,
% 2.98/1.57 ( binunionTILcontra
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 2.98/1.57 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(binunionTIRcontra_type,type,
% 2.98/1.57 binunionTIRcontra: $o ).
% 2.98/1.57
% 2.98/1.57 thf(binunionTIRcontra,definition,
% 2.98/1.57 ( binunionTIRcontra
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 2.98/1.57 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(inIntersectImpInUnion_type,type,
% 2.98/1.57 inIntersectImpInUnion: $o ).
% 2.98/1.57
% 2.98/1.57 thf(inIntersectImpInUnion,definition,
% 2.98/1.57 ( inIntersectImpInUnion
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Z: $i] :
% 2.98/1.57 ( ( in @ Z @ ( powerset @ A ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 2.98/1.57 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(inIntersectImpInUnion2_type,type,
% 2.98/1.57 inIntersectImpInUnion2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(inIntersectImpInUnion2,definition,
% 2.98/1.57 ( inIntersectImpInUnion2
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Z: $i] :
% 2.98/1.57 ( ( in @ Z @ ( powerset @ A ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 2.98/1.57 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(inIntersectImpInIntersectUnions_type,type,
% 2.98/1.57 inIntersectImpInIntersectUnions: $o ).
% 2.98/1.57
% 2.98/1.57 thf(inIntersectImpInIntersectUnions,definition,
% 2.98/1.57 ( inIntersectImpInIntersectUnions
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Z: $i] :
% 2.98/1.57 ( ( in @ Z @ ( powerset @ A ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 2.98/1.57 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(intersectInPowersetIntersectUnions_type,type,
% 2.98/1.57 intersectInPowersetIntersectUnions: $o ).
% 2.98/1.57
% 2.98/1.57 thf(intersectInPowersetIntersectUnions,definition,
% 2.98/1.57 ( intersectInPowersetIntersectUnions
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Z: $i] :
% 2.98/1.57 ( ( in @ Z @ ( powerset @ A ) )
% 2.98/1.57 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(inComplementUnionImpNotIn1_type,type,
% 2.98/1.57 inComplementUnionImpNotIn1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(inComplementUnionImpNotIn1,definition,
% 2.98/1.57 ( inComplementUnionImpNotIn1
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.98/1.57 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(inComplementUnionImpInComplement1_type,type,
% 2.98/1.57 inComplementUnionImpInComplement1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(inComplementUnionImpInComplement1,definition,
% 2.98/1.57 ( inComplementUnionImpInComplement1
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.98/1.57 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(binunionTE_type,type,
% 2.98/1.57 binunionTE: $o ).
% 2.98/1.57
% 2.98/1.57 thf(binunionTE,definition,
% 2.98/1.57 ( binunionTE
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Xphi: $o,Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 2.98/1.57 => ( ( ( in @ Xx @ X )
% 2.98/1.57 => Xphi )
% 2.98/1.57 => ( ( ( in @ Xx @ Y )
% 2.98/1.57 => Xphi )
% 2.98/1.57 => Xphi ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(binunionTEcontra_type,type,
% 2.98/1.57 binunionTEcontra: $o ).
% 2.98/1.57
% 2.98/1.57 thf(binunionTEcontra,definition,
% 2.98/1.57 ( binunionTEcontra
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ~ ( in @ Xx @ X )
% 2.98/1.57 => ( ~ ( in @ Xx @ Y )
% 2.98/1.57 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(demorgan2a1_type,type,
% 2.98/1.57 demorgan2a1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(demorgan2a1,definition,
% 2.98/1.57 ( demorgan2a1
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.98/1.57 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(complementUnionInPowersetComplement_type,type,
% 2.98/1.57 complementUnionInPowersetComplement: $o ).
% 2.98/1.57
% 2.98/1.57 thf(complementUnionInPowersetComplement,definition,
% 2.98/1.57 ( complementUnionInPowersetComplement
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(demorgan2a2_type,type,
% 2.98/1.57 demorgan2a2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(demorgan2a2,definition,
% 2.98/1.57 ( demorgan2a2
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.98/1.57 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(demorgan1a_type,type,
% 2.98/1.57 demorgan1a: $o ).
% 2.98/1.57
% 2.98/1.57 thf(demorgan1a,definition,
% 2.98/1.57 ( demorgan1a
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 2.98/1.57 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(demorgan1b_type,type,
% 2.98/1.57 demorgan1b: $o ).
% 2.98/1.57
% 2.98/1.57 thf(demorgan1b,definition,
% 2.98/1.57 ( demorgan1b
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 2.98/1.57 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(demorgan1_type,type,
% 2.98/1.57 demorgan1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(demorgan1,definition,
% 2.98/1.57 ( demorgan1
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 2.98/1.57 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(demorgan2a_type,type,
% 2.98/1.57 demorgan2a: $o ).
% 2.98/1.57
% 2.98/1.57 thf(demorgan2a,definition,
% 2.98/1.57 ( demorgan2a
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.98/1.57 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(demorgan2b2_type,type,
% 2.98/1.57 demorgan2b2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(demorgan2b2,definition,
% 2.98/1.57 ( demorgan2b2
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 2.98/1.57 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 2.98/1.57 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(demorgan2b_type,type,
% 2.98/1.57 demorgan2b: $o ).
% 2.98/1.57
% 2.98/1.57 thf(demorgan2b,definition,
% 2.98/1.57 ( demorgan2b
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 2.98/1.57 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(demorgan2_type,type,
% 2.98/1.57 demorgan2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(demorgan2,definition,
% 2.98/1.57 ( demorgan2
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 2.98/1.57 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(woz13rule0_type,type,
% 2.98/1.57 woz13rule0: $o ).
% 2.98/1.57
% 2.98/1.57 thf(woz13rule0,definition,
% 2.98/1.57 ( woz13rule0
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 2.98/1.57 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(woz13rule1_type,type,
% 2.98/1.57 woz13rule1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(woz13rule1,definition,
% 2.98/1.57 ( woz13rule1
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Z: $i] :
% 2.98/1.57 ( ( in @ Z @ ( powerset @ A ) )
% 2.98/1.57 => ( ( subset @ X @ Z )
% 2.98/1.57 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(woz13rule2_type,type,
% 2.98/1.57 woz13rule2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(woz13rule2,definition,
% 2.98/1.57 ( woz13rule2
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Z: $i] :
% 2.98/1.57 ( ( in @ Z @ ( powerset @ A ) )
% 2.98/1.57 => ( ( subset @ Y @ Z )
% 2.98/1.57 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(woz13rule3_type,type,
% 2.98/1.57 woz13rule3: $o ).
% 2.98/1.57
% 2.98/1.57 thf(woz13rule3,definition,
% 2.98/1.57 ( woz13rule3
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Z: $i] :
% 2.98/1.57 ( ( in @ Z @ ( powerset @ A ) )
% 2.98/1.57 => ( ( subset @ X @ Y )
% 2.98/1.57 => ( ( subset @ X @ Z )
% 2.98/1.57 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(woz13rule4_type,type,
% 2.98/1.57 woz13rule4: $o ).
% 2.98/1.57
% 2.98/1.57 thf(woz13rule4,definition,
% 2.98/1.57 ( woz13rule4
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Z: $i] :
% 2.98/1.57 ( ( in @ Z @ ( powerset @ A ) )
% 2.98/1.57 => ! [W: $i] :
% 2.98/1.57 ( ( in @ W @ ( powerset @ A ) )
% 2.98/1.57 => ( ( subset @ X @ Z )
% 2.98/1.57 => ( ( subset @ Y @ W )
% 2.98/1.57 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(woz1_1_type,type,
% 2.98/1.57 woz1_1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(woz1_1,definition,
% 2.98/1.57 ( woz1_1
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(woz1_2_type,type,
% 2.98/1.57 woz1_2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(woz1_2,definition,
% 2.98/1.57 ( woz1_2
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Z: $i] :
% 2.98/1.57 ( ( in @ Z @ ( powerset @ A ) )
% 2.98/1.57 => ! [W: $i] :
% 2.98/1.57 ( ( in @ W @ ( powerset @ A ) )
% 2.98/1.57 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 2.98/1.57 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(woz1_3_type,type,
% 2.98/1.57 woz1_3: $o ).
% 2.98/1.57
% 2.98/1.57 thf(woz1_3,definition,
% 2.98/1.57 ( woz1_3
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ! [Z: $i] :
% 2.98/1.57 ( ( in @ Z @ ( powerset @ A ) )
% 2.98/1.57 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(woz1_4_type,type,
% 2.98/1.57 woz1_4: $o ).
% 2.98/1.57
% 2.98/1.57 thf(woz1_4,definition,
% 2.98/1.57 ( woz1_4
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.98/1.57 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(woz1_5_type,type,
% 2.98/1.57 woz1_5: $o ).
% 2.98/1.57
% 2.98/1.57 thf(woz1_5,definition,
% 2.98/1.57 ( woz1_5
% 2.98/1.57 = ( ! [A: $i,X: $i] :
% 2.98/1.57 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.57 => ! [Y: $i] :
% 2.98/1.57 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.57 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(breln1_type,type,
% 2.98/1.57 breln1: $i > $i > $o ).
% 2.98/1.57
% 2.98/1.57 thf(breln1,definition,
% 2.98/1.57 ( breln1
% 2.98/1.57 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(breln1all2_type,type,
% 2.98/1.57 breln1all2: $o ).
% 2.98/1.57
% 2.98/1.57 thf(breln1all2,definition,
% 2.98/1.57 ( breln1all2
% 2.98/1.57 = ( ! [A: $i,R: $i] :
% 2.98/1.57 ( ( breln1 @ A @ R )
% 2.98/1.57 => ! [Xphi: $i > $o] :
% 2.98/1.57 ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ A )
% 2.98/1.57 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.98/1.57 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ R )
% 2.98/1.57 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(breln1Set_type,type,
% 2.98/1.57 breln1Set: $i > $i ).
% 2.98/1.57
% 2.98/1.57 thf(breln1SetBreln1_type,type,
% 2.98/1.57 breln1SetBreln1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(breln1SetBreln1,definition,
% 2.98/1.57 ( breln1SetBreln1
% 2.98/1.57 = ( ! [A: $i,R: $i] :
% 2.98/1.57 ( ( in @ R @ ( breln1Set @ A ) )
% 2.98/1.57 => ( breln1 @ A @ R ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(transitive_type,type,
% 2.98/1.57 transitive: $i > $i > $o ).
% 2.98/1.57
% 2.98/1.57 thf(antisymmetric_type,type,
% 2.98/1.57 antisymmetric: $i > $i > $o ).
% 2.98/1.57
% 2.98/1.57 thf(reflexive_type,type,
% 2.98/1.57 reflexive: $i > $i > $o ).
% 2.98/1.57
% 2.98/1.57 thf(refltransitive_type,type,
% 2.98/1.57 refltransitive: $i > $i > $o ).
% 2.98/1.57
% 2.98/1.57 thf(refllinearorder_type,type,
% 2.98/1.57 refllinearorder: $i > $i > $o ).
% 2.98/1.57
% 2.98/1.57 thf(reflwellordering_type,type,
% 2.98/1.57 reflwellordering: $i > $i > $o ).
% 2.98/1.57
% 2.98/1.57 thf(choice2fnsingleton_type,type,
% 2.98/1.57 choice2fnsingleton: $o ).
% 2.98/1.57
% 2.98/1.57 thf(choice2fnsingleton,definition,
% 2.98/1.57 ( choice2fnsingleton
% 2.98/1.57 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.98/1.57 ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ? [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ B )
% 2.98/1.57 & ( Xphi @ Xx @ Xy ) ) )
% 2.98/1.57 => ! [R: $i] :
% 2.98/1.57 ( ( in @ R @ ( breln1Set @ B ) )
% 2.98/1.57 => ( ( reflwellordering @ B @ R )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ( singleton
% 2.98/1.57 @ ( dsetconstr @ B
% 2.98/1.57 @ ^ [Xy: $i] :
% 2.98/1.57 ( ( Xphi @ Xx @ Xy )
% 2.98/1.57 & ! [Xz: $i] :
% 2.98/1.57 ( ( in @ Xz @ B )
% 2.98/1.57 => ( ( Xphi @ Xx @ Xz )
% 2.98/1.57 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(setOfPairsIsBReln1_type,type,
% 2.98/1.57 setOfPairsIsBReln1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(setOfPairsIsBReln1,definition,
% 2.98/1.57 ( setOfPairsIsBReln1
% 2.98/1.57 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 2.98/1.57 ( breln1 @ A
% 2.98/1.57 @ ( dpsetconstr @ A @ A
% 2.98/1.57 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(breln1all1_type,type,
% 2.98/1.57 breln1all1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(breln1all1,definition,
% 2.98/1.57 ( breln1all1
% 2.98/1.57 = ( ! [A: $i,R: $i] :
% 2.98/1.57 ( ( breln1 @ A @ R )
% 2.98/1.57 => ! [Xphi: $i > $o] :
% 2.98/1.57 ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ A )
% 2.98/1.57 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.98/1.57 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.98/1.57 => ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ R )
% 2.98/1.57 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(subbreln1_type,type,
% 2.98/1.57 subbreln1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(subbreln1,definition,
% 2.98/1.57 ( subbreln1
% 2.98/1.57 = ( ! [A: $i,R: $i] :
% 2.98/1.57 ( ( breln1 @ A @ R )
% 2.98/1.57 => ! [S: $i] :
% 2.98/1.57 ( ( breln1 @ A @ S )
% 2.98/1.57 => ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ A )
% 2.98/1.57 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.98/1.57 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.98/1.57 => ( subset @ R @ S ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(eqbreln1_type,type,
% 2.98/1.57 eqbreln1: $o ).
% 2.98/1.57
% 2.98/1.57 thf(eqbreln1,definition,
% 2.98/1.57 ( eqbreln1
% 2.98/1.57 = ( ! [A: $i,R: $i] :
% 2.98/1.57 ( ( breln1 @ A @ R )
% 2.98/1.57 => ! [S: $i] :
% 2.98/1.57 ( ( breln1 @ A @ S )
% 2.98/1.57 => ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ A )
% 2.98/1.57 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.98/1.57 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.98/1.57 => ( ! [Xx: $i] :
% 2.98/1.57 ( ( in @ Xx @ A )
% 2.98/1.57 => ! [Xy: $i] :
% 2.98/1.57 ( ( in @ Xy @ A )
% 2.98/1.57 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 2.98/1.57 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 2.98/1.57 => ( R = S ) ) ) ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(breln1invset_type,type,
% 2.98/1.57 breln1invset: $i > $i > $i ).
% 2.98/1.57
% 2.98/1.57 thf(breln1invset,definition,
% 2.98/1.57 ( breln1invset
% 2.98/1.57 = ( ^ [A: $i,R: $i] :
% 2.98/1.57 ( dpsetconstr @ A @ A
% 2.98/1.57 @ ^ [Xx: $i,Xy: $i] : ( in @ ( kpair @ Xy @ Xx ) @ R ) ) ) ) ).
