%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU814^1 : 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 : n002.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 09:37:26 AM UTC 2026
% Result : Theorem 13.72s 3.26s
% Output : Refutation 13.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 10
% Syntax : Number of formulae : 71 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 5605 (1522 equ; 0 cnn)
% Maximal formula atoms : 334 ( 78 avg)
% Number of connectives : 2930 ( 88 ~; 64 |;1038 &; 372 @)
% ( 7 <=>;1357 =>; 0 <=; 0 <~>)
% Maximal formula depth : 340 ( 37 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 685 ( 681 usr; 343 con; 0-6 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 138 ( 10 ^; 94 !; 34 ?; 138 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_184,type,
atmost1p: $i > $o ).
thf(func_def_185,type,
atleast2p: $i > $o ).
thf(func_def_186,type,
atmost2p: $i > $o ).
thf(func_def_187,type,
upairsetp: $i > $o ).
thf(func_def_191,type,
kfst: $i > $i ).
thf(func_def_203,type,
ksnd: $i > $i ).
thf(func_def_213,type,
breln: $i > $i > $i > $o ).
thf(func_def_214,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_222,type,
func: $i > $i > $i > $o ).
thf(func_def_223,type,
funcSet: $i > $i > $i ).
thf(func_def_226,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_232,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_259,type,
if: $i > $o > $i > $i > $i ).
thf(func_def_323,type,
breln1: $i > $i > $o ).
thf(func_def_325,type,
breln1Set: $i > $i ).
thf(func_def_327,type,
transitive: $i > $i > $o ).
thf(func_def_328,type,
antisymmetric: $i > $i > $o ).
thf(func_def_329,type,
reflexive: $i > $i > $o ).
thf(func_def_330,type,
refltransitive: $i > $i > $o ).
thf(func_def_331,type,
refllinearorder: $i > $i > $o ).
thf(func_def_332,type,
reflwellordering: $i > $i > $o ).
thf(func_def_338,type,
breln1invset: $i > $i > $i ).
thf(func_def_342,type,
breln1compset: $i > $i > $i > $i ).
thf(func_def_360,type,
image1: $i > ( $i > $i ) > $i ).
thf(func_def_364,type,
injective: $i > $i > $i > $o ).
thf(func_def_365,type,
injFuncSet: $i > $i > $i ).
thf(func_def_369,type,
surjective: $i > $i > $i > $o ).
thf(func_def_370,type,
surjFuncSet: $i > $i > $i ).
thf(func_def_378,type,
omegaS: $i > $i ).
thf(func_def_382,type,
peano3: $i > $i > $i > $o ).
thf(func_def_383,type,
peano4: $i > $i > $i > $o ).
thf(func_def_384,type,
peano5: $i > $i > $i > $o ).
thf(func_def_386,type,
peano: $i > $i > $i > $o ).
thf(func_def_387,type,
transitiveset: $i > $o ).
thf(func_def_405,type,
sP1: $i > $i > $o > $o ).
thf(func_def_406,type,
sP2: ( $i > $i ) > $i > $i > $o ).
thf(func_def_408,type,
sP4: $o > $i > $i > $i > $o ).
thf(func_def_409,type,
sP5: $i > $i > $i > $i > $o ).
thf(func_def_411,type,
sP7: ( $i > $o ) > $i > $i > $o ).
thf(func_def_413,type,
sP9: $i > ( $i > $o ) > $o ).
thf(func_def_415,type,
sP11: $i > ( $i > $o ) > $o ).
thf(func_def_417,type,
sP13: $o > $i > $i > $o ).
thf(func_def_419,type,
sP15: $i > $i > $o ).
thf(func_def_424,type,
sP20: $i > $i > $i > $i > $o ).
thf(func_def_425,type,
sP21: $i > $i > $i > $o ).
thf(func_def_426,type,
sP22: $o > $i > $i > $o ).
thf(func_def_427,type,
sP23: $i > $i > $i > $o ).
thf(func_def_428,type,
sP24: $i > $i > $i > $o ).
thf(func_def_429,type,
sP25: $i > ( $i > $o ) > $o ).
thf(func_def_431,type,
sP27: ( $i > $o ) > $i > $o ).
thf(func_def_433,type,
sP29: $i > $i > $i > $i > $o ).
thf(func_def_434,type,
sP30: $i > $i > $i > $i > $o ).
thf(func_def_435,type,
sP31: $i > ( $i > $o ) > $o ).
thf(func_def_436,type,
sP32: ( $i > $o ) > $i > $o ).
thf(func_def_437,type,
sP33: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_438,type,
sP34: ( $i > $i > $o ) > $i > $o ).
thf(func_def_443,type,
sP39: $i > $o ).
thf(func_def_444,type,
sP40: $i > $o ).
thf(func_def_445,type,
sP41: $i > $i > $o ).
thf(func_def_448,type,
sP44: $i > $i > $o > $o ).
thf(func_def_449,type,
sP45: $i > $i > $i > $o ).
thf(func_def_450,type,
sP46: $i > ( $i > $i ) > $i > $o ).
thf(func_def_452,type,
sP48: $i > $i > $i > $o ).
thf(func_def_453,type,
sP49: $i > $i > $i > $o ).
thf(func_def_454,type,
sP50: ( $i > $o ) > $i > $o ).
thf(func_def_455,type,
sP51: ( $i > $o ) > $i > $o ).
thf(func_def_456,type,
sP52: $i > $i > $i > $o ).
thf(func_def_457,type,
sP53: $i > ( $i > $i > $o ) > $i > $o ).
thf(func_def_458,type,
sP54: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_459,type,
sP55: ( $i > $o ) > $o ).
thf(func_def_460,type,
sP56: ( $i > $o ) > $i > $o ).
thf(func_def_461,type,
sP57: $i > ( $i > $o ) > $i > $i > $o ).
thf(func_def_462,type,
sP58: ( $i > $o ) > $o ).
thf(func_def_463,type,
sP59: $i > $i > $i > $o ).
thf(func_def_464,type,
sP60: $i > $o ).
thf(func_def_465,type,
sP61: ( $i > $o ) > $i > $o ).
thf(func_def_466,type,
sP62: ( $i > $o ) > $i > $i > $o ).
thf(func_def_467,type,
sP63: $i > ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_468,type,
sP64: $i > $i > $o ).
thf(func_def_470,type,
sP66: ( $i > $o ) > $i > $o ).
thf(func_def_473,type,
sP69: $i > ( $i > $i ) > $i > $o ).
thf(func_def_475,type,
sP71: $i > $i > $i > $o ).
thf(func_def_476,type,
sP72: $i > $i > $o ).
thf(func_def_477,type,
sP73: $i > $i > $o ).
thf(func_def_478,type,
sP74: $i > $i > $o ).
thf(func_def_479,type,
sP75: $i > $i > $o ).
thf(func_def_480,type,
sP76: $i > $o ).
thf(func_def_481,type,
sP77: $i > $i > $i > $i > $o ).
thf(func_def_482,type,
sP78: $i > ( $i > $i ) > $i > $o ).
thf(func_def_484,type,
sP80: ( $i > $o ) > $o ).
thf(func_def_485,type,
sP81: ( $i > $i ) > $i > $i > $o ).
thf(func_def_487,type,
sP83: $i > $i > $i > $i > $o > $i > $o ).
thf(func_def_488,type,
sP84: $i > $i > $i > $o ).
thf(func_def_490,type,
sP86: $i > ( $i > $o ) > $o ).
thf(func_def_492,type,
sP88: ( $i > $o ) > $o ).
thf(func_def_495,type,
sP91: ( $i > $o ) > $i > $o ).
thf(func_def_496,type,
sP92: ( $i > $o ) > $i > $i > $i > $o ).
thf(func_def_497,type,
sP93: $i > $i > $i > $o ).
thf(func_def_498,type,
sP94: $i > $i > $i > $o ).
thf(func_def_499,type,
sP95: $i > $i > $i > $o ).
thf(func_def_500,type,
sP96: $i > $i > $i > $i > $o ).
thf(func_def_501,type,
sP97: $i > $i > $i > $o ).
thf(func_def_502,type,
sP98: $i > $i > $i > $o ).
thf(func_def_503,type,
sP99: $i > $o > $i > $i > $o ).
thf(func_def_504,type,
sP100: $o > $i > $i > $i > $o ).
thf(func_def_505,type,
sP101: $i > ( $i > $o ) > $o ).
thf(func_def_506,type,
sP102: $i > $i > ( $i > $o ) > $o ).
thf(func_def_508,type,
sP104: ( $i > $o ) > $o ).
thf(func_def_509,type,
sP105: $i > $i > $i > $i > $i > $o ).
thf(func_def_514,type,
sK110: $i > $i > $i ).
thf(func_def_515,type,
sK111: $i > $o ).
thf(func_def_528,type,
sK124: $i > $i > $o > $i ).
thf(func_def_537,type,
sK133: $i > $o ).
thf(func_def_555,type,
sK151: $i > $o ).
thf(func_def_558,type,
sK154: $i > $i ).
thf(func_def_561,type,
sK157: $i > $i > ( $i > $i ) > $i ).
thf(func_def_562,type,
sK158: ( $i > $i ) > $i > $i > $i ).
thf(func_def_563,type,
sK159: $i > ( $i > $i ) > $i > $i > $i ).
thf(func_def_565,type,
sK161: $i > $i > $i > $i > $o ).
thf(func_def_572,type,
sK168: $i > $i ).
thf(func_def_599,type,
sK195: $i > $o ).
thf(func_def_600,type,
sK196: $i > $o ).
thf(func_def_601,type,
sK197: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_602,type,
sK198: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_621,type,
sK217: ( $i > $o ) > $i > $i > $i ).
thf(func_def_622,type,
sK218: $i > $o ).
thf(func_def_627,type,
sK223: $i > $i ).
thf(func_def_629,type,
sK225: $i > ( $i > $i ) > $i > $i ).
thf(func_def_633,type,
sK229: $i > $o ).
