%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU777^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 09:37:06 AM UTC 2026
% Result : Theorem 19.50s 4.13s
% Output : Refutation 17.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 4775 (1269 equ; 0 cnn)
% Maximal formula atoms : 298 ( 136 avg)
% Number of connectives : 2611 ( 32 ~; 17 |; 917 &; 448 @)
% ( 2 <=>;1195 =>; 0 <=; 0 <~>)
% Maximal formula depth : 307 ( 64 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 603 ( 600 usr; 303 con; 0-4 aty)
% Number of variables : 160 ( 56 ^; 71 !; 33 ?; 160 :)
% 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_354,type,
sP0: $i > $o > $i > $o ).
thf(func_def_355,type,
sP1: $i > ( $i > $o ) > $o ).
thf(func_def_357,type,
sP3: ( $i > $o ) > $o ).
thf(func_def_358,type,
sP4: $i > $i > $o ).
thf(func_def_360,type,
sP6: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_361,type,
sP7: ( $i > $i > $o ) > $i > $o ).
thf(func_def_363,type,
sP9: ( $i > $o ) > $i > $o ).
thf(func_def_367,type,
sP13: ( $i > $o ) > $i > $o ).
thf(func_def_368,type,
sP14: ( $i > $o ) > $i > $i > $i > $o ).
thf(func_def_369,type,
sP15: $o > $i > $i > $o ).
thf(func_def_371,type,
sP17: ( $i > $o ) > $i > $o ).
thf(func_def_372,type,
sP18: $i > $i > ( $i > $o ) > $o ).
thf(func_def_373,type,
sP19: ( $i > $o ) > $o ).
thf(func_def_374,type,
sP20: $i > $i > $i > $o ).
thf(func_def_375,type,
sP21: $i > $i > $i > $o > $o ).
thf(func_def_376,type,
sP22: $i > $o > $i > $i > $o ).
thf(func_def_379,type,
sP25: $i > $i > $i > $o ).
thf(func_def_381,type,
sP27: $i > $i > $o ).
thf(func_def_383,type,
sP29: $i > ( $i > $o ) > $o ).
thf(func_def_386,type,
sP32: $i > $i > $i > $o ).
thf(func_def_387,type,
sP33: $i > $i > $o ).
thf(func_def_388,type,
sP34: $i > $o ).
thf(func_def_389,type,
sP35: $i > $i > $o ).
thf(func_def_390,type,
sP36: $i > $i > $o ).
thf(func_def_391,type,
sP37: $i > $i > $o ).
thf(func_def_392,type,
sP38: $i > ( $i > $o ) > $o ).
thf(func_def_395,type,
sP41: $i > $i > $i > $i > $o ).
thf(func_def_396,type,
sP42: $i > $i > $i > $o ).
thf(func_def_397,type,
sP43: $i > $i > $i > $o ).
thf(func_def_398,type,
sP44: $i > $i > $i > $o ).
thf(func_def_399,type,
sP45: $i > ( $i > $i ) > $i > $o ).
thf(func_def_401,type,
sP47: $i > $i > ( $i > $o ) > $o ).
thf(func_def_402,type,
sP48: $i > $o ).
thf(func_def_403,type,
sP49: $i > ( $i > $o ) > $o ).
thf(func_def_405,type,
sP51: $i > $i > ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_406,type,
sP52: $i > $i > ( $i > $i ) > $o ).
thf(func_def_409,type,
sP55: $i > $i > $o ).
thf(func_def_411,type,
sP57: $i > $i > $i > $o ).
thf(func_def_413,type,
sP59: ( $i > $o ) > $o ).
thf(func_def_414,type,
sP60: $i > $i > $i > $o ).
thf(func_def_417,type,
sP63: ( $i > $o ) > $o ).
thf(func_def_418,type,
sP64: $i > $i > $o > $o ).
thf(func_def_419,type,
sP65: $i > $i > $i > $o ).
thf(func_def_420,type,
sP66: $i > $i > $i > $i > $o ).
thf(func_def_421,type,
sP67: $i > $i > $i > $i > $o ).
thf(func_def_422,type,
sP68: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_423,type,
sP69: $i > ( $i > $i > $o ) > $i > $o ).
thf(func_def_424,type,
sP70: $i > $o ).
thf(func_def_425,type,
sP71: $i > $o ).
thf(func_def_426,type,
sP72: ( $i > $o ) > $i > $o ).
thf(func_def_427,type,
sP73: ( $i > $o ) > $i > $o ).
thf(func_def_428,type,
sP74: ( $i > $o ) > $o ).
thf(func_def_429,type,
sP75: $o > $i > $i > $o ).
thf(func_def_430,type,
sP76: $i > $i > $i > $o ).
thf(func_def_431,type,
sP77: $i > $i > $i > $o ).
thf(func_def_432,type,
sP78: $i > $i > $i > $o ).
thf(func_def_435,type,
sP81: $i > ( $i > $o ) > $o ).
thf(func_def_436,type,
sP82: $i > ( $i > $o ) > $i > $i > $o ).
thf(func_def_437,type,
sP83: ( $i > $o ) > $i > $o ).
thf(func_def_438,type,
sP84: $i > $i > ( $i > $o ) > $o ).
thf(func_def_439,type,
sP85: $i > $i > $i > $i > $o ).
thf(func_def_440,type,
sP86: ( $i > $o ) > $i > $o ).
thf(func_def_442,type,
sP88: $i > ( $i > $o ) > $o ).
thf(func_def_443,type,
sP89: ( $i > $o ) > $i > $o ).
thf(func_def_444,type,
sP90: $i > $i > $i > $o ).
thf(func_def_445,type,
sP91: $i > $i > $i > $o ).
thf(func_def_446,type,
sP92: $i > $i > $i > $o ).
thf(func_def_473,type,
sK119: $i > $i ).
thf(func_def_479,type,
sK125: $i > $o > $i > $i ).
thf(func_def_485,type,
sK131: $i > $o ).
thf(func_def_487,type,
sK133: $i > ( $i > $o ) > $i ).
thf(func_def_488,type,
sK134: $i > ( $i > $o ) > $i ).
thf(func_def_499,type,
sK145: ( $i > $o ) > $i ).
thf(func_def_500,type,
sK146: $i > ( $i > $o ) > $i ).
thf(func_def_501,type,
sK147: $i > $o ).
thf(func_def_508,type,
sK154: $i > $i > $i ).
thf(func_def_530,type,
sK176: $i > $i > $o ).
thf(func_def_571,type,
sK217: $i > $i > $o ).
thf(func_def_585,type,
sK231: $i > $i > $o ).
thf(func_def_586,type,
sK232: ( $i > $i > $o ) > $i > $i ).
thf(func_def_587,type,
sK233: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_588,type,
sK234: ( $i > $i > $o ) > $i > $i ).
thf(func_def_589,type,
sK235: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_604,type,
sK250: $i > $o ).
thf(func_def_605,type,
sK251: ( $i > $o ) > $i > $i ).
thf(func_def_606,type,
sK252: ( $i > $o ) > $i > $i ).
thf(func_def_621,type,
sK267: $i > $i ).
thf(func_def_624,type,
sK270: $i > $i > ( $i > $i ) > $i ).
thf(func_def_629,type,
sK275: $i > $o ).
thf(func_def_631,type,
sK277: $i > $o ).
thf(func_def_638,type,
sK284: $i > $o ).
thf(func_def_639,type,
sK285: ( $i > $o ) > $i > $i ).
thf(func_def_642,type,
sK288: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_643,type,
sK289: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_644,type,
sK290: ( $i > $o ) > $i > $i ).
thf(func_def_648,type,
sK294: $i > $o ).
thf(func_def_653,type,
sK299: $i > $i > ( $i > $o ) > $i ).
thf(func_def_654,type,
sK300: $i > $i > ( $i > $o ) > $i ).
thf(func_def_655,type,
sK301: ( $i > $o ) > $i > $i ).
thf(func_def_658,type,
sK304: $i > $o ).
thf(func_def_660,type,
sK306: ( $i > $o ) > $i ).
thf(func_def_661,type,
sK307: ( $i > $o ) > $i ).
thf(func_def_662,type,
sK308: $i > $o ).
thf(func_def_672,type,
sK318: $i > $o ).
thf(func_def_675,type,
sK321: $i > $i > $o ).
thf(func_def_678,type,
sK324: $i > $i > $i > $i ).
thf(func_def_679,type,
sK325: $i > $i > $i > $i > $i ).
thf(func_def_702,type,
sK348: $i > $o ).
thf(func_def_703,type,
sK349: $i > $o ).
thf(func_def_704,type,
sK350: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_705,type,
sK351: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_709,type,
sK355: $i > $i ).
thf(func_def_712,type,
sK358: $i > $i > ( $i > $i ) > $i ).
thf(func_def_713,type,
sK359: $i > $i > $i > $i ).
thf(func_def_734,type,
sK380: $i > $i > $i ).
thf(func_def_740,type,
sK386: $i > $i > $i ).
thf(func_def_741,type,
sK387: $i > $i > $i ).
thf(func_def_742,type,
sK388: $i > $o ).
thf(func_def_744,type,
sK390: $i > ( $i > $o ) > $i ).
thf(func_def_745,type,
sK391: $i > ( $i > $o ) > $i ).
thf(func_def_757,type,
sK403: $i > $i ).
thf(func_def_759,type,
sK405: $i > ( $i > $i ) > $i > $i ).
thf(func_def_760,type,
sK406: $i > $i > $i ).
thf(func_def_761,type,
sK407: $i > $i > $i ).
thf(func_def_762,type,
sK408: $i > $i > $i > $i ).
thf(func_def_763,type,
sK409: $i > $i > $i ).
thf(func_def_764,type,
sK410: $i > $i > $i ).
thf(func_def_765,type,
sK411: $i > $i > $i ).
thf(func_def_766,type,
sK412: $i > $i > $i ).
thf(func_def_767,type,
sK413: $i > $i > $i ).
thf(func_def_768,type,
sK414: $i > $i ).
thf(func_def_769,type,
sK415: $i > $i ).
thf(func_def_770,type,
sK416: $i > $i ).
thf(func_def_771,type,
sK417: $i > $i ).
thf(func_def_772,type,
sK418: $i > $i > $i ).
thf(func_def_773,type,
sK419: $i > $i > $i ).
thf(func_def_774,type,
sK420: $i > $i > $i ).
thf(func_def_775,type,
sK421: $i > $i > $i > $i ).
thf(func_def_776,type,
sK422: $i > $i > $i > $i ).
thf(func_def_778,type,
sK424: $i > $i ).
thf(func_def_781,type,
sK427: $i > $o ).
thf(func_def_782,type,
sK428: ( $i > $o ) > $i > $i ).
thf(func_def_783,type,
sK429: $i > ( $i > $o ) > $i ).
thf(func_def_796,type,
sK442: $i > $i > $i ).
thf(func_def_802,type,
sK448: $i > $i ).
thf(func_def_805,type,
sK451: $i > $i > $i > $i ).
thf(func_def_806,type,
sK452: $i > $i > $i > $i > $i ).
thf(func_def_807,type,
sK453: $i > $i > $i > $i > $i ).
thf(func_def_808,type,
sK454: $i > $i > $i > $i > $i ).
thf(func_def_816,type,
sK462: $i > $i > $i > $i ).
thf(func_def_817,type,
sK463: $i > $i > $i > $i ).
thf(func_def_822,type,
sK468: $i > $i ).
thf(func_def_824,type,
sK470: $i > ( $i > $i ) > $i > $i ).
thf(func_def_825,type,
sK471: $i > ( $i > $i ) > $i > $i ).
thf(func_def_826,type,
sK472: $i > $i > ( $i > $o ) > $i ).
thf(func_def_828,type,
sK474: $i > $o ).
thf(func_def_837,type,
sK483: $i > $i > $i ).
thf(func_def_838,type,
sK484: $i > $i ).
thf(func_def_841,type,
sK487: $i > $o ).
thf(func_def_843,type,
sK489: $i > ( $i > $o ) > $i ).
thf(func_def_844,type,
sK490: $i > ( $i > $o ) > $i ).
thf(func_def_847,type,
sK493: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_848,type,
sK494: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_851,type,
sK497: $i > $o ).
thf(func_def_852,type,
sK498: $i > $o ).
thf(func_def_858,type,
sK504: $i > $o ).
thf(func_def_861,type,
sK507: $i > $i ).
thf(func_def_863,type,
sK509: $i > ( $i > $i ) > $i > $i ).
thf(func_def_864,type,
sK510: $i > $i > ( $i > $i ) > $i ).
thf(func_def_866,type,
sK512: $i > $i ).
thf(func_def_877,type,
sK523: $i > $o ).
thf(func_def_899,type,
sK545: $i > $i > $o ).
thf(func_def_911,type,
sK557: $i > $i > $i ).
thf(func_def_938,type,
sK584: $i > $i > $i ).
thf(func_def_953,type,
sK599: $i > ( $i > $o ) > $i ).
thf(func_def_954,type,
sK600: ( $i > $o ) > $i ).
thf(func_def_955,type,
sK601: $i > $o ).
thf(func_def_966,type,
sK612: $i > $i > $o ).
thf(func_def_979,type,
sK625: $i > $i > $i > $i ).
thf(func_def_980,type,
sK626: $i > $i > $i > $i ).
thf(func_def_988,type,
sK634: $i > $o ).
thf(func_def_989,type,
sK635: $i > $o ).
thf(func_def_990,type,
sK636: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_991,type,
sK637: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1001,type,
sK647: $i > $i > $i ).
thf(func_def_1004,type,
sK650: $i > ( $i > $o ) > $i ).
thf(func_def_1005,type,
sK651: ( $i > $o ) > $i ).
thf(func_def_1006,type,
sK652: $i > $o ).
thf(func_def_1025,type,
sK671: $i > $i > $i > $i ).
thf(func_def_1026,type,
sK672: $i > $i > $i > $o ).
thf(func_def_1052,type,
sK698: $i > $i > $i > $i > $i ).
thf(func_def_1053,type,
sK699: $i > $i > $i > $i > $i ).
thf(func_def_1054,type,
sK700: $i > $i > $i > $i > $i ).
thf(func_def_1055,type,
sK701: $i > $i > $i > $i > $i ).
thf(func_def_1064,type,
sK710: $i > $o ).
thf(func_def_1069,type,
sK715: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_1070,type,
sK716: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_1071,type,
sK717: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_1072,type,
sK718: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_1073,type,
sK719: $i > $i > $o ).
thf(func_def_1084,type,
sK730: $i > $i ).
thf(func_def_1085,type,
sK731: $i > $i ).
thf(func_def_1087,type,
sK733: $i > $i ).
thf(func_def_1089,type,
sK735: $i > $i > $i ).
thf(func_def_1098,type,
sK744: ( $i > $o ) > $i > $i ).
thf(func_def_1099,type,
sK745: ( $i > $o ) > $i > $i ).
thf(func_def_1100,type,
sK746: ( $i > $o ) > $i > $i ).
thf(func_def_1101,type,
sK747: $i > $o ).
thf(func_def_1107,type,
sK753: $i > $i > $o ).
thf(func_def_1114,type,
sK760: $i > $i > $o ).
thf(func_def_1118,type,
sK764: $i > $o ).
thf(func_def_1126,type,
sK772: $i > $o ).
thf(func_def_1131,type,
sK777: $i > $o ).
thf(func_def_1132,type,
sK778: ( $i > $o ) > $i ).
thf(func_def_1138,type,
sK784: $i > $o ).
thf(func_def_1143,type,
sK789: ( $i > $o ) > $i ).
thf(func_def_1144,type,
sK790: $i > ( $i > $o ) > $i ).
thf(func_def_1145,type,
sK791: $i > $o ).
thf(func_def_1146,type,
sK792: $i > $i > $i > $o ).
thf(func_def_1164,type,
sK810: $i > $i > $i > $i ).
thf(func_def_1175,type,
sK821: $i > $o ).
thf(func_def_1179,type,
sK825: $i > $i > $i > $i ).
thf(func_def_1180,type,
sK826: $i > $i > $i > $i > $i ).
thf(func_def_1190,type,
sK836: $i > $i ).
thf(func_def_1191,type,
sK837: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1208,type,
sK854: $i > $i > $i ).
thf(func_def_1239,type,
sK885: $i > $o ).
thf(func_def_1278,type,
sK924: $i > ( $i > $o ) > $i > $i > $i ).
thf(func_def_1279,type,
sK925: $i > ( $i > $o ) > $i > $i > $i ).
thf(func_def_1280,type,
sK926: $i > ( $i > $o ) > $i ).
thf(func_def_1284,type,
sK930: $i > $o ).
thf(func_def_1288,type,
sK934: $i > $o ).
thf(func_def_1312,type,
sK958: $i > $i > ( $i > $o ) > $i ).
thf(func_def_1313,type,
sK959: $i > $i > ( $i > $o ) > $i ).
thf(func_def_1314,type,
sK960: ( $i > $o ) > $i > $i ).
thf(func_def_1317,type,
sK963: $i > $o ).
thf(func_def_1321,type,
sK967: $i > $i > $i > $i > $i ).
thf(func_def_1322,type,
sK968: $i > $i > $i > $i > $i ).
thf(func_def_1333,type,
sK979: $i > $o ).
thf(func_def_1334,type,
sK980: ( $i > $o ) > $i > $i ).
thf(func_def_1335,type,
sK981: ( $i > $o ) > $i > $i ).
thf(func_def_1347,type,
sK993: ( $i > $o ) > $i > $i ).
thf(func_def_1348,type,
sK994: ( $i > $o ) > $i > $i ).
thf(func_def_1349,type,
sK995: $i > ( $i > $o ) > $i ).
thf(func_def_1350,type,
sK996: $i > $o ).
thf(func_def_1357,type,
sK1003: $i > $i > $o ).
thf(func_def_1359,type,
sK1005: $i > $i > $i > $i ).
thf(func_def_1360,type,
sK1006: $i > $i > $i > $i ).
thf(func_def_1361,type,
sK1007: $i > $i > $i > $i ).
thf(func_def_1362,type,
sK1008: $i > $i > $i > $i ).
thf(func_def_1376,type,
sK1022: $i > $o ).
thf(func_def_1384,type,
sK1030: $i > $i > $i > $i ).
thf(func_def_1385,type,
sK1031: $i > $i > $i > $i ).
thf(func_def_1400,type,
ph1046:
!>[X0: $tType] : X0 ).
thf(f13584,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f13529,f4004]) ).
thf(f4004,plain,
( ( in @ ( kpair @ sK580 @ sK581 ) @ sK579 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f2307]) ).
thf(f2307,plain,
( ( singletonprop = $true )
& ( ap2apEq2 = $true )
& ( woz1_1 = $true )
& ( setukpairinjR2 = $true )
& ( dpsetconstrEL1 = $true )
& ( demorgan2a1 = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( beta2 = $true )
& ( kfstpairEq = $true )
& ( binunionTIRcontra = $true )
& ( iftrue = $true )
& ( binunionTILcontra = $true )
& ( notdexE = $true )
& ( woz1_3 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( binintersectSubset2 = $true )
& ( ex1I = $true )
& ( woz13rule4 = $true )
& ( exuEu = $true )
& ( binintersectRsub = $true )
& ( nonemptyE1 = $true )
& ( binintersectSubset1 = $true )
& ( symdiffI1 = $true )
& ( descrp = $true )
& ( demorgan2a2 = $true )
& ( subsetE = $true )
& ( breln1invprop = $true )
& ( iftrueProp2 = $true )
& ( inIntersectImpInUnion = $true )
& ( binunionIR = $true )
& ( setminusER = $true )
& ( setunionE2 = $true )
& ( eqimpsubset2 = $true )
& ( apProp = $true )
& ( setoftrueEq = $true )
& ( omega__Cong = $true )
& ( powerset__Cong = $true )
& ( nonemptyI = $true )
& ( emptysetimpfalse = $true )
& ( powersetTE1 = $true )
& ( ex1I2 = $true )
& ( iffalseProp1 = $true )
& ( theeq = $true )
& ( cartprodsndpairEq = $true )
& ( dsetconstrEL = $true )
& ( subsetemptysetimpeq = $true )
& ( doubleComplementE1 = $true )
& ( setadjoinSub = $true )
& ( breln1all1 = $true )
& ( cartprodfstin = $true )
& ( iffalse = $true )
& ( emptysetE = $true )
& ( setukpairinjR12 = $true )
& ( subsetTrans = $true )
& ( funcGraphProp1 = $true )
& ( binunionEcases = $true )
& ( sepSubset = $true )
& ( iffalseProp2 = $true )
& ( setminusIRneg = $true )
& ( inCongP = $true )
& ( cartprodpairmemEL = $true )
& ( singletoninpowunion = $true )
& ( quantDeMorgan4 = $true )
& ( setminusERneg = $true )
& ( woz13rule3 = $true )
& ( funcinfuncset = $true )
& ( setOfPairsIsBReln = $true )
& ( kfstsingleton = $true )
& ( setextAx = $true )
& ( demorgan2b = $true )
& ( doubleComplementSub2 = $true )
& ( brelnall1 = $true )
& ( emptysetsubset = $true )
& ( setukpairinjL1 = $true )
& ( symdiffI2 = $true )
& ( singletoninpowerset = $true )
& ( woz1_5 = $true )
& ( lamProp = $true )
& ( ubforcartprodlem2 = $true )
& ( powersetAx = $true )
& ( eqbreln = $true )
& ( ksndpairEq = $true )
& ( upairsetE = $true )
& ( prop2setI = $true )
& ( brelnall2 = $true )
& ( powersetE = $true )
& ( cartprodmempair1 = $true )
& ( symdiffIneg2 = $true )
& ( ex1E2 = $true )
& ( setadjoinE = $true )
& ( cartprodpairin = $true )
& ( noeltsimpempty = $true )
& ( foundationAx = $true )
& ( setunionE = $true )
& ( woz13rule1 = $true )
& ( emptysetAx = $true )
& ( ap2apEq1 = $true )
& ( complementTE1 = $true )
& ( singletonsubset = $true )
& ( emptyInPowerset = $true )
& ( demorgan1a = $true )
& ( setminusELneg = $true )
& ( theprop = $true )
& ( powersetE1 = $true )
& ( upairsubunion = $true )
& ( demorgan2a = $true )
& ( emptyinunitempty = $true )
& ( setext = $true )
& ( ap2p = $true )
& ( setminusT_lem = $true )
& ( emptyI = $true )
& ( wellorderingAx = $true )
& ( subsetI2 = $true )
& ( doubleComplementEq = $true )
& ( setadjoinIL = $true )
& ( subsetRefl = $true )
& ( ubforcartprodlem1 = $true )
& ( eqimpsubset1 = $true )
& ( subbreln1 = $true )
& ( setunionsingleton1 = $true )
& ( funcext = $true )
& ( setadjoinIR = $true )
& ( woz13rule2 = $true )
& ( dsetconstrI = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( setminusEL = $true )
& ( disjointsetsI1 = $true )
& ( funcImageSingleton = $true )
& ( setminusSubset1 = $true )
& ( powersetI = $true )
& ( replAx = $true )
& ( funcextLem = $true )
& ( binintersectSubset5 = $true )
& ( binintersectER = $true )
& ( binunionRsub = $true )
& ( iftrueProp1 = $true )
& ( setextT = $true )
& ( exuE3e = $true )
& ( complementImpComplementIntersect = $true )
& ( exuE1 = $true )
& ( ifSingleton = $true )
& ( doubleComplementI1 = $true )
& ( dpsetconstrER = $true )
& ( quantDeMorgan2 = $true )
& ( powersetTI1 = $true )
& ( app = $true )
& ( notequalI1 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( exuI2 = $true )
& ( setminusILneg = $true )
& ( cartprodmempaircEq = $true )
& ( eta2 = $true )
& ( funcGraphProp2 = $true )
& ( subsetE2 = $true )
& ( setukpairinjL2 = $true )
& ( singletonsswitch = $true )
& ( complementTI1 = $true )
& ( ( breln1 @ sK578 @ sK579 )
= $true )
& ( $true
= ( in @ sK580 @ sK578 ) )
& ( ( in @ ( kpair @ sK581 @ sK580 ) @ ( breln1invset @ sK578 @ sK579 ) )
= $true )
& ( ( in @ ( kpair @ sK580 @ sK581 ) @ sK579 )
!= $true )
& ( $true
= ( in @ sK581 @ sK578 ) )
& ( setextsub = $true )
& ( prop2set2propI = $true )
& ( binintersectSubset3 = $true )
& ( setunionsingleton = $true )
& ( powersetsubset = $true )
& ( symdiffIneg1 = $true )
& ( upairset2E = $true )
& ( notinemptyset = $true )
& ( dpsetconstrI = $true )
& ( setukpairinjR1 = $true )
& ( woz1_2 = $true )
& ( eta1 = $true )
& ( setminusLsub = $true )
& ( exuE3u = $true )
& ( subsetI1 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( binintersectT_lem = $true )
& ( quantDeMorgan3 = $true )
& ( beta1 = $true )
& ( omegaSAx = $true )
& ( in__Cong = $true )
& ( funcGraphProp4 = $true )
& ( omegaIndAx = $true )
& ( setunion__Cong = $true )
& ( notinsingleton = $true )
& ( binunionTE = $true )
& ( upairequniteq = $true )
& ( singletonsuniq = $true )
& ( contraSubsetComplement = $true )
& ( subset2powerset = $true )
& ( powersetI1 = $true )
& ( complementTcontraSubset = $true )
& ( setminusSubset2 = $true )
& ( complementT_lem = $true )
& ( binunionE = $true )
& ( lamp = $true )
& ( ubforcartprodlem3 = $true )
& ( ksndsingleton = $true )
& ( exuI3 = $true )
& ( omega0Ax = $true )
& ( upairsetIL = $true )
& ( sepInPowerset = $true )
& ( symdiffE = $true )
& ( cartprodpairmemER = $true )
& ( bs114d = $true )
& ( breln1SetBreln1 = $true )
& ( secondinupair = $true )
& ( contrasubsetT1 = $true )
& ( funcGraphProp3 = $true )
& ( eqbreln1 = $true )
& ( upairset2IR = $true )
& ( binintersectTERcontra = $true )
& ( binunionLsub = $true )
& ( setunionI = $true )
& ( notsubsetI = $true )
& ( setadjoinAx = $true )
& ( binunionIL = $true )
& ( setminusI = $true )
& ( iftrueorfalse = $true )
& ( setOfPairsIsBReln1 = $true )
& ( nonemptyI1 = $true )
& ( demorgan2 = $true )
& ( upairinpowunion = $true )
& ( woz1_4 = $true )
& ( contrasubsetT2 = $true )
& ( contrasubsetT3 = $true )
& ( exu__Cong = $true )
& ( powersetT_lem = $true )
& ( setadjoinSub2 = $true )
& ( setunionsingleton2 = $true )
& ( vacuousDall = $true )
& ( dpsetconstrERa = $true )
& ( binunionTEcontra = $true )
& ( cartprodpairsurjEq = $true )
& ( binintersectLsub = $true )
& ( setukpairinjR11 = $true )
& ( doubleComplementSub1 = $true )
& ( notdallE = $true )
& ( setunionAx = $true )
& ( emptyinPowerset = $true )
& ( emptyset__Cong = $true )
& ( cartprodsndin = $true )
& ( ifp = $true )
& ( demorgan1 = $true )
& ( binintersectI = $true )
& ( infuncsetfunc = $true )
& ( prop2setE = $true )
& ( uniqinunit = $true )
& ( complementSubsetComplementIntersect = $true )
& ( kpairiskpair = $true )
& ( complementTnotintersectT = $true )
& ( subPowSU = $true )
& ( exuI1 = $true )
& ( inPowerset = $true )
& ( choice2fnsingleton = $true )
& ( nonemptyImpWitness = $true )
& ( setadjoin__Cong = $true )
& ( setukpairIR = $true )
& ( subsetTI = $true )
& ( binunionT_lem = $true )
& ( quantDeMorgan1 = $true )
& ( ex1E1 = $true )
& ( dsetconstr__Cong = $true )
& ( contrasubsetT = $true )
& ( exuE2 = $true )
& ( setadjoinOr = $true )
& ( binintersectSubset4 = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( eqinunit = $true )
& ( dpsetconstrEL2 = $true )
& ( setukpairIL = $true )
& ( setbeta = $true )
& ( breln1invI = $true )
& ( kpairp = $true )
& ( funcext2 = $true )
& ( setukpairinjL = $true )
& ( cartprodmempair = $true )
& ( lam2lamEq = $true )
& ( dpsetconstrSub = $true )
& ( emptyE1 = $true )
& ( demorgan2b2 = $true )
& ( binintersectEL = $true )
& ( cartprodfstpairEq = $true )
& ( subbreln = $true )
& ( descr__Cong = $true )
& ( lam2p = $true )
& ( kpairsurjEq = $true )
& ( binintersectTELcontra = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( breln1all2 = $true )
& ( setukpairinjR = $true )
& ( demorgan1b = $true )
& ( woz13rule0 = $true )
& ( upairsetIR = $true )
& ( dsetconstrER = $true )
& ( notequalI2 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK578,sK579,sK580,sK581])],[f1264,f2306,f2305,f2304]) ).
thf(f2304,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
& ? [X3: $i] :
( ( ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X0 @ X1 ) )
= $true )
& ( $true
!= ( in @ ( kpair @ X2 @ X3 ) @ X1 ) )
& ( ( in @ X3 @ X0 )
= $true ) ) ) )
=> ( ( ( breln1 @ sK578 @ sK579 )
= $true )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ sK578 ) )
& ? [X3: $i] :
( ( ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ sK578 @ sK579 ) )
= $true )
& ( ( in @ ( kpair @ X2 @ X3 ) @ sK579 )
!= $true )
& ( $true
= ( in @ X3 @ sK578 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2305,plain,
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ sK578 ) )
& ? [X3: $i] :
( ( ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ sK578 @ sK579 ) )
= $true )
& ( ( in @ ( kpair @ X2 @ X3 ) @ sK579 )
!= $true )
& ( $true
= ( in @ X3 @ sK578 ) ) ) )
=> ( ( $true
= ( in @ sK580 @ sK578 ) )
& ? [X3: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ sK580 ) @ ( breln1invset @ sK578 @ sK579 ) ) )
& ( ( in @ ( kpair @ sK580 @ X3 ) @ sK579 )
!= $true )
& ( $true
= ( in @ X3 @ sK578 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2306,plain,
( ? [X3: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ sK580 ) @ ( breln1invset @ sK578 @ sK579 ) ) )
& ( ( in @ ( kpair @ sK580 @ X3 ) @ sK579 )
!= $true )
& ( $true
= ( in @ X3 @ sK578 ) ) )
=> ( ( ( in @ ( kpair @ sK581 @ sK580 ) @ ( breln1invset @ sK578 @ sK579 ) )
= $true )
& ( ( in @ ( kpair @ sK580 @ sK581 ) @ sK579 )
!= $true )
& ( $true
= ( in @ sK581 @ sK578 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1264,plain,
( ( singletonprop = $true )
& ( ap2apEq2 = $true )
& ( woz1_1 = $true )
& ( setukpairinjR2 = $true )
& ( dpsetconstrEL1 = $true )
& ( demorgan2a1 = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( beta2 = $true )
& ( kfstpairEq = $true )
& ( binunionTIRcontra = $true )
& ( iftrue = $true )
& ( binunionTILcontra = $true )
& ( notdexE = $true )
& ( woz1_3 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( binintersectSubset2 = $true )
& ( ex1I = $true )
& ( woz13rule4 = $true )
& ( exuEu = $true )
& ( binintersectRsub = $true )
& ( nonemptyE1 = $true )
& ( binintersectSubset1 = $true )
& ( symdiffI1 = $true )
& ( descrp = $true )
& ( demorgan2a2 = $true )
& ( subsetE = $true )
& ( breln1invprop = $true )
& ( iftrueProp2 = $true )
& ( inIntersectImpInUnion = $true )
& ( binunionIR = $true )
& ( setminusER = $true )
& ( setunionE2 = $true )
& ( eqimpsubset2 = $true )
& ( apProp = $true )
& ( setoftrueEq = $true )
& ( omega__Cong = $true )
& ( powerset__Cong = $true )
& ( nonemptyI = $true )
& ( emptysetimpfalse = $true )
& ( powersetTE1 = $true )
& ( ex1I2 = $true )
& ( iffalseProp1 = $true )
& ( theeq = $true )
& ( cartprodsndpairEq = $true )
& ( dsetconstrEL = $true )
& ( subsetemptysetimpeq = $true )
& ( doubleComplementE1 = $true )
& ( setadjoinSub = $true )
& ( breln1all1 = $true )
& ( cartprodfstin = $true )
& ( iffalse = $true )
& ( emptysetE = $true )
& ( setukpairinjR12 = $true )
& ( subsetTrans = $true )
& ( funcGraphProp1 = $true )
& ( binunionEcases = $true )
& ( sepSubset = $true )
& ( iffalseProp2 = $true )
& ( setminusIRneg = $true )
& ( inCongP = $true )
& ( cartprodpairmemEL = $true )
& ( singletoninpowunion = $true )
& ( quantDeMorgan4 = $true )
& ( setminusERneg = $true )
& ( woz13rule3 = $true )
& ( funcinfuncset = $true )
& ( setOfPairsIsBReln = $true )
& ( kfstsingleton = $true )
& ( setextAx = $true )
& ( demorgan2b = $true )
& ( doubleComplementSub2 = $true )
& ( brelnall1 = $true )
& ( emptysetsubset = $true )
& ( setukpairinjL1 = $true )
& ( symdiffI2 = $true )
& ( singletoninpowerset = $true )
& ( woz1_5 = $true )
& ( lamProp = $true )
& ( ubforcartprodlem2 = $true )
& ( powersetAx = $true )
& ( eqbreln = $true )
& ( ksndpairEq = $true )
& ( upairsetE = $true )
& ( prop2setI = $true )
& ( brelnall2 = $true )
& ( powersetE = $true )
& ( cartprodmempair1 = $true )
& ( symdiffIneg2 = $true )
& ( ex1E2 = $true )
& ( setadjoinE = $true )
& ( cartprodpairin = $true )
& ( noeltsimpempty = $true )
& ( foundationAx = $true )
& ( setunionE = $true )
& ( woz13rule1 = $true )
& ( emptysetAx = $true )
& ( ap2apEq1 = $true )
& ( complementTE1 = $true )
& ( singletonsubset = $true )
& ( emptyInPowerset = $true )
& ( demorgan1a = $true )
& ( setminusELneg = $true )
& ( theprop = $true )
& ( powersetE1 = $true )
& ( upairsubunion = $true )
& ( demorgan2a = $true )
& ( emptyinunitempty = $true )
& ( setext = $true )
& ( ap2p = $true )
& ( setminusT_lem = $true )
& ( emptyI = $true )
& ( wellorderingAx = $true )
& ( subsetI2 = $true )
& ( doubleComplementEq = $true )
& ( setadjoinIL = $true )
& ( subsetRefl = $true )
& ( ubforcartprodlem1 = $true )
& ( eqimpsubset1 = $true )
& ( subbreln1 = $true )
& ( setunionsingleton1 = $true )
& ( funcext = $true )
& ( setadjoinIR = $true )
& ( woz13rule2 = $true )
& ( dsetconstrI = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( setminusEL = $true )
& ( disjointsetsI1 = $true )
& ( funcImageSingleton = $true )
& ( setminusSubset1 = $true )
& ( powersetI = $true )
& ( replAx = $true )
& ( funcextLem = $true )
& ( binintersectSubset5 = $true )
& ( binintersectER = $true )
& ( binunionRsub = $true )
& ( iftrueProp1 = $true )
& ( setextT = $true )
& ( exuE3e = $true )
& ( complementImpComplementIntersect = $true )
& ( exuE1 = $true )
& ( ifSingleton = $true )
& ( doubleComplementI1 = $true )
& ( dpsetconstrER = $true )
& ( quantDeMorgan2 = $true )
& ( powersetTI1 = $true )
& ( app = $true )
& ( notequalI1 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( exuI2 = $true )
& ( setminusILneg = $true )
& ( cartprodmempaircEq = $true )
& ( eta2 = $true )
& ( funcGraphProp2 = $true )
& ( subsetE2 = $true )
& ( setukpairinjL2 = $true )
& ( singletonsswitch = $true )
& ( complementTI1 = $true )
& ? [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
& ? [X2: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
& ? [X3: $i] :
( ( ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X0 @ X1 ) )
= $true )
& ( $true
!= ( in @ ( kpair @ X2 @ X3 ) @ X1 ) )
& ( ( in @ X3 @ X0 )
= $true ) ) ) )
& ( setextsub = $true )
& ( prop2set2propI = $true )
& ( binintersectSubset3 = $true )
& ( setunionsingleton = $true )
& ( powersetsubset = $true )
& ( symdiffIneg1 = $true )
& ( upairset2E = $true )
& ( notinemptyset = $true )
& ( dpsetconstrI = $true )
& ( setukpairinjR1 = $true )
& ( woz1_2 = $true )
& ( eta1 = $true )
& ( setminusLsub = $true )
& ( exuE3u = $true )
& ( subsetI1 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( binintersectT_lem = $true )
& ( quantDeMorgan3 = $true )
& ( beta1 = $true )
& ( omegaSAx = $true )
& ( in__Cong = $true )
& ( funcGraphProp4 = $true )
& ( omegaIndAx = $true )
& ( setunion__Cong = $true )
& ( notinsingleton = $true )
& ( binunionTE = $true )
& ( upairequniteq = $true )
& ( singletonsuniq = $true )
& ( contraSubsetComplement = $true )
& ( subset2powerset = $true )
& ( powersetI1 = $true )
& ( complementTcontraSubset = $true )
& ( setminusSubset2 = $true )
& ( complementT_lem = $true )
& ( binunionE = $true )
& ( lamp = $true )
& ( ubforcartprodlem3 = $true )
& ( ksndsingleton = $true )
& ( exuI3 = $true )
& ( omega0Ax = $true )
& ( upairsetIL = $true )
& ( sepInPowerset = $true )
& ( symdiffE = $true )
& ( cartprodpairmemER = $true )
& ( bs114d = $true )
& ( breln1SetBreln1 = $true )
& ( secondinupair = $true )
& ( contrasubsetT1 = $true )
& ( funcGraphProp3 = $true )
& ( eqbreln1 = $true )
& ( upairset2IR = $true )
& ( binintersectTERcontra = $true )
& ( binunionLsub = $true )
& ( setunionI = $true )
& ( notsubsetI = $true )
& ( setadjoinAx = $true )
& ( binunionIL = $true )
& ( setminusI = $true )
& ( iftrueorfalse = $true )
& ( setOfPairsIsBReln1 = $true )
& ( nonemptyI1 = $true )
& ( demorgan2 = $true )
& ( upairinpowunion = $true )
& ( woz1_4 = $true )
& ( contrasubsetT2 = $true )
& ( contrasubsetT3 = $true )
& ( exu__Cong = $true )
& ( powersetT_lem = $true )
& ( setadjoinSub2 = $true )
& ( setunionsingleton2 = $true )
& ( vacuousDall = $true )
& ( dpsetconstrERa = $true )
& ( binunionTEcontra = $true )
& ( cartprodpairsurjEq = $true )
& ( binintersectLsub = $true )
& ( setukpairinjR11 = $true )
& ( doubleComplementSub1 = $true )
& ( notdallE = $true )
& ( setunionAx = $true )
& ( emptyinPowerset = $true )
& ( emptyset__Cong = $true )
& ( cartprodsndin = $true )
& ( ifp = $true )
& ( demorgan1 = $true )
& ( binintersectI = $true )
& ( infuncsetfunc = $true )
& ( prop2setE = $true )
& ( uniqinunit = $true )
& ( complementSubsetComplementIntersect = $true )
& ( kpairiskpair = $true )
& ( complementTnotintersectT = $true )
& ( subPowSU = $true )
& ( exuI1 = $true )
& ( inPowerset = $true )
& ( choice2fnsingleton = $true )
& ( nonemptyImpWitness = $true )
& ( setadjoin__Cong = $true )
& ( setukpairIR = $true )
& ( subsetTI = $true )
& ( binunionT_lem = $true )
& ( quantDeMorgan1 = $true )
& ( ex1E1 = $true )
& ( dsetconstr__Cong = $true )
& ( contrasubsetT = $true )
& ( exuE2 = $true )
& ( setadjoinOr = $true )
& ( binintersectSubset4 = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( eqinunit = $true )
& ( dpsetconstrEL2 = $true )
& ( setukpairIL = $true )
& ( setbeta = $true )
& ( breln1invI = $true )
& ( kpairp = $true )
& ( funcext2 = $true )
& ( setukpairinjL = $true )
& ( cartprodmempair = $true )
& ( lam2lamEq = $true )
& ( dpsetconstrSub = $true )
& ( emptyE1 = $true )
& ( demorgan2b2 = $true )
& ( binintersectEL = $true )
& ( cartprodfstpairEq = $true )
& ( subbreln = $true )
& ( descr__Cong = $true )
& ( lam2p = $true )
& ( kpairsurjEq = $true )
& ( binintersectTELcontra = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( breln1all2 = $true )
& ( setukpairinjR = $true )
& ( demorgan1b = $true )
& ( woz13rule0 = $true )
& ( upairsetIR = $true )
& ( dsetconstrER = $true )
& ( notequalI2 = $true ) ),
inference(flattening,[status(thm)],[f1263]) ).
thf(f1263,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ ( kpair @ X2 @ X3 ) @ X1 ) )
& ( ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X0 @ X1 ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( $true
= ( in @ X2 @ X0 ) ) )
& ( $true
= ( breln1 @ X0 @ X1 ) ) )
& ( breln1invI = $true )
& ( breln1invprop = $true )
& ( eqbreln1 = $true )
& ( subbreln1 = $true )
& ( breln1all1 = $true )
& ( setOfPairsIsBReln1 = $true )
& ( choice2fnsingleton = $true )
& ( breln1SetBreln1 = $true )
& ( breln1all2 = $true )
& ( woz1_5 = $true )
& ( woz1_4 = $true )
& ( woz1_3 = $true )
& ( woz1_2 = $true )
& ( woz1_1 = $true )
& ( woz13rule4 = $true )
& ( woz13rule3 = $true )
& ( woz13rule2 = $true )
& ( woz13rule1 = $true )
& ( woz13rule0 = $true )
& ( demorgan2 = $true )
& ( demorgan2b = $true )
& ( demorgan2b2 = $true )
& ( demorgan2a = $true )
& ( demorgan1 = $true )
& ( demorgan1b = $true )
& ( demorgan1a = $true )
& ( demorgan2a2 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( demorgan2a1 = $true )
& ( binunionTEcontra = $true )
& ( binunionTE = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( inIntersectImpInUnion2 = $true )
& ( inIntersectImpInUnion = $true )
& ( binunionTIRcontra = $true )
& ( binunionTILcontra = $true )
& ( complementTcontraSubset = $true )
& ( contraSubsetComplement = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( complementSubsetComplementIntersect = $true )
& ( complementImpComplementIntersect = $true )
& ( complementTnotintersectT = $true )
& ( doubleComplementEq = $true )
& ( doubleComplementSub2 = $true )
& ( doubleComplementSub1 = $true )
& ( doubleComplementE1 = $true )
& ( doubleComplementI1 = $true )
& ( contrasubsetT3 = $true )
& ( contrasubsetT2 = $true )
& ( contrasubsetT1 = $true )
& ( contrasubsetT = $true )
& ( binintersectTERcontra = $true )
& ( binintersectTELcontra = $true )
& ( complementTE1 = $true )
& ( complementTI1 = $true )
& ( powersetTE1 = $true )
& ( powersetTI1 = $true )
& ( subsetTI = $true )
& ( setextT = $true )
& ( complementT_lem = $true )
& ( setminusT_lem = $true )
& ( powersetT_lem = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true )
& ( iftrueorfalse = $true )
& ( iffalse = $true )
& ( iftrue = $true )
& ( theeq = $true )
& ( ifp = $true )
& ( ifSingleton = $true )
& ( iftrueProp2 = $true )
& ( iftrueProp1 = $true )
& ( iffalseProp2 = $true )
& ( iffalseProp1 = $true )
& ( eta2 = $true )
& ( beta2 = $true )
& ( lam2lamEq = $true )
& ( eta1 = $true )
& ( beta1 = $true )
& ( ap2apEq2 = $true )
& ( ap2apEq1 = $true )
& ( funcext2 = $true )
& ( funcext = $true )
& ( eqbreln = $true )
& ( subbreln = $true )
& ( funcGraphProp4 = $true )
& ( funcextLem = $true )
& ( funcGraphProp2 = $true )
& ( funcGraphProp3 = $true )
& ( funcGraphProp1 = $true )
& ( ex1E2 = $true )
& ( brelnall2 = $true )
& ( brelnall1 = $true )
& ( lam2p = $true )
& ( lamp = $true )
& ( lamProp = $true )
& ( funcinfuncset = $true )
& ( ap2p = $true )
& ( infuncsetfunc = $true )
& ( app = $true )
& ( apProp = $true )
& ( funcImageSingleton = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrEL2 = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrERa = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrI = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodsndin = $true )
& ( kpairsurjEq = $true )
& ( ksndpairEq = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( setukpairinjR2 = $true )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f527]) ).
thf(f527,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ( ( ap2p = $true )
=> ( ( funcinfuncset = $true )
=> ( ( lamProp = $true )
=> ( ( lamp = $true )
=> ( ( lam2p = $true )
=> ( ( brelnall1 = $true )
=> ( ( brelnall2 = $true )
=> ( ( ex1E2 = $true )
=> ( ( funcGraphProp1 = $true )
=> ( ( funcGraphProp3 = $true )
=> ( ( funcGraphProp2 = $true )
=> ( ( funcextLem = $true )
=> ( ( funcGraphProp4 = $true )
=> ( ( subbreln = $true )
=> ( ( eqbreln = $true )
=> ( ( funcext = $true )
=> ( ( funcext2 = $true )
=> ( ( ap2apEq1 = $true )
=> ( ( ap2apEq2 = $true )
=> ( ( beta1 = $true )
=> ( ( eta1 = $true )
=> ( ( lam2lamEq = $true )
=> ( ( beta2 = $true )
=> ( ( eta2 = $true )
=> ( ( iffalseProp1 = $true )
=> ( ( iffalseProp2 = $true )
=> ( ( iftrueProp1 = $true )
=> ( ( iftrueProp2 = $true )
=> ( ( ifSingleton = $true )
=> ( ( ifp = $true )
=> ( ( theeq = $true )
=> ( ( iftrue = $true )
=> ( ( iffalse = $true )
=> ( ( iftrueorfalse = $true )
=> ( ( binintersectT_lem = $true )
=> ( ( binunionT_lem = $true )
=> ( ( powersetT_lem = $true )
=> ( ( setminusT_lem = $true )
=> ( ( complementT_lem = $true )
=> ( ( setextT = $true )
=> ( ( subsetTI = $true )
=> ( ( powersetTI1 = $true )
=> ( ( powersetTE1 = $true )
=> ( ( complementTI1 = $true )
=> ( ( complementTE1 = $true )
=> ( ( binintersectTELcontra = $true )
=> ( ( binintersectTERcontra = $true )
=> ( ( contrasubsetT = $true )
=> ( ( contrasubsetT1 = $true )
=> ( ( contrasubsetT2 = $true )
=> ( ( contrasubsetT3 = $true )
=> ( ( doubleComplementI1 = $true )
=> ( ( doubleComplementE1 = $true )
=> ( ( doubleComplementSub1 = $true )
=> ( ( doubleComplementSub2 = $true )
=> ( ( doubleComplementEq = $true )
=> ( ( complementTnotintersectT = $true )
=> ( ( complementImpComplementIntersect = $true )
=> ( ( complementSubsetComplementIntersect = $true )
=> ( ( complementInPowersetComplementIntersect = $true )
=> ( ( contraSubsetComplement = $true )
=> ( ( complementTcontraSubset = $true )
=> ( ( binunionTILcontra = $true )
=> ( ( binunionTIRcontra = $true )
=> ( ( inIntersectImpInUnion = $true )
=> ( ( inIntersectImpInUnion2 = $true )
=> ( ( inIntersectImpInIntersectUnions = $true )
=> ( ( intersectInPowersetIntersectUnions = $true )
=> ( ( inComplementUnionImpNotIn1 = $true )
=> ( ( inComplementUnionImpInComplement1 = $true )
=> ( ( binunionTE = $true )
=> ( ( binunionTEcontra = $true )
=> ( ( demorgan2a1 = $true )
=> ( ( complementUnionInPowersetComplement = $true )
=> ( ( demorgan2a2 = $true )
=> ( ( demorgan1a = $true )
=> ( ( demorgan1b = $true )
=> ( ( demorgan1 = $true )
=> ( ( demorgan2a = $true )
=> ( ( demorgan2b2 = $true )
=> ( ( demorgan2b = $true )
=> ( ( demorgan2 = $true )
=> ( ( woz13rule0 = $true )
=> ( ( woz13rule1 = $true )
=> ( ( woz13rule2 = $true )
=> ( ( woz13rule3 = $true )
=> ( ( woz13rule4 = $true )
=> ( ( woz1_1 = $true )
=> ( ( woz1_2 = $true )
=> ( ( woz1_3 = $true )
=> ( ( woz1_4 = $true )
=> ( ( woz1_5 = $true )
=> ( ( breln1all2 = $true )
=> ( ( breln1SetBreln1 = $true )
=> ( ( choice2fnsingleton = $true )
=> ( ( setOfPairsIsBReln1 = $true )
=> ( ( breln1all1 = $true )
=> ( ( subbreln1 = $true )
=> ( ( eqbreln1 = $true )
=> ( ( breln1invprop = $true )
=> ( ( breln1invI = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X0 @ X1 ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X0 @ X1 ) )
= $true )
=> ( $true
= ( in @ ( kpair @ X2 @ X3 ) @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f526]) ).
thf(f526,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X0 @ X1 ) )
=> ( in @ ( kpair @ X2 @ X3 ) @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f300]) ).
thf(f300,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ! [X3: $i,X13: $i] :
( ( breln1 @ X3 @ X13 )
=> ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X3 )
=> ( ( in @ ( kpair @ X2 @ X1 ) @ ( breln1invset @ X3 @ X13 ) )
=> ( in @ ( kpair @ X1 @ X2 ) @ X13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f299]) ).
thf(f299,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ! [X3: $i,X13: $i] :
( ( breln1 @ X3 @ X13 )
=> ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X3 )
=> ( ( in @ ( kpair @ X2 @ X1 ) @ ( breln1invset @ X3 @ X13 ) )
=> ( in @ ( kpair @ X1 @ X2 ) @ X13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4RsbB0Qymi/DTF2THF_10978.p',breln1invE) ).
thf(f13529,plain,
( ( in @ ( kpair @ sK580 @ sK581 ) @ sK579 )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f13528]) ).
thf(f13528,plain,
( ( ^ [Y0: $i,Y1: $i] : ( in @ ( kpair @ Y1 @ Y0 ) @ sK579 )
@ sK581
@ sK580 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f13519]) ).
thf(f13519,plain,
( ( ( ^ [Y0: $i,Y1: $i] : ( in @ ( kpair @ Y1 @ Y0 ) @ sK579 )
@ sK581
@ sK580 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f6197,f5980]) ).
thf(f5980,plain,
( ( in @ ( kpair @ sK581 @ sK580 )
@ ( dpsetconstr @ sK578 @ sK578
@ ^ [Y0: $i,Y1: $i] : ( in @ ( kpair @ Y1 @ Y0 ) @ sK579 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f5386]) ).
thf(f5386,plain,
( $true
= ( in @ ( kpair @ sK581 @ sK580 )
@ ( ^ [Y0: $i,Y1: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y2: $i,Y3: $i] : ( in @ ( kpair @ Y3 @ Y2 ) @ Y1 ) )
@ sK578
@ sK579 ) ) ),
inference(definition_unfolding,[status(thm)],[f4005,f3704]) ).
thf(f3704,plain,
( breln1invset
= ( ^ [Y0: $i,Y1: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y2: $i,Y3: $i] : ( in @ ( kpair @ Y3 @ Y2 ) @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f395]) ).
thf(f395,plain,
( breln1invset
= ( ^ [Y0: $i,Y1: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y2: $i,Y3: $i] : ( in @ ( kpair @ Y3 @ Y2 ) @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f394]) ).
thf(f394,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/sandbox/tmp/tmp.4RsbB0Qymi/DTF2THF_10978.p',breln1invset) ).
thf(f4005,plain,
( ( in @ ( kpair @ sK581 @ sK580 ) @ ( breln1invset @ sK578 @ sK579 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f2307]) ).
thf(f6197,plain,
! [X2: $i > $i > $o,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( in @ ( kpair @ X4 @ X0 ) @ ( dpsetconstr @ X3 @ X1 @ X2 ) )
!= $true )
| ( ( X2 @ X4 @ X0 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f6196]) ).
thf(f6196,plain,
! [X2: $i > $i > $o,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( in @ ( kpair @ X4 @ X0 )
@ ( dpsetconstr @ X3 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) ) )
| ( ( X2 @ X4 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f5585]) ).
thf(f5585,plain,
! [X2: $i > $i > $o,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
!= ( in @ ( kpair @ X4 @ X0 )
@ ( dpsetconstr @ X3 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) ) )
| ( $true != $true )
| ( ( X2 @ X4 @ X0 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f4447,f4022]) ).
thf(f4022,plain,
dpsetconstrER = $true,
inference(cnf_transformation,[status(thm)],[f2307]) ).
thf(f4447,plain,
! [X2: $i > $i > $o,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( X2 @ X4 @ X0 )
= $true )
| ( $true
!= ( in @ ( kpair @ X4 @ X0 )
@ ( dpsetconstr @ X3 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) ) )
| ( dpsetconstrER != $true ) ),
inference(cnf_transformation,[status(thm)],[f2633]) ).
thf(f2633,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $i > $o,X3: $i,X4: $i] :
( ( ( X2 @ X4 @ X0 )
= $true )
| ( $true
!= ( in @ ( kpair @ X4 @ X0 )
@ ( dpsetconstr @ X3 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) ) ) )
| ( dpsetconstrER != $true ) )
& ( ( dpsetconstrER = $true )
| ( ( ( sK760 @ sK762 @ sK758 )
!= $true )
& ( ( in @ ( kpair @ sK762 @ sK758 )
@ ( dpsetconstr @ sK761 @ sK759
@ ^ [Y0: $i,Y1: $i] : ( sK760 @ Y0 @ Y1 ) ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK758,sK759,sK760,sK761,sK762])],[f2631,f2632]) ).
thf(f2632,plain,
( ? [X5: $i,X6: $i,X7: $i > $i > $o,X8: $i,X9: $i] :
( ( ( X7 @ X9 @ X5 )
!= $true )
& ( ( in @ ( kpair @ X9 @ X5 )
@ ( dpsetconstr @ X8 @ X6
@ ^ [Y0: $i,Y1: $i] : ( X7 @ Y0 @ Y1 ) ) )
= $true ) )
=> ( ( ( sK760 @ sK762 @ sK758 )
!= $true )
& ( ( in @ ( kpair @ sK762 @ sK758 )
@ ( dpsetconstr @ sK761 @ sK759
@ ^ [Y0: $i,Y1: $i] : ( sK760 @ Y0 @ Y1 ) ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2631,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $i > $o,X3: $i,X4: $i] :
( ( ( X2 @ X4 @ X0 )
= $true )
| ( $true
!= ( in @ ( kpair @ X4 @ X0 )
@ ( dpsetconstr @ X3 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) ) ) )
| ( dpsetconstrER != $true ) )
& ( ( dpsetconstrER = $true )
| ? [X5: $i,X6: $i,X7: $i > $i > $o,X8: $i,X9: $i] :
( ( ( X7 @ X9 @ X5 )
!= $true )
& ( ( in @ ( kpair @ X9 @ X5 )
@ ( dpsetconstr @ X8 @ X6
@ ^ [Y0: $i,Y1: $i] : ( X7 @ Y0 @ Y1 ) ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f2630]) ).
thf(f2630,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $i > $o,X3: $i,X4: $i] :
( ( ( X2 @ X4 @ X0 )
= $true )
| ( $true
!= ( in @ ( kpair @ X4 @ X0 )
@ ( dpsetconstr @ X3 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) ) ) )
| ( dpsetconstrER != $true ) )
& ( ( dpsetconstrER = $true )
| ? [X0: $i,X1: $i,X2: $i > $i > $o,X3: $i,X4: $i] :
( ( ( X2 @ X4 @ X0 )
!= $true )
& ( $true
= ( in @ ( kpair @ X4 @ X0 )
@ ( dpsetconstr @ X3 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f975]) ).
thf(f975,plain,
( ! [X0: $i,X1: $i,X2: $i > $i > $o,X3: $i,X4: $i] :
( ( ( X2 @ X4 @ X0 )
= $true )
| ( $true
!= ( in @ ( kpair @ X4 @ X0 )
@ ( dpsetconstr @ X3 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) ) ) )
<=> ( dpsetconstrER = $true ) ),
inference(ennf_transformation,[status(thm)],[f499]) ).
thf(f499,plain,
( ! [X0: $i,X1: $i,X2: $i > $i > $o,X3: $i,X4: $i] :
( ( $true
= ( in @ ( kpair @ X4 @ X0 )
@ ( dpsetconstr @ X3 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) ) )
=> ( ( X2 @ X4 @ X0 )
= $true ) )
<=> ( dpsetconstrER = $true ) ),
inference(fool_elimination,[status(thm)],[f498]) ).
thf(f498,plain,
( dpsetconstrER
= ( ! [X0: $i,X1: $i,X2: $i > $i > $o,X3: $i,X4: $i] :
( ( in @ ( kpair @ X4 @ X0 )
@ ( dpsetconstr @ X3 @ X1
@ ^ [X5: $i,X6: $i] : ( X2 @ X5 @ X6 ) ) )
=> ( X2 @ X4 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f191]) ).
thf(f191,axiom,
( dpsetconstrER
= ( ! [X2: $i,X4: $i,X0: $i > $i > $o,X3: $i,X1: $i] :
( ( in @ ( kpair @ X1 @ X2 )
@ ( dpsetconstr @ X3 @ X4
@ ^ [X8: $i,X10: $i] : ( X0 @ X8 @ X10 ) ) )
=> ( X0 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4RsbB0Qymi/DTF2THF_10978.p',dpsetconstrER) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU777^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.31 % Computer : n014.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Feb 24 12:33:42 EST 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.42 ---- Original DTF file ---
% 0.15/0.42 thf(spec,logic,$$dhol).