% 2.98/1.57
% 2.98/1.57 thf(breln1invprop,conjecture,
% 2.98/1.57 ( setextAx
% 2.98/1.57 => ( emptysetAx
% 2.98/1.57 => ( setadjoinAx
% 2.98/1.57 => ( powersetAx
% 2.98/1.57 => ( setunionAx
% 2.98/1.57 => ( omega0Ax
% 2.98/1.57 => ( omegaSAx
% 2.98/1.57 => ( omegaIndAx
% 2.98/1.57 => ( replAx
% 2.98/1.57 => ( foundationAx
% 2.98/1.57 => ( wellorderingAx
% 2.98/1.57 => ( descrp
% 2.98/1.57 => ( dsetconstrI
% 2.98/1.57 => ( dsetconstrEL
% 2.98/1.57 => ( dsetconstrER
% 2.98/1.57 => ( exuE1
% 2.98/1.57 => ( prop2setE
% 2.98/1.57 => ( emptysetE
% 2.98/1.57 => ( emptysetimpfalse
% 2.98/1.57 => ( notinemptyset
% 2.98/1.57 => ( exuE3e
% 2.98/1.57 => ( setext
% 2.98/1.57 => ( emptyI
% 2.98/1.57 => ( noeltsimpempty
% 2.98/1.57 => ( setbeta
% 2.98/1.57 => ( nonemptyE1
% 2.98/1.57 => ( nonemptyI
% 2.98/1.57 => ( nonemptyI1
% 2.98/1.57 => ( setadjoinIL
% 2.98/1.57 => ( emptyinunitempty
% 2.98/1.57 => ( setadjoinIR
% 2.98/1.57 => ( setadjoinE
% 2.98/1.57 => ( setadjoinOr
% 2.98/1.57 => ( setoftrueEq
% 2.98/1.57 => ( powersetI
% 2.98/1.57 => ( emptyinPowerset
% 2.98/1.57 => ( emptyInPowerset
% 2.98/1.57 => ( powersetE
% 2.98/1.57 => ( setunionI
% 2.98/1.57 => ( setunionE
% 2.98/1.57 => ( subPowSU
% 2.98/1.57 => ( exuE2
% 2.98/1.57 => ( nonemptyImpWitness
% 2.98/1.57 => ( uniqinunit
% 2.98/1.57 => ( notinsingleton
% 2.98/1.57 => ( eqinunit
% 2.98/1.57 => ( singletonsswitch
% 2.98/1.57 => ( upairsetE
% 2.98/1.57 => ( upairsetIL
% 2.98/1.57 => ( upairsetIR
% 2.98/1.57 => ( emptyE1
% 2.98/1.57 => ( vacuousDall
% 2.98/1.57 => ( quantDeMorgan1
% 2.98/1.57 => ( quantDeMorgan2
% 2.98/1.57 => ( quantDeMorgan3
% 2.98/1.57 => ( quantDeMorgan4
% 2.98/1.57 => ( prop2setI
% 2.98/1.57 => ( prop2set2propI
% 2.98/1.57 => ( notdexE
% 2.98/1.57 => ( notdallE
% 2.98/1.57 => ( exuI1
% 2.98/1.57 => ( exuI3
% 2.98/1.57 => ( exuI2
% 2.98/1.57 => ( inCongP
% 2.98/1.57 => ( in__Cong
% 2.98/1.57 => ( exuE3u
% 2.98/1.57 => ( exu__Cong
% 2.98/1.57 => ( emptyset__Cong
% 2.98/1.57 => ( setadjoin__Cong
% 2.98/1.57 => ( powerset__Cong
% 2.98/1.57 => ( setunion__Cong
% 2.98/1.57 => ( omega__Cong
% 2.98/1.57 => ( exuEu
% 2.98/1.57 => ( descr__Cong
% 2.98/1.57 => ( dsetconstr__Cong
% 2.98/1.57 => ( subsetI1
% 2.98/1.57 => ( eqimpsubset2
% 2.98/1.57 => ( eqimpsubset1
% 2.98/1.57 => ( subsetI2
% 2.98/1.57 => ( emptysetsubset
% 2.98/1.57 => ( subsetE
% 2.98/1.57 => ( subsetE2
% 2.98/1.57 => ( notsubsetI
% 2.98/1.57 => ( notequalI1
% 2.98/1.57 => ( notequalI2
% 2.98/1.57 => ( subsetRefl
% 2.98/1.57 => ( subsetTrans
% 2.98/1.57 => ( setadjoinSub
% 2.98/1.57 => ( setadjoinSub2
% 2.98/1.57 => ( subset2powerset
% 2.98/1.57 => ( setextsub
% 2.98/1.57 => ( subsetemptysetimpeq
% 2.98/1.57 => ( powersetI1
% 2.98/1.57 => ( powersetE1
% 2.98/1.57 => ( inPowerset
% 2.98/1.57 => ( powersetsubset
% 2.98/1.57 => ( sepInPowerset
% 2.98/1.57 => ( sepSubset
% 2.98/1.57 => ( binunionIL
% 2.98/1.57 => ( upairset2IR
% 2.98/1.57 => ( binunionIR
% 2.98/1.57 => ( binunionEcases
% 2.98/1.57 => ( binunionE
% 2.98/1.57 => ( binunionLsub
% 2.98/1.57 => ( binunionRsub
% 2.98/1.57 => ( binintersectI
% 2.98/1.57 => ( binintersectSubset5
% 2.98/1.57 => ( binintersectEL
% 2.98/1.57 => ( binintersectLsub
% 2.98/1.57 => ( binintersectSubset2
% 2.98/1.57 => ( binintersectSubset3
% 2.98/1.57 => ( binintersectER
% 2.98/1.57 => ( disjointsetsI1
% 2.98/1.57 => ( binintersectRsub
% 2.98/1.57 => ( binintersectSubset4
% 2.98/1.57 => ( binintersectSubset1
% 2.98/1.57 => ( bs114d
% 2.98/1.57 => ( setminusI
% 2.98/1.57 => ( setminusEL
% 2.98/1.57 => ( setminusER
% 2.98/1.57 => ( setminusSubset2
% 2.98/1.57 => ( setminusERneg
% 2.98/1.57 => ( setminusELneg
% 2.98/1.57 => ( setminusILneg
% 2.98/1.57 => ( setminusIRneg
% 2.98/1.57 => ( setminusLsub
% 2.98/1.57 => ( setminusSubset1
% 2.98/1.57 => ( symdiffE
% 2.98/1.57 => ( symdiffI1
% 2.98/1.57 => ( symdiffI2
% 2.98/1.57 => ( symdiffIneg1
% 2.98/1.57 => ( symdiffIneg2
% 2.98/1.57 => ( secondinupair
% 2.98/1.57 => ( setukpairIL
% 2.98/1.57 => ( setukpairIR
% 2.98/1.57 => ( kpairiskpair
% 2.98/1.57 => ( kpairp
% 2.98/1.57 => ( singletonsubset
% 2.98/1.57 => ( singletoninpowerset
% 2.98/1.57 => ( singletoninpowunion
% 2.98/1.57 => ( upairset2E
% 2.98/1.57 => ( upairsubunion
% 2.98/1.57 => ( upairinpowunion
% 2.98/1.57 => ( ubforcartprodlem1
% 2.98/1.57 => ( ubforcartprodlem2
% 2.98/1.57 => ( ubforcartprodlem3
% 2.98/1.57 => ( cartprodpairin
% 2.98/1.57 => ( cartprodmempair1
% 2.98/1.57 => ( cartprodmempair
% 2.98/1.57 => ( setunionE2
% 2.98/1.57 => ( setunionsingleton1
% 2.98/1.57 => ( setunionsingleton2
% 2.98/1.57 => ( setunionsingleton
% 2.98/1.57 => ( singletonprop
% 2.98/1.57 => ( ex1E1
% 2.98/1.57 => ( ex1I
% 2.98/1.57 => ( ex1I2
% 2.98/1.57 => ( singletonsuniq
% 2.98/1.57 => ( setukpairinjL1
% 2.98/1.57 => ( kfstsingleton
% 2.98/1.57 => ( theprop
% 2.98/1.57 => ( kfstpairEq
% 2.98/1.57 => ( cartprodfstin
% 2.98/1.57 => ( setukpairinjL2
% 2.98/1.57 => ( setukpairinjL
% 2.98/1.57 => ( setukpairinjR11
% 2.98/1.57 => ( setukpairinjR12
% 2.98/1.57 => ( setukpairinjR1
% 2.98/1.57 => ( upairequniteq
% 2.98/1.57 => ( setukpairinjR2
% 2.98/1.57 => ( setukpairinjR
% 2.98/1.57 => ( ksndsingleton
% 2.98/1.57 => ( ksndpairEq
% 2.98/1.57 => ( kpairsurjEq
% 2.98/1.57 => ( cartprodsndin
% 2.98/1.57 => ( cartprodpairmemEL
% 2.98/1.57 => ( cartprodpairmemER
% 2.98/1.57 => ( cartprodmempaircEq
% 2.98/1.57 => ( cartprodfstpairEq
% 2.98/1.57 => ( cartprodsndpairEq
% 2.98/1.57 => ( cartprodpairsurjEq
% 2.98/1.57 => ( dpsetconstrI
% 2.98/1.57 => ( dpsetconstrSub
% 2.98/1.57 => ( setOfPairsIsBReln
% 2.98/1.57 => ( dpsetconstrERa
% 2.98/1.57 => ( dpsetconstrEL1
% 2.98/1.57 => ( dpsetconstrEL2
% 2.98/1.57 => ( dpsetconstrER
% 2.98/1.57 => ( funcImageSingleton
% 2.98/1.57 => ( apProp
% 2.98/1.57 => ( app
% 2.98/1.57 => ( infuncsetfunc
% 2.98/1.57 => ( ap2p
% 2.98/1.57 => ( funcinfuncset
% 2.98/1.57 => ( lamProp
% 2.98/1.57 => ( lamp
% 2.98/1.57 => ( lam2p
% 2.98/1.57 => ( brelnall1
% 2.98/1.57 => ( brelnall2
% 2.98/1.57 => ( ex1E2
% 2.98/1.57 => ( funcGraphProp1
% 2.98/1.57 => ( funcGraphProp3
% 2.98/1.57 => ( funcGraphProp2
% 2.98/1.57 => ( funcextLem
% 2.98/1.57 => ( funcGraphProp4
% 2.98/1.57 => ( subbreln
% 2.98/1.57 => ( eqbreln
% 2.98/1.57 => ( funcext
% 2.98/1.57 => ( funcext2
% 2.98/1.57 => ( ap2apEq1
% 2.98/1.57 => ( ap2apEq2
% 2.98/1.57 => ( beta1
% 2.98/1.57 => ( eta1
% 2.98/1.57 => ( lam2lamEq
% 2.98/1.57 => ( beta2
% 2.98/1.57 => ( eta2
% 2.98/1.57 => ( iffalseProp1
% 2.98/1.57 => ( iffalseProp2
% 2.98/1.57 => ( iftrueProp1
% 2.98/1.57 => ( iftrueProp2
% 2.98/1.57 => ( ifSingleton
% 2.98/1.57 => ( ifp
% 2.98/1.57 => ( theeq
% 2.98/1.57 => ( iftrue
% 2.98/1.57 => ( iffalse
% 2.98/1.57 => ( iftrueorfalse
% 2.98/1.57 => ( binintersectT_lem
% 2.98/1.57 => ( binunionT_lem
% 2.98/1.57 => ( powersetT_lem
% 2.98/1.57 => ( setminusT_lem
% 2.98/1.57 => ( complementT_lem
% 2.98/1.57 => ( setextT
% 2.98/1.57 => ( subsetTI
% 2.98/1.57 => ( powersetTI1
% 2.98/1.57 => ( powersetTE1
% 2.98/1.57 => ( complementTI1
% 2.98/1.57 => ( complementTE1
% 2.98/1.57 => ( binintersectTELcontra
% 2.98/1.57 => ( binintersectTERcontra
% 2.98/1.57 => ( contrasubsetT
% 2.98/1.57 => ( contrasubsetT1
% 2.98/1.57 => ( contrasubsetT2
% 2.98/1.57 => ( contrasubsetT3
% 2.98/1.57 => ( doubleComplementI1
% 2.98/1.57 => ( doubleComplementE1
% 2.98/1.57 => ( doubleComplementSub1
% 2.98/1.57 => ( doubleComplementSub2
% 2.98/1.57 => ( doubleComplementEq
% 2.98/1.57 => ( complementTnotintersectT
% 2.98/1.57 => ( complementImpComplementIntersect
% 2.98/1.57 => ( complementSubsetComplementIntersect
% 2.98/1.57 => ( complementInPowersetComplementIntersect
% 2.98/1.57 => ( contraSubsetComplement
% 2.98/1.57 => ( complementTcontraSubset
% 2.98/1.57 => ( binunionTILcontra
% 2.98/1.57 => ( binunionTIRcontra
% 2.98/1.57 => ( inIntersectImpInUnion
% 2.98/1.57 => ( inIntersectImpInUnion2
% 2.98/1.57 => ( inIntersectImpInIntersectUnions
% 2.98/1.57 => ( intersectInPowersetIntersectUnions
% 2.98/1.57 => ( inComplementUnionImpNotIn1
% 2.98/1.57 => ( inComplementUnionImpInComplement1
% 2.98/1.57 => ( binunionTE
% 2.98/1.57 => ( binunionTEcontra
% 2.98/1.57 => ( demorgan2a1
% 2.98/1.57 => ( complementUnionInPowersetComplement
% 2.98/1.57 => ( demorgan2a2
% 2.98/1.57 => ( demorgan1a
% 2.98/1.57 => ( demorgan1b
% 2.98/1.57 => ( demorgan1
% 2.98/1.57 => ( demorgan2a
% 2.98/1.57 => ( demorgan2b2
% 2.98/1.57 => ( demorgan2b
% 2.98/1.57 => ( demorgan2
% 2.98/1.57 => ( woz13rule0
% 2.98/1.57 => ( woz13rule1
% 2.98/1.57 => ( woz13rule2
% 2.98/1.57 => ( woz13rule3
% 2.98/1.57 => ( woz13rule4
% 2.98/1.57 => ( woz1_1
% 2.98/1.57 => ( woz1_2
% 2.98/1.57 => ( woz1_3
% 2.98/1.57 => ( woz1_4
% 2.98/1.57 => ( woz1_5
% 2.98/1.57 => ( breln1all2
% 2.98/1.57 => ( breln1SetBreln1
% 2.98/1.57 => ( choice2fnsingleton
% 2.98/1.57 => ( setOfPairsIsBReln1
% 2.98/1.57 => ( breln1all1
% 2.98/1.57 => ( subbreln1
% 2.98/1.57 => ( eqbreln1
% 2.98/1.57 => ! [A: $i,R: $i] :
% 2.98/1.57 ( ( breln1 @ A @ R )
% 2.98/1.57 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.98/1.57 ------------------------
% 3.09/1.60 % (2862)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_2668 for (2999ds/4Mi)
% 3.09/1.60 % (2861)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2668 for (2999ds/183Mi)
% 3.09/1.60 % (2865)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_2668 for (2999ds/2Mi)
% 3.09/1.60 % (2862)Instruction limit reached!
% 3.09/1.60 % (2862)------------------------------
% 3.09/1.60 % (2862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.60 % (2862)Termination reason: Unknown
% 3.09/1.60 % (2862)Termination phase: shuffling
% 3.09/1.60
% 3.09/1.60 % (2862)Memory used [KB]: 1535
% 3.09/1.60 % (2862)Time elapsed: 0.003 s
% 3.09/1.60 % (2862)Instructions burned: 5 (million)
% 3.09/1.60 % (2862)------------------------------
% 3.09/1.60 % (2862)------------------------------
% 3.09/1.60 % (2865)Instruction limit reached!
% 3.09/1.60 % (2865)------------------------------
% 3.09/1.60 % (2865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.60 % (2865)Termination reason: Unknown
% 3.09/1.60 % (2865)Termination phase: shuffling
% 3.09/1.60
% 3.09/1.60 % (2865)Memory used [KB]: 1535
% 3.09/1.60 % (2865)Time elapsed: 0.002 s
% 3.09/1.60 % (2865)Instructions burned: 3 (million)
% 3.09/1.60 % (2865)------------------------------
% 3.09/1.60 % (2865)------------------------------
% 3.09/1.61 % (2863)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_2668 for (2999ds/27Mi)
% 3.09/1.61 % (2864)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2668 for (2999ds/2Mi)
% 3.09/1.61 % (2867)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2668 for (2999ds/18Mi)
% 3.09/1.61 % (2866)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_2668 for (2999ds/275Mi)
% 3.09/1.61 % (2864)Instruction limit reached!
% 3.09/1.61 % (2864)------------------------------
% 3.09/1.61 % (2864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.61 % (2864)Termination reason: Unknown
% 3.09/1.61 % (2864)Termination phase: shuffling
% 3.09/1.61
% 3.09/1.61 % (2864)Memory used [KB]: 1535
% 3.09/1.61 % (2864)Time elapsed: 0.003 s
% 3.09/1.61 % (2864)Instructions burned: 3 (million)
% 3.09/1.61 % (2864)------------------------------
% 3.09/1.61 % (2864)------------------------------
% 3.09/1.61 % (2868)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2668 for (2999ds/3Mi)
% 3.09/1.61 % (2868)Instruction limit reached!
% 3.09/1.61 % (2868)------------------------------
% 3.09/1.61 % (2868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.61 % (2868)Termination reason: Unknown
% 3.09/1.61 % (2868)Termination phase: shuffling
% 3.09/1.61
% 3.09/1.61 % (2868)Memory used [KB]: 1535
% 3.09/1.61 % (2868)Time elapsed: 0.002 s
% 3.09/1.61 % (2868)Instructions burned: 3 (million)
% 3.09/1.61 % (2868)------------------------------
% 3.09/1.61 % (2868)------------------------------
% 3.09/1.61 % (2869)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_2668 for (2999ds/37Mi)
% 3.09/1.62 % (2863)Instruction limit reached!
% 3.09/1.62 % (2863)------------------------------
% 3.09/1.62 % (2863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.62 % (2863)Termination reason: Unknown
% 3.09/1.62 % (2863)Termination phase: shuffling
% 3.09/1.62
% 3.09/1.62 % (2863)Memory used [KB]: 2046
% 3.09/1.62 % (2863)Time elapsed: 0.014 s
% 3.09/1.62 % (2863)Instructions burned: 29 (million)
% 3.09/1.62 % (2863)------------------------------
% 3.09/1.62 % (2863)------------------------------
% 3.09/1.62 % (2867)Instruction limit reached!
% 3.09/1.62 % (2867)------------------------------
% 3.09/1.62 % (2867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.62 % (2867)Termination reason: Unknown
% 3.09/1.62 % (2867)Termination phase: shuffling
% 3.09/1.62
% 3.09/1.62 % (2867)Memory used [KB]: 1791
% 3.09/1.62 % (2867)Time elapsed: 0.013 s
% 3.09/1.62 % (2867)Instructions burned: 19 (million)
% 3.09/1.62 % (2867)------------------------------
% 3.09/1.62 % (2867)------------------------------
% 3.09/1.62 % (2871)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_2668 for (2999ds/3Mi)
% 3.09/1.62 % (2871)Instruction limit reached!
% 3.09/1.62 % (2871)------------------------------
% 3.09/1.62 % (2871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.62 % (2871)Termination reason: Unknown
% 3.09/1.62 % (2871)Termination phase: shuffling
% 3.09/1.62
% 3.09/1.62 % (2871)Memory used [KB]: 1535
% 3.09/1.62 % (2871)Time elapsed: 0.002 s
% 3.09/1.62 % (2871)Instructions burned: 3 (million)
% 3.09/1.62 % (2871)------------------------------
% 3.09/1.62 % (2871)------------------------------
% 3.09/1.62 % (2869)Instruction limit reached!
% 3.09/1.62 % (2869)------------------------------
% 3.09/1.62 % (2869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.62 % (2869)Termination reason: Unknown
% 3.09/1.62 % (2869)Termination phase: shuffling
% 3.09/1.62
% 3.09/1.62 % (2869)Memory used [KB]: 2302
% 3.09/1.62 % (2869)Time elapsed: 0.012 s
% 3.09/1.62 % (2869)Instructions burned: 38 (million)
% 3.09/1.62 % (2869)------------------------------
% 3.09/1.62 % (2869)------------------------------
% 3.09/1.63 % (2870)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_2668 for (2999ds/15Mi)
% 3.09/1.63 % (2872)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_2668 for (2999ds/1041Mi)
% 3.09/1.63 % (2874)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_2668 for (2999ds/16Mi)
% 3.09/1.63 % (2875)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_2668 for (2999ds/3Mi)
% 3.09/1.64 % (2875)Instruction limit reached!
% 3.09/1.64 % (2875)------------------------------
% 3.09/1.64 % (2875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.64 % (2875)Termination reason: Unknown
% 3.09/1.64 % (2875)Termination phase: shuffling
% 3.09/1.64
% 3.09/1.64 % (2875)Memory used [KB]: 1535
% 3.09/1.64 % (2875)Time elapsed: 0.002 s
% 3.09/1.64 % (2875)Instructions burned: 4 (million)
% 3.09/1.64 % (2875)------------------------------
% 3.09/1.64 % (2875)------------------------------
% 3.09/1.64 % (2870)Instruction limit reached!
% 3.09/1.64 % (2870)------------------------------
% 3.09/1.64 % (2870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.64 % (2870)Termination reason: Unknown
% 3.09/1.64 % (2870)Termination phase: shuffling
% 3.09/1.64
% 3.09/1.64 % (2870)Memory used [KB]: 1791
% 3.09/1.64 % (2870)Time elapsed: 0.011 s
% 3.09/1.64 % (2870)Instructions burned: 15 (million)
% 3.09/1.64 % (2870)------------------------------
% 3.09/1.64 % (2870)------------------------------
% 3.09/1.64 % (2874)Instruction limit reached!
% 3.09/1.64 % (2874)------------------------------
% 3.09/1.64 % (2874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.64 % (2874)Termination reason: Unknown
% 3.09/1.64 % (2874)Termination phase: shuffling
% 3.09/1.64
% 3.09/1.64 % (2874)Memory used [KB]: 1791
% 3.09/1.64 % (2874)Time elapsed: 0.006 s
% 3.09/1.64 % (2874)Instructions burned: 17 (million)
% 3.09/1.64 % (2874)------------------------------
% 3.09/1.64 % (2874)------------------------------
% 3.09/1.64 % (2873)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_2668 for (2999ds/7Mi)
% 3.09/1.64 % (2873)Instruction limit reached!
% 3.09/1.64 % (2873)------------------------------
% 3.09/1.64 % (2873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.64 % (2873)Termination reason: Unknown
% 3.09/1.64 % (2873)Termination phase: shuffling
% 3.09/1.64
% 3.09/1.64 % (2873)Memory used [KB]: 1535
% 3.09/1.64 % (2873)Time elapsed: 0.006 s
% 3.09/1.64 % (2873)Instructions burned: 7 (million)
% 3.09/1.64 % (2873)------------------------------
% 3.09/1.64 % (2873)------------------------------
% 3.09/1.65 % (2876)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_2668 for (2999ds/3Mi)
% 3.09/1.65 % (2876)Instruction limit reached!
% 3.09/1.65 % (2876)------------------------------
% 3.09/1.65 % (2876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.65 % (2876)Termination reason: Unknown
% 3.09/1.65 % (2876)Termination phase: shuffling
% 3.09/1.65
% 3.09/1.65 % (2876)Memory used [KB]: 1535
% 3.09/1.65 % (2876)Time elapsed: 0.002 s
% 3.09/1.65 % (2876)Instructions burned: 4 (million)
% 3.09/1.65 % (2876)------------------------------
% 3.09/1.65 % (2876)------------------------------
% 3.09/1.65 % (2878)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_2668 for (2999ds/3Mi)
% 3.09/1.65 % (2861)Instruction limit reached!
% 3.09/1.65 % (2861)------------------------------
% 3.09/1.65 % (2861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.65 % (2861)Termination reason: Unknown
% 3.09/1.65 % (2861)Termination phase: Saturation
% 3.09/1.65
% 3.09/1.65 % (2861)Memory used [KB]: 7419
% 3.09/1.65 % (2861)Time elapsed: 0.048 s
% 3.09/1.65 % (2861)Instructions burned: 183 (million)
% 3.09/1.65 % (2861)------------------------------
% 3.09/1.65 % (2861)------------------------------
% 3.09/1.65 % (2878)Instruction limit reached!
% 3.09/1.65 % (2878)------------------------------
% 3.09/1.65 % (2878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.65 % (2878)Termination reason: Unknown
% 3.09/1.65 % (2878)Termination phase: shuffling
% 3.09/1.65
% 3.09/1.65 % (2878)Memory used [KB]: 1535
% 3.09/1.65 % (2878)Time elapsed: 0.002 s
% 3.09/1.65 % (2878)Instructions burned: 3 (million)
% 3.09/1.65 % (2878)------------------------------
% 3.09/1.65 % (2878)------------------------------
% 3.09/1.66 % (2877)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_2668 for (2999ds/7Mi)
% 3.09/1.66 % (2880)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_2668 for (2999ds/18Mi)
% 3.09/1.66 % (2882)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_2668 for (2999ds/6Mi)
% 3.09/1.66 % (2877)Instruction limit reached!
% 3.09/1.66 % (2877)------------------------------
% 3.09/1.66 % (2877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.66 % (2877)Termination reason: Unknown
% 3.09/1.66 % (2877)Termination phase: shuffling
% 3.09/1.66
% 3.09/1.66 % (2877)Memory used [KB]: 1535
% 3.09/1.66 % (2877)Time elapsed: 0.006 s
% 3.09/1.66 % (2877)Instructions burned: 7 (million)
% 3.09/1.66 % (2877)------------------------------
% 3.09/1.66 % (2877)------------------------------
% 3.09/1.66 % (2882)Instruction limit reached!
% 3.09/1.66 % (2882)------------------------------
% 3.09/1.66 % (2882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.66 % (2882)Termination reason: Unknown
% 3.09/1.66 % (2882)Termination phase: shuffling
% 3.09/1.66
% 3.09/1.66 % (2882)Memory used [KB]: 1535
% 3.09/1.66 % (2882)Time elapsed: 0.003 s
% 3.09/1.66 % (2882)Instructions burned: 7 (million)
% 3.09/1.66 % (2882)------------------------------
% 3.09/1.66 % (2882)------------------------------
% 3.09/1.66 % (2879)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_2668 for (2999ds/4Mi)
% 3.09/1.66 % (2881)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_2668 for (2999ds/710Mi)
% 3.09/1.66 % (2880)Instruction limit reached!