thf(func_def_635,type,
sK231: $i > ( $i > $o ) > $i ).
thf(func_def_636,type,
sK232: $i > ( $i > $o ) > $i ).
thf(func_def_641,type,
sK237: $i > $o ).
thf(func_def_650,type,
sK246: $i > $o ).
thf(func_def_652,type,
sK248: $i > ( $i > $o ) > $i ).
thf(func_def_653,type,
sK249: $i > ( $i > $o ) > $i ).
thf(func_def_679,type,
sK275: $i > $i > $i ).
thf(func_def_685,type,
sK281: $i > $i > $i ).
thf(func_def_693,type,
sK289: $i > $i ).
thf(func_def_730,type,
sK326: $i > $o ).
thf(func_def_731,type,
sK327: ( $i > $o ) > $i > $i ).
thf(func_def_732,type,
sK328: $i > $i > $i > $i > $i ).
thf(func_def_739,type,
sK335: $i > $i > $o ).
thf(func_def_747,type,
sK343: $i > $i > $i > $i ).
thf(func_def_748,type,
sK344: $i > $i > $i > $i ).
thf(func_def_752,type,
sK348: $i > $i > $i ).
thf(func_def_755,type,
sK351: $i > $i > $i > $o ).
thf(func_def_759,type,
sK355: $i > $i > $i > $i ).
thf(func_def_766,type,
sK362: $i > $o ).
thf(func_def_768,type,
sK364: $i > ( $i > $o ) > $i ).
thf(func_def_769,type,
sK365: $i > ( $i > $o ) > $i ).
thf(func_def_778,type,
sK374: $i > $o ).
thf(func_def_780,type,
sK376: $i > ( $i > $o ) > $i ).
thf(func_def_781,type,
sK377: ( $i > $o ) > $i > $i ).
thf(func_def_786,type,
sK382: $i > $i > $i > $i > $i ).
thf(func_def_787,type,
sK383: $i > $i > $i > $i > $i ).
thf(func_def_788,type,
sK384: $i > $i > $i > $i > $i ).
thf(func_def_789,type,
sK385: $i > $i > $i > $i > $i ).
thf(func_def_797,type,
sK393: $i > $o ).
thf(func_def_798,type,
sK394: ( $i > $o ) > $i ).
thf(func_def_810,type,
sK406: ( $i > $o ) > $i > $i ).
thf(func_def_811,type,
sK407: ( $i > $o ) > $i > $i ).
thf(func_def_812,type,
sK408: $i > ( $i > $o ) > $i ).
thf(func_def_814,type,
sK410: $i > $o ).
thf(func_def_824,type,
sK420: $i > $i > $o ).
thf(func_def_842,type,
sK438: $i > $i > $o ).
thf(func_def_844,type,
sK440: $i > ( $i > $i > $o ) > $i ).
thf(func_def_845,type,
sK441: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_846,type,
sK442: ( $i > $i > $o ) > $i > $i ).
thf(func_def_847,type,
sK443: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_885,type,
sK481: $i > $i ).
thf(func_def_887,type,
sK483: $i > ( $i > $i ) > $i > $i ).
thf(func_def_894,type,
sK490: $i > $o ).
thf(func_def_912,type,
sK508: $i > $i > $i ).
thf(func_def_917,type,
sK513: $i > $o ).
thf(func_def_928,type,
sK524: $i > $i ).
thf(func_def_929,type,
sK525: ( $i > $i ) > $i > $i > $i ).
thf(func_def_938,type,
sK534: $i > $i ).
thf(func_def_939,type,
sK535: $i > $i ).
thf(func_def_950,type,
sK546: $i > $i > $o ).
thf(func_def_954,type,
sK550: $i > $i > $i ).
thf(func_def_960,type,
sK556: $i > $i ).
thf(func_def_962,type,
sK558: $i > ( $i > $i ) > $i > $i ).
thf(func_def_966,type,
sK562: $i > $i > $i > $i ).
thf(func_def_967,type,
sK563: $i > $i > $i > $o ).
thf(func_def_975,type,
sK571: $i > $i ).
thf(func_def_976,type,
sK572: ( $i > $i ) > $i > $i > $i ).
thf(func_def_977,type,
sK573: $i > ( $i > $i ) > $i > $i ).
thf(func_def_982,type,
sK578: $i > $i > $i > $i ).
thf(func_def_983,type,
sK579: $i > $i > $i > $i ).
thf(func_def_991,type,
sK587: ( $i > $o ) > $i > $i ).
thf(func_def_992,type,
sK588: ( $i > $o ) > $i > $i ).
thf(func_def_993,type,
sK589: ( $i > $o ) > $i > $i ).
thf(func_def_994,type,
sK590: $i > $o ).
thf(func_def_1007,type,
sK603: $i > $i > $i > $i ).
thf(func_def_1008,type,
sK604: $i > $i > $i > $i > $i ).
thf(func_def_1012,type,
sK608: $i > $o ).
thf(func_def_1036,type,
sK632: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_1037,type,
sK633: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_1038,type,
sK634: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_1039,type,
sK635: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_1042,type,
sK638: $i > $i > $o ).
thf(func_def_1053,type,
sK649: $i > $i ).
thf(func_def_1058,type,
sK654: $i > $o ).
thf(func_def_1061,type,
sK657: $i > ( $i > $o ) > $i ).
thf(func_def_1062,type,
sK658: ( $i > $o ) > $i ).
thf(func_def_1063,type,
sK659: $i > $o ).
thf(func_def_1064,type,
sK660: $i > ( $i > $o ) > $i > $i > $i ).
thf(func_def_1065,type,
sK661: $i > ( $i > $o ) > $i > $i > $i ).
thf(func_def_1066,type,
sK662: ( $i > $o ) > $i > $i ).
thf(func_def_1070,type,
sK666: $i > $o ).
thf(func_def_1079,type,
sK675: ( $i > $o ) > $i ).
thf(func_def_1080,type,
sK676: ( $i > $o ) > $i ).
thf(func_def_1081,type,
sK677: $i > $o ).
thf(func_def_1097,type,
sK693: $i > $i > $i > $i ).
thf(func_def_1102,type,
sK698: $i > $i > $o ).
thf(func_def_1109,type,
sK705: $i > $i > $i ).
thf(func_def_1110,type,
sK706: $i > $i ).
thf(func_def_1120,type,
sK716: ( $i > $o ) > $i > $i > $i ).
thf(func_def_1121,type,
sK717: ( $i > $o ) > $i > $i > $i ).
thf(func_def_1122,type,
sK718: ( $i > $o ) > $i > $i ).
thf(func_def_1125,type,
sK721: $i > $o ).
thf(func_def_1126,type,
sK722: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(func_def_1127,type,
sK723: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(func_def_1130,type,
sK726: $i > $o ).
thf(func_def_1131,type,
sK727: $i > $o ).
thf(func_def_1141,type,
sK737: $i > $i > $i ).
thf(func_def_1142,type,
sK738: $i > $i > $i ).
thf(func_def_1157,type,
sK753: $i > $o ).
thf(func_def_1158,type,
sK754: ( $i > $o ) > $i > $i ).
thf(func_def_1159,type,
sK755: ( $i > $o ) > $i > $i ).
thf(func_def_1162,type,
sK758: $i > $i ).
thf(func_def_1175,type,
sK771: $i > $i ).
thf(func_def_1179,type,
sK775: $i > $o ).
thf(func_def_1180,type,
sK776: $i > $o ).
thf(func_def_1181,type,
sK777: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1182,type,
sK778: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1183,type,
sK779: $i > $i ).
thf(func_def_1186,type,
sK782: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1197,type,
sK793: $i > $i ).
thf(func_def_1198,type,
sK794: $i > $i ).
thf(func_def_1199,type,
sK795: $i > $i ).
thf(func_def_1200,type,
sK796: $i > $i ).
thf(func_def_1201,type,
sK797: $i > $i > $i ).
thf(func_def_1202,type,
sK798: $i > $i > $i ).
thf(func_def_1203,type,
sK799: $i > $i > $i ).
thf(func_def_1204,type,
sK800: $i > $i > $i ).
thf(func_def_1205,type,
sK801: $i > $i > $i > $i ).
thf(func_def_1206,type,
sK802: $i > $i > $i ).
thf(func_def_1207,type,
sK803: $i > $i > $i ).
thf(func_def_1208,type,
sK804: $i > $i > $i ).
thf(func_def_1209,type,
sK805: $i > $i > $i ).
thf(func_def_1210,type,
sK806: $i > $i > $i ).
thf(func_def_1211,type,
sK807: $i > $i > $i ).
thf(func_def_1212,type,
sK808: $i > $i > $i > $i ).
thf(func_def_1213,type,
sK809: $i > $i > $i > $i ).
thf(func_def_1215,type,
sK811: $i > $i ).
thf(func_def_1216,type,
sK812: $i > $i > $i > $i > $i ).
thf(func_def_1217,type,
sK813: $i > $i > $i > $i > $i ).
thf(func_def_1223,type,
sK819: $i > $i ).
thf(func_def_1225,type,
sK821: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1226,type,
sK822: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1235,type,
sK831: ( $i > $o ) > $i ).
thf(func_def_1236,type,
sK832: $i > ( $i > $o ) > $i ).
thf(func_def_1237,type,
sK833: $i > $o ).
thf(func_def_1250,type,
sK846: $i > $i > $o ).
thf(func_def_1287,type,
sK883: $i > $i ).
thf(func_def_1289,type,
sK885: $i > $i ).
thf(func_def_1290,type,
sK886: $i > ( $i > $i ) > $i ).
thf(func_def_1291,type,
sK887: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1305,type,
sK901: $i > $i > $o ).
thf(func_def_1308,type,
sK904: $i > $i > $i > $i > $o > $i > $i ).
thf(func_def_1322,type,
sK918: $i > $i > $o ).
thf(func_def_1336,type,
sK932: $i > $o ).
thf(func_def_1338,type,
sK934: $i > ( $i > $o ) > $i ).