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 % File : SEU777^1 : TPTP v9.2.1. Released v3.7.0.
% 0.15/0.42 % Domain : Set Theory
% 0.15/0.42 % Problem : Binary Relations on a Set
% 0.15/0.42 % Version : Especial.
% 0.15/0.42 % English : (! A:i.! R:i.breln1 A R -> (! x:i.in x A -> (! y:i.in y A ->
% 0.15/0.42 % in (kpair y x) (breln1invset A R) -> in (kpair x y) R)))
% 0.15/0.42
% 0.15/0.42 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.15/0.42 % Source : [Bro08]
% 0.15/0.42 % Names : ZFC279g [Bro08]
% 0.15/0.42
% 0.15/0.42 % Status : Theorem
% 0.15/0.42 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.54 v8.1.0, 0.45 v7.5.0, 0.14 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.62 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.71 v5.5.0, 0.83 v5.4.0, 0.80 v5.2.0, 1.00 v3.7.0
% 0.15/0.42 % Syntax : Number of formulae : 639 ( 298 unt; 340 typ; 298 def)
% 0.15/0.42 % Number of atoms : 1801 ( 428 equ; 0 cnn)
% 0.15/0.42 % Maximal formula atoms : 298 ( 6 avg)
% 0.15/0.42 % Number of connectives : 3892 ( 73 ~; 12 |; 46 &;2823 @)
% 0.15/0.42 % ( 14 <=>; 924 =>; 0 <=; 0 <~>)
% 0.15/0.42 % Maximal formula depth : 306 ( 2 avg)
% 0.15/0.42 % Number of types : 2 ( 0 usr)
% 0.15/0.42 % Number of type conns : 154 ( 154 >; 0 *; 0 +; 0 <<)
% 0.15/0.42 % Number of symbols : 343 ( 340 usr; 297 con; 0-4 aty)
% 0.15/0.42 % Number of variables : 1035 ( 80 ^; 919 !; 36 ?;1035 :)
% 0.15/0.42 % SPC : TH0_THM_EQU_NAR
% 0.15/0.42
% 0.15/0.42 % Comments : http://mathgate.info/detsetitem.php?id=342
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 thf(in_type,type,
% 0.15/0.42 in: $i > $i > $o ).
% 0.15/0.42
% 0.15/0.42 thf(exu_type,type,
% 0.15/0.42 exu: ( $i > $o ) > $o ).
% 0.15/0.42
% 0.15/0.42 thf(exu,definition,
% 0.15/0.42 ( exu
% 0.15/0.42 = ( ^ [Xphi: $i > $o] :
% 0.15/0.42 ? [Xx: $i] :
% 0.15/0.42 ( ( Xphi @ Xx )
% 0.15/0.42 & ! [Xy: $i] :
% 0.15/0.42 ( ( Xphi @ Xy )
% 0.15/0.42 => ( Xx = Xy ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(setextAx_type,type,
% 0.15/0.42 setextAx: $o ).
% 0.15/0.42
% 0.15/0.42 thf(setextAx,definition,
% 0.15/0.42 ( setextAx
% 0.15/0.42 = ( ! [A: $i,B: $i] :
% 0.15/0.42 ( ! [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 <=> ( in @ Xx @ B ) )
% 0.15/0.42 => ( A = B ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(emptyset_type,type,
% 0.15/0.42 emptyset: $i ).
% 0.15/0.42
% 0.15/0.42 thf(emptysetAx_type,type,
% 0.15/0.42 emptysetAx: $o ).
% 0.15/0.42
% 0.15/0.42 thf(emptysetAx,definition,
% 0.15/0.42 ( emptysetAx
% 0.15/0.42 = ( ! [Xx: $i] :
% 0.15/0.42 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(setadjoin_type,type,
% 0.15/0.42 setadjoin: $i > $i > $i ).
% 0.15/0.42
% 0.15/0.42 thf(setadjoinAx_type,type,
% 0.15/0.42 setadjoinAx: $o ).
% 0.15/0.42
% 0.15/0.42 thf(setadjoinAx,definition,
% 0.15/0.42 ( setadjoinAx
% 0.15/0.42 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.15/0.42 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.15/0.42 <=> ( ( Xy = Xx )
% 0.15/0.42 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(powerset_type,type,
% 0.15/0.42 powerset: $i > $i ).
% 0.15/0.42
% 0.15/0.42 thf(powersetAx_type,type,
% 0.15/0.42 powersetAx: $o ).
% 0.15/0.42
% 0.15/0.42 thf(powersetAx,definition,
% 0.15/0.42 ( powersetAx
% 0.15/0.42 = ( ! [A: $i,B: $i] :
% 0.15/0.42 ( ( in @ B @ ( powerset @ A ) )
% 0.15/0.42 <=> ! [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ B )
% 0.15/0.42 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(setunion_type,type,
% 0.15/0.42 setunion: $i > $i ).
% 0.15/0.42
% 0.15/0.42 thf(setunionAx_type,type,
% 0.15/0.42 setunionAx: $o ).
% 0.15/0.42
% 0.15/0.42 thf(setunionAx,definition,
% 0.15/0.42 ( setunionAx
% 0.15/0.42 = ( ! [A: $i,Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ ( setunion @ A ) )
% 0.15/0.42 <=> ? [B: $i] :
% 0.15/0.42 ( ( in @ Xx @ B )
% 0.15/0.42 & ( in @ B @ A ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(omega_type,type,
% 0.15/0.42 omega: $i ).
% 0.15/0.42
% 0.15/0.42 thf(omega0Ax_type,type,
% 0.15/0.42 omega0Ax: $o ).
% 0.15/0.42
% 0.15/0.42 thf(omega0Ax,definition,
% 0.15/0.42 ( omega0Ax
% 0.15/0.42 = ( in @ emptyset @ omega ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(omegaSAx_type,type,
% 0.15/0.42 omegaSAx: $o ).
% 0.15/0.42
% 0.15/0.42 thf(omegaSAx,definition,
% 0.15/0.42 ( omegaSAx
% 0.15/0.42 = ( ! [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ omega )
% 0.15/0.42 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(omegaIndAx_type,type,
% 0.15/0.42 omegaIndAx: $o ).
% 0.15/0.42
% 0.15/0.42 thf(omegaIndAx,definition,
% 0.15/0.42 ( omegaIndAx
% 0.15/0.42 = ( ! [A: $i] :
% 0.15/0.42 ( ( ( in @ emptyset @ A )
% 0.15/0.42 & ! [Xx: $i] :
% 0.15/0.42 ( ( ( in @ Xx @ omega )
% 0.15/0.42 & ( in @ Xx @ A ) )
% 0.15/0.42 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.15/0.42 => ! [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ omega )
% 0.15/0.42 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(replAx_type,type,
% 0.15/0.42 replAx: $o ).
% 0.15/0.42
% 0.15/0.42 thf(replAx,definition,
% 0.15/0.42 ( replAx
% 0.15/0.42 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.15/0.42 ( ! [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 => ( exu
% 0.15/0.42 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.15/0.42 => ? [B: $i] :
% 0.15/0.42 ! [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ B )
% 0.15/0.42 <=> ? [Xy: $i] :
% 0.15/0.42 ( ( in @ Xy @ A )
% 0.15/0.42 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(foundationAx_type,type,
% 0.15/0.42 foundationAx: $o ).
% 0.15/0.42
% 0.15/0.42 thf(foundationAx,definition,
% 0.15/0.42 ( foundationAx
% 0.15/0.42 = ( ! [A: $i] :
% 0.15/0.42 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.15/0.42 => ? [B: $i] :
% 0.15/0.42 ( ( in @ B @ A )
% 0.15/0.42 & ~ ? [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ B )
% 0.15/0.42 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(wellorderingAx_type,type,
% 0.15/0.42 wellorderingAx: $o ).
% 0.15/0.42
% 0.15/0.42 thf(wellorderingAx,definition,
% 0.15/0.42 ( wellorderingAx
% 0.15/0.42 = ( ! [A: $i] :
% 0.15/0.42 ? [B: $i] :
% 0.15/0.42 ( ! [C: $i] :
% 0.15/0.42 ( ( in @ C @ B )
% 0.15/0.42 => ! [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ C )
% 0.15/0.42 => ( in @ Xx @ A ) ) )
% 0.15/0.42 & ! [Xx: $i,Xy: $i] :
% 0.15/0.42 ( ( ( in @ Xx @ A )
% 0.15/0.42 & ( in @ Xy @ A ) )
% 0.15/0.42 => ( ! [C: $i] :
% 0.15/0.42 ( ( in @ C @ B )
% 0.15/0.42 => ( ( in @ Xx @ C )
% 0.15/0.42 <=> ( in @ Xy @ C ) ) )
% 0.15/0.42 => ( Xx = Xy ) ) )
% 0.15/0.42 & ! [C: $i,D: $i] :
% 0.15/0.42 ( ( ( in @ C @ B )
% 0.15/0.42 & ( in @ D @ B ) )
% 0.15/0.42 => ( ! [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ C )
% 0.15/0.42 => ( in @ Xx @ D ) )
% 0.15/0.42 | ! [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ D )
% 0.15/0.42 => ( in @ Xx @ C ) ) ) )
% 0.15/0.42 & ! [C: $i] :
% 0.15/0.42 ( ( ! [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ C )
% 0.15/0.42 => ( in @ Xx @ A ) )
% 0.15/0.42 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.15/0.42 => ? [D: $i,Xx: $i] :
% 0.15/0.42 ( ( in @ D @ B )
% 0.15/0.42 & ( in @ Xx @ C )
% 0.15/0.42 & ~ ? [Xy: $i] :
% 0.15/0.42 ( ( in @ Xy @ D )
% 0.15/0.42 & ( in @ Xy @ C ) )
% 0.15/0.42 & ! [E: $i] :
% 0.15/0.42 ( ( in @ E @ B )
% 0.15/0.42 => ( ! [Xy: $i] :
% 0.15/0.42 ( ( in @ Xy @ E )
% 0.15/0.42 => ( in @ Xy @ D ) )
% 0.15/0.42 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(descr_type,type,
% 0.15/0.42 descr: ( $i > $o ) > $i ).
% 0.15/0.42
% 0.15/0.42 thf(descrp_type,type,
% 0.15/0.42 descrp: $o ).
% 0.15/0.42
% 0.15/0.42 thf(descrp,definition,
% 0.15/0.42 ( descrp
% 0.15/0.42 = ( ! [Xphi: $i > $o] :
% 0.15/0.42 ( ( exu
% 0.15/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.42 => ( Xphi
% 0.15/0.42 @ ( descr
% 0.15/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(dsetconstr_type,type,
% 0.15/0.42 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.15/0.42
% 0.15/0.42 thf(dsetconstrI_type,type,
% 0.15/0.42 dsetconstrI: $o ).
% 0.15/0.42
% 0.15/0.42 thf(dsetconstrI,definition,
% 0.15/0.42 ( dsetconstrI
% 0.15/0.42 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 => ( ( Xphi @ Xx )
% 0.15/0.42 => ( in @ Xx
% 0.15/0.42 @ ( dsetconstr @ A
% 0.15/0.42 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(dsetconstrEL_type,type,
% 0.15/0.42 dsetconstrEL: $o ).
% 0.15/0.42
% 0.15/0.42 thf(dsetconstrEL,definition,
% 0.15/0.42 ( dsetconstrEL
% 0.15/0.42 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.15/0.42 ( ( in @ Xx
% 0.15/0.42 @ ( dsetconstr @ A
% 0.15/0.42 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.15/0.42 => ( in @ Xx @ A ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(dsetconstrER_type,type,
% 0.15/0.42 dsetconstrER: $o ).
% 0.15/0.42
% 0.15/0.42 thf(dsetconstrER,definition,
% 0.15/0.42 ( dsetconstrER
% 0.15/0.42 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.15/0.42 ( ( in @ Xx
% 0.15/0.42 @ ( dsetconstr @ A
% 0.15/0.42 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.15/0.42 => ( Xphi @ Xx ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(exuE1_type,type,
% 0.15/0.42 exuE1: $o ).
% 0.15/0.42
% 0.15/0.42 thf(exuE1,definition,
% 0.15/0.42 ( exuE1
% 0.15/0.42 = ( ! [Xphi: $i > $o] :
% 0.15/0.42 ( ( exu
% 0.15/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.42 => ? [Xx: $i] :
% 0.15/0.42 ( ( Xphi @ Xx )
% 0.15/0.42 & ! [Xy: $i] :
% 0.15/0.42 ( ( Xphi @ Xy )
% 0.15/0.42 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(prop2set_type,type,
% 0.15/0.42 prop2set: $o > $i ).
% 0.15/0.42
% 0.15/0.42 thf(prop2setE_type,type,
% 0.15/0.42 prop2setE: $o ).
% 0.15/0.42
% 0.15/0.42 thf(prop2setE,definition,
% 0.15/0.42 ( prop2setE
% 0.15/0.42 = ( ! [Xphi: $o,Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.15/0.42 => Xphi ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(emptysetE_type,type,
% 0.15/0.42 emptysetE: $o ).
% 0.15/0.42
% 0.15/0.42 thf(emptysetE,definition,
% 0.15/0.42 ( emptysetE
% 0.15/0.42 = ( ! [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ emptyset )
% 0.15/0.42 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(emptysetimpfalse_type,type,
% 0.15/0.42 emptysetimpfalse: $o ).
% 0.15/0.42
% 0.15/0.42 thf(emptysetimpfalse,definition,
% 0.15/0.42 ( emptysetimpfalse
% 0.15/0.42 = ( ! [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ emptyset )
% 0.15/0.42 => $false ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(notinemptyset_type,type,
% 0.15/0.42 notinemptyset: $o ).
% 0.15/0.42
% 0.15/0.42 thf(notinemptyset,definition,
% 0.15/0.42 ( notinemptyset
% 0.15/0.42 = ( ! [Xx: $i] :
% 0.15/0.42 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(exuE3e_type,type,
% 0.15/0.42 exuE3e: $o ).
% 0.15/0.42
% 0.15/0.42 thf(exuE3e,definition,
% 0.15/0.42 ( exuE3e
% 0.15/0.42 = ( ! [Xphi: $i > $o] :
% 0.15/0.42 ( ( exu
% 0.15/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.42 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(setext_type,type,
% 0.15/0.42 setext: $o ).
% 0.15/0.42
% 0.15/0.42 thf(setext,definition,
% 0.15/0.42 ( setext
% 0.15/0.42 = ( ! [A: $i,B: $i] :
% 0.15/0.42 ( ! [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 => ( in @ Xx @ B ) )
% 0.15/0.42 => ( ! [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ B )
% 0.15/0.42 => ( in @ Xx @ A ) )
% 0.15/0.42 => ( A = B ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(emptyI_type,type,
% 0.15/0.42 emptyI: $o ).
% 0.15/0.42
% 0.15/0.42 thf(emptyI,definition,
% 0.15/0.42 ( emptyI
% 0.15/0.42 = ( ! [A: $i] :
% 0.15/0.42 ( ! [Xx: $i] :
% 0.15/0.42 ~ ( in @ Xx @ A )
% 0.15/0.42 => ( A = emptyset ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(noeltsimpempty_type,type,
% 0.15/0.42 noeltsimpempty: $o ).
% 0.15/0.42
% 0.15/0.42 thf(noeltsimpempty,definition,
% 0.15/0.42 ( noeltsimpempty
% 0.15/0.42 = ( ! [A: $i] :
% 0.15/0.42 ( ! [Xx: $i] :
% 0.15/0.42 ~ ( in @ Xx @ A )
% 0.15/0.42 => ( A = emptyset ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(setbeta_type,type,
% 0.15/0.42 setbeta: $o ).
% 0.15/0.42
% 0.15/0.42 thf(setbeta,definition,
% 0.15/0.42 ( setbeta
% 0.15/0.42 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 => ( ( in @ Xx
% 0.15/0.42 @ ( dsetconstr @ A
% 0.15/0.42 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.15/0.42 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(nonempty_type,type,
% 0.15/0.42 nonempty: $i > $o ).
% 0.15/0.42
% 0.15/0.42 thf(nonempty,definition,
% 0.15/0.42 ( nonempty
% 0.15/0.42 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(nonemptyE1_type,type,
% 0.15/0.42 nonemptyE1: $o ).
% 0.15/0.42
% 0.15/0.42 thf(nonemptyE1,definition,
% 0.15/0.42 ( nonemptyE1
% 0.15/0.42 = ( ! [A: $i] :
% 0.15/0.42 ( ( nonempty @ A )
% 0.15/0.42 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(nonemptyI_type,type,
% 0.15/0.42 nonemptyI: $o ).
% 0.15/0.42
% 0.15/0.42 thf(nonemptyI,definition,
% 0.15/0.42 ( nonemptyI
% 0.15/0.42 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 => ( ( Xphi @ Xx )
% 0.15/0.42 => ( nonempty
% 0.15/0.42 @ ( dsetconstr @ A
% 0.15/0.42 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(nonemptyI1_type,type,
% 0.15/0.42 nonemptyI1: $o ).
% 0.15/0.42
% 0.15/0.42 thf(nonemptyI1,definition,
% 0.15/0.42 ( nonemptyI1
% 0.15/0.42 = ( ! [A: $i] :
% 0.15/0.42 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.15/0.42 => ( nonempty @ A ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(setadjoinIL_type,type,
% 0.15/0.42 setadjoinIL: $o ).
% 0.15/0.42
% 0.15/0.42 thf(setadjoinIL,definition,
% 0.15/0.42 ( setadjoinIL
% 0.15/0.42 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(emptyinunitempty_type,type,
% 0.15/0.42 emptyinunitempty: $o ).
% 0.15/0.42
% 0.15/0.42 thf(emptyinunitempty,definition,
% 0.15/0.42 ( emptyinunitempty
% 0.15/0.42 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(setadjoinIR_type,type,
% 0.15/0.42 setadjoinIR: $o ).
% 0.15/0.42
% 0.15/0.42 thf(setadjoinIR,definition,
% 0.15/0.42 ( setadjoinIR
% 0.15/0.42 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.15/0.42 ( ( in @ Xy @ A )
% 0.15/0.42 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(setadjoinE_type,type,
% 0.15/0.42 setadjoinE: $o ).
% 0.15/0.42
% 0.15/0.42 thf(setadjoinE,definition,
% 0.15/0.42 ( setadjoinE
% 0.15/0.42 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.15/0.42 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.15/0.42 => ! [Xphi: $o] :
% 0.15/0.42 ( ( ( Xy = Xx )
% 0.15/0.42 => Xphi )
% 0.15/0.42 => ( ( ( in @ Xy @ A )
% 0.15/0.42 => Xphi )
% 0.15/0.42 => Xphi ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(setadjoinOr_type,type,
% 0.15/0.42 setadjoinOr: $o ).
% 0.15/0.42
% 0.15/0.42 thf(setadjoinOr,definition,
% 0.15/0.42 ( setadjoinOr
% 0.15/0.42 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.15/0.42 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.15/0.42 => ( ( Xy = Xx )
% 0.15/0.42 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(setoftrueEq_type,type,
% 0.15/0.42 setoftrueEq: $o ).
% 0.15/0.42
% 0.15/0.42 thf(setoftrueEq,definition,
% 0.15/0.42 ( setoftrueEq
% 0.15/0.42 = ( ! [A: $i] :
% 0.15/0.42 ( ( dsetconstr @ A
% 0.15/0.42 @ ^ [Xx: $i] : $true )
% 0.15/0.42 = A ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(powersetI_type,type,
% 0.15/0.42 powersetI: $o ).
% 0.15/0.42
% 0.15/0.42 thf(powersetI,definition,
% 0.15/0.42 ( powersetI
% 0.15/0.42 = ( ! [A: $i,B: $i] :
% 0.15/0.42 ( ! [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ B )
% 0.15/0.42 => ( in @ Xx @ A ) )
% 0.15/0.42 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(emptyinPowerset_type,type,
% 0.15/0.42 emptyinPowerset: $o ).
% 0.15/0.42
% 0.15/0.42 thf(emptyinPowerset,definition,
% 0.15/0.42 ( emptyinPowerset
% 0.15/0.42 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(emptyInPowerset_type,type,
% 0.15/0.42 emptyInPowerset: $o ).
% 0.15/0.42
% 0.15/0.42 thf(emptyInPowerset,definition,
% 0.15/0.42 ( emptyInPowerset
% 0.15/0.42 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(powersetE_type,type,
% 0.15/0.42 powersetE: $o ).
% 0.15/0.42
% 0.15/0.42 thf(powersetE,definition,
% 0.15/0.42 ( powersetE
% 0.15/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.42 ( ( in @ B @ ( powerset @ A ) )
% 0.15/0.42 => ( ( in @ Xx @ B )
% 0.15/0.42 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(setunionI_type,type,
% 0.15/0.42 setunionI: $o ).
% 0.15/0.42
% 0.15/0.42 thf(setunionI,definition,
% 0.15/0.42 ( setunionI
% 0.15/0.42 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.15/0.42 ( ( in @ Xx @ B )
% 0.15/0.42 => ( ( in @ B @ A )
% 0.15/0.42 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(setunionE_type,type,
% 0.15/0.42 setunionE: $o ).
% 0.15/0.42
% 0.15/0.42 thf(setunionE,definition,
% 0.15/0.42 ( setunionE
% 0.15/0.42 = ( ! [A: $i,Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ ( setunion @ A ) )
% 0.15/0.42 => ! [Xphi: $o] :
% 0.15/0.42 ( ! [B: $i] :
% 0.15/0.42 ( ( in @ Xx @ B )
% 0.15/0.42 => ( ( in @ B @ A )
% 0.15/0.42 => Xphi ) )
% 0.15/0.42 => Xphi ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(subPowSU_type,type,
% 0.15/0.42 subPowSU: $o ).
% 0.15/0.42
% 0.15/0.42 thf(subPowSU,definition,
% 0.15/0.42 ( subPowSU
% 0.15/0.42 = ( ! [A: $i,Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(exuE2_type,type,
% 0.15/0.42 exuE2: $o ).
% 0.15/0.42
% 0.15/0.42 thf(exuE2,definition,
% 0.15/0.42 ( exuE2
% 0.15/0.42 = ( ! [Xphi: $i > $o] :
% 0.15/0.42 ( ( exu
% 0.15/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.42 => ? [Xx: $i] :
% 0.15/0.42 ! [Xy: $i] :
% 0.15/0.42 ( ( Xphi @ Xy )
% 0.15/0.42 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(nonemptyImpWitness_type,type,
% 0.15/0.42 nonemptyImpWitness: $o ).
% 0.15/0.42
% 0.15/0.42 thf(nonemptyImpWitness,definition,
% 0.15/0.42 ( nonemptyImpWitness
% 0.15/0.42 = ( ! [A: $i] :
% 0.15/0.42 ( ( nonempty @ A )
% 0.15/0.42 => ? [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 & $true ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(uniqinunit_type,type,
% 0.15/0.42 uniqinunit: $o ).
% 0.15/0.42
% 0.15/0.42 thf(uniqinunit,definition,
% 0.15/0.42 ( uniqinunit
% 0.15/0.42 = ( ! [Xx: $i,Xy: $i] :
% 0.15/0.42 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.15/0.42 => ( Xx = Xy ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(notinsingleton_type,type,
% 0.15/0.42 notinsingleton: $o ).
% 0.15/0.42
% 0.15/0.42 thf(notinsingleton,definition,
% 0.15/0.42 ( notinsingleton
% 0.15/0.42 = ( ! [Xx: $i,Xy: $i] :
% 0.15/0.42 ( ( Xx != Xy )
% 0.15/0.42 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(eqinunit_type,type,
% 0.15/0.42 eqinunit: $o ).
% 0.15/0.42
% 0.15/0.42 thf(eqinunit,definition,
% 0.15/0.42 ( eqinunit
% 0.15/0.42 = ( ! [Xx: $i,Xy: $i] :
% 0.15/0.42 ( ( Xx = Xy )
% 0.15/0.42 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(singletonsswitch_type,type,
% 0.15/0.42 singletonsswitch: $o ).
% 0.15/0.42
% 0.15/0.42 thf(singletonsswitch,definition,
% 0.15/0.42 ( singletonsswitch
% 0.15/0.42 = ( ! [Xx: $i,Xy: $i] :
% 0.15/0.42 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.15/0.42 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(upairsetE_type,type,
% 0.15/0.42 upairsetE: $o ).
% 0.15/0.42
% 0.15/0.42 thf(upairsetE,definition,
% 0.15/0.42 ( upairsetE
% 0.15/0.42 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.15/0.42 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.15/0.42 => ( ( Xz = Xx )
% 0.15/0.42 | ( Xz = Xy ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(upairsetIL_type,type,
% 0.15/0.42 upairsetIL: $o ).
% 0.15/0.42
% 0.15/0.42 thf(upairsetIL,definition,
% 0.15/0.42 ( upairsetIL
% 0.15/0.42 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(upairsetIR_type,type,
% 0.15/0.42 upairsetIR: $o ).
% 0.15/0.42
% 0.15/0.42 thf(upairsetIR,definition,
% 0.15/0.42 ( upairsetIR
% 0.15/0.42 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(emptyE1_type,type,
% 0.15/0.42 emptyE1: $o ).
% 0.15/0.42
% 0.15/0.42 thf(emptyE1,definition,
% 0.15/0.42 ( emptyE1
% 0.15/0.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.15/0.42 ( ? [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 & ( Xphi @ Xx ) )
% 0.15/0.42 => ( ( ( dsetconstr @ A
% 0.15/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.42 = emptyset )
% 0.15/0.42 => $false ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(vacuousDall_type,type,
% 0.15/0.42 vacuousDall: $o ).
% 0.15/0.42
% 0.15/0.42 thf(vacuousDall,definition,
% 0.15/0.42 ( vacuousDall
% 0.15/0.42 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ emptyset )
% 0.15/0.42 => ( Xphi @ Xx ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(quantDeMorgan1_type,type,
% 0.15/0.42 quantDeMorgan1: $o ).
% 0.15/0.42
% 0.15/0.42 thf(quantDeMorgan1,definition,
% 0.15/0.42 ( quantDeMorgan1
% 0.15/0.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.15/0.42 ( ~ ! [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 => ( Xphi @ Xx ) )
% 0.15/0.42 => ? [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(quantDeMorgan2_type,type,
% 0.15/0.42 quantDeMorgan2: $o ).
% 0.15/0.42
% 0.15/0.42 thf(quantDeMorgan2,definition,
% 0.15/0.42 ( quantDeMorgan2
% 0.15/0.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.15/0.42 ( ! [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 => ~ ( Xphi @ Xx ) )
% 0.15/0.42 => ~ ? [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(quantDeMorgan3_type,type,
% 0.15/0.42 quantDeMorgan3: $o ).
% 0.15/0.42
% 0.15/0.42 thf(quantDeMorgan3,definition,
% 0.15/0.42 ( quantDeMorgan3
% 0.15/0.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.15/0.42 ( ~ ? [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 & ( Xphi @ Xx ) )
% 0.15/0.42 => ! [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(quantDeMorgan4_type,type,
% 0.15/0.42 quantDeMorgan4: $o ).
% 0.15/0.42
% 0.15/0.42 thf(quantDeMorgan4,definition,
% 0.15/0.42 ( quantDeMorgan4
% 0.15/0.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.15/0.42 ( ? [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 & ~ ( Xphi @ Xx ) )
% 0.15/0.42 => ~ ! [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(prop2setI_type,type,
% 0.15/0.42 prop2setI: $o ).
% 0.15/0.42
% 0.15/0.42 thf(prop2setI,definition,
% 0.15/0.42 ( prop2setI
% 0.15/0.42 = ( ! [Xphi: $o] :
% 0.15/0.42 ( Xphi
% 0.15/0.42 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(set2prop_type,type,
% 0.15/0.42 set2prop: $i > $o ).
% 0.15/0.42
% 0.15/0.42 thf(prop2set2propI_type,type,
% 0.15/0.42 prop2set2propI: $o ).
% 0.15/0.42
% 0.15/0.42 thf(prop2set2propI,definition,
% 0.15/0.42 ( prop2set2propI
% 0.15/0.42 = ( ! [Xphi: $o] :
% 0.15/0.42 ( Xphi
% 0.15/0.42 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(notdexE_type,type,
% 0.15/0.42 notdexE: $o ).
% 0.15/0.42
% 0.15/0.42 thf(notdexE,definition,
% 0.15/0.42 ( notdexE
% 0.15/0.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.15/0.42 ( ~ ? [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 & ( Xphi @ Xx ) )
% 0.15/0.42 => ! [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(notdallE_type,type,
% 0.15/0.42 notdallE: $o ).
% 0.15/0.42
% 0.15/0.42 thf(notdallE,definition,
% 0.15/0.42 ( notdallE
% 0.15/0.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.15/0.42 ( ~ ! [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 => ( Xphi @ Xx ) )
% 0.15/0.42 => ? [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(exuI1_type,type,
% 0.15/0.42 exuI1: $o ).
% 0.15/0.42
% 0.15/0.42 thf(exuI1,definition,
% 0.15/0.42 ( exuI1
% 0.15/0.42 = ( ! [Xphi: $i > $o] :
% 0.15/0.42 ( ? [Xx: $i] :
% 0.15/0.42 ( ( Xphi @ Xx )
% 0.15/0.42 & ! [Xy: $i] :
% 0.15/0.42 ( ( Xphi @ Xy )
% 0.15/0.42 => ( Xx = Xy ) ) )
% 0.15/0.42 => ( exu
% 0.15/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(exuI3_type,type,
% 0.15/0.42 exuI3: $o ).
% 0.15/0.42
% 0.15/0.42 thf(exuI3,definition,
% 0.15/0.42 ( exuI3
% 0.15/0.42 = ( ! [Xphi: $i > $o] :
% 0.15/0.42 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.15/0.42 => ( ! [Xx: $i,Xy: $i] :
% 0.15/0.42 ( ( Xphi @ Xx )
% 0.15/0.42 => ( ( Xphi @ Xy )
% 0.15/0.42 => ( Xx = Xy ) ) )
% 0.15/0.42 => ( exu
% 0.15/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(exuI2_type,type,
% 0.15/0.42 exuI2: $o ).
% 0.15/0.42
% 0.15/0.42 thf(exuI2,definition,
% 0.15/0.42 ( exuI2
% 0.15/0.42 = ( ! [Xphi: $i > $o] :
% 0.15/0.42 ( ? [Xx: $i] :
% 0.15/0.42 ! [Xy: $i] :
% 0.15/0.42 ( ( Xphi @ Xy )
% 0.15/0.42 <=> ( Xy = Xx ) )
% 0.15/0.42 => ( exu
% 0.15/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(inCongP_type,type,
% 0.15/0.42 inCongP: $o ).
% 0.15/0.42
% 0.15/0.42 thf(inCongP,definition,
% 0.15/0.42 ( inCongP
% 0.15/0.42 = ( ! [A: $i,B: $i] :
% 0.15/0.42 ( ( A = B )
% 0.15/0.42 => ! [Xx: $i,Xy: $i] :
% 0.15/0.42 ( ( Xx = Xy )
% 0.15/0.42 => ( ( in @ Xx @ A )
% 0.15/0.42 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(in__Cong_type,type,
% 0.15/0.42 in__Cong: $o ).
% 0.15/0.42
% 0.15/0.42 thf(in__Cong,definition,
% 0.15/0.42 ( in__Cong
% 0.15/0.42 = ( ! [A: $i,B: $i] :
% 0.15/0.42 ( ( A = B )
% 0.15/0.42 => ! [Xx: $i,Xy: $i] :
% 0.15/0.42 ( ( Xx = Xy )
% 0.15/0.42 => ( ( in @ Xx @ A )
% 0.15/0.42 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(exuE3u_type,type,
% 0.15/0.42 exuE3u: $o ).
% 0.15/0.42
% 0.15/0.42 thf(exuE3u,definition,
% 0.15/0.42 ( exuE3u
% 0.15/0.42 = ( ! [Xphi: $i > $o] :
% 0.15/0.42 ( ( exu
% 0.15/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.42 => ! [Xx: $i,Xy: $i] :
% 0.15/0.42 ( ( Xphi @ Xx )
% 0.15/0.42 => ( ( Xphi @ Xy )
% 0.15/0.42 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(exu__Cong_type,type,
% 0.15/0.42 exu__Cong: $o ).
% 0.15/0.42
% 0.15/0.42 thf(exu__Cong,definition,
% 0.15/0.42 ( exu__Cong
% 0.15/0.42 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.15/0.42 ( ! [Xx: $i,Xy: $i] :
% 0.15/0.42 ( ( Xx = Xy )
% 0.15/0.42 => ( ( Xphi @ Xx )
% 0.15/0.42 <=> ( Xpsi @ Xy ) ) )
% 0.15/0.42 => ( ( exu
% 0.15/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.42 <=> ( exu
% 0.15/0.42 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(emptyset__Cong_type,type,
% 0.15/0.42 emptyset__Cong: $o ).
% 0.15/0.42
% 0.15/0.42 thf(emptyset__Cong,definition,
% 0.15/0.42 ( emptyset__Cong
% 0.15/0.42 = ( emptyset = emptyset ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(setadjoin__Cong_type,type,
% 0.15/0.42 setadjoin__Cong: $o ).
% 0.15/0.42
% 0.15/0.42 thf(setadjoin__Cong,definition,
% 0.15/0.42 ( setadjoin__Cong
% 0.15/0.42 = ( ! [Xx: $i,Xy: $i] :
% 0.15/0.42 ( ( Xx = Xy )
% 0.15/0.42 => ! [Xz: $i,Xu: $i] :
% 0.15/0.42 ( ( Xz = Xu )
% 0.15/0.42 => ( ( setadjoin @ Xx @ Xz )
% 0.15/0.42 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(powerset__Cong_type,type,
% 0.15/0.42 powerset__Cong: $o ).
% 0.15/0.42
% 0.15/0.42 thf(powerset__Cong,definition,
% 0.15/0.42 ( powerset__Cong
% 0.15/0.42 = ( ! [A: $i,B: $i] :
% 0.15/0.42 ( ( A = B )
% 0.15/0.42 => ( ( powerset @ A )
% 0.15/0.42 = ( powerset @ B ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(setunion__Cong_type,type,
% 0.15/0.42 setunion__Cong: $o ).
% 0.15/0.42
% 0.15/0.42 thf(setunion__Cong,definition,
% 0.15/0.42 ( setunion__Cong
% 0.15/0.42 = ( ! [A: $i,B: $i] :
% 0.15/0.42 ( ( A = B )
% 0.15/0.42 => ( ( setunion @ A )
% 0.15/0.42 = ( setunion @ B ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(omega__Cong_type,type,
% 0.15/0.42 omega__Cong: $o ).
% 0.15/0.42
% 0.15/0.42 thf(omega__Cong,definition,
% 0.15/0.42 ( omega__Cong
% 0.15/0.42 = ( omega = omega ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(exuEu_type,type,
% 0.15/0.42 exuEu: $o ).
% 0.15/0.42
% 0.15/0.42 thf(exuEu,definition,
% 0.15/0.42 ( exuEu
% 0.15/0.42 = ( ! [Xphi: $i > $o] :
% 0.15/0.42 ( ( exu
% 0.15/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.42 => ! [Xx: $i,Xy: $i] :
% 0.15/0.42 ( ( Xphi @ Xx )
% 0.15/0.42 => ( ( Xphi @ Xy )
% 0.15/0.42 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(descr__Cong_type,type,
% 0.15/0.42 descr__Cong: $o ).
% 0.15/0.42
% 0.15/0.42 thf(descr__Cong,definition,
% 0.15/0.42 ( descr__Cong
% 0.15/0.42 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.15/0.42 ( ! [Xx: $i,Xy: $i] :
% 0.15/0.42 ( ( Xx = Xy )
% 0.15/0.42 => ( ( Xphi @ Xx )
% 0.15/0.42 <=> ( Xpsi @ Xy ) ) )
% 0.15/0.42 => ( ( exu
% 0.15/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.42 => ( ( exu
% 0.15/0.42 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.15/0.42 => ( ( descr
% 0.15/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.42 = ( descr
% 0.15/0.42 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(dsetconstr__Cong_type,type,
% 0.15/0.42 dsetconstr__Cong: $o ).
% 0.15/0.42
% 0.15/0.42 thf(dsetconstr__Cong,definition,
% 0.15/0.42 ( dsetconstr__Cong
% 0.15/0.42 = ( ! [A: $i,B: $i] :
% 0.15/0.42 ( ( A = B )
% 0.15/0.42 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.15/0.42 ( ! [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 => ! [Xy: $i] :
% 0.15/0.42 ( ( in @ Xy @ B )
% 0.15/0.42 => ( ( Xx = Xy )
% 0.15/0.42 => ( ( Xphi @ Xx )
% 0.15/0.42 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.15/0.42 => ( ( dsetconstr @ A
% 0.15/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.42 = ( dsetconstr @ B
% 0.15/0.42 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(subset_type,type,
% 0.15/0.42 subset: $i > $i > $o ).
% 0.15/0.42
% 0.15/0.42 thf(disjoint_type,type,
% 0.15/0.42 disjoint: $i > $i > $o ).
% 0.15/0.42
% 0.15/0.42 thf(setsmeet_type,type,
% 0.15/0.42 setsmeet: $i > $i > $o ).
% 0.15/0.42
% 0.15/0.42 thf(subsetI1_type,type,
% 0.15/0.42 subsetI1: $o ).
% 0.15/0.42
% 0.15/0.42 thf(subsetI1,definition,
% 0.15/0.42 ( subsetI1
% 0.15/0.42 = ( ! [A: $i,B: $i] :
% 0.15/0.42 ( ! [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 => ( in @ Xx @ B ) )
% 0.15/0.42 => ( subset @ A @ B ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(eqimpsubset2_type,type,
% 0.15/0.42 eqimpsubset2: $o ).
% 0.15/0.42
% 0.15/0.42 thf(eqimpsubset2,definition,
% 0.15/0.42 ( eqimpsubset2
% 0.15/0.42 = ( ! [A: $i,B: $i] :
% 0.15/0.42 ( ( A = B )
% 0.15/0.42 => ( subset @ B @ A ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(eqimpsubset1_type,type,
% 0.15/0.42 eqimpsubset1: $o ).
% 0.15/0.42
% 0.15/0.42 thf(eqimpsubset1,definition,
% 0.15/0.42 ( eqimpsubset1
% 0.15/0.42 = ( ! [A: $i,B: $i] :
% 0.15/0.42 ( ( A = B )
% 0.15/0.42 => ( subset @ A @ B ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(subsetI2_type,type,
% 0.15/0.42 subsetI2: $o ).
% 0.15/0.42
% 0.15/0.42 thf(subsetI2,definition,
% 0.15/0.42 ( subsetI2
% 0.15/0.42 = ( ! [A: $i,B: $i] :
% 0.15/0.42 ( ! [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 => ( in @ Xx @ B ) )
% 0.15/0.42 => ( subset @ A @ B ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(emptysetsubset_type,type,
% 0.15/0.42 emptysetsubset: $o ).
% 0.15/0.42
% 0.15/0.42 thf(emptysetsubset,definition,
% 0.15/0.42 ( emptysetsubset
% 0.15/0.42 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(subsetE_type,type,
% 0.15/0.42 subsetE: $o ).
% 0.15/0.42
% 0.15/0.42 thf(subsetE,definition,
% 0.15/0.42 ( subsetE
% 0.15/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.42 ( ( subset @ A @ B )
% 0.15/0.42 => ( ( in @ Xx @ A )
% 0.15/0.42 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(subsetE2_type,type,
% 0.15/0.42 subsetE2: $o ).
% 0.15/0.42
% 0.15/0.42 thf(subsetE2,definition,
% 0.15/0.42 ( subsetE2
% 0.15/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.42 ( ( subset @ A @ B )
% 0.15/0.42 => ( ~ ( in @ Xx @ B )
% 0.15/0.42 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(notsubsetI_type,type,
% 0.15/0.42 notsubsetI: $o ).
% 0.15/0.42
% 0.15/0.42 thf(notsubsetI,definition,
% 0.15/0.42 ( notsubsetI
% 0.15/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 => ( ~ ( in @ Xx @ B )
% 0.15/0.42 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(notequalI1_type,type,
% 0.15/0.42 notequalI1: $o ).
% 0.15/0.42
% 0.15/0.42 thf(notequalI1,definition,
% 0.15/0.42 ( notequalI1
% 0.15/0.42 = ( ! [A: $i,B: $i] :
% 0.15/0.42 ( ~ ( subset @ A @ B )
% 0.15/0.42 => ( A != B ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(notequalI2_type,type,
% 0.15/0.42 notequalI2: $o ).
% 0.15/0.42
% 0.15/0.42 thf(notequalI2,definition,
% 0.15/0.42 ( notequalI2
% 0.15/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 => ( ~ ( in @ Xx @ B )
% 0.15/0.42 => ( A != B ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(subsetRefl_type,type,
% 0.15/0.42 subsetRefl: $o ).
% 0.15/0.42
% 0.15/0.42 thf(subsetRefl,definition,
% 0.15/0.42 ( subsetRefl
% 0.15/0.42 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(subsetTrans_type,type,
% 0.15/0.42 subsetTrans: $o ).
% 0.15/0.42
% 0.15/0.42 thf(subsetTrans,definition,
% 0.15/0.42 ( subsetTrans
% 0.15/0.42 = ( ! [A: $i,B: $i,C: $i] :
% 0.15/0.42 ( ( subset @ A @ B )
% 0.15/0.42 => ( ( subset @ B @ C )
% 0.15/0.42 => ( subset @ A @ C ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(setadjoinSub_type,type,
% 0.15/0.42 setadjoinSub: $o ).
% 0.15/0.42
% 0.15/0.42 thf(setadjoinSub,definition,
% 0.15/0.42 ( setadjoinSub
% 0.15/0.42 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(setadjoinSub2_type,type,
% 0.15/0.42 setadjoinSub2: $o ).
% 0.15/0.42
% 0.15/0.42 thf(setadjoinSub2,definition,
% 0.15/0.42 ( setadjoinSub2
% 0.15/0.42 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.15/0.42 ( ( subset @ A @ B )
% 0.15/0.42 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(subset2powerset_type,type,
% 0.15/0.42 subset2powerset: $o ).
% 0.15/0.42
% 0.15/0.42 thf(subset2powerset,definition,
% 0.15/0.42 ( subset2powerset
% 0.15/0.42 = ( ! [A: $i,B: $i] :
% 0.15/0.42 ( ( subset @ A @ B )
% 0.15/0.42 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(setextsub_type,type,
% 0.15/0.42 setextsub: $o ).
% 0.15/0.42
% 0.15/0.42 thf(setextsub,definition,
% 0.15/0.42 ( setextsub
% 0.15/0.42 = ( ! [A: $i,B: $i] :
% 0.15/0.42 ( ( subset @ A @ B )
% 0.15/0.42 => ( ( subset @ B @ A )
% 0.15/0.42 => ( A = B ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(subsetemptysetimpeq_type,type,
% 0.15/0.42 subsetemptysetimpeq: $o ).
% 0.15/0.42
% 0.15/0.42 thf(subsetemptysetimpeq,definition,
% 0.15/0.42 ( subsetemptysetimpeq
% 0.15/0.42 = ( ! [A: $i] :
% 0.15/0.42 ( ( subset @ A @ emptyset )
% 0.15/0.42 => ( A = emptyset ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(powersetI1_type,type,
% 0.15/0.42 powersetI1: $o ).
% 0.15/0.42
% 0.15/0.42 thf(powersetI1,definition,
% 0.15/0.42 ( powersetI1
% 0.15/0.42 = ( ! [A: $i,B: $i] :
% 0.15/0.42 ( ( subset @ B @ A )
% 0.15/0.42 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(powersetE1_type,type,
% 0.15/0.42 powersetE1: $o ).
% 0.15/0.42
% 0.15/0.42 thf(powersetE1,definition,
% 0.15/0.42 ( powersetE1
% 0.15/0.42 = ( ! [A: $i,B: $i] :
% 0.15/0.42 ( ( in @ B @ ( powerset @ A ) )
% 0.15/0.42 => ( subset @ B @ A ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(inPowerset_type,type,
% 0.15/0.42 inPowerset: $o ).
% 0.15/0.42
% 0.15/0.42 thf(inPowerset,definition,
% 0.15/0.42 ( inPowerset
% 0.15/0.42 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(powersetsubset_type,type,
% 0.15/0.42 powersetsubset: $o ).
% 0.15/0.42
% 0.15/0.42 thf(powersetsubset,definition,
% 0.15/0.42 ( powersetsubset
% 0.15/0.42 = ( ! [A: $i,B: $i] :
% 0.15/0.42 ( ( subset @ A @ B )
% 0.15/0.42 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(sepInPowerset_type,type,
% 0.15/0.42 sepInPowerset: $o ).
% 0.15/0.42
% 0.15/0.42 thf(sepInPowerset,definition,
% 0.15/0.42 ( sepInPowerset
% 0.15/0.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.15/0.42 ( in
% 0.15/0.42 @ ( dsetconstr @ A
% 0.15/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.42 @ ( powerset @ A ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(sepSubset_type,type,
% 0.15/0.42 sepSubset: $o ).
% 0.15/0.42
% 0.15/0.42 thf(sepSubset,definition,
% 0.15/0.42 ( sepSubset
% 0.15/0.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.15/0.42 ( subset
% 0.15/0.42 @ ( dsetconstr @ A
% 0.15/0.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.42 @ A ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(binunion_type,type,
% 0.15/0.42 binunion: $i > $i > $i ).
% 0.15/0.42
% 0.15/0.42 thf(binunionIL_type,type,
% 0.15/0.42 binunionIL: $o ).
% 0.15/0.42
% 0.15/0.42 thf(binunionIL,definition,
% 0.15/0.42 ( binunionIL
% 0.15/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(upairset2IR_type,type,
% 0.15/0.42 upairset2IR: $o ).
% 0.15/0.42
% 0.15/0.42 thf(upairset2IR,definition,
% 0.15/0.42 ( upairset2IR
% 0.15/0.42 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(binunionIR_type,type,
% 0.15/0.42 binunionIR: $o ).
% 0.15/0.42
% 0.15/0.42 thf(binunionIR,definition,
% 0.15/0.42 ( binunionIR
% 0.15/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ B )
% 0.15/0.42 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(binunionEcases_type,type,
% 0.15/0.42 binunionEcases: $o ).
% 0.15/0.42
% 0.15/0.42 thf(binunionEcases,definition,
% 0.15/0.42 ( binunionEcases
% 0.15/0.42 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.15/0.42 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.15/0.42 => ( ( ( in @ Xx @ A )
% 0.15/0.42 => Xphi )
% 0.15/0.42 => ( ( ( in @ Xx @ B )
% 0.15/0.42 => Xphi )
% 0.15/0.42 => Xphi ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(binunionE_type,type,
% 0.15/0.42 binunionE: $o ).
% 0.15/0.42
% 0.15/0.42 thf(binunionE,definition,
% 0.15/0.42 ( binunionE
% 0.15/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.15/0.42 => ( ( in @ Xx @ A )
% 0.15/0.42 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(binunionLsub_type,type,
% 0.15/0.42 binunionLsub: $o ).
% 0.15/0.42
% 0.15/0.42 thf(binunionLsub,definition,
% 0.15/0.42 ( binunionLsub
% 0.15/0.42 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(binunionRsub_type,type,
% 0.15/0.42 binunionRsub: $o ).
% 0.15/0.42
% 0.15/0.42 thf(binunionRsub,definition,
% 0.15/0.42 ( binunionRsub
% 0.15/0.42 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(binintersect_type,type,
% 0.15/0.42 binintersect: $i > $i > $i ).
% 0.15/0.42
% 0.15/0.42 thf(binintersectI_type,type,
% 0.15/0.42 binintersectI: $o ).
% 0.15/0.42
% 0.15/0.42 thf(binintersectI,definition,
% 0.15/0.42 ( binintersectI
% 0.15/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 => ( ( in @ Xx @ B )
% 0.15/0.42 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(binintersectSubset5_type,type,
% 0.15/0.42 binintersectSubset5: $o ).
% 0.15/0.42
% 0.15/0.42 thf(binintersectSubset5,definition,
% 0.15/0.42 ( binintersectSubset5
% 0.15/0.42 = ( ! [A: $i,B: $i,C: $i] :
% 0.15/0.42 ( ( subset @ C @ A )
% 0.15/0.42 => ( ( subset @ C @ B )
% 0.15/0.42 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(binintersectEL_type,type,
% 0.15/0.42 binintersectEL: $o ).
% 0.15/0.42
% 0.15/0.42 thf(binintersectEL,definition,
% 0.15/0.42 ( binintersectEL
% 0.15/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.15/0.42 => ( in @ Xx @ A ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(binintersectLsub_type,type,
% 0.15/0.42 binintersectLsub: $o ).
% 0.15/0.42
% 0.15/0.42 thf(binintersectLsub,definition,
% 0.15/0.42 ( binintersectLsub
% 0.15/0.42 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(binintersectSubset2_type,type,
% 0.15/0.42 binintersectSubset2: $o ).
% 0.15/0.42
% 0.15/0.42 thf(binintersectSubset2,definition,
% 0.15/0.42 ( binintersectSubset2
% 0.15/0.42 = ( ! [A: $i,B: $i] :
% 0.15/0.42 ( ( subset @ A @ B )
% 0.15/0.42 => ( ( binintersect @ A @ B )
% 0.15/0.42 = A ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(binintersectSubset3_type,type,
% 0.15/0.42 binintersectSubset3: $o ).
% 0.15/0.42
% 0.15/0.42 thf(binintersectSubset3,definition,
% 0.15/0.42 ( binintersectSubset3
% 0.15/0.42 = ( ! [A: $i,B: $i] :
% 0.15/0.42 ( ( ( binintersect @ A @ B )
% 0.15/0.42 = B )
% 0.15/0.42 => ( subset @ B @ A ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(binintersectER_type,type,
% 0.15/0.42 binintersectER: $o ).
% 0.15/0.42
% 0.15/0.42 thf(binintersectER,definition,
% 0.15/0.42 ( binintersectER
% 0.15/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.15/0.42 => ( in @ Xx @ B ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(disjointsetsI1_type,type,
% 0.15/0.42 disjointsetsI1: $o ).
% 0.15/0.42
% 0.15/0.42 thf(disjointsetsI1,definition,
% 0.15/0.42 ( disjointsetsI1
% 0.15/0.42 = ( ! [A: $i,B: $i] :
% 0.15/0.42 ( ~ ? [Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 & ( in @ Xx @ B ) )
% 0.15/0.42 => ( ( binintersect @ A @ B )
% 0.15/0.42 = emptyset ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(binintersectRsub_type,type,
% 0.15/0.42 binintersectRsub: $o ).
% 0.15/0.42
% 0.15/0.42 thf(binintersectRsub,definition,
% 0.15/0.42 ( binintersectRsub
% 0.15/0.42 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(binintersectSubset4_type,type,
% 0.15/0.42 binintersectSubset4: $o ).
% 0.15/0.42
% 0.15/0.42 thf(binintersectSubset4,definition,
% 0.15/0.42 ( binintersectSubset4
% 0.15/0.42 = ( ! [A: $i,B: $i] :
% 0.15/0.42 ( ( subset @ B @ A )
% 0.15/0.42 => ( ( binintersect @ A @ B )
% 0.15/0.42 = B ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(binintersectSubset1_type,type,
% 0.15/0.42 binintersectSubset1: $o ).
% 0.15/0.42
% 0.15/0.42 thf(binintersectSubset1,definition,
% 0.15/0.42 ( binintersectSubset1
% 0.15/0.42 = ( ! [A: $i,B: $i] :
% 0.15/0.42 ( ( ( binintersect @ A @ B )
% 0.15/0.42 = A )
% 0.15/0.42 => ( subset @ A @ B ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(bs114d_type,type,
% 0.15/0.42 bs114d: $o ).
% 0.15/0.42
% 0.15/0.42 thf(bs114d,definition,
% 0.15/0.42 ( bs114d
% 0.15/0.42 = ( ! [A: $i,B: $i,C: $i] :
% 0.15/0.42 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.15/0.42 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(regular_type,type,
% 0.15/0.42 regular: $i > $o ).
% 0.15/0.42
% 0.15/0.42 thf(setminus_type,type,
% 0.15/0.42 setminus: $i > $i > $i ).
% 0.15/0.42
% 0.15/0.42 thf(setminusI_type,type,
% 0.15/0.42 setminusI: $o ).
% 0.15/0.42
% 0.15/0.42 thf(setminusI,definition,
% 0.15/0.42 ( setminusI
% 0.15/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 => ( ~ ( in @ Xx @ B )
% 0.15/0.42 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(setminusEL_type,type,
% 0.15/0.42 setminusEL: $o ).
% 0.15/0.42
% 0.15/0.42 thf(setminusEL,definition,
% 0.15/0.42 ( setminusEL
% 0.15/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.15/0.42 => ( in @ Xx @ A ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(setminusER_type,type,
% 0.15/0.42 setminusER: $o ).
% 0.15/0.42
% 0.15/0.42 thf(setminusER,definition,
% 0.15/0.42 ( setminusER
% 0.15/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.15/0.42 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(setminusSubset2_type,type,
% 0.15/0.42 setminusSubset2: $o ).
% 0.15/0.42
% 0.15/0.42 thf(setminusSubset2,definition,
% 0.15/0.42 ( setminusSubset2
% 0.15/0.42 = ( ! [A: $i,B: $i] :
% 0.15/0.42 ( ( subset @ A @ B )
% 0.15/0.42 => ( ( setminus @ A @ B )
% 0.15/0.42 = emptyset ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(setminusERneg_type,type,
% 0.15/0.42 setminusERneg: $o ).
% 0.15/0.42
% 0.15/0.42 thf(setminusERneg,definition,
% 0.15/0.42 ( setminusERneg
% 0.15/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.42 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.15/0.42 => ( ( in @ Xx @ A )
% 0.15/0.42 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(setminusELneg_type,type,
% 0.15/0.42 setminusELneg: $o ).
% 0.15/0.42
% 0.15/0.42 thf(setminusELneg,definition,
% 0.15/0.42 ( setminusELneg
% 0.15/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.42 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.15/0.42 => ( ~ ( in @ Xx @ B )
% 0.15/0.42 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(setminusILneg_type,type,
% 0.15/0.42 setminusILneg: $o ).
% 0.15/0.42
% 0.15/0.42 thf(setminusILneg,definition,
% 0.15/0.42 ( setminusILneg
% 0.15/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.42 ( ~ ( in @ Xx @ A )
% 0.15/0.42 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(setminusIRneg_type,type,
% 0.15/0.42 setminusIRneg: $o ).
% 0.15/0.42
% 0.15/0.42 thf(setminusIRneg,definition,
% 0.15/0.42 ( setminusIRneg
% 0.15/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ B )
% 0.15/0.42 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(setminusLsub_type,type,
% 0.15/0.42 setminusLsub: $o ).
% 0.15/0.42
% 0.15/0.42 thf(setminusLsub,definition,
% 0.15/0.42 ( setminusLsub
% 0.15/0.42 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(setminusSubset1_type,type,
% 0.15/0.42 setminusSubset1: $o ).
% 0.15/0.42
% 0.15/0.42 thf(setminusSubset1,definition,
% 0.15/0.42 ( setminusSubset1
% 0.15/0.42 = ( ! [A: $i,B: $i] :
% 0.15/0.42 ( ( ( setminus @ A @ B )
% 0.15/0.42 = emptyset )
% 0.15/0.42 => ( subset @ A @ B ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(symdiff_type,type,
% 0.15/0.42 symdiff: $i > $i > $i ).
% 0.15/0.42
% 0.15/0.42 thf(symdiffE_type,type,
% 0.15/0.42 symdiffE: $o ).
% 0.15/0.42
% 0.15/0.42 thf(symdiffE,definition,
% 0.15/0.42 ( symdiffE
% 0.15/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.15/0.42 => ! [Xphi: $o] :
% 0.15/0.42 ( ( ( in @ Xx @ A )
% 0.15/0.42 => ( ~ ( in @ Xx @ B )
% 0.15/0.42 => Xphi ) )
% 0.15/0.42 => ( ( ~ ( in @ Xx @ A )
% 0.15/0.42 => ( ( in @ Xx @ B )
% 0.15/0.42 => Xphi ) )
% 0.15/0.42 => Xphi ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(symdiffI1_type,type,
% 0.15/0.42 symdiffI1: $o ).
% 0.15/0.42
% 0.15/0.42 thf(symdiffI1,definition,
% 0.15/0.42 ( symdiffI1
% 0.15/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 => ( ~ ( in @ Xx @ B )
% 0.15/0.42 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(symdiffI2_type,type,
% 0.15/0.42 symdiffI2: $o ).
% 0.15/0.42
% 0.15/0.42 thf(symdiffI2,definition,
% 0.15/0.42 ( symdiffI2
% 0.15/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.42 ( ~ ( in @ Xx @ A )
% 0.15/0.42 => ( ( in @ Xx @ B )
% 0.15/0.42 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(symdiffIneg1_type,type,
% 0.15/0.42 symdiffIneg1: $o ).
% 0.15/0.42
% 0.15/0.42 thf(symdiffIneg1,definition,
% 0.15/0.42 ( symdiffIneg1
% 0.15/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 => ( ( in @ Xx @ B )
% 0.15/0.42 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(symdiffIneg2_type,type,
% 0.15/0.42 symdiffIneg2: $o ).