% 3.09/1.66 % (2880)------------------------------
% 3.09/1.66 % (2880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.66 % (2880)Termination reason: Unknown
% 3.09/1.66 % (2880)Termination phase: shuffling
% 3.09/1.66
% 3.09/1.66 % (2880)Memory used [KB]: 1791
% 3.09/1.66 % (2880)Time elapsed: 0.007 s
% 3.09/1.66 % (2880)Instructions burned: 20 (million)
% 3.09/1.66 % (2880)------------------------------
% 3.09/1.66 % (2880)------------------------------
% 3.09/1.66 % (2879)Instruction limit reached!
% 3.09/1.66 % (2879)------------------------------
% 3.09/1.66 % (2879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.66 % (2879)Termination reason: Unknown
% 3.09/1.66 % (2879)Termination phase: shuffling
% 3.09/1.66
% 3.09/1.66 % (2879)Memory used [KB]: 1535
% 3.09/1.66 % (2879)Time elapsed: 0.005 s
% 3.09/1.66 % (2879)Instructions burned: 5 (million)
% 3.09/1.66 % (2879)------------------------------
% 3.09/1.66 % (2879)------------------------------
% 3.09/1.67 % (2884)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_2668 for (2999ds/21Mi)
% 3.09/1.67 % (2885)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_2668 for (2999ds/5Mi)
% 3.09/1.67 % (2885)Instruction limit reached!
% 3.09/1.67 % (2885)------------------------------
% 3.09/1.67 % (2885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.67 % (2885)Termination reason: Unknown
% 3.09/1.67 % (2885)Termination phase: shuffling
% 3.09/1.67
% 3.09/1.67 % (2885)Memory used [KB]: 1535
% 3.09/1.67 % (2885)Time elapsed: 0.003 s
% 3.09/1.67 % (2885)Instructions burned: 5 (million)
% 3.09/1.67 % (2885)------------------------------
% 3.09/1.67 % (2885)------------------------------
% 3.09/1.68 % (2883)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_2668 for (2999ds/902Mi)
% 3.09/1.68 % (2884)Instruction limit reached!
% 3.09/1.68 % (2884)------------------------------
% 3.09/1.68 % (2884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.68 % (2884)Termination reason: Unknown
% 3.09/1.68 % (2884)Termination phase: shuffling
% 3.09/1.68
% 3.09/1.68 % (2884)Memory used [KB]: 1918
% 3.09/1.68 % (2884)Time elapsed: 0.008 s
% 3.09/1.68 % (2884)Instructions burned: 24 (million)
% 3.09/1.68 % (2884)------------------------------
% 3.09/1.68 % (2884)------------------------------
% 3.09/1.68 % (2886)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_2668 for (2999ds/6Mi)
% 3.09/1.68 % (2887)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_2668 for (2999ds/377Mi)
% 3.09/1.68 % (2886)Instruction limit reached!
% 3.09/1.68 % (2886)------------------------------
% 3.09/1.68 % (2886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.68 % (2886)Termination reason: Unknown
% 3.09/1.68 % (2886)Termination phase: shuffling
% 3.09/1.68
% 3.09/1.68 % (2886)Memory used [KB]: 1535
% 3.09/1.68 % (2886)Time elapsed: 0.006 s
% 3.09/1.68 % (2886)Instructions burned: 7 (million)
% 3.09/1.68 % (2886)------------------------------
% 3.09/1.68 % (2886)------------------------------
% 3.09/1.68 % (2888)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_2668 for (2999ds/779Mi)
% 3.09/1.70 % (2889)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_2668 for (2999ds/19Mi)
% 3.09/1.71 % (2889)Instruction limit reached!
% 3.09/1.71 % (2889)------------------------------
% 3.09/1.71 % (2889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.71 % (2889)Termination reason: Unknown
% 3.09/1.71 % (2889)Termination phase: shuffling
% 3.09/1.71
% 3.09/1.71 % (2889)Memory used [KB]: 1918
% 3.09/1.71 % (2889)Time elapsed: 0.009 s
% 3.09/1.71 % (2889)Instructions burned: 20 (million)
% 3.09/1.71 % (2889)------------------------------
% 3.09/1.71 % (2889)------------------------------
% 3.09/1.72 % (2890)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_2668 for (2998ds/879Mi)
% 3.09/1.74 % (2866)Instruction limit reached!
% 3.09/1.74 % (2866)------------------------------
% 3.09/1.74 % (2866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.74 % (2866)Termination reason: Unknown
% 3.09/1.74 % (2866)Termination phase: Saturation
% 3.09/1.74
% 3.09/1.74 % (2866)Memory used [KB]: 10234
% 3.09/1.74 % (2866)Time elapsed: 0.131 s
% 3.09/1.74 % (2866)Instructions burned: 275 (million)
% 3.09/1.74 % (2866)------------------------------
% 3.09/1.74 % (2866)------------------------------
% 3.09/1.75 % (2891)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_2668 for (2998ds/17Mi)
% 3.09/1.75 % (2891)Instruction limit reached!
% 3.09/1.75 % (2891)------------------------------
% 3.09/1.75 % (2891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.75 % (2891)Termination reason: Unknown
% 3.09/1.75 % (2891)Termination phase: shuffling
% 3.09/1.75
% 3.09/1.75 % (2891)Memory used [KB]: 1791
% 3.09/1.75 % (2891)Time elapsed: 0.006 s
% 3.09/1.75 % (2891)Instructions burned: 17 (million)
% 3.09/1.75 % (2891)------------------------------
% 3.09/1.75 % (2891)------------------------------
% 3.09/1.76 % (2892)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_2668 for (2998ds/3Mi)
% 3.09/1.77 % (2892)Instruction limit reached!
% 3.09/1.77 % (2892)------------------------------
% 3.09/1.77 % (2892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.77 % (2892)Termination reason: Unknown
% 3.09/1.77 % (2892)Termination phase: shuffling
% 3.09/1.77
% 3.09/1.77 % (2892)Memory used [KB]: 1535
% 3.09/1.77 % (2892)Time elapsed: 0.002 s
% 3.09/1.77 % (2892)Instructions burned: 4 (million)
% 3.09/1.77 % (2892)------------------------------
% 3.09/1.77 % (2892)------------------------------
% 3.09/1.78 % (2893)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_2668 for (2998ds/30Mi)
% 3.09/1.78 % (2887)Instruction limit reached!
% 3.09/1.78 % (2887)------------------------------
% 3.09/1.78 % (2887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.78 % (2887)Termination reason: Unknown
% 3.09/1.78 % (2887)Termination phase: Saturation
% 3.09/1.78
% 3.09/1.78 % (2887)Memory used [KB]: 9338
% 3.09/1.78 % (2887)Time elapsed: 0.102 s
% 3.09/1.78 % (2887)Instructions burned: 377 (million)
% 3.09/1.78 % (2887)------------------------------
% 3.09/1.78 % (2887)------------------------------
% 3.09/1.79 % (2893)Instruction limit reached!
% 3.09/1.79 % (2893)------------------------------
% 3.09/1.79 % (2893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.79 % (2893)Termination reason: Unknown
% 3.09/1.79 % (2893)Termination phase: shuffling
% 3.09/1.79
% 3.09/1.79 % (2893)Memory used [KB]: 2174
% 3.09/1.79 % (2893)Time elapsed: 0.010 s
% 3.09/1.79 % (2893)Instructions burned: 31 (million)
% 3.09/1.79 % (2893)------------------------------
% 3.09/1.79 % (2893)------------------------------
% 3.09/1.79 % (2894)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_2668 for (2998ds/127Mi)
% 3.09/1.80 % (2895)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_2668 for (2998ds/100Mi)
% 3.09/1.81 % (2883)Refutation not found, incomplete strategy
% 3.09/1.81 % (2883)------------------------------
% 3.09/1.81 % (2883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.81 % (2883)Termination reason: Refutation not found, incomplete strategy
% 3.09/1.81
% 3.09/1.81
% 3.09/1.81 % (2883)Memory used [KB]: 10874
% 3.09/1.81 % (2883)Time elapsed: 0.140 s
% 3.09/1.81 % (2883)Instructions burned: 424 (million)
% 3.09/1.81 % (2883)------------------------------
% 3.09/1.81 % (2883)------------------------------
% 3.09/1.82 % (2895)Instruction limit reached!
% 3.09/1.82 % (2895)------------------------------
% 3.09/1.82 % (2895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.82 % (2895)Termination reason: Unknown
% 3.09/1.82 % (2895)Termination phase: Property scanning
% 3.09/1.82
% 3.09/1.82 % (2895)Memory used [KB]: 2686
% 3.09/1.82 % (2895)Time elapsed: 0.029 s
% 3.09/1.82 % (2895)Instructions burned: 100 (million)
% 3.09/1.82 % (2895)------------------------------
% 3.09/1.82 % (2895)------------------------------
% 3.09/1.83 % (2896)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_2668 for (2997ds/3Mi)
% 3.09/1.83 % (2894)Instruction limit reached!
% 3.09/1.83 % (2894)------------------------------
% 3.09/1.83 % (2894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.83 % (2894)Termination reason: Unknown
% 3.09/1.83 % (2894)Termination phase: Property scanning
% 3.09/1.83
% 3.09/1.83 % (2894)Memory used [KB]: 2814
% 3.09/1.83 % (2894)Time elapsed: 0.034 s
% 3.09/1.83 % (2894)Instructions burned: 129 (million)
% 3.09/1.83 % (2894)------------------------------
% 3.09/1.83 % (2894)------------------------------
% 3.09/1.83 % (2896)Instruction limit reached!
% 3.09/1.83 % (2896)------------------------------
% 3.09/1.83 % (2896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.83 % (2896)Termination reason: Unknown
% 3.09/1.83 % (2896)Termination phase: shuffling
% 3.09/1.83
% 3.09/1.83 % (2896)Memory used [KB]: 1535
% 3.09/1.83 % (2896)Time elapsed: 0.002 s
% 3.09/1.83 % (2896)Instructions burned: 3 (million)
% 3.09/1.83 % (2896)------------------------------
% 3.09/1.83 % (2896)------------------------------
% 3.09/1.83 % (2897)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_2668 for (2997ds/20Mi)
% 3.09/1.84 % (2899)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_2668 for (2997ds/107Mi)
% 3.09/1.84 % (2898)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_2668 for (2997ds/86Mi)
% 3.09/1.84 % (2897)Instruction limit reached!
% 3.09/1.84 % (2897)------------------------------
% 3.09/1.84 % (2897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.84 % (2897)Termination reason: Unknown
% 3.09/1.84 % (2897)Termination phase: shuffling
% 3.09/1.84
% 3.09/1.84 % (2897)Memory used [KB]: 1791
% 3.09/1.84 % (2897)Time elapsed: 0.008 s
% 3.09/1.84 % (2897)Instructions burned: 20 (million)
% 3.09/1.84 % (2897)------------------------------
% 3.09/1.84 % (2897)------------------------------
% 3.09/1.85 % (2900)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_2668 for (2997ds/39Mi)
% 3.09/1.86 % (2898)Instruction limit reached!
% 3.09/1.86 % (2898)------------------------------
% 3.09/1.86 % (2898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.86 % (2898)Termination reason: Unknown
% 3.09/1.86 % (2898)Termination phase: Property scanning
% 3.09/1.86
% 3.09/1.86 % (2898)Memory used [KB]: 2558
% 3.09/1.86 % (2898)Time elapsed: 0.026 s
% 3.09/1.86 % (2898)Instructions burned: 89 (million)
% 3.09/1.86 % (2898)------------------------------
% 3.09/1.86 % (2898)------------------------------
% 3.09/1.86 % (2900)Instruction limit reached!
% 3.09/1.86 % (2900)------------------------------
% 3.09/1.86 % (2900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.86 % (2900)Termination reason: Unknown
% 3.09/1.86 % (2900)Termination phase: shuffling
% 3.09/1.86
% 3.09/1.86 % (2900)Memory used [KB]: 2302
% 3.09/1.86 % (2900)Time elapsed: 0.013 s
% 3.09/1.86 % (2900)Instructions burned: 40 (million)
% 3.09/1.86 % (2900)------------------------------
% 3.09/1.86 % (2900)------------------------------
% 3.09/1.86 % (2899)Instruction limit reached!
% 3.09/1.86 % (2899)------------------------------
% 3.09/1.86 % (2899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.86 % (2899)Termination reason: Unknown
% 3.09/1.86 % (2899)Termination phase: SInE selection
% 3.09/1.86
% 3.09/1.86 % (2899)Memory used [KB]: 2558
% 3.09/1.86 % (2899)Time elapsed: 0.029 s
% 3.09/1.86 % (2899)Instructions burned: 110 (million)
% 3.09/1.86 % (2899)------------------------------
% 3.09/1.86 % (2899)------------------------------
% 3.09/1.87 % (2901)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_2668 for (2997ds/448Mi)
% 3.09/1.87 % (2903)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_2668 for (2997ds/98Mi)
% 3.09/1.87 % (2902)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_2668 for (2997ds/46Mi)
% 3.09/1.88 % (2888)Instruction limit reached!
% 3.09/1.88 % (2888)------------------------------
% 3.09/1.88 % (2888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.88 % (2888)Termination reason: Unknown
% 3.09/1.88 % (2888)Termination phase: Saturation
% 3.09/1.88
% 3.09/1.88 % (2888)Memory used [KB]: 7675
% 3.09/1.88 % (2888)Time elapsed: 0.194 s
% 3.09/1.88 % (2888)Instructions burned: 779 (million)
% 3.09/1.88 % (2888)------------------------------
% 3.09/1.88 % (2888)------------------------------
% 3.09/1.88 % (2881)Instruction limit reached!
% 3.09/1.88 % (2881)------------------------------
% 3.09/1.88 % (2881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.88 % (2881)Termination reason: Unknown
% 3.09/1.88 % (2881)Termination phase: Saturation
% 3.09/1.88
% 3.09/1.88 % (2881)Memory used [KB]: 12153
% 3.09/1.88 % (2881)Time elapsed: 0.220 s
% 3.09/1.88 % (2881)Instructions burned: 711 (million)
% 3.09/1.88 % (2881)------------------------------
% 3.09/1.88 % (2881)------------------------------
% 3.09/1.89 % (2904)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_2668 for (2997ds/507Mi)
% 3.09/1.89 % (2902)Instruction limit reached!
% 3.09/1.89 % (2902)------------------------------
% 3.09/1.89 % (2902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.89 % (2902)Termination reason: Unknown
% 3.09/1.89 % (2902)Termination phase: shuffling
% 3.09/1.89
% 3.09/1.89 % (2902)Memory used [KB]: 2430
% 3.09/1.89 % (2902)Time elapsed: 0.015 s
% 3.09/1.89 % (2902)Instructions burned: 48 (million)
% 3.09/1.89 % (2902)------------------------------
% 3.09/1.89 % (2902)------------------------------
% 3.09/1.89 % (2905)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_2668 for (2997ds/149Mi)
% 3.09/1.90 % (2906)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_2668 for (2997ds/39Mi)
% 3.09/1.90 % (2903)Instruction limit reached!
% 3.09/1.90 % (2903)------------------------------
% 3.09/1.90 % (2903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.90 % (2903)Termination reason: Unknown
% 3.09/1.90 % (2903)Termination phase: Property scanning
% 3.09/1.90
% 3.09/1.90 % (2903)Memory used [KB]: 2686
% 3.09/1.90 % (2903)Time elapsed: 0.027 s
% 3.09/1.90 % (2903)Instructions burned: 100 (million)
% 3.09/1.90 % (2903)------------------------------
% 3.09/1.90 % (2903)------------------------------
% 3.09/1.91 % (2907)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_2668 for (2996ds/6Mi)
% 3.09/1.91 % (2906)Instruction limit reached!
% 3.09/1.91 % (2906)------------------------------
% 3.09/1.91 % (2906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.91 % (2906)Termination reason: Unknown
% 3.09/1.91 % (2906)Termination phase: shuffling
% 3.09/1.91
% 3.09/1.91 % (2906)Memory used [KB]: 2302
% 3.09/1.91 % (2906)Time elapsed: 0.013 s
% 3.09/1.91 % (2906)Instructions burned: 41 (million)
% 3.09/1.91 % (2906)------------------------------
% 3.09/1.91 % (2906)------------------------------
% 3.09/1.91 % (2907)Instruction limit reached!
% 3.09/1.91 % (2907)------------------------------
% 3.09/1.91 % (2907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.91 % (2907)Termination reason: Unknown
% 3.09/1.91 % (2907)Termination phase: shuffling
% 3.09/1.91
% 3.09/1.91 % (2907)Memory used [KB]: 1663
% 3.09/1.91 % (2907)Time elapsed: 0.003 s
% 3.09/1.91 % (2907)Instructions burned: 7 (million)
% 3.09/1.91 % (2907)------------------------------
% 3.09/1.91 % (2907)------------------------------
% 3.09/1.91 % (2872)Instruction limit reached!
% 3.09/1.91 % (2872)------------------------------
% 3.09/1.91 % (2872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.91 % (2872)Termination reason: Unknown
% 3.09/1.91 % (2872)Termination phase: Saturation
% 3.09/1.91
% 3.09/1.91 % (2872)Memory used [KB]: 16502
% 3.09/1.91 % (2872)Time elapsed: 0.282 s
% 3.09/1.91 % (2872)Instructions burned: 1043 (million)
% 3.09/1.91 % (2872)------------------------------
% 3.09/1.91 % (2872)------------------------------
% 3.09/1.92 % (2909)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_2668 for (2996ds/47Mi)
% 3.09/1.92 % (2908)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_2668 for (2996ds/1087Mi)
% 3.09/1.92 % (2910)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_2668 for (2996ds/44Mi)
% 3.09/1.93 % (2905)Instruction limit reached!
% 3.09/1.93 % (2905)------------------------------
% 3.09/1.93 % (2905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.93 % (2905)Termination reason: Unknown
% 3.09/1.93 % (2905)Termination phase: Twee Goal Transformation
% 3.09/1.93
% 3.09/1.93 % (2905)Memory used [KB]: 3070
% 3.09/1.93 % (2905)Time elapsed: 0.040 s
% 3.09/1.93 % (2905)Instructions burned: 149 (million)
% 3.09/1.93 % (2905)------------------------------
% 3.09/1.93 % (2905)------------------------------
% 3.09/1.93 % (2909)Instruction limit reached!
% 3.09/1.93 % (2909)------------------------------
% 3.09/1.93 % (2909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.93 % (2909)Termination reason: Unknown
% 3.09/1.93 % (2909)Termination phase: shuffling
% 3.09/1.93
% 3.09/1.93 % (2909)Memory used [KB]: 2430
% 3.09/1.93 % (2909)Time elapsed: 0.015 s
% 3.09/1.93 % (2909)Instructions burned: 49 (million)
% 3.09/1.93 % (2909)------------------------------
% 3.09/1.93 % (2909)------------------------------
% 3.09/1.94 % (2910)Instruction limit reached!
% 3.09/1.94 % (2910)------------------------------
% 3.09/1.94 % (2910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.94 % (2910)Termination reason: Unknown
% 3.09/1.94 % (2910)Termination phase: shuffling
% 3.09/1.94
% 3.09/1.94 % (2910)Memory used [KB]: 2430
% 3.09/1.94 % (2910)Time elapsed: 0.014 s
% 3.09/1.94 % (2910)Instructions burned: 46 (million)
% 3.09/1.94 % (2910)------------------------------
% 3.09/1.94 % (2910)------------------------------
% 3.09/1.94 % (2911)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_2668 for (2996ds/432Mi)
% 3.09/1.94 % (2912)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_2668 for (2996ds/62Mi)
% 3.09/1.94 % (2913)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_2668 for (2996ds/31Mi)
% 3.09/1.95 % (2913)Instruction limit reached!
% 3.09/1.95 % (2913)------------------------------
% 3.09/1.95 % (2913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.95 % (2913)Termination reason: Unknown
% 3.09/1.95 % (2913)Termination phase: shuffling
% 3.09/1.95
% 3.09/1.95 % (2913)Memory used [KB]: 2174
% 3.09/1.95 % (2913)Time elapsed: 0.010 s
% 3.09/1.95 % (2913)Instructions burned: 33 (million)
% 3.09/1.95 % (2913)------------------------------
% 3.09/1.95 % (2913)------------------------------
% 3.09/1.96 % (2912)Instruction limit reached!