thf(func_def_1339,type,
sK935: $i > ( $i > $o ) > $i ).
thf(func_def_1340,type,
sK936: $i > ( $i > $o ) > $i ).
thf(func_def_1341,type,
sK937: ( $i > $o ) > $i ).
thf(func_def_1342,type,
sK938: $i > $o ).
thf(func_def_1349,type,
sK945: $i > $i ).
thf(func_def_1352,type,
sK948: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1359,type,
sK955: $i > $o ).
thf(func_def_1365,type,
sK961: $i > $i > $o ).
thf(func_def_1392,type,
sK988: $i > $o ).
thf(func_def_1398,type,
sK994: $i > $i ).
thf(func_def_1407,type,
sK1003: $i > $i > $i ).
thf(func_def_1413,type,
sK1009: $i > $o ).
thf(func_def_1420,type,
sK1016: $i > $o ).
thf(func_def_1438,type,
sK1034: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_1439,type,
sK1035: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_1440,type,
sK1036: ( $i > $o ) > $i > $i ).
thf(func_def_1444,type,
sK1040: $i > $o ).
thf(func_def_1477,type,
sK1073: $i > $i > $i > $i ).
thf(func_def_1478,type,
sK1074: $i > $i > $i > $i > $i ).
thf(func_def_1496,type,
sK1092: $i > $i > $i > $i ).
thf(func_def_1497,type,
sK1093: $i > $i > $i > $i ).
thf(func_def_1498,type,
sK1094: $i > $i > $i > $i ).
thf(func_def_1499,type,
sK1095: $i > $i > $i > $i ).
thf(func_def_1516,type,
sK1112: $i > $i ).
thf(func_def_1521,type,
sK1117: $i > $i > $i > $i ).
thf(func_def_1522,type,
sK1118: $i > $i > $i > $i > $i ).
thf(func_def_1523,type,
sK1119: $i > $i > $i > $i > $i ).
thf(func_def_1524,type,
sK1120: $i > $i > $i > $i > $i ).
thf(func_def_1539,type,
sK1135: $i > $i > $i > $i ).
thf(func_def_1540,type,
sK1136: $i > $i > $i > $i ).
thf(func_def_1556,type,
sK1152: $i > $i > ( $i > $o ) > $i ).
thf(func_def_1557,type,
sK1153: $i > $i > ( $i > $o ) > $i ).
thf(func_def_1558,type,
sK1154: $i > ( $i > $o ) > $i ).
thf(func_def_1561,type,
sK1157: $i > $o ).
thf(func_def_1571,type,
sK1167: $i > $i > $i ).
thf(func_def_1573,type,
sK1169: ( $i > $o ) > $i ).
thf(func_def_1574,type,
sK1170: $i > ( $i > $o ) > $i ).
thf(func_def_1575,type,
sK1171: $i > $o ).
thf(func_def_1579,type,
sK1175: $i > $o ).
thf(func_def_1582,type,
sK1178: $i > $i > $i > $i > $i > $i ).
thf(func_def_1589,type,
sK1185: $i > $i ).
thf(func_def_1590,type,
sK1186: $i > $i ).
thf(func_def_1591,type,
sK1187: $i > $i ).
thf(func_def_1592,type,
ph1188:
!>[X0: $tType] : X0 ).
thf(f12158,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f12145]) ).
thf(f12145,plain,
$true = $false,
inference(backward_demodulation,[status(thm)],[f5042,f12120]) ).
thf(f12120,plain,
( $false
= ( in @ sK1042 @ sK1041 ) ),
inference(trivial_inequality_removal,[status(thm)],[f12113]) ).
thf(f12113,plain,
( ( $true != $true )
| ( $false
= ( in @ sK1042 @ sK1041 ) ) ),
inference(superposition,[status(thm)],[f12019,f6924]) ).
thf(f6924,plain,
! [X1: $i] :
( ( $true
= ( subset @ X1 @ sK1041 ) )
| ( $false
= ( in @ X1 @ sK1041 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f6923]) ).
thf(f6923,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK1041 )
=> ( subset @ X1 @ sK1041 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f6922]) ).
thf(f6922,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK1041 )
=> ( subset @ Y0 @ sK1041 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f6921]) ).
thf(f6921,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK1041 )
=> ( subset @ Y0 @ sK1041 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f6556]) ).
thf(f6556,plain,
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) )
@ sK1041 ) ),
inference(definition_unfolding,[status(thm)],[f5044,f4246]) ).
thf(f4246,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f394]) ).
thf(f394,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f393]) ).
thf(f393,plain,
( transitiveset
= ( ^ [X0: $i] :
! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f331]) ).
thf(f331,axiom,
( transitiveset
= ( ^ [X3: $i] :
! [X11: $i] :
( ( in @ X11 @ X3 )
=> ( subset @ X11 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zuy6gBFKOi/DTF2THF_17963.p',transitiveset) ).
thf(f5044,plain,
( ( transitiveset @ sK1041 )
= $true ),
inference(cnf_transformation,[status(thm)],[f3260]) ).
thf(f3260,plain,
( ( doubleComplementE1 = $true )
& ( iffalseProp1 = $true )
& ( powersetTE1 = $true )
& ( notinemptyset = $true )
& ( brelnall1 = $true )
& ( ubforcartprodlem1 = $true )
& ( dpsetconstrI = $true )
& ( breln1unionE = $true )
& ( woz1_4 = $true )
& ( subsetI2 = $true )
& ( funcGraphProp2 = $true )
& ( injFuncInInjFuncSet = $true )
& ( binunionTE = $true )
& ( disjointsetsI1 = $true )
& ( iftrueProp2 = $true )
& ( setukpairinjR = $true )
& ( emptysetsubset = $true )
& ( setunionAx = $true )
& ( leftInvIsSurj = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( binintersectSubset3 = $true )
& ( symdiffI1 = $true )
& ( surjCantorThm = $true )
& ( subsetI1 = $true )
& ( setukpairinjR2 = $true )
& ( setukpairinjL = $true )
& ( surjFuncSetFuncSurj = $true )
& ( funcinfuncset = $true )
& ( image1Ex1 = $true )
& ( breln1compprop = $true )
& ( setunionI = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodmempair1 = $true )
& ( notinself = $true )
& ( setminusI = $true )
& ( setminusIRneg = $true )
& ( contraSubsetComplement = $true )
& ( emptyI = $true )
& ( peano0notS = $true )
& ( lam2p = $true )
& ( inCongP = $true )
& ( transitivesetOp1 = $true )
& ( nonemptyI = $true )
& ( woz13rule3 = $true )
& ( singletonsubset = $true )
& ( powersetE = $true )
& ( setadjoinSub = $true )
& ( notsubsetI = $true )
& ( prop2setI = $true )
& ( woz2B = $true )
& ( contrasubsetT1 = $true )
& ( vacuousDall = $true )
& ( cartprodmempaircEq = $true )
& ( quantDeMorgan1 = $true )
& ( contrasubsetT = $true )
& ( cartprodsndin = $true )
& ( funcext = $true )
& ( setminusER = $true )
& ( setukpairinjL1 = $true )
& ( image1I = $true )
& ( binintersectTELcontra = $true )
& ( funcGraphProp4 = $true )
& ( iffalse = $true )
& ( binintTransitive = $true )
& ( binintersectTERcontra = $true )
& ( binintersectEL = $true )
& ( funcGraphProp1 = $true )
& ( infuncsetfunc = $true )
& ( binintersectER = $true )
& ( complementImpComplementIntersect = $true )
& ( app = $true )
& ( setunionsingleton2 = $true )
& ( image1Equiv = $true )
& ( breln1unionIR = $true )
& ( wellorderingAx = $true )
& ( breln1unionI = $true )
& ( setukpairinjR11 = $true )
& ( breln1all1 = $true )
& ( upairset2IR = $true )
& ( emptyE1 = $true )
& ( binunionLsub = $true )
& ( subsetTrans = $true )
& ( setukpairinjR1 = $true )
& ( subbreln1 = $true )
& ( subsetE = $true )
& ( ap2apEq2 = $true )
& ( emptyset__Cong = $true )
& ( injFuncSetFuncInj = $true )
& ( binunionT_lem = $true )
& ( complementTI1 = $true )
& ( noeltsimpempty = $true )
& ( setextAx = $true )
& ( binintersectLsub = $true )
& ( kfstsingleton = $true )
& ( doubleComplementEq = $true )
& ( setextT = $true )
& ( subsetRefl = $true )
& ( foundation2 = $true )
& ( uniqinunit = $true )
& ( woz1_5 = $true )
& ( doubleComplementSub1 = $true )
& ( setminusSubset2 = $true )
& ( subsetemptysetimpeq = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrEL2 = $true )
& ( setadjoin__Cong = $true )
& ( woz13rule0 = $true )
& ( emptysetimpfalse = $true )
& ( woz13rule1 = $true )
& ( dpsetconstrER = $true )
& ( quantDeMorgan4 = $true )
& ( beta1 = $true )
& ( complementTE1 = $true )
& ( dsetconstr__Cong = $true )
& ( injFuncSetFuncIn = $true )
& ( singletoninpowunion = $true )
& ( exuI2 = $true )
& ( notinself2 = $true )
& ( woz13rule2 = $true )
& ( demorgan1b = $true )
& ( subsetTI = $true )
& ( breln1compI = $true )
& ( eqbreln1 = $true )
& ( setext = $true )
& ( apProp = $true )
& ( exuE3e = $true )
& ( setadjoinSub2 = $true )
& ( setminusILneg = $true )
& ( kpairp = $true )
& ( eqbreln = $true )
& ( emptyinunitempty = $true )
& ( eta1 = $true )