% 0.15/0.42
% 0.15/0.42 thf(symdiffIneg2,definition,
% 0.15/0.42 ( symdiffIneg2
% 0.15/0.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.42 ( ~ ( in @ Xx @ A )
% 0.15/0.42 => ( ~ ( in @ Xx @ B )
% 0.15/0.42 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(iskpair_type,type,
% 0.15/0.42 iskpair: $i > $o ).
% 0.15/0.42
% 0.15/0.42 thf(secondinupair_type,type,
% 0.15/0.42 secondinupair: $o ).
% 0.15/0.42
% 0.15/0.42 thf(secondinupair,definition,
% 0.15/0.42 ( secondinupair
% 0.15/0.42 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(setukpairIL_type,type,
% 0.15/0.42 setukpairIL: $o ).
% 0.15/0.42
% 0.15/0.42 thf(setukpairIL,definition,
% 0.15/0.42 ( setukpairIL
% 0.15/0.42 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(setukpairIR_type,type,
% 0.15/0.42 setukpairIR: $o ).
% 0.15/0.42
% 0.15/0.42 thf(setukpairIR,definition,
% 0.15/0.42 ( setukpairIR
% 0.15/0.42 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(kpairiskpair_type,type,
% 0.15/0.42 kpairiskpair: $o ).
% 0.15/0.42
% 0.15/0.42 thf(kpairiskpair,definition,
% 0.15/0.42 ( kpairiskpair
% 0.15/0.42 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(kpair_type,type,
% 0.15/0.42 kpair: $i > $i > $i ).
% 0.15/0.42
% 0.15/0.42 thf(kpairp_type,type,
% 0.15/0.42 kpairp: $o ).
% 0.15/0.42
% 0.15/0.42 thf(kpairp,definition,
% 0.15/0.42 ( kpairp
% 0.15/0.42 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(cartprod_type,type,
% 0.15/0.42 cartprod: $i > $i > $i ).
% 0.15/0.42
% 0.15/0.42 thf(singletonsubset_type,type,
% 0.15/0.42 singletonsubset: $o ).
% 0.15/0.42
% 0.15/0.42 thf(singletonsubset,definition,
% 0.15/0.42 ( singletonsubset
% 0.15/0.42 = ( ! [A: $i,Xx: $i] :
% 0.15/0.42 ( ( in @ Xx @ A )
% 0.15/0.42 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(singletoninpowerset_type,type,
% 0.15/0.43 singletoninpowerset: $o ).
% 0.15/0.43
% 0.15/0.43 thf(singletoninpowerset,definition,
% 0.15/0.43 ( singletoninpowerset
% 0.15/0.43 = ( ! [A: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(singletoninpowunion_type,type,
% 0.15/0.43 singletoninpowunion: $o ).
% 0.15/0.43
% 0.15/0.43 thf(singletoninpowunion,definition,
% 0.15/0.43 ( singletoninpowunion
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(upairset2E_type,type,
% 0.15/0.43 upairset2E: $o ).
% 0.15/0.43
% 0.15/0.43 thf(upairset2E,definition,
% 0.15/0.43 ( upairset2E
% 0.15/0.43 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.15/0.43 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.15/0.43 => ( ( Xz = Xx )
% 0.15/0.43 | ( Xz = Xy ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(upairsubunion_type,type,
% 0.15/0.43 upairsubunion: $o ).
% 0.15/0.43
% 0.15/0.43 thf(upairsubunion,definition,
% 0.15/0.43 ( upairsubunion
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ B )
% 0.15/0.43 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(upairinpowunion_type,type,
% 0.15/0.43 upairinpowunion: $o ).
% 0.15/0.43
% 0.15/0.43 thf(upairinpowunion,definition,
% 0.15/0.43 ( upairinpowunion
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ B )
% 0.15/0.43 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(ubforcartprodlem1_type,type,
% 0.15/0.43 ubforcartprodlem1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(ubforcartprodlem1,definition,
% 0.15/0.43 ( ubforcartprodlem1
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ B )
% 0.15/0.43 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(ubforcartprodlem2_type,type,
% 0.15/0.43 ubforcartprodlem2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(ubforcartprodlem2,definition,
% 0.15/0.43 ( ubforcartprodlem2
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ B )
% 0.15/0.43 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(ubforcartprodlem3_type,type,
% 0.15/0.43 ubforcartprodlem3: $o ).
% 0.15/0.43
% 0.15/0.43 thf(ubforcartprodlem3,definition,
% 0.15/0.43 ( ubforcartprodlem3
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ B )
% 0.15/0.43 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(cartprodpairin_type,type,
% 0.15/0.43 cartprodpairin: $o ).
% 0.15/0.43
% 0.15/0.43 thf(cartprodpairin,definition,
% 0.15/0.43 ( cartprodpairin
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ B )
% 0.15/0.43 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(cartprodmempair1_type,type,
% 0.15/0.43 cartprodmempair1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(cartprodmempair1,definition,
% 0.15/0.43 ( cartprodmempair1
% 0.15/0.43 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.15/0.43 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.15/0.43 => ? [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 & ? [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ B )
% 0.15/0.43 & ( Xu
% 0.15/0.43 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(cartprodmempair_type,type,
% 0.15/0.43 cartprodmempair: $o ).
% 0.15/0.43
% 0.15/0.43 thf(cartprodmempair,definition,
% 0.15/0.43 ( cartprodmempair
% 0.15/0.43 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.15/0.43 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.15/0.43 => ( iskpair @ Xu ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setunionE2_type,type,
% 0.15/0.43 setunionE2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setunionE2,definition,
% 0.15/0.43 ( setunionE2
% 0.15/0.43 = ( ! [A: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ ( setunion @ A ) )
% 0.15/0.43 => ? [X: $i] :
% 0.15/0.43 ( ( in @ X @ A )
% 0.15/0.43 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setunionsingleton1_type,type,
% 0.15/0.43 setunionsingleton1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setunionsingleton1,definition,
% 0.15/0.43 ( setunionsingleton1
% 0.15/0.43 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setunionsingleton2_type,type,
% 0.15/0.43 setunionsingleton2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setunionsingleton2,definition,
% 0.15/0.43 ( setunionsingleton2
% 0.15/0.43 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setunionsingleton_type,type,
% 0.15/0.43 setunionsingleton: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setunionsingleton,definition,
% 0.15/0.43 ( setunionsingleton
% 0.15/0.43 = ( ! [Xx: $i] :
% 0.15/0.43 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.15/0.43 = Xx ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(singleton_type,type,
% 0.15/0.43 singleton: $i > $o ).
% 0.15/0.43
% 0.15/0.43 thf(singletonprop_type,type,
% 0.15/0.43 singletonprop: $o ).
% 0.15/0.43
% 0.15/0.43 thf(singletonprop,definition,
% 0.15/0.43 ( singletonprop
% 0.15/0.43 = ( ! [A: $i,Xphi: $i > $o] :
% 0.15/0.43 ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ A )
% 0.15/0.43 => ( ( Xphi @ Xx )
% 0.15/0.43 => ( ( Xphi @ Xy )
% 0.15/0.43 => ( Xx = Xy ) ) ) ) )
% 0.15/0.43 => ( ? [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 & ( Xphi @ Xx ) )
% 0.15/0.43 => ( singleton
% 0.15/0.43 @ ( dsetconstr @ A
% 0.15/0.43 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(ex1_type,type,
% 0.15/0.43 ex1: $i > ( $i > $o ) > $o ).
% 0.15/0.43
% 0.15/0.43 thf(ex1E1_type,type,
% 0.15/0.43 ex1E1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(ex1E1,definition,
% 0.15/0.43 ( ex1E1
% 0.15/0.43 = ( ! [A: $i,Xphi: $i > $o] :
% 0.15/0.43 ( ( ex1 @ A
% 0.15/0.43 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.43 => ? [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(ex1I_type,type,
% 0.15/0.43 ex1I: $o ).
% 0.15/0.43
% 0.15/0.43 thf(ex1I,definition,
% 0.15/0.43 ( ex1I
% 0.15/0.43 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( Xphi @ Xx )
% 0.15/0.43 => ( ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ A )
% 0.15/0.43 => ( ( Xphi @ Xy )
% 0.15/0.43 => ( Xy = Xx ) ) )
% 0.15/0.43 => ( ex1 @ A
% 0.15/0.43 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(ex1I2_type,type,
% 0.15/0.43 ex1I2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(ex1I2,definition,
% 0.15/0.43 ( ex1I2
% 0.15/0.43 = ( ! [A: $i,Xphi: $i > $o] :
% 0.15/0.43 ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ A )
% 0.15/0.43 => ( ( Xphi @ Xx )
% 0.15/0.43 => ( ( Xphi @ Xy )
% 0.15/0.43 => ( Xx = Xy ) ) ) ) )
% 0.15/0.43 => ( ? [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 & ( Xphi @ Xx ) )
% 0.15/0.43 => ( ex1 @ A
% 0.15/0.43 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(singletonsuniq_type,type,
% 0.15/0.43 singletonsuniq: $o ).
% 0.15/0.43
% 0.15/0.43 thf(singletonsuniq,definition,
% 0.15/0.43 ( singletonsuniq
% 0.15/0.43 = ( ! [Xx: $i,Xy: $i] :
% 0.15/0.43 ( ( ( setadjoin @ Xx @ emptyset )
% 0.15/0.43 = ( setadjoin @ Xy @ emptyset ) )
% 0.15/0.43 => ( Xx = Xy ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(atmost1p_type,type,
% 0.15/0.43 atmost1p: $i > $o ).
% 0.15/0.43
% 0.15/0.43 thf(atleast2p_type,type,
% 0.15/0.43 atleast2p: $i > $o ).
% 0.15/0.43
% 0.15/0.43 thf(atmost2p_type,type,
% 0.15/0.43 atmost2p: $i > $o ).
% 0.15/0.43
% 0.15/0.43 thf(upairsetp_type,type,
% 0.15/0.43 upairsetp: $i > $o ).
% 0.15/0.43
% 0.15/0.43 thf(setukpairinjL1_type,type,
% 0.15/0.43 setukpairinjL1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setukpairinjL1,definition,
% 0.15/0.43 ( setukpairinjL1
% 0.15/0.43 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.15/0.43 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.15/0.43 => ( Xx = Xz ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(kfstsingleton_type,type,
% 0.15/0.43 kfstsingleton: $o ).
% 0.15/0.43
% 0.15/0.43 thf(kfstsingleton,definition,
% 0.15/0.43 ( kfstsingleton
% 0.15/0.43 = ( ! [Xu: $i] :
% 0.15/0.43 ( ( iskpair @ Xu )
% 0.15/0.43 => ( singleton
% 0.15/0.43 @ ( dsetconstr @ ( setunion @ Xu )
% 0.15/0.43 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(theprop_type,type,
% 0.15/0.43 theprop: $o ).
% 0.15/0.43
% 0.15/0.43 thf(theprop,definition,
% 0.15/0.43 ( theprop
% 0.15/0.43 = ( ! [X: $i] :
% 0.15/0.43 ( ( singleton @ X )
% 0.15/0.43 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(kfst_type,type,
% 0.15/0.43 kfst: $i > $i ).
% 0.15/0.43
% 0.15/0.43 thf(kfstpairEq_type,type,
% 0.15/0.43 kfstpairEq: $o ).
% 0.15/0.43
% 0.15/0.43 thf(kfstpairEq,definition,
% 0.15/0.43 ( kfstpairEq
% 0.15/0.43 = ( ! [Xx: $i,Xy: $i] :
% 0.15/0.43 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.15/0.43 = Xx ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(cartprodfstin_type,type,
% 0.15/0.43 cartprodfstin: $o ).
% 0.15/0.43
% 0.15/0.43 thf(cartprodfstin,definition,
% 0.15/0.43 ( cartprodfstin
% 0.15/0.43 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.15/0.43 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.15/0.43 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setukpairinjL2_type,type,
% 0.15/0.43 setukpairinjL2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setukpairinjL2,definition,
% 0.15/0.43 ( setukpairinjL2
% 0.15/0.43 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.15/0.43 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.15/0.43 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.15/0.43 => ( Xx = Xz ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setukpairinjL_type,type,
% 0.15/0.43 setukpairinjL: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setukpairinjL,definition,
% 0.15/0.43 ( setukpairinjL
% 0.15/0.43 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.15/0.43 ( ( ( kpair @ Xx @ Xy )
% 0.15/0.43 = ( kpair @ Xz @ Xu ) )
% 0.15/0.43 => ( Xx = Xz ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setukpairinjR11_type,type,
% 0.15/0.43 setukpairinjR11: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setukpairinjR11,definition,
% 0.15/0.43 ( setukpairinjR11
% 0.15/0.43 = ( ! [Xx: $i,Xy: $i] :
% 0.15/0.43 ( ( Xx = Xy )
% 0.15/0.43 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.15/0.43 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setukpairinjR12_type,type,
% 0.15/0.43 setukpairinjR12: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setukpairinjR12,definition,
% 0.15/0.43 ( setukpairinjR12
% 0.15/0.43 = ( ! [Xx: $i,Xy: $i] :
% 0.15/0.43 ( ( Xx = Xy )
% 0.15/0.43 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.15/0.43 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setukpairinjR1_type,type,
% 0.15/0.43 setukpairinjR1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setukpairinjR1,definition,
% 0.15/0.43 ( setukpairinjR1
% 0.15/0.43 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.15/0.43 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.15/0.43 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.15/0.43 => ( ( Xz = Xu )
% 0.15/0.43 => ( Xy = Xu ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(upairequniteq_type,type,
% 0.15/0.43 upairequniteq: $o ).
% 0.15/0.43
% 0.15/0.43 thf(upairequniteq,definition,
% 0.15/0.43 ( upairequniteq
% 0.15/0.43 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.15/0.43 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.15/0.43 = ( setadjoin @ Xz @ emptyset ) )
% 0.15/0.43 => ( Xx = Xy ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setukpairinjR2_type,type,
% 0.15/0.43 setukpairinjR2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setukpairinjR2,definition,
% 0.15/0.43 ( setukpairinjR2
% 0.15/0.43 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.15/0.43 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.15/0.43 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.15/0.43 => ( Xy = Xu ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setukpairinjR_type,type,
% 0.15/0.43 setukpairinjR: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setukpairinjR,definition,
% 0.15/0.43 ( setukpairinjR
% 0.15/0.43 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.15/0.43 ( ( ( kpair @ Xx @ Xy )
% 0.15/0.43 = ( kpair @ Xz @ Xu ) )
% 0.15/0.43 => ( Xy = Xu ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(ksndsingleton_type,type,
% 0.15/0.43 ksndsingleton: $o ).
% 0.15/0.43
% 0.15/0.43 thf(ksndsingleton,definition,
% 0.15/0.43 ( ksndsingleton
% 0.15/0.43 = ( ! [Xu: $i] :
% 0.15/0.43 ( ( iskpair @ Xu )
% 0.15/0.43 => ( singleton
% 0.15/0.43 @ ( dsetconstr @ ( setunion @ Xu )
% 0.15/0.43 @ ^ [Xx: $i] :
% 0.15/0.43 ( Xu
% 0.15/0.43 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(ksnd_type,type,
% 0.15/0.43 ksnd: $i > $i ).
% 0.15/0.43
% 0.15/0.43 thf(ksndpairEq_type,type,
% 0.15/0.43 ksndpairEq: $o ).
% 0.15/0.43
% 0.15/0.43 thf(ksndpairEq,definition,
% 0.15/0.43 ( ksndpairEq
% 0.15/0.43 = ( ! [Xx: $i,Xy: $i] :
% 0.15/0.43 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.15/0.43 = Xy ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(kpairsurjEq_type,type,
% 0.15/0.43 kpairsurjEq: $o ).
% 0.15/0.43
% 0.15/0.43 thf(kpairsurjEq,definition,
% 0.15/0.43 ( kpairsurjEq
% 0.15/0.43 = ( ! [Xu: $i] :
% 0.15/0.43 ( ( iskpair @ Xu )
% 0.15/0.43 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.15/0.43 = Xu ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(cartprodsndin_type,type,
% 0.15/0.43 cartprodsndin: $o ).
% 0.15/0.43
% 0.15/0.43 thf(cartprodsndin,definition,
% 0.15/0.43 ( cartprodsndin
% 0.15/0.43 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.15/0.43 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.15/0.43 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(cartprodpairmemEL_type,type,
% 0.15/0.43 cartprodpairmemEL: $o ).
% 0.15/0.43
% 0.15/0.43 thf(cartprodpairmemEL,definition,
% 0.15/0.43 ( cartprodpairmemEL
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.15/0.43 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.15/0.43 => ( in @ Xx @ A ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(cartprodpairmemER_type,type,
% 0.15/0.43 cartprodpairmemER: $o ).
% 0.15/0.43
% 0.15/0.43 thf(cartprodpairmemER,definition,
% 0.15/0.43 ( cartprodpairmemER
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.15/0.43 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.15/0.43 => ( in @ Xy @ B ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(cartprodmempaircEq_type,type,
% 0.15/0.43 cartprodmempaircEq: $o ).
% 0.15/0.43
% 0.15/0.43 thf(cartprodmempaircEq,definition,
% 0.15/0.43 ( cartprodmempaircEq
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ B )
% 0.15/0.43 => ( ( kpair @ Xx @ Xy )
% 0.15/0.43 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(cartprodfstpairEq_type,type,
% 0.15/0.43 cartprodfstpairEq: $o ).
% 0.15/0.43
% 0.15/0.43 thf(cartprodfstpairEq,definition,
% 0.15/0.43 ( cartprodfstpairEq
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ B )
% 0.15/0.43 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.15/0.43 = Xx ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(cartprodsndpairEq_type,type,
% 0.15/0.43 cartprodsndpairEq: $o ).
% 0.15/0.43
% 0.15/0.43 thf(cartprodsndpairEq,definition,
% 0.15/0.43 ( cartprodsndpairEq
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ B )
% 0.15/0.43 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.15/0.43 = Xy ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(cartprodpairsurjEq_type,type,
% 0.15/0.43 cartprodpairsurjEq: $o ).
% 0.15/0.43
% 0.15/0.43 thf(cartprodpairsurjEq,definition,
% 0.15/0.43 ( cartprodpairsurjEq
% 0.15/0.43 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.15/0.43 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.15/0.43 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.15/0.43 = Xu ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(breln_type,type,
% 0.15/0.43 breln: $i > $i > $i > $o ).
% 0.15/0.43
% 0.15/0.43 thf(breln,definition,
% 0.15/0.43 ( breln
% 0.15/0.43 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(dpsetconstr_type,type,
% 0.15/0.43 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.15/0.43
% 0.15/0.43 thf(dpsetconstrI_type,type,
% 0.15/0.43 dpsetconstrI: $o ).
% 0.15/0.43
% 0.15/0.43 thf(dpsetconstrI,definition,
% 0.15/0.43 ( dpsetconstrI
% 0.15/0.43 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ B )
% 0.15/0.43 => ( ( Xphi @ Xx @ Xy )
% 0.15/0.43 => ( in @ ( kpair @ Xx @ Xy )
% 0.15/0.43 @ ( dpsetconstr @ A @ B
% 0.15/0.43 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(dpsetconstrSub_type,type,
% 0.15/0.43 dpsetconstrSub: $o ).
% 0.15/0.43
% 0.15/0.43 thf(dpsetconstrSub,definition,
% 0.15/0.43 ( dpsetconstrSub
% 0.15/0.43 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.15/0.43 ( subset
% 0.15/0.43 @ ( dpsetconstr @ A @ B
% 0.15/0.43 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.15/0.43 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setOfPairsIsBReln_type,type,
% 0.15/0.43 setOfPairsIsBReln: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setOfPairsIsBReln,definition,
% 0.15/0.43 ( setOfPairsIsBReln
% 0.15/0.43 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.15/0.43 ( breln @ A @ B
% 0.15/0.43 @ ( dpsetconstr @ A @ B
% 0.15/0.43 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(dpsetconstrERa_type,type,
% 0.15/0.43 dpsetconstrERa: $o ).
% 0.15/0.43
% 0.15/0.43 thf(dpsetconstrERa,definition,
% 0.15/0.43 ( dpsetconstrERa
% 0.15/0.43 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ B )
% 0.15/0.43 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.15/0.43 @ ( dpsetconstr @ A @ B
% 0.15/0.43 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.15/0.43 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(dpsetconstrEL1_type,type,
% 0.15/0.43 dpsetconstrEL1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(dpsetconstrEL1,definition,
% 0.15/0.43 ( dpsetconstrEL1
% 0.15/0.43 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.15/0.43 ( ( in @ ( kpair @ Xx @ Xy )
% 0.15/0.43 @ ( dpsetconstr @ A @ B
% 0.15/0.43 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.15/0.43 => ( in @ Xx @ A ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(dpsetconstrEL2_type,type,
% 0.15/0.43 dpsetconstrEL2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(dpsetconstrEL2,definition,
% 0.15/0.43 ( dpsetconstrEL2
% 0.15/0.43 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.15/0.43 ( ( in @ ( kpair @ Xx @ Xy )
% 0.15/0.43 @ ( dpsetconstr @ A @ B
% 0.15/0.43 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.15/0.43 => ( in @ Xy @ B ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(dpsetconstrER_type,type,
% 0.15/0.43 dpsetconstrER: $o ).
% 0.15/0.43
% 0.15/0.43 thf(dpsetconstrER,definition,
% 0.15/0.43 ( dpsetconstrER
% 0.15/0.43 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.15/0.43 ( ( in @ ( kpair @ Xx @ Xy )
% 0.15/0.43 @ ( dpsetconstr @ A @ B
% 0.15/0.43 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.15/0.43 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(func_type,type,
% 0.15/0.43 func: $i > $i > $i > $o ).
% 0.15/0.43
% 0.15/0.43 thf(funcSet_type,type,
% 0.15/0.43 funcSet: $i > $i > $i ).
% 0.15/0.43
% 0.15/0.43 thf(funcImageSingleton_type,type,
% 0.15/0.43 funcImageSingleton: $o ).
% 0.15/0.43
% 0.15/0.43 thf(funcImageSingleton,definition,
% 0.15/0.43 ( funcImageSingleton
% 0.15/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.15/0.43 ( ( func @ A @ B @ Xf )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( singleton
% 0.15/0.43 @ ( dsetconstr @ B
% 0.15/0.43 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(apProp_type,type,
% 0.15/0.43 apProp: $o ).
% 0.15/0.43
% 0.15/0.43 thf(apProp,definition,
% 0.15/0.43 ( apProp
% 0.15/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.15/0.43 ( ( func @ A @ B @ Xf )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( in
% 0.15/0.43 @ ( setunion
% 0.15/0.43 @ ( dsetconstr @ B
% 0.15/0.43 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.15/0.43 @ B ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(ap_type,type,
% 0.15/0.43 ap: $i > $i > $i > $i > $i ).
% 0.15/0.43
% 0.15/0.43 thf(app_type,type,
% 0.15/0.43 app: $o ).
% 0.15/0.43
% 0.15/0.43 thf(app,definition,
% 0.15/0.43 ( app
% 0.15/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.15/0.43 ( ( func @ A @ B @ Xf )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(infuncsetfunc_type,type,
% 0.15/0.43 infuncsetfunc: $o ).
% 0.15/0.43
% 0.15/0.43 thf(infuncsetfunc,definition,
% 0.15/0.43 ( infuncsetfunc
% 0.15/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.15/0.43 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.15/0.43 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(ap2p_type,type,
% 0.15/0.43 ap2p: $o ).
% 0.15/0.43
% 0.15/0.43 thf(ap2p,definition,
% 0.15/0.43 ( ap2p
% 0.15/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.15/0.43 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(funcinfuncset_type,type,
% 0.15/0.43 funcinfuncset: $o ).
% 0.15/0.43
% 0.15/0.43 thf(funcinfuncset,definition,
% 0.15/0.43 ( funcinfuncset
% 0.15/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.15/0.43 ( ( func @ A @ B @ Xf )
% 0.15/0.43 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(lamProp_type,type,
% 0.15/0.43 lamProp: $o ).
% 0.15/0.43
% 0.15/0.43 thf(lamProp,definition,
% 0.15/0.43 ( lamProp
% 0.15/0.43 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.15/0.43 ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.15/0.43 => ( func @ A @ B
% 0.15/0.43 @ ( dpsetconstr @ A @ B
% 0.15/0.43 @ ^ [Xx: $i,Xy: $i] :
% 0.15/0.43 ( ( Xf @ Xx )
% 0.15/0.43 = Xy ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(lam_type,type,
% 0.15/0.43 lam: $i > $i > ( $i > $i ) > $i ).
% 0.15/0.43
% 0.15/0.43 thf(lamp_type,type,
% 0.15/0.43 lamp: $o ).
% 0.15/0.43
% 0.15/0.43 thf(lamp,definition,
% 0.15/0.43 ( lamp
% 0.15/0.43 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.15/0.43 ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.15/0.43 => ( func @ A @ B
% 0.15/0.43 @ ( lam @ A @ B
% 0.15/0.43 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(lam2p_type,type,
% 0.15/0.43 lam2p: $o ).
% 0.15/0.43
% 0.15/0.43 thf(lam2p,definition,
% 0.15/0.43 ( lam2p
% 0.15/0.43 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.15/0.43 ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.15/0.43 => ( in
% 0.15/0.43 @ ( lam @ A @ B
% 0.15/0.43 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.15/0.43 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(brelnall1_type,type,
% 0.15/0.43 brelnall1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(brelnall1,definition,
% 0.15/0.43 ( brelnall1
% 0.15/0.43 = ( ! [A: $i,B: $i,R: $i] :
% 0.15/0.43 ( ( breln @ A @ B @ R )
% 0.15/0.43 => ! [Xphi: $i > $o] :
% 0.15/0.43 ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ B )
% 0.15/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.15/0.43 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ R )
% 0.15/0.43 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(brelnall2_type,type,
% 0.15/0.43 brelnall2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(brelnall2,definition,
% 0.15/0.43 ( brelnall2
% 0.15/0.43 = ( ! [A: $i,B: $i,R: $i] :
% 0.15/0.43 ( ( breln @ A @ B @ R )
% 0.15/0.43 => ! [Xphi: $i > $o] :
% 0.15/0.43 ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ B )
% 0.15/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.15/0.43 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ R )
% 0.15/0.43 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(ex1E2_type,type,
% 0.15/0.43 ex1E2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(ex1E2,definition,
% 0.15/0.43 ( ex1E2
% 0.15/0.43 = ( ! [A: $i,Xphi: $i > $o] :
% 0.15/0.43 ( ( ex1 @ A
% 0.15/0.43 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ A )
% 0.15/0.43 => ( ( Xphi @ Xx )
% 0.15/0.43 => ( ( Xphi @ Xy )
% 0.15/0.43 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(funcGraphProp1_type,type,
% 0.15/0.43 funcGraphProp1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(funcGraphProp1,definition,
% 0.15/0.43 ( funcGraphProp1
% 0.15/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.15/0.43 ( ( func @ A @ B @ Xf )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(funcGraphProp3_type,type,
% 0.15/0.43 funcGraphProp3: $o ).
% 0.15/0.43
% 0.15/0.43 thf(funcGraphProp3,definition,
% 0.15/0.43 ( funcGraphProp3
% 0.15/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.15/0.43 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(funcGraphProp2_type,type,
% 0.15/0.43 funcGraphProp2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(funcGraphProp2,definition,
% 0.15/0.43 ( funcGraphProp2
% 0.15/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.15/0.43 ( ( func @ A @ B @ Xf )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ B )
% 0.15/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.15/0.43 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.15/0.43 = Xy ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(funcextLem_type,type,
% 0.15/0.43 funcextLem: $o ).
% 0.15/0.43
% 0.15/0.43 thf(funcextLem,definition,
% 0.15/0.43 ( funcextLem
% 0.15/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.15/0.43 ( ( func @ A @ B @ Xf )
% 0.15/0.43 => ! [Xg: $i] :
% 0.15/0.43 ( ( func @ A @ B @ Xg )
% 0.15/0.43 => ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.15/0.43 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ B )
% 0.15/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 0.15/0.43 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(funcGraphProp4_type,type,
% 0.15/0.43 funcGraphProp4: $o ).
% 0.15/0.43
% 0.15/0.43 thf(funcGraphProp4,definition,
% 0.15/0.43 ( funcGraphProp4
% 0.15/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.15/0.43 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ B )
% 0.15/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.15/0.43 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.15/0.43 = Xy ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(subbreln_type,type,
% 0.15/0.43 subbreln: $o ).
% 0.15/0.43
% 0.15/0.43 thf(subbreln,definition,
% 0.15/0.43 ( subbreln
% 0.15/0.43 = ( ! [A: $i,B: $i,R: $i] :
% 0.15/0.43 ( ( breln @ A @ B @ R )
% 0.15/0.43 => ! [S: $i] :
% 0.15/0.43 ( ( breln @ A @ B @ S )
% 0.15/0.43 => ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ B )
% 0.15/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.15/0.43 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.15/0.43 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(eqbreln_type,type,
% 0.15/0.43 eqbreln: $o ).
% 0.15/0.43
% 0.15/0.43 thf(eqbreln,definition,
% 0.15/0.43 ( eqbreln
% 0.15/0.43 = ( ! [A: $i,B: $i,R: $i] :
% 0.15/0.43 ( ( breln @ A @ B @ R )
% 0.15/0.43 => ! [S: $i] :
% 0.15/0.43 ( ( breln @ A @ B @ S )
% 0.15/0.43 => ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ B )
% 0.15/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.15/0.43 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.15/0.43 => ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ B )
% 0.15/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.15/0.43 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.15/0.43 => ( R = S ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(funcext_type,type,
% 0.15/0.43 funcext: $o ).
% 0.15/0.43
% 0.15/0.43 thf(funcext,definition,
% 0.15/0.43 ( funcext
% 0.15/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.15/0.43 ( ( func @ A @ B @ Xf )
% 0.15/0.43 => ! [Xg: $i] :
% 0.15/0.43 ( ( func @ A @ B @ Xg )
% 0.15/0.43 => ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.15/0.43 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.15/0.43 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(funcext2_type,type,
% 0.15/0.43 funcext2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(funcext2,definition,
% 0.15/0.43 ( funcext2
% 0.15/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.15/0.43 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.15/0.43 => ! [Xg: $i] :
% 0.15/0.43 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 0.15/0.43 => ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.15/0.43 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.15/0.43 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(ap2apEq1_type,type,
% 0.15/0.43 ap2apEq1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(ap2apEq1,definition,
% 0.15/0.43 ( ap2apEq1
% 0.15/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.15/0.43 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.15/0.43 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(ap2apEq2_type,type,
% 0.15/0.43 ap2apEq2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(ap2apEq2,definition,
% 0.15/0.43 ( ap2apEq2
% 0.15/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.15/0.43 ( ( func @ A @ B @ Xf )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.15/0.43 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(beta1_type,type,
% 0.15/0.43 beta1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(beta1,definition,
% 0.15/0.43 ( beta1
% 0.15/0.43 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.15/0.43 ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( ap @ A @ B
% 0.15/0.43 @ ( lam @ A @ B
% 0.15/0.43 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.15/0.43 @ Xx )
% 0.15/0.43 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(eta1_type,type,
% 0.15/0.43 eta1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(eta1,definition,
% 0.15/0.43 ( eta1
% 0.15/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.15/0.43 ( ( func @ A @ B @ Xf )
% 0.15/0.43 => ( ( lam @ A @ B
% 0.15/0.43 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.15/0.43 = Xf ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(lam2lamEq_type,type,
% 0.15/0.43 lam2lamEq: $o ).
% 0.15/0.43
% 0.15/0.43 thf(lam2lamEq,definition,
% 0.15/0.43 ( lam2lamEq
% 0.15/0.43 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.15/0.43 ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.15/0.43 => ( ( lam @ A @ B
% 0.15/0.43 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.15/0.43 = ( lam @ A @ B
% 0.15/0.43 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(beta2_type,type,
% 0.15/0.43 beta2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(beta2,definition,
% 0.15/0.43 ( beta2
% 0.15/0.43 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.15/0.43 ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( ap @ A @ B
% 0.15/0.43 @ ( lam @ A @ B
% 0.15/0.43 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.15/0.43 @ Xx )
% 0.15/0.43 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(eta2_type,type,
% 0.15/0.43 eta2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(eta2,definition,
% 0.15/0.43 ( eta2
% 0.15/0.43 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.15/0.43 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.15/0.43 => ( ( lam @ A @ B
% 0.15/0.43 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.15/0.43 = Xf ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(iffalseProp1_type,type,
% 0.15/0.43 iffalseProp1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(iffalseProp1,definition,
% 0.15/0.43 ( iffalseProp1
% 0.15/0.43 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ A )
% 0.15/0.43 => ( ~ Xphi
% 0.15/0.43 => ( in @ Xy
% 0.15/0.43 @ ( dsetconstr @ A
% 0.15/0.43 @ ^ [Xz: $i] :
% 0.15/0.43 ( ( Xphi
% 0.15/0.43 & ( Xz = Xx ) )
% 0.15/0.43 | ( ~ Xphi
% 0.15/0.43 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(iffalseProp2_type,type,
% 0.15/0.43 iffalseProp2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(iffalseProp2,definition,
% 0.15/0.43 ( iffalseProp2
% 0.15/0.43 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ A )
% 0.15/0.43 => ( ~ Xphi
% 0.15/0.43 => ( ( dsetconstr @ A
% 0.15/0.43 @ ^ [Xz: $i] :
% 0.15/0.43 ( ( Xphi
% 0.15/0.43 & ( Xz = Xx ) )
% 0.15/0.43 | ( ~ Xphi
% 0.15/0.43 & ( Xz = Xy ) ) ) )
% 0.15/0.43 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(iftrueProp1_type,type,
% 0.15/0.43 iftrueProp1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(iftrueProp1,definition,
% 0.15/0.43 ( iftrueProp1
% 0.15/0.43 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ A )
% 0.15/0.43 => ( Xphi
% 0.15/0.43 => ( in @ Xx
% 0.15/0.43 @ ( dsetconstr @ A
% 0.15/0.43 @ ^ [Xz: $i] :
% 0.15/0.43 ( ( Xphi
% 0.15/0.43 & ( Xz = Xx ) )
% 0.15/0.43 | ( ~ Xphi
% 0.15/0.43 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(iftrueProp2_type,type,
% 0.15/0.43 iftrueProp2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(iftrueProp2,definition,
% 0.15/0.43 ( iftrueProp2
% 0.15/0.43 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ A )
% 0.15/0.43 => ( Xphi
% 0.15/0.43 => ( ( dsetconstr @ A
% 0.15/0.43 @ ^ [Xz: $i] :
% 0.15/0.43 ( ( Xphi
% 0.15/0.43 & ( Xz = Xx ) )
% 0.15/0.43 | ( ~ Xphi
% 0.15/0.43 & ( Xz = Xy ) ) ) )
% 0.15/0.43 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(ifSingleton_type,type,
% 0.15/0.43 ifSingleton: $o ).
% 0.15/0.43
% 0.15/0.43 thf(ifSingleton,definition,
% 0.15/0.43 ( ifSingleton
% 0.15/0.43 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ A )
% 0.15/0.43 => ( singleton
% 0.15/0.43 @ ( dsetconstr @ A
% 0.15/0.43 @ ^ [Xz: $i] :
% 0.15/0.43 ( ( Xphi
% 0.15/0.43 & ( Xz = Xx ) )
% 0.15/0.43 | ( ~ Xphi
% 0.15/0.43 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(if_type,type,
% 0.15/0.43 if: $i > $o > $i > $i > $i ).
% 0.15/0.43
% 0.15/0.43 thf(ifp_type,type,
% 0.15/0.43 ifp: $o ).
% 0.15/0.43
% 0.15/0.43 thf(ifp,definition,
% 0.15/0.43 ( ifp
% 0.15/0.43 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ A )
% 0.15/0.43 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(theeq_type,type,
% 0.15/0.43 theeq: $o ).
% 0.15/0.43
% 0.15/0.43 thf(theeq,definition,
% 0.15/0.43 ( theeq
% 0.15/0.43 = ( ! [X: $i] :
% 0.15/0.43 ( ( singleton @ X )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ X )
% 0.15/0.43 => ( ( setunion @ X )
% 0.15/0.43 = Xx ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(iftrue_type,type,
% 0.15/0.43 iftrue: $o ).
% 0.15/0.43
% 0.15/0.43 thf(iftrue,definition,
% 0.15/0.43 ( iftrue
% 0.15/0.43 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ A )
% 0.15/0.43 => ( Xphi
% 0.15/0.43 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.15/0.43 = Xx ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(iffalse_type,type,
% 0.15/0.43 iffalse: $o ).
% 0.15/0.43
% 0.15/0.43 thf(iffalse,definition,
% 0.15/0.43 ( iffalse
% 0.15/0.43 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ A )
% 0.15/0.43 => ( ~ Xphi
% 0.15/0.43 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.15/0.43 = Xy ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(iftrueorfalse_type,type,
% 0.15/0.43 iftrueorfalse: $o ).
% 0.15/0.43
% 0.15/0.43 thf(iftrueorfalse,definition,
% 0.15/0.43 ( iftrueorfalse
% 0.15/0.43 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ A )
% 0.15/0.43 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(binintersectT_lem_type,type,
% 0.15/0.43 binintersectT_lem: $o ).
% 0.15/0.43
% 0.15/0.43 thf(binintersectT_lem,definition,
% 0.15/0.43 ( binintersectT_lem
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(binunionT_lem_type,type,
% 0.15/0.43 binunionT_lem: $o ).
% 0.15/0.43
% 0.15/0.43 thf(binunionT_lem,definition,
% 0.15/0.43 ( binunionT_lem
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(powersetT_lem_type,type,
% 0.15/0.43 powersetT_lem: $o ).
% 0.15/0.43
% 0.15/0.43 thf(powersetT_lem,definition,
% 0.15/0.43 ( powersetT_lem
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setminusT_lem_type,type,
% 0.15/0.43 setminusT_lem: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setminusT_lem,definition,
% 0.15/0.43 ( setminusT_lem
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(complementT_lem_type,type,
% 0.15/0.43 complementT_lem: $o ).
% 0.15/0.43
% 0.15/0.43 thf(complementT_lem,definition,
% 0.15/0.43 ( complementT_lem
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setextT_type,type,
% 0.15/0.43 setextT: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setextT,definition,
% 0.15/0.43 ( setextT
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx @ X )
% 0.15/0.43 => ( in @ Xx @ Y ) ) )
% 0.15/0.43 => ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx @ Y )
% 0.15/0.43 => ( in @ Xx @ X ) ) )
% 0.15/0.43 => ( X = Y ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(subsetTI_type,type,
% 0.15/0.43 subsetTI: $o ).
% 0.15/0.43
% 0.15/0.43 thf(subsetTI,definition,
% 0.15/0.43 ( subsetTI
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx @ X )
% 0.15/0.43 => ( in @ Xx @ Y ) ) )
% 0.15/0.43 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(powersetTI1_type,type,
% 0.15/0.43 powersetTI1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(powersetTI1,definition,
% 0.15/0.43 ( powersetTI1
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx @ X )
% 0.15/0.43 => ( in @ Xx @ Y ) ) )
% 0.15/0.43 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(powersetTE1_type,type,
% 0.15/0.43 powersetTE1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(powersetTE1,definition,
% 0.15/0.43 ( powersetTE1
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ X @ ( powerset @ Y ) )
% 0.15/0.43 => ( ( in @ Xx @ X )
% 0.15/0.43 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(complementTI1_type,type,
% 0.15/0.43 complementTI1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(complementTI1,definition,
% 0.15/0.43 ( complementTI1
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx @ X )
% 0.15/0.43 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(complementTE1_type,type,
% 0.15/0.43 complementTE1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(complementTE1,definition,
% 0.15/0.43 ( complementTE1
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 0.15/0.43 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(binintersectTELcontra_type,type,
% 0.15/0.43 binintersectTELcontra: $o ).
% 0.15/0.43
% 0.15/0.43 thf(binintersectTELcontra,definition,
% 0.15/0.43 ( binintersectTELcontra
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ~ ( in @ Xx @ X )
% 0.15/0.43 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(binintersectTERcontra_type,type,
% 0.15/0.43 binintersectTERcontra: $o ).
% 0.15/0.43
% 0.15/0.43 thf(binintersectTERcontra,definition,
% 0.15/0.43 ( binintersectTERcontra
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ~ ( in @ Xx @ Y )
% 0.15/0.43 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(contrasubsetT_type,type,
% 0.15/0.43 contrasubsetT: $o ).
% 0.15/0.43
% 0.15/0.43 thf(contrasubsetT,definition,
% 0.15/0.43 ( contrasubsetT
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.15/0.43 => ( ( in @ Xx @ Y )
% 0.15/0.43 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(contrasubsetT1_type,type,
% 0.15/0.43 contrasubsetT1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(contrasubsetT1,definition,
% 0.15/0.43 ( contrasubsetT1
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( subset @ X @ Y )
% 0.15/0.43 => ( ~ ( in @ Xx @ Y )
% 0.15/0.43 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(contrasubsetT2_type,type,
% 0.15/0.43 contrasubsetT2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(contrasubsetT2,definition,
% 0.15/0.43 ( contrasubsetT2
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ( ( subset @ X @ Y )
% 0.15/0.43 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(contrasubsetT3_type,type,
% 0.15/0.43 contrasubsetT3: $o ).
% 0.15/0.43
% 0.15/0.43 thf(contrasubsetT3,definition,
% 0.15/0.43 ( contrasubsetT3
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 0.15/0.43 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(doubleComplementI1_type,type,
% 0.15/0.43 doubleComplementI1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(doubleComplementI1,definition,
% 0.15/0.43 ( doubleComplementI1
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx @ X )
% 0.15/0.43 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(doubleComplementE1_type,type,
% 0.15/0.43 doubleComplementE1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(doubleComplementE1,definition,
% 0.15/0.43 ( doubleComplementE1
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 0.15/0.43 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(doubleComplementSub1_type,type,
% 0.15/0.43 doubleComplementSub1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(doubleComplementSub1,definition,
% 0.15/0.43 ( doubleComplementSub1
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(doubleComplementSub2_type,type,
% 0.15/0.43 doubleComplementSub2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(doubleComplementSub2,definition,
% 0.15/0.43 ( doubleComplementSub2
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(doubleComplementEq_type,type,
% 0.15/0.43 doubleComplementEq: $o ).
% 0.15/0.43
% 0.15/0.43 thf(doubleComplementEq,definition,
% 0.15/0.43 ( doubleComplementEq
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ( X
% 0.15/0.43 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(complementTnotintersectT_type,type,
% 0.15/0.43 complementTnotintersectT: $o ).
% 0.15/0.43
% 0.15/0.43 thf(complementTnotintersectT,definition,
% 0.15/0.43 ( complementTnotintersectT
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.15/0.43 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(complementImpComplementIntersect_type,type,
% 0.15/0.43 complementImpComplementIntersect: $o ).
% 0.15/0.43
% 0.15/0.43 thf(complementImpComplementIntersect,definition,
% 0.15/0.43 ( complementImpComplementIntersect
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.15/0.43 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(complementSubsetComplementIntersect_type,type,
% 0.15/0.43 complementSubsetComplementIntersect: $o ).
% 0.15/0.43
% 0.15/0.43 thf(complementSubsetComplementIntersect,definition,
% 0.15/0.43 ( complementSubsetComplementIntersect
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(complementInPowersetComplementIntersect_type,type,
% 0.15/0.43 complementInPowersetComplementIntersect: $o ).
% 0.15/0.43
% 0.15/0.43 thf(complementInPowersetComplementIntersect,definition,
% 0.15/0.43 ( complementInPowersetComplementIntersect
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(contraSubsetComplement_type,type,
% 0.15/0.43 contraSubsetComplement: $o ).
% 0.15/0.43
% 0.15/0.43 thf(contraSubsetComplement,definition,
% 0.15/0.43 ( contraSubsetComplement
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx @ Y )
% 0.15/0.43 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(complementTcontraSubset_type,type,
% 0.15/0.43 complementTcontraSubset: $o ).
% 0.15/0.43
% 0.15/0.43 thf(complementTcontraSubset,definition,
% 0.15/0.43 ( complementTcontraSubset
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.15/0.43 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(binunionTILcontra_type,type,
% 0.15/0.43 binunionTILcontra: $o ).
% 0.15/0.43
% 0.15/0.43 thf(binunionTILcontra,definition,
% 0.15/0.43 ( binunionTILcontra
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.15/0.43 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(binunionTIRcontra_type,type,
% 0.15/0.43 binunionTIRcontra: $o ).
% 0.15/0.43
% 0.15/0.43 thf(binunionTIRcontra,definition,
% 0.15/0.43 ( binunionTIRcontra
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.15/0.43 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(inIntersectImpInUnion_type,type,
% 0.15/0.43 inIntersectImpInUnion: $o ).
% 0.15/0.43
% 0.15/0.43 thf(inIntersectImpInUnion,definition,
% 0.15/0.43 ( inIntersectImpInUnion
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Z: $i] :
% 0.15/0.43 ( ( in @ Z @ ( powerset @ A ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.15/0.43 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(inIntersectImpInUnion2_type,type,
% 0.15/0.43 inIntersectImpInUnion2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(inIntersectImpInUnion2,definition,
% 0.15/0.43 ( inIntersectImpInUnion2
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Z: $i] :
% 0.15/0.43 ( ( in @ Z @ ( powerset @ A ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.15/0.43 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(inIntersectImpInIntersectUnions_type,type,
% 0.15/0.43 inIntersectImpInIntersectUnions: $o ).
% 0.15/0.43
% 0.15/0.43 thf(inIntersectImpInIntersectUnions,definition,
% 0.15/0.43 ( inIntersectImpInIntersectUnions
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Z: $i] :
% 0.15/0.43 ( ( in @ Z @ ( powerset @ A ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.15/0.43 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(intersectInPowersetIntersectUnions_type,type,
% 0.15/0.43 intersectInPowersetIntersectUnions: $o ).
% 0.15/0.43
% 0.15/0.43 thf(intersectInPowersetIntersectUnions,definition,
% 0.15/0.43 ( intersectInPowersetIntersectUnions
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Z: $i] :
% 0.15/0.43 ( ( in @ Z @ ( powerset @ A ) )
% 0.15/0.43 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(inComplementUnionImpNotIn1_type,type,
% 0.15/0.43 inComplementUnionImpNotIn1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(inComplementUnionImpNotIn1,definition,
% 0.15/0.43 ( inComplementUnionImpNotIn1
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.15/0.43 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(inComplementUnionImpInComplement1_type,type,
% 0.15/0.43 inComplementUnionImpInComplement1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(inComplementUnionImpInComplement1,definition,
% 0.15/0.43 ( inComplementUnionImpInComplement1
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.15/0.43 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(binunionTE_type,type,
% 0.15/0.43 binunionTE: $o ).
% 0.15/0.43
% 0.15/0.43 thf(binunionTE,definition,
% 0.15/0.43 ( binunionTE
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Xphi: $o,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.15/0.43 => ( ( ( in @ Xx @ X )
% 0.15/0.43 => Xphi )
% 0.15/0.43 => ( ( ( in @ Xx @ Y )
% 0.15/0.43 => Xphi )
% 0.15/0.43 => Xphi ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(binunionTEcontra_type,type,
% 0.15/0.43 binunionTEcontra: $o ).
% 0.15/0.43
% 0.15/0.43 thf(binunionTEcontra,definition,
% 0.15/0.43 ( binunionTEcontra
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ~ ( in @ Xx @ X )
% 0.15/0.43 => ( ~ ( in @ Xx @ Y )
% 0.15/0.43 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(demorgan2a1_type,type,
% 0.15/0.43 demorgan2a1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(demorgan2a1,definition,
% 0.15/0.43 ( demorgan2a1
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.15/0.43 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(complementUnionInPowersetComplement_type,type,
% 0.15/0.43 complementUnionInPowersetComplement: $o ).
% 0.15/0.43
% 0.15/0.43 thf(complementUnionInPowersetComplement,definition,
% 0.15/0.43 ( complementUnionInPowersetComplement
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(demorgan2a2_type,type,
% 0.15/0.43 demorgan2a2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(demorgan2a2,definition,
% 0.15/0.43 ( demorgan2a2
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.15/0.43 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(demorgan1a_type,type,
% 0.15/0.43 demorgan1a: $o ).
% 0.15/0.43
% 0.15/0.43 thf(demorgan1a,definition,
% 0.15/0.43 ( demorgan1a
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 0.15/0.43 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(demorgan1b_type,type,
% 0.15/0.43 demorgan1b: $o ).
% 0.15/0.43
% 0.15/0.43 thf(demorgan1b,definition,
% 0.15/0.43 ( demorgan1b
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.15/0.43 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(demorgan1_type,type,
% 0.15/0.43 demorgan1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(demorgan1,definition,
% 0.15/0.43 ( demorgan1
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 0.15/0.43 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(demorgan2a_type,type,
% 0.15/0.43 demorgan2a: $o ).
% 0.15/0.43
% 0.15/0.43 thf(demorgan2a,definition,
% 0.15/0.43 ( demorgan2a
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.15/0.43 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(demorgan2b2_type,type,
% 0.15/0.43 demorgan2b2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(demorgan2b2,definition,
% 0.15/0.43 ( demorgan2b2
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.15/0.43 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 0.15/0.43 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(demorgan2b_type,type,
% 0.15/0.43 demorgan2b: $o ).
% 0.15/0.43
% 0.15/0.43 thf(demorgan2b,definition,
% 0.15/0.43 ( demorgan2b
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.15/0.43 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(demorgan2_type,type,
% 0.15/0.43 demorgan2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(demorgan2,definition,
% 0.15/0.43 ( demorgan2
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 0.15/0.43 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(woz13rule0_type,type,
% 0.15/0.43 woz13rule0: $o ).
% 0.15/0.43
% 0.15/0.43 thf(woz13rule0,definition,
% 0.15/0.43 ( woz13rule0
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.15/0.43 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(woz13rule1_type,type,
% 0.15/0.43 woz13rule1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(woz13rule1,definition,
% 0.15/0.43 ( woz13rule1
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Z: $i] :
% 0.15/0.43 ( ( in @ Z @ ( powerset @ A ) )
% 0.15/0.43 => ( ( subset @ X @ Z )
% 0.15/0.43 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(woz13rule2_type,type,
% 0.15/0.43 woz13rule2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(woz13rule2,definition,
% 0.15/0.43 ( woz13rule2
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Z: $i] :
% 0.15/0.43 ( ( in @ Z @ ( powerset @ A ) )
% 0.15/0.43 => ( ( subset @ Y @ Z )
% 0.15/0.43 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(woz13rule3_type,type,
% 0.15/0.43 woz13rule3: $o ).
% 0.15/0.43
% 0.15/0.43 thf(woz13rule3,definition,
% 0.15/0.43 ( woz13rule3
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Z: $i] :
% 0.15/0.43 ( ( in @ Z @ ( powerset @ A ) )
% 0.15/0.43 => ( ( subset @ X @ Y )
% 0.15/0.43 => ( ( subset @ X @ Z )
% 0.15/0.43 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(woz13rule4_type,type,
% 0.15/0.43 woz13rule4: $o ).
% 0.15/0.43
% 0.15/0.43 thf(woz13rule4,definition,
% 0.15/0.43 ( woz13rule4
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Z: $i] :
% 0.15/0.43 ( ( in @ Z @ ( powerset @ A ) )
% 0.15/0.43 => ! [W: $i] :
% 0.15/0.43 ( ( in @ W @ ( powerset @ A ) )
% 0.15/0.43 => ( ( subset @ X @ Z )
% 0.15/0.43 => ( ( subset @ Y @ W )
% 0.15/0.43 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(woz1_1_type,type,
% 0.15/0.43 woz1_1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(woz1_1,definition,
% 0.15/0.43 ( woz1_1
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(woz1_2_type,type,
% 0.15/0.43 woz1_2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(woz1_2,definition,
% 0.15/0.43 ( woz1_2
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Z: $i] :
% 0.15/0.43 ( ( in @ Z @ ( powerset @ A ) )
% 0.15/0.43 => ! [W: $i] :
% 0.15/0.43 ( ( in @ W @ ( powerset @ A ) )
% 0.15/0.43 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 0.15/0.43 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(woz1_3_type,type,
% 0.15/0.43 woz1_3: $o ).
% 0.15/0.43
% 0.15/0.43 thf(woz1_3,definition,
% 0.15/0.43 ( woz1_3
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ! [Z: $i] :
% 0.15/0.43 ( ( in @ Z @ ( powerset @ A ) )
% 0.15/0.43 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(woz1_4_type,type,
% 0.15/0.43 woz1_4: $o ).
% 0.15/0.43
% 0.15/0.43 thf(woz1_4,definition,
% 0.15/0.43 ( woz1_4
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.15/0.43 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(woz1_5_type,type,
% 0.15/0.43 woz1_5: $o ).
% 0.15/0.43
% 0.15/0.43 thf(woz1_5,definition,
% 0.15/0.43 ( woz1_5
% 0.15/0.43 = ( ! [A: $i,X: $i] :
% 0.15/0.43 ( ( in @ X @ ( powerset @ A ) )
% 0.15/0.43 => ! [Y: $i] :
% 0.15/0.43 ( ( in @ Y @ ( powerset @ A ) )
% 0.15/0.43 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(breln1_type,type,
% 0.15/0.43 breln1: $i > $i > $o ).
% 0.15/0.43
% 0.15/0.43 thf(breln1,definition,
% 0.15/0.43 ( breln1
% 0.15/0.43 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(breln1all2_type,type,
% 0.15/0.43 breln1all2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(breln1all2,definition,
% 0.15/0.43 ( breln1all2
% 0.15/0.43 = ( ! [A: $i,R: $i] :
% 0.15/0.43 ( ( breln1 @ A @ R )
% 0.15/0.43 => ! [Xphi: $i > $o] :
% 0.15/0.43 ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ A )
% 0.15/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.15/0.43 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ R )
% 0.15/0.43 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(breln1Set_type,type,
% 0.15/0.43 breln1Set: $i > $i ).
% 0.15/0.43
% 0.15/0.43 thf(breln1SetBreln1_type,type,
% 0.15/0.43 breln1SetBreln1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(breln1SetBreln1,definition,
% 0.15/0.43 ( breln1SetBreln1
% 0.15/0.43 = ( ! [A: $i,R: $i] :
% 0.15/0.43 ( ( in @ R @ ( breln1Set @ A ) )
% 0.15/0.43 => ( breln1 @ A @ R ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(transitive_type,type,
% 0.15/0.43 transitive: $i > $i > $o ).
% 0.15/0.43
% 0.15/0.43 thf(antisymmetric_type,type,
% 0.15/0.43 antisymmetric: $i > $i > $o ).
% 0.15/0.43
% 0.15/0.43 thf(reflexive_type,type,
% 0.15/0.43 reflexive: $i > $i > $o ).
% 0.15/0.43
% 0.15/0.43 thf(refltransitive_type,type,
% 0.15/0.43 refltransitive: $i > $i > $o ).
% 0.15/0.43
% 0.15/0.43 thf(refllinearorder_type,type,
% 0.15/0.43 refllinearorder: $i > $i > $o ).
% 0.15/0.43
% 0.15/0.43 thf(reflwellordering_type,type,
% 0.15/0.43 reflwellordering: $i > $i > $o ).
% 0.15/0.43
% 0.15/0.43 thf(choice2fnsingleton_type,type,
% 0.15/0.43 choice2fnsingleton: $o ).
% 0.15/0.43
% 0.15/0.43 thf(choice2fnsingleton,definition,
% 0.15/0.43 ( choice2fnsingleton
% 0.15/0.43 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.15/0.43 ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ? [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ B )
% 0.15/0.43 & ( Xphi @ Xx @ Xy ) ) )
% 0.15/0.43 => ! [R: $i] :
% 0.15/0.43 ( ( in @ R @ ( breln1Set @ B ) )
% 0.15/0.43 => ( ( reflwellordering @ B @ R )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( singleton
% 0.15/0.43 @ ( dsetconstr @ B
% 0.15/0.43 @ ^ [Xy: $i] :
% 0.15/0.43 ( ( Xphi @ Xx @ Xy )
% 0.15/0.43 & ! [Xz: $i] :
% 0.15/0.43 ( ( in @ Xz @ B )
% 0.15/0.43 => ( ( Xphi @ Xx @ Xz )
% 0.15/0.43 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setOfPairsIsBReln1_type,type,
% 0.15/0.43 setOfPairsIsBReln1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setOfPairsIsBReln1,definition,
% 0.15/0.43 ( setOfPairsIsBReln1
% 0.15/0.43 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 0.15/0.43 ( breln1 @ A
% 0.15/0.43 @ ( dpsetconstr @ A @ A
% 0.15/0.43 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(breln1all1_type,type,
% 0.15/0.43 breln1all1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(breln1all1,definition,
% 0.15/0.43 ( breln1all1
% 0.15/0.43 = ( ! [A: $i,R: $i] :
% 0.15/0.43 ( ( breln1 @ A @ R )
% 0.15/0.43 => ! [Xphi: $i > $o] :
% 0.15/0.43 ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ A )
% 0.15/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.15/0.43 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ R )
% 0.15/0.43 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(subbreln1_type,type,
% 0.15/0.43 subbreln1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(subbreln1,definition,
% 0.15/0.43 ( subbreln1
% 0.15/0.43 = ( ! [A: $i,R: $i] :
% 0.15/0.43 ( ( breln1 @ A @ R )
% 0.15/0.43 => ! [S: $i] :
% 0.15/0.43 ( ( breln1 @ A @ S )
% 0.15/0.43 => ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ A )
% 0.15/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.15/0.43 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.15/0.43 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(eqbreln1_type,type,
% 0.15/0.43 eqbreln1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(eqbreln1,definition,
% 0.15/0.43 ( eqbreln1
% 0.15/0.43 = ( ! [A: $i,R: $i] :
% 0.15/0.43 ( ( breln1 @ A @ R )
% 0.15/0.43 => ! [S: $i] :
% 0.15/0.43 ( ( breln1 @ A @ S )
% 0.15/0.43 => ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ A )
% 0.15/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.15/0.43 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.15/0.43 => ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ A )
% 0.15/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.15/0.43 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.15/0.43 => ( R = S ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(breln1invset_type,type,
% 0.15/0.43 breln1invset: $i > $i > $i ).