% 3.09/1.96 % (2912)------------------------------
% 3.09/1.96 % (2912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.96 % (2912)Termination reason: Unknown
% 3.09/1.96 % (2912)Termination phase: Property scanning
% 3.09/1.96
% 3.09/1.96 % (2912)Memory used [KB]: 2558
% 3.09/1.96 % (2912)Time elapsed: 0.018 s
% 3.09/1.96 % (2912)Instructions burned: 66 (million)
% 3.09/1.96 % (2912)------------------------------
% 3.09/1.96 % (2912)------------------------------
% 3.09/1.96 % (2914)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_2668 for (2996ds/96Mi)
% 3.09/1.97 % (2915)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_2668 for (2996ds/453Mi)
% 3.09/1.99 % (2914)Instruction limit reached!
% 3.09/1.99 % (2914)------------------------------
% 3.09/1.99 % (2914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.99 % (2914)Termination reason: Unknown
% 3.09/1.99 % (2914)Termination phase: Property scanning
% 3.09/1.99
% 3.09/1.99 % (2914)Memory used [KB]: 2686
% 3.09/1.99 % (2914)Time elapsed: 0.027 s
% 3.09/1.99 % (2914)Instructions burned: 97 (million)
% 3.09/1.99 % (2914)------------------------------
% 3.09/1.99 % (2914)------------------------------
% 3.09/1.99 % (2901)Instruction limit reached!
% 3.09/1.99 % (2901)------------------------------
% 3.09/1.99 % (2901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/1.99 % (2901)Termination reason: Unknown
% 3.09/1.99 % (2901)Termination phase: Saturation
% 3.09/1.99
% 3.09/1.99 % (2901)Memory used [KB]: 7547
% 3.09/1.99 % (2901)Time elapsed: 0.121 s
% 3.09/1.99 % (2901)Instructions burned: 449 (million)
% 3.09/1.99 % (2901)------------------------------
% 3.09/1.99 % (2901)------------------------------
% 3.09/2.00 % (2916)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_2668 for (2995ds/71Mi)
% 3.09/2.00 % (2890)Instruction limit reached!
% 3.09/2.00 % (2890)------------------------------
% 3.09/2.00 % (2890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.09/2.00 % (2890)Termination reason: Unknown
% 3.09/2.00 % (2890)Termination phase: Saturation
% 3.09/2.00
% 3.09/2.00 % (2890)Memory used [KB]: 10234
% 3.09/2.00 % (2890)Time elapsed: 0.282 s
% 3.09/2.00 % (2890)Instructions burned: 880 (million)
% 3.09/2.00 % (2890)------------------------------
% 3.09/2.00 % (2890)------------------------------
% 3.09/2.00 % (2917)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_2668 for (2995ds/83Mi)
% 3.09/2.01 % (2918)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_2668 for (2995ds/11Mi)
% 5.96/2.02 % (2918)Instruction limit reached!
% 5.96/2.02 % (2918)------------------------------
% 5.96/2.02 % (2918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.02 % (2918)Termination reason: Unknown
% 5.96/2.02 % (2918)Termination phase: shuffling
% 5.96/2.02
% 5.96/2.02 % (2918)Memory used [KB]: 1791
% 5.96/2.02 % (2918)Time elapsed: 0.005 s
% 5.96/2.02 % (2918)Instructions burned: 13 (million)
% 5.96/2.02 % (2918)------------------------------
% 5.96/2.02 % (2918)------------------------------
% 5.96/2.02 % (2916)Instruction limit reached!
% 5.96/2.02 % (2916)------------------------------
% 5.96/2.02 % (2916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.02 % (2916)Termination reason: Unknown
% 5.96/2.02 % (2916)Termination phase: Property scanning
% 5.96/2.02
% 5.96/2.02 % (2916)Memory used [KB]: 2558
% 5.96/2.02 % (2916)Time elapsed: 0.020 s
% 5.96/2.02 % (2916)Instructions burned: 72 (million)
% 5.96/2.02 % (2916)------------------------------
% 5.96/2.02 % (2916)------------------------------
% 5.96/2.03 % (2919)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_2668 for (2995ds/41Mi)
% 5.96/2.03 % (2917)Instruction limit reached!
% 5.96/2.03 % (2917)------------------------------
% 5.96/2.03 % (2917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.03 % (2917)Termination reason: Unknown
% 5.96/2.03 % (2917)Termination phase: Property scanning
% 5.96/2.03
% 5.96/2.03 % (2917)Memory used [KB]: 2558
% 5.96/2.03 % (2917)Time elapsed: 0.025 s
% 5.96/2.03 % (2917)Instructions burned: 86 (million)
% 5.96/2.03 % (2917)------------------------------
% 5.96/2.03 % (2917)------------------------------
% 5.96/2.03 % (2920)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_2668 for (2995ds/6Mi)
% 5.96/2.03 % (2920)Instruction limit reached!
% 5.96/2.03 % (2920)------------------------------
% 5.96/2.03 % (2920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.03 % (2920)Termination reason: Unknown
% 5.96/2.03 % (2920)Termination phase: shuffling
% 5.96/2.03
% 5.96/2.03 % (2920)Memory used [KB]: 1535
% 5.96/2.03 % (2920)Time elapsed: 0.003 s
% 5.96/2.03 % (2920)Instructions burned: 7 (million)
% 5.96/2.03 % (2920)------------------------------
% 5.96/2.03 % (2920)------------------------------
% 5.96/2.03 % (2904)Instruction limit reached!
% 5.96/2.03 % (2904)------------------------------
% 5.96/2.03 % (2904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.03 % (2904)Termination reason: Unknown
% 5.96/2.03 % (2904)Termination phase: Saturation
% 5.96/2.03
% 5.96/2.03 % (2904)Memory used [KB]: 8187
% 5.96/2.03 % (2904)Time elapsed: 0.146 s
% 5.96/2.03 % (2904)Instructions burned: 509 (million)
% 5.96/2.03 % (2904)------------------------------
% 5.96/2.03 % (2904)------------------------------
% 5.96/2.04 % (2921)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_2668 for (2995ds/150Mi)
% 5.96/2.04 % (2919)Instruction limit reached!
% 5.96/2.04 % (2919)------------------------------
% 5.96/2.04 % (2919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.04 % (2919)Termination reason: Unknown
% 5.96/2.04 % (2919)Termination phase: shuffling
% 5.96/2.04
% 5.96/2.04 % (2919)Memory used [KB]: 2302
% 5.96/2.04 % (2919)Time elapsed: 0.013 s
% 5.96/2.04 % (2919)Instructions burned: 42 (million)
% 5.96/2.04 % (2919)------------------------------
% 5.96/2.04 % (2919)------------------------------
% 5.96/2.04 % (2922)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_2668 for (2995ds/343Mi)
% 5.96/2.04 % (2923)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_2668 for (2995ds/109Mi)
% 5.96/2.05 % (2911)Instruction limit reached!
% 5.96/2.05 % (2911)------------------------------
% 5.96/2.05 % (2911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.05 % (2911)Termination reason: Unknown
% 5.96/2.05 % (2911)Termination phase: Saturation
% 5.96/2.05
% 5.96/2.05 % (2911)Memory used [KB]: 3070
% 5.96/2.05 % (2911)Time elapsed: 0.109 s
% 5.96/2.05 % (2911)Instructions burned: 433 (million)
% 5.96/2.05 % (2911)------------------------------
% 5.96/2.05 % (2911)------------------------------
% 5.96/2.05 % (2924)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_2668 for (2995ds/253Mi)
% 5.96/2.06 % (2925)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_2668 for (2995ds/140Mi)
% 5.96/2.07 % (2923)Instruction limit reached!
% 5.96/2.07 % (2923)------------------------------
% 5.96/2.07 % (2923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.07 % (2923)Termination reason: Unknown
% 5.96/2.07 % (2923)Termination phase: SInE selection
% 5.96/2.07
% 5.96/2.07 % (2923)Memory used [KB]: 2558
% 5.96/2.07 % (2923)Time elapsed: 0.029 s
% 5.96/2.07 % (2923)Instructions burned: 111 (million)
% 5.96/2.07 % (2923)------------------------------
% 5.96/2.07 % (2923)------------------------------
% 5.96/2.08 % (2926)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_2668 for (2995ds/614Mi)
% 5.96/2.08 % (2921)Instruction limit reached!
% 5.96/2.08 % (2921)------------------------------
% 5.96/2.08 % (2921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.08 % (2921)Termination reason: Unknown
% 5.96/2.08 % (2921)Termination phase: Property scanning
% 5.96/2.08
% 5.96/2.08 % (2921)Memory used [KB]: 5117
% 5.96/2.08 % (2921)Time elapsed: 0.045 s
% 5.96/2.08 % (2921)Instructions burned: 150 (million)
% 5.96/2.08 % (2921)------------------------------
% 5.96/2.08 % (2921)------------------------------
% 5.96/2.08 % (2915)Instruction limit reached!
% 5.96/2.08 % (2915)------------------------------
% 5.96/2.08 % (2915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.08 % (2915)Termination reason: Unknown
% 5.96/2.08 % (2915)Termination phase: Saturation
% 5.96/2.08
% 5.96/2.08 % (2915)Memory used [KB]: 7547
% 5.96/2.08 % (2915)Time elapsed: 0.114 s
% 5.96/2.08 % (2915)Instructions burned: 454 (million)
% 5.96/2.08 % (2915)------------------------------
% 5.96/2.08 % (2915)------------------------------
% 5.96/2.09 % (2927)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_2668 for (2995ds/202Mi)
% 5.96/2.09 % (2925)Instruction limit reached!
% 5.96/2.09 % (2925)------------------------------
% 5.96/2.09 % (2925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.96/2.09 % (2925)Termination reason: Unknown
% 5.96/2.09 % (2925)Termination phase: Function definition elimination
% 5.96/2.09
% 5.96/2.09 % (2925)Memory used [KB]: 2814
% 5.96/2.09 % (2925)Time elapsed: 0.037 s
% 5.96/2.09 % (2925)Instructions burned: 140 (million)
% 5.96/2.09 % (2925)------------------------------
% 5.96/2.09 % (2925)------------------------------
% 5.96/2.09 % (2928)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_2668 for (2995ds/339Mi)
% 5.96/2.10 % (2929)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_2668 for (2994ds/283Mi)
% 6.45/2.12 % (2924)Instruction limit reached!
% 6.45/2.12 % (2924)------------------------------
% 6.45/2.12 % (2924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.45/2.12 % (2924)Termination reason: Unknown
% 6.45/2.12 % (2924)Termination phase: Saturation
% 6.45/2.12
% 6.45/2.12 % (2924)Memory used [KB]: 5628
% 6.45/2.12 % (2924)Time elapsed: 0.074 s
% 6.45/2.12 % (2924)Instructions burned: 253 (million)
% 6.45/2.12 % (2924)------------------------------
% 6.45/2.12 % (2924)------------------------------
% 6.45/2.13 % (2922)Instruction limit reached!
% 6.45/2.13 % (2922)------------------------------
% 6.45/2.13 % (2922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.45/2.13 % (2922)Termination reason: Unknown
% 6.45/2.13 % (2922)Termination phase: Saturation
% 6.45/2.13
% 6.45/2.13 % (2922)Memory used [KB]: 8315
% 6.45/2.13 % (2922)Time elapsed: 0.091 s
% 6.45/2.13 % (2922)Instructions burned: 346 (million)
% 6.45/2.13 % (2922)------------------------------
% 6.45/2.13 % (2922)------------------------------
% 6.45/2.13 % (2930)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_2668 for (2994ds/134Mi)
% 6.45/2.14 % (2931)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_2668 for (2994ds/298Mi)
% 6.45/2.15 % (2927)Instruction limit reached!
% 6.45/2.15 % (2927)------------------------------
% 6.45/2.15 % (2927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.45/2.15 % (2927)Termination reason: Unknown
% 6.45/2.15 % (2927)Termination phase: Property scanning
% 6.45/2.15
% 6.45/2.15 % (2927)Memory used [KB]: 5245
% 6.45/2.15 % (2927)Time elapsed: 0.058 s
% 6.45/2.15 % (2927)Instructions burned: 202 (million)
% 6.45/2.15 % (2927)------------------------------
% 6.45/2.15 % (2927)------------------------------
% 6.45/2.16 % (2932)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_2668 for (2994ds/192Mi)
% 6.45/2.17 % (2930)Instruction limit reached!
% 6.45/2.17 % (2930)------------------------------
% 6.45/2.17 % (2930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.45/2.17 % (2930)Termination reason: Unknown
% 6.45/2.17 % (2930)Termination phase: Property scanning
% 6.45/2.17
% 6.45/2.17 % (2930)Memory used [KB]: 2814
% 6.45/2.17 % (2930)Time elapsed: 0.036 s
% 6.45/2.17 % (2930)Instructions burned: 137 (million)
% 6.45/2.17 % (2930)------------------------------
% 6.45/2.17 % (2930)------------------------------
% 6.45/2.17 % (2929)Instruction limit reached!
% 6.45/2.17 % (2929)------------------------------
% 6.45/2.17 % (2929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.45/2.17 % (2929)Termination reason: Unknown
% 6.45/2.17 % (2929)Termination phase: Saturation
% 6.45/2.17
% 6.45/2.17 % (2929)Memory used [KB]: 7547
% 6.45/2.17 % (2929)Time elapsed: 0.072 s
% 6.45/2.17 % (2929)Instructions burned: 283 (million)
% 6.45/2.17 % (2929)------------------------------
% 6.45/2.17 % (2929)------------------------------
% 6.45/2.18 % (2933)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_2668 for (2994ds/258Mi)
% 6.45/2.18 % (2934)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_2668 for (2994ds/90Mi)
% 6.45/2.19 % (2928)Instruction limit reached!
% 6.45/2.19 % (2928)------------------------------
% 6.45/2.19 % (2928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.45/2.19 % (2928)Termination reason: Unknown
% 6.45/2.19 % (2928)Termination phase: Saturation
% 6.45/2.19
% 6.45/2.19 % (2928)Memory used [KB]: 7803
% 6.45/2.19 % (2928)Time elapsed: 0.095 s
% 6.45/2.19 % (2928)Instructions burned: 341 (million)
% 6.45/2.19 % (2928)------------------------------
% 6.45/2.19 % (2928)------------------------------
% 7.00/2.20 % (2935)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_2668 for (2994ds/231Mi)
% 7.00/2.21 % (2934)Instruction limit reached!
% 7.00/2.21 % (2934)------------------------------
% 7.00/2.21 % (2934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.00/2.21 % (2934)Termination reason: Unknown
% 7.00/2.21 % (2934)Termination phase: Preprocessing 3
% 7.00/2.21
% 7.00/2.21 % (2934)Memory used [KB]: 2686
% 7.00/2.21 % (2934)Time elapsed: 0.026 s
% 7.00/2.21 % (2934)Instructions burned: 91 (million)
% 7.00/2.21 % (2934)------------------------------
% 7.00/2.21 % (2934)------------------------------
% 7.00/2.21 % (2932)Instruction limit reached!
% 7.00/2.21 % (2932)------------------------------
% 7.00/2.21 % (2932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.00/2.21 % (2932)Termination reason: Unknown
% 7.00/2.21 % (2932)Termination phase: Saturation
% 7.00/2.21
% 7.00/2.21 % (2932)Memory used [KB]: 7547
% 7.00/2.21 % (2932)Time elapsed: 0.051 s
% 7.00/2.21 % (2932)Instructions burned: 193 (million)
% 7.00/2.21 % (2932)------------------------------
% 7.00/2.21 % (2932)------------------------------
% 7.00/2.21 % (2931)Instruction limit reached!
% 7.00/2.21 % (2931)------------------------------
% 7.00/2.21 % (2931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.00/2.21 % (2931)Termination reason: Unknown
% 7.00/2.21 % (2931)Termination phase: Saturation
% 7.00/2.21
% 7.00/2.21 % (2931)Memory used [KB]: 7547
% 7.00/2.21 % (2931)Time elapsed: 0.076 s
% 7.00/2.21 % (2931)Instructions burned: 299 (million)
% 7.00/2.21 % (2931)------------------------------
% 7.00/2.21 % (2931)------------------------------
% 7.00/2.22 % (2936)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_2668 for (2993ds/458Mi)
% 7.00/2.22 % (2937)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_2668 for (2993ds/31Mi)
% 7.00/2.22 % (2938)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_2668 for (2993ds/297Mi)
% 7.00/2.23 % (2937)Instruction limit reached!
% 7.00/2.23 % (2937)------------------------------
% 7.00/2.23 % (2937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.00/2.23 % (2937)Termination reason: Unknown
% 7.00/2.23 % (2937)Termination phase: shuffling
% 7.00/2.23
% 7.00/2.23 % (2937)Memory used [KB]: 2046
% 7.00/2.23 % (2937)Time elapsed: 0.010 s
% 7.00/2.23 % (2937)Instructions burned: 32 (million)
% 7.00/2.23 % (2937)------------------------------
% 7.00/2.23 % (2937)------------------------------
% 7.00/2.24 % (2939)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_2668 for (2993ds/987Mi)
% 7.00/2.24 % (2933)Instruction limit reached!
% 7.00/2.24 % (2933)------------------------------
% 7.00/2.24 % (2933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.00/2.24 % (2933)Termination reason: Unknown
% 7.00/2.24 % (2933)Termination phase: Saturation
% 7.00/2.24
% 7.00/2.24 % (2933)Memory used [KB]: 7931
% 7.00/2.24 % (2933)Time elapsed: 0.069 s
% 7.00/2.24 % (2933)Instructions burned: 258 (million)
% 7.00/2.24 % (2933)------------------------------
% 7.00/2.24 % (2933)------------------------------
% 7.00/2.25 % (2940)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_2668 for (2993ds/182Mi)
% 7.00/2.26 % (2926)Instruction limit reached!
% 7.00/2.26 % (2926)------------------------------
% 7.00/2.26 % (2926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.00/2.26 % (2926)Termination reason: Unknown
% 7.00/2.26 % (2926)Termination phase: Saturation
% 7.00/2.26
% 7.00/2.26 % (2926)Memory used [KB]: 10106
% 7.00/2.26 % (2926)Time elapsed: 0.177 s
% 7.00/2.26 % (2926)Instructions burned: 617 (million)
% 7.00/2.26 % (2926)------------------------------
% 7.00/2.26 % (2926)------------------------------
% 7.00/2.26 % (2935)Instruction limit reached!
% 7.00/2.26 % (2935)------------------------------
% 7.00/2.26 % (2935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.00/2.26 % (2935)Termination reason: Unknown
% 7.00/2.26 % (2935)Termination phase: Saturation
% 7.00/2.26
% 7.00/2.26 % (2935)Memory used [KB]: 8443
% 7.00/2.26 % (2935)Time elapsed: 0.061 s
% 7.00/2.26 % (2935)Instructions burned: 232 (million)
% 7.00/2.26 % (2935)------------------------------
% 7.00/2.26 % (2935)------------------------------
% 7.00/2.27 % (2941)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_2668 for (2993ds/182Mi)
% 7.00/2.27 % (2942)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_2668 for (2993ds/154Mi)
% 7.00/2.30 % (2938)Instruction limit reached!
% 7.00/2.30 % (2938)------------------------------
% 7.00/2.30 % (2938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.00/2.30 % (2938)Termination reason: Unknown
% 7.00/2.30 % (2938)Termination phase: Saturation
% 7.00/2.30
% 7.00/2.30 % (2938)Memory used [KB]: 7547
% 7.00/2.30 % (2938)Time elapsed: 0.074 s
% 7.00/2.30 % (2938)Instructions burned: 298 (million)
% 7.00/2.30 % (2938)------------------------------
% 7.00/2.30 % (2938)------------------------------
% 7.72/2.30 % (2940)Instruction limit reached!
% 7.72/2.30 % (2940)------------------------------
% 7.72/2.30 % (2940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.30 % (2940)Termination reason: Unknown
% 7.72/2.30 % (2940)Termination phase: Saturation
% 7.72/2.30
% 7.72/2.30 % (2940)Memory used [KB]: 7419
% 7.72/2.30 % (2940)Time elapsed: 0.048 s
% 7.72/2.30 % (2940)Instructions burned: 185 (million)
% 7.72/2.30 % (2940)------------------------------
% 7.72/2.30 % (2940)------------------------------
% 7.72/2.31 % (2942)Instruction limit reached!
% 7.72/2.31 % (2942)------------------------------
% 7.72/2.31 % (2942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.31 % (2942)Termination reason: Unknown
% 7.72/2.31 % (2942)Termination phase: Property scanning
% 7.72/2.31
% 7.72/2.31 % (2942)Memory used [KB]: 2686
% 7.72/2.31 % (2942)Time elapsed: 0.040 s
% 7.72/2.31 % (2942)Instructions burned: 157 (million)
% 7.72/2.31 % (2942)------------------------------
% 7.72/2.31 % (2942)------------------------------
% 7.72/2.31 % (2943)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_2668 for (2992ds/79Mi)
% 7.72/2.31 % (2944)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_2668 for (2992ds/216Mi)
% 7.72/2.31 % (2945)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_2668 for (2992ds/114Mi)
% 7.72/2.32 % (2941)Instruction limit reached!