& ( demorgan2a1 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( woz13rule4 = $true )
& ( sepInPowerset = $true )
& ( binunionTEcontra = $true )
& ( powersetE1 = $true )
& ( in__Cong = $true )
& ( lam2lamEq = $true )
& ( surjFuncSetFuncIn = $true )
& ( setadjoinE = $true )
& ( exuE2 = $true )
& ( setOfPairsIsBReln1 = $true )
& ( ifSingleton = $true )
& ( exuI3 = $true )
& ( setadjoinIR = $true )
& ( setukpairinjL2 = $true )
& ( subPowSU = $true )
& ( singletoninpowerset = $true )
& ( omegaSclos = $true )
& ( demorgan2 = $true )
& ( eqimpsubset2 = $true )
& ( symdiffIneg2 = $true )
& ( binintersectSubset1 = $true )
& ( complementT_lem = $true )
& ( woz1_3 = $true )
& ( emptyinPowerset = $true )
& ( complementSubsetComplementIntersect = $true )
& ( powersetTI1 = $true )
& ( cartprodfstpairEq = $true )
& ( contrasubsetT2 = $true )
& ( upairinpowunion = $true )
& ( funcGraphProp3 = $true )
& ( demorgan2b2 = $true )
& ( funcext2 = $true )
& ( setadjoinAx = $true )
& ( cartprodmempair = $true )
& ( upairequniteq = $true )
& ( omegaIndAx = $true )
& ( setadjoinIL = $true )
& ( kpairsurjEq = $true )
& ( funcextLem = $true )
& ( iftrueProp1 = $true )
& ( demorgan1a = $true )
& ( emptysetE = $true )
& ( foundationAx = $true )
& ( theprop = $true )
& ( doubleComplementSub2 = $true )
& ( binunionE = $true )
& ( ksndsingleton = $true )
& ( dsetconstrEL = $true )
& ( kpairiskpair = $true )
& ( subbreln = $true )
& ( ex1I = $true )
& ( symdiffI2 = $true )
& ( setunionsingleton1 = $true )
& ( woz1_1 = $true )
& ( woz1_2 = $true )
& ( setextsub = $true )
& ( brelnall2 = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( binintersectRsub = $true )
& ( iftrue = $true )
& ( emptyInPowerset = $true )
& ( breln1unionprop = $true )
& ( binintersectSubset4 = $true )
& ( upairset2E = $true )
& ( subset2powerset = $true )
& ( dsetconstrI = $true )
& ( exu__Cong = $true )
& ( breln1compEex = $true )
& ( complementTcontraSubset = $true )
& ( omegaSAx = $true )
& ( setunion__Cong = $true )
& ( exuEu = $true )
& ( dsetconstrER = $true )
& ( image1E = $true )
& ( notequalI2 = $true )
& ( upairsetIR = $true )
& ( notinsingleton = $true )
& ( setminusT_lem = $true )
& ( breln1all2 = $true )
& ( notequalI1 = $true )
& ( breln1SetBreln1 = $true )
& ( powersetT_lem = $true )
& ( replAx = $true )
& ( binunionIR = $true )
& ( ap2p = $true )
& ( singletonsswitch = $true )
& ( binintersectSubset2 = $true )
& ( ifp = $true )
& ( prop2set2propI = $true )
& ( binintersectT_lem = $true )
& ( prop2setE = $true )
& ( setadjoinOr = $true )
& ( woz2Ex = $true )
& ( inIntersectImpInUnion = $true )
& ( subsetE2 = $true )
& ( binunionTILcontra = $true )
& ( omega__Cong = $true )
& ( breln1compE = $true )
& ( demorgan1 = $true )
& ( cartprodfstin = $true )
& ( ksndpairEq = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodpairin = $true )
& ( contrasubsetT3 = $true )
& ( woz2A = $true )
& ( kfstpairEq = $true )
& ( cartprodpairmemER = $true )
& ( ( transitiveset @ sK1041 )
= $true )
& ( $true
= ( in @ sK1043 @ sK1042 ) )
& ( $true
= ( in @ sK1042 @ sK1041 ) )
& ( ( in @ sK1043 @ sK1041 )
!= $true )
& ( choice2fnsingleton = $true )
& ( funcImageSingleton = $true )
& ( setukpairinjR12 = $true )
& ( exuE3u = $true )
& ( singletonprop = $true )
& ( iftrueorfalse = $true )
& ( ex1E1 = $true )
& ( doubleComplementI1 = $true )
& ( eqimpsubset1 = $true )
& ( notdallE = $true )
& ( nonemptyI1 = $true )
& ( breln1invE = $true )
& ( breln1invprop = $true )
& ( sepSubset = $true )
& ( powersetI1 = $true )
& ( iffalseProp2 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( quantDeMorgan2 = $true )
& ( nonemptyImpWitness = $true )
& ( bs114d = $true )
& ( inIntersectImpInUnion2 = $true )
& ( omegaSp = $true )
& ( ex1E2 = $true )
& ( setminusLsub = $true )
& ( setunionE = $true )
& ( eta2 = $true )
& ( breln1unionEcases = $true )
& ( powerset__Cong = $true )
& ( powersetAx = $true )
& ( upairsetIL = $true )
& ( setoftrueEq = $true )
& ( binunionRsub = $true )
& ( demorgan2b = $true )
& ( setbeta = $true )
& ( binunionIL = $true )
& ( dpsetconstrERa = $true )
& ( image1Ex = $true )
& ( secondinupair = $true )
& ( demorgan2a2 = $true )
& ( lamp = $true )
& ( cartprodpairsurjEq = $true )
& ( setminusERneg = $true )
& ( omega0Ax = $true )
& ( setukpairIR = $true )
& ( ubforcartprodlem3 = $true )
& ( exuI1 = $true )
& ( breln1unionIL = $true )
& ( binunionTIRcontra = $true )
& ( breln1invI = $true )
& ( eqinunit = $true )
& ( singletonsuniq = $true )
& ( upairsubunion = $true )
& ( binintersectI = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( symdiffE = $true )
& ( setukpairIL = $true )
& ( setminusEL = $true )
& ( ubforcartprodlem2 = $true )
& ( upairsetE = $true )
& ( quantDeMorgan3 = $true )
& ( powersetI = $true )
& ( lamProp = $true )
& ( binunionEcases = $true )
& ( dpsetconstrSub = $true )
& ( binintersectSubset5 = $true )
& ( descrp = $true )
& ( descr__Cong = $true )
& ( ex1I2 = $true )
& ( setminusELneg = $true )
& ( breln1unionCommutes = $true )
& ( theeq = $true )
& ( complementTnotintersectT = $true )
& ( beta2 = $true )
& ( setunionsingleton = $true )
& ( ap2apEq1 = $true )
& ( symdiffIneg1 = $true )
& ( emptysetAx = $true )
& ( notdexE = $true )
& ( nonemptyE1 = $true )
& ( demorgan2a = $true )
& ( setunionE2 = $true )
& ( setminusSubset1 = $true )
& ( inPowerset = $true )
& ( powersetsubset = $true )
& ( exuE1 = $true )
& ( woz2W = $true )
& ( setOfPairsIsBReln = $true )
& ( peanoSinj = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1041,sK1042,sK1043])],[f1384,f3259,f3258]) ).
thf(f3258,plain,
( ? [X0: $i] :
( ( $true
= ( transitiveset @ X0 ) )
& ? [X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
& ( $true
= ( in @ X1 @ X0 ) )
& ( $true
!= ( in @ X2 @ X0 ) ) ) )
=> ( ( ( transitiveset @ sK1041 )
= $true )
& ? [X2: $i,X1: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
& ( $true
= ( in @ X1 @ sK1041 ) )
& ( $true
!= ( in @ X2 @ sK1041 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f3259,plain,
( ? [X2: $i,X1: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
& ( $true
= ( in @ X1 @ sK1041 ) )
& ( $true
!= ( in @ X2 @ sK1041 ) ) )
=> ( ( $true
= ( in @ sK1043 @ sK1042 ) )
& ( $true
= ( in @ sK1042 @ sK1041 ) )
& ( ( in @ sK1043 @ sK1041 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1384,plain,
( ( doubleComplementE1 = $true )
& ( iffalseProp1 = $true )
& ( powersetTE1 = $true )
& ( notinemptyset = $true )
& ( brelnall1 = $true )
& ( ubforcartprodlem1 = $true )
& ( dpsetconstrI = $true )
& ( breln1unionE = $true )
& ( woz1_4 = $true )
& ( subsetI2 = $true )
& ( funcGraphProp2 = $true )
& ( injFuncInInjFuncSet = $true )
& ( binunionTE = $true )
& ( disjointsetsI1 = $true )
& ( iftrueProp2 = $true )
& ( setukpairinjR = $true )
& ( emptysetsubset = $true )
& ( setunionAx = $true )
& ( leftInvIsSurj = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( binintersectSubset3 = $true )
& ( symdiffI1 = $true )
& ( surjCantorThm = $true )
& ( subsetI1 = $true )
& ( setukpairinjR2 = $true )
& ( setukpairinjL = $true )
& ( surjFuncSetFuncSurj = $true )
& ( funcinfuncset = $true )
& ( image1Ex1 = $true )
& ( breln1compprop = $true )
& ( setunionI = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodmempair1 = $true )
& ( notinself = $true )
& ( setminusI = $true )
& ( setminusIRneg = $true )
& ( contraSubsetComplement = $true )
& ( emptyI = $true )
& ( peano0notS = $true )
& ( lam2p = $true )
& ( inCongP = $true )
& ( transitivesetOp1 = $true )
& ( nonemptyI = $true )
& ( woz13rule3 = $true )
& ( singletonsubset = $true )
& ( powersetE = $true )
& ( setadjoinSub = $true )
& ( notsubsetI = $true )
& ( prop2setI = $true )
& ( woz2B = $true )
& ( contrasubsetT1 = $true )
& ( vacuousDall = $true )