% 0.15/0.43
% 0.15/0.43 thf(breln1invset,definition,
% 0.15/0.43 ( breln1invset
% 0.15/0.43 = ( ^ [A: $i,R: $i] :
% 0.15/0.43 ( dpsetconstr @ A @ A
% 0.15/0.43 @ ^ [Xx: $i,Xy: $i] : ( in @ ( kpair @ Xy @ Xx ) @ R ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(breln1invprop_type,type,
% 0.15/0.43 breln1invprop: $o ).
% 0.15/0.43
% 0.15/0.43 thf(breln1invprop,definition,
% 0.15/0.43 ( breln1invprop
% 0.15/0.43 = ( ! [A: $i,R: $i] :
% 0.15/0.43 ( ( breln1 @ A @ R )
% 0.15/0.43 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(breln1invI_type,type,
% 0.15/0.43 breln1invI: $o ).
% 0.15/0.43
% 0.15/0.43 thf(breln1invI,definition,
% 0.15/0.43 ( breln1invI
% 0.15/0.43 = ( ! [A: $i,R: $i] :
% 0.15/0.43 ( ( breln1 @ A @ R )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ A )
% 0.15/0.43 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.15/0.43 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(breln1invE,conjecture,
% 0.15/0.43 ( setextAx
% 0.15/0.43 => ( emptysetAx
% 0.15/0.43 => ( setadjoinAx
% 0.15/0.43 => ( powersetAx
% 0.15/0.43 => ( setunionAx
% 0.15/0.43 => ( omega0Ax
% 0.15/0.43 => ( omegaSAx
% 0.15/0.43 => ( omegaIndAx
% 0.15/0.43 => ( replAx
% 0.15/0.43 => ( foundationAx
% 0.15/0.43 => ( wellorderingAx
% 0.15/0.43 => ( descrp
% 0.15/0.43 => ( dsetconstrI
% 0.15/0.43 => ( dsetconstrEL
% 0.15/0.43 => ( dsetconstrER
% 0.15/0.43 => ( exuE1
% 0.15/0.43 => ( prop2setE
% 0.15/0.43 => ( emptysetE
% 0.15/0.43 => ( emptysetimpfalse
% 0.15/0.43 => ( notinemptyset
% 0.15/0.43 => ( exuE3e
% 0.15/0.43 => ( setext
% 0.15/0.43 => ( emptyI
% 0.15/0.43 => ( noeltsimpempty
% 0.15/0.43 => ( setbeta
% 0.15/0.43 => ( nonemptyE1
% 0.15/0.43 => ( nonemptyI
% 0.15/0.43 => ( nonemptyI1
% 0.15/0.43 => ( setadjoinIL
% 0.15/0.43 => ( emptyinunitempty
% 0.15/0.43 => ( setadjoinIR
% 0.15/0.43 => ( setadjoinE
% 0.15/0.43 => ( setadjoinOr
% 0.15/0.43 => ( setoftrueEq
% 0.15/0.43 => ( powersetI
% 0.15/0.43 => ( emptyinPowerset
% 0.15/0.43 => ( emptyInPowerset
% 0.15/0.43 => ( powersetE
% 0.15/0.43 => ( setunionI
% 0.15/0.43 => ( setunionE
% 0.15/0.43 => ( subPowSU
% 0.15/0.43 => ( exuE2
% 0.15/0.43 => ( nonemptyImpWitness
% 0.15/0.43 => ( uniqinunit
% 0.15/0.43 => ( notinsingleton
% 0.15/0.43 => ( eqinunit
% 0.15/0.43 => ( singletonsswitch
% 0.15/0.43 => ( upairsetE
% 0.15/0.43 => ( upairsetIL
% 0.15/0.43 => ( upairsetIR
% 0.15/0.43 => ( emptyE1
% 0.15/0.43 => ( vacuousDall
% 0.15/0.43 => ( quantDeMorgan1
% 0.15/0.43 => ( quantDeMorgan2
% 0.15/0.43 => ( quantDeMorgan3
% 0.15/0.43 => ( quantDeMorgan4
% 0.15/0.43 => ( prop2setI
% 0.15/0.43 => ( prop2set2propI
% 0.15/0.43 => ( notdexE
% 0.15/0.43 => ( notdallE
% 0.15/0.43 => ( exuI1
% 0.15/0.43 => ( exuI3
% 0.15/0.43 => ( exuI2
% 0.15/0.43 => ( inCongP
% 0.15/0.43 => ( in__Cong
% 0.15/0.43 => ( exuE3u
% 0.15/0.43 => ( exu__Cong
% 0.15/0.43 => ( emptyset__Cong
% 0.15/0.43 => ( setadjoin__Cong
% 0.15/0.43 => ( powerset__Cong
% 0.15/0.43 => ( setunion__Cong
% 0.15/0.43 => ( omega__Cong
% 0.15/0.43 => ( exuEu
% 0.15/0.43 => ( descr__Cong
% 0.15/0.43 => ( dsetconstr__Cong
% 0.15/0.43 => ( subsetI1
% 0.15/0.43 => ( eqimpsubset2
% 0.15/0.43 => ( eqimpsubset1
% 0.15/0.43 => ( subsetI2
% 0.15/0.43 => ( emptysetsubset
% 0.15/0.43 => ( subsetE
% 0.15/0.43 => ( subsetE2
% 0.15/0.43 => ( notsubsetI
% 0.15/0.43 => ( notequalI1
% 0.15/0.43 => ( notequalI2
% 0.15/0.43 => ( subsetRefl
% 0.15/0.43 => ( subsetTrans
% 0.15/0.43 => ( setadjoinSub
% 0.15/0.43 => ( setadjoinSub2
% 0.15/0.43 => ( subset2powerset
% 0.15/0.43 => ( setextsub
% 0.15/0.43 => ( subsetemptysetimpeq
% 0.15/0.43 => ( powersetI1
% 0.15/0.43 => ( powersetE1
% 0.15/0.43 => ( inPowerset
% 0.15/0.43 => ( powersetsubset
% 0.15/0.43 => ( sepInPowerset
% 0.15/0.43 => ( sepSubset
% 0.15/0.43 => ( binunionIL
% 0.15/0.43 => ( upairset2IR
% 0.15/0.43 => ( binunionIR
% 0.15/0.43 => ( binunionEcases
% 0.15/0.43 => ( binunionE
% 0.15/0.43 => ( binunionLsub
% 0.15/0.43 => ( binunionRsub
% 0.15/0.43 => ( binintersectI
% 0.15/0.43 => ( binintersectSubset5
% 0.15/0.43 => ( binintersectEL
% 0.15/0.43 => ( binintersectLsub
% 0.15/0.43 => ( binintersectSubset2
% 0.15/0.43 => ( binintersectSubset3
% 0.15/0.43 => ( binintersectER
% 0.15/0.43 => ( disjointsetsI1
% 0.15/0.43 => ( binintersectRsub
% 0.15/0.43 => ( binintersectSubset4
% 0.15/0.43 => ( binintersectSubset1
% 0.15/0.43 => ( bs114d
% 0.15/0.43 => ( setminusI
% 0.15/0.43 => ( setminusEL
% 0.15/0.43 => ( setminusER
% 0.15/0.43 => ( setminusSubset2
% 0.15/0.43 => ( setminusERneg
% 0.15/0.43 => ( setminusELneg
% 0.15/0.43 => ( setminusILneg
% 0.15/0.43 => ( setminusIRneg
% 0.15/0.43 => ( setminusLsub
% 0.15/0.43 => ( setminusSubset1
% 0.15/0.43 => ( symdiffE
% 0.15/0.43 => ( symdiffI1
% 0.15/0.43 => ( symdiffI2
% 0.15/0.43 => ( symdiffIneg1
% 0.15/0.43 => ( symdiffIneg2
% 0.15/0.43 => ( secondinupair
% 0.15/0.43 => ( setukpairIL
% 0.15/0.43 => ( setukpairIR
% 0.15/0.43 => ( kpairiskpair
% 0.15/0.43 => ( kpairp
% 0.15/0.43 => ( singletonsubset
% 0.15/0.43 => ( singletoninpowerset
% 0.15/0.43 => ( singletoninpowunion
% 0.15/0.43 => ( upairset2E
% 0.15/0.43 => ( upairsubunion
% 0.15/0.43 => ( upairinpowunion
% 0.15/0.43 => ( ubforcartprodlem1
% 0.15/0.43 => ( ubforcartprodlem2
% 0.15/0.43 => ( ubforcartprodlem3
% 0.15/0.43 => ( cartprodpairin
% 0.15/0.43 => ( cartprodmempair1
% 0.15/0.43 => ( cartprodmempair
% 0.15/0.43 => ( setunionE2
% 0.15/0.43 => ( setunionsingleton1
% 0.15/0.43 => ( setunionsingleton2
% 0.15/0.43 => ( setunionsingleton
% 0.15/0.43 => ( singletonprop
% 0.15/0.43 => ( ex1E1
% 0.15/0.43 => ( ex1I
% 0.15/0.43 => ( ex1I2
% 0.15/0.43 => ( singletonsuniq
% 0.15/0.43 => ( setukpairinjL1
% 0.15/0.43 => ( kfstsingleton
% 0.15/0.43 => ( theprop
% 0.15/0.43 => ( kfstpairEq
% 0.15/0.43 => ( cartprodfstin
% 0.15/0.43 => ( setukpairinjL2
% 0.15/0.43 => ( setukpairinjL
% 0.15/0.43 => ( setukpairinjR11
% 0.15/0.43 => ( setukpairinjR12
% 0.15/0.43 => ( setukpairinjR1
% 0.15/0.43 => ( upairequniteq
% 0.15/0.43 => ( setukpairinjR2
% 0.15/0.43 => ( setukpairinjR
% 0.15/0.43 => ( ksndsingleton
% 0.15/0.43 => ( ksndpairEq
% 0.15/0.43 => ( kpairsurjEq
% 0.15/0.43 => ( cartprodsndin
% 0.15/0.43 => ( cartprodpairmemEL
% 0.15/0.43 => ( cartprodpairmemER
% 0.15/0.43 => ( cartprodmempaircEq
% 0.15/0.43 => ( cartprodfstpairEq
% 0.15/0.43 => ( cartprodsndpairEq
% 0.15/0.43 => ( cartprodpairsurjEq
% 0.15/0.43 => ( dpsetconstrI
% 0.15/0.43 => ( dpsetconstrSub
% 0.15/0.43 => ( setOfPairsIsBReln
% 0.15/0.43 => ( dpsetconstrERa
% 0.15/0.43 => ( dpsetconstrEL1
% 0.15/0.43 => ( dpsetconstrEL2
% 0.15/0.43 => ( dpsetconstrER
% 0.15/0.43 => ( funcImageSingleton
% 0.15/0.43 => ( apProp
% 0.15/0.43 => ( app
% 0.15/0.43 => ( infuncsetfunc
% 0.15/0.43 => ( ap2p
% 0.15/0.43 => ( funcinfuncset
% 0.15/0.43 => ( lamProp
% 0.15/0.43 => ( lamp
% 0.15/0.43 => ( lam2p
% 0.15/0.43 => ( brelnall1
% 0.15/0.43 => ( brelnall2
% 0.15/0.43 => ( ex1E2
% 0.15/0.43 => ( funcGraphProp1
% 0.15/0.43 => ( funcGraphProp3
% 0.15/0.43 => ( funcGraphProp2
% 0.15/0.43 => ( funcextLem
% 0.15/0.43 => ( funcGraphProp4
% 0.15/0.43 => ( subbreln
% 0.15/0.43 => ( eqbreln
% 0.15/0.43 => ( funcext
% 0.15/0.43 => ( funcext2
% 0.15/0.43 => ( ap2apEq1
% 0.15/0.43 => ( ap2apEq2
% 0.15/0.43 => ( beta1
% 0.15/0.43 => ( eta1
% 0.15/0.43 => ( lam2lamEq
% 0.15/0.43 => ( beta2
% 0.15/0.43 => ( eta2
% 0.15/0.43 => ( iffalseProp1
% 0.15/0.43 => ( iffalseProp2
% 0.15/0.43 => ( iftrueProp1
% 0.15/0.43 => ( iftrueProp2
% 0.15/0.43 => ( ifSingleton
% 0.15/0.43 => ( ifp
% 0.15/0.43 => ( theeq
% 0.15/0.43 => ( iftrue
% 0.15/0.43 => ( iffalse
% 0.15/0.43 => ( iftrueorfalse
% 0.15/0.43 => ( binintersectT_lem
% 0.15/0.43 => ( binunionT_lem
% 0.15/0.43 => ( powersetT_lem
% 0.15/0.43 => ( setminusT_lem
% 0.15/0.43 => ( complementT_lem
% 0.15/0.43 => ( setextT
% 0.15/0.43 => ( subsetTI
% 0.15/0.43 => ( powersetTI1
% 0.15/0.43 => ( powersetTE1
% 0.15/0.43 => ( complementTI1
% 0.15/0.43 => ( complementTE1
% 0.15/0.43 => ( binintersectTELcontra
% 0.15/0.43 => ( binintersectTERcontra
% 0.15/0.43 => ( contrasubsetT
% 0.15/0.43 => ( contrasubsetT1
% 0.15/0.43 => ( contrasubsetT2
% 0.15/0.43 => ( contrasubsetT3
% 0.15/0.43 => ( doubleComplementI1
% 0.15/0.43 => ( doubleComplementE1
% 0.15/0.43 => ( doubleComplementSub1
% 0.15/0.43 => ( doubleComplementSub2
% 0.15/0.43 => ( doubleComplementEq
% 0.15/0.43 => ( complementTnotintersectT
% 0.15/0.43 => ( complementImpComplementIntersect
% 0.15/0.43 => ( complementSubsetComplementIntersect
% 0.15/0.43 => ( complementInPowersetComplementIntersect
% 0.15/0.43 => ( contraSubsetComplement
% 0.15/0.43 => ( complementTcontraSubset
% 0.15/0.43 => ( binunionTILcontra
% 0.15/0.43 => ( binunionTIRcontra
% 0.15/0.43 => ( inIntersectImpInUnion
% 0.15/0.43 => ( inIntersectImpInUnion2
% 0.15/0.43 => ( inIntersectImpInIntersectUnions
% 0.15/0.43 => ( intersectInPowersetIntersectUnions
% 0.15/0.43 => ( inComplementUnionImpNotIn1
% 0.15/0.43 => ( inComplementUnionImpInComplement1
% 0.15/0.43 => ( binunionTE
% 0.15/0.43 => ( binunionTEcontra
% 0.15/0.43 => ( demorgan2a1
% 0.15/0.43 => ( complementUnionInPowersetComplement
% 0.15/0.43 => ( demorgan2a2
% 0.15/0.43 => ( demorgan1a
% 0.15/0.43 => ( demorgan1b
% 0.15/0.43 => ( demorgan1
% 0.15/0.43 => ( demorgan2a
% 0.15/0.43 => ( demorgan2b2
% 0.15/0.43 => ( demorgan2b
% 0.15/0.43 => ( demorgan2
% 0.15/0.43 => ( woz13rule0
% 0.15/0.43 => ( woz13rule1
% 0.15/0.43 => ( woz13rule2
% 0.15/0.43 => ( woz13rule3
% 0.15/0.43 => ( woz13rule4
% 0.15/0.43 => ( woz1_1
% 0.15/0.43 => ( woz1_2
% 0.15/0.43 => ( woz1_3
% 0.15/0.43 => ( woz1_4
% 0.15/0.43 => ( woz1_5
% 0.15/0.43 => ( breln1all2
% 0.15/0.43 => ( breln1SetBreln1
% 0.15/0.43 => ( choice2fnsingleton
% 0.15/0.43 => ( setOfPairsIsBReln1
% 0.15/0.43 => ( breln1all1
% 0.15/0.43 => ( subbreln1
% 0.15/0.43 => ( eqbreln1
% 0.15/0.43 => ( breln1invprop
% 0.15/0.43 => ( breln1invI
% 0.15/0.43 => ! [A: $i,R: $i] :
% 0.15/0.43 ( ( breln1 @ A @ R )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ A )
% 0.15/0.43 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 0.15/0.43 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 %------------------------------------------------------------------------------
% 0.15/0.43 ------------------------
% 2.95/1.57 ---- Embedded in THF ---
% 2.95/1.57 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.95/1.57 %%% Generated on Tue Feb 24 12:33:43 EST 2026
% 2.95/1.57 %%% using '$$dhol' embedding, version 1.3.0.
% 2.95/1.57 %%% Logic specification used:
% 2.95/1.57 %%% thf(spec, logic, $$dhol).
% 2.95/1.57
% 2.95/1.57 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.4RsbB0Qymi/DTF2DTF10978.p
% See solution above
% 2.95/1.57 ------------------------
% 3.08/1.60 ---- Cleaned THF ---
% 3.08/1.60 thf(in_type,type,
% 3.08/1.60 in: $i > $i > $o ).
% 3.08/1.60
% 3.08/1.60 thf(exu_type,type,
% 3.08/1.60 exu: ( $i > $o ) > $o ).
% 3.08/1.60
% 3.08/1.60 thf(exu,definition,
% 3.08/1.60 ( exu
% 3.08/1.60 = ( ^ [Xphi: $i > $o] :
% 3.08/1.60 ? [Xx: $i] :
% 3.08/1.60 ( ( Xphi @ Xx )
% 3.08/1.60 & ! [Xy: $i] :
% 3.08/1.60 ( ( Xphi @ Xy )
% 3.08/1.60 => ( Xx = Xy ) ) ) ) ) ).
% 3.08/1.60
% 3.08/1.60 thf(setextAx_type,type,
% 3.08/1.60 setextAx: $o ).
% 3.08/1.60
% 3.08/1.60 thf(setextAx,definition,
% 3.08/1.60 ( setextAx
% 3.08/1.60 = ( ! [A: $i,B: $i] :
% 3.08/1.60 ( ! [Xx: $i] :
% 3.08/1.60 ( ( in @ Xx @ A )
% 3.08/1.60 <=> ( in @ Xx @ B ) )
% 3.08/1.60 => ( A = B ) ) ) ) ).
% 3.08/1.60
% 3.08/1.60 thf(emptyset_type,type,
% 3.08/1.60 emptyset: $i ).
% 3.08/1.60
% 3.08/1.60 thf(emptysetAx_type,type,
% 3.08/1.60 emptysetAx: $o ).
% 3.08/1.60
% 3.08/1.60 thf(emptysetAx,definition,
% 3.08/1.60 ( emptysetAx
% 3.08/1.60 = ( ! [Xx: $i] :
% 3.08/1.60 ~ ( in @ Xx @ emptyset ) ) ) ).
% 3.08/1.60
% 3.08/1.60 thf(setadjoin_type,type,
% 3.08/1.60 setadjoin: $i > $i > $i ).
% 3.08/1.60
% 3.08/1.60 thf(setadjoinAx_type,type,
% 3.08/1.60 setadjoinAx: $o ).
% 3.08/1.60
% 3.08/1.60 thf(setadjoinAx,definition,
% 3.08/1.60 ( setadjoinAx
% 3.08/1.60 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.08/1.60 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.08/1.60 <=> ( ( Xy = Xx )
% 3.08/1.60 | ( in @ Xy @ A ) ) ) ) ) ).
% 3.08/1.60
% 3.08/1.60 thf(powerset_type,type,
% 3.08/1.60 powerset: $i > $i ).
% 3.08/1.60
% 3.08/1.60 thf(powersetAx_type,type,
% 3.08/1.60 powersetAx: $o ).
% 3.08/1.60
% 3.08/1.60 thf(powersetAx,definition,
% 3.08/1.60 ( powersetAx
% 3.08/1.60 = ( ! [A: $i,B: $i] :
% 3.08/1.60 ( ( in @ B @ ( powerset @ A ) )
% 3.08/1.60 <=> ! [Xx: $i] :
% 3.08/1.60 ( ( in @ Xx @ B )
% 3.08/1.60 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.08/1.60
% 3.08/1.60 thf(setunion_type,type,
% 3.08/1.60 setunion: $i > $i ).
% 3.08/1.60
% 3.08/1.60 thf(setunionAx_type,type,
% 3.08/1.60 setunionAx: $o ).
% 3.08/1.60
% 3.08/1.60 thf(setunionAx,definition,
% 3.08/1.60 ( setunionAx
% 3.08/1.60 = ( ! [A: $i,Xx: $i] :
% 3.08/1.60 ( ( in @ Xx @ ( setunion @ A ) )
% 3.08/1.60 <=> ? [B: $i] :
% 3.08/1.60 ( ( in @ Xx @ B )
% 3.08/1.60 & ( in @ B @ A ) ) ) ) ) ).
% 3.08/1.60
% 3.08/1.60 thf(omega_type,type,
% 3.08/1.60 omega: $i ).
% 3.08/1.60
% 3.08/1.60 thf(omega0Ax_type,type,
% 3.08/1.60 omega0Ax: $o ).
% 3.08/1.60
% 3.08/1.60 thf(omega0Ax,definition,
% 3.08/1.60 ( omega0Ax
% 3.08/1.60 = ( in @ emptyset @ omega ) ) ).
% 3.08/1.60
% 3.08/1.60 thf(omegaSAx_type,type,
% 3.08/1.60 omegaSAx: $o ).
% 3.08/1.60
% 3.08/1.60 thf(omegaSAx,definition,
% 3.08/1.60 ( omegaSAx
% 3.08/1.60 = ( ! [Xx: $i] :
% 3.08/1.60 ( ( in @ Xx @ omega )
% 3.08/1.60 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 3.08/1.60
% 3.08/1.60 thf(omegaIndAx_type,type,
% 3.08/1.60 omegaIndAx: $o ).
% 3.08/1.60
% 3.08/1.60 thf(omegaIndAx,definition,
% 3.08/1.60 ( omegaIndAx
% 3.08/1.60 = ( ! [A: $i] :
% 3.08/1.60 ( ( ( in @ emptyset @ A )
% 3.08/1.60 & ! [Xx: $i] :
% 3.08/1.60 ( ( ( in @ Xx @ omega )
% 3.08/1.60 & ( in @ Xx @ A ) )
% 3.08/1.60 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 3.08/1.60 => ! [Xx: $i] :
% 3.08/1.60 ( ( in @ Xx @ omega )
% 3.08/1.60 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.08/1.60
% 3.08/1.60 thf(replAx_type,type,
% 3.08/1.60 replAx: $o ).
% 3.08/1.60
% 3.08/1.60 thf(replAx,definition,
% 3.08/1.60 ( replAx
% 3.08/1.60 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 3.08/1.60 ( ! [Xx: $i] :
% 3.08/1.60 ( ( in @ Xx @ A )
% 3.08/1.60 => ( exu
% 3.08/1.60 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 3.08/1.60 => ? [B: $i] :
% 3.08/1.60 ! [Xx: $i] :
% 3.08/1.60 ( ( in @ Xx @ B )
% 3.08/1.60 <=> ? [Xy: $i] :
% 3.08/1.60 ( ( in @ Xy @ A )
% 3.08/1.60 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 3.08/1.60
% 3.08/1.60 thf(foundationAx_type,type,
% 3.08/1.60 foundationAx: $o ).
% 3.08/1.60
% 3.08/1.60 thf(foundationAx,definition,
% 3.08/1.60 ( foundationAx
% 3.08/1.60 = ( ! [A: $i] :
% 3.08/1.60 ( ? [Xx: $i] : ( in @ Xx @ A )
% 3.08/1.60 => ? [B: $i] :
% 3.08/1.60 ( ( in @ B @ A )
% 3.08/1.60 & ~ ? [Xx: $i] :
% 3.08/1.60 ( ( in @ Xx @ B )
% 3.08/1.60 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 3.08/1.60
% 3.08/1.60 thf(wellorderingAx_type,type,
% 3.08/1.60 wellorderingAx: $o ).
% 3.08/1.60
% 3.08/1.60 thf(wellorderingAx,definition,
% 3.08/1.60 ( wellorderingAx
% 3.08/1.60 = ( ! [A: $i] :
% 3.08/1.60 ? [B: $i] :
% 3.08/1.60 ( ! [C: $i] :
% 3.08/1.60 ( ( in @ C @ B )
% 3.08/1.60 => ! [Xx: $i] :
% 3.08/1.60 ( ( in @ Xx @ C )
% 3.08/1.60 => ( in @ Xx @ A ) ) )
% 3.08/1.60 & ! [Xx: $i,Xy: $i] :
% 3.08/1.60 ( ( ( in @ Xx @ A )
% 3.08/1.60 & ( in @ Xy @ A ) )
% 3.08/1.60 => ( ! [C: $i] :
% 3.08/1.60 ( ( in @ C @ B )
% 3.08/1.60 => ( ( in @ Xx @ C )
% 3.08/1.60 <=> ( in @ Xy @ C ) ) )
% 3.08/1.60 => ( Xx = Xy ) ) )
% 3.08/1.60 & ! [C: $i,D: $i] :
% 3.08/1.60 ( ( ( in @ C @ B )
% 3.08/1.60 & ( in @ D @ B ) )
% 3.08/1.60 => ( ! [Xx: $i] :
% 3.08/1.60 ( ( in @ Xx @ C )
% 3.08/1.60 => ( in @ Xx @ D ) )
% 3.08/1.60 | ! [Xx: $i] :
% 3.08/1.60 ( ( in @ Xx @ D )
% 3.08/1.61 => ( in @ Xx @ C ) ) ) )
% 3.08/1.61 & ! [C: $i] :
% 3.08/1.61 ( ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ C )
% 3.08/1.61 => ( in @ Xx @ A ) )
% 3.08/1.61 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 3.08/1.61 => ? [D: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ D @ B )
% 3.08/1.61 & ( in @ Xx @ C )
% 3.08/1.61 & ~ ? [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ D )
% 3.08/1.61 & ( in @ Xy @ C ) )
% 3.08/1.61 & ! [E: $i] :
% 3.08/1.61 ( ( in @ E @ B )
% 3.08/1.61 => ( ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ E )
% 3.08/1.61 => ( in @ Xy @ D ) )
% 3.08/1.61 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(descr_type,type,
% 3.08/1.61 descr: ( $i > $o ) > $i ).
% 3.08/1.61
% 3.08/1.61 thf(descrp_type,type,
% 3.08/1.61 descrp: $o ).
% 3.08/1.61
% 3.08/1.61 thf(descrp,definition,
% 3.08/1.61 ( descrp
% 3.08/1.61 = ( ! [Xphi: $i > $o] :
% 3.08/1.61 ( ( exu
% 3.08/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.61 => ( Xphi
% 3.08/1.61 @ ( descr
% 3.08/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(dsetconstr_type,type,
% 3.08/1.61 dsetconstr: $i > ( $i > $o ) > $i ).
% 3.08/1.61
% 3.08/1.61 thf(dsetconstrI_type,type,
% 3.08/1.61 dsetconstrI: $o ).
% 3.08/1.61
% 3.08/1.61 thf(dsetconstrI,definition,
% 3.08/1.61 ( dsetconstrI
% 3.08/1.61 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( Xphi @ Xx )
% 3.08/1.61 => ( in @ Xx
% 3.08/1.61 @ ( dsetconstr @ A
% 3.08/1.61 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(dsetconstrEL_type,type,
% 3.08/1.61 dsetconstrEL: $o ).
% 3.08/1.61
% 3.08/1.61 thf(dsetconstrEL,definition,
% 3.08/1.61 ( dsetconstrEL
% 3.08/1.61 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx
% 3.08/1.61 @ ( dsetconstr @ A
% 3.08/1.61 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.08/1.61 => ( in @ Xx @ A ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(dsetconstrER_type,type,
% 3.08/1.61 dsetconstrER: $o ).
% 3.08/1.61
% 3.08/1.61 thf(dsetconstrER,definition,
% 3.08/1.61 ( dsetconstrER
% 3.08/1.61 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx
% 3.08/1.61 @ ( dsetconstr @ A
% 3.08/1.61 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.08/1.61 => ( Xphi @ Xx ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(exuE1_type,type,
% 3.08/1.61 exuE1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(exuE1,definition,
% 3.08/1.61 ( exuE1
% 3.08/1.61 = ( ! [Xphi: $i > $o] :
% 3.08/1.61 ( ( exu
% 3.08/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.61 => ? [Xx: $i] :
% 3.08/1.61 ( ( Xphi @ Xx )
% 3.08/1.61 & ! [Xy: $i] :
% 3.08/1.61 ( ( Xphi @ Xy )
% 3.08/1.61 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(prop2set_type,type,
% 3.08/1.61 prop2set: $o > $i ).
% 3.08/1.61
% 3.08/1.61 thf(prop2setE_type,type,
% 3.08/1.61 prop2setE: $o ).
% 3.08/1.61
% 3.08/1.61 thf(prop2setE,definition,
% 3.08/1.61 ( prop2setE
% 3.08/1.61 = ( ! [Xphi: $o,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 3.08/1.61 => Xphi ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(emptysetE_type,type,
% 3.08/1.61 emptysetE: $o ).
% 3.08/1.61
% 3.08/1.61 thf(emptysetE,definition,
% 3.08/1.61 ( emptysetE
% 3.08/1.61 = ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ emptyset )
% 3.08/1.61 => ! [Xphi: $o] : Xphi ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(emptysetimpfalse_type,type,
% 3.08/1.61 emptysetimpfalse: $o ).
% 3.08/1.61
% 3.08/1.61 thf(emptysetimpfalse,definition,
% 3.08/1.61 ( emptysetimpfalse
% 3.08/1.61 = ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ emptyset )
% 3.08/1.61 => $false ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(notinemptyset_type,type,
% 3.08/1.61 notinemptyset: $o ).
% 3.08/1.61
% 3.08/1.61 thf(notinemptyset,definition,
% 3.08/1.61 ( notinemptyset
% 3.08/1.61 = ( ! [Xx: $i] :
% 3.08/1.61 ~ ( in @ Xx @ emptyset ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(exuE3e_type,type,
% 3.08/1.61 exuE3e: $o ).
% 3.08/1.61
% 3.08/1.61 thf(exuE3e,definition,
% 3.08/1.61 ( exuE3e
% 3.08/1.61 = ( ! [Xphi: $i > $o] :
% 3.08/1.61 ( ( exu
% 3.08/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.61 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setext_type,type,
% 3.08/1.61 setext: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setext,definition,
% 3.08/1.61 ( setext
% 3.08/1.61 = ( ! [A: $i,B: $i] :
% 3.08/1.61 ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( in @ Xx @ B ) )
% 3.08/1.61 => ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ B )
% 3.08/1.61 => ( in @ Xx @ A ) )
% 3.08/1.61 => ( A = B ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(emptyI_type,type,
% 3.08/1.61 emptyI: $o ).
% 3.08/1.61
% 3.08/1.61 thf(emptyI,definition,
% 3.08/1.61 ( emptyI
% 3.08/1.61 = ( ! [A: $i] :
% 3.08/1.61 ( ! [Xx: $i] :
% 3.08/1.61 ~ ( in @ Xx @ A )
% 3.08/1.61 => ( A = emptyset ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(noeltsimpempty_type,type,
% 3.08/1.61 noeltsimpempty: $o ).
% 3.08/1.61
% 3.08/1.61 thf(noeltsimpempty,definition,
% 3.08/1.61 ( noeltsimpempty
% 3.08/1.61 = ( ! [A: $i] :
% 3.08/1.61 ( ! [Xx: $i] :
% 3.08/1.61 ~ ( in @ Xx @ A )
% 3.08/1.61 => ( A = emptyset ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setbeta_type,type,
% 3.08/1.61 setbeta: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setbeta,definition,
% 3.08/1.61 ( setbeta
% 3.08/1.61 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( in @ Xx
% 3.08/1.61 @ ( dsetconstr @ A
% 3.08/1.61 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.08/1.61 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(nonempty_type,type,
% 3.08/1.61 nonempty: $i > $o ).
% 3.08/1.61
% 3.08/1.61 thf(nonempty,definition,
% 3.08/1.61 ( nonempty
% 3.08/1.61 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(nonemptyE1_type,type,
% 3.08/1.61 nonemptyE1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(nonemptyE1,definition,
% 3.08/1.61 ( nonemptyE1
% 3.08/1.61 = ( ! [A: $i] :
% 3.08/1.61 ( ( nonempty @ A )
% 3.08/1.61 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(nonemptyI_type,type,
% 3.08/1.61 nonemptyI: $o ).
% 3.08/1.61
% 3.08/1.61 thf(nonemptyI,definition,
% 3.08/1.61 ( nonemptyI
% 3.08/1.61 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( Xphi @ Xx )
% 3.08/1.61 => ( nonempty
% 3.08/1.61 @ ( dsetconstr @ A
% 3.08/1.61 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(nonemptyI1_type,type,
% 3.08/1.61 nonemptyI1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(nonemptyI1,definition,
% 3.08/1.61 ( nonemptyI1
% 3.08/1.61 = ( ! [A: $i] :
% 3.08/1.61 ( ? [Xx: $i] : ( in @ Xx @ A )
% 3.08/1.61 => ( nonempty @ A ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setadjoinIL_type,type,
% 3.08/1.61 setadjoinIL: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setadjoinIL,definition,
% 3.08/1.61 ( setadjoinIL
% 3.08/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(emptyinunitempty_type,type,
% 3.08/1.61 emptyinunitempty: $o ).
% 3.08/1.61
% 3.08/1.61 thf(emptyinunitempty,definition,
% 3.08/1.61 ( emptyinunitempty
% 3.08/1.61 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setadjoinIR_type,type,
% 3.08/1.61 setadjoinIR: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setadjoinIR,definition,
% 3.08/1.61 ( setadjoinIR
% 3.08/1.61 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ A )
% 3.08/1.61 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setadjoinE_type,type,
% 3.08/1.61 setadjoinE: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setadjoinE,definition,
% 3.08/1.61 ( setadjoinE
% 3.08/1.61 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.08/1.61 => ! [Xphi: $o] :
% 3.08/1.61 ( ( ( Xy = Xx )
% 3.08/1.61 => Xphi )
% 3.08/1.61 => ( ( ( in @ Xy @ A )
% 3.08/1.61 => Xphi )
% 3.08/1.61 => Xphi ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setadjoinOr_type,type,
% 3.08/1.61 setadjoinOr: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setadjoinOr,definition,
% 3.08/1.61 ( setadjoinOr
% 3.08/1.61 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.08/1.61 => ( ( Xy = Xx )
% 3.08/1.61 | ( in @ Xy @ A ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setoftrueEq_type,type,
% 3.08/1.61 setoftrueEq: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setoftrueEq,definition,
% 3.08/1.61 ( setoftrueEq
% 3.08/1.61 = ( ! [A: $i] :
% 3.08/1.61 ( ( dsetconstr @ A
% 3.08/1.61 @ ^ [Xx: $i] : $true )
% 3.08/1.61 = A ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(powersetI_type,type,
% 3.08/1.61 powersetI: $o ).
% 3.08/1.61
% 3.08/1.61 thf(powersetI,definition,
% 3.08/1.61 ( powersetI
% 3.08/1.61 = ( ! [A: $i,B: $i] :
% 3.08/1.61 ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ B )
% 3.08/1.61 => ( in @ Xx @ A ) )
% 3.08/1.61 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(emptyinPowerset_type,type,
% 3.08/1.61 emptyinPowerset: $o ).
% 3.08/1.61
% 3.08/1.61 thf(emptyinPowerset,definition,
% 3.08/1.61 ( emptyinPowerset
% 3.08/1.61 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(emptyInPowerset_type,type,
% 3.08/1.61 emptyInPowerset: $o ).
% 3.08/1.61
% 3.08/1.61 thf(emptyInPowerset,definition,
% 3.08/1.61 ( emptyInPowerset
% 3.08/1.61 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(powersetE_type,type,
% 3.08/1.61 powersetE: $o ).
% 3.08/1.61
% 3.08/1.61 thf(powersetE,definition,
% 3.08/1.61 ( powersetE
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ B @ ( powerset @ A ) )
% 3.08/1.61 => ( ( in @ Xx @ B )
% 3.08/1.61 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setunionI_type,type,
% 3.08/1.61 setunionI: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setunionI,definition,
% 3.08/1.61 ( setunionI
% 3.08/1.61 = ( ! [A: $i,Xx: $i,B: $i] :
% 3.08/1.61 ( ( in @ Xx @ B )
% 3.08/1.61 => ( ( in @ B @ A )
% 3.08/1.61 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setunionE_type,type,
% 3.08/1.61 setunionE: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setunionE,definition,
% 3.08/1.61 ( setunionE
% 3.08/1.61 = ( ! [A: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ ( setunion @ A ) )
% 3.08/1.61 => ! [Xphi: $o] :
% 3.08/1.61 ( ! [B: $i] :
% 3.08/1.61 ( ( in @ Xx @ B )
% 3.08/1.61 => ( ( in @ B @ A )
% 3.08/1.61 => Xphi ) )
% 3.08/1.61 => Xphi ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(subPowSU_type,type,
% 3.08/1.61 subPowSU: $o ).
% 3.08/1.61
% 3.08/1.61 thf(subPowSU,definition,
% 3.08/1.61 ( subPowSU
% 3.08/1.61 = ( ! [A: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(exuE2_type,type,
% 3.08/1.61 exuE2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(exuE2,definition,
% 3.08/1.61 ( exuE2
% 3.08/1.61 = ( ! [Xphi: $i > $o] :
% 3.08/1.61 ( ( exu
% 3.08/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.61 => ? [Xx: $i] :
% 3.08/1.61 ! [Xy: $i] :
% 3.08/1.61 ( ( Xphi @ Xy )
% 3.08/1.61 <=> ( Xy = Xx ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(nonemptyImpWitness_type,type,
% 3.08/1.61 nonemptyImpWitness: $o ).
% 3.08/1.61
% 3.08/1.61 thf(nonemptyImpWitness,definition,
% 3.08/1.61 ( nonemptyImpWitness
% 3.08/1.61 = ( ! [A: $i] :
% 3.08/1.61 ( ( nonempty @ A )
% 3.08/1.61 => ? [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 & $true ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(uniqinunit_type,type,
% 3.08/1.61 uniqinunit: $o ).
% 3.08/1.61
% 3.08/1.61 thf(uniqinunit,definition,
% 3.08/1.61 ( uniqinunit
% 3.08/1.61 = ( ! [Xx: $i,Xy: $i] :
% 3.08/1.61 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.08/1.61 => ( Xx = Xy ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(notinsingleton_type,type,
% 3.08/1.61 notinsingleton: $o ).
% 3.08/1.61
% 3.08/1.61 thf(notinsingleton,definition,
% 3.08/1.61 ( notinsingleton
% 3.08/1.61 = ( ! [Xx: $i,Xy: $i] :
% 3.08/1.61 ( ( Xx != Xy )
% 3.08/1.61 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(eqinunit_type,type,
% 3.08/1.61 eqinunit: $o ).
% 3.08/1.61
% 3.08/1.61 thf(eqinunit,definition,
% 3.08/1.61 ( eqinunit
% 3.08/1.61 = ( ! [Xx: $i,Xy: $i] :
% 3.08/1.61 ( ( Xx = Xy )
% 3.08/1.61 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(singletonsswitch_type,type,
% 3.08/1.61 singletonsswitch: $o ).
% 3.08/1.61
% 3.08/1.61 thf(singletonsswitch,definition,
% 3.08/1.61 ( singletonsswitch
% 3.08/1.61 = ( ! [Xx: $i,Xy: $i] :
% 3.08/1.61 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.08/1.61 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(upairsetE_type,type,
% 3.08/1.61 upairsetE: $o ).
% 3.08/1.61
% 3.08/1.61 thf(upairsetE,definition,
% 3.08/1.61 ( upairsetE
% 3.08/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.08/1.61 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 3.08/1.61 => ( ( Xz = Xx )
% 3.08/1.61 | ( Xz = Xy ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(upairsetIL_type,type,
% 3.08/1.61 upairsetIL: $o ).
% 3.08/1.61
% 3.08/1.61 thf(upairsetIL,definition,
% 3.08/1.61 ( upairsetIL
% 3.08/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(upairsetIR_type,type,
% 3.08/1.61 upairsetIR: $o ).
% 3.08/1.61
% 3.08/1.61 thf(upairsetIR,definition,
% 3.08/1.61 ( upairsetIR
% 3.08/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(emptyE1_type,type,
% 3.08/1.61 emptyE1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(emptyE1,definition,
% 3.08/1.61 ( emptyE1
% 3.08/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 3.08/1.61 ( ? [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 & ( Xphi @ Xx ) )
% 3.08/1.61 => ( ( ( dsetconstr @ A
% 3.08/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.61 = emptyset )
% 3.08/1.61 => $false ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(vacuousDall_type,type,
% 3.08/1.61 vacuousDall: $o ).
% 3.08/1.61
% 3.08/1.61 thf(vacuousDall,definition,
% 3.08/1.61 ( vacuousDall
% 3.08/1.61 = ( ! [Xphi: $i > $o,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ emptyset )
% 3.08/1.61 => ( Xphi @ Xx ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(quantDeMorgan1_type,type,
% 3.08/1.61 quantDeMorgan1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(quantDeMorgan1,definition,
% 3.08/1.61 ( quantDeMorgan1
% 3.08/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 3.08/1.61 ( ~ ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( Xphi @ Xx ) )
% 3.08/1.61 => ? [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(quantDeMorgan2_type,type,
% 3.08/1.61 quantDeMorgan2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(quantDeMorgan2,definition,
% 3.08/1.61 ( quantDeMorgan2
% 3.08/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 3.08/1.61 ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ~ ( Xphi @ Xx ) )
% 3.08/1.61 => ~ ? [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 & ( Xphi @ Xx ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(quantDeMorgan3_type,type,
% 3.08/1.61 quantDeMorgan3: $o ).
% 3.08/1.61
% 3.08/1.61 thf(quantDeMorgan3,definition,
% 3.08/1.61 ( quantDeMorgan3
% 3.08/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 3.08/1.61 ( ~ ? [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 & ( Xphi @ Xx ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(quantDeMorgan4_type,type,
% 3.08/1.61 quantDeMorgan4: $o ).
% 3.08/1.61
% 3.08/1.61 thf(quantDeMorgan4,definition,
% 3.08/1.61 ( quantDeMorgan4
% 3.08/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 3.08/1.61 ( ? [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 & ~ ( Xphi @ Xx ) )
% 3.08/1.61 => ~ ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( Xphi @ Xx ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(prop2setI_type,type,
% 3.08/1.61 prop2setI: $o ).
% 3.08/1.61
% 3.08/1.61 thf(prop2setI,definition,
% 3.08/1.61 ( prop2setI
% 3.08/1.61 = ( ! [Xphi: $o] :
% 3.08/1.61 ( Xphi
% 3.08/1.61 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(set2prop_type,type,
% 3.08/1.61 set2prop: $i > $o ).
% 3.08/1.61
% 3.08/1.61 thf(prop2set2propI_type,type,
% 3.08/1.61 prop2set2propI: $o ).
% 3.08/1.61
% 3.08/1.61 thf(prop2set2propI,definition,
% 3.08/1.61 ( prop2set2propI
% 3.08/1.61 = ( ! [Xphi: $o] :
% 3.08/1.61 ( Xphi
% 3.08/1.61 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(notdexE_type,type,
% 3.08/1.61 notdexE: $o ).
% 3.08/1.61
% 3.08/1.61 thf(notdexE,definition,
% 3.08/1.61 ( notdexE
% 3.08/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 3.08/1.61 ( ~ ? [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 & ( Xphi @ Xx ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(notdallE_type,type,
% 3.08/1.61 notdallE: $o ).
% 3.08/1.61
% 3.08/1.61 thf(notdallE,definition,
% 3.08/1.61 ( notdallE
% 3.08/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 3.08/1.61 ( ~ ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( Xphi @ Xx ) )
% 3.08/1.61 => ? [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(exuI1_type,type,
% 3.08/1.61 exuI1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(exuI1,definition,
% 3.08/1.61 ( exuI1
% 3.08/1.61 = ( ! [Xphi: $i > $o] :
% 3.08/1.61 ( ? [Xx: $i] :
% 3.08/1.61 ( ( Xphi @ Xx )
% 3.08/1.61 & ! [Xy: $i] :
% 3.08/1.61 ( ( Xphi @ Xy )
% 3.08/1.61 => ( Xx = Xy ) ) )
% 3.08/1.61 => ( exu
% 3.08/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(exuI3_type,type,
% 3.08/1.61 exuI3: $o ).
% 3.08/1.61
% 3.08/1.61 thf(exuI3,definition,
% 3.08/1.61 ( exuI3
% 3.08/1.61 = ( ! [Xphi: $i > $o] :
% 3.08/1.61 ( ? [Xx: $i] : ( Xphi @ Xx )
% 3.08/1.61 => ( ! [Xx: $i,Xy: $i] :
% 3.08/1.61 ( ( Xphi @ Xx )
% 3.08/1.61 => ( ( Xphi @ Xy )
% 3.08/1.61 => ( Xx = Xy ) ) )
% 3.08/1.61 => ( exu
% 3.08/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(exuI2_type,type,
% 3.08/1.61 exuI2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(exuI2,definition,
% 3.08/1.61 ( exuI2
% 3.08/1.61 = ( ! [Xphi: $i > $o] :
% 3.08/1.61 ( ? [Xx: $i] :
% 3.08/1.61 ! [Xy: $i] :
% 3.08/1.61 ( ( Xphi @ Xy )
% 3.08/1.61 <=> ( Xy = Xx ) )
% 3.08/1.61 => ( exu
% 3.08/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(inCongP_type,type,
% 3.08/1.61 inCongP: $o ).
% 3.08/1.61
% 3.08/1.61 thf(inCongP,definition,
% 3.08/1.61 ( inCongP
% 3.08/1.61 = ( ! [A: $i,B: $i] :
% 3.08/1.61 ( ( A = B )
% 3.08/1.61 => ! [Xx: $i,Xy: $i] :
% 3.08/1.61 ( ( Xx = Xy )
% 3.08/1.61 => ( ( in @ Xx @ A )
% 3.08/1.61 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(in__Cong_type,type,
% 3.08/1.61 in__Cong: $o ).
% 3.08/1.61
% 3.08/1.61 thf(in__Cong,definition,
% 3.08/1.61 ( in__Cong
% 3.08/1.61 = ( ! [A: $i,B: $i] :
% 3.08/1.61 ( ( A = B )
% 3.08/1.61 => ! [Xx: $i,Xy: $i] :
% 3.08/1.61 ( ( Xx = Xy )
% 3.08/1.61 => ( ( in @ Xx @ A )
% 3.08/1.61 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(exuE3u_type,type,
% 3.08/1.61 exuE3u: $o ).
% 3.08/1.61
% 3.08/1.61 thf(exuE3u,definition,
% 3.08/1.61 ( exuE3u
% 3.08/1.61 = ( ! [Xphi: $i > $o] :
% 3.08/1.61 ( ( exu
% 3.08/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.61 => ! [Xx: $i,Xy: $i] :
% 3.08/1.61 ( ( Xphi @ Xx )
% 3.08/1.61 => ( ( Xphi @ Xy )
% 3.08/1.61 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(exu__Cong_type,type,
% 3.08/1.61 exu__Cong: $o ).
% 3.08/1.61
% 3.08/1.61 thf(exu__Cong,definition,
% 3.08/1.61 ( exu__Cong
% 3.08/1.61 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.08/1.61 ( ! [Xx: $i,Xy: $i] :
% 3.08/1.61 ( ( Xx = Xy )
% 3.08/1.61 => ( ( Xphi @ Xx )
% 3.08/1.61 <=> ( Xpsi @ Xy ) ) )
% 3.08/1.61 => ( ( exu
% 3.08/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.61 <=> ( exu
% 3.08/1.61 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(emptyset__Cong_type,type,
% 3.08/1.61 emptyset__Cong: $o ).
% 3.08/1.61
% 3.08/1.61 thf(emptyset__Cong,definition,
% 3.08/1.61 ( emptyset__Cong
% 3.08/1.61 = ( emptyset = emptyset ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setadjoin__Cong_type,type,
% 3.08/1.61 setadjoin__Cong: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setadjoin__Cong,definition,
% 3.08/1.61 ( setadjoin__Cong
% 3.08/1.61 = ( ! [Xx: $i,Xy: $i] :
% 3.08/1.61 ( ( Xx = Xy )
% 3.08/1.61 => ! [Xz: $i,Xu: $i] :
% 3.08/1.61 ( ( Xz = Xu )
% 3.08/1.61 => ( ( setadjoin @ Xx @ Xz )
% 3.08/1.61 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(powerset__Cong_type,type,
% 3.08/1.61 powerset__Cong: $o ).
% 3.08/1.61
% 3.08/1.61 thf(powerset__Cong,definition,
% 3.08/1.61 ( powerset__Cong
% 3.08/1.61 = ( ! [A: $i,B: $i] :
% 3.08/1.61 ( ( A = B )
% 3.08/1.61 => ( ( powerset @ A )
% 3.08/1.61 = ( powerset @ B ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setunion__Cong_type,type,
% 3.08/1.61 setunion__Cong: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setunion__Cong,definition,
% 3.08/1.61 ( setunion__Cong
% 3.08/1.61 = ( ! [A: $i,B: $i] :
% 3.08/1.61 ( ( A = B )
% 3.08/1.61 => ( ( setunion @ A )
% 3.08/1.61 = ( setunion @ B ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(omega__Cong_type,type,
% 3.08/1.61 omega__Cong: $o ).
% 3.08/1.61
% 3.08/1.61 thf(omega__Cong,definition,
% 3.08/1.61 ( omega__Cong
% 3.08/1.61 = ( omega = omega ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(exuEu_type,type,
% 3.08/1.61 exuEu: $o ).
% 3.08/1.61
% 3.08/1.61 thf(exuEu,definition,
% 3.08/1.61 ( exuEu
% 3.08/1.61 = ( ! [Xphi: $i > $o] :
% 3.08/1.61 ( ( exu
% 3.08/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.61 => ! [Xx: $i,Xy: $i] :
% 3.08/1.61 ( ( Xphi @ Xx )
% 3.08/1.61 => ( ( Xphi @ Xy )
% 3.08/1.61 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(descr__Cong_type,type,
% 3.08/1.61 descr__Cong: $o ).
% 3.08/1.61
% 3.08/1.61 thf(descr__Cong,definition,
% 3.08/1.61 ( descr__Cong
% 3.08/1.61 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.08/1.61 ( ! [Xx: $i,Xy: $i] :
% 3.08/1.61 ( ( Xx = Xy )
% 3.08/1.61 => ( ( Xphi @ Xx )
% 3.08/1.61 <=> ( Xpsi @ Xy ) ) )
% 3.08/1.61 => ( ( exu
% 3.08/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.61 => ( ( exu
% 3.08/1.61 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 3.08/1.61 => ( ( descr
% 3.08/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.61 = ( descr
% 3.08/1.61 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(dsetconstr__Cong_type,type,
% 3.08/1.61 dsetconstr__Cong: $o ).
% 3.08/1.61
% 3.08/1.61 thf(dsetconstr__Cong,definition,
% 3.08/1.61 ( dsetconstr__Cong
% 3.08/1.61 = ( ! [A: $i,B: $i] :
% 3.08/1.61 ( ( A = B )
% 3.08/1.61 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.08/1.61 ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ B )
% 3.08/1.61 => ( ( Xx = Xy )
% 3.08/1.61 => ( ( Xphi @ Xx )
% 3.08/1.61 <=> ( Xpsi @ Xy ) ) ) ) )
% 3.08/1.61 => ( ( dsetconstr @ A
% 3.08/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.61 = ( dsetconstr @ B
% 3.08/1.61 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(subset_type,type,
% 3.08/1.61 subset: $i > $i > $o ).
% 3.08/1.61
% 3.08/1.61 thf(disjoint_type,type,
% 3.08/1.61 disjoint: $i > $i > $o ).
% 3.08/1.61
% 3.08/1.61 thf(setsmeet_type,type,
% 3.08/1.61 setsmeet: $i > $i > $o ).
% 3.08/1.61
% 3.08/1.61 thf(subsetI1_type,type,
% 3.08/1.61 subsetI1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(subsetI1,definition,
% 3.08/1.61 ( subsetI1
% 3.08/1.61 = ( ! [A: $i,B: $i] :
% 3.08/1.61 ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( in @ Xx @ B ) )
% 3.08/1.61 => ( subset @ A @ B ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(eqimpsubset2_type,type,
% 3.08/1.61 eqimpsubset2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(eqimpsubset2,definition,
% 3.08/1.61 ( eqimpsubset2
% 3.08/1.61 = ( ! [A: $i,B: $i] :
% 3.08/1.61 ( ( A = B )
% 3.08/1.61 => ( subset @ B @ A ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(eqimpsubset1_type,type,
% 3.08/1.61 eqimpsubset1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(eqimpsubset1,definition,
% 3.08/1.61 ( eqimpsubset1
% 3.08/1.61 = ( ! [A: $i,B: $i] :
% 3.08/1.61 ( ( A = B )
% 3.08/1.61 => ( subset @ A @ B ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(subsetI2_type,type,
% 3.08/1.61 subsetI2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(subsetI2,definition,
% 3.08/1.61 ( subsetI2
% 3.08/1.61 = ( ! [A: $i,B: $i] :
% 3.08/1.61 ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( in @ Xx @ B ) )
% 3.08/1.61 => ( subset @ A @ B ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(emptysetsubset_type,type,
% 3.08/1.61 emptysetsubset: $o ).
% 3.08/1.61
% 3.08/1.61 thf(emptysetsubset,definition,
% 3.08/1.61 ( emptysetsubset
% 3.08/1.61 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(subsetE_type,type,
% 3.08/1.61 subsetE: $o ).
% 3.08/1.61
% 3.08/1.61 thf(subsetE,definition,
% 3.08/1.61 ( subsetE
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ( subset @ A @ B )
% 3.08/1.61 => ( ( in @ Xx @ A )
% 3.08/1.61 => ( in @ Xx @ B ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(subsetE2_type,type,
% 3.08/1.61 subsetE2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(subsetE2,definition,
% 3.08/1.61 ( subsetE2
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ( subset @ A @ B )
% 3.08/1.61 => ( ~ ( in @ Xx @ B )
% 3.08/1.61 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(notsubsetI_type,type,
% 3.08/1.61 notsubsetI: $o ).
% 3.08/1.61
% 3.08/1.61 thf(notsubsetI,definition,
% 3.08/1.61 ( notsubsetI
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ~ ( in @ Xx @ B )
% 3.08/1.61 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(notequalI1_type,type,
% 3.08/1.61 notequalI1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(notequalI1,definition,
% 3.08/1.61 ( notequalI1
% 3.08/1.61 = ( ! [A: $i,B: $i] :
% 3.08/1.61 ( ~ ( subset @ A @ B )
% 3.08/1.61 => ( A != B ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(notequalI2_type,type,
% 3.08/1.61 notequalI2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(notequalI2,definition,
% 3.08/1.61 ( notequalI2
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ~ ( in @ Xx @ B )
% 3.08/1.61 => ( A != B ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(subsetRefl_type,type,
% 3.08/1.61 subsetRefl: $o ).
% 3.08/1.61
% 3.08/1.61 thf(subsetRefl,definition,
% 3.08/1.61 ( subsetRefl
% 3.08/1.61 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(subsetTrans_type,type,
% 3.08/1.61 subsetTrans: $o ).
% 3.08/1.61
% 3.08/1.61 thf(subsetTrans,definition,
% 3.08/1.61 ( subsetTrans
% 3.08/1.61 = ( ! [A: $i,B: $i,C: $i] :
% 3.08/1.61 ( ( subset @ A @ B )
% 3.08/1.61 => ( ( subset @ B @ C )
% 3.08/1.61 => ( subset @ A @ C ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setadjoinSub_type,type,
% 3.08/1.61 setadjoinSub: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setadjoinSub,definition,
% 3.08/1.61 ( setadjoinSub
% 3.08/1.61 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setadjoinSub2_type,type,
% 3.08/1.61 setadjoinSub2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setadjoinSub2,definition,
% 3.08/1.61 ( setadjoinSub2
% 3.08/1.61 = ( ! [A: $i,Xx: $i,B: $i] :
% 3.08/1.61 ( ( subset @ A @ B )
% 3.08/1.61 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(subset2powerset_type,type,
% 3.08/1.61 subset2powerset: $o ).
% 3.08/1.61
% 3.08/1.61 thf(subset2powerset,definition,
% 3.08/1.61 ( subset2powerset
% 3.08/1.61 = ( ! [A: $i,B: $i] :
% 3.08/1.61 ( ( subset @ A @ B )
% 3.08/1.61 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setextsub_type,type,
% 3.08/1.61 setextsub: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setextsub,definition,
% 3.08/1.61 ( setextsub
% 3.08/1.61 = ( ! [A: $i,B: $i] :
% 3.08/1.61 ( ( subset @ A @ B )
% 3.08/1.61 => ( ( subset @ B @ A )
% 3.08/1.61 => ( A = B ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(subsetemptysetimpeq_type,type,
% 3.08/1.61 subsetemptysetimpeq: $o ).
% 3.08/1.61
% 3.08/1.61 thf(subsetemptysetimpeq,definition,
% 3.08/1.61 ( subsetemptysetimpeq
% 3.08/1.61 = ( ! [A: $i] :
% 3.08/1.61 ( ( subset @ A @ emptyset )
% 3.08/1.61 => ( A = emptyset ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(powersetI1_type,type,
% 3.08/1.61 powersetI1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(powersetI1,definition,
% 3.08/1.61 ( powersetI1
% 3.08/1.61 = ( ! [A: $i,B: $i] :
% 3.08/1.61 ( ( subset @ B @ A )
% 3.08/1.61 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(powersetE1_type,type,
% 3.08/1.61 powersetE1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(powersetE1,definition,
% 3.08/1.61 ( powersetE1
% 3.08/1.61 = ( ! [A: $i,B: $i] :
% 3.08/1.61 ( ( in @ B @ ( powerset @ A ) )
% 3.08/1.61 => ( subset @ B @ A ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(inPowerset_type,type,
% 3.08/1.61 inPowerset: $o ).