% 7.72/2.32 % (2941)------------------------------
% 7.72/2.32 % (2941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.32 % (2941)Termination reason: Unknown
% 7.72/2.32 % (2941)Termination phase: Property scanning
% 7.72/2.32
% 7.72/2.32 % (2941)Memory used [KB]: 5117
% 7.72/2.32 % (2941)Time elapsed: 0.052 s
% 7.72/2.32 % (2941)Instructions burned: 183 (million)
% 7.72/2.32 % (2941)------------------------------
% 7.72/2.32 % (2941)------------------------------
% 7.72/2.32 % (2908)Instruction limit reached!
% 7.72/2.32 % (2908)------------------------------
% 7.72/2.32 % (2908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.32 % (2908)Termination reason: Unknown
% 7.72/2.32 % (2908)Termination phase: Saturation
% 7.72/2.32
% 7.72/2.32 % (2908)Memory used [KB]: 12665
% 7.72/2.32 % (2908)Time elapsed: 0.421 s
% 7.72/2.32 % (2908)Instructions burned: 1087 (million)
% 7.72/2.32 % (2908)------------------------------
% 7.72/2.32 % (2908)------------------------------
% 7.72/2.33 % (2943)Instruction limit reached!
% 7.72/2.33 % (2943)------------------------------
% 7.72/2.33 % (2943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.33 % (2943)Termination reason: Unknown
% 7.72/2.33 % (2943)Termination phase: Property scanning
% 7.72/2.33
% 7.72/2.33 % (2943)Memory used [KB]: 2558
% 7.72/2.33 % (2943)Time elapsed: 0.022 s
% 7.72/2.33 % (2943)Instructions burned: 79 (million)
% 7.72/2.33 % (2943)------------------------------
% 7.72/2.33 % (2943)------------------------------
% 7.72/2.33 % (2946)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_2668 for (2992ds/922Mi)
% 7.72/2.33 % (2947)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_2668 for (2992ds/182Mi)
% 7.72/2.34 % (2948)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_2668 for (2992ds/164Mi)
% 7.72/2.34 % (2936)Instruction limit reached!
% 7.72/2.34 % (2936)------------------------------
% 7.72/2.34 % (2936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.34 % (2936)Termination reason: Unknown
% 7.72/2.34 % (2936)Termination phase: Saturation
% 7.72/2.34
% 7.72/2.34 % (2936)Memory used [KB]: 9722
% 7.72/2.34 % (2936)Time elapsed: 0.126 s
% 7.72/2.34 % (2936)Instructions burned: 460 (million)
% 7.72/2.34 % (2936)------------------------------
% 7.72/2.34 % (2936)------------------------------
% 7.72/2.34 % (2945)Instruction limit reached!
% 7.72/2.34 % (2945)------------------------------
% 7.72/2.34 % (2945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.34 % (2945)Termination reason: Unknown
% 7.72/2.34 % (2945)Termination phase: Property scanning
% 7.72/2.34
% 7.72/2.34 % (2945)Memory used [KB]: 2686
% 7.72/2.34 % (2945)Time elapsed: 0.031 s
% 7.72/2.34 % (2945)Instructions burned: 117 (million)
% 7.72/2.34 % (2945)------------------------------
% 7.72/2.34 % (2945)------------------------------
% 7.72/2.35 % (2949)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_2668 for (2992ds/50Mi)
% 7.72/2.35 % (2950)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_2668 for (2992ds/368Mi)
% 7.72/2.36 % (2944)Instruction limit reached!
% 7.72/2.36 % (2944)------------------------------
% 7.72/2.36 % (2944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.36 % (2944)Termination reason: Unknown
% 7.72/2.36 % (2944)Termination phase: Property scanning
% 7.72/2.36
% 7.72/2.36 % (2944)Memory used [KB]: 2814
% 7.72/2.36 % (2944)Time elapsed: 0.055 s
% 7.72/2.36 % (2944)Instructions burned: 220 (million)
% 7.72/2.36 % (2944)------------------------------
% 7.72/2.36 % (2944)------------------------------
% 7.72/2.37 % (2949)Instruction limit reached!
% 7.72/2.37 % (2949)------------------------------
% 7.72/2.37 % (2949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.37 % (2949)Termination reason: Unknown
% 7.72/2.37 % (2949)Termination phase: shuffling
% 7.72/2.37
% 7.72/2.37 % (2949)Memory used [KB]: 2430
% 7.72/2.37 % (2949)Time elapsed: 0.015 s
% 7.72/2.37 % (2949)Instructions burned: 53 (million)
% 7.72/2.37 % (2949)------------------------------
% 7.72/2.37 % (2949)------------------------------
% 7.72/2.37 % (2951)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_2668 for (2992ds/1021Mi)
% 7.72/2.37 % (2952)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_2668 for (2992ds/267Mi)
% 7.72/2.38 % (2947)Instruction limit reached!
% 7.72/2.38 % (2947)------------------------------
% 7.72/2.38 % (2947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.38 % (2947)Termination reason: Unknown
% 7.72/2.38 % (2947)Termination phase: Saturation
% 7.72/2.38
% 7.72/2.38 % (2947)Memory used [KB]: 7547
% 7.72/2.38 % (2947)Time elapsed: 0.047 s
% 7.72/2.38 % (2947)Instructions burned: 184 (million)
% 7.72/2.38 % (2947)------------------------------
% 7.72/2.38 % (2947)------------------------------
% 7.72/2.38 % (2948)Instruction limit reached!
% 7.72/2.38 % (2948)------------------------------
% 7.72/2.38 % (2948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.38 % (2948)Termination reason: Unknown
% 7.72/2.38 % (2948)Termination phase: Function definition elimination
% 7.72/2.38
% 7.72/2.38 % (2948)Memory used [KB]: 2814
% 7.72/2.38 % (2948)Time elapsed: 0.042 s
% 7.72/2.38 % (2948)Instructions burned: 164 (million)
% 7.72/2.38 % (2948)------------------------------
% 7.72/2.38 % (2948)------------------------------
% 7.72/2.39 % (2953)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_2668 for (2992ds/204Mi)
% 7.72/2.39 % (2954)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_2668 for (2992ds/26Mi)
% 7.72/2.39 % (2954)Instruction limit reached!
% 7.72/2.39 % (2954)------------------------------
% 7.72/2.39 % (2954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.39 % (2954)Termination reason: Unknown
% 7.72/2.39 % (2954)Termination phase: shuffling
% 7.72/2.39
% 7.72/2.39 % (2954)Memory used [KB]: 1918
% 7.72/2.39 % (2954)Time elapsed: 0.008 s
% 7.72/2.39 % (2954)Instructions burned: 26 (million)
% 7.72/2.39 % (2954)------------------------------
% 7.72/2.39 % (2954)------------------------------
% 8.35/2.40 % (2955)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_2668 for (2991ds/53Mi)
% 8.35/2.42 % (2955)Instruction limit reached!
% 8.35/2.42 % (2955)------------------------------
% 8.35/2.42 % (2955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.35/2.42 % (2955)Termination reason: Unknown
% 8.35/2.42 % (2955)Termination phase: shuffling
% 8.35/2.42
% 8.35/2.42 % (2955)Memory used [KB]: 2558
% 8.35/2.42 % (2955)Time elapsed: 0.016 s
% 8.35/2.42 % (2955)Instructions burned: 54 (million)
% 8.35/2.42 % (2955)------------------------------
% 8.35/2.42 % (2955)------------------------------
% 8.35/2.43 % (2956)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_2668 for (2991ds/4436Mi)
% 8.35/2.44 % (2953)Instruction limit reached!
% 8.35/2.44 % (2953)------------------------------
% 8.35/2.44 % (2953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.35/2.44 % (2953)Termination reason: Unknown
% 8.35/2.44 % (2953)Termination phase: Property scanning
% 8.35/2.44
% 8.35/2.44 % (2953)Memory used [KB]: 2942
% 8.35/2.44 % (2953)Time elapsed: 0.053 s
% 8.35/2.44 % (2953)Instructions burned: 207 (million)
% 8.35/2.44 % (2953)------------------------------
% 8.35/2.44 % (2953)------------------------------
% 8.35/2.44 % (2952)Instruction limit reached!
% 8.35/2.44 % (2952)------------------------------
% 8.35/2.44 % (2952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.35/2.44 % (2952)Termination reason: Unknown
% 8.35/2.44 % (2952)Termination phase: Saturation
% 8.35/2.44
% 8.35/2.44 % (2952)Memory used [KB]: 7547
% 8.35/2.44 % (2952)Time elapsed: 0.068 s
% 8.35/2.44 % (2952)Instructions burned: 269 (million)
% 8.35/2.44 % (2952)------------------------------
% 8.35/2.44 % (2952)------------------------------
% 8.35/2.45 % (2957)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_2668 for (2991ds/1539Mi)
% 8.35/2.45 % (2958)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_2668 for (2991ds/408Mi)
% 8.35/2.45 % (2950)Instruction limit reached!
% 8.35/2.45 % (2950)------------------------------
% 8.35/2.45 % (2950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.35/2.45 % (2950)Termination reason: Unknown
% 8.35/2.45 % (2950)Termination phase: Saturation
% 8.35/2.45
% 8.35/2.45 % (2950)Memory used [KB]: 9338
% 8.35/2.45 % (2950)Time elapsed: 0.099 s
% 8.35/2.45 % (2950)Instructions burned: 370 (million)
% 8.35/2.45 % (2950)------------------------------
% 8.35/2.45 % (2950)------------------------------
% 8.35/2.46 % (2959)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_2668 for (2991ds/5205Mi)
% 8.35/2.48 % (2939)Instruction limit reached!
% 8.35/2.48 % (2939)------------------------------
% 8.35/2.48 % (2939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.35/2.48 % (2939)Termination reason: Unknown
% 8.35/2.48 % (2939)Termination phase: Saturation
% 8.35/2.48
% 8.35/2.48 % (2939)Memory used [KB]: 16375
% 8.35/2.48 % (2939)Time elapsed: 0.250 s
% 8.35/2.48 % (2939)Instructions burned: 989 (million)
% 8.35/2.48 % (2939)------------------------------
% 8.35/2.48 % (2939)------------------------------
% 8.35/2.50 % (2960)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_2668 for (2990ds/1913Mi)
% 8.88/2.57 % (2958)Instruction limit reached!
% 8.88/2.57 % (2958)------------------------------
% 8.88/2.57 % (2958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.88/2.57 % (2958)Termination reason: Unknown
% 8.88/2.57 % (2958)Termination phase: Saturation
% 8.88/2.57
% 8.88/2.57 % (2958)Memory used [KB]: 11385
% 8.88/2.57 % (2958)Time elapsed: 0.120 s
% 8.88/2.57 % (2958)Instructions burned: 410 (million)
% 8.88/2.57 % (2958)------------------------------
% 8.88/2.57 % (2958)------------------------------
% 8.88/2.58 % (2961)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_2668 for (2990ds/4350Mi)
% 9.00/2.61 % (2946)Instruction limit reached!
% 9.00/2.61 % (2946)------------------------------
% 9.00/2.61 % (2946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.00/2.61 % (2946)Termination reason: Unknown
% 9.00/2.61 % (2946)Termination phase: Saturation
% 9.00/2.61
% 9.00/2.61 % (2946)Memory used [KB]: 12409
% 9.00/2.61 % (2946)Time elapsed: 0.304 s
% 9.00/2.61 % (2946)Instructions burned: 922 (million)
% 9.00/2.61 % (2946)------------------------------
% 9.00/2.61 % (2946)------------------------------
% 9.00/2.62 % (2962)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_2668 for (2989ds/68Mi)
% 9.00/2.64 % (2962)Instruction limit reached!
% 9.00/2.64 % (2962)------------------------------
% 9.00/2.64 % (2962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.00/2.64 % (2962)Termination reason: Unknown
% 9.00/2.64 % (2962)Termination phase: Property scanning
% 9.00/2.64
% 9.00/2.64 % (2962)Memory used [KB]: 2558
% 9.00/2.64 % (2962)Time elapsed: 0.020 s
% 9.00/2.64 % (2962)Instructions burned: 71 (million)
% 9.00/2.64 % (2962)------------------------------
% 9.00/2.64 % (2962)------------------------------
% 9.00/2.65 % (2963)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_2668 for (2989ds/358Mi)
% 9.00/2.69 % (2951)Instruction limit reached!
% 9.00/2.69 % (2951)------------------------------
% 9.00/2.69 % (2951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.00/2.69 % (2951)Termination reason: Unknown
% 9.00/2.69 % (2951)Termination phase: Saturation
% 9.00/2.69
% 9.00/2.69 % (2951)Memory used [KB]: 12920
% 9.00/2.69 % (2951)Time elapsed: 0.320 s
% 9.00/2.69 % (2951)Instructions burned: 1024 (million)
% 9.00/2.69 % (2951)------------------------------
% 9.00/2.69 % (2951)------------------------------
% 9.66/2.70 % (2964)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_2668 for (2988ds/31Mi)
% 9.66/2.71 % (2964)Instruction limit reached!
% 9.66/2.71 % (2964)------------------------------
% 9.66/2.71 % (2964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.66/2.71 % (2964)Termination reason: Unknown
% 9.66/2.71 % (2964)Termination phase: shuffling
% 9.66/2.71
% 9.66/2.71 % (2964)Memory used [KB]: 2174
% 9.66/2.71 % (2964)Time elapsed: 0.010 s
% 9.66/2.71 % (2964)Instructions burned: 31 (million)
% 9.66/2.71 % (2964)------------------------------
% 9.66/2.71 % (2964)------------------------------
% 9.66/2.72 % (2965)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_2668 for (2988ds/279Mi)
% 9.66/2.74 % (2963)Instruction limit reached!
% 9.66/2.74 % (2963)------------------------------
% 9.66/2.74 % (2963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.66/2.74 % (2963)Termination reason: Unknown
% 9.66/2.74 % (2963)Termination phase: Saturation
% 9.66/2.74
% 9.66/2.74 % (2963)Memory used [KB]: 8443
% 9.66/2.74 % (2963)Time elapsed: 0.094 s
% 9.66/2.74 % (2963)Instructions burned: 358 (million)
% 9.66/2.74 % (2963)------------------------------
% 9.66/2.74 % (2963)------------------------------
% 9.66/2.75 % (2966)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_2668 for (2988ds/258Mi)
% 9.66/2.79 % (2965)Instruction limit reached!
% 9.66/2.79 % (2965)------------------------------
% 9.66/2.79 % (2965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.66/2.79 % (2965)Termination reason: Unknown
% 9.66/2.79 % (2965)Termination phase: Saturation
% 9.66/2.79
% 9.66/2.79 % (2965)Memory used [KB]: 7547
% 9.66/2.79 % (2965)Time elapsed: 0.070 s
% 9.66/2.79 % (2965)Instructions burned: 279 (million)
% 9.66/2.79 % (2965)------------------------------
% 9.66/2.79 % (2965)------------------------------
% 9.86/2.80 % (2967)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_2668 for (2987ds/26Mi)
% 9.86/2.81 % (2967)Instruction limit reached!
% 9.86/2.81 % (2967)------------------------------
% 9.86/2.81 % (2967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.86/2.81 % (2967)Termination reason: Unknown
% 9.86/2.81 % (2967)Termination phase: shuffling
% 9.86/2.81
% 9.86/2.81 % (2967)Memory used [KB]: 1918
% 9.86/2.81 % (2967)Time elapsed: 0.008 s
% 9.86/2.81 % (2967)Instructions burned: 26 (million)
% 9.86/2.81 % (2967)------------------------------
% 9.86/2.81 % (2967)------------------------------
% 9.86/2.82 % (2968)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_2668 for (2987ds/995Mi)
% 9.86/2.82 % (2966)Instruction limit reached!
% 9.86/2.82 % (2966)------------------------------
% 9.86/2.82 % (2966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.86/2.82 % (2966)Termination reason: Unknown
% 9.86/2.82 % (2966)Termination phase: Saturation
% 9.86/2.82
% 9.86/2.82 % (2966)Memory used [KB]: 8315
% 9.86/2.82 % (2966)Time elapsed: 0.069 s
% 9.86/2.82 % (2966)Instructions burned: 260 (million)
% 9.86/2.82 % (2966)------------------------------
% 9.86/2.82 % (2966)------------------------------
% 9.86/2.83 % (2969)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_2668 for (2987ds/373Mi)
% 9.95/2.92 % (2957)Instruction limit reached!
% 9.95/2.92 % (2957)------------------------------
% 9.95/2.92 % (2957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.95/2.92 % (2957)Termination reason: Unknown
% 9.95/2.92 % (2957)Termination phase: Saturation
% 9.95/2.92
% 9.95/2.92 % (2957)Memory used [KB]: 11001
% 9.95/2.92 % (2957)Time elapsed: 0.469 s
% 9.95/2.92 % (2957)Instructions burned: 1539 (million)
% 9.95/2.92 % (2957)------------------------------
% 9.95/2.92 % (2957)------------------------------
% 9.95/2.92 % (2969)Instruction limit reached!
% 9.95/2.92 % (2969)------------------------------
% 9.95/2.92 % (2969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.95/2.92 % (2969)Termination reason: Unknown
% 9.95/2.92 % (2969)Termination phase: Saturation
% 9.95/2.92
% 9.95/2.92 % (2969)Memory used [KB]: 9338
% 9.95/2.92 % (2969)Time elapsed: 0.099 s
% 9.95/2.92 % (2969)Instructions burned: 374 (million)
% 9.95/2.92 % (2969)------------------------------
% 9.95/2.92 % (2969)------------------------------
% 9.95/2.93 % (2970)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_2668 for (2986ds/253Mi)
% 9.95/2.93 % (2971)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_2668 for (2986ds/832Mi)
% 9.95/2.99 % (2970)Instruction limit reached!
% 9.95/2.99 % (2970)------------------------------
% 9.95/2.99 % (2970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.95/2.99 % (2970)Termination reason: Unknown
% 9.95/2.99 % (2970)Termination phase: Saturation
% 9.95/2.99
% 9.95/2.99 % (2970)Memory used [KB]: 7547
% 9.95/2.99 % (2970)Time elapsed: 0.067 s
% 9.95/2.99 % (2970)Instructions burned: 256 (million)
% 9.95/2.99 % (2970)------------------------------
% 9.95/2.99 % (2970)------------------------------
% 9.95/3.00 % (2972)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_2668 for (2985ds/668Mi)
% 13.03/3.03 % (2956)First to succeed.
% 13.03/3.04 % (2956)Refutation found. Thanks to Tanya!
% 13.03/3.04 % SZS status Theorem for DTF2THF_2668
% 13.03/3.04 % SZS output start Proof for DTF2THF_2668
% 13.03/3.04 thf(func_def_0, type, in: $i > $i > $o).
% 13.03/3.04 thf(func_def_1, type, exu: ($i > $o) > $o).
% 13.03/3.04 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 13.03/3.04 thf(func_def_8, type, powerset: $i > $i).
% 13.03/3.04 thf(func_def_10, type, setunion: $i > $i).
% 13.03/3.04 thf(func_def_19, type, descr: ($i > $o) > $i).
% 13.03/3.04 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 13.03/3.04 thf(func_def_26, type, prop2set: $o > $i).
% 13.03/3.04 thf(func_def_36, type, nonempty: $i > $o).
% 13.03/3.04 thf(func_def_69, type, set2prop: $i > $o).
% 13.03/3.04 thf(func_def_88, type, subset: $i > $i > $o).
% 13.03/3.04 thf(func_def_89, type, disjoint: $i > $i > $o).
% 13.03/3.04 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 13.03/3.04 thf(func_def_114, type, binunion: $i > $i > $i).
% 13.03/3.04 thf(func_def_122, type, binintersect: $i > $i > $i).
% 13.03/3.04 thf(func_def_135, type, regular: $i > $o).
% 13.03/3.04 thf(func_def_136, type, setminus: $i > $i > $i).
% 13.03/3.04 thf(func_def_147, type, symdiff: $i > $i > $i).
% 13.03/3.04 thf(func_def_153, type, iskpair: $i > $o).
% 13.03/3.04 thf(func_def_158, type, kpair: $i > $i > $i).
% 13.03/3.04 thf(func_def_160, type, cartprod: $i > $i > $i).
% 13.03/3.04 thf(func_def_177, type, singleton: $i > $o).
% 13.03/3.04 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 13.03/3.04 thf(func_def_184, type, atmost1p: $i > $o).
% 13.03/3.04 thf(func_def_185, type, atleast2p: $i > $o).
% 13.03/3.04 thf(func_def_186, type, atmost2p: $i > $o).
% 13.03/3.04 thf(func_def_187, type, upairsetp: $i > $o).