& ( cartprodmempaircEq = $true )
& ( quantDeMorgan1 = $true )
& ( contrasubsetT = $true )
& ( cartprodsndin = $true )
& ( funcext = $true )
& ( setminusER = $true )
& ( setukpairinjL1 = $true )
& ( image1I = $true )
& ( binintersectTELcontra = $true )
& ( funcGraphProp4 = $true )
& ( iffalse = $true )
& ( binintTransitive = $true )
& ( binintersectTERcontra = $true )
& ( binintersectEL = $true )
& ( funcGraphProp1 = $true )
& ( infuncsetfunc = $true )
& ( binintersectER = $true )
& ( complementImpComplementIntersect = $true )
& ( app = $true )
& ( setunionsingleton2 = $true )
& ( image1Equiv = $true )
& ( breln1unionIR = $true )
& ( wellorderingAx = $true )
& ( breln1unionI = $true )
& ( setukpairinjR11 = $true )
& ( breln1all1 = $true )
& ( upairset2IR = $true )
& ( emptyE1 = $true )
& ( binunionLsub = $true )
& ( subsetTrans = $true )
& ( setukpairinjR1 = $true )
& ( subbreln1 = $true )
& ( subsetE = $true )
& ( ap2apEq2 = $true )
& ( emptyset__Cong = $true )
& ( injFuncSetFuncInj = $true )
& ( binunionT_lem = $true )
& ( complementTI1 = $true )
& ( noeltsimpempty = $true )
& ( setextAx = $true )
& ( binintersectLsub = $true )
& ( kfstsingleton = $true )
& ( doubleComplementEq = $true )
& ( setextT = $true )
& ( subsetRefl = $true )
& ( foundation2 = $true )
& ( uniqinunit = $true )
& ( woz1_5 = $true )
& ( doubleComplementSub1 = $true )
& ( setminusSubset2 = $true )
& ( subsetemptysetimpeq = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrEL2 = $true )
& ( setadjoin__Cong = $true )
& ( woz13rule0 = $true )
& ( emptysetimpfalse = $true )
& ( woz13rule1 = $true )
& ( dpsetconstrER = $true )
& ( quantDeMorgan4 = $true )
& ( beta1 = $true )
& ( complementTE1 = $true )
& ( dsetconstr__Cong = $true )
& ( injFuncSetFuncIn = $true )
& ( singletoninpowunion = $true )
& ( exuI2 = $true )
& ( notinself2 = $true )
& ( woz13rule2 = $true )
& ( demorgan1b = $true )
& ( subsetTI = $true )
& ( breln1compI = $true )
& ( eqbreln1 = $true )
& ( setext = $true )
& ( apProp = $true )
& ( exuE3e = $true )
& ( setadjoinSub2 = $true )
& ( setminusILneg = $true )
& ( kpairp = $true )
& ( eqbreln = $true )
& ( emptyinunitempty = $true )
& ( eta1 = $true )
& ( demorgan2a1 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( woz13rule4 = $true )
& ( sepInPowerset = $true )
& ( binunionTEcontra = $true )
& ( powersetE1 = $true )
& ( in__Cong = $true )
& ( lam2lamEq = $true )
& ( surjFuncSetFuncIn = $true )
& ( setadjoinE = $true )
& ( exuE2 = $true )
& ( setOfPairsIsBReln1 = $true )
& ( ifSingleton = $true )
& ( exuI3 = $true )
& ( setadjoinIR = $true )
& ( setukpairinjL2 = $true )
& ( subPowSU = $true )
& ( singletoninpowerset = $true )
& ( omegaSclos = $true )
& ( demorgan2 = $true )
& ( eqimpsubset2 = $true )
& ( symdiffIneg2 = $true )
& ( binintersectSubset1 = $true )
& ( complementT_lem = $true )
& ( woz1_3 = $true )
& ( emptyinPowerset = $true )
& ( complementSubsetComplementIntersect = $true )
& ( powersetTI1 = $true )
& ( cartprodfstpairEq = $true )
& ( contrasubsetT2 = $true )
& ( upairinpowunion = $true )
& ( funcGraphProp3 = $true )
& ( demorgan2b2 = $true )
& ( funcext2 = $true )
& ( setadjoinAx = $true )
& ( cartprodmempair = $true )
& ( upairequniteq = $true )
& ( omegaIndAx = $true )
& ( setadjoinIL = $true )
& ( kpairsurjEq = $true )
& ( funcextLem = $true )
& ( iftrueProp1 = $true )
& ( demorgan1a = $true )
& ( emptysetE = $true )
& ( foundationAx = $true )
& ( theprop = $true )
& ( doubleComplementSub2 = $true )
& ( binunionE = $true )
& ( ksndsingleton = $true )
& ( dsetconstrEL = $true )
& ( kpairiskpair = $true )
& ( subbreln = $true )
& ( ex1I = $true )
& ( symdiffI2 = $true )
& ( setunionsingleton1 = $true )
& ( woz1_1 = $true )
& ( woz1_2 = $true )
& ( setextsub = $true )
& ( brelnall2 = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( binintersectRsub = $true )
& ( iftrue = $true )
& ( emptyInPowerset = $true )
& ( breln1unionprop = $true )
& ( binintersectSubset4 = $true )
& ( upairset2E = $true )
& ( subset2powerset = $true )
& ( dsetconstrI = $true )
& ( exu__Cong = $true )
& ( breln1compEex = $true )
& ( complementTcontraSubset = $true )
& ( omegaSAx = $true )
& ( setunion__Cong = $true )
& ( exuEu = $true )
& ( dsetconstrER = $true )
& ( image1E = $true )
& ( notequalI2 = $true )
& ( upairsetIR = $true )
& ( notinsingleton = $true )
& ( setminusT_lem = $true )
& ( breln1all2 = $true )
& ( notequalI1 = $true )
& ( breln1SetBreln1 = $true )
& ( powersetT_lem = $true )
& ( replAx = $true )
& ( binunionIR = $true )
& ( ap2p = $true )
& ( singletonsswitch = $true )
& ( binintersectSubset2 = $true )
& ( ifp = $true )
& ( prop2set2propI = $true )
& ( binintersectT_lem = $true )
& ( prop2setE = $true )
& ( setadjoinOr = $true )
& ( woz2Ex = $true )
& ( inIntersectImpInUnion = $true )
& ( subsetE2 = $true )
& ( binunionTILcontra = $true )
& ( omega__Cong = $true )
& ( breln1compE = $true )
& ( demorgan1 = $true )
& ( cartprodfstin = $true )
& ( ksndpairEq = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodpairin = $true )
& ( contrasubsetT3 = $true )
& ( woz2A = $true )
& ( kfstpairEq = $true )
& ( cartprodpairmemER = $true )
& ? [X0: $i] :
( ( $true
= ( transitiveset @ X0 ) )
& ? [X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
& ( $true
= ( in @ X1 @ X0 ) )
& ( $true
!= ( in @ X2 @ X0 ) ) ) )
& ( choice2fnsingleton = $true )
& ( funcImageSingleton = $true )
& ( setukpairinjR12 = $true )
& ( exuE3u = $true )
& ( singletonprop = $true )
& ( iftrueorfalse = $true )
& ( ex1E1 = $true )
& ( doubleComplementI1 = $true )
& ( eqimpsubset1 = $true )
& ( notdallE = $true )
& ( nonemptyI1 = $true )
& ( breln1invE = $true )
& ( breln1invprop = $true )
& ( sepSubset = $true )
& ( powersetI1 = $true )
& ( iffalseProp2 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( quantDeMorgan2 = $true )
& ( nonemptyImpWitness = $true )
& ( bs114d = $true )
& ( inIntersectImpInUnion2 = $true )
& ( omegaSp = $true )
& ( ex1E2 = $true )
& ( setminusLsub = $true )
& ( setunionE = $true )
& ( eta2 = $true )
& ( breln1unionEcases = $true )
& ( powerset__Cong = $true )
& ( powersetAx = $true )
& ( upairsetIL = $true )
& ( setoftrueEq = $true )
& ( binunionRsub = $true )
& ( demorgan2b = $true )
& ( setbeta = $true )
& ( binunionIL = $true )
& ( dpsetconstrERa = $true )
& ( image1Ex = $true )
& ( secondinupair = $true )
& ( demorgan2a2 = $true )
& ( lamp = $true )
& ( cartprodpairsurjEq = $true )
& ( setminusERneg = $true )
& ( omega0Ax = $true )
& ( setukpairIR = $true )
& ( ubforcartprodlem3 = $true )
& ( exuI1 = $true )
& ( breln1unionIL = $true )
& ( binunionTIRcontra = $true )
& ( breln1invI = $true )
& ( eqinunit = $true )
& ( singletonsuniq = $true )
& ( upairsubunion = $true )
& ( binintersectI = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( symdiffE = $true )
& ( setukpairIL = $true )
& ( setminusEL = $true )
& ( ubforcartprodlem2 = $true )
& ( upairsetE = $true )
& ( quantDeMorgan3 = $true )
& ( powersetI = $true )
& ( lamProp = $true )
& ( binunionEcases = $true )
& ( dpsetconstrSub = $true )
& ( binintersectSubset5 = $true )
& ( descrp = $true )
& ( descr__Cong = $true )
& ( ex1I2 = $true )
& ( setminusELneg = $true )
& ( breln1unionCommutes = $true )
& ( theeq = $true )
& ( complementTnotintersectT = $true )
& ( beta2 = $true )
& ( setunionsingleton = $true )
& ( ap2apEq1 = $true )
& ( symdiffIneg1 = $true )
& ( emptysetAx = $true )
& ( notdexE = $true )
& ( nonemptyE1 = $true )
& ( demorgan2a = $true )
& ( setunionE2 = $true )
& ( setminusSubset1 = $true )
& ( inPowerset = $true )
& ( powersetsubset = $true )
& ( exuE1 = $true )
& ( woz2W = $true )
& ( setOfPairsIsBReln = $true )
& ( peanoSinj = $true ) ),
inference(flattening,[status(thm)],[f1383]) ).