% 3.08/1.61
% 3.08/1.61 thf(inPowerset,definition,
% 3.08/1.61 ( inPowerset
% 3.08/1.61 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(powersetsubset_type,type,
% 3.08/1.61 powersetsubset: $o ).
% 3.08/1.61
% 3.08/1.61 thf(powersetsubset,definition,
% 3.08/1.61 ( powersetsubset
% 3.08/1.61 = ( ! [A: $i,B: $i] :
% 3.08/1.61 ( ( subset @ A @ B )
% 3.08/1.61 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(sepInPowerset_type,type,
% 3.08/1.61 sepInPowerset: $o ).
% 3.08/1.61
% 3.08/1.61 thf(sepInPowerset,definition,
% 3.08/1.61 ( sepInPowerset
% 3.08/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 3.08/1.61 ( in
% 3.08/1.61 @ ( dsetconstr @ A
% 3.08/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.61 @ ( powerset @ A ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(sepSubset_type,type,
% 3.08/1.61 sepSubset: $o ).
% 3.08/1.61
% 3.08/1.61 thf(sepSubset,definition,
% 3.08/1.61 ( sepSubset
% 3.08/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 3.08/1.61 ( subset
% 3.08/1.61 @ ( dsetconstr @ A
% 3.08/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.61 @ A ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(binunion_type,type,
% 3.08/1.61 binunion: $i > $i > $i ).
% 3.08/1.61
% 3.08/1.61 thf(binunionIL_type,type,
% 3.08/1.61 binunionIL: $o ).
% 3.08/1.61
% 3.08/1.61 thf(binunionIL,definition,
% 3.08/1.61 ( binunionIL
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(upairset2IR_type,type,
% 3.08/1.61 upairset2IR: $o ).
% 3.08/1.61
% 3.08/1.61 thf(upairset2IR,definition,
% 3.08/1.61 ( upairset2IR
% 3.08/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(binunionIR_type,type,
% 3.08/1.61 binunionIR: $o ).
% 3.08/1.61
% 3.08/1.61 thf(binunionIR,definition,
% 3.08/1.61 ( binunionIR
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ B )
% 3.08/1.61 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(binunionEcases_type,type,
% 3.08/1.61 binunionEcases: $o ).
% 3.08/1.61
% 3.08/1.61 thf(binunionEcases,definition,
% 3.08/1.61 ( binunionEcases
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 3.08/1.61 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 3.08/1.61 => ( ( ( in @ Xx @ A )
% 3.08/1.61 => Xphi )
% 3.08/1.61 => ( ( ( in @ Xx @ B )
% 3.08/1.61 => Xphi )
% 3.08/1.61 => Xphi ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(binunionE_type,type,
% 3.08/1.61 binunionE: $o ).
% 3.08/1.61
% 3.08/1.61 thf(binunionE,definition,
% 3.08/1.61 ( binunionE
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 3.08/1.61 => ( ( in @ Xx @ A )
% 3.08/1.61 | ( in @ Xx @ B ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(binunionLsub_type,type,
% 3.08/1.61 binunionLsub: $o ).
% 3.08/1.61
% 3.08/1.61 thf(binunionLsub,definition,
% 3.08/1.61 ( binunionLsub
% 3.08/1.61 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(binunionRsub_type,type,
% 3.08/1.61 binunionRsub: $o ).
% 3.08/1.61
% 3.08/1.61 thf(binunionRsub,definition,
% 3.08/1.61 ( binunionRsub
% 3.08/1.61 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(binintersect_type,type,
% 3.08/1.61 binintersect: $i > $i > $i ).
% 3.08/1.61
% 3.08/1.61 thf(binintersectI_type,type,
% 3.08/1.61 binintersectI: $o ).
% 3.08/1.61
% 3.08/1.61 thf(binintersectI,definition,
% 3.08/1.61 ( binintersectI
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( in @ Xx @ B )
% 3.08/1.61 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(binintersectSubset5_type,type,
% 3.08/1.61 binintersectSubset5: $o ).
% 3.08/1.61
% 3.08/1.61 thf(binintersectSubset5,definition,
% 3.08/1.61 ( binintersectSubset5
% 3.08/1.61 = ( ! [A: $i,B: $i,C: $i] :
% 3.08/1.61 ( ( subset @ C @ A )
% 3.08/1.61 => ( ( subset @ C @ B )
% 3.08/1.61 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(binintersectEL_type,type,
% 3.08/1.61 binintersectEL: $o ).
% 3.08/1.61
% 3.08/1.61 thf(binintersectEL,definition,
% 3.08/1.61 ( binintersectEL
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 3.08/1.61 => ( in @ Xx @ A ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(binintersectLsub_type,type,
% 3.08/1.61 binintersectLsub: $o ).
% 3.08/1.61
% 3.08/1.61 thf(binintersectLsub,definition,
% 3.08/1.61 ( binintersectLsub
% 3.08/1.61 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(binintersectSubset2_type,type,
% 3.08/1.61 binintersectSubset2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(binintersectSubset2,definition,
% 3.08/1.61 ( binintersectSubset2
% 3.08/1.61 = ( ! [A: $i,B: $i] :
% 3.08/1.61 ( ( subset @ A @ B )
% 3.08/1.61 => ( ( binintersect @ A @ B )
% 3.08/1.61 = A ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(binintersectSubset3_type,type,
% 3.08/1.61 binintersectSubset3: $o ).
% 3.08/1.61
% 3.08/1.61 thf(binintersectSubset3,definition,
% 3.08/1.61 ( binintersectSubset3
% 3.08/1.61 = ( ! [A: $i,B: $i] :
% 3.08/1.61 ( ( ( binintersect @ A @ B )
% 3.08/1.61 = B )
% 3.08/1.61 => ( subset @ B @ A ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(binintersectER_type,type,
% 3.08/1.61 binintersectER: $o ).
% 3.08/1.61
% 3.08/1.61 thf(binintersectER,definition,
% 3.08/1.61 ( binintersectER
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 3.08/1.61 => ( in @ Xx @ B ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(disjointsetsI1_type,type,
% 3.08/1.61 disjointsetsI1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(disjointsetsI1,definition,
% 3.08/1.61 ( disjointsetsI1
% 3.08/1.61 = ( ! [A: $i,B: $i] :
% 3.08/1.61 ( ~ ? [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 & ( in @ Xx @ B ) )
% 3.08/1.61 => ( ( binintersect @ A @ B )
% 3.08/1.61 = emptyset ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(binintersectRsub_type,type,
% 3.08/1.61 binintersectRsub: $o ).
% 3.08/1.61
% 3.08/1.61 thf(binintersectRsub,definition,
% 3.08/1.61 ( binintersectRsub
% 3.08/1.61 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(binintersectSubset4_type,type,
% 3.08/1.61 binintersectSubset4: $o ).
% 3.08/1.61
% 3.08/1.61 thf(binintersectSubset4,definition,
% 3.08/1.61 ( binintersectSubset4
% 3.08/1.61 = ( ! [A: $i,B: $i] :
% 3.08/1.61 ( ( subset @ B @ A )
% 3.08/1.61 => ( ( binintersect @ A @ B )
% 3.08/1.61 = B ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(binintersectSubset1_type,type,
% 3.08/1.61 binintersectSubset1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(binintersectSubset1,definition,
% 3.08/1.61 ( binintersectSubset1
% 3.08/1.61 = ( ! [A: $i,B: $i] :
% 3.08/1.61 ( ( ( binintersect @ A @ B )
% 3.08/1.61 = A )
% 3.08/1.61 => ( subset @ A @ B ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(bs114d_type,type,
% 3.08/1.61 bs114d: $o ).
% 3.08/1.61
% 3.08/1.61 thf(bs114d,definition,
% 3.08/1.61 ( bs114d
% 3.08/1.61 = ( ! [A: $i,B: $i,C: $i] :
% 3.08/1.61 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 3.08/1.61 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(regular_type,type,
% 3.08/1.61 regular: $i > $o ).
% 3.08/1.61
% 3.08/1.61 thf(setminus_type,type,
% 3.08/1.61 setminus: $i > $i > $i ).
% 3.08/1.61
% 3.08/1.61 thf(setminusI_type,type,
% 3.08/1.61 setminusI: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setminusI,definition,
% 3.08/1.61 ( setminusI
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ~ ( in @ Xx @ B )
% 3.08/1.61 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setminusEL_type,type,
% 3.08/1.61 setminusEL: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setminusEL,definition,
% 3.08/1.61 ( setminusEL
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 3.08/1.61 => ( in @ Xx @ A ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setminusER_type,type,
% 3.08/1.61 setminusER: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setminusER,definition,
% 3.08/1.61 ( setminusER
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 3.08/1.61 => ~ ( in @ Xx @ B ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setminusSubset2_type,type,
% 3.08/1.61 setminusSubset2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setminusSubset2,definition,
% 3.08/1.61 ( setminusSubset2
% 3.08/1.61 = ( ! [A: $i,B: $i] :
% 3.08/1.61 ( ( subset @ A @ B )
% 3.08/1.61 => ( ( setminus @ A @ B )
% 3.08/1.61 = emptyset ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setminusERneg_type,type,
% 3.08/1.61 setminusERneg: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setminusERneg,definition,
% 3.08/1.61 ( setminusERneg
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 3.08/1.61 => ( ( in @ Xx @ A )
% 3.08/1.61 => ( in @ Xx @ B ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setminusELneg_type,type,
% 3.08/1.61 setminusELneg: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setminusELneg,definition,
% 3.08/1.61 ( setminusELneg
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 3.08/1.61 => ( ~ ( in @ Xx @ B )
% 3.08/1.61 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setminusILneg_type,type,
% 3.08/1.61 setminusILneg: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setminusILneg,definition,
% 3.08/1.61 ( setminusILneg
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ~ ( in @ Xx @ A )
% 3.08/1.61 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setminusIRneg_type,type,
% 3.08/1.61 setminusIRneg: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setminusIRneg,definition,
% 3.08/1.61 ( setminusIRneg
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ B )
% 3.08/1.61 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setminusLsub_type,type,
% 3.08/1.61 setminusLsub: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setminusLsub,definition,
% 3.08/1.61 ( setminusLsub
% 3.08/1.61 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setminusSubset1_type,type,
% 3.08/1.61 setminusSubset1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setminusSubset1,definition,
% 3.08/1.61 ( setminusSubset1
% 3.08/1.61 = ( ! [A: $i,B: $i] :
% 3.08/1.61 ( ( ( setminus @ A @ B )
% 3.08/1.61 = emptyset )
% 3.08/1.61 => ( subset @ A @ B ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(symdiff_type,type,
% 3.08/1.61 symdiff: $i > $i > $i ).
% 3.08/1.61
% 3.08/1.61 thf(symdiffE_type,type,
% 3.08/1.61 symdiffE: $o ).
% 3.08/1.61
% 3.08/1.61 thf(symdiffE,definition,
% 3.08/1.61 ( symdiffE
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 3.08/1.61 => ! [Xphi: $o] :
% 3.08/1.61 ( ( ( in @ Xx @ A )
% 3.08/1.61 => ( ~ ( in @ Xx @ B )
% 3.08/1.61 => Xphi ) )
% 3.08/1.61 => ( ( ~ ( in @ Xx @ A )
% 3.08/1.61 => ( ( in @ Xx @ B )
% 3.08/1.61 => Xphi ) )
% 3.08/1.61 => Xphi ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(symdiffI1_type,type,
% 3.08/1.61 symdiffI1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(symdiffI1,definition,
% 3.08/1.61 ( symdiffI1
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ~ ( in @ Xx @ B )
% 3.08/1.61 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(symdiffI2_type,type,
% 3.08/1.61 symdiffI2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(symdiffI2,definition,
% 3.08/1.61 ( symdiffI2
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ~ ( in @ Xx @ A )
% 3.08/1.61 => ( ( in @ Xx @ B )
% 3.08/1.61 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(symdiffIneg1_type,type,
% 3.08/1.61 symdiffIneg1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(symdiffIneg1,definition,
% 3.08/1.61 ( symdiffIneg1
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( in @ Xx @ B )
% 3.08/1.61 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(symdiffIneg2_type,type,
% 3.08/1.61 symdiffIneg2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(symdiffIneg2,definition,
% 3.08/1.61 ( symdiffIneg2
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ~ ( in @ Xx @ A )
% 3.08/1.61 => ( ~ ( in @ Xx @ B )
% 3.08/1.61 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(iskpair_type,type,
% 3.08/1.61 iskpair: $i > $o ).
% 3.08/1.61
% 3.08/1.61 thf(secondinupair_type,type,
% 3.08/1.61 secondinupair: $o ).
% 3.08/1.61
% 3.08/1.61 thf(secondinupair,definition,
% 3.08/1.61 ( secondinupair
% 3.08/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setukpairIL_type,type,
% 3.08/1.61 setukpairIL: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setukpairIL,definition,
% 3.08/1.61 ( setukpairIL
% 3.08/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setukpairIR_type,type,
% 3.08/1.61 setukpairIR: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setukpairIR,definition,
% 3.08/1.61 ( setukpairIR
% 3.08/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(kpairiskpair_type,type,
% 3.08/1.61 kpairiskpair: $o ).
% 3.08/1.61
% 3.08/1.61 thf(kpairiskpair,definition,
% 3.08/1.61 ( kpairiskpair
% 3.08/1.61 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(kpair_type,type,
% 3.08/1.61 kpair: $i > $i > $i ).
% 3.08/1.61
% 3.08/1.61 thf(kpairp_type,type,
% 3.08/1.61 kpairp: $o ).
% 3.08/1.61
% 3.08/1.61 thf(kpairp,definition,
% 3.08/1.61 ( kpairp
% 3.08/1.61 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(cartprod_type,type,
% 3.08/1.61 cartprod: $i > $i > $i ).
% 3.08/1.61
% 3.08/1.61 thf(singletonsubset_type,type,
% 3.08/1.61 singletonsubset: $o ).
% 3.08/1.61
% 3.08/1.61 thf(singletonsubset,definition,
% 3.08/1.61 ( singletonsubset
% 3.08/1.61 = ( ! [A: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(singletoninpowerset_type,type,
% 3.08/1.61 singletoninpowerset: $o ).
% 3.08/1.61
% 3.08/1.61 thf(singletoninpowerset,definition,
% 3.08/1.61 ( singletoninpowerset
% 3.08/1.61 = ( ! [A: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(singletoninpowunion_type,type,
% 3.08/1.61 singletoninpowunion: $o ).
% 3.08/1.61
% 3.08/1.61 thf(singletoninpowunion,definition,
% 3.08/1.61 ( singletoninpowunion
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(upairset2E_type,type,
% 3.08/1.61 upairset2E: $o ).
% 3.08/1.61
% 3.08/1.61 thf(upairset2E,definition,
% 3.08/1.61 ( upairset2E
% 3.08/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.08/1.61 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 3.08/1.61 => ( ( Xz = Xx )
% 3.08/1.61 | ( Xz = Xy ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(upairsubunion_type,type,
% 3.08/1.61 upairsubunion: $o ).
% 3.08/1.61
% 3.08/1.61 thf(upairsubunion,definition,
% 3.08/1.61 ( upairsubunion
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ B )
% 3.08/1.61 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(upairinpowunion_type,type,
% 3.08/1.61 upairinpowunion: $o ).
% 3.08/1.61
% 3.08/1.61 thf(upairinpowunion,definition,
% 3.08/1.61 ( upairinpowunion
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ B )
% 3.08/1.61 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(ubforcartprodlem1_type,type,
% 3.08/1.61 ubforcartprodlem1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(ubforcartprodlem1,definition,
% 3.08/1.61 ( ubforcartprodlem1
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ B )
% 3.08/1.61 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(ubforcartprodlem2_type,type,
% 3.08/1.61 ubforcartprodlem2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(ubforcartprodlem2,definition,
% 3.08/1.61 ( ubforcartprodlem2
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ B )
% 3.08/1.61 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(ubforcartprodlem3_type,type,
% 3.08/1.61 ubforcartprodlem3: $o ).
% 3.08/1.61
% 3.08/1.61 thf(ubforcartprodlem3,definition,
% 3.08/1.61 ( ubforcartprodlem3
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ B )
% 3.08/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(cartprodpairin_type,type,
% 3.08/1.61 cartprodpairin: $o ).
% 3.08/1.61
% 3.08/1.61 thf(cartprodpairin,definition,
% 3.08/1.61 ( cartprodpairin
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ B )
% 3.08/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(cartprodmempair1_type,type,
% 3.08/1.61 cartprodmempair1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(cartprodmempair1,definition,
% 3.08/1.61 ( cartprodmempair1
% 3.08/1.61 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.08/1.61 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.08/1.61 => ? [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 & ? [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ B )
% 3.08/1.61 & ( Xu
% 3.08/1.61 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(cartprodmempair_type,type,
% 3.08/1.61 cartprodmempair: $o ).
% 3.08/1.61
% 3.08/1.61 thf(cartprodmempair,definition,
% 3.08/1.61 ( cartprodmempair
% 3.08/1.61 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.08/1.61 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.08/1.61 => ( iskpair @ Xu ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setunionE2_type,type,
% 3.08/1.61 setunionE2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setunionE2,definition,
% 3.08/1.61 ( setunionE2
% 3.08/1.61 = ( ! [A: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ ( setunion @ A ) )
% 3.08/1.61 => ? [X: $i] :
% 3.08/1.61 ( ( in @ X @ A )
% 3.08/1.61 & ( in @ Xx @ X ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setunionsingleton1_type,type,
% 3.08/1.61 setunionsingleton1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setunionsingleton1,definition,
% 3.08/1.61 ( setunionsingleton1
% 3.08/1.61 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setunionsingleton2_type,type,
% 3.08/1.61 setunionsingleton2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setunionsingleton2,definition,
% 3.08/1.61 ( setunionsingleton2
% 3.08/1.61 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setunionsingleton_type,type,
% 3.08/1.61 setunionsingleton: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setunionsingleton,definition,
% 3.08/1.61 ( setunionsingleton
% 3.08/1.61 = ( ! [Xx: $i] :
% 3.08/1.61 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 3.08/1.61 = Xx ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(singleton_type,type,
% 3.08/1.61 singleton: $i > $o ).
% 3.08/1.61
% 3.08/1.61 thf(singletonprop_type,type,
% 3.08/1.61 singletonprop: $o ).
% 3.08/1.61
% 3.08/1.61 thf(singletonprop,definition,
% 3.08/1.61 ( singletonprop
% 3.08/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 3.08/1.61 ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ A )
% 3.08/1.61 => ( ( Xphi @ Xx )
% 3.08/1.61 => ( ( Xphi @ Xy )
% 3.08/1.61 => ( Xx = Xy ) ) ) ) )
% 3.08/1.61 => ( ? [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 & ( Xphi @ Xx ) )
% 3.08/1.61 => ( singleton
% 3.08/1.61 @ ( dsetconstr @ A
% 3.08/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(ex1_type,type,
% 3.08/1.61 ex1: $i > ( $i > $o ) > $o ).
% 3.08/1.61
% 3.08/1.61 thf(ex1E1_type,type,
% 3.08/1.61 ex1E1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(ex1E1,definition,
% 3.08/1.61 ( ex1E1
% 3.08/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 3.08/1.61 ( ( ex1 @ A
% 3.08/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.61 => ? [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 & ( Xphi @ Xx ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(ex1I_type,type,
% 3.08/1.61 ex1I: $o ).
% 3.08/1.61
% 3.08/1.61 thf(ex1I,definition,
% 3.08/1.61 ( ex1I
% 3.08/1.61 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( Xphi @ Xx )
% 3.08/1.61 => ( ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ A )
% 3.08/1.61 => ( ( Xphi @ Xy )
% 3.08/1.61 => ( Xy = Xx ) ) )
% 3.08/1.61 => ( ex1 @ A
% 3.08/1.61 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(ex1I2_type,type,
% 3.08/1.61 ex1I2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(ex1I2,definition,
% 3.08/1.61 ( ex1I2
% 3.08/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 3.08/1.61 ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ A )
% 3.08/1.61 => ( ( Xphi @ Xx )
% 3.08/1.61 => ( ( Xphi @ Xy )
% 3.08/1.61 => ( Xx = Xy ) ) ) ) )
% 3.08/1.61 => ( ? [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 & ( Xphi @ Xx ) )
% 3.08/1.61 => ( ex1 @ A
% 3.08/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(singletonsuniq_type,type,
% 3.08/1.61 singletonsuniq: $o ).
% 3.08/1.61
% 3.08/1.61 thf(singletonsuniq,definition,
% 3.08/1.61 ( singletonsuniq
% 3.08/1.61 = ( ! [Xx: $i,Xy: $i] :
% 3.08/1.61 ( ( ( setadjoin @ Xx @ emptyset )
% 3.08/1.61 = ( setadjoin @ Xy @ emptyset ) )
% 3.08/1.61 => ( Xx = Xy ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(atmost1p_type,type,
% 3.08/1.61 atmost1p: $i > $o ).
% 3.08/1.61
% 3.08/1.61 thf(atleast2p_type,type,
% 3.08/1.61 atleast2p: $i > $o ).
% 3.08/1.61
% 3.08/1.61 thf(atmost2p_type,type,
% 3.08/1.61 atmost2p: $i > $o ).
% 3.08/1.61
% 3.08/1.61 thf(upairsetp_type,type,
% 3.08/1.61 upairsetp: $i > $o ).
% 3.08/1.61
% 3.08/1.61 thf(setukpairinjL1_type,type,
% 3.08/1.61 setukpairinjL1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setukpairinjL1,definition,
% 3.08/1.61 ( setukpairinjL1
% 3.08/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.08/1.61 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 3.08/1.61 => ( Xx = Xz ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(kfstsingleton_type,type,
% 3.08/1.61 kfstsingleton: $o ).
% 3.08/1.61
% 3.08/1.61 thf(kfstsingleton,definition,
% 3.08/1.61 ( kfstsingleton
% 3.08/1.61 = ( ! [Xu: $i] :
% 3.08/1.61 ( ( iskpair @ Xu )
% 3.08/1.61 => ( singleton
% 3.08/1.61 @ ( dsetconstr @ ( setunion @ Xu )
% 3.08/1.61 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(theprop_type,type,
% 3.08/1.61 theprop: $o ).
% 3.08/1.61
% 3.08/1.61 thf(theprop,definition,
% 3.08/1.61 ( theprop
% 3.08/1.61 = ( ! [X: $i] :
% 3.08/1.61 ( ( singleton @ X )
% 3.08/1.61 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(kfst_type,type,
% 3.08/1.61 kfst: $i > $i ).
% 3.08/1.61
% 3.08/1.61 thf(kfstpairEq_type,type,
% 3.08/1.61 kfstpairEq: $o ).
% 3.08/1.61
% 3.08/1.61 thf(kfstpairEq,definition,
% 3.08/1.61 ( kfstpairEq
% 3.08/1.61 = ( ! [Xx: $i,Xy: $i] :
% 3.08/1.61 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 3.08/1.61 = Xx ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(cartprodfstin_type,type,
% 3.08/1.61 cartprodfstin: $o ).
% 3.08/1.61
% 3.08/1.61 thf(cartprodfstin,definition,
% 3.08/1.61 ( cartprodfstin
% 3.08/1.61 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.08/1.61 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.08/1.61 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setukpairinjL2_type,type,
% 3.08/1.61 setukpairinjL2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setukpairinjL2,definition,
% 3.08/1.61 ( setukpairinjL2
% 3.08/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.08/1.61 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.08/1.61 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.08/1.61 => ( Xx = Xz ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setukpairinjL_type,type,
% 3.08/1.61 setukpairinjL: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setukpairinjL,definition,
% 3.08/1.61 ( setukpairinjL
% 3.08/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.08/1.61 ( ( ( kpair @ Xx @ Xy )
% 3.08/1.61 = ( kpair @ Xz @ Xu ) )
% 3.08/1.61 => ( Xx = Xz ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setukpairinjR11_type,type,
% 3.08/1.61 setukpairinjR11: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setukpairinjR11,definition,
% 3.08/1.61 ( setukpairinjR11
% 3.08/1.61 = ( ! [Xx: $i,Xy: $i] :
% 3.08/1.61 ( ( Xx = Xy )
% 3.08/1.61 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.08/1.61 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setukpairinjR12_type,type,
% 3.08/1.61 setukpairinjR12: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setukpairinjR12,definition,
% 3.08/1.61 ( setukpairinjR12
% 3.08/1.61 = ( ! [Xx: $i,Xy: $i] :
% 3.08/1.61 ( ( Xx = Xy )
% 3.08/1.61 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.08/1.61 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setukpairinjR1_type,type,
% 3.08/1.61 setukpairinjR1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setukpairinjR1,definition,
% 3.08/1.61 ( setukpairinjR1
% 3.08/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.08/1.61 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.08/1.61 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.08/1.61 => ( ( Xz = Xu )
% 3.08/1.61 => ( Xy = Xu ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(upairequniteq_type,type,
% 3.08/1.61 upairequniteq: $o ).
% 3.08/1.61
% 3.08/1.61 thf(upairequniteq,definition,
% 3.08/1.61 ( upairequniteq
% 3.08/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.08/1.61 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.08/1.61 = ( setadjoin @ Xz @ emptyset ) )
% 3.08/1.61 => ( Xx = Xy ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setukpairinjR2_type,type,
% 3.08/1.61 setukpairinjR2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setukpairinjR2,definition,
% 3.08/1.61 ( setukpairinjR2
% 3.08/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.08/1.61 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.08/1.61 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.08/1.61 => ( Xy = Xu ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setukpairinjR_type,type,
% 3.08/1.61 setukpairinjR: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setukpairinjR,definition,
% 3.08/1.61 ( setukpairinjR
% 3.08/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.08/1.61 ( ( ( kpair @ Xx @ Xy )
% 3.08/1.61 = ( kpair @ Xz @ Xu ) )
% 3.08/1.61 => ( Xy = Xu ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(ksndsingleton_type,type,
% 3.08/1.61 ksndsingleton: $o ).
% 3.08/1.61
% 3.08/1.61 thf(ksndsingleton,definition,
% 3.08/1.61 ( ksndsingleton
% 3.08/1.61 = ( ! [Xu: $i] :
% 3.08/1.61 ( ( iskpair @ Xu )
% 3.08/1.61 => ( singleton
% 3.08/1.61 @ ( dsetconstr @ ( setunion @ Xu )
% 3.08/1.61 @ ^ [Xx: $i] :
% 3.08/1.61 ( Xu
% 3.08/1.61 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(ksnd_type,type,
% 3.08/1.61 ksnd: $i > $i ).
% 3.08/1.61
% 3.08/1.61 thf(ksndpairEq_type,type,
% 3.08/1.61 ksndpairEq: $o ).
% 3.08/1.61
% 3.08/1.61 thf(ksndpairEq,definition,
% 3.08/1.61 ( ksndpairEq
% 3.08/1.61 = ( ! [Xx: $i,Xy: $i] :
% 3.08/1.61 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 3.08/1.61 = Xy ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(kpairsurjEq_type,type,
% 3.08/1.61 kpairsurjEq: $o ).
% 3.08/1.61
% 3.08/1.61 thf(kpairsurjEq,definition,
% 3.08/1.61 ( kpairsurjEq
% 3.08/1.61 = ( ! [Xu: $i] :
% 3.08/1.61 ( ( iskpair @ Xu )
% 3.08/1.61 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 3.08/1.61 = Xu ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(cartprodsndin_type,type,
% 3.08/1.61 cartprodsndin: $o ).
% 3.08/1.61
% 3.08/1.61 thf(cartprodsndin,definition,
% 3.08/1.61 ( cartprodsndin
% 3.08/1.61 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.08/1.61 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.08/1.61 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(cartprodpairmemEL_type,type,
% 3.08/1.61 cartprodpairmemEL: $o ).
% 3.08/1.61
% 3.08/1.61 thf(cartprodpairmemEL,definition,
% 3.08/1.61 ( cartprodpairmemEL
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 3.08/1.61 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 3.08/1.61 => ( in @ Xx @ A ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(cartprodpairmemER_type,type,
% 3.08/1.61 cartprodpairmemER: $o ).
% 3.08/1.61
% 3.08/1.61 thf(cartprodpairmemER,definition,
% 3.08/1.61 ( cartprodpairmemER
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 3.08/1.61 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 3.08/1.61 => ( in @ Xy @ B ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(cartprodmempaircEq_type,type,
% 3.08/1.61 cartprodmempaircEq: $o ).
% 3.08/1.61
% 3.08/1.61 thf(cartprodmempaircEq,definition,
% 3.08/1.61 ( cartprodmempaircEq
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ B )
% 3.08/1.61 => ( ( kpair @ Xx @ Xy )
% 3.08/1.61 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(cartprodfstpairEq_type,type,
% 3.08/1.61 cartprodfstpairEq: $o ).
% 3.08/1.61
% 3.08/1.61 thf(cartprodfstpairEq,definition,
% 3.08/1.61 ( cartprodfstpairEq
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ B )
% 3.08/1.61 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 3.08/1.61 = Xx ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(cartprodsndpairEq_type,type,
% 3.08/1.61 cartprodsndpairEq: $o ).
% 3.08/1.61
% 3.08/1.61 thf(cartprodsndpairEq,definition,
% 3.08/1.61 ( cartprodsndpairEq
% 3.08/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ B )
% 3.08/1.61 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 3.08/1.61 = Xy ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(cartprodpairsurjEq_type,type,
% 3.08/1.61 cartprodpairsurjEq: $o ).
% 3.08/1.61
% 3.08/1.61 thf(cartprodpairsurjEq,definition,
% 3.08/1.61 ( cartprodpairsurjEq
% 3.08/1.61 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.08/1.61 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.08/1.61 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 3.08/1.61 = Xu ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(breln_type,type,
% 3.08/1.61 breln: $i > $i > $i > $o ).
% 3.08/1.61
% 3.08/1.61 thf(breln,definition,
% 3.08/1.61 ( breln
% 3.08/1.61 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(dpsetconstr_type,type,
% 3.08/1.61 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 3.08/1.61
% 3.08/1.61 thf(dpsetconstrI_type,type,
% 3.08/1.61 dpsetconstrI: $o ).
% 3.08/1.61
% 3.08/1.61 thf(dpsetconstrI,definition,
% 3.08/1.61 ( dpsetconstrI
% 3.08/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ B )
% 3.08/1.61 => ( ( Xphi @ Xx @ Xy )
% 3.08/1.61 => ( in @ ( kpair @ Xx @ Xy )
% 3.08/1.61 @ ( dpsetconstr @ A @ B
% 3.08/1.61 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(dpsetconstrSub_type,type,
% 3.08/1.61 dpsetconstrSub: $o ).
% 3.08/1.61
% 3.08/1.61 thf(dpsetconstrSub,definition,
% 3.08/1.61 ( dpsetconstrSub
% 3.08/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.08/1.61 ( subset
% 3.08/1.61 @ ( dpsetconstr @ A @ B
% 3.08/1.61 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 3.08/1.61 @ ( cartprod @ A @ B ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setOfPairsIsBReln_type,type,
% 3.08/1.61 setOfPairsIsBReln: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setOfPairsIsBReln,definition,
% 3.08/1.61 ( setOfPairsIsBReln
% 3.08/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.08/1.61 ( breln @ A @ B
% 3.08/1.61 @ ( dpsetconstr @ A @ B
% 3.08/1.61 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(dpsetconstrERa_type,type,
% 3.08/1.61 dpsetconstrERa: $o ).
% 3.08/1.61
% 3.08/1.61 thf(dpsetconstrERa,definition,
% 3.08/1.61 ( dpsetconstrERa
% 3.08/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ B )
% 3.08/1.61 => ( ( in @ ( kpair @ Xx @ Xy )
% 3.08/1.61 @ ( dpsetconstr @ A @ B
% 3.08/1.61 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.08/1.61 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(dpsetconstrEL1_type,type,
% 3.08/1.61 dpsetconstrEL1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(dpsetconstrEL1,definition,
% 3.08/1.61 ( dpsetconstrEL1
% 3.08/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.08/1.61 ( ( in @ ( kpair @ Xx @ Xy )
% 3.08/1.61 @ ( dpsetconstr @ A @ B
% 3.08/1.61 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.08/1.61 => ( in @ Xx @ A ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(dpsetconstrEL2_type,type,
% 3.08/1.61 dpsetconstrEL2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(dpsetconstrEL2,definition,
% 3.08/1.61 ( dpsetconstrEL2
% 3.08/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.08/1.61 ( ( in @ ( kpair @ Xx @ Xy )
% 3.08/1.61 @ ( dpsetconstr @ A @ B
% 3.08/1.61 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.08/1.61 => ( in @ Xy @ B ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(dpsetconstrER_type,type,
% 3.08/1.61 dpsetconstrER: $o ).
% 3.08/1.61
% 3.08/1.61 thf(dpsetconstrER,definition,
% 3.08/1.61 ( dpsetconstrER
% 3.08/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.08/1.61 ( ( in @ ( kpair @ Xx @ Xy )
% 3.08/1.61 @ ( dpsetconstr @ A @ B
% 3.08/1.61 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.08/1.61 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(func_type,type,
% 3.08/1.61 func: $i > $i > $i > $o ).
% 3.08/1.61
% 3.08/1.61 thf(funcSet_type,type,
% 3.08/1.61 funcSet: $i > $i > $i ).
% 3.08/1.61
% 3.08/1.61 thf(funcImageSingleton_type,type,
% 3.08/1.61 funcImageSingleton: $o ).
% 3.08/1.61
% 3.08/1.61 thf(funcImageSingleton,definition,
% 3.08/1.61 ( funcImageSingleton
% 3.08/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.61 ( ( func @ A @ B @ Xf )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( singleton
% 3.08/1.61 @ ( dsetconstr @ B
% 3.08/1.61 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(apProp_type,type,
% 3.08/1.61 apProp: $o ).
% 3.08/1.61
% 3.08/1.61 thf(apProp,definition,
% 3.08/1.61 ( apProp
% 3.08/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.61 ( ( func @ A @ B @ Xf )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( in
% 3.08/1.61 @ ( setunion
% 3.08/1.61 @ ( dsetconstr @ B
% 3.08/1.61 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 3.08/1.61 @ B ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(ap_type,type,
% 3.08/1.61 ap: $i > $i > $i > $i > $i ).
% 3.08/1.61
% 3.08/1.61 thf(app_type,type,
% 3.08/1.61 app: $o ).
% 3.08/1.61
% 3.08/1.61 thf(app,definition,
% 3.08/1.61 ( app
% 3.08/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.61 ( ( func @ A @ B @ Xf )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(infuncsetfunc_type,type,
% 3.08/1.61 infuncsetfunc: $o ).
% 3.08/1.61
% 3.08/1.61 thf(infuncsetfunc,definition,
% 3.08/1.61 ( infuncsetfunc
% 3.08/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.61 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.08/1.61 => ( func @ A @ B @ Xf ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(ap2p_type,type,
% 3.08/1.61 ap2p: $o ).
% 3.08/1.61
% 3.08/1.61 thf(ap2p,definition,
% 3.08/1.61 ( ap2p
% 3.08/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.61 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(funcinfuncset_type,type,
% 3.08/1.61 funcinfuncset: $o ).
% 3.08/1.61
% 3.08/1.61 thf(funcinfuncset,definition,
% 3.08/1.61 ( funcinfuncset
% 3.08/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.61 ( ( func @ A @ B @ Xf )
% 3.08/1.61 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(lamProp_type,type,
% 3.08/1.61 lamProp: $o ).
% 3.08/1.61
% 3.08/1.61 thf(lamProp,definition,
% 3.08/1.61 ( lamProp
% 3.08/1.61 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.08/1.61 ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.08/1.61 => ( func @ A @ B
% 3.08/1.61 @ ( dpsetconstr @ A @ B
% 3.08/1.61 @ ^ [Xx: $i,Xy: $i] :
% 3.08/1.61 ( ( Xf @ Xx )
% 3.08/1.61 = Xy ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(lam_type,type,
% 3.08/1.61 lam: $i > $i > ( $i > $i ) > $i ).
% 3.08/1.61
% 3.08/1.61 thf(lamp_type,type,
% 3.08/1.61 lamp: $o ).
% 3.08/1.61
% 3.08/1.61 thf(lamp,definition,
% 3.08/1.61 ( lamp
% 3.08/1.61 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.08/1.61 ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.08/1.61 => ( func @ A @ B
% 3.08/1.61 @ ( lam @ A @ B
% 3.08/1.61 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(lam2p_type,type,
% 3.08/1.61 lam2p: $o ).
% 3.08/1.61
% 3.08/1.61 thf(lam2p,definition,
% 3.08/1.61 ( lam2p
% 3.08/1.61 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.08/1.61 ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.08/1.61 => ( in
% 3.08/1.61 @ ( lam @ A @ B
% 3.08/1.61 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 3.08/1.61 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(brelnall1_type,type,
% 3.08/1.61 brelnall1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(brelnall1,definition,
% 3.08/1.61 ( brelnall1
% 3.08/1.61 = ( ! [A: $i,B: $i,R: $i] :
% 3.08/1.61 ( ( breln @ A @ B @ R )
% 3.08/1.61 => ! [Xphi: $i > $o] :
% 3.08/1.61 ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ B )
% 3.08/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.08/1.61 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ R )
% 3.08/1.61 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(brelnall2_type,type,
% 3.08/1.61 brelnall2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(brelnall2,definition,
% 3.08/1.61 ( brelnall2
% 3.08/1.61 = ( ! [A: $i,B: $i,R: $i] :
% 3.08/1.61 ( ( breln @ A @ B @ R )
% 3.08/1.61 => ! [Xphi: $i > $o] :
% 3.08/1.61 ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ B )
% 3.08/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.08/1.61 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ R )
% 3.08/1.61 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(ex1E2_type,type,
% 3.08/1.61 ex1E2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(ex1E2,definition,
% 3.08/1.61 ( ex1E2
% 3.08/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 3.08/1.61 ( ( ex1 @ A
% 3.08/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ A )
% 3.08/1.61 => ( ( Xphi @ Xx )
% 3.08/1.61 => ( ( Xphi @ Xy )
% 3.08/1.61 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(funcGraphProp1_type,type,
% 3.08/1.61 funcGraphProp1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(funcGraphProp1,definition,
% 3.08/1.61 ( funcGraphProp1
% 3.08/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.61 ( ( func @ A @ B @ Xf )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(funcGraphProp3_type,type,
% 3.08/1.61 funcGraphProp3: $o ).
% 3.08/1.61
% 3.08/1.61 thf(funcGraphProp3,definition,
% 3.08/1.61 ( funcGraphProp3
% 3.08/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.61 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(funcGraphProp2_type,type,
% 3.08/1.61 funcGraphProp2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(funcGraphProp2,definition,
% 3.08/1.61 ( funcGraphProp2
% 3.08/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.61 ( ( func @ A @ B @ Xf )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ B )
% 3.08/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 3.08/1.61 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.08/1.61 = Xy ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(funcextLem_type,type,
% 3.08/1.61 funcextLem: $o ).
% 3.08/1.61
% 3.08/1.61 thf(funcextLem,definition,
% 3.08/1.61 ( funcextLem
% 3.08/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.61 ( ( func @ A @ B @ Xf )
% 3.08/1.61 => ! [Xg: $i] :
% 3.08/1.61 ( ( func @ A @ B @ Xg )
% 3.08/1.61 => ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.08/1.61 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ B )
% 3.08/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 3.08/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(funcGraphProp4_type,type,
% 3.08/1.61 funcGraphProp4: $o ).
% 3.08/1.61
% 3.08/1.61 thf(funcGraphProp4,definition,
% 3.08/1.61 ( funcGraphProp4
% 3.08/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.61 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ B )
% 3.08/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 3.08/1.61 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.08/1.61 = Xy ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(subbreln_type,type,
% 3.08/1.61 subbreln: $o ).
% 3.08/1.61
% 3.08/1.61 thf(subbreln,definition,
% 3.08/1.61 ( subbreln
% 3.08/1.61 = ( ! [A: $i,B: $i,R: $i] :
% 3.08/1.61 ( ( breln @ A @ B @ R )
% 3.08/1.61 => ! [S: $i] :
% 3.08/1.61 ( ( breln @ A @ B @ S )
% 3.08/1.61 => ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ B )
% 3.08/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.08/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.08/1.61 => ( subset @ R @ S ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(eqbreln_type,type,
% 3.08/1.61 eqbreln: $o ).
% 3.08/1.61
% 3.08/1.61 thf(eqbreln,definition,
% 3.08/1.61 ( eqbreln
% 3.08/1.61 = ( ! [A: $i,B: $i,R: $i] :
% 3.08/1.61 ( ( breln @ A @ B @ R )
% 3.08/1.61 => ! [S: $i] :
% 3.08/1.61 ( ( breln @ A @ B @ S )
% 3.08/1.61 => ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ B )
% 3.08/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.08/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.08/1.61 => ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ B )
% 3.08/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.08/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 3.08/1.61 => ( R = S ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(funcext_type,type,
% 3.08/1.61 funcext: $o ).
% 3.08/1.61
% 3.08/1.61 thf(funcext,definition,
% 3.08/1.61 ( funcext
% 3.08/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.61 ( ( func @ A @ B @ Xf )
% 3.08/1.61 => ! [Xg: $i] :
% 3.08/1.61 ( ( func @ A @ B @ Xg )
% 3.08/1.61 => ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.08/1.61 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.08/1.61 => ( Xf = Xg ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(funcext2_type,type,
% 3.08/1.61 funcext2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(funcext2,definition,
% 3.08/1.61 ( funcext2
% 3.08/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.61 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.08/1.61 => ! [Xg: $i] :
% 3.08/1.61 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 3.08/1.61 => ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.08/1.61 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.08/1.61 => ( Xf = Xg ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(ap2apEq1_type,type,
% 3.08/1.61 ap2apEq1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(ap2apEq1,definition,
% 3.08/1.61 ( ap2apEq1
% 3.08/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.61 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.08/1.61 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(ap2apEq2_type,type,
% 3.08/1.61 ap2apEq2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(ap2apEq2,definition,
% 3.08/1.61 ( ap2apEq2
% 3.08/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.61 ( ( func @ A @ B @ Xf )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.08/1.61 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(beta1_type,type,
% 3.08/1.61 beta1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(beta1,definition,
% 3.08/1.61 ( beta1
% 3.08/1.61 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.08/1.61 ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( ap @ A @ B
% 3.08/1.61 @ ( lam @ A @ B
% 3.08/1.61 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 3.08/1.61 @ Xx )
% 3.08/1.61 = ( Xf @ Xx ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(eta1_type,type,
% 3.08/1.61 eta1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(eta1,definition,
% 3.08/1.61 ( eta1
% 3.08/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.61 ( ( func @ A @ B @ Xf )
% 3.08/1.61 => ( ( lam @ A @ B
% 3.08/1.61 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 3.08/1.61 = Xf ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(lam2lamEq_type,type,
% 3.08/1.61 lam2lamEq: $o ).
% 3.08/1.61
% 3.08/1.61 thf(lam2lamEq,definition,
% 3.08/1.61 ( lam2lamEq
% 3.08/1.61 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.08/1.61 ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.08/1.61 => ( ( lam @ A @ B
% 3.08/1.61 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 3.08/1.61 = ( lam @ A @ B
% 3.08/1.61 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(beta2_type,type,
% 3.08/1.61 beta2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(beta2,definition,
% 3.08/1.61 ( beta2
% 3.08/1.61 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.08/1.61 ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( ap @ A @ B
% 3.08/1.61 @ ( lam @ A @ B
% 3.08/1.61 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 3.08/1.61 @ Xx )
% 3.08/1.61 = ( Xf @ Xx ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(eta2_type,type,
% 3.08/1.61 eta2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(eta2,definition,
% 3.08/1.61 ( eta2
% 3.08/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.08/1.61 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.08/1.61 => ( ( lam @ A @ B
% 3.08/1.61 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 3.08/1.61 = Xf ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(iffalseProp1_type,type,
% 3.08/1.61 iffalseProp1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(iffalseProp1,definition,
% 3.08/1.61 ( iffalseProp1
% 3.08/1.61 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ A )
% 3.08/1.61 => ( ~ Xphi
% 3.08/1.61 => ( in @ Xy
% 3.08/1.61 @ ( dsetconstr @ A
% 3.08/1.61 @ ^ [Xz: $i] :
% 3.08/1.61 ( ( Xphi
% 3.08/1.61 & ( Xz = Xx ) )
% 3.08/1.61 | ( ~ Xphi
% 3.08/1.61 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(iffalseProp2_type,type,
% 3.08/1.61 iffalseProp2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(iffalseProp2,definition,
% 3.08/1.61 ( iffalseProp2
% 3.08/1.61 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ A )
% 3.08/1.61 => ( ~ Xphi
% 3.08/1.61 => ( ( dsetconstr @ A
% 3.08/1.61 @ ^ [Xz: $i] :
% 3.08/1.61 ( ( Xphi
% 3.08/1.61 & ( Xz = Xx ) )
% 3.08/1.61 | ( ~ Xphi
% 3.08/1.61 & ( Xz = Xy ) ) ) )
% 3.08/1.61 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(iftrueProp1_type,type,
% 3.08/1.61 iftrueProp1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(iftrueProp1,definition,
% 3.08/1.61 ( iftrueProp1
% 3.08/1.61 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ A )
% 3.08/1.61 => ( Xphi
% 3.08/1.61 => ( in @ Xx
% 3.08/1.61 @ ( dsetconstr @ A
% 3.08/1.61 @ ^ [Xz: $i] :
% 3.08/1.61 ( ( Xphi
% 3.08/1.61 & ( Xz = Xx ) )
% 3.08/1.61 | ( ~ Xphi
% 3.08/1.61 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(iftrueProp2_type,type,
% 3.08/1.61 iftrueProp2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(iftrueProp2,definition,
% 3.08/1.61 ( iftrueProp2
% 3.08/1.61 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ A )
% 3.08/1.61 => ( Xphi
% 3.08/1.61 => ( ( dsetconstr @ A
% 3.08/1.61 @ ^ [Xz: $i] :
% 3.08/1.61 ( ( Xphi
% 3.08/1.61 & ( Xz = Xx ) )
% 3.08/1.61 | ( ~ Xphi
% 3.08/1.61 & ( Xz = Xy ) ) ) )
% 3.08/1.61 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(ifSingleton_type,type,
% 3.08/1.61 ifSingleton: $o ).
% 3.08/1.61
% 3.08/1.61 thf(ifSingleton,definition,
% 3.08/1.61 ( ifSingleton
% 3.08/1.61 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ A )
% 3.08/1.61 => ( singleton
% 3.08/1.61 @ ( dsetconstr @ A
% 3.08/1.61 @ ^ [Xz: $i] :
% 3.08/1.61 ( ( Xphi
% 3.08/1.61 & ( Xz = Xx ) )
% 3.08/1.61 | ( ~ Xphi
% 3.08/1.61 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(if_type,type,
% 3.08/1.61 if: $i > $o > $i > $i > $i ).
% 3.08/1.61
% 3.08/1.61 thf(ifp_type,type,
% 3.08/1.61 ifp: $o ).
% 3.08/1.61
% 3.08/1.61 thf(ifp,definition,
% 3.08/1.61 ( ifp
% 3.08/1.61 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ A )
% 3.08/1.61 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(theeq_type,type,
% 3.08/1.61 theeq: $o ).
% 3.08/1.61
% 3.08/1.61 thf(theeq,definition,
% 3.08/1.61 ( theeq
% 3.08/1.61 = ( ! [X: $i] :
% 3.08/1.61 ( ( singleton @ X )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ X )
% 3.08/1.61 => ( ( setunion @ X )
% 3.08/1.61 = Xx ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(iftrue_type,type,
% 3.08/1.61 iftrue: $o ).
% 3.08/1.61
% 3.08/1.61 thf(iftrue,definition,
% 3.08/1.61 ( iftrue
% 3.08/1.61 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ A )
% 3.08/1.61 => ( Xphi
% 3.08/1.61 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 3.08/1.61 = Xx ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(iffalse_type,type,
% 3.08/1.61 iffalse: $o ).
% 3.08/1.61
% 3.08/1.61 thf(iffalse,definition,
% 3.08/1.61 ( iffalse
% 3.08/1.61 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ A )
% 3.08/1.61 => ( ~ Xphi
% 3.08/1.61 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 3.08/1.61 = Xy ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(iftrueorfalse_type,type,
% 3.08/1.61 iftrueorfalse: $o ).
% 3.08/1.61
% 3.08/1.61 thf(iftrueorfalse,definition,
% 3.08/1.61 ( iftrueorfalse
% 3.08/1.61 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ A )
% 3.08/1.61 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(binintersectT_lem_type,type,
% 3.08/1.61 binintersectT_lem: $o ).
% 3.08/1.61
% 3.08/1.61 thf(binintersectT_lem,definition,
% 3.08/1.61 ( binintersectT_lem
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(binunionT_lem_type,type,
% 3.08/1.61 binunionT_lem: $o ).
% 3.08/1.61
% 3.08/1.61 thf(binunionT_lem,definition,
% 3.08/1.61 ( binunionT_lem
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(powersetT_lem_type,type,
% 3.08/1.61 powersetT_lem: $o ).
% 3.08/1.61
% 3.08/1.61 thf(powersetT_lem,definition,
% 3.08/1.61 ( powersetT_lem
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setminusT_lem_type,type,
% 3.08/1.61 setminusT_lem: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setminusT_lem,definition,
% 3.08/1.61 ( setminusT_lem
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(complementT_lem_type,type,
% 3.08/1.61 complementT_lem: $o ).
% 3.08/1.61
% 3.08/1.61 thf(complementT_lem,definition,
% 3.08/1.61 ( complementT_lem
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setextT_type,type,
% 3.08/1.61 setextT: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setextT,definition,
% 3.08/1.61 ( setextT
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( in @ Xx @ X )
% 3.08/1.61 => ( in @ Xx @ Y ) ) )
% 3.08/1.61 => ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( in @ Xx @ Y )
% 3.08/1.61 => ( in @ Xx @ X ) ) )
% 3.08/1.61 => ( X = Y ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(subsetTI_type,type,
% 3.08/1.61 subsetTI: $o ).
% 3.08/1.61
% 3.08/1.61 thf(subsetTI,definition,
% 3.08/1.61 ( subsetTI
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( in @ Xx @ X )
% 3.08/1.61 => ( in @ Xx @ Y ) ) )
% 3.08/1.61 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(powersetTI1_type,type,
% 3.08/1.61 powersetTI1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(powersetTI1,definition,
% 3.08/1.61 ( powersetTI1
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( in @ Xx @ X )
% 3.08/1.61 => ( in @ Xx @ Y ) ) )
% 3.08/1.61 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(powersetTE1_type,type,
% 3.08/1.61 powersetTE1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(powersetTE1,definition,
% 3.08/1.61 ( powersetTE1
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( in @ X @ ( powerset @ Y ) )
% 3.08/1.61 => ( ( in @ Xx @ X )
% 3.08/1.61 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(complementTI1_type,type,
% 3.08/1.61 complementTI1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(complementTI1,definition,
% 3.08/1.61 ( complementTI1
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( in @ Xx @ X )
% 3.08/1.61 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(complementTE1_type,type,
% 3.08/1.61 complementTE1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(complementTE1,definition,
% 3.08/1.61 ( complementTE1
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 3.08/1.61 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(binintersectTELcontra_type,type,
% 3.08/1.61 binintersectTELcontra: $o ).
% 3.08/1.61
% 3.08/1.61 thf(binintersectTELcontra,definition,
% 3.08/1.61 ( binintersectTELcontra
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ~ ( in @ Xx @ X )
% 3.08/1.61 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(binintersectTERcontra_type,type,
% 3.08/1.61 binintersectTERcontra: $o ).
% 3.08/1.61
% 3.08/1.61 thf(binintersectTERcontra,definition,
% 3.08/1.61 ( binintersectTERcontra
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ~ ( in @ Xx @ Y )
% 3.08/1.61 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(contrasubsetT_type,type,
% 3.08/1.61 contrasubsetT: $o ).
% 3.08/1.61
% 3.08/1.61 thf(contrasubsetT,definition,
% 3.08/1.61 ( contrasubsetT
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.08/1.61 => ( ( in @ Xx @ Y )
% 3.08/1.61 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(contrasubsetT1_type,type,
% 3.08/1.61 contrasubsetT1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(contrasubsetT1,definition,
% 3.08/1.61 ( contrasubsetT1
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( subset @ X @ Y )
% 3.08/1.61 => ( ~ ( in @ Xx @ Y )
% 3.08/1.61 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(contrasubsetT2_type,type,
% 3.08/1.61 contrasubsetT2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(contrasubsetT2,definition,
% 3.08/1.61 ( contrasubsetT2
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ( ( subset @ X @ Y )
% 3.08/1.61 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(contrasubsetT3_type,type,
% 3.08/1.61 contrasubsetT3: $o ).
% 3.08/1.61
% 3.08/1.61 thf(contrasubsetT3,definition,
% 3.08/1.61 ( contrasubsetT3
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 3.08/1.61 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(doubleComplementI1_type,type,
% 3.08/1.61 doubleComplementI1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(doubleComplementI1,definition,
% 3.08/1.61 ( doubleComplementI1
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( in @ Xx @ X )
% 3.08/1.61 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(doubleComplementE1_type,type,
% 3.08/1.61 doubleComplementE1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(doubleComplementE1,definition,
% 3.08/1.61 ( doubleComplementE1
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 3.08/1.61 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(doubleComplementSub1_type,type,
% 3.08/1.61 doubleComplementSub1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(doubleComplementSub1,definition,
% 3.08/1.61 ( doubleComplementSub1
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(doubleComplementSub2_type,type,
% 3.08/1.61 doubleComplementSub2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(doubleComplementSub2,definition,
% 3.08/1.61 ( doubleComplementSub2
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(doubleComplementEq_type,type,
% 3.08/1.61 doubleComplementEq: $o ).
% 3.08/1.61
% 3.08/1.61 thf(doubleComplementEq,definition,
% 3.08/1.61 ( doubleComplementEq
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ( X
% 3.08/1.61 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(complementTnotintersectT_type,type,
% 3.08/1.61 complementTnotintersectT: $o ).
% 3.08/1.61
% 3.08/1.61 thf(complementTnotintersectT,definition,
% 3.08/1.61 ( complementTnotintersectT
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.08/1.61 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(complementImpComplementIntersect_type,type,
% 3.08/1.61 complementImpComplementIntersect: $o ).
% 3.08/1.61
% 3.08/1.61 thf(complementImpComplementIntersect,definition,
% 3.08/1.61 ( complementImpComplementIntersect
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.08/1.61 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(complementSubsetComplementIntersect_type,type,
% 3.08/1.61 complementSubsetComplementIntersect: $o ).
% 3.08/1.61
% 3.08/1.61 thf(complementSubsetComplementIntersect,definition,
% 3.08/1.61 ( complementSubsetComplementIntersect
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(complementInPowersetComplementIntersect_type,type,
% 3.08/1.61 complementInPowersetComplementIntersect: $o ).
% 3.08/1.61
% 3.08/1.61 thf(complementInPowersetComplementIntersect,definition,
% 3.08/1.61 ( complementInPowersetComplementIntersect
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(contraSubsetComplement_type,type,
% 3.08/1.61 contraSubsetComplement: $o ).
% 3.08/1.61
% 3.08/1.61 thf(contraSubsetComplement,definition,
% 3.08/1.61 ( contraSubsetComplement
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( in @ Xx @ Y )
% 3.08/1.61 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(complementTcontraSubset_type,type,
% 3.08/1.61 complementTcontraSubset: $o ).
% 3.08/1.61
% 3.08/1.61 thf(complementTcontraSubset,definition,
% 3.08/1.61 ( complementTcontraSubset
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.08/1.61 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(binunionTILcontra_type,type,
% 3.08/1.61 binunionTILcontra: $o ).
% 3.08/1.61
% 3.08/1.61 thf(binunionTILcontra,definition,
% 3.08/1.61 ( binunionTILcontra
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.08/1.61 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(binunionTIRcontra_type,type,
% 3.08/1.61 binunionTIRcontra: $o ).
% 3.08/1.61
% 3.08/1.61 thf(binunionTIRcontra,definition,
% 3.08/1.61 ( binunionTIRcontra
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.08/1.61 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(inIntersectImpInUnion_type,type,
% 3.08/1.61 inIntersectImpInUnion: $o ).
% 3.08/1.61
% 3.08/1.61 thf(inIntersectImpInUnion,definition,
% 3.08/1.61 ( inIntersectImpInUnion
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Z: $i] :
% 3.08/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.08/1.61 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(inIntersectImpInUnion2_type,type,
% 3.08/1.61 inIntersectImpInUnion2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(inIntersectImpInUnion2,definition,
% 3.08/1.61 ( inIntersectImpInUnion2
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Z: $i] :
% 3.08/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.08/1.61 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(inIntersectImpInIntersectUnions_type,type,
% 3.08/1.61 inIntersectImpInIntersectUnions: $o ).
% 3.08/1.61
% 3.08/1.61 thf(inIntersectImpInIntersectUnions,definition,
% 3.08/1.61 ( inIntersectImpInIntersectUnions
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Z: $i] :
% 3.08/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.08/1.61 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(intersectInPowersetIntersectUnions_type,type,
% 3.08/1.61 intersectInPowersetIntersectUnions: $o ).
% 3.08/1.61
% 3.08/1.61 thf(intersectInPowersetIntersectUnions,definition,
% 3.08/1.61 ( intersectInPowersetIntersectUnions
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Z: $i] :
% 3.08/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 3.08/1.61 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(inComplementUnionImpNotIn1_type,type,
% 3.08/1.61 inComplementUnionImpNotIn1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(inComplementUnionImpNotIn1,definition,
% 3.08/1.61 ( inComplementUnionImpNotIn1
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.08/1.61 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(inComplementUnionImpInComplement1_type,type,
% 3.08/1.61 inComplementUnionImpInComplement1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(inComplementUnionImpInComplement1,definition,
% 3.08/1.61 ( inComplementUnionImpInComplement1
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.08/1.61 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(binunionTE_type,type,
% 3.08/1.61 binunionTE: $o ).