% 13.03/3.04 thf(func_def_191, type, kfst: $i > $i).
% 13.03/3.04 thf(func_def_203, type, ksnd: $i > $i).
% 13.03/3.04 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 13.03/3.04 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 13.03/3.04 thf(func_def_222, type, func: $i > $i > $i > $o).
% 13.03/3.04 thf(func_def_223, type, funcSet: $i > $i > $i).
% 13.03/3.04 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 13.03/3.04 thf(func_def_259, type, if: $i > $o > $i > $i > $i).
% 13.03/3.04 thf(func_def_323, type, breln1: $i > $i > $o).
% 13.03/3.04 thf(func_def_325, type, breln1Set: $i > $i).
% 13.03/3.04 thf(func_def_327, type, transitive: $i > $i > $o).
% 13.03/3.04 thf(func_def_328, type, antisymmetric: $i > $i > $o).
% 13.03/3.04 thf(func_def_329, type, reflexive: $i > $i > $o).
% 13.03/3.04 thf(func_def_330, type, refltransitive: $i > $i > $o).
% 13.03/3.04 thf(func_def_331, type, refllinearorder: $i > $i > $o).
% 13.03/3.04 thf(func_def_332, type, reflwellordering: $i > $i > $o).
% 13.03/3.04 thf(func_def_338, type, breln1invset: $i > $i > $i).
% 13.03/3.04 thf(func_def_352, type, sP0: $i > $i > $i > $o).
% 13.03/3.04 thf(func_def_353, type, sP1: $i > $i > $o).
% 13.03/3.04 thf(func_def_354, type, sP2: $i > $i > $o).
% 13.03/3.04 thf(func_def_355, type, sP3: $i > $i > $o).
% 13.03/3.04 thf(func_def_356, type, sP4: $i > $i > $o).
% 13.03/3.04 thf(func_def_357, type, sP5: $i > $o).
% 13.03/3.04 thf(func_def_359, type, sP7: $i > $i > $i > $o > $o).
% 13.03/3.04 thf(func_def_360, type, sP8: $o > $i > $i > $i > $o).
% 13.03/3.04 thf(func_def_363, type, sP11: $i > $i > $i > $i > $o).
% 13.03/3.04 thf(func_def_364, type, sP12: $i > $i > $i > $i > $o).
% 13.03/3.04 thf(func_def_365, type, sP13: $o > $i > $i > $o).
% 13.03/3.04 thf(func_def_366, type, sP14: $i > $i > $i > $o).
% 13.03/3.04 thf(func_def_367, type, sP15: $i > $i > $i > $o).
% 13.03/3.04 thf(func_def_370, type, sP18: $i > $i > $o).
% 13.03/3.04 thf(func_def_372, type, sP20: ($i > $o) > $i > $o).
% 13.03/3.04 thf(func_def_373, type, sP21: ($i > $o) > $i > $i > $o).
% 13.03/3.04 thf(func_def_375, type, sP23: $i > $i > $i > $i > $o).
% 13.03/3.04 thf(func_def_376, type, sP24: $i > $o > $i > $o).
% 13.03/3.04 thf(func_def_377, type, sP25: $i > $i > $i > $o).
% 13.03/3.04 thf(func_def_378, type, sP26: $i > ($i > $o) > ($i > $o) > $i > $o).
% 13.03/3.04 thf(func_def_379, type, sP27: ($i > $o) > $i > $o).
% 13.03/3.04 thf(func_def_381, type, sP29: $i > ($i > $o) > $o).
% 13.03/3.04 thf(func_def_382, type, sP30: $i > ($i > $o) > $i > $o).
% 13.03/3.04 thf(func_def_383, type, sP31: $i > ($i > $o) > $o).
% 13.03/3.04 thf(func_def_385, type, sP33: ($i > $o) > $i > $o).
% 13.03/3.04 thf(func_def_386, type, sP34: $i > $i > ($i > $o) > $i > $o).
% 13.03/3.04 thf(func_def_389, type, sP37: $i > $i > $i > $o).
% 13.03/3.04 thf(func_def_390, type, sP38: $i > ($i > $i > $o) > $i > $o).
% 13.03/3.04 thf(func_def_391, type, sP39: $i > ($i > $i > $o) > $o).
% 13.03/3.04 thf(func_def_393, type, sP41: ($i > $o) > $o).
% 13.03/3.04 thf(func_def_394, type, sP42: $i > ($i > $o) > $o).
% 13.03/3.04 thf(func_def_396, type, sP44: $i > $i > $i > $o).
% 13.03/3.04 thf(func_def_397, type, sP45: $i > $i > $o > $o).
% 13.03/3.04 thf(func_def_399, type, sP47: $i > ($i > $o) > $o).
% 13.03/3.04 thf(func_def_400, type, sP48: ($i > $o) > $i > $o).
% 13.03/3.04 thf(func_def_401, type, sP49: $i > $i > $i > $o).
% 13.03/3.04 thf(func_def_402, type, sP50: $i > $i > $i > $o).
% 13.03/3.04 thf(func_def_404, type, sP52: $i > ($i > $o) > $o).
% 13.03/3.04 thf(func_def_406, type, sP54: ($i > $o) > $o).
% 13.03/3.04 thf(func_def_407, type, sP55: $i > ($i > $o) > $o).
% 13.03/3.04 thf(func_def_408, type, sP56: $i > ($i > $o) > $o).
% 13.03/3.04 thf(func_def_409, type, sP57: ($i > $o) > $i > $o).
% 13.03/3.04 thf(func_def_411, type, sP59: ($i > $o) > $o).
% 13.03/3.04 thf(func_def_412, type, sP60: $i > $i > $i > $o).
% 13.03/3.04 thf(func_def_414, type, sP62: $i > $i > $i > $i > $o).
% 13.03/3.04 thf(func_def_415, type, sP63: $i > $i > $i > $o).
% 13.03/3.04 thf(func_def_416, type, sP64: $i > $i > $o).
% 13.03/3.04 thf(func_def_418, type, sP66: ($i > $o) > $i > $o).
% 13.03/3.04 thf(func_def_419, type, sP67: $i > $i > ($i > $o) > $i > $o).
% 13.03/3.04 thf(func_def_420, type, sP68: $i > ($i > $i) > $i > $o).
% 13.03/3.04 thf(func_def_423, type, sP71: ($i > $o) > $o).
% 13.03/3.04 thf(func_def_424, type, sP72: $i > ($i > $o) > $i > $o).
% 13.03/3.04 thf(func_def_425, type, sP73: $i > ($i > $o) > $o).
% 13.03/3.04 thf(func_def_428, type, sP76: $i > $i > $o).
% 13.03/3.04 thf(func_def_430, type, sP78: $i > $i > ($i > $i) > $o).
% 13.03/3.04 thf(func_def_433, type, sP81: $i > $o).
% 13.03/3.04 thf(func_def_434, type, sP82: $i > $o).
% 13.03/3.04 thf(func_def_435, type, sP83: $i > $i > $i > $o).
% 13.03/3.04 thf(func_def_436, type, sP84: $i > ($i > $i > $o) > $i > $o).
% 13.03/3.04 thf(func_def_437, type, sP85: $i > $i > ($i > $i > $o) > $o).
% 13.03/3.04 thf(func_def_438, type, sP86: $i > $o).
% 13.03/3.04 thf(func_def_439, type, sP87: $i > $i > $i > $o).
% 13.03/3.04 thf(func_def_440, type, sP88: $o > $i > $i > $o).
% 13.03/3.04 thf(func_def_441, type, sP89: $i > $i > $i > $o).
% 13.03/3.04 thf(func_def_442, type, sP90: ($i > $o) > $o).
% 13.03/3.04 thf(func_def_443, type, sP91: $i > $i > $i > $o).
% 13.03/3.04 thf(func_def_444, type, sP92: $i > $i > $i > $o).
% 13.03/3.04 thf(func_def_456, type, sK104: $i > $i).
% 13.03/3.04 thf(func_def_457, type, sK105: $i > $i).
% 13.03/3.04 thf(func_def_458, type, sK106: $i > $i).
% 13.03/3.04 thf(func_def_459, type, sK107: $i > $i).
% 13.03/3.04 thf(func_def_460, type, sK108: $i > $i > $i).
% 13.03/3.04 thf(func_def_461, type, sK109: $i > $i > $i).
% 13.03/3.04 thf(func_def_462, type, sK110: $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_463, type, sK111: $i > $i > $i).
% 13.03/3.04 thf(func_def_464, type, sK112: $i > $i > $i).
% 13.03/3.04 thf(func_def_465, type, sK113: $i > $i > $i).
% 13.03/3.04 thf(func_def_466, type, sK114: $i > $i > $i).
% 13.03/3.04 thf(func_def_467, type, sK115: $i > $i > $i).
% 13.03/3.04 thf(func_def_468, type, sK116: $i > $i > $i).
% 13.03/3.04 thf(func_def_469, type, sK117: $i > $i > $i).
% 13.03/3.04 thf(func_def_470, type, sK118: $i > $i > $i).
% 13.03/3.04 thf(func_def_471, type, sK119: $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_472, type, sK120: $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_474, type, sK122: $i > $i).
% 13.03/3.04 thf(func_def_481, type, sK129: $i > $o).
% 13.03/3.04 thf(func_def_482, type, sK130: $i > $o).
% 13.03/3.04 thf(func_def_483, type, sK131: ($i > $o) > ($i > $o) > $i).
% 13.03/3.04 thf(func_def_484, type, sK132: ($i > $o) > ($i > $o) > $i).
% 13.03/3.04 thf(func_def_502, type, sK150: $i > $i).
% 13.03/3.04 thf(func_def_525, type, sK173: $i > $i > $i).
% 13.03/3.04 thf(func_def_548, type, sK196: $i > $i > $o).
% 13.03/3.04 thf(func_def_562, type, sK210: $i > $i > $i).
% 13.03/3.04 thf(func_def_579, type, sK227: $i > $i > $o).
% 13.03/3.04 thf(func_def_584, type, sK232: $i > $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_585, type, sK233: $i > $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_586, type, sK234: $i > $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_587, type, sK235: $i > $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_605, type, sK253: $i > $i > $i > $o).
% 13.03/3.04 thf(func_def_609, type, sK257: $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_610, type, sK258: $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_614, type, sK262: $i > $i > $o).
% 13.03/3.04 thf(func_def_621, type, sK269: $i > $i).
% 13.03/3.04 thf(func_def_622, type, sK270: ($i > $i) > $i > $i > $i).
% 13.03/3.04 thf(func_def_643, type, sK291: $i > $i > $o).
% 13.03/3.04 thf(func_def_656, type, sK304: $i > $i).
% 13.03/3.04 thf(func_def_657, type, sK305: ($i > $i) > $i > $i > $i).
% 13.03/3.04 thf(func_def_659, type, sK307: $i > $i > $o).
% 13.03/3.04 thf(func_def_675, type, sK323: $i > $o).
% 13.03/3.04 thf(func_def_681, type, sK329: $i > $o).
% 13.03/3.04 thf(func_def_693, type, sK341: $i > $i > $i).
% 13.03/3.04 thf(func_def_694, type, sK342: $i > $i > $i).
% 13.03/3.04 thf(func_def_699, type, sK347: ($i > $o) > $i > $i > $i).
% 13.03/3.04 thf(func_def_700, type, sK348: ($i > $o) > $i > $i > $i).
% 13.03/3.04 thf(func_def_701, type, sK349: ($i > $o) > $i > $i).
% 13.03/3.04 thf(func_def_704, type, sK352: $i > $o).
% 13.03/3.04 thf(func_def_707, type, sK355: $i > $i > $i).
% 13.03/3.04 thf(func_def_722, type, sK370: $i > $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_723, type, sK371: $i > $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_728, type, sK376: $i > $o > $i > $i).
% 13.03/3.04 thf(func_def_741, type, sK389: $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_742, type, sK390: $i > $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_746, type, sK394: $i > ($i > $o) > ($i > $o) > $i > $i).
% 13.03/3.04 thf(func_def_747, type, sK395: $i > ($i > $o) > ($i > $o) > $i > $i).
% 13.03/3.04 thf(func_def_750, type, sK398: $i > $o).
% 13.03/3.04 thf(func_def_751, type, sK399: $i > $o).
% 13.03/3.04 thf(func_def_755, type, sK403: $i > $i > $o).
% 13.03/3.04 thf(func_def_771, type, sK419: $i > $o).
% 13.03/3.04 thf(func_def_772, type, sK420: ($i > $o) > $i > $i).
% 13.03/3.04 thf(func_def_773, type, sK421: ($i > $o) > $i > $i).
% 13.03/3.04 thf(func_def_776, type, sK424: $i > $i > $o).
% 13.03/3.04 thf(func_def_789, type, sK437: $i > ($i > $o) > $i > $i).
% 13.03/3.04 thf(func_def_790, type, sK438: $i > ($i > $o) > $i > $i).
% 13.03/3.04 thf(func_def_791, type, sK439: $i > ($i > $o) > $i).
% 13.03/3.04 thf(func_def_794, type, sK442: $i > $o).
% 13.03/3.04 thf(func_def_799, type, sK447: $i > $o).
% 13.03/3.04 thf(func_def_801, type, sK449: $i > ($i > $o) > $i).
% 13.03/3.04 thf(func_def_802, type, sK450: $i > ($i > $o) > $i).
% 13.03/3.04 thf(func_def_823, type, sK471: $i > $i).
% 13.03/3.04 thf(func_def_827, type, sK475: $i > $o).
% 13.03/3.04 thf(func_def_828, type, sK476: $i > $i > ($i > $o) > $i > $i).
% 13.03/3.04 thf(func_def_829, type, sK477: $i > $i > ($i > $o) > $i > $i).
% 13.03/3.04 thf(func_def_830, type, sK478: ($i > $o) > $i > $i).
% 13.03/3.04 thf(func_def_834, type, sK482: $i > $o).
% 13.03/3.04 thf(func_def_853, type, sK501: $i > $i).
% 13.03/3.04 thf(func_def_854, type, sK502: ($i > $i) > $i > $i > $i).
% 13.03/3.04 thf(func_def_857, type, sK505: $i > $o).
% 13.03/3.04 thf(func_def_859, type, sK507: $i > ($i > $o) > $i).
% 13.03/3.04 thf(func_def_866, type, sK514: $i > $o).
% 13.03/3.04 thf(func_def_867, type, sK515: $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_868, type, sK516: $i > $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_888, type, sK536: $i > $i).
% 13.03/3.04 thf(func_def_893, type, sK541: $i > $o).
% 13.03/3.04 thf(func_def_900, type, sK548: $i > $o).
% 13.03/3.04 thf(func_def_926, type, sK574: $i > $i > $o).
% 13.03/3.04 thf(func_def_927, type, sK575: ($i > $i > $o) > $i > $i).
% 13.03/3.04 thf(func_def_928, type, sK576: $i > $i > ($i > $i > $o) > $i).
% 13.03/3.04 thf(func_def_929, type, sK577: $i > ($i > $i > $o) > $i).
% 13.03/3.04 thf(func_def_930, type, sK578: $i > ($i > $i > $o) > $i > $i).
% 13.03/3.04 thf(func_def_932, type, sK580: $i > $o).
% 13.03/3.04 thf(func_def_937, type, sK585: $i > $i).
% 13.03/3.04 thf(func_def_954, type, sK602: $i > $o).
% 13.03/3.04 thf(func_def_964, type, sK612: $i > $o).
% 13.03/3.04 thf(func_def_971, type, sK619: ($i > $o) > $i).
% 13.03/3.04 thf(func_def_972, type, sK620: ($i > $o) > $i).
% 13.03/3.04 thf(func_def_973, type, sK621: $i > $o).
% 13.03/3.04 thf(func_def_978, type, sK626: $i > $i > $o).
% 13.03/3.04 thf(func_def_981, type, sK629: $i > $o).
% 13.03/3.04 thf(func_def_1005, type, sK653: $i > $o).
% 13.03/3.04 thf(func_def_1006, type, sK654: ($i > $o) > $i > $i).
% 13.03/3.04 thf(func_def_1007, type, sK655: $i > ($i > $o) > $i).
% 13.03/3.04 thf(func_def_1008, type, sK656: $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_1020, type, sK668: ($i > $o) > $i > $i).
% 13.03/3.04 thf(func_def_1021, type, sK669: ($i > $o) > $i > $i).
% 13.03/3.04 thf(func_def_1022, type, sK670: $i > ($i > $o) > $i).
% 13.03/3.04 thf(func_def_1024, type, sK672: $i > $o).
% 13.03/3.04 thf(func_def_1039, type, sK687: $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_1040, type, sK688: $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_1057, type, sK705: $i > $i > $i).
% 13.03/3.04 thf(func_def_1058, type, sK706: $i > $o).
% 13.03/3.04 thf(func_def_1060, type, sK708: $i > ($i > $o) > $i).
% 13.03/3.04 thf(func_def_1061, type, sK709: $i > ($i > $o) > $i).
% 13.03/3.04 thf(func_def_1067, type, sK715: ($i > $o) > $i).
% 13.03/3.04 thf(func_def_1068, type, sK716: $i > ($i > $o) > $i).
% 13.03/3.04 thf(func_def_1069, type, sK717: $i > $o).
% 13.03/3.04 thf(func_def_1079, type, sK727: $i > ($i > $o) > $i).
% 13.03/3.04 thf(func_def_1080, type, sK728: $i > ($i > $o) > $i).
% 13.03/3.04 thf(func_def_1081, type, sK729: $i > ($i > $o) > $i).
% 13.03/3.04 thf(func_def_1082, type, sK730: $i > $o).
% 13.03/3.04 thf(func_def_1085, type, sK733: $i > $o).
% 13.03/3.04 thf(func_def_1086, type, sK734: ($i > $o) > $i > $i).
% 13.03/3.04 thf(func_def_1087, type, sK735: ($i > $o) > $i > $i).
% 13.03/3.04 thf(func_def_1090, type, sK738: $i > $o).
% 13.03/3.04 thf(func_def_1091, type, sK739: ($i > $o) > $i).
% 13.03/3.04 thf(func_def_1101, type, sK749: $i > ($i > $o) > $i).
% 13.03/3.04 thf(func_def_1102, type, sK750: ($i > $o) > $i).
% 13.03/3.04 thf(func_def_1103, type, sK751: $i > $o).
% 13.03/3.04 thf(func_def_1126, type, sK774: $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_1127, type, sK775: $i > $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_1128, type, sK776: $i > $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_1129, type, sK777: $i > $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_1135, type, sK783: $i > $i > $i).
% 13.03/3.04 thf(func_def_1141, type, sK789: $i > $i > $i).
% 13.03/3.04 thf(func_def_1147, type, sK795: $i > $i > ($i > $o) > $i > $i).
% 13.03/3.04 thf(func_def_1148, type, sK796: $i > $i > ($i > $o) > $i > $i).
% 13.03/3.04 thf(func_def_1149, type, sK797: ($i > $o) > $i > $i).
% 13.03/3.04 thf(func_def_1153, type, sK801: $i > $o).
% 13.03/3.04 thf(func_def_1174, type, sK822: $i > $i).
% 13.03/3.04 thf(func_def_1176, type, sK824: $i > ($i > $i) > $i > $i).
% 13.03/3.04 thf(func_def_1177, type, sK825: $i > ($i > $i) > $i > $i).
% 13.03/3.04 thf(func_def_1206, type, sK854: $i > $i > $i).
% 13.03/3.04 thf(func_def_1212, type, sK860: ($i > $o) > $i).
% 13.03/3.04 thf(func_def_1213, type, sK861: $i > ($i > $o) > $i).
% 13.03/3.04 thf(func_def_1214, type, sK862: $i > $o).
% 13.03/3.04 thf(func_def_1220, type, sK868: $i > ($i > $o) > $i > $i).
% 13.03/3.04 thf(func_def_1222, type, sK870: $i > $o).
% 13.03/3.04 thf(func_def_1226, type, sK874: $i > $o).
% 13.03/3.04 thf(func_def_1228, type, sK876: $i > ($i > $o) > $i).
% 13.03/3.04 thf(func_def_1229, type, sK877: $i > ($i > $o) > $i).
% 13.03/3.04 thf(func_def_1236, type, sK884: $i > $o).
% 13.03/3.04 thf(func_def_1237, type, sK885: $i > $i).
% 13.03/3.04 thf(func_def_1240, type, sK888: $i > $i > ($i > $i) > $i).
% 13.03/3.04 thf(func_def_1243, type, sK891: $i > $i > $i).
% 13.03/3.04 thf(func_def_1266, type, sK914: $i > $i).
% 13.03/3.04 thf(func_def_1268, type, sK916: $i > ($i > $i) > $i > $i).
% 13.03/3.04 thf(func_def_1269, type, sK917: $i > $i > ($i > $i) > $i).