thf(f1383,plain,
( ? [X0: $i] :
( ? [X1: $i,X2: $i] :
( ( $true
!= ( in @ X2 @ X0 ) )
& ( $true
= ( in @ X2 @ X1 ) )
& ( $true
= ( in @ X1 @ X0 ) ) )
& ( $true
= ( transitiveset @ X0 ) ) )
& ( binintTransitive = $true )
& ( transitivesetOp1 = $true )
& ( peanoSinj = $true )
& ( peano0notS = $true )
& ( omegaSclos = $true )
& ( omegaSp = $true )
& ( notinself2 = $true )
& ( notinself = $true )
& ( foundation2 = $true )
& ( surjCantorThm = $true )
& ( leftInvIsSurj = $true )
& ( surjFuncSetFuncSurj = $true )
& ( surjFuncSetFuncIn = $true )
& ( injFuncSetFuncInj = $true )
& ( injFuncSetFuncIn = $true )
& ( injFuncInInjFuncSet = $true )
& ( image1I = $true )
& ( image1E = $true )
& ( image1Equiv = $true )
& ( image1Ex1 = $true )
& ( image1Ex = $true )
& ( woz2B = $true )
& ( woz2A = $true )
& ( woz2W = $true )
& ( woz2Ex = $true )
& ( breln1unionCommutes = $true )
& ( breln1unionEcases = $true )
& ( breln1unionE = $true )
& ( breln1unionI = $true )
& ( breln1unionIR = $true )
& ( breln1unionIL = $true )
& ( breln1unionprop = $true )
& ( breln1compEex = $true )
& ( breln1compE = $true )
& ( breln1compI = $true )
& ( breln1compprop = $true )
& ( breln1invE = $true )
& ( breln1invI = $true )
& ( breln1invprop = $true )
& ( eqbreln1 = $true )
& ( subbreln1 = $true )
& ( breln1all1 = $true )
& ( setOfPairsIsBReln1 = $true )
& ( choice2fnsingleton = $true )
& ( breln1SetBreln1 = $true )
& ( breln1all2 = $true )
& ( woz1_5 = $true )
& ( woz1_4 = $true )
& ( woz1_3 = $true )
& ( woz1_2 = $true )
& ( woz1_1 = $true )
& ( woz13rule4 = $true )
& ( woz13rule3 = $true )
& ( woz13rule2 = $true )
& ( woz13rule1 = $true )
& ( woz13rule0 = $true )
& ( demorgan2 = $true )
& ( demorgan2b = $true )
& ( demorgan2b2 = $true )
& ( demorgan2a = $true )
& ( demorgan1 = $true )
& ( demorgan1b = $true )
& ( demorgan1a = $true )
& ( demorgan2a2 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( demorgan2a1 = $true )
& ( binunionTEcontra = $true )
& ( binunionTE = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( inIntersectImpInUnion2 = $true )
& ( inIntersectImpInUnion = $true )
& ( binunionTIRcontra = $true )
& ( binunionTILcontra = $true )
& ( complementTcontraSubset = $true )
& ( contraSubsetComplement = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( complementSubsetComplementIntersect = $true )
& ( complementImpComplementIntersect = $true )
& ( complementTnotintersectT = $true )
& ( doubleComplementEq = $true )
& ( doubleComplementSub2 = $true )
& ( doubleComplementSub1 = $true )
& ( doubleComplementE1 = $true )
& ( doubleComplementI1 = $true )
& ( contrasubsetT3 = $true )
& ( contrasubsetT2 = $true )
& ( contrasubsetT1 = $true )
& ( contrasubsetT = $true )
& ( binintersectTERcontra = $true )
& ( binintersectTELcontra = $true )
& ( complementTE1 = $true )
& ( complementTI1 = $true )
& ( powersetTE1 = $true )
& ( powersetTI1 = $true )
& ( subsetTI = $true )
& ( setextT = $true )
& ( complementT_lem = $true )
& ( setminusT_lem = $true )
& ( powersetT_lem = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true )
& ( iftrueorfalse = $true )
& ( iffalse = $true )
& ( iftrue = $true )
& ( theeq = $true )
& ( ifp = $true )
& ( ifSingleton = $true )
& ( iftrueProp2 = $true )
& ( iftrueProp1 = $true )
& ( iffalseProp2 = $true )
& ( iffalseProp1 = $true )
& ( eta2 = $true )
& ( beta2 = $true )
& ( lam2lamEq = $true )
& ( eta1 = $true )
& ( beta1 = $true )
& ( ap2apEq2 = $true )
& ( ap2apEq1 = $true )
& ( funcext2 = $true )
& ( funcext = $true )
& ( eqbreln = $true )
& ( subbreln = $true )
& ( funcGraphProp4 = $true )
& ( funcextLem = $true )
& ( funcGraphProp2 = $true )
& ( funcGraphProp3 = $true )
& ( funcGraphProp1 = $true )
& ( ex1E2 = $true )
& ( brelnall2 = $true )
& ( brelnall1 = $true )
& ( lam2p = $true )
& ( lamp = $true )
& ( lamProp = $true )
& ( funcinfuncset = $true )
& ( ap2p = $true )
& ( infuncsetfunc = $true )
& ( app = $true )
& ( apProp = $true )
& ( funcImageSingleton = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrEL2 = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrERa = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrI = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodsndin = $true )
& ( kpairsurjEq = $true )
& ( ksndpairEq = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( setukpairinjR2 = $true )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f368]) ).
thf(f368,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ( ( ap2p = $true )
=> ( ( funcinfuncset = $true )
=> ( ( lamProp = $true )
=> ( ( lamp = $true )
=> ( ( lam2p = $true )
=> ( ( brelnall1 = $true )
=> ( ( brelnall2 = $true )
=> ( ( ex1E2 = $true )
=> ( ( funcGraphProp1 = $true )
=> ( ( funcGraphProp3 = $true )
=> ( ( funcGraphProp2 = $true )
=> ( ( funcextLem = $true )
=> ( ( funcGraphProp4 = $true )
=> ( ( subbreln = $true )
=> ( ( eqbreln = $true )
=> ( ( funcext = $true )
=> ( ( funcext2 = $true )
=> ( ( ap2apEq1 = $true )
=> ( ( ap2apEq2 = $true )
=> ( ( beta1 = $true )
=> ( ( eta1 = $true )
=> ( ( lam2lamEq = $true )
=> ( ( beta2 = $true )
=> ( ( eta2 = $true )
=> ( ( iffalseProp1 = $true )
=> ( ( iffalseProp2 = $true )
=> ( ( iftrueProp1 = $true )
=> ( ( iftrueProp2 = $true )
=> ( ( ifSingleton = $true )
=> ( ( ifp = $true )
=> ( ( theeq = $true )
=> ( ( iftrue = $true )
=> ( ( iffalse = $true )
=> ( ( iftrueorfalse = $true )
=> ( ( binintersectT_lem = $true )
=> ( ( binunionT_lem = $true )
=> ( ( powersetT_lem = $true )
=> ( ( setminusT_lem = $true )
=> ( ( complementT_lem = $true )
=> ( ( setextT = $true )
=> ( ( subsetTI = $true )
=> ( ( powersetTI1 = $true )
=> ( ( powersetTE1 = $true )
=> ( ( complementTI1 = $true )
=> ( ( complementTE1 = $true )
=> ( ( binintersectTELcontra = $true )
=> ( ( binintersectTERcontra = $true )
=> ( ( contrasubsetT = $true )
=> ( ( contrasubsetT1 = $true )
=> ( ( contrasubsetT2 = $true )
=> ( ( contrasubsetT3 = $true )
=> ( ( doubleComplementI1 = $true )
=> ( ( doubleComplementE1 = $true )
=> ( ( doubleComplementSub1 = $true )
=> ( ( doubleComplementSub2 = $true )
=> ( ( doubleComplementEq = $true )
=> ( ( complementTnotintersectT = $true )
=> ( ( complementImpComplementIntersect = $true )
=> ( ( complementSubsetComplementIntersect = $true )
=> ( ( complementInPowersetComplementIntersect = $true )
=> ( ( contraSubsetComplement = $true )
=> ( ( complementTcontraSubset = $true )
=> ( ( binunionTILcontra = $true )
=> ( ( binunionTIRcontra = $true )
=> ( ( inIntersectImpInUnion = $true )
=> ( ( inIntersectImpInUnion2 = $true )
=> ( ( inIntersectImpInIntersectUnions = $true )
=> ( ( intersectInPowersetIntersectUnions = $true )
=> ( ( inComplementUnionImpNotIn1 = $true )
=> ( ( inComplementUnionImpInComplement1 = $true )
=> ( ( binunionTE = $true )
=> ( ( binunionTEcontra = $true )
=> ( ( demorgan2a1 = $true )
=> ( ( complementUnionInPowersetComplement = $true )
=> ( ( demorgan2a2 = $true )
=> ( ( demorgan1a = $true )
=> ( ( demorgan1b = $true )
=> ( ( demorgan1 = $true )
=> ( ( demorgan2a = $true )
=> ( ( demorgan2b2 = $true )
=> ( ( demorgan2b = $true )
=> ( ( demorgan2 = $true )
=> ( ( woz13rule0 = $true )
=> ( ( woz13rule1 = $true )
=> ( ( woz13rule2 = $true )
=> ( ( woz13rule3 = $true )
=> ( ( woz13rule4 = $true )
=> ( ( woz1_1 = $true )
=> ( ( woz1_2 = $true )
=> ( ( woz1_3 = $true )
=> ( ( woz1_4 = $true )
=> ( ( woz1_5 = $true )
=> ( ( breln1all2 = $true )
=> ( ( breln1SetBreln1 = $true )
=> ( ( choice2fnsingleton = $true )
=> ( ( setOfPairsIsBReln1 = $true )
=> ( ( breln1all1 = $true )
=> ( ( subbreln1 = $true )
=> ( ( eqbreln1 = $true )
=> ( ( breln1invprop = $true )
=> ( ( breln1invI = $true )
=> ( ( breln1invE = $true )
=> ( ( breln1compprop = $true )
=> ( ( breln1compI = $true )
=> ( ( breln1compE = $true )
=> ( ( breln1compEex = $true )
=> ( ( breln1unionprop = $true )
=> ( ( breln1unionIL = $true )
=> ( ( breln1unionIR = $true )
=> ( ( breln1unionI = $true )
=> ( ( breln1unionE = $true )
=> ( ( breln1unionEcases = $true )
=> ( ( breln1unionCommutes = $true )
=> ( ( woz2Ex = $true )
=> ( ( woz2W = $true )
=> ( ( woz2A = $true )
=> ( ( woz2B = $true )
=> ( ( image1Ex = $true )
=> ( ( image1Ex1 = $true )
=> ( ( image1Equiv = $true )
=> ( ( image1E = $true )
=> ( ( image1I = $true )
=> ( ( injFuncInInjFuncSet = $true )
=> ( ( injFuncSetFuncIn = $true )
=> ( ( injFuncSetFuncInj = $true )
=> ( ( surjFuncSetFuncIn = $true )
=> ( ( surjFuncSetFuncSurj = $true )
=> ( ( leftInvIsSurj = $true )
=> ( ( surjCantorThm = $true )
=> ( ( foundation2 = $true )
=> ( ( notinself = $true )
=> ( ( notinself2 = $true )
=> ( ( omegaSp = $true )
=> ( ( omegaSclos = $true )
=> ( ( peano0notS = $true )
=> ( ( peanoSinj = $true )
=> ( ( transitivesetOp1 = $true )
=> ( ( binintTransitive = $true )
=> ! [X0: $i] :
( ( $true
= ( transitiveset @ X0 ) )
=> ! [X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
=> ( ( $true
= ( in @ X2 @ X1 ) )
=> ( $true
= ( in @ X2 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f367]) ).