% 3.08/1.61
% 3.08/1.61 thf(binunionTE,definition,
% 3.08/1.61 ( binunionTE
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Xphi: $o,Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.08/1.61 => ( ( ( in @ Xx @ X )
% 3.08/1.61 => Xphi )
% 3.08/1.61 => ( ( ( in @ Xx @ Y )
% 3.08/1.61 => Xphi )
% 3.08/1.61 => Xphi ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(binunionTEcontra_type,type,
% 3.08/1.61 binunionTEcontra: $o ).
% 3.08/1.61
% 3.08/1.61 thf(binunionTEcontra,definition,
% 3.08/1.61 ( binunionTEcontra
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ~ ( in @ Xx @ X )
% 3.08/1.61 => ( ~ ( in @ Xx @ Y )
% 3.08/1.61 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(demorgan2a1_type,type,
% 3.08/1.61 demorgan2a1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(demorgan2a1,definition,
% 3.08/1.61 ( demorgan2a1
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.08/1.61 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(complementUnionInPowersetComplement_type,type,
% 3.08/1.61 complementUnionInPowersetComplement: $o ).
% 3.08/1.61
% 3.08/1.61 thf(complementUnionInPowersetComplement,definition,
% 3.08/1.61 ( complementUnionInPowersetComplement
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(demorgan2a2_type,type,
% 3.08/1.61 demorgan2a2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(demorgan2a2,definition,
% 3.08/1.61 ( demorgan2a2
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.08/1.61 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(demorgan1a_type,type,
% 3.08/1.61 demorgan1a: $o ).
% 3.08/1.61
% 3.08/1.61 thf(demorgan1a,definition,
% 3.08/1.61 ( demorgan1a
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 3.08/1.61 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(demorgan1b_type,type,
% 3.08/1.61 demorgan1b: $o ).
% 3.08/1.61
% 3.08/1.61 thf(demorgan1b,definition,
% 3.08/1.61 ( demorgan1b
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 3.08/1.61 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(demorgan1_type,type,
% 3.08/1.61 demorgan1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(demorgan1,definition,
% 3.08/1.61 ( demorgan1
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 3.08/1.61 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(demorgan2a_type,type,
% 3.08/1.61 demorgan2a: $o ).
% 3.08/1.61
% 3.08/1.61 thf(demorgan2a,definition,
% 3.08/1.61 ( demorgan2a
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.08/1.61 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(demorgan2b2_type,type,
% 3.08/1.61 demorgan2b2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(demorgan2b2,definition,
% 3.08/1.61 ( demorgan2b2
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.08/1.61 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 3.08/1.61 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(demorgan2b_type,type,
% 3.08/1.61 demorgan2b: $o ).
% 3.08/1.61
% 3.08/1.61 thf(demorgan2b,definition,
% 3.08/1.61 ( demorgan2b
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 3.08/1.61 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(demorgan2_type,type,
% 3.08/1.61 demorgan2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(demorgan2,definition,
% 3.08/1.61 ( demorgan2
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 3.08/1.61 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(woz13rule0_type,type,
% 3.08/1.61 woz13rule0: $o ).
% 3.08/1.61
% 3.08/1.61 thf(woz13rule0,definition,
% 3.08/1.61 ( woz13rule0
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.08/1.61 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(woz13rule1_type,type,
% 3.08/1.61 woz13rule1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(woz13rule1,definition,
% 3.08/1.61 ( woz13rule1
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Z: $i] :
% 3.08/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 3.08/1.61 => ( ( subset @ X @ Z )
% 3.08/1.61 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(woz13rule2_type,type,
% 3.08/1.61 woz13rule2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(woz13rule2,definition,
% 3.08/1.61 ( woz13rule2
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Z: $i] :
% 3.08/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 3.08/1.61 => ( ( subset @ Y @ Z )
% 3.08/1.61 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(woz13rule3_type,type,
% 3.08/1.61 woz13rule3: $o ).
% 3.08/1.61
% 3.08/1.61 thf(woz13rule3,definition,
% 3.08/1.61 ( woz13rule3
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Z: $i] :
% 3.08/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 3.08/1.61 => ( ( subset @ X @ Y )
% 3.08/1.61 => ( ( subset @ X @ Z )
% 3.08/1.61 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(woz13rule4_type,type,
% 3.08/1.61 woz13rule4: $o ).
% 3.08/1.61
% 3.08/1.61 thf(woz13rule4,definition,
% 3.08/1.61 ( woz13rule4
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Z: $i] :
% 3.08/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 3.08/1.61 => ! [W: $i] :
% 3.08/1.61 ( ( in @ W @ ( powerset @ A ) )
% 3.08/1.61 => ( ( subset @ X @ Z )
% 3.08/1.61 => ( ( subset @ Y @ W )
% 3.08/1.61 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(woz1_1_type,type,
% 3.08/1.61 woz1_1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(woz1_1,definition,
% 3.08/1.61 ( woz1_1
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(woz1_2_type,type,
% 3.08/1.61 woz1_2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(woz1_2,definition,
% 3.08/1.61 ( woz1_2
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Z: $i] :
% 3.08/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 3.08/1.61 => ! [W: $i] :
% 3.08/1.61 ( ( in @ W @ ( powerset @ A ) )
% 3.08/1.61 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 3.08/1.61 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(woz1_3_type,type,
% 3.08/1.61 woz1_3: $o ).
% 3.08/1.61
% 3.08/1.61 thf(woz1_3,definition,
% 3.08/1.61 ( woz1_3
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ! [Z: $i] :
% 3.08/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 3.08/1.61 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(woz1_4_type,type,
% 3.08/1.61 woz1_4: $o ).
% 3.08/1.61
% 3.08/1.61 thf(woz1_4,definition,
% 3.08/1.61 ( woz1_4
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.08/1.61 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(woz1_5_type,type,
% 3.08/1.61 woz1_5: $o ).
% 3.08/1.61
% 3.08/1.61 thf(woz1_5,definition,
% 3.08/1.61 ( woz1_5
% 3.08/1.61 = ( ! [A: $i,X: $i] :
% 3.08/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.08/1.61 => ! [Y: $i] :
% 3.08/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.08/1.61 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(breln1_type,type,
% 3.08/1.61 breln1: $i > $i > $o ).
% 3.08/1.61
% 3.08/1.61 thf(breln1,definition,
% 3.08/1.61 ( breln1
% 3.08/1.61 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(breln1all2_type,type,
% 3.08/1.61 breln1all2: $o ).
% 3.08/1.61
% 3.08/1.61 thf(breln1all2,definition,
% 3.08/1.61 ( breln1all2
% 3.08/1.61 = ( ! [A: $i,R: $i] :
% 3.08/1.61 ( ( breln1 @ A @ R )
% 3.08/1.61 => ! [Xphi: $i > $o] :
% 3.08/1.61 ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ A )
% 3.08/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.08/1.61 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ R )
% 3.08/1.61 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(breln1Set_type,type,
% 3.08/1.61 breln1Set: $i > $i ).
% 3.08/1.61
% 3.08/1.61 thf(breln1SetBreln1_type,type,
% 3.08/1.61 breln1SetBreln1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(breln1SetBreln1,definition,
% 3.08/1.61 ( breln1SetBreln1
% 3.08/1.61 = ( ! [A: $i,R: $i] :
% 3.08/1.61 ( ( in @ R @ ( breln1Set @ A ) )
% 3.08/1.61 => ( breln1 @ A @ R ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(transitive_type,type,
% 3.08/1.61 transitive: $i > $i > $o ).
% 3.08/1.61
% 3.08/1.61 thf(antisymmetric_type,type,
% 3.08/1.61 antisymmetric: $i > $i > $o ).
% 3.08/1.61
% 3.08/1.61 thf(reflexive_type,type,
% 3.08/1.61 reflexive: $i > $i > $o ).
% 3.08/1.61
% 3.08/1.61 thf(refltransitive_type,type,
% 3.08/1.61 refltransitive: $i > $i > $o ).
% 3.08/1.61
% 3.08/1.61 thf(refllinearorder_type,type,
% 3.08/1.61 refllinearorder: $i > $i > $o ).
% 3.08/1.61
% 3.08/1.61 thf(reflwellordering_type,type,
% 3.08/1.61 reflwellordering: $i > $i > $o ).
% 3.08/1.61
% 3.08/1.61 thf(choice2fnsingleton_type,type,
% 3.08/1.61 choice2fnsingleton: $o ).
% 3.08/1.61
% 3.08/1.61 thf(choice2fnsingleton,definition,
% 3.08/1.61 ( choice2fnsingleton
% 3.08/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.08/1.61 ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ? [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ B )
% 3.08/1.61 & ( Xphi @ Xx @ Xy ) ) )
% 3.08/1.61 => ! [R: $i] :
% 3.08/1.61 ( ( in @ R @ ( breln1Set @ B ) )
% 3.08/1.61 => ( ( reflwellordering @ B @ R )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ( singleton
% 3.08/1.61 @ ( dsetconstr @ B
% 3.08/1.61 @ ^ [Xy: $i] :
% 3.08/1.61 ( ( Xphi @ Xx @ Xy )
% 3.08/1.61 & ! [Xz: $i] :
% 3.08/1.61 ( ( in @ Xz @ B )
% 3.08/1.61 => ( ( Xphi @ Xx @ Xz )
% 3.08/1.61 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(setOfPairsIsBReln1_type,type,
% 3.08/1.61 setOfPairsIsBReln1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(setOfPairsIsBReln1,definition,
% 3.08/1.61 ( setOfPairsIsBReln1
% 3.08/1.61 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 3.08/1.61 ( breln1 @ A
% 3.08/1.61 @ ( dpsetconstr @ A @ A
% 3.08/1.61 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(breln1all1_type,type,
% 3.08/1.61 breln1all1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(breln1all1,definition,
% 3.08/1.61 ( breln1all1
% 3.08/1.61 = ( ! [A: $i,R: $i] :
% 3.08/1.61 ( ( breln1 @ A @ R )
% 3.08/1.61 => ! [Xphi: $i > $o] :
% 3.08/1.61 ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ A )
% 3.08/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.08/1.61 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ R )
% 3.08/1.61 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(subbreln1_type,type,
% 3.08/1.61 subbreln1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(subbreln1,definition,
% 3.08/1.61 ( subbreln1
% 3.08/1.61 = ( ! [A: $i,R: $i] :
% 3.08/1.61 ( ( breln1 @ A @ R )
% 3.08/1.61 => ! [S: $i] :
% 3.08/1.61 ( ( breln1 @ A @ S )
% 3.08/1.61 => ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ A )
% 3.08/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.08/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.08/1.61 => ( subset @ R @ S ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(eqbreln1_type,type,
% 3.08/1.61 eqbreln1: $o ).
% 3.08/1.61
% 3.08/1.61 thf(eqbreln1,definition,
% 3.08/1.61 ( eqbreln1
% 3.08/1.61 = ( ! [A: $i,R: $i] :
% 3.08/1.61 ( ( breln1 @ A @ R )
% 3.08/1.61 => ! [S: $i] :
% 3.08/1.61 ( ( breln1 @ A @ S )
% 3.08/1.61 => ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ A )
% 3.08/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.08/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.08/1.61 => ( ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ A )
% 3.08/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.08/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 3.08/1.61 => ( R = S ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(breln1invset_type,type,
% 3.08/1.61 breln1invset: $i > $i > $i ).
% 3.08/1.61
% 3.08/1.61 thf(breln1invset,definition,
% 3.08/1.61 ( breln1invset
% 3.08/1.61 = ( ^ [A: $i,R: $i] :
% 3.08/1.61 ( dpsetconstr @ A @ A
% 3.08/1.61 @ ^ [Xx: $i,Xy: $i] : ( in @ ( kpair @ Xy @ Xx ) @ R ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(breln1invprop_type,type,
% 3.08/1.61 breln1invprop: $o ).
% 3.08/1.61
% 3.08/1.61 thf(breln1invprop,definition,
% 3.08/1.61 ( breln1invprop
% 3.08/1.61 = ( ! [A: $i,R: $i] :
% 3.08/1.61 ( ( breln1 @ A @ R )
% 3.08/1.61 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(breln1invI_type,type,
% 3.08/1.61 breln1invI: $o ).
% 3.08/1.61
% 3.08/1.61 thf(breln1invI,definition,
% 3.08/1.61 ( breln1invI
% 3.08/1.61 = ( ! [A: $i,R: $i] :
% 3.08/1.61 ( ( breln1 @ A @ R )
% 3.08/1.61 => ! [Xx: $i] :
% 3.08/1.61 ( ( in @ Xx @ A )
% 3.08/1.61 => ! [Xy: $i] :
% 3.08/1.61 ( ( in @ Xy @ A )
% 3.08/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.08/1.61 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
% 3.08/1.61
% 3.08/1.61 thf(breln1invE,conjecture,
% 3.08/1.61 ( setextAx
% 3.08/1.61 => ( emptysetAx
% 3.08/1.61 => ( setadjoinAx
% 3.08/1.61 => ( powersetAx
% 3.08/1.61 => ( setunionAx
% 3.08/1.61 => ( omega0Ax
% 3.08/1.61 => ( omegaSAx
% 3.08/1.61 => ( omegaIndAx
% 3.08/1.61 => ( replAx
% 3.08/1.61 => ( foundationAx
% 3.08/1.61 => ( wellorderingAx
% 3.08/1.61 => ( descrp
% 3.08/1.61 => ( dsetconstrI
% 3.08/1.61 => ( dsetconstrEL
% 3.08/1.61 => ( dsetconstrER
% 3.08/1.61 => ( exuE1
% 3.08/1.61 => ( prop2setE
% 3.08/1.61 => ( emptysetE
% 3.08/1.61 => ( emptysetimpfalse
% 3.08/1.61 => ( notinemptyset
% 3.08/1.61 => ( exuE3e
% 3.08/1.61 => ( setext
% 3.08/1.61 => ( emptyI
% 3.08/1.61 => ( noeltsimpempty
% 3.08/1.61 => ( setbeta
% 3.08/1.61 => ( nonemptyE1
% 3.08/1.61 => ( nonemptyI
% 3.08/1.61 => ( nonemptyI1
% 3.08/1.61 => ( setadjoinIL
% 3.08/1.61 => ( emptyinunitempty
% 3.08/1.61 => ( setadjoinIR
% 3.08/1.61 => ( setadjoinE
% 3.08/1.61 => ( setadjoinOr
% 3.08/1.61 => ( setoftrueEq
% 3.08/1.61 => ( powersetI
% 3.08/1.61 => ( emptyinPowerset
% 3.08/1.61 => ( emptyInPowerset
% 3.08/1.61 => ( powersetE
% 3.08/1.61 => ( setunionI
% 3.08/1.61 => ( setunionE
% 3.08/1.61 => ( subPowSU
% 3.08/1.61 => ( exuE2
% 3.08/1.61 => ( nonemptyImpWitness
% 3.08/1.61 => ( uniqinunit
% 3.08/1.61 => ( notinsingleton
% 3.08/1.61 => ( eqinunit
% 3.08/1.61 => ( singletonsswitch
% 3.08/1.61 => ( upairsetE
% 3.08/1.61 => ( upairsetIL
% 3.08/1.61 => ( upairsetIR
% 3.08/1.61 => ( emptyE1
% 3.08/1.61 => ( vacuousDall
% 3.08/1.61 => ( quantDeMorgan1
% 3.08/1.61 => ( quantDeMorgan2
% 3.08/1.61 => ( quantDeMorgan3
% 3.08/1.61 => ( quantDeMorgan4
% 3.08/1.61 => ( prop2setI
% 3.08/1.61 => ( prop2set2propI
% 3.08/1.61 => ( notdexE
% 3.08/1.61 => ( notdallE
% 3.08/1.61 => ( exuI1
% 3.08/1.61 => ( exuI3
% 3.08/1.61 => ( exuI2
% 3.08/1.61 => ( inCongP
% 3.08/1.61 => ( in__Cong
% 3.08/1.61 => ( exuE3u
% 3.08/1.61 => ( exu__Cong
% 3.08/1.61 => ( emptyset__Cong
% 3.08/1.61 => ( setadjoin__Cong
% 3.08/1.61 => ( powerset__Cong
% 3.08/1.61 => ( setunion__Cong
% 3.08/1.61 => ( omega__Cong
% 3.08/1.61 => ( exuEu
% 3.08/1.61 => ( descr__Cong
% 3.08/1.61 => ( dsetconstr__Cong
% 3.08/1.61 => ( subsetI1
% 3.08/1.61 => ( eqimpsubset2
% 3.08/1.61 => ( eqimpsubset1
% 3.08/1.61 => ( subsetI2
% 3.08/1.61 => ( emptysetsubset
% 3.08/1.61 => ( subsetE
% 3.08/1.61 => ( subsetE2
% 3.08/1.61 => ( notsubsetI
% 3.08/1.61 => ( notequalI1
% 3.08/1.61 => ( notequalI2
% 3.08/1.61 => ( subsetRefl
% 3.08/1.61 => ( subsetTrans
% 3.08/1.61 => ( setadjoinSub
% 3.08/1.61 => ( setadjoinSub2
% 3.08/1.61 => ( subset2powerset
% 3.08/1.61 => ( setextsub
% 3.08/1.61 => ( subsetemptysetimpeq
% 3.08/1.61 => ( powersetI1
% 3.08/1.61 => ( powersetE1
% 3.08/1.61 => ( inPowerset
% 3.08/1.61 => ( powersetsubset
% 3.08/1.61 => ( sepInPowerset
% 3.08/1.61 => ( sepSubset
% 3.08/1.61 => ( binunionIL
% 3.08/1.61 => ( upairset2IR
% 3.08/1.61 => ( binunionIR
% 3.08/1.61 => ( binunionEcases
% 3.08/1.61 => ( binunionE
% 3.08/1.61 => ( binunionLsub
% 3.08/1.61 => ( binunionRsub
% 3.08/1.61 => ( binintersectI
% 3.08/1.61 => ( binintersectSubset5
% 3.08/1.61 => ( binintersectEL
% 3.08/1.61 => ( binintersectLsub
% 3.08/1.61 => ( binintersectSubset2
% 3.08/1.61 => ( binintersectSubset3
% 3.08/1.61 => ( binintersectER
% 3.08/1.61 => ( disjointsetsI1
% 3.08/1.61 => ( binintersectRsub
% 3.08/1.61 => ( binintersectSubset4
% 3.08/1.61 => ( binintersectSubset1
% 3.08/1.61 => ( bs114d
% 3.08/1.61 => ( setminusI
% 3.08/1.61 => ( setminusEL
% 3.08/1.61 => ( setminusER
% 3.08/1.61 => ( setminusSubset2
% 3.08/1.61 => ( setminusERneg
% 3.08/1.61 => ( setminusELneg
% 3.08/1.61 => ( setminusILneg
% 3.08/1.61 => ( setminusIRneg
% 3.08/1.61 => ( setminusLsub
% 3.08/1.61 => ( setminusSubset1
% 3.08/1.61 => ( symdiffE
% 3.08/1.61 => ( symdiffI1
% 3.08/1.61 => ( symdiffI2
% 3.08/1.61 => ( symdiffIneg1
% 3.08/1.61 => ( symdiffIneg2
% 3.08/1.61 => ( secondinupair
% 3.08/1.61 => ( setukpairIL
% 3.08/1.61 => ( setukpairIR
% 3.08/1.61 => ( kpairiskpair
% 3.08/1.61 => ( kpairp
% 3.08/1.61 => ( singletonsubset
% 3.08/1.61 => ( singletoninpowerset
% 3.08/1.61 => ( singletoninpowunion
% 3.08/1.61 => ( upairset2E
% 3.08/1.61 => ( upairsubunion
% 3.08/1.61 => ( upairinpowunion
% 3.08/1.61 => ( ubforcartprodlem1
% 3.08/1.61 => ( ubforcartprodlem2
% 3.08/1.61 => ( ubforcartprodlem3
% 3.08/1.61 => ( cartprodpairin
% 3.08/1.61 => ( cartprodmempair1
% 3.08/1.61 => ( cartprodmempair
% 3.08/1.61 => ( setunionE2
% 3.08/1.61 => ( setunionsingleton1
% 3.08/1.61 => ( setunionsingleton2
% 3.08/1.61 => ( setunionsingleton
% 3.08/1.61 => ( singletonprop
% 3.08/1.61 => ( ex1E1
% 3.08/1.61 => ( ex1I
% 3.08/1.61 => ( ex1I2
% 3.08/1.61 => ( singletonsuniq
% 3.08/1.61 => ( setukpairinjL1
% 3.08/1.61 => ( kfstsingleton
% 3.08/1.61 => ( theprop
% 3.08/1.61 => ( kfstpairEq
% 3.08/1.61 => ( cartprodfstin
% 3.08/1.61 => ( setukpairinjL2
% 3.08/1.61 => ( setukpairinjL
% 3.08/1.61 => ( setukpairinjR11
% 3.08/1.61 => ( setukpairinjR12
% 3.08/1.61 => ( setukpairinjR1
% 3.08/1.61 => ( upairequniteq
% 3.08/1.61 => ( setukpairinjR2
% 3.08/1.61 => ( setukpairinjR
% 3.08/1.61 => ( ksndsingleton
% 3.08/1.61 => ( ksndpairEq
% 3.08/1.61 => ( kpairsurjEq
% 3.08/1.61 => ( cartprodsndin
% 3.08/1.61 => ( cartprodpairmemEL
% 3.08/1.61 => ( cartprodpairmemER
% 3.08/1.61 => ( cartprodmempaircEq
% 3.08/1.61 => ( cartprodfstpairEq
% 3.08/1.61 => ( cartprodsndpairEq
% 3.08/1.61 => ( cartprodpairsurjEq
% 3.08/1.61 => ( dpsetconstrI
% 3.08/1.61 => ( dpsetconstrSub
% 3.08/1.61 => ( setOfPairsIsBReln
% 3.08/1.61 => ( dpsetconstrERa
% 3.08/1.61 => ( dpsetconstrEL1
% 3.08/1.61 => ( dpsetconstrEL2
% 3.08/1.61 => ( dpsetconstrER
% 3.08/1.61 => ( funcImageSingleton
% 3.08/1.61 => ( apProp
% 3.08/1.61 => ( app
% 3.08/1.61 => ( infuncsetfunc
% 3.08/1.61 => ( ap2p
% 3.08/1.61 => ( funcinfuncset
% 3.08/1.61 => ( lamProp
% 3.08/1.61 => ( lamp
% 3.08/1.61 => ( lam2p
% 3.08/1.61 => ( brelnall1
% 3.08/1.61 => ( brelnall2
% 3.08/1.61 => ( ex1E2
% 3.08/1.61 => ( funcGraphProp1
% 3.08/1.61 => ( funcGraphProp3
% 3.08/1.61 => ( funcGraphProp2
% 3.08/1.61 => ( funcextLem
% 3.08/1.61 => ( funcGraphProp4
% 3.08/1.61 => ( subbreln
% 3.08/1.61 => ( eqbreln
% 3.08/1.61 => ( funcext
% 3.08/1.61 => ( funcext2
% 3.08/1.61 => ( ap2apEq1
% 3.08/1.61 => ( ap2apEq2
% 3.08/1.61 => ( beta1
% 3.08/1.61 => ( eta1
% 3.08/1.61 => ( lam2lamEq
% 3.08/1.61 => ( beta2
% 3.08/1.61 => ( eta2
% 3.08/1.61 => ( iffalseProp1
% 3.08/1.61 => ( iffalseProp2
% 3.08/1.61 => ( iftrueProp1
% 3.08/1.61 => ( iftrueProp2
% 3.08/1.61 => ( ifSingleton
% 3.08/1.61 => ( ifp
% 3.08/1.61 => ( theeq
% 3.08/1.61 => ( iftrue
% 3.08/1.61 => ( iffalse
% 3.08/1.61 => ( iftrueorfalse
% 3.08/1.61 => ( binintersectT_lem
% 3.08/1.61 => ( binunionT_lem
% 3.08/1.61 => ( powersetT_lem
% 3.08/1.61 => ( setminusT_lem
% 3.08/1.61 => ( complementT_lem
% 3.08/1.61 => ( setextT
% 3.08/1.61 => ( subsetTI
% 3.08/1.61 => ( powersetTI1
% 3.08/1.61 => ( powersetTE1
% 3.08/1.61 => ( complementTI1
% 3.08/1.62 => ( complementTE1
% 3.08/1.62 => ( binintersectTELcontra
% 3.08/1.62 => ( binintersectTERcontra
% 3.08/1.62 => ( contrasubsetT
% 3.08/1.62 => ( contrasubsetT1
% 3.08/1.62 => ( contrasubsetT2
% 3.08/1.62 => ( contrasubsetT3
% 3.08/1.62 => ( doubleComplementI1
% 3.08/1.62 => ( doubleComplementE1
% 3.08/1.62 => ( doubleComplementSub1
% 3.08/1.62 => ( doubleComplementSub2
% 3.08/1.62 => ( doubleComplementEq
% 3.08/1.62 => ( complementTnotintersectT
% 3.08/1.62 => ( complementImpComplementIntersect
% 3.08/1.62 => ( complementSubsetComplementIntersect
% 3.08/1.62 => ( complementInPowersetComplementIntersect
% 3.08/1.62 => ( contraSubsetComplement
% 3.08/1.62 => ( complementTcontraSubset
% 3.08/1.62 => ( binunionTILcontra
% 3.08/1.62 => ( binunionTIRcontra
% 3.08/1.62 => ( inIntersectImpInUnion
% 3.08/1.62 => ( inIntersectImpInUnion2
% 3.08/1.62 => ( inIntersectImpInIntersectUnions
% 3.08/1.62 => ( intersectInPowersetIntersectUnions
% 3.08/1.62 => ( inComplementUnionImpNotIn1
% 3.08/1.62 => ( inComplementUnionImpInComplement1
% 3.08/1.62 => ( binunionTE
% 3.08/1.62 => ( binunionTEcontra
% 3.08/1.62 => ( demorgan2a1
% 3.08/1.62 => ( complementUnionInPowersetComplement
% 3.08/1.62 => ( demorgan2a2
% 3.08/1.62 => ( demorgan1a
% 3.08/1.62 => ( demorgan1b
% 3.08/1.62 => ( demorgan1
% 3.08/1.62 => ( demorgan2a
% 3.08/1.62 => ( demorgan2b2
% 3.08/1.62 => ( demorgan2b
% 3.08/1.62 => ( demorgan2
% 3.08/1.62 => ( woz13rule0
% 3.08/1.62 => ( woz13rule1
% 3.08/1.62 => ( woz13rule2
% 3.08/1.62 => ( woz13rule3
% 3.08/1.62 => ( woz13rule4
% 3.08/1.62 => ( woz1_1
% 3.08/1.62 => ( woz1_2
% 3.08/1.62 => ( woz1_3
% 3.08/1.62 => ( woz1_4
% 3.08/1.62 => ( woz1_5
% 3.08/1.62 => ( breln1all2
% 3.08/1.62 => ( breln1SetBreln1
% 3.08/1.62 => ( choice2fnsingleton
% 3.08/1.62 => ( setOfPairsIsBReln1
% 3.08/1.62 => ( breln1all1
% 3.08/1.62 => ( subbreln1
% 3.08/1.62 => ( eqbreln1
% 3.08/1.62 => ( breln1invprop
% 3.08/1.62 => ( breln1invI
% 3.08/1.62 => ! [A: $i,R: $i] :
% 3.08/1.62 ( ( breln1 @ A @ R )
% 3.08/1.62 => ! [Xx: $i] :
% 3.08/1.62 ( ( in @ Xx @ A )
% 3.08/1.62 => ! [Xy: $i] :
% 3.08/1.62 ( ( in @ Xy @ A )
% 3.08/1.62 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 3.08/1.62 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.08/1.62 ------------------------
% 3.08/1.64 % (11087)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10978 for (2999ds/183Mi)
% 3.08/1.65 % (11088)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_10978 for (2999ds/4Mi)
% 3.08/1.65 % (11089)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_10978 for (2999ds/27Mi)
% 3.08/1.65 % (11090)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10978 for (2999ds/2Mi)
% 3.08/1.65 % (11092)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_10978 for (2999ds/275Mi)
% 3.08/1.65 % (11091)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_10978 for (2999ds/2Mi)
% 3.08/1.65 % (11093)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10978 for (2999ds/18Mi)
% 3.08/1.65 % (11090)Instruction limit reached!
% 3.08/1.65 % (11090)------------------------------
% 3.08/1.65 % (11090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.65 % (11090)Termination reason: Unknown
% 3.08/1.65 % (11091)Instruction limit reached!
% 3.08/1.65 % (11091)------------------------------
% 3.08/1.65 % (11091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.65 % (11091)Termination reason: Unknown
% 3.08/1.65 % (11091)Termination phase: shuffling
% 3.08/1.65
% 3.08/1.65 % (11091)Memory used [KB]: 1535
% 3.08/1.65 % (11091)Time elapsed: 0.003 s
% 3.08/1.65 % (11091)Instructions burned: 2 (million)
% 3.08/1.65 % (11091)------------------------------
% 3.08/1.65 % (11091)------------------------------
% 3.08/1.65 % (11090)Termination phase: shuffling
% 3.08/1.65
% 3.08/1.65 % (11090)Memory used [KB]: 1535
% 3.08/1.65 % (11090)Time elapsed: 0.003 s
% 3.08/1.65 % (11090)Instructions burned: 2 (million)
% 3.08/1.65 % (11090)------------------------------
% 3.08/1.65 % (11090)------------------------------
% 3.08/1.65 % (11088)Instruction limit reached!
% 3.08/1.65 % (11088)------------------------------
% 3.08/1.65 % (11088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.65 % (11088)Termination reason: Unknown
% 3.08/1.65 % (11088)Termination phase: shuffling
% 3.08/1.65
% 3.08/1.65 % (11088)Memory used [KB]: 1535
% 3.08/1.65 % (11088)Time elapsed: 0.004 s
% 3.08/1.65 % (11088)Instructions burned: 5 (million)
% 3.08/1.65 % (11088)------------------------------
% 3.08/1.65 % (11088)------------------------------
% 3.08/1.66 % (11093)Instruction limit reached!
% 3.08/1.66 % (11093)------------------------------
% 3.08/1.66 % (11093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.66 % (11093)Termination reason: Unknown
% 3.08/1.66 % (11093)Termination phase: shuffling
% 3.08/1.66
% 3.08/1.66 % (11093)Memory used [KB]: 1791
% 3.08/1.66 % (11093)Time elapsed: 0.011 s
% 3.08/1.66 % (11093)Instructions burned: 18 (million)
% 3.08/1.66 % (11093)------------------------------
% 3.08/1.66 % (11093)------------------------------
% 3.08/1.66 % (11089)Instruction limit reached!
% 3.08/1.66 % (11089)------------------------------
% 3.08/1.66 % (11089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.66 % (11089)Termination reason: Unknown
% 3.08/1.66 % (11089)Termination phase: shuffling
% 3.08/1.66
% 3.08/1.66 % (11089)Memory used [KB]: 2046
% 3.08/1.66 % (11089)Time elapsed: 0.014 s
% 3.08/1.66 % (11089)Instructions burned: 27 (million)
% 3.08/1.66 % (11089)------------------------------
% 3.08/1.66 % (11089)------------------------------
% 3.08/1.67 % (11094)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10978 for (2999ds/3Mi)
% 3.08/1.67 % (11095)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_10978 for (2999ds/37Mi)
% 3.08/1.67 % (11096)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_10978 for (2999ds/15Mi)
% 3.08/1.67 % (11094)Instruction limit reached!
% 3.08/1.67 % (11094)------------------------------
% 3.08/1.67 % (11094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.67 % (11094)Termination reason: Unknown
% 3.08/1.67 % (11094)Termination phase: shuffling
% 3.08/1.67
% 3.08/1.67 % (11094)Memory used [KB]: 1535
% 3.08/1.67 % (11094)Time elapsed: 0.003 s
% 3.08/1.67 % (11094)Instructions burned: 3 (million)
% 3.08/1.67 % (11094)------------------------------
% 3.08/1.67 % (11094)------------------------------
% 3.08/1.67 % (11097)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_10978 for (2999ds/3Mi)
% 3.08/1.67 % (11096)Instruction limit reached!
% 3.08/1.67 % (11096)------------------------------
% 3.08/1.67 % (11096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.67 % (11096)Termination reason: Unknown
% 3.08/1.67 % (11096)Termination phase: shuffling
% 3.08/1.67
% 3.08/1.67 % (11096)Memory used [KB]: 1791
% 3.08/1.67 % (11096)Time elapsed: 0.009 s
% 3.08/1.67 % (11096)Instructions burned: 16 (million)
% 3.08/1.67 % (11096)------------------------------
% 3.08/1.67 % (11096)------------------------------
% 3.08/1.67 % (11097)Instruction limit reached!
% 3.08/1.67 % (11097)------------------------------
% 3.08/1.67 % (11097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.67 % (11097)Termination reason: Unknown
% 3.08/1.67 % (11097)Termination phase: shuffling
% 3.08/1.67
% 3.08/1.67 % (11097)Memory used [KB]: 1535
% 3.08/1.67 % (11097)Time elapsed: 0.003 s
% 3.08/1.67 % (11097)Instructions burned: 3 (million)
% 3.08/1.67 % (11097)------------------------------
% 3.08/1.67 % (11097)------------------------------
% 3.08/1.68 % (11098)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_10978 for (2999ds/1041Mi)
% 3.08/1.68 % (11095)Instruction limit reached!
% 3.08/1.68 % (11095)------------------------------
% 3.08/1.68 % (11095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.68 % (11095)Termination reason: Unknown
% 3.08/1.68 % (11095)Termination phase: shuffling
% 3.08/1.68
% 3.08/1.68 % (11095)Memory used [KB]: 2302
% 3.08/1.68 % (11095)Time elapsed: 0.018 s
% 3.08/1.68 % (11095)Instructions burned: 37 (million)
% 3.08/1.68 % (11095)------------------------------
% 3.08/1.68 % (11095)------------------------------
% 3.08/1.68 % (11099)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_10978 for (2999ds/7Mi)
% 3.08/1.69 % (11099)Instruction limit reached!
% 3.08/1.69 % (11099)------------------------------
% 3.08/1.69 % (11099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.69 % (11099)Termination reason: Unknown
% 3.08/1.69 % (11099)Termination phase: shuffling
% 3.08/1.69
% 3.08/1.69 % (11099)Memory used [KB]: 1663
% 3.08/1.69 % (11099)Time elapsed: 0.005 s
% 3.08/1.69 % (11099)Instructions burned: 8 (million)
% 3.08/1.69 % (11099)------------------------------
% 3.08/1.69 % (11099)------------------------------
% 3.08/1.69 % (11087)Instruction limit reached!
% 3.08/1.69 % (11087)------------------------------
% 3.08/1.69 % (11087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.69 % (11087)Termination reason: Unknown
% 3.08/1.69 % (11087)Termination phase: Saturation
% 3.08/1.69
% 3.08/1.69 % (11087)Memory used [KB]: 7419
% 3.08/1.69 % (11087)Time elapsed: 0.049 s
% 3.08/1.69 % (11087)Instructions burned: 186 (million)
% 3.08/1.69 % (11087)------------------------------
% 3.08/1.69 % (11087)------------------------------
% 3.08/1.69 % (11100)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_10978 for (2999ds/16Mi)
% 3.08/1.69 % (11101)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_10978 for (2999ds/3Mi)
% 3.08/1.69 % (11101)Instruction limit reached!
% 3.08/1.69 % (11101)------------------------------
% 3.08/1.69 % (11101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.69 % (11101)Termination reason: Unknown
% 3.08/1.69 % (11101)Termination phase: shuffling
% 3.08/1.69
% 3.08/1.69 % (11101)Memory used [KB]: 1535
% 3.08/1.69 % (11101)Time elapsed: 0.003 s
% 3.08/1.69 % (11101)Instructions burned: 3 (million)
% 3.08/1.69 % (11101)------------------------------
% 3.08/1.69 % (11101)------------------------------
% 3.11/1.70 % (11100)Instruction limit reached!
% 3.11/1.70 % (11100)------------------------------
% 3.11/1.70 % (11100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.70 % (11100)Termination reason: Unknown
% 3.11/1.70 % (11100)Termination phase: shuffling
% 3.11/1.70
% 3.11/1.70 % (11100)Memory used [KB]: 1791
% 3.11/1.70 % (11100)Time elapsed: 0.009 s
% 3.11/1.70 % (11100)Instructions burned: 16 (million)
% 3.11/1.70 % (11100)------------------------------
% 3.11/1.70 % (11100)------------------------------
% 3.11/1.70 % (11104)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_10978 for (2999ds/3Mi)
% 3.11/1.70 % (11102)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_10978 for (2999ds/3Mi)
% 3.11/1.70 % (11104)Instruction limit reached!
% 3.11/1.70 % (11104)------------------------------
% 3.11/1.70 % (11104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.70 % (11104)Termination reason: Unknown
% 3.11/1.70 % (11104)Termination phase: shuffling
% 3.11/1.70
% 3.11/1.70 % (11104)Memory used [KB]: 1535
% 3.11/1.70 % (11104)Time elapsed: 0.002 s
% 3.11/1.70 % (11104)Instructions burned: 3 (million)
% 3.11/1.70 % (11104)------------------------------
% 3.11/1.70 % (11104)------------------------------
% 3.11/1.70 % (11102)Instruction limit reached!
% 3.11/1.70 % (11102)------------------------------
% 3.11/1.70 % (11102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.70 % (11102)Termination reason: Unknown
% 3.11/1.70 % (11102)Termination phase: shuffling
% 3.11/1.70
% 3.11/1.70 % (11102)Memory used [KB]: 1535
% 3.11/1.70 % (11102)Time elapsed: 0.003 s
% 3.11/1.70 % (11102)Instructions burned: 3 (million)
% 3.11/1.70 % (11102)------------------------------
% 3.11/1.70 % (11102)------------------------------
% 3.11/1.70 % (11103)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_10978 for (2999ds/7Mi)
% 3.11/1.71 % (11103)Instruction limit reached!
% 3.11/1.71 % (11103)------------------------------
% 3.11/1.71 % (11103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.71 % (11103)Termination reason: Unknown
% 3.11/1.71 % (11103)Termination phase: shuffling
% 3.11/1.71
% 3.11/1.71 % (11103)Memory used [KB]: 1663
% 3.11/1.71 % (11103)Time elapsed: 0.005 s
% 3.11/1.71 % (11103)Instructions burned: 7 (million)
% 3.11/1.71 % (11103)------------------------------
% 3.11/1.71 % (11103)------------------------------
% 3.11/1.71 % (11107)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_10978 for (2999ds/710Mi)
% 3.11/1.71 % (11105)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_10978 for (2999ds/4Mi)
% 3.11/1.71 % (11105)Instruction limit reached!
% 3.11/1.71 % (11105)------------------------------
% 3.11/1.71 % (11105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.71 % (11105)Termination reason: Unknown
% 3.11/1.71 % (11105)Termination phase: shuffling
% 3.11/1.71
% 3.11/1.71 % (11105)Memory used [KB]: 1535
% 3.11/1.71 % (11105)Time elapsed: 0.004 s
% 3.11/1.71 % (11105)Instructions burned: 5 (million)
% 3.11/1.71 % (11105)------------------------------
% 3.11/1.71 % (11105)------------------------------
% 3.11/1.71 % (11106)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_10978 for (2999ds/18Mi)
% 3.11/1.72 % (11108)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_10978 for (2999ds/6Mi)
% 3.11/1.72 % (11108)Instruction limit reached!
% 3.11/1.72 % (11108)------------------------------
% 3.11/1.72 % (11108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.72 % (11108)Termination reason: Unknown
% 3.11/1.72 % (11108)Termination phase: shuffling
% 3.11/1.72
% 3.11/1.72 % (11108)Memory used [KB]: 1535
% 3.11/1.72 % (11108)Time elapsed: 0.004 s
% 3.11/1.72 % (11108)Instructions burned: 6 (million)
% 3.11/1.72 % (11108)------------------------------
% 3.11/1.72 % (11108)------------------------------
% 3.11/1.72 % (11106)Instruction limit reached!
% 3.11/1.72 % (11106)------------------------------
% 3.11/1.72 % (11106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.72 % (11106)Termination reason: Unknown
% 3.11/1.72 % (11106)Termination phase: shuffling
% 3.11/1.72
% 3.11/1.72 % (11106)Memory used [KB]: 1791
% 3.11/1.72 % (11106)Time elapsed: 0.010 s
% 3.11/1.72 % (11106)Instructions burned: 19 (million)
% 3.11/1.72 % (11106)------------------------------
% 3.11/1.72 % (11106)------------------------------
% 3.11/1.72 % (11109)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_10978 for (2999ds/902Mi)
% 3.11/1.73 % (11110)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_10978 for (2999ds/21Mi)
% 3.11/1.74 % (11110)Instruction limit reached!
% 3.11/1.74 % (11110)------------------------------
% 3.11/1.74 % (11110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.74 % (11110)Termination reason: Unknown
% 3.11/1.74 % (11110)Termination phase: shuffling
% 3.11/1.74
% 3.11/1.74 % (11110)Memory used [KB]: 1918
% 3.11/1.74 % (11110)Time elapsed: 0.011 s
% 3.11/1.74 % (11110)Instructions burned: 21 (million)
% 3.11/1.74 % (11110)------------------------------
% 3.11/1.74 % (11110)------------------------------
% 3.11/1.74 % (11112)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_10978 for (2999ds/6Mi)
% 3.11/1.74 % (11111)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_10978 for (2999ds/5Mi)
% 3.11/1.74 % (11112)Instruction limit reached!
% 3.11/1.74 % (11112)------------------------------
% 3.11/1.74 % (11112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.74 % (11112)Termination reason: Unknown
% 3.11/1.74 % (11112)Termination phase: shuffling
% 3.11/1.74
% 3.11/1.74 % (11112)Memory used [KB]: 1663
% 3.11/1.74 % (11112)Time elapsed: 0.005 s
% 3.11/1.74 % (11112)Instructions burned: 7 (million)
% 3.11/1.74 % (11112)------------------------------
% 3.11/1.74 % (11112)------------------------------
% 3.11/1.74 % (11111)Instruction limit reached!
% 3.11/1.74 % (11111)------------------------------
% 3.11/1.74 % (11111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.74 % (11111)Termination reason: Unknown
% 3.11/1.74 % (11111)Termination phase: shuffling
% 3.11/1.74
% 3.11/1.74 % (11111)Memory used [KB]: 1535
% 3.11/1.74 % (11111)Time elapsed: 0.004 s
% 3.11/1.74 % (11111)Instructions burned: 5 (million)
% 3.11/1.74 % (11111)------------------------------
% 3.11/1.74 % (11111)------------------------------
% 3.11/1.76 % (11113)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_10978 for (2998ds/377Mi)
% 3.11/1.76 % (11114)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_10978 for (2998ds/779Mi)
% 3.11/1.76 % (11115)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_10978 for (2998ds/19Mi)
% 3.11/1.77 % (11115)Instruction limit reached!
% 3.11/1.77 % (11115)------------------------------
% 3.11/1.77 % (11115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.77 % (11115)Termination reason: Unknown
% 3.11/1.77 % (11115)Termination phase: shuffling
% 3.11/1.77
% 3.11/1.77 % (11115)Memory used [KB]: 1918
% 3.11/1.77 % (11115)Time elapsed: 0.011 s
% 3.11/1.77 % (11115)Instructions burned: 20 (million)
% 3.11/1.77 % (11115)------------------------------
% 3.11/1.77 % (11115)------------------------------
% 3.11/1.77 % (11092)Instruction limit reached!
% 3.11/1.77 % (11092)------------------------------
% 3.11/1.77 % (11092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.77 % (11092)Termination reason: Unknown
% 3.11/1.77 % (11092)Termination phase: Saturation
% 3.11/1.77
% 3.11/1.77 % (11092)Memory used [KB]: 10234
% 3.11/1.77 % (11092)Time elapsed: 0.129 s
% 3.11/1.77 % (11092)Instructions burned: 275 (million)
% 3.11/1.77 % (11092)------------------------------
% 3.11/1.77 % (11092)------------------------------
% 3.11/1.79 % (11116)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_10978 for (2998ds/879Mi)
% 3.11/1.79 % (11117)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_10978 for (2998ds/17Mi)
% 3.11/1.80 % (11117)Instruction limit reached!
% 3.11/1.80 % (11117)------------------------------
% 3.11/1.80 % (11117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.80 % (11117)Termination reason: Unknown
% 3.11/1.80 % (11117)Termination phase: shuffling
% 3.11/1.80
% 3.11/1.80 % (11117)Memory used [KB]: 1918
% 3.11/1.80 % (11117)Time elapsed: 0.007 s
% 3.11/1.80 % (11117)Instructions burned: 19 (million)
% 3.11/1.80 % (11117)------------------------------
% 3.11/1.80 % (11117)------------------------------
% 3.11/1.81 % (11119)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_10978 for (2998ds/3Mi)
% 3.11/1.81 % (11119)Instruction limit reached!
% 3.11/1.81 % (11119)------------------------------
% 3.11/1.81 % (11119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.81 % (11119)Termination reason: Unknown
% 3.11/1.81 % (11119)Termination phase: shuffling
% 3.11/1.81
% 3.11/1.81 % (11119)Memory used [KB]: 1535
% 3.11/1.81 % (11119)Time elapsed: 0.003 s
% 3.11/1.81 % (11119)Instructions burned: 6 (million)
% 3.11/1.81 % (11119)------------------------------
% 3.11/1.81 % (11119)------------------------------
% 3.11/1.82 % (11120)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_10978 for (2998ds/30Mi)
% 3.11/1.83 % (11120)Instruction limit reached!
% 3.11/1.83 % (11120)------------------------------
% 3.11/1.83 % (11120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.83 % (11120)Termination reason: Unknown
% 3.11/1.83 % (11120)Termination phase: shuffling
% 3.11/1.83
% 3.11/1.83 % (11120)Memory used [KB]: 2174
% 3.11/1.83 % (11120)Time elapsed: 0.010 s
% 3.11/1.83 % (11120)Instructions burned: 32 (million)
% 3.11/1.83 % (11120)------------------------------
% 3.11/1.83 % (11120)------------------------------
% 3.11/1.84 % (11121)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_10978 for (2998ds/127Mi)
% 3.11/1.87 % (11121)Instruction limit reached!
% 3.11/1.87 % (11121)------------------------------
% 3.11/1.87 % (11121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.87 % (11121)Termination reason: Unknown
% 3.11/1.87 % (11121)Termination phase: Property scanning
% 3.11/1.87
% 3.11/1.87 % (11121)Memory used [KB]: 2814
% 3.11/1.87 % (11121)Time elapsed: 0.034 s
% 3.11/1.87 % (11121)Instructions burned: 128 (million)
% 3.11/1.87 % (11121)------------------------------
% 3.11/1.87 % (11121)------------------------------
% 3.11/1.89 % (11122)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_10978 for (2997ds/100Mi)
% 3.11/1.92 % (11122)Instruction limit reached!
% 3.11/1.92 % (11122)------------------------------
% 3.11/1.92 % (11122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.92 % (11122)Termination reason: Unknown
% 3.11/1.92 % (11122)Termination phase: Property scanning
% 3.11/1.92
% 3.11/1.92 % (11122)Memory used [KB]: 2686
% 3.11/1.92 % (11122)Time elapsed: 0.027 s
% 3.11/1.92 % (11122)Instructions burned: 101 (million)
% 3.11/1.92 % (11122)------------------------------
% 3.11/1.92 % (11122)------------------------------
% 3.11/1.92 % (11113)Instruction limit reached!
% 3.11/1.92 % (11113)------------------------------
% 3.11/1.92 % (11113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.92 % (11113)Termination reason: Unknown
% 3.11/1.92 % (11113)Termination phase: Saturation
% 3.11/1.92
% 3.11/1.92 % (11113)Memory used [KB]: 9338
% 3.11/1.92 % (11113)Time elapsed: 0.169 s
% 3.11/1.92 % (11113)Instructions burned: 378 (million)
% 3.11/1.92 % (11113)------------------------------
% 3.11/1.92 % (11113)------------------------------
% 3.11/1.93 % (11123)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_10978 for (2997ds/3Mi)
% 3.11/1.93 % (11123)Instruction limit reached!
% 3.11/1.93 % (11123)------------------------------
% 3.11/1.93 % (11123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.93 % (11123)Termination reason: Unknown
% 3.11/1.93 % (11123)Termination phase: shuffling
% 3.11/1.93
% 3.11/1.93 % (11123)Memory used [KB]: 1535
% 3.11/1.93 % (11123)Time elapsed: 0.003 s
% 3.11/1.93 % (11123)Instructions burned: 6 (million)
% 3.11/1.93 % (11123)------------------------------
% 3.11/1.93 % (11123)------------------------------
% 3.11/1.94 % (11125)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_10978 for (2997ds/86Mi)
% 3.11/1.94 % (11124)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_10978 for (2997ds/20Mi)
% 3.11/1.95 % (11124)Instruction limit reached!
% 3.11/1.95 % (11124)------------------------------
% 3.11/1.95 % (11124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.95 % (11124)Termination reason: Unknown
% 3.11/1.95 % (11124)Termination phase: shuffling
% 3.11/1.95
% 3.11/1.95 % (11124)Memory used [KB]: 1918
% 3.11/1.95 % (11124)Time elapsed: 0.012 s
% 3.11/1.95 % (11124)Instructions burned: 21 (million)
% 3.11/1.95 % (11124)------------------------------
% 3.11/1.95 % (11124)------------------------------
% 3.11/1.96 % (11125)Instruction limit reached!
% 3.11/1.96 % (11125)------------------------------
% 3.11/1.96 % (11125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.96 % (11125)Termination reason: Unknown
% 3.11/1.96 % (11125)Termination phase: Property scanning
% 3.11/1.96
% 3.11/1.96 % (11125)Memory used [KB]: 2558
% 3.11/1.96 % (11125)Time elapsed: 0.024 s
% 3.11/1.96 % (11125)Instructions burned: 89 (million)
% 3.11/1.96 % (11125)------------------------------
% 3.11/1.96 % (11125)------------------------------
% 3.11/1.97 % (11126)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_10978 for (2996ds/107Mi)
% 3.11/1.97 % (11127)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_10978 for (2996ds/39Mi)
% 3.11/1.98 % (11127)Instruction limit reached!
% 3.11/1.98 % (11127)------------------------------
% 3.11/1.98 % (11127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.98 % (11127)Termination reason: Unknown
% 3.11/1.98 % (11127)Termination phase: shuffling
% 3.11/1.98
% 3.11/1.98 % (11127)Memory used [KB]: 2302
% 3.11/1.98 % (11127)Time elapsed: 0.012 s
% 3.11/1.98 % (11127)Instructions burned: 41 (million)
% 3.11/1.98 % (11127)------------------------------
% 3.11/1.98 % (11127)------------------------------
% 3.11/1.99 % (11128)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_10978 for (2996ds/448Mi)
% 3.11/2.00 % (11107)Instruction limit reached!
% 3.11/2.00 % (11107)------------------------------
% 3.11/2.00 % (11107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/2.00 % (11107)Termination reason: Unknown
% 3.11/2.00 % (11107)Termination phase: Saturation
% 3.11/2.00
% 3.11/2.00 % (11107)Memory used [KB]: 11513
% 3.11/2.00 % (11107)Time elapsed: 0.295 s
% 3.11/2.00 % (11107)Instructions burned: 710 (million)
% 3.11/2.00 % (11107)------------------------------
% 3.11/2.00 % (11107)------------------------------
% 3.11/2.01 % (11126)Instruction limit reached!
% 3.11/2.01 % (11126)------------------------------
% 3.11/2.01 % (11126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/2.01 % (11126)Termination reason: Unknown
% 3.11/2.01 % (11126)Termination phase: SInE selection
% 3.11/2.01
% 3.11/2.01 % (11126)Memory used [KB]: 2558
% 3.11/2.01 % (11126)Time elapsed: 0.048 s
% 3.11/2.01 % (11126)Instructions burned: 107 (million)
% 3.11/2.01 % (11126)------------------------------
% 3.11/2.01 % (11126)------------------------------
% 5.65/2.02 % (11130)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_10978 for (2996ds/98Mi)
% 5.65/2.02 % (11129)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_10978 for (2996ds/46Mi)
% 5.65/2.05 % (11129)Instruction limit reached!
% 5.65/2.05 % (11129)------------------------------
% 5.65/2.05 % (11129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.05 % (11129)Termination reason: Unknown
% 5.65/2.05 % (11129)Termination phase: shuffling
% 5.65/2.05
% 5.65/2.05 % (11129)Memory used [KB]: 2430
% 5.65/2.05 % (11129)Time elapsed: 0.023 s
% 5.65/2.05 % (11129)Instructions burned: 46 (million)
% 5.65/2.05 % (11129)------------------------------
% 5.65/2.05 % (11129)------------------------------
% 5.65/2.05 % (11130)Instruction limit reached!
% 5.65/2.05 % (11130)------------------------------
% 5.65/2.05 % (11130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.05 % (11130)Termination reason: Unknown
% 5.65/2.05 % (11130)Termination phase: Property scanning
% 5.65/2.05
% 5.65/2.05 % (11130)Memory used [KB]: 2686
% 5.65/2.05 % (11130)Time elapsed: 0.027 s
% 5.65/2.05 % (11130)Instructions burned: 101 (million)
% 5.65/2.05 % (11130)------------------------------
% 5.65/2.05 % (11130)------------------------------
% 5.65/2.06 % (11114)Instruction limit reached!
% 5.65/2.06 % (11114)------------------------------
% 5.65/2.06 % (11114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.06 % (11114)Termination reason: Unknown
% 5.65/2.06 % (11114)Termination phase: Saturation
% 5.65/2.06
% 5.65/2.06 % (11114)Memory used [KB]: 7675
% 5.65/2.06 % (11114)Time elapsed: 0.302 s
% 5.65/2.06 % (11114)Instructions burned: 781 (million)
% 5.65/2.06 % (11114)------------------------------
% 5.65/2.06 % (11114)------------------------------
% 5.65/2.06 % (11133)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_10978 for (2995ds/149Mi)
% 5.65/2.06 % (11132)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_10978 for (2995ds/507Mi)
% 5.65/2.07 % (11098)Instruction limit reached!
% 5.65/2.07 % (11098)------------------------------
% 5.65/2.07 % (11098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.07 % (11098)Termination reason: Unknown
% 5.65/2.07 % (11098)Termination phase: Saturation
% 5.65/2.07
% 5.65/2.07 % (11098)Memory used [KB]: 16630
% 5.65/2.07 % (11098)Time elapsed: 0.394 s
% 5.65/2.07 % (11098)Instructions burned: 1042 (million)
% 5.65/2.07 % (11098)------------------------------
% 5.65/2.07 % (11098)------------------------------
% 5.65/2.07 % (11134)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_10978 for (2995ds/39Mi)
% 5.65/2.09 % (11135)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_10978 for (2995ds/6Mi)
% 5.65/2.09 % (11134)Instruction limit reached!
% 5.65/2.09 % (11134)------------------------------
% 5.65/2.09 % (11134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.09 % (11134)Termination reason: Unknown
% 5.65/2.09 % (11134)Termination phase: shuffling
% 5.65/2.09
% 5.65/2.09 % (11134)Memory used [KB]: 2302
% 5.65/2.09 % (11134)Time elapsed: 0.019 s
% 5.65/2.09 % (11134)Instructions burned: 39 (million)
% 5.65/2.09 % (11134)------------------------------
% 5.65/2.09 % (11134)------------------------------
% 5.65/2.09 % (11135)Instruction limit reached!
% 5.65/2.09 % (11135)------------------------------
% 5.65/2.09 % (11135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.09 % (11135)Termination reason: Unknown
% 5.65/2.09 % (11135)Termination phase: shuffling
% 5.65/2.09
% 5.65/2.09 % (11135)Memory used [KB]: 1663
% 5.65/2.09 % (11135)Time elapsed: 0.005 s
% 5.65/2.09 % (11135)Instructions burned: 7 (million)
% 5.65/2.09 % (11135)------------------------------
% 5.65/2.09 % (11135)------------------------------
% 5.65/2.10 % (11133)Instruction limit reached!
% 5.65/2.10 % (11133)------------------------------
% 5.65/2.10 % (11133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.65/2.10 % (11133)Termination reason: Unknown
% 5.65/2.10 % (11133)Termination phase: Twee Goal Transformation
% 5.65/2.10
% 5.65/2.10 % (11133)Memory used [KB]: 3070
% 5.65/2.10 % (11133)Time elapsed: 0.040 s
% 5.65/2.10 % (11133)Instructions burned: 151 (million)
% 5.65/2.10 % (11133)------------------------------
% 5.65/2.10 % (11133)------------------------------
% 5.65/2.11 % (11136)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_10978 for (2995ds/1087Mi)
% 5.65/2.11 % (11138)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_10978 for (2995ds/44Mi)
% 5.65/2.11 % (11137)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_10978 for (2995ds/47Mi)
% 6.28/2.12 % (11138)Instruction limit reached!
% 6.28/2.12 % (11138)------------------------------
% 6.28/2.12 % (11138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.12 % (11138)Termination reason: Unknown
% 6.28/2.12 % (11138)Termination phase: shuffling
% 6.28/2.12
% 6.28/2.12 % (11138)Memory used [KB]: 2430
% 6.28/2.12 % (11138)Time elapsed: 0.014 s
% 6.28/2.12 % (11138)Instructions burned: 47 (million)
% 6.28/2.12 % (11138)------------------------------
% 6.28/2.12 % (11138)------------------------------
% 6.28/2.13 % (11139)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_10978 for (2995ds/432Mi)
% 6.28/2.13 % (11137)Instruction limit reached!