% 13.03/3.04 thf(func_def_1293, type, sK941: $i > $o).
% 13.03/3.04 thf(func_def_1294, type, sK942: $i > $o).
% 13.03/3.04 thf(func_def_1295, type, sK943: ($i > $o) > ($i > $o) > $i).
% 13.03/3.04 thf(func_def_1296, type, sK944: ($i > $o) > ($i > $o) > $i).
% 13.03/3.04 thf(func_def_1297, type, sK945: $i > $o).
% 13.03/3.04 thf(func_def_1302, type, sK950: $i > $i).
% 13.03/3.04 thf(func_def_1303, type, sK951: $i > $i).
% 13.03/3.04 thf(func_def_1309, type, sK957: $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_1322, type, sK970: $i > $i > ($i > $i > $o) > $i).
% 13.03/3.04 thf(func_def_1323, type, sK971: $i > $i > ($i > $i > $o) > $i).
% 13.03/3.04 thf(func_def_1324, type, sK972: $i > ($i > $i > $o) > $i > $i).
% 13.03/3.04 thf(func_def_1325, type, sK973: $i > ($i > $i > $o) > $i > $i).
% 13.03/3.04 thf(func_def_1328, type, sK976: $i > $i > $o).
% 13.03/3.04 thf(func_def_1339, type, sK987: $i > $i > $i).
% 13.03/3.04 thf(func_def_1340, type, sK988: $i > $i).
% 13.03/3.04 thf(func_def_1349, type, sK997: $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_1350, type, sK998: $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_1362, type, sK1010: $i > $i > $i > $o).
% 13.03/3.04 thf(func_def_1363, type, sK1011: $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_1367, type, sK1015: $i > ($i > $o) > $i).
% 13.03/3.04 thf(func_def_1368, type, sK1016: ($i > $o) > $i).
% 13.03/3.04 thf(func_def_1369, type, sK1017: $i > $o).
% 13.03/3.04 thf(func_def_1370, type, sK1018: $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_1371, type, sK1019: $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_1372, type, sK1020: $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_1373, type, sK1021: $i > $i > $i > $i).
% 13.03/3.04 thf(func_def_1387, type, sK1035: $i > $o).
% 13.03/3.04 thf(func_def_1390, type, ph1038: !>[X0: $tType]:(X0)).
% 13.03/3.04 thf(f11829,plain,(
% 13.03/3.04 $false),
% 13.03/3.04 inference(subsumption_resolution,[status(thm)],[f6264,f5973])).
% 13.03/3.04 thf(f5973,plain,(
% 13.03/3.04 ( ! [X2 : $i,X0 : $i > $i > $o,X1 : $i] : (($true = (breln @ X1 @ X2 @ (dpsetconstr @ X1 @ X2 @ X0)))) )),
% 13.03/3.04 inference(beta_eta_normalization,[status(thm)],[f5972])).
% 13.03/3.04 thf(f5972,plain,(
% 13.03/3.04 ( ! [X2 : $i,X0 : $i > $i > $o,X1 : $i] : (($true = (breln @ X1 @ X2 @ (dpsetconstr @ X1 @ X2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X0 @ Y0 @ Y1)))))))) )),
% 13.03/3.04 inference(trivial_inequality_removal,[status(thm)],[f5183])).
% 13.03/3.04 thf(f5183,plain,(
% 13.03/3.04 ( ! [X2 : $i,X0 : $i > $i > $o,X1 : $i] : (($true = (breln @ X1 @ X2 @ (dpsetconstr @ X1 @ X2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X0 @ Y0 @ Y1))))))) | ($true != $true)) )),
% 13.03/3.04 inference(definition_unfolding,[status(thm)],[f3585,f4420])).
% 13.03/3.04 thf(f4420,plain,(
% 13.03/3.04 (setOfPairsIsBReln = $true)),
% 13.03/3.04 inference(cnf_transformation,[status(thm)],[f2811])).
% 13.03/3.04 thf(f2811,plain,(
% 13.03/3.04 (iftrueorfalse = $true) & (powersetI = $true) & (demorgan2a = $true) & (ksndpairEq = $true) & (subset2powerset = $true) & (kpairp = $true) & (complementTI1 = $true) & (setminusSubset2 = $true) & (binunionTILcontra = $true) & (demorgan2a2 = $true) & (binintersectER = $true) & (powersetTI1 = $true) & (setbeta = $true) & (symdiffIneg1 = $true) & (notequalI1 = $true) & (upairsetE = $true) & (setadjoinSub2 = $true) & (funcext = $true) & (demorgan1b = $true) & (omegaIndAx = $true) & (setunionAx = $true) & (iftrue = $true) & (subbreln = $true) & (cartprodsndin = $true) & (woz1_5 = $true) & (doubleComplementE1 = $true) & (setunionI = $true) & (woz13rule2 = $true) & (foundationAx = $true) & (complementT_lem = $true) & (in__Cong = $true) & (woz1_2 = $true) & (notsubsetI = $true) & (nonemptyImpWitness = $true) & (eqinunit = $true) & (setOfPairsIsBReln1 = $true) & (subsetE2 = $true) & (complementTE1 = $true) & (binunionIR = $true) & (inIntersectImpInUnion = $true) & (complementSubsetComplementIntersect = $true) & (notequalI2 = $true) & (app = $true) & (complementImpComplementIntersect = $true) & (cartprodsndpairEq = $true) & (eqbreln1 = $true) & (cartprodfstpairEq = $true) & (complementUnionInPowersetComplement = $true) & (exuE3u = $true) & (noeltsimpempty = $true) & (binunionTEcontra = $true) & (secondinupair = $true) & (powersetAx = $true) & (binunionIL = $true) & (setminusER = $true) & (wellorderingAx = $true) & (dpsetconstrER = $true) & (powersetE = $true) & (binintersectTELcontra = $true) & (demorgan1 = $true) & (beta1 = $true) & (sepSubset = $true) & (setadjoinOr = $true) & (setukpairinjR = $true) & (setextAx = $true) & (eta2 = $true) & (choice2fnsingleton = $true) & (breln1all2 = $true) & (exuE2 = $true) & (setukpairinjL2 = $true) & (eqimpsubset2 = $true) & (vacuousDall = $true) & (setadjoin__Cong = $true) & (exuI3 = $true) & (setukpairinjR11 = $true) & (demorgan1a = $true) & (iffalseProp1 = $true) & (iftrueProp2 = $true) & (cartprodpairin = $true) & (singletonprop = $true) & (setadjoinE = $true) & (cartprodfstin = $true) & (binunionE = $true) & (prop2set2propI = $true) & (woz13rule3 = $true) & (binintersectLsub = $true) & (funcGraphProp1 = $true) & (nonemptyE1 = $true) & (kfstsingleton = $true) & (replAx = $true) & (upairinpowunion = $true) & (ubforcartprodlem1 = $true) & (ap2apEq1 = $true) & (singletonsubset = $true) & (descr__Cong = $true) & (binintersectSubset2 = $true) & (contrasubsetT1 = $true) & (nonemptyI1 = $true) & (disjointsetsI1 = $true) & (theeq = $true) & (notinemptyset = $true) & (inIntersectImpInUnion2 = $true) & (exuE3e = $true) & (doubleComplementSub1 = $true) & (binintersectEL = $true) & (brelnall1 = $true) & (iffalse = $true) & (funcImageSingleton = $true) & (ubforcartprodlem3 = $true) & (omega__Cong = $true) & (ap2p = $true) & (cartprodmempaircEq = $true) & (complementTcontraSubset = $true) & (dsetconstrEL = $true) & (emptysetimpfalse = $true) & (lamp = $true) & (ap2apEq2 = $true) & (prop2setI = $true) & (subsetTI = $true) & (setadjoinIR = $true) & (setukpairIR = $true) & (emptyinunitempty = $true) & (binintersectRsub = $true) & (binintersectTERcontra = $true) & (setadjoinAx = $true) & (singletoninpowunion = $true) & (funcinfuncset = $true) & (symdiffI2 = $true) & (complementTnotintersectT = $true) & (dsetconstrI = $true) & (binunionTIRcontra = $true) & (binintersectSubset3 = $true) & (powerset__Cong = $true) & (complementInPowersetComplementIntersect = $true) & (kfstpairEq = $true) & (cartprodpairmemEL = $true) & (cartprodpairmemER = $true) & (notdallE = $true) & (ex1E2 = $true) & (inIntersectImpInIntersectUnions = $true) & (binintersectSubset5 = $true) & (subsetTrans = $true) & (breln1SetBreln1 = $true) & (setunionsingleton2 = $true) & (subsetRefl = $true) & (demorgan2 = $true) & (ubforcartprodlem2 = $true) & (setminusT_lem = $true) & (descrp = $true) & (demorgan2a1 = $true) & (setextT = $true) & (dpsetconstrEL1 = $true) & (demorgan2b2 = $true) & (setOfPairsIsBReln = $true) & (quantDeMorgan3 = $true) & (lam2p = $true) & (singletonsuniq = $true) & (symdiffE = $true) & (powersetT_lem = $true) & (emptysetE = $true) & (binintersectT_lem = $true) & (exuEu = $true) & (setunionsingleton = $true) & (cartprodpairsurjEq = $true) & (inComplementUnionImpNotIn1 = $true) & (ex1E1 = $true) & (dsetconstr__Cong = $true) & (subsetemptysetimpeq = $true) & (setminusLsub = $true) & (subsetI2 = $true) & (emptyI = $true) & (emptyset__Cong = $true) & (setminusELneg = $true) & (theprop = $true) & (setukpairinjL1 = $true) & (exu__Cong = $true) & (contrasubsetT3 = $true) & (symdiffIneg2 = $true) & (upairequniteq = $true) & (powersetI1 = $true) & (upairset2IR = $true) & (doubleComplementI1 = $true) & (binunionTE = $true) & (demorgan2b = $true) & (symdiffI1 = $true) & (dpsetconstrI = $true) & (powersetsubset = $true) & (contraSubsetComplement = $true) & (setminusILneg = $true) & (omegaSAx = $true) & (exuI2 = $true) & (doubleComplementEq = $true) & (funcGraphProp3 = $true) & (((breln1 @ sK880 @ (breln1invset @ sK880 @ sK881)) != $true) & ($true = (breln1 @ sK880 @ sK881))) & (setextsub = $true) & (subsetE = $true) & (setunion__Cong = $true) & (setukpairinjL = $true) & (upairsetIR = $true) & (woz13rule0 = $true) & (emptyInPowerset = $true) & (iftrueProp1 = $true) & (setukpairinjR1 = $true) & (setukpairIL = $true) & (infuncsetfunc = $true) & (dpsetconstrERa = $true) & (setukpairinjR2 = $true) & (exuE1 = $true) & (binunionT_lem = $true) & (woz13rule4 = $true) & (setminusERneg = $true) & (funcextLem = $true) & (ex1I2 = $true) & (emptyinPowerset = $true) & (setoftrueEq = $true) & (contrasubsetT2 = $true) & (lam2lamEq = $true) & (prop2setE = $true) & (woz1_4 = $true) & (inComplementUnionImpInComplement1 = $true) & (eta1 = $true) & (quantDeMorgan4 = $true) & (emptysetsubset = $true) & (breln1all1 = $true) & (setminusI = $true) & (setunionsingleton1 = $true) & (emptysetAx = $true) & (intersectInPowersetIntersectUnions = $true) & (setunionE2 = $true) & (dsetconstrER = $true) & (upairsubunion = $true) & (beta2 = $true) & (binintersectSubset4 = $true) & (setukpairinjR12 = $true) & (binunionEcases = $true) & (woz1_3 = $true) & (inPowerset = $true) & (eqimpsubset1 = $true) & (woz1_1 = $true) & (brelnall2 = $true) & (ex1I = $true) & (setminusEL = $true) & (upairsetIL = $true) & (setadjoinIL = $true) & (bs114d = $true) & (notdexE = $true) & (binintersectSubset1 = $true) & (cartprodmempair1 = $true) & (iffalseProp2 = $true) & (funcGraphProp4 = $true) & (ksndsingleton = $true) & (subbreln1 = $true) & (upairset2E = $true) & (dpsetconstrEL2 = $true) & (singletonsswitch = $true) & (notinsingleton = $true) & (nonemptyI = $true) & (subsetI1 = $true) & (quantDeMorgan2 = $true) & (subPowSU = $true) & (singletoninpowerset = $true) & (powersetE1 = $true) & (binunionRsub = $true) & (omega0Ax = $true) & (setunionE = $true) & (contrasubsetT = $true) & (kpairsurjEq = $true) & (setminusIRneg = $true) & (funcext2 = $true) & (lamProp = $true) & (powersetTE1 = $true) & (inCongP = $true) & (setext = $true) & (setminusSubset1 = $true) & (dpsetconstrSub = $true) & (doubleComplementSub2 = $true) & (eqbreln = $true) & (uniqinunit = $true) & (ifSingleton = $true) & (quantDeMorgan1 = $true) & (woz13rule1 = $true) & (binintersectI = $true) & (binunionLsub = $true) & (exuI1 = $true) & (apProp = $true) & (funcGraphProp2 = $true) & (sepInPowerset = $true) & (ifp = $true) & (setadjoinSub = $true) & (kpairiskpair = $true) & (cartprodmempair = $true) & (emptyE1 = $true)),
% 13.03/3.04 inference(skolemisation,[status(esa),new_symbols(skolem,[sK880,sK881])],[f989,f2810])).
% 13.03/3.04 thf(f2810,plain,(
% 13.03/3.04 ? [X0 : $i,X1 : $i] : (($true != (breln1 @ X0 @ (breln1invset @ X0 @ X1))) & ($true = (breln1 @ X0 @ X1))) => (((breln1 @ sK880 @ (breln1invset @ sK880 @ sK881)) != $true) & ($true = (breln1 @ sK880 @ sK881)))),
% 13.03/3.04 introduced(definition,[],[choice_axiom])).
% 13.03/3.04 thf(f989,plain,(
% 13.03/3.04 (iftrueorfalse = $true) & (powersetI = $true) & (demorgan2a = $true) & (ksndpairEq = $true) & (subset2powerset = $true) & (kpairp = $true) & (complementTI1 = $true) & (setminusSubset2 = $true) & (binunionTILcontra = $true) & (demorgan2a2 = $true) & (binintersectER = $true) & (powersetTI1 = $true) & (setbeta = $true) & (symdiffIneg1 = $true) & (notequalI1 = $true) & (upairsetE = $true) & (setadjoinSub2 = $true) & (funcext = $true) & (demorgan1b = $true) & (omegaIndAx = $true) & (setunionAx = $true) & (iftrue = $true) & (subbreln = $true) & (cartprodsndin = $true) & (woz1_5 = $true) & (doubleComplementE1 = $true) & (setunionI = $true) & (woz13rule2 = $true) & (foundationAx = $true) & (complementT_lem = $true) & (in__Cong = $true) & (woz1_2 = $true) & (notsubsetI = $true) & (nonemptyImpWitness = $true) & (eqinunit = $true) & (setOfPairsIsBReln1 = $true) & (subsetE2 = $true) & (complementTE1 = $true) & (binunionIR = $true) & (inIntersectImpInUnion = $true) & (complementSubsetComplementIntersect = $true) & (notequalI2 = $true) & (app = $true) & (complementImpComplementIntersect = $true) & (cartprodsndpairEq = $true) & (eqbreln1 = $true) & (cartprodfstpairEq = $true) & (complementUnionInPowersetComplement = $true) & (exuE3u = $true) & (noeltsimpempty = $true) & (binunionTEcontra = $true) & (secondinupair = $true) & (powersetAx = $true) & (binunionIL = $true) & (setminusER = $true) & (wellorderingAx = $true) & (dpsetconstrER = $true) & (powersetE = $true) & (binintersectTELcontra = $true) & (demorgan1 = $true) & (beta1 = $true) & (sepSubset = $true) & (setadjoinOr = $true) & (setukpairinjR = $true) & (setextAx = $true) & (eta2 = $true) & (choice2fnsingleton = $true) & (breln1all2 = $true) & (exuE2 = $true) & (setukpairinjL2 = $true) & (eqimpsubset2 = $true) & (vacuousDall = $true) & (setadjoin__Cong = $true) & (exuI3 = $true) & (setukpairinjR11 = $true) & (demorgan1a = $true) & (iffalseProp1 = $true) & (iftrueProp2 = $true) & (cartprodpairin = $true) & (singletonprop = $true) & (setadjoinE = $true) & (cartprodfstin = $true) & (binunionE = $true) & (prop2set2propI = $true) & (woz13rule3 = $true) & (binintersectLsub = $true) & (funcGraphProp1 = $true) & (nonemptyE1 = $true) & (kfstsingleton = $true) & (replAx = $true) & (upairinpowunion = $true) & (ubforcartprodlem1 = $true) & (ap2apEq1 = $true) & (singletonsubset = $true) & (descr__Cong = $true) & (binintersectSubset2 = $true) & (contrasubsetT1 = $true) & (nonemptyI1 = $true) & (disjointsetsI1 = $true) & (theeq = $true) & (notinemptyset = $true) & (inIntersectImpInUnion2 = $true) & (exuE3e = $true) & (doubleComplementSub1 = $true) & (binintersectEL = $true) & (brelnall1 = $true) & (iffalse = $true) & (funcImageSingleton = $true) & (ubforcartprodlem3 = $true) & (omega__Cong = $true) & (ap2p = $true) & (cartprodmempaircEq = $true) & (complementTcontraSubset = $true) & (dsetconstrEL = $true) & (emptysetimpfalse = $true) & (lamp = $true) & (ap2apEq2 = $true) & (prop2setI = $true) & (subsetTI = $true) & (setadjoinIR = $true) & (setukpairIR = $true) & (emptyinunitempty = $true) & (binintersectRsub = $true) & (binintersectTERcontra = $true) & (setadjoinAx = $true) & (singletoninpowunion = $true) & (funcinfuncset = $true) & (symdiffI2 = $true) & (complementTnotintersectT = $true) & (dsetconstrI = $true) & (binunionTIRcontra = $true) & (binintersectSubset3 = $true) & (powerset__Cong = $true) & (complementInPowersetComplementIntersect = $true) & (kfstpairEq = $true) & (cartprodpairmemEL = $true) & (cartprodpairmemER = $true) & (notdallE = $true) & (ex1E2 = $true) & (inIntersectImpInIntersectUnions = $true) & (binintersectSubset5 = $true) & (subsetTrans = $true) & (breln1SetBreln1 = $true) & (setunionsingleton2 = $true) & (subsetRefl = $true) & (demorgan2 = $true) & (ubforcartprodlem2 = $true) & (setminusT_lem = $true) & (descrp = $true) & (demorgan2a1 = $true) & (setextT = $true) & (dpsetconstrEL1 = $true) & (demorgan2b2 = $true) & (setOfPairsIsBReln = $true) & (quantDeMorgan3 = $true) & (lam2p = $true) & (singletonsuniq = $true) & (symdiffE = $true) & (powersetT_lem = $true) & (emptysetE = $true) & (binintersectT_lem = $true) & (exuEu = $true) & (setunionsingleton = $true) & (cartprodpairsurjEq = $true) & (inComplementUnionImpNotIn1 = $true) & (ex1E1 = $true) & (dsetconstr__Cong = $true) & (subsetemptysetimpeq = $true) & (setminusLsub = $true) & (subsetI2 = $true) & (emptyI = $true) & (emptyset__Cong = $true) & (setminusELneg = $true) & (theprop = $true) & (setukpairinjL1 = $true) & (exu__Cong = $true) & (contrasubsetT3 = $true) & (symdiffIneg2 = $true) & (upairequniteq = $true) & (powersetI1 = $true) & (upairset2IR = $true) & (doubleComplementI1 = $true) & (binunionTE = $true) & (demorgan2b = $true) & (symdiffI1 = $true) & (dpsetconstrI = $true) & (powersetsubset = $true) & (contraSubsetComplement = $true) & (setminusILneg = $true) & (omegaSAx = $true) & (exuI2 = $true) & (doubleComplementEq = $true) & (funcGraphProp3 = $true) & ? [X0 : $i,X1 : $i] : (($true != (breln1 @ X0 @ (breln1invset @ X0 @ X1))) & ($true = (breln1 @ X0 @ X1))) & (setextsub = $true) & (subsetE = $true) & (setunion__Cong = $true) & (setukpairinjL = $true) & (upairsetIR = $true) & (woz13rule0 = $true) & (emptyInPowerset = $true) & (iftrueProp1 = $true) & (setukpairinjR1 = $true) & (setukpairIL = $true) & (infuncsetfunc = $true) & (dpsetconstrERa = $true) & (setukpairinjR2 = $true) & (exuE1 = $true) & (binunionT_lem = $true) & (woz13rule4 = $true) & (setminusERneg = $true) & (funcextLem = $true) & (ex1I2 = $true) & (emptyinPowerset = $true) & (setoftrueEq = $true) & (contrasubsetT2 = $true) & (lam2lamEq = $true) & (prop2setE = $true) & (woz1_4 = $true) & (inComplementUnionImpInComplement1 = $true) & (eta1 = $true) & (quantDeMorgan4 = $true) & (emptysetsubset = $true) & (breln1all1 = $true) & (setminusI = $true) & (setunionsingleton1 = $true) & (emptysetAx = $true) & (intersectInPowersetIntersectUnions = $true) & (setunionE2 = $true) & (dsetconstrER = $true) & (upairsubunion = $true) & (beta2 = $true) & (binintersectSubset4 = $true) & (setukpairinjR12 = $true) & (binunionEcases = $true) & (woz1_3 = $true) & (inPowerset = $true) & (eqimpsubset1 = $true) & (woz1_1 = $true) & (brelnall2 = $true) & (ex1I = $true) & (setminusEL = $true) & (upairsetIL = $true) & (setadjoinIL = $true) & (bs114d = $true) & (notdexE = $true) & (binintersectSubset1 = $true) & (cartprodmempair1 = $true) & (iffalseProp2 = $true) & (funcGraphProp4 = $true) & (ksndsingleton = $true) & (subbreln1 = $true) & (upairset2E = $true) & (dpsetconstrEL2 = $true) & (singletonsswitch = $true) & (notinsingleton = $true) & (nonemptyI = $true) & (subsetI1 = $true) & (quantDeMorgan2 = $true) & (subPowSU = $true) & (singletoninpowerset = $true) & (powersetE1 = $true) & (binunionRsub = $true) & (omega0Ax = $true) & (setunionE = $true) & (contrasubsetT = $true) & (kpairsurjEq = $true) & (setminusIRneg = $true) & (funcext2 = $true) & (lamProp = $true) & (powersetTE1 = $true) & (inCongP = $true) & (setext = $true) & (setminusSubset1 = $true) & (dpsetconstrSub = $true) & (doubleComplementSub2 = $true) & (eqbreln = $true) & (uniqinunit = $true) & (ifSingleton = $true) & (quantDeMorgan1 = $true) & (woz13rule1 = $true) & (binintersectI = $true) & (binunionLsub = $true) & (exuI1 = $true) & (apProp = $true) & (funcGraphProp2 = $true) & (sepInPowerset = $true) & (ifp = $true) & (setadjoinSub = $true) & (kpairiskpair = $true) & (cartprodmempair = $true) & (emptyE1 = $true)),
% 13.03/3.04 inference(flattening,[status(thm)],[f988])).