thf(f367,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( breln1compprop
=> ( breln1compI
=> ( breln1compE
=> ( breln1compEex
=> ( breln1unionprop
=> ( breln1unionIL
=> ( breln1unionIR
=> ( breln1unionI
=> ( breln1unionE
=> ( breln1unionEcases
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ( woz2B
=> ( image1Ex
=> ( image1Ex1
=> ( image1Equiv
=> ( image1E
=> ( image1I
=> ( injFuncInInjFuncSet
=> ( injFuncSetFuncIn
=> ( injFuncSetFuncInj
=> ( surjFuncSetFuncIn
=> ( surjFuncSetFuncSurj
=> ( leftInvIsSurj
=> ( surjCantorThm
=> ( foundation2
=> ( notinself
=> ( notinself2
=> ( omegaSp
=> ( omegaSclos
=> ( peano0notS
=> ( peanoSinj
=> ( transitivesetOp1
=> ( binintTransitive
=> ! [X0: $i] :
( ( transitiveset @ X0 )
=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f335]) ).
thf(f335,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( breln1compprop
=> ( breln1compI
=> ( breln1compE
=> ( breln1compEex
=> ( breln1unionprop
=> ( breln1unionIL
=> ( breln1unionIR
=> ( breln1unionI
=> ( breln1unionE
=> ( breln1unionEcases
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ( woz2B
=> ( image1Ex
=> ( image1Ex1
=> ( image1Equiv
=> ( image1E
=> ( image1I
=> ( injFuncInInjFuncSet
=> ( injFuncSetFuncIn
=> ( injFuncSetFuncInj
=> ( surjFuncSetFuncIn
=> ( surjFuncSetFuncSurj
=> ( leftInvIsSurj
=> ( surjCantorThm
=> ( foundation2
=> ( notinself
=> ( notinself2
=> ( omegaSp
=> ( omegaSclos
=> ( peano0notS
=> ( peanoSinj
=> ( transitivesetOp1
=> ( binintTransitive
=> ! [X11: $i] :
( ( transitiveset @ X11 )
=> ! [X3: $i,X1: $i] :
( ( in @ X3 @ X11 )
=> ( ( in @ X1 @ X3 )
=> ( in @ X1 @ X11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f334]) ).
thf(f334,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( breln1compprop
=> ( breln1compI
=> ( breln1compE
=> ( breln1compEex
=> ( breln1unionprop
=> ( breln1unionIL
=> ( breln1unionIR
=> ( breln1unionI
=> ( breln1unionE
=> ( breln1unionEcases
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ( woz2B
=> ( image1Ex
=> ( image1Ex1
=> ( image1Equiv
=> ( image1E
=> ( image1I
=> ( injFuncInInjFuncSet
=> ( injFuncSetFuncIn
=> ( injFuncSetFuncInj
=> ( surjFuncSetFuncIn
=> ( surjFuncSetFuncSurj
=> ( leftInvIsSurj
=> ( surjCantorThm
=> ( foundation2
=> ( notinself
=> ( notinself2
=> ( omegaSp
=> ( omegaSclos
=> ( peano0notS
=> ( peanoSinj
=> ( transitivesetOp1
=> ( binintTransitive
=> ! [X11: $i] :
( ( transitiveset @ X11 )
=> ! [X3: $i,X1: $i] :
( ( in @ X3 @ X11 )
=> ( ( in @ X1 @ X3 )
=> ( in @ X1 @ X11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zuy6gBFKOi/DTF2THF_17963.p',transitivesetOp2) ).
thf(f12019,plain,
( ( subset @ sK1042 @ sK1041 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f12017]) ).
thf(f12017,plain,
( ( ( subset @ sK1042 @ sK1041 )
!= $true )
| ( sK1042 != sK1042 ) ),
inference(superposition,[status(thm)],[f11946,f6953]) ).
thf(f6953,plain,
! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X1 )
| ( $true
!= ( subset @ X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f6139]) ).
thf(f6139,plain,
! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X1 )
| ( $true != $true )
| ( $true
!= ( subset @ X1 @ X0 ) ) ),
inference(definition_unfolding,[status(thm)],[f4393,f5089]) ).
thf(f5089,plain,
binintersectSubset4 = $true,
inference(cnf_transformation,[status(thm)],[f3260]) ).
thf(f4393,plain,
! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X1 )
| ( $true
!= ( subset @ X1 @ X0 ) )
| ( binintersectSubset4 != $true ) ),
inference(cnf_transformation,[status(thm)],[f2624]) ).
thf(f2624,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X1 )
| ( $true
!= ( subset @ X1 @ X0 ) ) )
| ( binintersectSubset4 != $true ) )
& ( ( binintersectSubset4 = $true )
| ( ( ( binintersect @ sK667 @ sK668 )
!= sK668 )
& ( $true
= ( subset @ sK668 @ sK667 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK667,sK668])],[f2622,f2623]) ).
thf(f2623,plain,
( ? [X2: $i,X3: $i] :
( ( ( binintersect @ X2 @ X3 )
!= X3 )
& ( $true
= ( subset @ X3 @ X2 ) ) )
=> ( ( ( binintersect @ sK667 @ sK668 )
!= sK668 )
& ( $true
= ( subset @ sK668 @ sK667 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2622,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X1 )
| ( $true
!= ( subset @ X1 @ X0 ) ) )
| ( binintersectSubset4 != $true ) )
& ( ( binintersectSubset4 = $true )
| ? [X2: $i,X3: $i] :
( ( ( binintersect @ X2 @ X3 )
!= X3 )
& ( $true
= ( subset @ X3 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f2621]) ).
thf(f2621,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X1 )
| ( $true
!= ( subset @ X1 @ X0 ) ) )
| ( binintersectSubset4 != $true ) )
& ( ( binintersectSubset4 = $true )
| ? [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
!= X1 )
& ( $true
= ( subset @ X1 @ X0 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f1239]) ).
thf(f1239,plain,
( ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X1 )
| ( $true
!= ( subset @ X1 @ X0 ) ) )
<=> ( binintersectSubset4 = $true ) ),
inference(ennf_transformation,[status(thm)],[f944]) ).
thf(f944,plain,
( ( binintersectSubset4 = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
=> ( ( binintersect @ X0 @ X1 )
= X1 ) ) ),
inference(fool_elimination,[status(thm)],[f943]) ).
thf(f943,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
=> ( ( binintersect @ X0 @ X1 )
= X1 ) )
= binintersectSubset4 ),
inference(rectify,[status(thm)],[f117]) ).
thf(f117,axiom,
! [X3: $i,X4: $i] :
( ( ( subset @ X4 @ X3 )
=> ( ( binintersect @ X3 @ X4 )
= X4 ) )
= binintersectSubset4 ),
file('/export/starexec/sandbox/tmp/tmp.zuy6gBFKOi/DTF2THF_17963.p',binintersectSubset4) ).
thf(f11946,plain,
( sK1042
!= ( binintersect @ sK1041 @ sK1042 ) ),
inference(trivial_inequality_removal,[status(thm)],[f11938]) ).
thf(f11938,plain,
( ( $true != $true )
| ( sK1042
!= ( binintersect @ sK1041 @ sK1042 ) ) ),
inference(superposition,[status(thm)],[f9724,f5043]) ).
thf(f5043,plain,
( $true
= ( in @ sK1043 @ sK1042 ) ),
inference(cnf_transformation,[status(thm)],[f3260]) ).
thf(f9724,plain,
! [X0: $i] :
( ( $true
!= ( in @ sK1043 @ X0 ) )
| ( ( binintersect @ sK1041 @ X0 )
!= X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f9721]) ).
thf(f9721,plain,
! [X0: $i] :
( ( $true
!= ( in @ sK1043 @ X0 ) )
| ( ( binintersect @ sK1041 @ X0 )
!= X0 )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f8878,f6900]) ).
thf(f6900,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ( ( binintersect @ X0 @ X1 )
!= X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f5712]) ).
thf(f5712,plain,
! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
!= X1 )
| ( $true != $true )
| ( $true
= ( subset @ X1 @ X0 ) ) ),
inference(definition_unfolding,[status(thm)],[f3801,f5266]) ).
thf(f5266,plain,
binintersectSubset3 = $true,
inference(cnf_transformation,[status(thm)],[f3260]) ).
thf(f3801,plain,
! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
!= X1 )
| ( $true
= ( subset @ X1 @ X0 ) )
| ( binintersectSubset3 != $true ) ),
inference(cnf_transformation,[status(thm)],[f1949]) ).