% 6.28/2.13 % (11137)------------------------------
% 6.28/2.13 % (11137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.13 % (11137)Termination reason: Unknown
% 6.28/2.13 % (11137)Termination phase: shuffling
% 6.28/2.13
% 6.28/2.13 % (11137)Memory used [KB]: 2430
% 6.28/2.13 % (11137)Time elapsed: 0.023 s
% 6.28/2.13 % (11137)Instructions burned: 47 (million)
% 6.28/2.13 % (11137)------------------------------
% 6.28/2.13 % (11137)------------------------------
% 6.28/2.15 % (11140)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_10978 for (2994ds/62Mi)
% 6.28/2.16 % (11109)Instruction limit reached!
% 6.28/2.16 % (11109)------------------------------
% 6.28/2.16 % (11109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.16 % (11109)Termination reason: Unknown
% 6.28/2.16 % (11109)Termination phase: Saturation
% 6.28/2.16
% 6.28/2.16 % (11109)Memory used [KB]: 12792
% 6.28/2.16 % (11109)Time elapsed: 0.438 s
% 6.28/2.16 % (11109)Instructions burned: 902 (million)
% 6.28/2.16 % (11109)------------------------------
% 6.28/2.16 % (11109)------------------------------
% 6.28/2.17 % (11140)Instruction limit reached!
% 6.28/2.17 % (11140)------------------------------
% 6.28/2.17 % (11140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.17 % (11140)Termination reason: Unknown
% 6.28/2.17 % (11140)Termination phase: Property scanning
% 6.28/2.17
% 6.28/2.17 % (11140)Memory used [KB]: 2558
% 6.28/2.17 % (11140)Time elapsed: 0.029 s
% 6.28/2.17 % (11140)Instructions burned: 62 (million)
% 6.28/2.17 % (11140)------------------------------
% 6.28/2.17 % (11140)------------------------------
% 6.28/2.18 % (11128)Instruction limit reached!
% 6.28/2.18 % (11128)------------------------------
% 6.28/2.18 % (11128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.18 % (11128)Termination reason: Unknown
% 6.28/2.18 % (11128)Termination phase: Saturation
% 6.28/2.18
% 6.28/2.18 % (11128)Memory used [KB]: 7547
% 6.28/2.18 % (11128)Time elapsed: 0.184 s
% 6.28/2.18 % (11128)Instructions burned: 448 (million)
% 6.28/2.18 % (11128)------------------------------
% 6.28/2.18 % (11128)------------------------------
% 6.28/2.18 % (11142)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_10978 for (2994ds/31Mi)
% 6.28/2.19 % (11116)Instruction limit reached!
% 6.28/2.19 % (11116)------------------------------
% 6.28/2.19 % (11116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.19 % (11116)Termination reason: Unknown
% 6.28/2.19 % (11116)Termination phase: Saturation
% 6.28/2.19
% 6.28/2.19 % (11116)Memory used [KB]: 10234
% 6.28/2.19 % (11116)Time elapsed: 0.400 s
% 6.28/2.19 % (11116)Instructions burned: 880 (million)
% 6.28/2.19 % (11116)------------------------------
% 6.28/2.19 % (11116)------------------------------
% 6.28/2.19 % (11143)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_10978 for (2994ds/96Mi)
% 6.28/2.19 % (11142)Instruction limit reached!
% 6.28/2.19 % (11142)------------------------------
% 6.28/2.19 % (11142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.19 % (11142)Termination reason: Unknown
% 6.28/2.19 % (11142)Termination phase: shuffling
% 6.28/2.19
% 6.28/2.19 % (11142)Memory used [KB]: 2046
% 6.28/2.19 % (11142)Time elapsed: 0.010 s
% 6.28/2.19 % (11142)Instructions burned: 32 (million)
% 6.28/2.19 % (11142)------------------------------
% 6.28/2.19 % (11142)------------------------------
% 6.28/2.19 % (11144)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_10978 for (2994ds/453Mi)
% 6.62/2.21 % (11145)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_10978 for (2994ds/71Mi)
% 6.62/2.21 % (11146)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_10978 for (2994ds/83Mi)
% 6.62/2.23 % (11143)Instruction limit reached!
% 6.62/2.23 % (11143)------------------------------
% 6.62/2.23 % (11143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.23 % (11143)Termination reason: Unknown
% 6.62/2.23 % (11143)Termination phase: Property scanning
% 6.62/2.23
% 6.62/2.23 % (11143)Memory used [KB]: 2814
% 6.62/2.23 % (11143)Time elapsed: 0.045 s
% 6.62/2.23 % (11143)Instructions burned: 97 (million)
% 6.62/2.23 % (11143)------------------------------
% 6.62/2.23 % (11143)------------------------------
% 6.62/2.24 % (11145)Instruction limit reached!
% 6.62/2.24 % (11145)------------------------------
% 6.62/2.24 % (11145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.24 % (11145)Termination reason: Unknown
% 6.62/2.24 % (11145)Termination phase: Property scanning
% 6.62/2.24
% 6.62/2.24 % (11145)Memory used [KB]: 2558
% 6.62/2.24 % (11145)Time elapsed: 0.034 s
% 6.62/2.24 % (11145)Instructions burned: 71 (million)
% 6.62/2.24 % (11145)------------------------------
% 6.62/2.24 % (11145)------------------------------
% 6.62/2.25 % (11146)Instruction limit reached!
% 6.62/2.25 % (11146)------------------------------
% 6.62/2.25 % (11146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.25 % (11146)Termination reason: Unknown
% 6.62/2.25 % (11146)Termination phase: Property scanning
% 6.62/2.25
% 6.62/2.25 % (11146)Memory used [KB]: 2558
% 6.62/2.25 % (11146)Time elapsed: 0.040 s
% 6.62/2.25 % (11146)Instructions burned: 84 (million)
% 6.62/2.25 % (11146)------------------------------
% 6.62/2.25 % (11146)------------------------------
% 6.62/2.25 % (11147)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_10978 for (2993ds/11Mi)
% 6.62/2.25 % (11148)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_10978 for (2993ds/41Mi)
% 6.62/2.26 % (11147)Instruction limit reached!
% 6.62/2.26 % (11147)------------------------------
% 6.62/2.26 % (11147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.26 % (11147)Termination reason: Unknown
% 6.62/2.26 % (11147)Termination phase: shuffling
% 6.62/2.26
% 6.62/2.26 % (11147)Memory used [KB]: 1663
% 6.62/2.26 % (11147)Time elapsed: 0.006 s
% 6.62/2.26 % (11147)Instructions burned: 11 (million)
% 6.62/2.26 % (11147)------------------------------
% 6.62/2.26 % (11147)------------------------------
% 6.62/2.26 % (11149)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_10978 for (2993ds/6Mi)
% 6.62/2.27 % (11139)Instruction limit reached!
% 6.62/2.27 % (11139)------------------------------
% 6.62/2.27 % (11139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.27 % (11139)Termination reason: Unknown
% 6.62/2.27 % (11139)Termination phase: Saturation
% 6.62/2.27
% 6.62/2.27 % (11139)Memory used [KB]: 3070
% 6.62/2.27 % (11139)Time elapsed: 0.137 s
% 6.62/2.27 % (11139)Instructions burned: 435 (million)
% 6.62/2.27 % (11139)------------------------------
% 6.62/2.27 % (11139)------------------------------
% 6.62/2.27 % (11149)Instruction limit reached!
% 6.62/2.27 % (11149)------------------------------
% 6.62/2.27 % (11149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.27 % (11149)Termination reason: Unknown
% 6.62/2.27 % (11149)Termination phase: shuffling
% 6.62/2.27
% 6.62/2.27 % (11149)Memory used [KB]: 1663
% 6.62/2.27 % (11149)Time elapsed: 0.005 s
% 6.62/2.27 % (11149)Instructions burned: 8 (million)
% 6.62/2.27 % (11149)------------------------------
% 6.62/2.27 % (11149)------------------------------
% 6.62/2.27 % (11148)Instruction limit reached!
% 6.62/2.27 % (11148)------------------------------
% 6.62/2.27 % (11148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.27 % (11148)Termination reason: Unknown
% 6.62/2.27 % (11148)Termination phase: shuffling
% 6.62/2.27
% 6.62/2.27 % (11148)Memory used [KB]: 2430
% 6.62/2.27 % (11148)Time elapsed: 0.018 s
% 6.62/2.27 % (11148)Instructions burned: 44 (million)
% 6.62/2.27 % (11148)------------------------------
% 6.62/2.27 % (11148)------------------------------
% 6.62/2.27 % (11150)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_10978 for (2993ds/150Mi)
% 6.62/2.28 % (11153)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_10978 for (2993ds/253Mi)
% 6.62/2.28 % (11151)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_10978 for (2993ds/343Mi)
% 6.62/2.28 % (11152)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_10978 for (2993ds/109Mi)
% 6.62/2.30 % (11132)Instruction limit reached!
% 6.62/2.30 % (11132)------------------------------
% 6.62/2.30 % (11132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.30 % (11132)Termination reason: Unknown
% 6.62/2.30 % (11132)Termination phase: Saturation
% 7.00/2.30
% 7.00/2.30 % (11132)Memory used [KB]: 8187
% 7.00/2.30 % (11132)Time elapsed: 0.236 s
% 7.00/2.30 % (11132)Instructions burned: 508 (million)
% 7.00/2.30 % (11132)------------------------------
% 7.00/2.30 % (11132)------------------------------
% 7.00/2.31 % (11154)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_10978 for (2993ds/140Mi)
% 7.00/2.33 % (11152)Instruction limit reached!
% 7.00/2.33 % (11152)------------------------------
% 7.00/2.33 % (11152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.00/2.33 % (11152)Termination reason: Unknown
% 7.00/2.33 % (11152)Termination phase: SInE selection
% 7.00/2.33
% 7.00/2.33 % (11152)Memory used [KB]: 2558
% 7.00/2.33 % (11152)Time elapsed: 0.049 s
% 7.00/2.33 % (11152)Instructions burned: 110 (million)
% 7.00/2.33 % (11152)------------------------------
% 7.00/2.33 % (11152)------------------------------
% 7.00/2.34 % (11150)Instruction limit reached!
% 7.00/2.34 % (11150)------------------------------
% 7.00/2.34 % (11150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.00/2.34 % (11150)Termination reason: Unknown
% 7.00/2.34 % (11150)Termination phase: Property scanning
% 7.00/2.34
% 7.00/2.34 % (11150)Memory used [KB]: 5245
% 7.00/2.34 % (11150)Time elapsed: 0.073 s
% 7.00/2.34 % (11150)Instructions burned: 150 (million)
% 7.00/2.34 % (11150)------------------------------
% 7.00/2.34 % (11150)------------------------------
% 7.00/2.35 % (11155)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_10978 for (2993ds/614Mi)
% 7.00/2.35 % (11153)Instruction limit reached!
% 7.00/2.35 % (11153)------------------------------
% 7.00/2.35 % (11153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.00/2.35 % (11153)Termination reason: Unknown
% 7.00/2.35 % (11153)Termination phase: Saturation
% 7.00/2.35
% 7.00/2.35 % (11153)Memory used [KB]: 5628
% 7.00/2.35 % (11153)Time elapsed: 0.072 s
% 7.00/2.35 % (11153)Instructions burned: 255 (million)
% 7.00/2.35 % (11153)------------------------------
% 7.00/2.35 % (11153)------------------------------
% 7.00/2.36 % (11156)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_10978 for (2992ds/202Mi)
% 7.00/2.36 % (11157)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_10978 for (2992ds/339Mi)
% 7.00/2.38 % (11154)Instruction limit reached!
% 7.00/2.38 % (11154)------------------------------
% 7.00/2.38 % (11154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.00/2.38 % (11154)Termination reason: Unknown
% 7.00/2.38 % (11154)Termination phase: Function definition elimination
% 7.00/2.38
% 7.00/2.38 % (11154)Memory used [KB]: 2814
% 7.00/2.38 % (11154)Time elapsed: 0.064 s
% 7.00/2.38 % (11154)Instructions burned: 140 (million)
% 7.00/2.38 % (11154)------------------------------
% 7.00/2.38 % (11154)------------------------------
% 7.00/2.38 % (11144)Instruction limit reached!
% 7.00/2.38 % (11144)------------------------------
% 7.00/2.38 % (11144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.00/2.38 % (11144)Termination reason: Unknown
% 7.00/2.38 % (11144)Termination phase: Saturation
% 7.00/2.38
% 7.00/2.38 % (11144)Memory used [KB]: 7675
% 7.00/2.38 % (11144)Time elapsed: 0.187 s
% 7.00/2.38 % (11144)Instructions burned: 454 (million)
% 7.00/2.38 % (11144)------------------------------
% 7.00/2.38 % (11144)------------------------------
% 7.00/2.39 % (11158)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_10978 for (2992ds/283Mi)
% 7.77/2.40 % (11159)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_10978 for (2992ds/134Mi)
% 7.77/2.43 % (11151)Instruction limit reached!
% 7.77/2.43 % (11151)------------------------------
% 7.77/2.43 % (11151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.43 % (11151)Termination reason: Unknown
% 7.77/2.43 % (11151)Termination phase: Saturation
% 7.77/2.43
% 7.77/2.43 % (11151)Memory used [KB]: 8315
% 7.77/2.43 % (11151)Time elapsed: 0.150 s
% 7.77/2.43 % (11151)Instructions burned: 343 (million)
% 7.77/2.43 % (11151)------------------------------
% 7.77/2.43 % (11151)------------------------------
% 7.77/2.45 % (11156)Instruction limit reached!
% 7.77/2.45 % (11156)------------------------------
% 7.77/2.45 % (11156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.45 % (11156)Termination reason: Unknown
% 7.77/2.45 % (11156)Termination phase: Property scanning
% 7.77/2.45
% 7.77/2.45 % (11156)Memory used [KB]: 5245
% 7.77/2.45 % (11156)Time elapsed: 0.095 s
% 7.77/2.45 % (11156)Instructions burned: 202 (million)
% 7.77/2.45 % (11156)------------------------------
% 7.77/2.45 % (11156)------------------------------
% 7.77/2.45 % (11160)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_10978 for (2992ds/298Mi)
% 7.77/2.46 % (11159)Instruction limit reached!
% 7.77/2.46 % (11159)------------------------------
% 7.77/2.46 % (11159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.46 % (11159)Termination reason: Unknown
% 7.77/2.46 % (11159)Termination phase: Function definition elimination
% 7.77/2.46
% 7.77/2.46 % (11159)Memory used [KB]: 2814
% 7.77/2.46 % (11159)Time elapsed: 0.062 s
% 7.77/2.46 % (11159)Instructions burned: 136 (million)
% 7.77/2.46 % (11159)------------------------------
% 7.77/2.46 % (11159)------------------------------
% 7.77/2.47 % (11162)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_10978 for (2991ds/258Mi)
% 7.77/2.47 % (11161)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_10978 for (2991ds/192Mi)
% 8.12/2.51 % (11158)Instruction limit reached!
% 8.12/2.51 % (11158)------------------------------
% 8.12/2.51 % (11158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.12/2.51 % (11158)Termination reason: Unknown
% 8.12/2.51 % (11158)Termination phase: Saturation
% 8.12/2.51
% 8.12/2.51 % (11158)Memory used [KB]: 7547
% 8.12/2.51 % (11158)Time elapsed: 0.119 s
% 8.12/2.51 % (11158)Instructions burned: 284 (million)
% 8.12/2.51 % (11158)------------------------------
% 8.12/2.51 % (11158)------------------------------
% 8.12/2.51 % (11157)Instruction limit reached!
% 8.12/2.51 % (11157)------------------------------
% 8.12/2.51 % (11157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.12/2.51 % (11157)Termination reason: Unknown
% 8.12/2.51 % (11157)Termination phase: Saturation
% 8.12/2.51
% 8.12/2.51 % (11157)Memory used [KB]: 8187
% 8.12/2.51 % (11157)Time elapsed: 0.153 s
% 8.12/2.51 % (11157)Instructions burned: 339 (million)
% 8.12/2.51 % (11157)------------------------------
% 8.12/2.51 % (11157)------------------------------
% 8.12/2.53 % (11163)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_10978 for (2991ds/90Mi)
% 8.12/2.53 % (11164)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_10978 for (2991ds/231Mi)
% 8.12/2.55 % (11136)Instruction limit reached!
% 8.12/2.55 % (11136)------------------------------
% 8.12/2.55 % (11136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.12/2.55 % (11136)Termination reason: Unknown
% 8.12/2.55 % (11136)Termination phase: Saturation
% 8.12/2.55
% 8.12/2.55 % (11136)Memory used [KB]: 12665
% 8.12/2.55 % (11136)Time elapsed: 0.444 s
% 8.12/2.55 % (11136)Instructions burned: 1089 (million)
% 8.12/2.55 % (11136)------------------------------
% 8.12/2.55 % (11136)------------------------------
% 8.12/2.56 % (11161)Instruction limit reached!
% 8.12/2.56 % (11161)------------------------------
% 8.12/2.56 % (11161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.12/2.56 % (11161)Termination reason: Unknown
% 8.12/2.56 % (11161)Termination phase: Saturation
% 8.12/2.56
% 8.12/2.56 % (11161)Memory used [KB]: 7547
% 8.12/2.56 % (11161)Time elapsed: 0.086 s
% 8.12/2.56 % (11161)Instructions burned: 194 (million)
% 8.12/2.56 % (11161)------------------------------
% 8.12/2.56 % (11161)------------------------------
% 8.12/2.56 % (11165)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_10978 for (2990ds/458Mi)
% 8.12/2.57 % (11163)Instruction limit reached!
% 8.12/2.57 % (11163)------------------------------
% 8.12/2.57 % (11163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.12/2.57 % (11163)Termination reason: Unknown
% 8.12/2.57 % (11163)Termination phase: Property scanning
% 8.12/2.57
% 8.12/2.57 % (11163)Memory used [KB]: 2558
% 8.12/2.57 % (11163)Time elapsed: 0.042 s
% 8.12/2.57 % (11163)Instructions burned: 90 (million)
% 8.12/2.57 % (11163)------------------------------
% 8.12/2.57 % (11163)------------------------------
% 8.12/2.58 % (11166)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_10978 for (2990ds/31Mi)
% 8.12/2.58 % (11160)Instruction limit reached!
% 8.12/2.58 % (11160)------------------------------
% 8.12/2.58 % (11160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.12/2.58 % (11160)Termination reason: Unknown
% 8.12/2.58 % (11160)Termination phase: Saturation
% 8.12/2.58
% 8.12/2.58 % (11160)Memory used [KB]: 7547
% 8.12/2.58 % (11160)Time elapsed: 0.126 s
% 8.12/2.58 % (11160)Instructions burned: 298 (million)
% 8.12/2.58 % (11160)------------------------------
% 8.12/2.58 % (11160)------------------------------
% 8.12/2.58 % (11167)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_10978 for (2990ds/297Mi)
% 8.12/2.59 % (11162)Instruction limit reached!
% 8.12/2.59 % (11162)------------------------------
% 8.12/2.59 % (11162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.12/2.59 % (11162)Termination reason: Unknown
% 8.12/2.59 % (11162)Termination phase: Saturation
% 8.12/2.59
% 8.12/2.59 % (11162)Memory used [KB]: 7803
% 8.12/2.59 % (11162)Time elapsed: 0.115 s
% 8.12/2.59 % (11162)Instructions burned: 260 (million)
% 8.12/2.59 % (11162)------------------------------
% 8.12/2.59 % (11162)------------------------------
% 8.12/2.59 % (11166)Instruction limit reached!
% 8.12/2.59 % (11166)------------------------------
% 8.12/2.59 % (11166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.12/2.59 % (11166)Termination reason: Unknown
% 8.12/2.59 % (11166)Termination phase: shuffling
% 8.12/2.59
% 8.12/2.59 % (11166)Memory used [KB]: 2046
% 8.12/2.59 % (11166)Time elapsed: 0.016 s
% 8.12/2.59 % (11166)Instructions burned: 31 (million)
% 8.12/2.59 % (11166)------------------------------
% 8.12/2.59 % (11166)------------------------------
% 9.33/2.60 % (11168)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_10978 for (2990ds/987Mi)
% 9.33/2.60 % (11169)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_10978 for (2990ds/182Mi)
% 9.33/2.61 % (11170)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_10978 for (2990ds/182Mi)
% 9.33/2.63 % (11155)Instruction limit reached!
% 9.33/2.63 % (11155)------------------------------
% 9.33/2.63 % (11155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.33/2.63 % (11155)Termination reason: Unknown
% 9.33/2.63 % (11155)Termination phase: Saturation
% 9.33/2.63
% 9.33/2.63 % (11155)Memory used [KB]: 10234
% 9.33/2.63 % (11155)Time elapsed: 0.286 s
% 9.33/2.63 % (11155)Instructions burned: 614 (million)
% 9.33/2.63 % (11155)------------------------------
% 9.33/2.63 % (11155)------------------------------
% 9.33/2.63 % (11164)Instruction limit reached!
% 9.33/2.63 % (11164)------------------------------
% 9.33/2.63 % (11164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.33/2.63 % (11164)Termination reason: Unknown
% 9.33/2.63 % (11164)Termination phase: Saturation
% 9.33/2.63
% 9.33/2.63 % (11164)Memory used [KB]: 8443
% 9.33/2.63 % (11164)Time elapsed: 0.103 s
% 9.33/2.63 % (11164)Instructions burned: 232 (million)
% 9.33/2.63 % (11164)------------------------------
% 9.33/2.63 % (11164)------------------------------
% 9.33/2.65 % (11171)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_10978 for (2989ds/154Mi)
% 9.33/2.65 % (11172)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_10978 for (2989ds/79Mi)
% 9.33/2.68 % (11169)Instruction limit reached!
% 9.33/2.68 % (11169)------------------------------
% 9.33/2.68 % (11169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.33/2.68 % (11169)Termination reason: Unknown
% 9.33/2.68 % (11169)Termination phase: Saturation
% 9.33/2.68
% 9.33/2.68 % (11169)Memory used [KB]: 7419
% 9.33/2.68 % (11169)Time elapsed: 0.081 s
% 9.33/2.68 % (11169)Instructions burned: 182 (million)
% 9.33/2.68 % (11169)------------------------------
% 9.33/2.68 % (11169)------------------------------
% 9.33/2.68 % (11172)Instruction limit reached!
% 9.33/2.68 % (11172)------------------------------
% 9.33/2.68 % (11172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.33/2.68 % (11172)Termination reason: Unknown
% 9.33/2.68 % (11172)Termination phase: Property scanning
% 9.33/2.68
% 9.33/2.68 % (11172)Memory used [KB]: 2558
% 9.33/2.68 % (11172)Time elapsed: 0.038 s
% 9.33/2.68 % (11172)Instructions burned: 80 (million)
% 9.33/2.68 % (11172)------------------------------
% 9.33/2.68 % (11172)------------------------------
% 9.33/2.69 % (11170)Instruction limit reached!
% 9.33/2.69 % (11170)------------------------------
% 9.33/2.69 % (11170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.33/2.69 % (11170)Termination reason: Unknown
% 9.33/2.69 % (11170)Termination phase: Property scanning
% 9.33/2.69
% 9.33/2.69 % (11170)Memory used [KB]: 5245
% 9.33/2.69 % (11170)Time elapsed: 0.086 s
% 9.33/2.69 % (11170)Instructions burned: 182 (million)
% 9.33/2.69 % (11170)------------------------------
% 9.33/2.69 % (11170)------------------------------
% 10.00/2.70 % (11173)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_10978 for (2989ds/216Mi)
% 10.00/2.70 % (11174)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_10978 for (2989ds/114Mi)
% 10.00/2.70 % (11171)Instruction limit reached!
% 10.00/2.70 % (11171)------------------------------
% 10.00/2.70 % (11171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.00/2.70 % (11171)Termination reason: Unknown
% 10.00/2.70 % (11171)Termination phase: Property scanning
% 10.00/2.70
% 10.00/2.70 % (11171)Memory used [KB]: 2814
% 10.00/2.70 % (11171)Time elapsed: 0.055 s
% 10.00/2.70 % (11171)Instructions burned: 157 (million)
% 10.00/2.70 % (11171)------------------------------
% 10.00/2.70 % (11171)------------------------------
% 10.00/2.71 % (11167)Instruction limit reached!
% 10.00/2.71 % (11167)------------------------------
% 10.00/2.71 % (11167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.00/2.71 % (11167)Termination reason: Unknown
% 10.00/2.71 % (11167)Termination phase: Saturation
% 10.00/2.71
% 10.00/2.71 % (11167)Memory used [KB]: 7547
% 10.00/2.71 % (11167)Time elapsed: 0.125 s
% 10.00/2.71 % (11167)Instructions burned: 299 (million)
% 10.00/2.71 % (11167)------------------------------
% 10.00/2.71 % (11167)------------------------------
% 10.00/2.71 % (11175)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_10978 for (2989ds/922Mi)
% 10.00/2.71 % (11165)Instruction limit reached!
% 10.00/2.71 % (11165)------------------------------
% 10.00/2.71 % (11165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.00/2.71 % (11165)Termination reason: Unknown
% 10.00/2.71 % (11165)Termination phase: Saturation
% 10.00/2.71
% 10.00/2.71 % (11165)Memory used [KB]: 9722
% 10.00/2.71 % (11165)Time elapsed: 0.153 s
% 10.00/2.71 % (11165)Instructions burned: 459 (million)
% 10.00/2.71 % (11165)------------------------------
% 10.00/2.71 % (11165)------------------------------
% 10.00/2.72 % (11176)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_10978 for (2989ds/182Mi)
% 10.00/2.73 % (11177)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_10978 for (2989ds/164Mi)
% 10.00/2.73 % (11178)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_10978 for (2989ds/50Mi)
% 10.00/2.75 % (11178)Instruction limit reached!
% 10.00/2.75 % (11178)------------------------------
% 10.00/2.75 % (11178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.00/2.75 % (11178)Termination reason: Unknown
% 10.00/2.75 % (11178)Termination phase: shuffling
% 10.00/2.75
% 10.00/2.75 % (11178)Memory used [KB]: 2430
% 10.00/2.75 % (11178)Time elapsed: 0.024 s
% 10.00/2.75 % (11178)Instructions burned: 50 (million)
% 10.00/2.75 % (11178)------------------------------
% 10.00/2.75 % (11178)------------------------------
% 10.00/2.75 % (11174)Instruction limit reached!
% 10.00/2.75 % (11174)------------------------------
% 10.00/2.75 % (11174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.00/2.75 % (11174)Termination reason: Unknown
% 10.00/2.75 % (11174)Termination phase: Property scanning
% 10.00/2.75
% 10.00/2.75 % (11174)Memory used [KB]: 2814
% 10.00/2.75 % (11174)Time elapsed: 0.052 s
% 10.00/2.75 % (11174)Instructions burned: 114 (million)
% 10.00/2.75 % (11174)------------------------------
% 10.00/2.75 % (11174)------------------------------
% 10.00/2.77 % (11180)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_10978 for (2988ds/1021Mi)
% 10.00/2.77 % (11179)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_10978 for (2988ds/368Mi)
% 10.00/2.79 % (11173)Instruction limit reached!
% 10.00/2.79 % (11173)------------------------------
% 10.00/2.79 % (11173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.00/2.79 % (11173)Termination reason: Unknown
% 10.00/2.79 % (11173)Termination phase: Property scanning
% 10.00/2.79
% 10.00/2.79 % (11173)Memory used [KB]: 2814
% 10.00/2.79 % (11173)Time elapsed: 0.091 s
% 10.00/2.79 % (11173)Instructions burned: 216 (million)
% 10.00/2.79 % (11173)------------------------------
% 10.00/2.79 % (11173)------------------------------
% 10.00/2.80 % (11176)Instruction limit reached!
% 10.00/2.80 % (11176)------------------------------
% 10.00/2.80 % (11176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.00/2.80 % (11176)Termination reason: Unknown
% 10.00/2.80 % (11176)Termination phase: Saturation
% 10.00/2.80
% 10.00/2.80 % (11176)Memory used [KB]: 7291
% 10.00/2.80 % (11176)Time elapsed: 0.080 s
% 10.00/2.80 % (11176)Instructions burned: 182 (million)
% 10.00/2.80 % (11176)------------------------------
% 10.00/2.80 % (11176)------------------------------
% 10.58/2.80 % (11177)Instruction limit reached!
% 10.58/2.80 % (11177)------------------------------
% 10.58/2.80 % (11177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.58/2.80 % (11177)Termination reason: Unknown
% 10.58/2.80 % (11177)Termination phase: Function definition elimination
% 10.58/2.80
% 10.58/2.80 % (11177)Memory used [KB]: 2814
% 10.58/2.80 % (11177)Time elapsed: 0.070 s
% 10.58/2.80 % (11177)Instructions burned: 164 (million)
% 10.58/2.80 % (11177)------------------------------
% 10.58/2.80 % (11177)------------------------------
% 10.58/2.81 % (11182)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_10978 for (2988ds/267Mi)
% 10.58/2.81 % (11184)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_10978 for (2988ds/26Mi)
% 10.58/2.82 % (11183)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_10978 for (2988ds/204Mi)
% 10.58/2.83 % (11184)Instruction limit reached!
% 10.58/2.83 % (11184)------------------------------
% 10.58/2.83 % (11184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.58/2.83 % (11184)Termination reason: Unknown
% 10.58/2.83 % (11184)Termination phase: shuffling
% 10.58/2.83
% 10.58/2.83 % (11184)Memory used [KB]: 2174
% 10.58/2.83 % (11184)Time elapsed: 0.014 s
% 10.58/2.83 % (11184)Instructions burned: 27 (million)
% 10.58/2.83 % (11184)------------------------------
% 10.58/2.83 % (11184)------------------------------
% 10.58/2.84 % (11185)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_10978 for (2988ds/53Mi)
% 10.58/2.87 % (11185)Instruction limit reached!
% 10.58/2.87 % (11185)------------------------------
% 10.58/2.87 % (11185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.58/2.87 % (11185)Termination reason: Unknown
% 10.58/2.87 % (11185)Termination phase: shuffling
% 10.58/2.87
% 10.58/2.87 % (11185)Memory used [KB]: 2558
% 10.58/2.87 % (11185)Time elapsed: 0.026 s
% 10.58/2.87 % (11185)Instructions burned: 54 (million)
% 10.58/2.87 % (11185)------------------------------
% 10.58/2.87 % (11185)------------------------------
% 10.58/2.88 % (11186)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_10978 for (2987ds/4436Mi)
% 10.83/2.92 % (11182)Instruction limit reached!
% 10.83/2.92 % (11182)------------------------------
% 10.83/2.92 % (11182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.83/2.92 % (11182)Termination reason: Unknown
% 10.83/2.92 % (11182)Termination phase: Saturation
% 10.83/2.92
% 10.83/2.92 % (11182)Memory used [KB]: 7547
% 10.83/2.92 % (11182)Time elapsed: 0.113 s
% 10.83/2.92 % (11182)Instructions burned: 268 (million)
% 10.83/2.92 % (11182)------------------------------
% 10.83/2.92 % (11182)------------------------------
% 10.83/2.92 % (11183)Instruction limit reached!
% 10.83/2.92 % (11183)------------------------------
% 10.83/2.92 % (11183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.83/2.92 % (11183)Termination reason: Unknown
% 10.83/2.92 % (11183)Termination phase: Property scanning
% 10.83/2.92
% 10.83/2.92 % (11183)Memory used [KB]: 2942
% 10.83/2.92 % (11183)Time elapsed: 0.057 s
% 10.83/2.92 % (11183)Instructions burned: 206 (million)
% 10.83/2.92 % (11183)------------------------------
% 10.83/2.92 % (11183)------------------------------
% 10.83/2.93 % (11179)Instruction limit reached!
% 10.83/2.93 % (11179)------------------------------
% 10.83/2.93 % (11179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.83/2.93 % (11179)Termination reason: Unknown
% 10.83/2.93 % (11179)Termination phase: Saturation
% 10.83/2.93
% 10.83/2.93 % (11179)Memory used [KB]: 9338
% 10.83/2.93 % (11179)Time elapsed: 0.166 s
% 10.83/2.93 % (11179)Instructions burned: 369 (million)
% 10.83/2.93 % (11179)------------------------------
% 10.83/2.93 % (11179)------------------------------
% 10.83/2.93 % (11188)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_10978 for (2987ds/408Mi)
% 10.83/2.94 % (11187)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_10978 for (2987ds/1539Mi)
% 10.83/2.95 % (11189)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_10978 for (2986ds/5205Mi)
% 10.83/2.98 % (11168)Instruction limit reached!
% 10.83/2.98 % (11168)------------------------------
% 10.83/2.98 % (11168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.83/2.98 % (11168)Termination reason: Unknown
% 10.83/2.98 % (11168)Termination phase: Saturation
% 10.83/2.98
% 10.83/2.98 % (11168)Memory used [KB]: 16758
% 10.83/2.98 % (11168)Time elapsed: 0.385 s
% 10.83/2.98 % (11168)Instructions burned: 988 (million)
% 10.83/2.98 % (11168)------------------------------
% 10.83/2.98 % (11168)------------------------------
% 10.83/2.99 % (11190)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_10978 for (2986ds/1913Mi)
% 12.50/3.09 % (11188)Instruction limit reached!
% 12.50/3.09 % (11188)------------------------------
% 12.50/3.09 % (11188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.50/3.09 % (11188)Termination reason: Unknown
% 12.50/3.09 % (11188)Termination phase: Saturation
% 12.50/3.09
% 12.50/3.09 % (11188)Memory used [KB]: 11641
% 12.50/3.09 % (11188)Time elapsed: 0.158 s
% 12.50/3.09 % (11188)Instructions burned: 408 (million)
% 12.50/3.09 % (11188)------------------------------
% 12.50/3.09 % (11188)------------------------------
% 12.50/3.11 % (11193)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_10978 for (2985ds/4350Mi)
% 13.21/3.13 % (11175)Instruction limit reached!
% 13.21/3.13 % (11175)------------------------------
% 13.21/3.13 % (11175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.21/3.13 % (11175)Termination reason: Unknown
% 13.21/3.13 % (11175)Termination phase: Saturation
% 13.21/3.13
% 13.21/3.13 % (11175)Memory used [KB]: 11897
% 13.21/3.13 % (11175)Time elapsed: 0.433 s
% 13.21/3.13 % (11175)Instructions burned: 922 (million)
% 13.21/3.13 % (11175)------------------------------
% 13.21/3.13 % (11175)------------------------------
% 13.21/3.15 % (11194)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_10978 for (2985ds/68Mi)
% 13.21/3.18 % (11194)Instruction limit reached!
% 13.21/3.18 % (11194)------------------------------
% 13.21/3.18 % (11194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.21/3.18 % (11194)Termination reason: Unknown
% 13.21/3.18 % (11194)Termination phase: Property scanning
% 13.21/3.18
% 13.21/3.18 % (11194)Memory used [KB]: 2558
% 13.21/3.18 % (11194)Time elapsed: 0.033 s
% 13.21/3.18 % (11194)Instructions burned: 69 (million)
% 13.21/3.18 % (11194)------------------------------
% 13.21/3.18 % (11194)------------------------------
% 13.21/3.19 % (11195)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_10978 for (2984ds/358Mi)
% 13.66/3.27 % (11180)Instruction limit reached!
% 13.66/3.27 % (11180)------------------------------
% 13.66/3.27 % (11180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.66/3.27 % (11180)Termination reason: Unknown
% 13.66/3.27 % (11180)Termination phase: Saturation
% 13.66/3.27
% 13.66/3.27 % (11180)Memory used [KB]: 12920
% 13.66/3.27 % (11180)Time elapsed: 0.508 s
% 13.66/3.27 % (11180)Instructions burned: 1022 (million)
% 13.66/3.27 % (11180)------------------------------
% 13.66/3.27 % (11180)------------------------------
% 13.66/3.29 % (11196)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_10978 for (2983ds/31Mi)
% 14.16/3.31 % (11196)Instruction limit reached!
% 14.16/3.31 % (11196)------------------------------
% 14.16/3.31 % (11196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.16/3.31 % (11196)Termination reason: Unknown
% 14.16/3.31 % (11196)Termination phase: shuffling
% 14.16/3.31
% 14.16/3.31 % (11196)Memory used [KB]: 2046
% 14.16/3.31 % (11196)Time elapsed: 0.017 s
% 14.16/3.31 % (11196)Instructions burned: 32 (million)
% 14.16/3.31 % (11196)------------------------------
% 14.16/3.31 % (11196)------------------------------
% 14.16/3.32 % (11197)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_10978 for (2983ds/279Mi)
% 14.16/3.35 % (11195)Instruction limit reached!
% 14.16/3.35 % (11195)------------------------------
% 14.16/3.35 % (11195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.16/3.35 % (11195)Termination reason: Unknown
% 14.16/3.35 % (11195)Termination phase: Saturation
% 14.16/3.35
% 14.16/3.35 % (11195)Memory used [KB]: 8571
% 14.16/3.35 % (11195)Time elapsed: 0.158 s
% 14.16/3.35 % (11195)Instructions burned: 359 (million)
% 14.16/3.35 % (11195)------------------------------
% 14.16/3.35 % (11195)------------------------------
% 14.16/3.37 % (11198)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_10978 for (2982ds/258Mi)
% 14.77/3.42 % (11197)Instruction limit reached!
% 14.77/3.42 % (11197)------------------------------
% 14.77/3.42 % (11197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.77/3.42 % (11197)Termination reason: Unknown
% 14.77/3.42 % (11197)Termination phase: Saturation
% 14.77/3.42
% 14.77/3.42 % (11197)Memory used [KB]: 7547
% 14.77/3.42 % (11197)Time elapsed: 0.086 s
% 14.77/3.42 % (11197)Instructions burned: 279 (million)
% 14.77/3.42 % (11197)------------------------------
% 14.77/3.42 % (11197)------------------------------
% 14.77/3.44 % (11199)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_10978 for (2982ds/26Mi)
% 14.77/3.45 % (11198)Instruction limit reached!
% 14.77/3.45 % (11198)------------------------------
% 14.77/3.45 % (11198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.77/3.45 % (11198)Termination reason: Unknown
% 14.77/3.45 % (11198)Termination phase: Saturation
% 14.77/3.45
% 14.77/3.45 % (11198)Memory used [KB]: 8315
% 14.77/3.45 % (11198)Time elapsed: 0.069 s
% 14.77/3.45 % (11198)Instructions burned: 260 (million)
% 14.77/3.45 % (11198)------------------------------
% 14.77/3.45 % (11198)------------------------------
% 14.77/3.45 % (11199)Instruction limit reached!
% 14.77/3.45 % (11199)------------------------------
% 14.77/3.45 % (11199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.77/3.45 % (11199)Termination reason: Unknown
% 14.77/3.45 % (11199)Termination phase: shuffling
% 14.77/3.45
% 14.77/3.45 % (11199)Memory used [KB]: 1918
% 14.77/3.45 % (11199)Time elapsed: 0.013 s
% 14.77/3.45 % (11199)Instructions burned: 26 (million)
% 14.77/3.45 % (11199)------------------------------
% 14.77/3.45 % (11199)------------------------------
% 14.77/3.46 % (11200)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_10978 for (2981ds/995Mi)
% 14.77/3.47 % (11201)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_10978 for (2981ds/373Mi)
% 15.37/3.58 % (11201)Instruction limit reached!
% 15.37/3.58 % (11201)------------------------------
% 15.37/3.58 % (11201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.37/3.58 % (11201)Termination reason: Unknown
% 15.37/3.58 % (11201)Termination phase: Saturation
% 15.37/3.58
% 15.37/3.58 % (11201)Memory used [KB]: 9466
% 15.37/3.58 % (11201)Time elapsed: 0.109 s
% 15.37/3.58 % (11201)Instructions burned: 376 (million)
% 15.37/3.58 % (11201)------------------------------
% 15.37/3.58 % (11201)------------------------------
% 15.37/3.59 % (11203)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_10978 for (2980ds/253Mi)
% 15.89/3.65 % (11203)Instruction limit reached!
% 15.89/3.65 % (11203)------------------------------
% 15.89/3.65 % (11203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.89/3.65 % (11203)Termination reason: Unknown
% 15.89/3.65 % (11203)Termination phase: Saturation
% 15.89/3.65
% 15.89/3.65 % (11203)Memory used [KB]: 7547
% 15.89/3.65 % (11203)Time elapsed: 0.065 s
% 15.89/3.65 % (11203)Instructions burned: 254 (million)
% 15.89/3.65 % (11203)------------------------------
% 15.89/3.65 % (11203)------------------------------
% 15.89/3.66 % (11204)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_10978 for (2979ds/832Mi)
% 15.89/3.68 % (11187)Instruction limit reached!
% 15.89/3.68 % (11187)------------------------------
% 15.89/3.68 % (11187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.89/3.68 % (11187)Termination reason: Unknown
% 15.89/3.68 % (11187)Termination phase: Saturation
% 15.89/3.68
% 15.89/3.68 % (11187)Memory used [KB]: 11001
% 15.89/3.68 % (11187)Time elapsed: 0.751 s
% 15.89/3.68 % (11187)Instructions burned: 1539 (million)
% 15.89/3.68 % (11187)------------------------------
% 15.89/3.68 % (11187)------------------------------
% 16.36/3.70 % (11205)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_10978 for (2979ds/668Mi)
% 16.66/3.81 % (11190)Instruction limit reached!
% 16.66/3.81 % (11190)------------------------------
% 16.66/3.81 % (11190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.66/3.81 % (11190)Termination reason: Unknown
% 16.66/3.81 % (11190)Termination phase: Saturation
% 16.66/3.81
% 16.66/3.81 % (11190)Memory used [KB]: 6268
% 16.66/3.81 % (11190)Time elapsed: 0.829 s
% 16.66/3.81 % (11190)Instructions burned: 1916 (million)
% 16.66/3.81 % (11190)------------------------------
% 16.66/3.81 % (11190)------------------------------
% 16.66/3.82 % (11206)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_10978 for (2978ds/40Mi)
% 16.66/3.82 % (11200)Instruction limit reached!
% 16.66/3.82 % (11200)------------------------------
% 16.66/3.82 % (11200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.66/3.82 % (11200)Termination reason: Unknown
% 16.66/3.82 % (11200)Termination phase: Saturation
% 16.66/3.82
% 16.66/3.82 % (11200)Memory used [KB]: 16630
% 16.66/3.82 % (11200)Time elapsed: 0.362 s
% 16.66/3.82 % (11200)Instructions burned: 996 (million)
% 16.66/3.82 % (11200)------------------------------
% 16.66/3.82 % (11200)------------------------------
% 16.66/3.83 % (11206)Instruction limit reached!
% 16.66/3.83 % (11206)------------------------------
% 16.66/3.83 % (11206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.66/3.83 % (11206)Termination reason: Unknown
% 16.66/3.83 % (11206)Termination phase: shuffling
% 16.66/3.83
% 16.66/3.83 % (11206)Memory used [KB]: 2302
% 16.66/3.83 % (11206)Time elapsed: 0.013 s
% 16.66/3.83 % (11206)Instructions burned: 43 (million)
% 16.66/3.83 % (11206)------------------------------
% 16.66/3.83 % (11206)------------------------------
% 16.66/3.84 % (11208)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_10978 for (2978ds/187Mi)
% 16.66/3.84 % (11207)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_10978 for (2978ds/294Mi)
% 16.66/3.89 % (11208)Instruction limit reached!
% 16.66/3.89 % (11208)------------------------------
% 16.66/3.89 % (11208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.66/3.89 % (11208)Termination reason: Unknown
% 16.66/3.89 % (11208)Termination phase: Saturation
% 16.66/3.89
% 16.66/3.89 % (11208)Memory used [KB]: 7419
% 16.66/3.89 % (11208)Time elapsed: 0.048 s
% 16.66/3.89 % (11208)Instructions burned: 188 (million)
% 16.66/3.89 % (11208)------------------------------
% 16.66/3.89 % (11208)------------------------------
% 17.33/3.90 % (11209)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_10978 for (2977ds/371Mi)
% 17.33/3.96 % (11207)Instruction limit reached!
% 17.33/3.96 % (11207)------------------------------
% 17.33/3.96 % (11207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.33/3.96 % (11207)Termination reason: Unknown
% 17.33/3.96 % (11207)Termination phase: Saturation
% 17.33/3.96
% 17.33/3.96 % (11207)Memory used [KB]: 7547
% 17.33/3.96 % (11207)Time elapsed: 0.124 s
% 17.33/3.96 % (11207)Instructions burned: 295 (million)
% 17.33/3.96 % (11207)------------------------------
% 17.33/3.96 % (11207)------------------------------
% 17.33/3.97 % (11205)Instruction limit reached!
% 17.33/3.97 % (11205)------------------------------
% 17.33/3.97 % (11205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.33/3.97 % (11205)Termination reason: Unknown
% 17.33/3.97 % (11205)Termination phase: Saturation
% 17.33/3.97
% 17.33/3.97 % (11205)Memory used [KB]: 13688
% 17.33/3.97 % (11205)Time elapsed: 0.265 s
% 17.33/3.97 % (11205)Instructions burned: 668 (million)
% 17.33/3.97 % (11205)------------------------------
% 17.33/3.97 % (11205)------------------------------
% 17.33/3.98 % (11210)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_10978 for (2976ds/1827Mi)
% 17.33/3.98 % (11211)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_10978 for (2976ds/70Mi)
% 17.33/3.99 % (11204)Instruction limit reached!
% 17.33/3.99 % (11204)------------------------------
% 17.33/3.99 % (11204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.33/3.99 % (11204)Termination reason: Unknown
% 17.33/3.99 % (11204)Termination phase: Saturation
% 17.33/3.99
% 17.33/3.99 % (11204)Memory used [KB]: 11769
% 17.33/3.99 % (11204)Time elapsed: 0.347 s
% 17.33/3.99 % (11204)Instructions burned: 832 (million)
% 17.33/3.99 % (11204)------------------------------
% 17.33/3.99 % (11204)------------------------------
% 17.33/4.01 % (11212)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_10978 for (2976ds/316Mi)
% 17.33/4.01 % (11211)Instruction limit reached!
% 17.33/4.01 % (11211)------------------------------
% 17.33/4.01 % (11211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.33/4.01 % (11211)Termination reason: Unknown
% 17.33/4.01 % (11211)Termination phase: Property scanning
% 17.33/4.01
% 17.33/4.01 % (11211)Memory used [KB]: 2558
% 17.33/4.01 % (11211)Time elapsed: 0.033 s
% 17.33/4.01 % (11211)Instructions burned: 71 (million)
% 17.33/4.01 % (11211)------------------------------
% 17.33/4.01 % (11211)------------------------------
% 19.50/4.03 % (11213)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_10978 for (2976ds/932Mi)
% 19.50/4.05 % (11209)Instruction limit reached!
% 19.50/4.05 % (11209)------------------------------
% 19.50/4.05 % (11209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.50/4.05 % (11209)Termination reason: Unknown
% 19.50/4.05 % (11209)Termination phase: Saturation
% 19.50/4.05
% 19.50/4.05 % (11209)Memory used [KB]: 9210
% 19.50/4.05 % (11209)Time elapsed: 0.156 s
% 19.50/4.05 % (11209)Instructions burned: 372 (million)
% 19.50/4.05 % (11209)------------------------------
% 19.50/4.05 % (11209)------------------------------
% 19.50/4.07 % (11215)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_10978 for (2975ds/4714Mi)
% 19.50/4.12 % (11186)First to succeed.
% 19.50/4.13 % (11186)Refutation found. Thanks to Tanya!
% 19.50/4.13 % SZS status Theorem for DTF2THF_10978
% 19.50/4.13 % SZS output start Proof for DTF2THF_10978
% 19.50/4.13 thf(func_def_0, type, in: $i > $i > $o).
% 19.50/4.13 thf(func_def_1, type, exu: ($i > $o) > $o).
% 19.50/4.13 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 19.50/4.13 thf(func_def_8, type, powerset: $i > $i).
% 19.50/4.13 thf(func_def_10, type, setunion: $i > $i).
% 19.50/4.13 thf(func_def_19, type, descr: ($i > $o) > $i).
% 19.50/4.13 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 19.50/4.13 thf(func_def_26, type, prop2set: $o > $i).
% 19.50/4.13 thf(func_def_36, type, nonempty: $i > $o).
% 19.50/4.13 thf(func_def_69, type, set2prop: $i > $o).
% 19.50/4.13 thf(func_def_88, type, subset: $i > $i > $o).
% 19.50/4.13 thf(func_def_89, type, disjoint: $i > $i > $o).
% 19.50/4.13 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 19.50/4.13 thf(func_def_114, type, binunion: $i > $i > $i).
% 19.50/4.13 thf(func_def_122, type, binintersect: $i > $i > $i).
% 19.50/4.13 thf(func_def_135, type, regular: $i > $o).
% 19.50/4.13 thf(func_def_136, type, setminus: $i > $i > $i).
% 19.50/4.13 thf(func_def_147, type, symdiff: $i > $i > $i).
% 19.50/4.13 thf(func_def_153, type, iskpair: $i > $o).
% 19.50/4.13 thf(func_def_158, type, kpair: $i > $i > $i).
% 19.50/4.13 thf(func_def_160, type, cartprod: $i > $i > $i).
% 19.50/4.13 thf(func_def_177, type, singleton: $i > $o).
% 19.50/4.13 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 19.50/4.13 thf(func_def_184, type, atmost1p: $i > $o).
% 19.50/4.13 thf(func_def_185, type, atleast2p: $i > $o).
% 19.50/4.13 thf(func_def_186, type, atmost2p: $i > $o).
% 19.50/4.13 thf(func_def_187, type, upairsetp: $i > $o).
% 19.50/4.13 thf(func_def_191, type, kfst: $i > $i).
% 19.50/4.13 thf(func_def_203, type, ksnd: $i > $i).
% 19.50/4.13 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 19.50/4.13 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 19.50/4.13 thf(func_def_222, type, func: $i > $i > $i > $o).
% 19.50/4.13 thf(func_def_223, type, funcSet: $i > $i > $i).
% 19.50/4.13 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 19.50/4.13 thf(func_def_259, type, if: $i > $o > $i > $i > $i).
% 19.50/4.13 thf(func_def_323, type, breln1: $i > $i > $o).
% 19.50/4.13 thf(func_def_325, type, breln1Set: $i > $i).
% 19.50/4.13 thf(func_def_327, type, transitive: $i > $i > $o).
% 19.50/4.13 thf(func_def_328, type, antisymmetric: $i > $i > $o).
% 19.50/4.13 thf(func_def_329, type, reflexive: $i > $i > $o).
% 19.50/4.13 thf(func_def_330, type, refltransitive: $i > $i > $o).
% 19.50/4.13 thf(func_def_331, type, refllinearorder: $i > $i > $o).
% 19.50/4.13 thf(func_def_332, type, reflwellordering: $i > $i > $o).
% 19.50/4.13 thf(func_def_338, type, breln1invset: $i > $i > $i).
% 19.50/4.13 thf(func_def_354, type, sP0: $i > $o > $i > $o).
% 19.50/4.13 thf(func_def_355, type, sP1: $i > ($i > $o) > $o).
% 19.50/4.13 thf(func_def_357, type, sP3: ($i > $o) > $o).
% 19.50/4.13 thf(func_def_358, type, sP4: $i > $i > $o).
% 19.50/4.13 thf(func_def_360, type, sP6: ($i > $i > $o) > $i > $i > $o).
% 19.50/4.13 thf(func_def_361, type, sP7: ($i > $i > $o) > $i > $o).
% 19.50/4.13 thf(func_def_363, type, sP9: ($i > $o) > $i > $o).
% 19.50/4.13 thf(func_def_367, type, sP13: ($i > $o) > $i > $o).
% 19.50/4.13 thf(func_def_368, type, sP14: ($i > $o) > $i > $i > $i > $o).
% 19.50/4.13 thf(func_def_369, type, sP15: $o > $i > $i > $o).
% 19.50/4.13 thf(func_def_371, type, sP17: ($i > $o) > $i > $o).
% 19.50/4.13 thf(func_def_372, type, sP18: $i > $i > ($i > $o) > $o).
% 19.50/4.13 thf(func_def_373, type, sP19: ($i > $o) > $o).
% 19.50/4.13 thf(func_def_374, type, sP20: $i > $i > $i > $o).
% 19.50/4.13 thf(func_def_375, type, sP21: $i > $i > $i > $o > $o).
% 19.50/4.13 thf(func_def_376, type, sP22: $i > $o > $i > $i > $o).
% 19.50/4.13 thf(func_def_379, type, sP25: $i > $i > $i > $o).
% 19.50/4.13 thf(func_def_381, type, sP27: $i > $i > $o).
% 19.50/4.13 thf(func_def_383, type, sP29: $i > ($i > $o) > $o).
% 19.50/4.13 thf(func_def_386, type, sP32: $i > $i > $i > $o).
% 19.50/4.13 thf(func_def_387, type, sP33: $i > $i > $o).
% 19.50/4.13 thf(func_def_388, type, sP34: $i > $o).
% 19.50/4.13 thf(func_def_389, type, sP35: $i > $i > $o).
% 19.50/4.13 thf(func_def_390, type, sP36: $i > $i > $o).
% 19.50/4.13 thf(func_def_391, type, sP37: $i > $i > $o).
% 19.50/4.13 thf(func_def_392, type, sP38: $i > ($i > $o) > $o).
% 19.50/4.13 thf(func_def_395, type, sP41: $i > $i > $i > $i > $o).
% 19.50/4.13 thf(func_def_396, type, sP42: $i > $i > $i > $o).
% 19.50/4.13 thf(func_def_397, type, sP43: $i > $i > $i > $o).
% 19.50/4.13 thf(func_def_398, type, sP44: $i > $i > $i > $o).
% 19.50/4.13 thf(func_def_399, type, sP45: $i > ($i > $i) > $i > $o).
% 19.50/4.13 thf(func_def_401, type, sP47: $i > $i > ($i > $o) > $o).
% 19.50/4.13 thf(func_def_402, type, sP48: $i > $o).
% 19.50/4.13 thf(func_def_403, type, sP49: $i > ($i > $o) > $o).
% 19.50/4.13 thf(func_def_405, type, sP51: $i > $i > ($i > $o) > ($i > $o) > $o).
% 19.50/4.13 thf(func_def_406, type, sP52: $i > $i > ($i > $i) > $o).
% 19.50/4.13 thf(func_def_409, type, sP55: $i > $i > $o).
% 19.50/4.13 thf(func_def_411, type, sP57: $i > $i > $i > $o).
% 19.50/4.13 thf(func_def_413, type, sP59: ($i > $o) > $o).
% 19.50/4.13 thf(func_def_414, type, sP60: $i > $i > $i > $o).
% 19.50/4.13 thf(func_def_417, type, sP63: ($i > $o) > $o).
% 19.50/4.13 thf(func_def_418, type, sP64: $i > $i > $o > $o).
% 19.50/4.13 thf(func_def_419, type, sP65: $i > $i > $i > $o).
% 19.50/4.13 thf(func_def_420, type, sP66: $i > $i > $i > $i > $o).
% 19.50/4.13 thf(func_def_421, type, sP67: $i > $i > $i > $i > $o).
% 19.50/4.13 thf(func_def_422, type, sP68: ($i > $i > $o) > $i > $i > $o).
% 19.50/4.13 thf(func_def_423, type, sP69: $i > ($i > $i > $o) > $i > $o).
% 19.50/4.13 thf(func_def_424, type, sP70: $i > $o).
% 19.50/4.13 thf(func_def_425, type, sP71: $i > $o).
% 19.50/4.13 thf(func_def_426, type, sP72: ($i > $o) > $i > $o).
% 19.50/4.13 thf(func_def_427, type, sP73: ($i > $o) > $i > $o).
% 19.50/4.13 thf(func_def_428, type, sP74: ($i > $o) > $o).
% 19.50/4.13 thf(func_def_429, type, sP75: $o > $i > $i > $o).
% 19.50/4.13 thf(func_def_430, type, sP76: $i > $i > $i > $o).
% 19.50/4.13 thf(func_def_431, type, sP77: $i > $i > $i > $o).
% 19.50/4.13 thf(func_def_432, type, sP78: $i > $i > $i > $o).
% 19.50/4.13 thf(func_def_435, type, sP81: $i > ($i > $o) > $o).
% 19.50/4.13 thf(func_def_436, type, sP82: $i > ($i > $o) > $i > $i > $o).
% 19.50/4.13 thf(func_def_437, type, sP83: ($i > $o) > $i > $o).
% 19.50/4.13 thf(func_def_438, type, sP84: $i > $i > ($i > $o) > $o).
% 19.50/4.13 thf(func_def_439, type, sP85: $i > $i > $i > $i > $o).
% 19.50/4.13 thf(func_def_440, type, sP86: ($i > $o) > $i > $o).
% 19.50/4.13 thf(func_def_442, type, sP88: $i > ($i > $o) > $o).
% 19.50/4.13 thf(func_def_443, type, sP89: ($i > $o) > $i > $o).
% 19.50/4.13 thf(func_def_444, type, sP90: $i > $i > $i > $o).
% 19.50/4.13 thf(func_def_445, type, sP91: $i > $i > $i > $o).
% 19.50/4.13 thf(func_def_446, type, sP92: $i > $i > $i > $o).
% 19.50/4.13 thf(func_def_473, type, sK119: $i > $i).
% 19.50/4.13 thf(func_def_479, type, sK125: $i > $o > $i > $i).
% 19.50/4.13 thf(func_def_485, type, sK131: $i > $o).
% 19.50/4.13 thf(func_def_487, type, sK133: $i > ($i > $o) > $i).
% 19.50/4.13 thf(func_def_488, type, sK134: $i > ($i > $o) > $i).
% 19.50/4.13 thf(func_def_499, type, sK145: ($i > $o) > $i).
% 19.50/4.13 thf(func_def_500, type, sK146: $i > ($i > $o) > $i).
% 19.50/4.13 thf(func_def_501, type, sK147: $i > $o).
% 19.50/4.13 thf(func_def_508, type, sK154: $i > $i > $i).