% 13.03/3.04 thf(f988,plain,(
% 13.03/3.04 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (($true != (breln1 @ X0 @ (breln1invset @ X0 @ X1))) & ($true = (breln1 @ X0 @ X1))) & (eqbreln1 = $true)) & (subbreln1 = $true)) & (breln1all1 = $true)) & (setOfPairsIsBReln1 = $true)) & (choice2fnsingleton = $true)) & (breln1SetBreln1 = $true)) & (breln1all2 = $true)) & (woz1_5 = $true)) & (woz1_4 = $true)) & (woz1_3 = $true)) & (woz1_2 = $true)) & (woz1_1 = $true)) & (woz13rule4 = $true)) & (woz13rule3 = $true)) & (woz13rule2 = $true)) & (woz13rule1 = $true)) & (woz13rule0 = $true)) & (demorgan2 = $true)) & (demorgan2b = $true)) & (demorgan2b2 = $true)) & (demorgan2a = $true)) & (demorgan1 = $true)) & (demorgan1b = $true)) & (demorgan1a = $true)) & (demorgan2a2 = $true)) & (complementUnionInPowersetComplement = $true)) & (demorgan2a1 = $true)) & (binunionTEcontra = $true)) & (binunionTE = $true)) & (inComplementUnionImpInComplement1 = $true)) & (inComplementUnionImpNotIn1 = $true)) & (intersectInPowersetIntersectUnions = $true)) & (inIntersectImpInIntersectUnions = $true)) & (inIntersectImpInUnion2 = $true)) & (inIntersectImpInUnion = $true)) & (binunionTIRcontra = $true)) & (binunionTILcontra = $true)) & (complementTcontraSubset = $true)) & (contraSubsetComplement = $true)) & (complementInPowersetComplementIntersect = $true)) & (complementSubsetComplementIntersect = $true)) & (complementImpComplementIntersect = $true)) & (complementTnotintersectT = $true)) & (doubleComplementEq = $true)) & (doubleComplementSub2 = $true)) & (doubleComplementSub1 = $true)) & (doubleComplementE1 = $true)) & (doubleComplementI1 = $true)) & (contrasubsetT3 = $true)) & (contrasubsetT2 = $true)) & (contrasubsetT1 = $true)) & (contrasubsetT = $true)) & (binintersectTERcontra = $true)) & (binintersectTELcontra = $true)) & (complementTE1 = $true)) & (complementTI1 = $true)) & (powersetTE1 = $true)) & (powersetTI1 = $true)) & (subsetTI = $true)) & (setextT = $true)) & (complementT_lem = $true)) & (setminusT_lem = $true)) & (powersetT_lem = $true)) & (binunionT_lem = $true)) & (binintersectT_lem = $true)) & (iftrueorfalse = $true)) & (iffalse = $true)) & (iftrue = $true)) & (theeq = $true)) & (ifp = $true)) & (ifSingleton = $true)) & (iftrueProp2 = $true)) & (iftrueProp1 = $true)) & (iffalseProp2 = $true)) & (iffalseProp1 = $true)) & (eta2 = $true)) & (beta2 = $true)) & (lam2lamEq = $true)) & (eta1 = $true)) & (beta1 = $true)) & (ap2apEq2 = $true)) & (ap2apEq1 = $true)) & (funcext2 = $true)) & (funcext = $true)) & (eqbreln = $true)) & (subbreln = $true)) & (funcGraphProp4 = $true)) & (funcextLem = $true)) & (funcGraphProp2 = $true)) & (funcGraphProp3 = $true)) & (funcGraphProp1 = $true)) & (ex1E2 = $true)) & (brelnall2 = $true)) & (brelnall1 = $true)) & (lam2p = $true)) & (lamp = $true)) & (lamProp = $true)) & (funcinfuncset = $true)) & (ap2p = $true)) & (infuncsetfunc = $true)) & (app = $true)) & (apProp = $true)) & (funcImageSingleton = $true)) & (dpsetconstrER = $true)) & (dpsetconstrEL2 = $true)) & (dpsetconstrEL1 = $true)) & (dpsetconstrERa = $true)) & (setOfPairsIsBReln = $true)) & (dpsetconstrSub = $true)) & (dpsetconstrI = $true)) & (cartprodpairsurjEq = $true)) & (cartprodsndpairEq = $true)) & (cartprodfstpairEq = $true)) & (cartprodmempaircEq = $true)) & (cartprodpairmemER = $true)) & (cartprodpairmemEL = $true)) & (cartprodsndin = $true)) & (kpairsurjEq = $true)) & (ksndpairEq = $true)) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (setukpairinjR2 = $true)) & (upairequniteq = $true)) & (setukpairinjR1 = $true)) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 13.03/3.04 inference(ennf_transformation,[status(thm)],[f444])).
% 13.03/3.04 thf(f444,plain,(
% 13.03/3.04 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ((upairequniteq = $true) => ((setukpairinjR2 = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ((ksndpairEq = $true) => ((kpairsurjEq = $true) => ((cartprodsndin = $true) => ((cartprodpairmemEL = $true) => ((cartprodpairmemER = $true) => ((cartprodmempaircEq = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ((cartprodpairsurjEq = $true) => ((dpsetconstrI = $true) => ((dpsetconstrSub = $true) => ((setOfPairsIsBReln = $true) => ((dpsetconstrERa = $true) => ((dpsetconstrEL1 = $true) => ((dpsetconstrEL2 = $true) => ((dpsetconstrER = $true) => ((funcImageSingleton = $true) => ((apProp = $true) => ((app = $true) => ((infuncsetfunc = $true) => ((ap2p = $true) => ((funcinfuncset = $true) => ((lamProp = $true) => ((lamp = $true) => ((lam2p = $true) => ((brelnall1 = $true) => ((brelnall2 = $true) => ((ex1E2 = $true) => ((funcGraphProp1 = $true) => ((funcGraphProp3 = $true) => ((funcGraphProp2 = $true) => ((funcextLem = $true) => ((funcGraphProp4 = $true) => ((subbreln = $true) => ((eqbreln = $true) => ((funcext = $true) => ((funcext2 = $true) => ((ap2apEq1 = $true) => ((ap2apEq2 = $true) => ((beta1 = $true) => ((eta1 = $true) => ((lam2lamEq = $true) => ((beta2 = $true) => ((eta2 = $true) => ((iffalseProp1 = $true) => ((iffalseProp2 = $true) => ((iftrueProp1 = $true) => ((iftrueProp2 = $true) => ((ifSingleton = $true) => ((ifp = $true) => ((theeq = $true) => ((iftrue = $true) => ((iffalse = $true) => ((iftrueorfalse = $true) => ((binintersectT_lem = $true) => ((binunionT_lem = $true) => ((powersetT_lem = $true) => ((setminusT_lem = $true) => ((complementT_lem = $true) => ((setextT = $true) => ((subsetTI = $true) => ((powersetTI1 = $true) => ((powersetTE1 = $true) => ((complementTI1 = $true) => ((complementTE1 = $true) => ((binintersectTELcontra = $true) => ((binintersectTERcontra = $true) => ((contrasubsetT = $true) => ((contrasubsetT1 = $true) => ((contrasubsetT2 = $true) => ((contrasubsetT3 = $true) => ((doubleComplementI1 = $true) => ((doubleComplementE1 = $true) => ((doubleComplementSub1 = $true) => ((doubleComplementSub2 = $true) => ((doubleComplementEq = $true) => ((complementTnotintersectT = $true) => ((complementImpComplementIntersect = $true) => ((complementSubsetComplementIntersect = $true) => ((complementInPowersetComplementIntersect = $true) => ((contraSubsetComplement = $true) => ((complementTcontraSubset = $true) => ((binunionTILcontra = $true) => ((binunionTIRcontra = $true) => ((inIntersectImpInUnion = $true) => ((inIntersectImpInUnion2 = $true) => ((inIntersectImpInIntersectUnions = $true) => ((intersectInPowersetIntersectUnions = $true) => ((inComplementUnionImpNotIn1 = $true) => ((inComplementUnionImpInComplement1 = $true) => ((binunionTE = $true) => ((binunionTEcontra = $true) => ((demorgan2a1 = $true) => ((complementUnionInPowersetComplement = $true) => ((demorgan2a2 = $true) => ((demorgan1a = $true) => ((demorgan1b = $true) => ((demorgan1 = $true) => ((demorgan2a = $true) => ((demorgan2b2 = $true) => ((demorgan2b = $true) => ((demorgan2 = $true) => ((woz13rule0 = $true) => ((woz13rule1 = $true) => ((woz13rule2 = $true) => ((woz13rule3 = $true) => ((woz13rule4 = $true) => ((woz1_1 = $true) => ((woz1_2 = $true) => ((woz1_3 = $true) => ((woz1_4 = $true) => ((woz1_5 = $true) => ((breln1all2 = $true) => ((breln1SetBreln1 = $true) => ((choice2fnsingleton = $true) => ((setOfPairsIsBReln1 = $true) => ((breln1all1 = $true) => ((subbreln1 = $true) => ((eqbreln1 = $true) => ! [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) => ($true = (breln1 @ X0 @ (breln1invset @ X0 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 13.03/3.04 inference(fool_elimination,[status(thm)],[f443])).
% 13.03/3.04 thf(f443,plain,(
% 13.03/3.04 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (eqbreln1 => ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => (breln1 @ X0 @ (breln1invset @ X0 @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 13.03/3.04 inference(rectify,[status(thm)],[f298])).
% 13.03/3.04 thf(f298,negated_conjecture,(
% 13.03/3.04 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (eqbreln1 => ! [X3 : $i,X13 : $i] : ((breln1 @ X3 @ X13) => (breln1 @ X3 @ (breln1invset @ X3 @ X13))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 13.03/3.04 inference(negated_conjecture,[status(cth)],[f297])).
% 13.03/3.04 thf(f297,conjecture,(
% 13.03/3.04 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (eqbreln1 => ! [X3 : $i,X13 : $i] : ((breln1 @ X3 @ X13) => (breln1 @ X3 @ (breln1invset @ X3 @ X13)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 13.03/3.04 file('/export/starexec/sandbox2/tmp/tmp.VPOVQ5G1w9/DTF2THF_2668.p',breln1invprop)).
% 13.03/3.04 thf(f3585,plain,(
% 13.03/3.04 ( ! [X2 : $i,X0 : $i > $i > $o,X1 : $i] : (($true = (breln @ X1 @ X2 @ (dpsetconstr @ X1 @ X2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X0 @ Y0 @ Y1))))))) | (setOfPairsIsBReln != $true)) )),
% 13.03/3.04 inference(cnf_transformation,[status(thm)],[f2006])).
% 13.03/3.04 thf(f2006,plain,(
% 13.03/3.04 (! [X0 : $i > $i > $o,X1 : $i,X2 : $i] : ($true = (breln @ X1 @ X2 @ (dpsetconstr @ X1 @ X2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X0 @ Y0 @ Y1))))))) | (setOfPairsIsBReln != $true)) & ((setOfPairsIsBReln = $true) | ($true != (breln @ sK425 @ sK426 @ (dpsetconstr @ sK425 @ sK426 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK424 @ Y0 @ Y1))))))))),
% 13.03/3.04 inference(skolemisation,[status(esa),new_symbols(skolem,[sK424,sK425,sK426])],[f2004,f2005])).
% 13.03/3.04 thf(f2005,plain,(
% 13.03/3.04 ? [X3 : $i > $i > $o,X4 : $i,X5 : $i] : ($true != (breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X3 @ Y0 @ Y1))))))) => ($true != (breln @ sK425 @ sK426 @ (dpsetconstr @ sK425 @ sK426 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK424 @ Y0 @ Y1)))))))),
% 13.03/3.04 introduced(definition,[],[choice_axiom])).
% 13.03/3.04 thf(f2004,plain,(
% 13.03/3.04 (! [X0 : $i > $i > $o,X1 : $i,X2 : $i] : ($true = (breln @ X1 @ X2 @ (dpsetconstr @ X1 @ X2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X0 @ Y0 @ Y1))))))) | (setOfPairsIsBReln != $true)) & ((setOfPairsIsBReln = $true) | ? [X3 : $i > $i > $o,X4 : $i,X5 : $i] : ($true != (breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X3 @ Y0 @ Y1))))))))),
% 13.03/3.04 inference(rectify,[status(thm)],[f2003])).
% 13.03/3.04 thf(f2003,plain,(
% 13.03/3.04 (! [X0 : $i > $i > $o,X1 : $i,X2 : $i] : ($true = (breln @ X1 @ X2 @ (dpsetconstr @ X1 @ X2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X0 @ Y0 @ Y1))))))) | (setOfPairsIsBReln != $true)) & ((setOfPairsIsBReln = $true) | ? [X0 : $i > $i > $o,X1 : $i,X2 : $i] : ($true != (breln @ X1 @ X2 @ (dpsetconstr @ X1 @ X2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X0 @ Y0 @ Y1))))))))),
% 13.03/3.04 inference(nnf_transformation,[status(thm)],[f522])).
% 13.03/3.04 thf(f522,plain,(
% 13.03/3.04 ! [X0 : $i > $i > $o,X1 : $i,X2 : $i] : ($true = (breln @ X1 @ X2 @ (dpsetconstr @ X1 @ X2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X0 @ Y0 @ Y1))))))) <=> (setOfPairsIsBReln = $true)),
% 13.03/3.04 inference(fool_elimination,[status(thm)],[f521])).
% 13.03/3.04 thf(f521,plain,(
% 13.03/3.04 (! [X0 : $i > $i > $o,X1 : $i,X2 : $i] : (breln @ X1 @ X2 @ (dpsetconstr @ X1 @ X2 @ (^[X3 : $i, X4 : $i] : (X0 @ X3 @ X4)))) = setOfPairsIsBReln)),
% 13.03/3.04 inference(rectify,[status(thm)],[f187])).
% 13.03/3.04 thf(f187,axiom,(
% 13.03/3.04 (! [X0 : $i > $i > $o,X3 : $i,X4 : $i] : (breln @ X3 @ X4 @ (dpsetconstr @ X3 @ X4 @ (^[X1 : $i, X2 : $i] : (X0 @ X1 @ X2)))) = setOfPairsIsBReln)),
% 13.03/3.04 file('/export/starexec/sandbox2/tmp/tmp.VPOVQ5G1w9/DTF2THF_2668.p',setOfPairsIsBReln)).
% 13.03/3.04 thf(f6264,plain,(
% 13.03/3.04 ($true != (breln @ sK880 @ sK880 @ (dpsetconstr @ sK880 @ sK880 @ (^[Y0 : $i]: ((^[Y1 : $i]: (in @ (kpair @ Y1 @ Y0) @ sK881)))))))),
% 13.03/3.04 inference(beta_eta_normalization,[status(thm)],[f5698])).
% 13.03/3.04 thf(f5698,plain,(
% 13.03/3.04 ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))) @ sK880 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (in @ (kpair @ Y3 @ Y2) @ Y1)))))))) @ sK880 @ sK881)))),
% 13.03/3.04 inference(definition_unfolding,[status(thm)],[f4380,f3514,f3332])).
% 13.03/3.04 thf(f3332,plain,(
% 13.03/3.04 (breln1invset = (^[Y0 : $i]: ((^[Y1 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (in @ (kpair @ Y3 @ Y2) @ Y1)))))))))),
% 13.03/3.04 inference(cnf_transformation,[status(thm)],[f747])).
% 13.03/3.04 thf(f747,plain,(
% 13.03/3.04 (breln1invset = (^[Y0 : $i]: ((^[Y1 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (in @ (kpair @ Y3 @ Y2) @ Y1)))))))))),
% 13.03/3.04 inference(fool_elimination,[status(thm)],[f746])).
% 13.03/3.04 thf(f746,plain,(
% 13.03/3.04 (breln1invset = (^[X0 : $i, X1 : $i] : (dpsetconstr @ X0 @ X0 @ (^[X2 : $i, X3 : $i] : (in @ (kpair @ X3 @ X2) @ X1)))))),
% 13.03/3.04 inference(rectify,[status(thm)],[f296])).
% 13.03/3.04 thf(f296,axiom,(
% 13.03/3.04 (breln1invset = (^[X3 : $i, X13 : $i] : (dpsetconstr @ X3 @ X3 @ (^[X1 : $i, X2 : $i] : (in @ (kpair @ X2 @ X1) @ X13)))))),
% 13.03/3.04 file('/export/starexec/sandbox2/tmp/tmp.VPOVQ5G1w9/DTF2THF_2668.p',breln1invset)).
% 13.03/3.04 thf(f3514,plain,(
% 13.03/3.04 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 13.03/3.04 inference(cnf_transformation,[status(thm)],[f751])).
% 13.03/3.04 thf(f751,plain,(
% 13.03/3.04 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 13.03/3.04 inference(fool_elimination,[status(thm)],[f750])).
% 13.03/3.04 thf(f750,plain,(
% 13.03/3.04 (breln1 = (^[X0 : $i, X1 : $i] : (breln @ X0 @ X0 @ X1)))),
% 13.03/3.04 inference(rectify,[status(thm)],[f288])).
% 13.03/3.04 thf(f288,axiom,(
% 13.03/3.04 (breln1 = (^[X3 : $i, X13 : $i] : (breln @ X3 @ X3 @ X13)))),
% 13.03/3.04 file('/export/starexec/sandbox2/tmp/tmp.VPOVQ5G1w9/DTF2THF_2668.p',breln1)).
% 13.03/3.04 thf(f4380,plain,(
% 13.03/3.04 ((breln1 @ sK880 @ (breln1invset @ sK880 @ sK881)) != $true)),
% 13.03/3.04 inference(cnf_transformation,[status(thm)],[f2811])).
% 13.03/3.04 % SZS output end Proof for DTF2THF_2668
% 13.03/3.04 % (2956)------------------------------
% 13.03/3.04 % (2956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.03/3.04 % (2956)Termination reason: Refutation
% 13.03/3.04
% 13.03/3.04 % (2956)Memory used [KB]: 13688
% 13.03/3.04 % (2956)Time elapsed: 0.611 s
% 13.03/3.04 % (2956)Instructions burned: 1939 (million)
% 13.03/3.04 % (2956)------------------------------
% 13.03/3.04 % (2956)------------------------------
% 13.03/3.04 % (2860)Success in time 1.43 s
%------------------------------------------------------------------------------