% 19.50/4.13 thf(func_def_530, type, sK176: $i > $i > $o).
% 19.50/4.13 thf(func_def_571, type, sK217: $i > $i > $o).
% 19.50/4.13 thf(func_def_585, type, sK231: $i > $i > $o).
% 19.50/4.13 thf(func_def_586, type, sK232: ($i > $i > $o) > $i > $i).
% 19.50/4.13 thf(func_def_587, type, sK233: $i > ($i > $i > $o) > $i > $i).
% 19.50/4.13 thf(func_def_588, type, sK234: ($i > $i > $o) > $i > $i).
% 19.50/4.13 thf(func_def_589, type, sK235: ($i > $i > $o) > $i > $i > $i).
% 19.50/4.13 thf(func_def_604, type, sK250: $i > $o).
% 19.50/4.13 thf(func_def_605, type, sK251: ($i > $o) > $i > $i).
% 19.50/4.13 thf(func_def_606, type, sK252: ($i > $o) > $i > $i).
% 19.50/4.13 thf(func_def_621, type, sK267: $i > $i).
% 19.50/4.13 thf(func_def_624, type, sK270: $i > $i > ($i > $i) > $i).
% 19.50/4.13 thf(func_def_629, type, sK275: $i > $o).
% 19.50/4.13 thf(func_def_631, type, sK277: $i > $o).
% 19.50/4.13 thf(func_def_638, type, sK284: $i > $o).
% 19.50/4.13 thf(func_def_639, type, sK285: ($i > $o) > $i > $i).
% 19.50/4.13 thf(func_def_642, type, sK288: ($i > $o) > $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_643, type, sK289: ($i > $o) > $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_644, type, sK290: ($i > $o) > $i > $i).
% 19.50/4.13 thf(func_def_648, type, sK294: $i > $o).
% 19.50/4.13 thf(func_def_653, type, sK299: $i > $i > ($i > $o) > $i).
% 19.50/4.13 thf(func_def_654, type, sK300: $i > $i > ($i > $o) > $i).
% 19.50/4.13 thf(func_def_655, type, sK301: ($i > $o) > $i > $i).
% 19.50/4.13 thf(func_def_658, type, sK304: $i > $o).
% 19.50/4.13 thf(func_def_660, type, sK306: ($i > $o) > $i).
% 19.50/4.13 thf(func_def_661, type, sK307: ($i > $o) > $i).
% 19.50/4.13 thf(func_def_662, type, sK308: $i > $o).
% 19.50/4.13 thf(func_def_672, type, sK318: $i > $o).
% 19.50/4.13 thf(func_def_675, type, sK321: $i > $i > $o).
% 19.50/4.13 thf(func_def_678, type, sK324: $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_679, type, sK325: $i > $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_702, type, sK348: $i > $o).
% 19.50/4.13 thf(func_def_703, type, sK349: $i > $o).
% 19.50/4.13 thf(func_def_704, type, sK350: ($i > $o) > ($i > $o) > $i).
% 19.50/4.13 thf(func_def_705, type, sK351: ($i > $o) > ($i > $o) > $i).
% 19.50/4.13 thf(func_def_709, type, sK355: $i > $i).
% 19.50/4.13 thf(func_def_712, type, sK358: $i > $i > ($i > $i) > $i).
% 19.50/4.13 thf(func_def_713, type, sK359: $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_734, type, sK380: $i > $i > $i).
% 19.50/4.13 thf(func_def_740, type, sK386: $i > $i > $i).
% 19.50/4.13 thf(func_def_741, type, sK387: $i > $i > $i).
% 19.50/4.13 thf(func_def_742, type, sK388: $i > $o).
% 19.50/4.13 thf(func_def_744, type, sK390: $i > ($i > $o) > $i).
% 19.50/4.13 thf(func_def_745, type, sK391: $i > ($i > $o) > $i).
% 19.50/4.13 thf(func_def_757, type, sK403: $i > $i).
% 19.50/4.13 thf(func_def_759, type, sK405: $i > ($i > $i) > $i > $i).
% 19.50/4.13 thf(func_def_760, type, sK406: $i > $i > $i).
% 19.50/4.13 thf(func_def_761, type, sK407: $i > $i > $i).
% 19.50/4.13 thf(func_def_762, type, sK408: $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_763, type, sK409: $i > $i > $i).
% 19.50/4.13 thf(func_def_764, type, sK410: $i > $i > $i).
% 19.50/4.13 thf(func_def_765, type, sK411: $i > $i > $i).
% 19.50/4.13 thf(func_def_766, type, sK412: $i > $i > $i).
% 19.50/4.13 thf(func_def_767, type, sK413: $i > $i > $i).
% 19.50/4.13 thf(func_def_768, type, sK414: $i > $i).
% 19.50/4.13 thf(func_def_769, type, sK415: $i > $i).
% 19.50/4.13 thf(func_def_770, type, sK416: $i > $i).
% 19.50/4.13 thf(func_def_771, type, sK417: $i > $i).
% 19.50/4.13 thf(func_def_772, type, sK418: $i > $i > $i).
% 19.50/4.13 thf(func_def_773, type, sK419: $i > $i > $i).
% 19.50/4.13 thf(func_def_774, type, sK420: $i > $i > $i).
% 19.50/4.13 thf(func_def_775, type, sK421: $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_776, type, sK422: $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_778, type, sK424: $i > $i).
% 19.50/4.13 thf(func_def_781, type, sK427: $i > $o).
% 19.50/4.13 thf(func_def_782, type, sK428: ($i > $o) > $i > $i).
% 19.50/4.13 thf(func_def_783, type, sK429: $i > ($i > $o) > $i).
% 19.50/4.13 thf(func_def_796, type, sK442: $i > $i > $i).
% 19.50/4.13 thf(func_def_802, type, sK448: $i > $i).
% 19.50/4.13 thf(func_def_805, type, sK451: $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_806, type, sK452: $i > $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_807, type, sK453: $i > $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_808, type, sK454: $i > $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_816, type, sK462: $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_817, type, sK463: $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_822, type, sK468: $i > $i).
% 19.50/4.13 thf(func_def_824, type, sK470: $i > ($i > $i) > $i > $i).
% 19.50/4.13 thf(func_def_825, type, sK471: $i > ($i > $i) > $i > $i).
% 19.50/4.13 thf(func_def_826, type, sK472: $i > $i > ($i > $o) > $i).
% 19.50/4.13 thf(func_def_828, type, sK474: $i > $o).
% 19.50/4.13 thf(func_def_837, type, sK483: $i > $i > $i).
% 19.50/4.13 thf(func_def_838, type, sK484: $i > $i).
% 19.50/4.13 thf(func_def_841, type, sK487: $i > $o).
% 19.50/4.13 thf(func_def_843, type, sK489: $i > ($i > $o) > $i).
% 19.50/4.13 thf(func_def_844, type, sK490: $i > ($i > $o) > $i).
% 19.50/4.13 thf(func_def_847, type, sK493: $i > $i > ($i > $o) > ($i > $o) > $i).
% 19.50/4.13 thf(func_def_848, type, sK494: $i > $i > ($i > $o) > ($i > $o) > $i).
% 19.50/4.13 thf(func_def_851, type, sK497: $i > $o).
% 19.50/4.13 thf(func_def_852, type, sK498: $i > $o).
% 19.50/4.13 thf(func_def_858, type, sK504: $i > $o).
% 19.50/4.13 thf(func_def_861, type, sK507: $i > $i).
% 19.50/4.13 thf(func_def_863, type, sK509: $i > ($i > $i) > $i > $i).
% 19.50/4.13 thf(func_def_864, type, sK510: $i > $i > ($i > $i) > $i).
% 19.50/4.13 thf(func_def_866, type, sK512: $i > $i).
% 19.50/4.13 thf(func_def_877, type, sK523: $i > $o).
% 19.50/4.13 thf(func_def_899, type, sK545: $i > $i > $o).
% 19.50/4.13 thf(func_def_911, type, sK557: $i > $i > $i).
% 19.50/4.13 thf(func_def_938, type, sK584: $i > $i > $i).
% 19.50/4.13 thf(func_def_953, type, sK599: $i > ($i > $o) > $i).
% 19.50/4.13 thf(func_def_954, type, sK600: ($i > $o) > $i).
% 19.50/4.13 thf(func_def_955, type, sK601: $i > $o).
% 19.50/4.13 thf(func_def_966, type, sK612: $i > $i > $o).
% 19.50/4.13 thf(func_def_979, type, sK625: $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_980, type, sK626: $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_988, type, sK634: $i > $o).
% 19.50/4.13 thf(func_def_989, type, sK635: $i > $o).
% 19.50/4.13 thf(func_def_990, type, sK636: ($i > $o) > ($i > $o) > $i).
% 19.50/4.13 thf(func_def_991, type, sK637: ($i > $o) > ($i > $o) > $i).
% 19.50/4.13 thf(func_def_1001, type, sK647: $i > $i > $i).
% 19.50/4.13 thf(func_def_1004, type, sK650: $i > ($i > $o) > $i).
% 19.50/4.13 thf(func_def_1005, type, sK651: ($i > $o) > $i).
% 19.50/4.13 thf(func_def_1006, type, sK652: $i > $o).
% 19.50/4.13 thf(func_def_1025, type, sK671: $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_1026, type, sK672: $i > $i > $i > $o).
% 19.50/4.13 thf(func_def_1052, type, sK698: $i > $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_1053, type, sK699: $i > $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_1054, type, sK700: $i > $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_1055, type, sK701: $i > $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_1064, type, sK710: $i > $o).
% 19.50/4.13 thf(func_def_1069, type, sK715: $i > ($i > $i > $o) > $i > $i).
% 19.50/4.13 thf(func_def_1070, type, sK716: $i > ($i > $i > $o) > $i > $i).
% 19.50/4.13 thf(func_def_1071, type, sK717: ($i > $i > $o) > $i > $i > $i).
% 19.50/4.13 thf(func_def_1072, type, sK718: ($i > $i > $o) > $i > $i > $i).
% 19.50/4.13 thf(func_def_1073, type, sK719: $i > $i > $o).
% 19.50/4.13 thf(func_def_1084, type, sK730: $i > $i).
% 19.50/4.13 thf(func_def_1085, type, sK731: $i > $i).
% 19.50/4.13 thf(func_def_1087, type, sK733: $i > $i).
% 19.50/4.13 thf(func_def_1089, type, sK735: $i > $i > $i).
% 19.50/4.13 thf(func_def_1098, type, sK744: ($i > $o) > $i > $i).
% 19.50/4.13 thf(func_def_1099, type, sK745: ($i > $o) > $i > $i).
% 19.50/4.13 thf(func_def_1100, type, sK746: ($i > $o) > $i > $i).
% 19.50/4.13 thf(func_def_1101, type, sK747: $i > $o).
% 19.50/4.13 thf(func_def_1107, type, sK753: $i > $i > $o).
% 19.50/4.13 thf(func_def_1114, type, sK760: $i > $i > $o).
% 19.50/4.13 thf(func_def_1118, type, sK764: $i > $o).
% 19.50/4.13 thf(func_def_1126, type, sK772: $i > $o).
% 19.50/4.13 thf(func_def_1131, type, sK777: $i > $o).
% 19.50/4.13 thf(func_def_1132, type, sK778: ($i > $o) > $i).
% 19.50/4.13 thf(func_def_1138, type, sK784: $i > $o).
% 19.50/4.13 thf(func_def_1143, type, sK789: ($i > $o) > $i).
% 19.50/4.13 thf(func_def_1144, type, sK790: $i > ($i > $o) > $i).
% 19.50/4.13 thf(func_def_1145, type, sK791: $i > $o).
% 19.50/4.13 thf(func_def_1146, type, sK792: $i > $i > $i > $o).
% 19.50/4.13 thf(func_def_1164, type, sK810: $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_1175, type, sK821: $i > $o).
% 19.50/4.13 thf(func_def_1179, type, sK825: $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_1180, type, sK826: $i > $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_1190, type, sK836: $i > $i).
% 19.50/4.13 thf(func_def_1191, type, sK837: ($i > $i) > $i > $i > $i).
% 19.50/4.13 thf(func_def_1208, type, sK854: $i > $i > $i).
% 19.50/4.13 thf(func_def_1239, type, sK885: $i > $o).
% 19.50/4.13 thf(func_def_1278, type, sK924: $i > ($i > $o) > $i > $i > $i).
% 19.50/4.13 thf(func_def_1279, type, sK925: $i > ($i > $o) > $i > $i > $i).
% 19.50/4.13 thf(func_def_1280, type, sK926: $i > ($i > $o) > $i).
% 19.50/4.13 thf(func_def_1284, type, sK930: $i > $o).
% 19.50/4.13 thf(func_def_1288, type, sK934: $i > $o).
% 19.50/4.13 thf(func_def_1312, type, sK958: $i > $i > ($i > $o) > $i).
% 19.50/4.13 thf(func_def_1313, type, sK959: $i > $i > ($i > $o) > $i).
% 19.50/4.13 thf(func_def_1314, type, sK960: ($i > $o) > $i > $i).
% 19.50/4.13 thf(func_def_1317, type, sK963: $i > $o).
% 19.50/4.13 thf(func_def_1321, type, sK967: $i > $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_1322, type, sK968: $i > $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_1333, type, sK979: $i > $o).
% 19.50/4.13 thf(func_def_1334, type, sK980: ($i > $o) > $i > $i).
% 19.50/4.13 thf(func_def_1335, type, sK981: ($i > $o) > $i > $i).
% 19.50/4.13 thf(func_def_1347, type, sK993: ($i > $o) > $i > $i).
% 19.50/4.13 thf(func_def_1348, type, sK994: ($i > $o) > $i > $i).
% 19.50/4.13 thf(func_def_1349, type, sK995: $i > ($i > $o) > $i).
% 19.50/4.13 thf(func_def_1350, type, sK996: $i > $o).
% 19.50/4.13 thf(func_def_1357, type, sK1003: $i > $i > $o).
% 19.50/4.13 thf(func_def_1359, type, sK1005: $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_1360, type, sK1006: $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_1361, type, sK1007: $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_1362, type, sK1008: $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_1376, type, sK1022: $i > $o).
% 19.50/4.13 thf(func_def_1384, type, sK1030: $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_1385, type, sK1031: $i > $i > $i > $i).
% 19.50/4.13 thf(func_def_1400, type, ph1046: !>[X0: $tType]:(X0)).
% 19.50/4.13 thf(f13584,plain,(
% 19.50/4.13 $false),
% 19.50/4.13 inference(subsumption_resolution,[status(thm)],[f13529,f4004])).
% 19.50/4.13 thf(f4004,plain,(
% 19.50/4.13 ((in @ (kpair @ sK580 @ sK581) @ sK579) != $true)),
% 19.50/4.13 inference(cnf_transformation,[status(thm)],[f2307])).
% 19.50/4.13 thf(f2307,plain,(
% 19.50/4.13 (singletonprop = $true) & (ap2apEq2 = $true) & (woz1_1 = $true) & (setukpairinjR2 = $true) & (dpsetconstrEL1 = $true) & (demorgan2a1 = $true) & (inIntersectImpInIntersectUnions = $true) & (beta2 = $true) & (kfstpairEq = $true) & (binunionTIRcontra = $true) & (iftrue = $true) & (binunionTILcontra = $true) & (notdexE = $true) & (woz1_3 = $true) & (complementUnionInPowersetComplement = $true) & (binintersectSubset2 = $true) & (ex1I = $true) & (woz13rule4 = $true) & (exuEu = $true) & (binintersectRsub = $true) & (nonemptyE1 = $true) & (binintersectSubset1 = $true) & (symdiffI1 = $true) & (descrp = $true) & (demorgan2a2 = $true) & (subsetE = $true) & (breln1invprop = $true) & (iftrueProp2 = $true) & (inIntersectImpInUnion = $true) & (binunionIR = $true) & (setminusER = $true) & (setunionE2 = $true) & (eqimpsubset2 = $true) & (apProp = $true) & (setoftrueEq = $true) & (omega__Cong = $true) & (powerset__Cong = $true) & (nonemptyI = $true) & (emptysetimpfalse = $true) & (powersetTE1 = $true) & (ex1I2 = $true) & (iffalseProp1 = $true) & (theeq = $true) & (cartprodsndpairEq = $true) & (dsetconstrEL = $true) & (subsetemptysetimpeq = $true) & (doubleComplementE1 = $true) & (setadjoinSub = $true) & (breln1all1 = $true) & (cartprodfstin = $true) & (iffalse = $true) & (emptysetE = $true) & (setukpairinjR12 = $true) & (subsetTrans = $true) & (funcGraphProp1 = $true) & (binunionEcases = $true) & (sepSubset = $true) & (iffalseProp2 = $true) & (setminusIRneg = $true) & (inCongP = $true) & (cartprodpairmemEL = $true) & (singletoninpowunion = $true) & (quantDeMorgan4 = $true) & (setminusERneg = $true) & (woz13rule3 = $true) & (funcinfuncset = $true) & (setOfPairsIsBReln = $true) & (kfstsingleton = $true) & (setextAx = $true) & (demorgan2b = $true) & (doubleComplementSub2 = $true) & (brelnall1 = $true) & (emptysetsubset = $true) & (setukpairinjL1 = $true) & (symdiffI2 = $true) & (singletoninpowerset = $true) & (woz1_5 = $true) & (lamProp = $true) & (ubforcartprodlem2 = $true) & (powersetAx = $true) & (eqbreln = $true) & (ksndpairEq = $true) & (upairsetE = $true) & (prop2setI = $true) & (brelnall2 = $true) & (powersetE = $true) & (cartprodmempair1 = $true) & (symdiffIneg2 = $true) & (ex1E2 = $true) & (setadjoinE = $true) & (cartprodpairin = $true) & (noeltsimpempty = $true) & (foundationAx = $true) & (setunionE = $true) & (woz13rule1 = $true) & (emptysetAx = $true) & (ap2apEq1 = $true) & (complementTE1 = $true) & (singletonsubset = $true) & (emptyInPowerset = $true) & (demorgan1a = $true) & (setminusELneg = $true) & (theprop = $true) & (powersetE1 = $true) & (upairsubunion = $true) & (demorgan2a = $true) & (emptyinunitempty = $true) & (setext = $true) & (ap2p = $true) & (setminusT_lem = $true) & (emptyI = $true) & (wellorderingAx = $true) & (subsetI2 = $true) & (doubleComplementEq = $true) & (setadjoinIL = $true) & (subsetRefl = $true) & (ubforcartprodlem1 = $true) & (eqimpsubset1 = $true) & (subbreln1 = $true) & (setunionsingleton1 = $true) & (funcext = $true) & (setadjoinIR = $true) & (woz13rule2 = $true) & (dsetconstrI = $true) & (inComplementUnionImpInComplement1 = $true) & (setminusEL = $true) & (disjointsetsI1 = $true) & (funcImageSingleton = $true) & (setminusSubset1 = $true) & (powersetI = $true) & (replAx = $true) & (funcextLem = $true) & (binintersectSubset5 = $true) & (binintersectER = $true) & (binunionRsub = $true) & (iftrueProp1 = $true) & (setextT = $true) & (exuE3e = $true) & (complementImpComplementIntersect = $true) & (exuE1 = $true) & (ifSingleton = $true) & (doubleComplementI1 = $true) & (dpsetconstrER = $true) & (quantDeMorgan2 = $true) & (powersetTI1 = $true) & (app = $true) & (notequalI1 = $true) & (inIntersectImpInUnion2 = $true) & (exuI2 = $true) & (setminusILneg = $true) & (cartprodmempaircEq = $true) & (eta2 = $true) & (funcGraphProp2 = $true) & (subsetE2 = $true) & (setukpairinjL2 = $true) & (singletonsswitch = $true) & (complementTI1 = $true) & (((breln1 @ sK578 @ sK579) = $true) & (($true = (in @ sK580 @ sK578)) & (((in @ (kpair @ sK581 @ sK580) @ (breln1invset @ sK578 @ sK579)) = $true) & ((in @ (kpair @ sK580 @ sK581) @ sK579) != $true) & ($true = (in @ sK581 @ sK578))))) & (setextsub = $true) & (prop2set2propI = $true) & (binintersectSubset3 = $true) & (setunionsingleton = $true) & (powersetsubset = $true) & (symdiffIneg1 = $true) & (upairset2E = $true) & (notinemptyset = $true) & (dpsetconstrI = $true) & (setukpairinjR1 = $true) & (woz1_2 = $true) & (eta1 = $true) & (setminusLsub = $true) & (exuE3u = $true) & (subsetI1 = $true) & (inComplementUnionImpNotIn1 = $true) & (binintersectT_lem = $true) & (quantDeMorgan3 = $true) & (beta1 = $true) & (omegaSAx = $true) & (in__Cong = $true) & (funcGraphProp4 = $true) & (omegaIndAx = $true) & (setunion__Cong = $true) & (notinsingleton = $true) & (binunionTE = $true) & (upairequniteq = $true) & (singletonsuniq = $true) & (contraSubsetComplement = $true) & (subset2powerset = $true) & (powersetI1 = $true) & (complementTcontraSubset = $true) & (setminusSubset2 = $true) & (complementT_lem = $true) & (binunionE = $true) & (lamp = $true) & (ubforcartprodlem3 = $true) & (ksndsingleton = $true) & (exuI3 = $true) & (omega0Ax = $true) & (upairsetIL = $true) & (sepInPowerset = $true) & (symdiffE = $true) & (cartprodpairmemER = $true) & (bs114d = $true) & (breln1SetBreln1 = $true) & (secondinupair = $true) & (contrasubsetT1 = $true) & (funcGraphProp3 = $true) & (eqbreln1 = $true) & (upairset2IR = $true) & (binintersectTERcontra = $true) & (binunionLsub = $true) & (setunionI = $true) & (notsubsetI = $true) & (setadjoinAx = $true) & (binunionIL = $true) & (setminusI = $true) & (iftrueorfalse = $true) & (setOfPairsIsBReln1 = $true) & (nonemptyI1 = $true) & (demorgan2 = $true) & (upairinpowunion = $true) & (woz1_4 = $true) & (contrasubsetT2 = $true) & (contrasubsetT3 = $true) & (exu__Cong = $true) & (powersetT_lem = $true) & (setadjoinSub2 = $true) & (setunionsingleton2 = $true) & (vacuousDall = $true) & (dpsetconstrERa = $true) & (binunionTEcontra = $true) & (cartprodpairsurjEq = $true) & (binintersectLsub = $true) & (setukpairinjR11 = $true) & (doubleComplementSub1 = $true) & (notdallE = $true) & (setunionAx = $true) & (emptyinPowerset = $true) & (emptyset__Cong = $true) & (cartprodsndin = $true) & (ifp = $true) & (demorgan1 = $true) & (binintersectI = $true) & (infuncsetfunc = $true) & (prop2setE = $true) & (uniqinunit = $true) & (complementSubsetComplementIntersect = $true) & (kpairiskpair = $true) & (complementTnotintersectT = $true) & (subPowSU = $true) & (exuI1 = $true) & (inPowerset = $true) & (choice2fnsingleton = $true) & (nonemptyImpWitness = $true) & (setadjoin__Cong = $true) & (setukpairIR = $true) & (subsetTI = $true) & (binunionT_lem = $true) & (quantDeMorgan1 = $true) & (ex1E1 = $true) & (dsetconstr__Cong = $true) & (contrasubsetT = $true) & (exuE2 = $true) & (setadjoinOr = $true) & (binintersectSubset4 = $true) & (complementInPowersetComplementIntersect = $true) & (eqinunit = $true) & (dpsetconstrEL2 = $true) & (setukpairIL = $true) & (setbeta = $true) & (breln1invI = $true) & (kpairp = $true) & (funcext2 = $true) & (setukpairinjL = $true) & (cartprodmempair = $true) & (lam2lamEq = $true) & (dpsetconstrSub = $true) & (emptyE1 = $true) & (demorgan2b2 = $true) & (binintersectEL = $true) & (cartprodfstpairEq = $true) & (subbreln = $true) & (descr__Cong = $true) & (lam2p = $true) & (kpairsurjEq = $true) & (binintersectTELcontra = $true) & (intersectInPowersetIntersectUnions = $true) & (breln1all2 = $true) & (setukpairinjR = $true) & (demorgan1b = $true) & (woz13rule0 = $true) & (upairsetIR = $true) & (dsetconstrER = $true) & (notequalI2 = $true)),
% 19.50/4.13 inference(skolemisation,[status(esa),new_symbols(skolem,[sK578,sK579,sK580,sK581])],[f1264,f2306,f2305,f2304])).
% 19.50/4.13 thf(f2304,plain,(
% 19.50/4.13 ? [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) & ? [X2 : $i] : (($true = (in @ X2 @ X0)) & ? [X3 : $i] : (((in @ (kpair @ X3 @ X2) @ (breln1invset @ X0 @ X1)) = $true) & ($true != (in @ (kpair @ X2 @ X3) @ X1)) & ((in @ X3 @ X0) = $true)))) => (((breln1 @ sK578 @ sK579) = $true) & ? [X2 : $i] : (($true = (in @ X2 @ sK578)) & ? [X3 : $i] : (((in @ (kpair @ X3 @ X2) @ (breln1invset @ sK578 @ sK579)) = $true) & ((in @ (kpair @ X2 @ X3) @ sK579) != $true) & ($true = (in @ X3 @ sK578)))))),
% 19.50/4.13 introduced(definition,[],[choice_axiom])).
% 19.50/4.13 thf(f2305,plain,(
% 19.50/4.13 ? [X2 : $i] : (($true = (in @ X2 @ sK578)) & ? [X3 : $i] : (((in @ (kpair @ X3 @ X2) @ (breln1invset @ sK578 @ sK579)) = $true) & ((in @ (kpair @ X2 @ X3) @ sK579) != $true) & ($true = (in @ X3 @ sK578)))) => (($true = (in @ sK580 @ sK578)) & ? [X3 : $i] : (($true = (in @ (kpair @ X3 @ sK580) @ (breln1invset @ sK578 @ sK579))) & ((in @ (kpair @ sK580 @ X3) @ sK579) != $true) & ($true = (in @ X3 @ sK578))))),
% 19.50/4.13 introduced(definition,[],[choice_axiom])).
% 19.50/4.13 thf(f2306,plain,(
% 19.50/4.13 ? [X3 : $i] : (($true = (in @ (kpair @ X3 @ sK580) @ (breln1invset @ sK578 @ sK579))) & ((in @ (kpair @ sK580 @ X3) @ sK579) != $true) & ($true = (in @ X3 @ sK578))) => (((in @ (kpair @ sK581 @ sK580) @ (breln1invset @ sK578 @ sK579)) = $true) & ((in @ (kpair @ sK580 @ sK581) @ sK579) != $true) & ($true = (in @ sK581 @ sK578)))),
% 19.50/4.13 introduced(definition,[],[choice_axiom])).
% 19.50/4.13 thf(f1264,plain,(
% 19.50/4.13 (singletonprop = $true) & (ap2apEq2 = $true) & (woz1_1 = $true) & (setukpairinjR2 = $true) & (dpsetconstrEL1 = $true) & (demorgan2a1 = $true) & (inIntersectImpInIntersectUnions = $true) & (beta2 = $true) & (kfstpairEq = $true) & (binunionTIRcontra = $true) & (iftrue = $true) & (binunionTILcontra = $true) & (notdexE = $true) & (woz1_3 = $true) & (complementUnionInPowersetComplement = $true) & (binintersectSubset2 = $true) & (ex1I = $true) & (woz13rule4 = $true) & (exuEu = $true) & (binintersectRsub = $true) & (nonemptyE1 = $true) & (binintersectSubset1 = $true) & (symdiffI1 = $true) & (descrp = $true) & (demorgan2a2 = $true) & (subsetE = $true) & (breln1invprop = $true) & (iftrueProp2 = $true) & (inIntersectImpInUnion = $true) & (binunionIR = $true) & (setminusER = $true) & (setunionE2 = $true) & (eqimpsubset2 = $true) & (apProp = $true) & (setoftrueEq = $true) & (omega__Cong = $true) & (powerset__Cong = $true) & (nonemptyI = $true) & (emptysetimpfalse = $true) & (powersetTE1 = $true) & (ex1I2 = $true) & (iffalseProp1 = $true) & (theeq = $true) & (cartprodsndpairEq = $true) & (dsetconstrEL = $true) & (subsetemptysetimpeq = $true) & (doubleComplementE1 = $true) & (setadjoinSub = $true) & (breln1all1 = $true) & (cartprodfstin = $true) & (iffalse = $true) & (emptysetE = $true) & (setukpairinjR12 = $true) & (subsetTrans = $true) & (funcGraphProp1 = $true) & (binunionEcases = $true) & (sepSubset = $true) & (iffalseProp2 = $true) & (setminusIRneg = $true) & (inCongP = $true) & (cartprodpairmemEL = $true) & (singletoninpowunion = $true) & (quantDeMorgan4 = $true) & (setminusERneg = $true) & (woz13rule3 = $true) & (funcinfuncset = $true) & (setOfPairsIsBReln = $true) & (kfstsingleton = $true) & (setextAx = $true) & (demorgan2b = $true) & (doubleComplementSub2 = $true) & (brelnall1 = $true) & (emptysetsubset = $true) & (setukpairinjL1 = $true) & (symdiffI2 = $true) & (singletoninpowerset = $true) & (woz1_5 = $true) & (lamProp = $true) & (ubforcartprodlem2 = $true) & (powersetAx = $true) & (eqbreln = $true) & (ksndpairEq = $true) & (upairsetE = $true) & (prop2setI = $true) & (brelnall2 = $true) & (powersetE = $true) & (cartprodmempair1 = $true) & (symdiffIneg2 = $true) & (ex1E2 = $true) & (setadjoinE = $true) & (cartprodpairin = $true) & (noeltsimpempty = $true) & (foundationAx = $true) & (setunionE = $true) & (woz13rule1 = $true) & (emptysetAx = $true) & (ap2apEq1 = $true) & (complementTE1 = $true) & (singletonsubset = $true) & (emptyInPowerset = $true) & (demorgan1a = $true) & (setminusELneg = $true) & (theprop = $true) & (powersetE1 = $true) & (upairsubunion = $true) & (demorgan2a = $true) & (emptyinunitempty = $true) & (setext = $true) & (ap2p = $true) & (setminusT_lem = $true) & (emptyI = $true) & (wellorderingAx = $true) & (subsetI2 = $true) & (doubleComplementEq = $true) & (setadjoinIL = $true) & (subsetRefl = $true) & (ubforcartprodlem1 = $true) & (eqimpsubset1 = $true) & (subbreln1 = $true) & (setunionsingleton1 = $true) & (funcext = $true) & (setadjoinIR = $true) & (woz13rule2 = $true) & (dsetconstrI = $true) & (inComplementUnionImpInComplement1 = $true) & (setminusEL = $true) & (disjointsetsI1 = $true) & (funcImageSingleton = $true) & (setminusSubset1 = $true) & (powersetI = $true) & (replAx = $true) & (funcextLem = $true) & (binintersectSubset5 = $true) & (binintersectER = $true) & (binunionRsub = $true) & (iftrueProp1 = $true) & (setextT = $true) & (exuE3e = $true) & (complementImpComplementIntersect = $true) & (exuE1 = $true) & (ifSingleton = $true) & (doubleComplementI1 = $true) & (dpsetconstrER = $true) & (quantDeMorgan2 = $true) & (powersetTI1 = $true) & (app = $true) & (notequalI1 = $true) & (inIntersectImpInUnion2 = $true) & (exuI2 = $true) & (setminusILneg = $true) & (cartprodmempaircEq = $true) & (eta2 = $true) & (funcGraphProp2 = $true) & (subsetE2 = $true) & (setukpairinjL2 = $true) & (singletonsswitch = $true) & (complementTI1 = $true) & ? [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) & ? [X2 : $i] : (($true = (in @ X2 @ X0)) & ? [X3 : $i] : (((in @ (kpair @ X3 @ X2) @ (breln1invset @ X0 @ X1)) = $true) & ($true != (in @ (kpair @ X2 @ X3) @ X1)) & ((in @ X3 @ X0) = $true)))) & (setextsub = $true) & (prop2set2propI = $true) & (binintersectSubset3 = $true) & (setunionsingleton = $true) & (powersetsubset = $true) & (symdiffIneg1 = $true) & (upairset2E = $true) & (notinemptyset = $true) & (dpsetconstrI = $true) & (setukpairinjR1 = $true) & (woz1_2 = $true) & (eta1 = $true) & (setminusLsub = $true) & (exuE3u = $true) & (subsetI1 = $true) & (inComplementUnionImpNotIn1 = $true) & (binintersectT_lem = $true) & (quantDeMorgan3 = $true) & (beta1 = $true) & (omegaSAx = $true) & (in__Cong = $true) & (funcGraphProp4 = $true) & (omegaIndAx = $true) & (setunion__Cong = $true) & (notinsingleton = $true) & (binunionTE = $true) & (upairequniteq = $true) & (singletonsuniq = $true) & (contraSubsetComplement = $true) & (subset2powerset = $true) & (powersetI1 = $true) & (complementTcontraSubset = $true) & (setminusSubset2 = $true) & (complementT_lem = $true) & (binunionE = $true) & (lamp = $true) & (ubforcartprodlem3 = $true) & (ksndsingleton = $true) & (exuI3 = $true) & (omega0Ax = $true) & (upairsetIL = $true) & (sepInPowerset = $true) & (symdiffE = $true) & (cartprodpairmemER = $true) & (bs114d = $true) & (breln1SetBreln1 = $true) & (secondinupair = $true) & (contrasubsetT1 = $true) & (funcGraphProp3 = $true) & (eqbreln1 = $true) & (upairset2IR = $true) & (binintersectTERcontra = $true) & (binunionLsub = $true) & (setunionI = $true) & (notsubsetI = $true) & (setadjoinAx = $true) & (binunionIL = $true) & (setminusI = $true) & (iftrueorfalse = $true) & (setOfPairsIsBReln1 = $true) & (nonemptyI1 = $true) & (demorgan2 = $true) & (upairinpowunion = $true) & (woz1_4 = $true) & (contrasubsetT2 = $true) & (contrasubsetT3 = $true) & (exu__Cong = $true) & (powersetT_lem = $true) & (setadjoinSub2 = $true) & (setunionsingleton2 = $true) & (vacuousDall = $true) & (dpsetconstrERa = $true) & (binunionTEcontra = $true) & (cartprodpairsurjEq = $true) & (binintersectLsub = $true) & (setukpairinjR11 = $true) & (doubleComplementSub1 = $true) & (notdallE = $true) & (setunionAx = $true) & (emptyinPowerset = $true) & (emptyset__Cong = $true) & (cartprodsndin = $true) & (ifp = $true) & (demorgan1 = $true) & (binintersectI = $true) & (infuncsetfunc = $true) & (prop2setE = $true) & (uniqinunit = $true) & (complementSubsetComplementIntersect = $true) & (kpairiskpair = $true) & (complementTnotintersectT = $true) & (subPowSU = $true) & (exuI1 = $true) & (inPowerset = $true) & (choice2fnsingleton = $true) & (nonemptyImpWitness = $true) & (setadjoin__Cong = $true) & (setukpairIR = $true) & (subsetTI = $true) & (binunionT_lem = $true) & (quantDeMorgan1 = $true) & (ex1E1 = $true) & (dsetconstr__Cong = $true) & (contrasubsetT = $true) & (exuE2 = $true) & (setadjoinOr = $true) & (binintersectSubset4 = $true) & (complementInPowersetComplementIntersect = $true) & (eqinunit = $true) & (dpsetconstrEL2 = $true) & (setukpairIL = $true) & (setbeta = $true) & (breln1invI = $true) & (kpairp = $true) & (funcext2 = $true) & (setukpairinjL = $true) & (cartprodmempair = $true) & (lam2lamEq = $true) & (dpsetconstrSub = $true) & (emptyE1 = $true) & (demorgan2b2 = $true) & (binintersectEL = $true) & (cartprodfstpairEq = $true) & (subbreln = $true) & (descr__Cong = $true) & (lam2p = $true) & (kpairsurjEq = $true) & (binintersectTELcontra = $true) & (intersectInPowersetIntersectUnions = $true) & (breln1all2 = $true) & (setukpairinjR = $true) & (demorgan1b = $true) & (woz13rule0 = $true) & (upairsetIR = $true) & (dsetconstrER = $true) & (notequalI2 = $true)),
% 19.50/4.13 inference(flattening,[status(thm)],[f1263])).
% 19.50/4.13 thf(f1263,plain,(
% 19.50/4.13 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : ((($true != (in @ (kpair @ X2 @ X3) @ X1)) & ((in @ (kpair @ X3 @ X2) @ (breln1invset @ X0 @ X1)) = $true)) & ((in @ X3 @ X0) = $true)) & ($true = (in @ X2 @ X0))) & ($true = (breln1 @ X0 @ X1))) & (breln1invI = $true)) & (breln1invprop = $true)) & (eqbreln1 = $true)) & (subbreln1 = $true)) & (breln1all1 = $true)) & (setOfPairsIsBReln1 = $true)) & (choice2fnsingleton = $true)) & (breln1SetBreln1 = $true)) & (breln1all2 = $true)) & (woz1_5 = $true)) & (woz1_4 = $true)) & (woz1_3 = $true)) & (woz1_2 = $true)) & (woz1_1 = $true)) & (woz13rule4 = $true)) & (woz13rule3 = $true)) & (woz13rule2 = $true)) & (woz13rule1 = $true)) & (woz13rule0 = $true)) & (demorgan2 = $true)) & (demorgan2b = $true)) & (demorgan2b2 = $true)) & (demorgan2a = $true)) & (demorgan1 = $true)) & (demorgan1b = $true)) & (demorgan1a = $true)) & (demorgan2a2 = $true)) & (complementUnionInPowersetComplement = $true)) & (demorgan2a1 = $true)) & (binunionTEcontra = $true)) & (binunionTE = $true)) & (inComplementUnionImpInComplement1 = $true)) & (inComplementUnionImpNotIn1 = $true)) & (intersectInPowersetIntersectUnions = $true)) & (inIntersectImpInIntersectUnions = $true)) & (inIntersectImpInUnion2 = $true)) & (inIntersectImpInUnion = $true)) & (binunionTIRcontra = $true)) & (binunionTILcontra = $true)) & (complementTcontraSubset = $true)) & (contraSubsetComplement = $true)) & (complementInPowersetComplementIntersect = $true)) & (complementSubsetComplementIntersect = $true)) & (complementImpComplementIntersect = $true)) & (complementTnotintersectT = $true)) & (doubleComplementEq = $true)) & (doubleComplementSub2 = $true)) & (doubleComplementSub1 = $true)) & (doubleComplementE1 = $true)) & (doubleComplementI1 = $true)) & (contrasubsetT3 = $true)) & (contrasubsetT2 = $true)) & (contrasubsetT1 = $true)) & (contrasubsetT = $true)) & (binintersectTERcontra = $true)) & (binintersectTELcontra = $true)) & (complementTE1 = $true)) & (complementTI1 = $true)) & (powersetTE1 = $true)) & (powersetTI1 = $true)) & (subsetTI = $true)) & (setextT = $true)) & (complementT_lem = $true)) & (setminusT_lem = $true)) & (powersetT_lem = $true)) & (binunionT_lem = $true)) & (binintersectT_lem = $true)) & (iftrueorfalse = $true)) & (iffalse = $true)) & (iftrue = $true)) & (theeq = $true)) & (ifp = $true)) & (ifSingleton = $true)) & (iftrueProp2 = $true)) & (iftrueProp1 = $true)) & (iffalseProp2 = $true)) & (iffalseProp1 = $true)) & (eta2 = $true)) & (beta2 = $true)) & (lam2lamEq = $true)) & (eta1 = $true)) & (beta1 = $true)) & (ap2apEq2 = $true)) & (ap2apEq1 = $true)) & (funcext2 = $true)) & (funcext = $true)) & (eqbreln = $true)) & (subbreln = $true)) & (funcGraphProp4 = $true)) & (funcextLem = $true)) & (funcGraphProp2 = $true)) & (funcGraphProp3 = $true)) & (funcGraphProp1 = $true)) & (ex1E2 = $true)) & (brelnall2 = $true)) & (brelnall1 = $true)) & (lam2p = $true)) & (lamp = $true)) & (lamProp = $true)) & (funcinfuncset = $true)) & (ap2p = $true)) & (infuncsetfunc = $true)) & (app = $true)) & (apProp = $true)) & (funcImageSingleton = $true)) & (dpsetconstrER = $true)) & (dpsetconstrEL2 = $true)) & (dpsetconstrEL1 = $true)) & (dpsetconstrERa = $true)) & (setOfPairsIsBReln = $true)) & (dpsetconstrSub = $true)) & (dpsetconstrI = $true)) & (cartprodpairsurjEq = $true)) & (cartprodsndpairEq = $true)) & (cartprodfstpairEq = $true)) & (cartprodmempaircEq = $true)) & (cartprodpairmemER = $true)) & (cartprodpairmemEL = $true)) & (cartprodsndin = $true)) & (kpairsurjEq = $true)) & (ksndpairEq = $true)) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (setukpairinjR2 = $true)) & (upairequniteq = $true)) & (setukpairinjR1 = $true)) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 19.50/4.13 inference(ennf_transformation,[status(thm)],[f527])).
% 19.50/4.13 thf(f527,plain,(
% 19.50/4.13 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ((upairequniteq = $true) => ((setukpairinjR2 = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ((ksndpairEq = $true) => ((kpairsurjEq = $true) => ((cartprodsndin = $true) => ((cartprodpairmemEL = $true) => ((cartprodpairmemER = $true) => ((cartprodmempaircEq = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ((cartprodpairsurjEq = $true) => ((dpsetconstrI = $true) => ((dpsetconstrSub = $true) => ((setOfPairsIsBReln = $true) => ((dpsetconstrERa = $true) => ((dpsetconstrEL1 = $true) => ((dpsetconstrEL2 = $true) => ((dpsetconstrER = $true) => ((funcImageSingleton = $true) => ((apProp = $true) => ((app = $true) => ((infuncsetfunc = $true) => ((ap2p = $true) => ((funcinfuncset = $true) => ((lamProp = $true) => ((lamp = $true) => ((lam2p = $true) => ((brelnall1 = $true) => ((brelnall2 = $true) => ((ex1E2 = $true) => ((funcGraphProp1 = $true) => ((funcGraphProp3 = $true) => ((funcGraphProp2 = $true) => ((funcextLem = $true) => ((funcGraphProp4 = $true) => ((subbreln = $true) => ((eqbreln = $true) => ((funcext = $true) => ((funcext2 = $true) => ((ap2apEq1 = $true) => ((ap2apEq2 = $true) => ((beta1 = $true) => ((eta1 = $true) => ((lam2lamEq = $true) => ((beta2 = $true) => ((eta2 = $true) => ((iffalseProp1 = $true) => ((iffalseProp2 = $true) => ((iftrueProp1 = $true) => ((iftrueProp2 = $true) => ((ifSingleton = $true) => ((ifp = $true) => ((theeq = $true) => ((iftrue = $true) => ((iffalse = $true) => ((iftrueorfalse = $true) => ((binintersectT_lem = $true) => ((binunionT_lem = $true) => ((powersetT_lem = $true) => ((setminusT_lem = $true) => ((complementT_lem = $true) => ((setextT = $true) => ((subsetTI = $true) => ((powersetTI1 = $true) => ((powersetTE1 = $true) => ((complementTI1 = $true) => ((complementTE1 = $true) => ((binintersectTELcontra = $true) => ((binintersectTERcontra = $true) => ((contrasubsetT = $true) => ((contrasubsetT1 = $true) => ((contrasubsetT2 = $true) => ((contrasubsetT3 = $true) => ((doubleComplementI1 = $true) => ((doubleComplementE1 = $true) => ((doubleComplementSub1 = $true) => ((doubleComplementSub2 = $true) => ((doubleComplementEq = $true) => ((complementTnotintersectT = $true) => ((complementImpComplementIntersect = $true) => ((complementSubsetComplementIntersect = $true) => ((complementInPowersetComplementIntersect = $true) => ((contraSubsetComplement = $true) => ((complementTcontraSubset = $true) => ((binunionTILcontra = $true) => ((binunionTIRcontra = $true) => ((inIntersectImpInUnion = $true) => ((inIntersectImpInUnion2 = $true) => ((inIntersectImpInIntersectUnions = $true) => ((intersectInPowersetIntersectUnions = $true) => ((inComplementUnionImpNotIn1 = $true) => ((inComplementUnionImpInComplement1 = $true) => ((binunionTE = $true) => ((binunionTEcontra = $true) => ((demorgan2a1 = $true) => ((complementUnionInPowersetComplement = $true) => ((demorgan2a2 = $true) => ((demorgan1a = $true) => ((demorgan1b = $true) => ((demorgan1 = $true) => ((demorgan2a = $true) => ((demorgan2b2 = $true) => ((demorgan2b = $true) => ((demorgan2 = $true) => ((woz13rule0 = $true) => ((woz13rule1 = $true) => ((woz13rule2 = $true) => ((woz13rule3 = $true) => ((woz13rule4 = $true) => ((woz1_1 = $true) => ((woz1_2 = $true) => ((woz1_3 = $true) => ((woz1_4 = $true) => ((woz1_5 = $true) => ((breln1all2 = $true) => ((breln1SetBreln1 = $true) => ((choice2fnsingleton = $true) => ((setOfPairsIsBReln1 = $true) => ((breln1all1 = $true) => ((subbreln1 = $true) => ((eqbreln1 = $true) => ((breln1invprop = $true) => ((breln1invI = $true) => ! [X0 : $i,X1 : $i] : (($true = (breln1 @ X0 @ X1)) => ! [X2 : $i] : (($true = (in @ X2 @ X0)) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => (((in @ (kpair @ X3 @ X2) @ (breln1invset @ X0 @ X1)) = $true) => ($true = (in @ (kpair @ X2 @ X3) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 19.50/4.13 inference(fool_elimination,[status(thm)],[f526])).
% 19.50/4.13 thf(f526,plain,(
% 19.50/4.13 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (eqbreln1 => (breln1invprop => (breln1invI => ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ (kpair @ X3 @ X2) @ (breln1invset @ X0 @ X1)) => (in @ (kpair @ X2 @ X3) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 19.50/4.13 inference(rectify,[status(thm)],[f300])).
% 19.50/4.13 thf(f300,negated_conjecture,(
% 19.50/4.13 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (eqbreln1 => (breln1invprop => (breln1invI => ! [X3 : $i,X13 : $i] : ((breln1 @ X3 @ X13) => ! [X1 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X3) => ((in @ (kpair @ X2 @ X1) @ (breln1invset @ X3 @ X13)) => (in @ (kpair @ X1 @ X2) @ X13))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 17.58/4.13 inference(negated_conjecture,[status(cth)],[f299])).
% 17.58/4.13 thf(f299,conjecture,(
% 17.58/4.13 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (eqbreln1 => (breln1invprop => (breln1invI => ! [X3 : $i,X13 : $i] : ((breln1 @ X3 @ X13) => ! [X1 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X3) => ((in @ (kpair @ X2 @ X1) @ (breln1invset @ X3 @ X13)) => (in @ (kpair @ X1 @ X2) @ X13)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 17.58/4.13 file('/export/starexec/sandbox/tmp/tmp.4RsbB0Qymi/DTF2THF_10978.p',breln1invE)).
% 17.58/4.13 thf(f13529,plain,(
% 17.58/4.13 ((in @ (kpair @ sK580 @ sK581) @ sK579) = $true)),
% 17.58/4.13 inference(beta_eta_normalization,[status(thm)],[f13528])).
% 17.58/4.13 thf(f13528,plain,(
% 17.58/4.13 (((^[Y0 : $i]: ((^[Y1 : $i]: (in @ (kpair @ Y1 @ Y0) @ sK579)))) @ sK581 @ sK580) = $true)),
% 17.58/4.13 inference(trivial_inequality_removal,[status(thm)],[f13519])).
% 17.58/4.13 thf(f13519,plain,(
% 17.58/4.13 (((^[Y0 : $i]: ((^[Y1 : $i]: (in @ (kpair @ Y1 @ Y0) @ sK579)))) @ sK581 @ sK580) = $true) | ($true != $true)),
% 17.58/4.13 inference(superposition,[status(thm)],[f6197,f5980])).
% 17.58/4.13 thf(f5980,plain,(
% 17.58/4.13 ((in @ (kpair @ sK581 @ sK580) @ (dpsetconstr @ sK578 @ sK578 @ (^[Y0 : $i]: ((^[Y1 : $i]: (in @ (kpair @ Y1 @ Y0) @ sK579)))))) = $true)),
% 17.58/4.13 inference(beta_eta_normalization,[status(thm)],[f5386])).
% 17.58/4.13 thf(f5386,plain,(
% 17.58/4.13 ($true = (in @ (kpair @ sK581 @ sK580) @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (in @ (kpair @ Y3 @ Y2) @ Y1)))))))) @ sK578 @ sK579)))),
% 17.58/4.13 inference(definition_unfolding,[status(thm)],[f4005,f3704])).
% 17.58/4.13 thf(f3704,plain,(
% 17.58/4.13 (breln1invset = (^[Y0 : $i]: ((^[Y1 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (in @ (kpair @ Y3 @ Y2) @ Y1)))))))))),
% 17.58/4.13 inference(cnf_transformation,[status(thm)],[f395])).
% 17.58/4.13 thf(f395,plain,(
% 17.58/4.13 (breln1invset = (^[Y0 : $i]: ((^[Y1 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (in @ (kpair @ Y3 @ Y2) @ Y1)))))))))),
% 17.58/4.13 inference(fool_elimination,[status(thm)],[f394])).
% 17.58/4.13 thf(f394,plain,(
% 17.58/4.13 (breln1invset = (^[X0 : $i, X1 : $i] : (dpsetconstr @ X0 @ X0 @ (^[X2 : $i, X3 : $i] : (in @ (kpair @ X3 @ X2) @ X1)))))),
% 17.58/4.13 inference(rectify,[status(thm)],[f296])).
% 17.58/4.13 thf(f296,axiom,(
% 17.58/4.13 (breln1invset = (^[X3 : $i, X13 : $i] : (dpsetconstr @ X3 @ X3 @ (^[X1 : $i, X2 : $i] : (in @ (kpair @ X2 @ X1) @ X13)))))),
% 17.58/4.13 file('/export/starexec/sandbox/tmp/tmp.4RsbB0Qymi/DTF2THF_10978.p',breln1invset)).
% 17.58/4.13 thf(f4005,plain,(
% 17.58/4.13 ((in @ (kpair @ sK581 @ sK580) @ (breln1invset @ sK578 @ sK579)) = $true)),
% 17.58/4.13 inference(cnf_transformation,[status(thm)],[f2307])).
% 17.58/4.13 thf(f6197,plain,(
% 17.58/4.13 ( ! [X2 : $i > $i > $o,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((in @ (kpair @ X4 @ X0) @ (dpsetconstr @ X3 @ X1 @ X2)) != $true) | ((X2 @ X4 @ X0) = $true)) )),
% 17.58/4.13 inference(beta_eta_normalization,[status(thm)],[f6196])).
% 17.58/4.13 thf(f6196,plain,(
% 17.58/4.13 ( ! [X2 : $i > $i > $o,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (in @ (kpair @ X4 @ X0) @ (dpsetconstr @ X3 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1))))))) | ((X2 @ X4 @ X0) = $true)) )),
% 17.58/4.13 inference(trivial_inequality_removal,[status(thm)],[f5585])).
% 17.58/4.13 thf(f5585,plain,(
% 17.58/4.13 ( ! [X2 : $i > $i > $o,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (in @ (kpair @ X4 @ X0) @ (dpsetconstr @ X3 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1))))))) | ($true != $true) | ((X2 @ X4 @ X0) = $true)) )),
% 17.58/4.13 inference(definition_unfolding,[status(thm)],[f4447,f4022])).
% 17.58/4.13 thf(f4022,plain,(
% 17.58/4.13 (dpsetconstrER = $true)),
% 17.58/4.13 inference(cnf_transformation,[status(thm)],[f2307])).
% 17.58/4.13 thf(f4447,plain,(
% 17.58/4.13 ( ! [X2 : $i > $i > $o,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((X2 @ X4 @ X0) = $true) | ($true != (in @ (kpair @ X4 @ X0) @ (dpsetconstr @ X3 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1))))))) | (dpsetconstrER != $true)) )),
% 17.58/4.13 inference(cnf_transformation,[status(thm)],[f2633])).
% 17.58/4.13 thf(f2633,plain,(
% 17.58/4.13 (! [X0 : $i,X1 : $i,X2 : $i > $i > $o,X3 : $i,X4 : $i] : (((X2 @ X4 @ X0) = $true) | ($true != (in @ (kpair @ X4 @ X0) @ (dpsetconstr @ X3 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1)))))))) | (dpsetconstrER != $true)) & ((dpsetconstrER = $true) | (((sK760 @ sK762 @ sK758) != $true) & ((in @ (kpair @ sK762 @ sK758) @ (dpsetconstr @ sK761 @ sK759 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK760 @ Y0 @ Y1)))))) = $true)))),
% 17.58/4.13 inference(skolemisation,[status(esa),new_symbols(skolem,[sK758,sK759,sK760,sK761,sK762])],[f2631,f2632])).
% 17.58/4.13 thf(f2632,plain,(
% 17.58/4.13 ? [X5 : $i,X6 : $i,X7 : $i > $i > $o,X8 : $i,X9 : $i] : (((X7 @ X9 @ X5) != $true) & ((in @ (kpair @ X9 @ X5) @ (dpsetconstr @ X8 @ X6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X7 @ Y0 @ Y1)))))) = $true)) => (((sK760 @ sK762 @ sK758) != $true) & ((in @ (kpair @ sK762 @ sK758) @ (dpsetconstr @ sK761 @ sK759 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK760 @ Y0 @ Y1)))))) = $true))),
% 17.58/4.13 introduced(definition,[],[choice_axiom])).
% 17.58/4.13 thf(f2631,plain,(
% 17.58/4.13 (! [X0 : $i,X1 : $i,X2 : $i > $i > $o,X3 : $i,X4 : $i] : (((X2 @ X4 @ X0) = $true) | ($true != (in @ (kpair @ X4 @ X0) @ (dpsetconstr @ X3 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1)))))))) | (dpsetconstrER != $true)) & ((dpsetconstrER = $true) | ? [X5 : $i,X6 : $i,X7 : $i > $i > $o,X8 : $i,X9 : $i] : (((X7 @ X9 @ X5) != $true) & ((in @ (kpair @ X9 @ X5) @ (dpsetconstr @ X8 @ X6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X7 @ Y0 @ Y1)))))) = $true)))),
% 17.58/4.13 inference(rectify,[status(thm)],[f2630])).
% 17.58/4.13 thf(f2630,plain,(
% 17.58/4.13 (! [X0 : $i,X1 : $i,X2 : $i > $i > $o,X3 : $i,X4 : $i] : (((X2 @ X4 @ X0) = $true) | ($true != (in @ (kpair @ X4 @ X0) @ (dpsetconstr @ X3 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1)))))))) | (dpsetconstrER != $true)) & ((dpsetconstrER = $true) | ? [X0 : $i,X1 : $i,X2 : $i > $i > $o,X3 : $i,X4 : $i] : (((X2 @ X4 @ X0) != $true) & ($true = (in @ (kpair @ X4 @ X0) @ (dpsetconstr @ X3 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1)))))))))),
% 17.58/4.13 inference(nnf_transformation,[status(thm)],[f975])).
% 17.58/4.13 thf(f975,plain,(
% 17.58/4.13 ! [X0 : $i,X1 : $i,X2 : $i > $i > $o,X3 : $i,X4 : $i] : (((X2 @ X4 @ X0) = $true) | ($true != (in @ (kpair @ X4 @ X0) @ (dpsetconstr @ X3 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1)))))))) <=> (dpsetconstrER = $true)),
% 17.58/4.13 inference(ennf_transformation,[status(thm)],[f499])).
% 17.58/4.13 thf(f499,plain,(
% 17.58/4.13 ! [X0 : $i,X1 : $i,X2 : $i > $i > $o,X3 : $i,X4 : $i] : (($true = (in @ (kpair @ X4 @ X0) @ (dpsetconstr @ X3 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1))))))) => ((X2 @ X4 @ X0) = $true)) <=> (dpsetconstrER = $true)),
% 17.58/4.13 inference(fool_elimination,[status(thm)],[f498])).
% 17.58/4.13 thf(f498,plain,(
% 17.58/4.13 (dpsetconstrER = ! [X0 : $i,X1 : $i,X2 : $i > $i > $o,X3 : $i,X4 : $i] : ((in @ (kpair @ X4 @ X0) @ (dpsetconstr @ X3 @ X1 @ (^[X5 : $i, X6 : $i] : (X2 @ X5 @ X6)))) => (X2 @ X4 @ X0)))),
% 17.58/4.13 inference(rectify,[status(thm)],[f191])).
% 17.58/4.13 thf(f191,axiom,(
% 17.58/4.13 (dpsetconstrER = ! [X2 : $i,X4 : $i,X0 : $i > $i > $o,X3 : $i,X1 : $i] : ((in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10)))) => (X0 @ X1 @ X2)))),
% 17.58/4.13 file('/export/starexec/sandbox/tmp/tmp.4RsbB0Qymi/DTF2THF_10978.p',dpsetconstrER)).
% 17.58/4.13 % SZS output end Proof for DTF2THF_10978
% 17.58/4.13 % (11186)------------------------------
% 17.58/4.13 % (11186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.58/4.13 % (11186)Termination reason: Refutation
% 17.58/4.13
% 17.58/4.13 % (11186)Memory used [KB]: 14200
% 17.58/4.13 % (11186)Time elapsed: 1.242 s
% 17.58/4.13 % (11186)Instructions burned: 2470 (million)
% 17.58/4.13 % (11186)------------------------------
% 17.58/4.13 % (11186)------------------------------
% 17.58/4.13 % (11086)Success in time 2.507 s
%------------------------------------------------------------------------------