thf(f1949,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
!= X1 )
| ( $true
= ( subset @ X1 @ X0 ) ) )
| ( binintersectSubset3 != $true ) )
& ( ( binintersectSubset3 = $true )
| ( ( ( binintersect @ sK282 @ sK283 )
= sK283 )
& ( ( subset @ sK283 @ sK282 )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK282,sK283])],[f1947,f1948]) ).
thf(f1948,plain,
( ? [X2: $i,X3: $i] :
( ( ( binintersect @ X2 @ X3 )
= X3 )
& ( $true
!= ( subset @ X3 @ X2 ) ) )
=> ( ( ( binintersect @ sK282 @ sK283 )
= sK283 )
& ( ( subset @ sK283 @ sK282 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1947,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
!= X1 )
| ( $true
= ( subset @ X1 @ X0 ) ) )
| ( binintersectSubset3 != $true ) )
& ( ( binintersectSubset3 = $true )
| ? [X2: $i,X3: $i] :
( ( ( binintersect @ X2 @ X3 )
= X3 )
& ( $true
!= ( subset @ X3 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f1946]) ).
thf(f1946,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
!= X1 )
| ( $true
= ( subset @ X1 @ X0 ) ) )
| ( binintersectSubset3 != $true ) )
& ( ( binintersectSubset3 = $true )
| ? [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X1 )
& ( $true
!= ( subset @ X1 @ X0 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f1152]) ).
thf(f1152,plain,
( ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
!= X1 )
| ( $true
= ( subset @ X1 @ X0 ) ) )
<=> ( binintersectSubset3 = $true ) ),
inference(ennf_transformation,[status(thm)],[f918]) ).
thf(f918,plain,
( ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X1 )
=> ( $true
= ( subset @ X1 @ X0 ) ) )
<=> ( binintersectSubset3 = $true ) ),
inference(fool_elimination,[status(thm)],[f917]) ).
thf(f917,plain,
! [X0: $i,X1: $i] :
( ( ( ( binintersect @ X0 @ X1 )
= X1 )
=> ( subset @ X1 @ X0 ) )
= binintersectSubset3 ),
inference(rectify,[status(thm)],[f113]) ).
thf(f113,axiom,
! [X3: $i,X4: $i] :
( ( ( ( binintersect @ X3 @ X4 )
= X4 )
=> ( subset @ X4 @ X3 ) )
= binintersectSubset3 ),
file('/export/starexec/sandbox/tmp/tmp.zuy6gBFKOi/DTF2THF_17963.p',binintersectSubset3) ).
thf(f8878,plain,
! [X0: $i] :
( ( $true
!= ( subset @ X0 @ sK1041 ) )
| ( $true
!= ( in @ sK1043 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f8862]) ).
thf(f8862,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( in @ sK1043 @ X0 ) )
| ( $true
!= ( subset @ X0 @ sK1041 ) ) ),
inference(superposition,[status(thm)],[f5041,f6851]) ).
thf(f6851,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
!= ( subset @ X2 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f6264]) ).
thf(f6264,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
| ( $true != $true )
| ( $true
!= ( subset @ X2 @ X1 ) )
| ( $true
!= ( in @ X0 @ X2 ) ) ),
inference(definition_unfolding,[status(thm)],[f4559,f5202]) ).
thf(f5202,plain,
subsetE = $true,
inference(cnf_transformation,[status(thm)],[f3260]) ).
thf(f4559,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
!= ( subset @ X2 @ X1 ) )
| ( subsetE != $true ) ),
inference(cnf_transformation,[status(thm)],[f2817]) ).
thf(f2817,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
!= ( subset @ X2 @ X1 ) ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ( ( ( in @ sK772 @ sK773 )
!= $true )
& ( $true
= ( in @ sK772 @ sK774 ) )
& ( $true
= ( subset @ sK774 @ sK773 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK772,sK773,sK774])],[f2815,f2816]) ).
thf(f2816,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
!= $true )
& ( $true
= ( in @ X3 @ X5 ) )
& ( ( subset @ X5 @ X4 )
= $true ) )
=> ( ( ( in @ sK772 @ sK773 )
!= $true )
& ( $true
= ( in @ sK772 @ sK774 ) )
& ( $true
= ( subset @ sK774 @ sK773 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2815,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
!= ( subset @ X2 @ X1 ) ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
!= $true )
& ( $true
= ( in @ X3 @ X5 ) )
& ( ( subset @ X5 @ X4 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f2814]) ).
thf(f2814,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
!= ( subset @ X2 @ X1 ) ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
& ( $true
= ( in @ X0 @ X2 ) )
& ( $true
= ( subset @ X2 @ X1 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f1256]) ).
thf(f1256,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
!= ( subset @ X2 @ X1 ) ) )
<=> ( subsetE = $true ) ),
inference(flattening,[status(thm)],[f1255]) ).
thf(f1255,plain,
( ( subsetE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
!= ( subset @ X2 @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f938]) ).
thf(f938,plain,
( ( subsetE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( subset @ X2 @ X1 ) )
=> ( ( $true
= ( in @ X0 @ X2 ) )
=> ( $true
= ( in @ X0 @ X1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f937]) ).
thf(f937,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X1 )
=> ( ( in @ X0 @ X2 )
=> ( in @ X0 @ X1 ) ) )
= subsetE ),
inference(rectify,[status(thm)],[f83]) ).
thf(f83,axiom,
! [X1: $i,X4: $i,X3: $i] :
( ( ( subset @ X3 @ X4 )
=> ( ( in @ X1 @ X3 )
=> ( in @ X1 @ X4 ) ) )
= subsetE ),
file('/export/starexec/sandbox/tmp/tmp.zuy6gBFKOi/DTF2THF_17963.p',subsetE) ).
thf(f5041,plain,
( ( in @ sK1043 @ sK1041 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f3260]) ).
thf(f5042,plain,
( $true
= ( in @ sK1042 @ sK1041 ) ),
inference(cnf_transformation,[status(thm)],[f3260]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU814^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n002.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:35:03 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.26/0.47 ---- Original DTF file ---
% 0.26/0.47 thf(spec,logic,$$dhol).
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 % File : SEU814^1 : TPTP v9.2.1. Released v3.7.0.
% 0.26/0.47 % Domain : Set Theory
% 0.26/0.47 % Problem : Transitive Sets
% 0.26/0.47 % Version : Especial.
% 0.26/0.47 % English : (! X:i.transitiveset X -> (! A:i.! x:i.in A X -> in x A ->
% 0.26/0.47 % in x X))
% 0.26/0.47
% 0.26/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.26/0.47 % Source : [Bro08]
% 0.26/0.47 % Names : ZFC316g [Bro08]
% 0.26/0.47
% 0.26/0.47 % Status : Theorem
% 0.26/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0, 1.00 v3.7.0
% 0.26/0.47 % Syntax : Number of formulae : 723 ( 333 unt; 389 typ; 333 def)
% 0.26/0.47 % Number of atoms : 2048 ( 478 equ; 0 cnn)
% 0.26/0.47 % Maximal formula atoms : 334 ( 6 avg)
% 0.26/0.47 % Number of connectives : 4457 ( 77 ~; 14 |; 54 &;3239 @)
% 0.26/0.47 % ( 17 <=>;1056 =>; 0 <=; 0 <~>)
% 0.26/0.47 % Maximal formula depth : 339 ( 2 avg)
% 0.26/0.47 % Number of types : 2 ( 0 usr)
% 0.26/0.47 % Number of type conns : 190 ( 190 >; 0 *; 0 +; 0 <<)
% 0.26/0.47 % Number of symbols : 392 ( 389 usr; 334 con; 0-4 aty)
% 0.26/0.47 % Number of variables : 1160 ( 76 ^;1040 !; 44 ?;1160 :)
% 0.26/0.47 % SPC : TH0_THM_EQU_NAR
% 0.26/0.47
% 0.26/0.47 % Comments : http://mathgate.info/detsetitem.php?id=502
% 0.26/0.47 %------------------------------------------------------------------------------
% 0.26/0.47 thf(in_type,type,
% 0.26/0.47 in: $i > $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(exu_type,type,
% 0.26/0.47 exu: ( $i > $o ) > $o ).
% 0.26/0.47
% 0.26/0.47 thf(exu,definition,
% 0.26/0.47 ( exu
% 0.26/0.47 = ( ^ [Xphi: $i > $o] :
% 0.26/0.47 ? [Xx: $i] :
% 0.26/0.47 ( ( Xphi @ Xx )
% 0.26/0.47 & ! [Xy: $i] :
% 0.26/0.47 ( ( Xphi @ Xy )
% 0.26/0.47 => ( Xx = Xy ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setextAx_type,type,
% 0.26/0.47 setextAx: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setextAx,definition,
% 0.26/0.47 ( setextAx
% 0.26/0.47 = ( ! [A: $i,B: $i] :
% 0.26/0.47 ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 <=> ( in @ Xx @ B ) )
% 0.26/0.47 => ( A = B ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(emptyset_type,type,
% 0.26/0.47 emptyset: $i ).
% 0.26/0.47
% 0.26/0.47 thf(emptysetAx_type,type,
% 0.26/0.47 emptysetAx: $o ).
% 0.26/0.47
% 0.26/0.47 thf(emptysetAx,definition,
% 0.26/0.47 ( emptysetAx
% 0.26/0.47 = ( ! [Xx: $i] :
% 0.26/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setadjoin_type,type,
% 0.26/0.47 setadjoin: $i > $i > $i ).
% 0.26/0.47
% 0.26/0.47 thf(setadjoinAx_type,type,
% 0.26/0.47 setadjoinAx: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setadjoinAx,definition,
% 0.26/0.47 ( setadjoinAx
% 0.26/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.26/0.47 <=> ( ( Xy = Xx )
% 0.26/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(powerset_type,type,
% 0.26/0.47 powerset: $i > $i ).
% 0.26/0.47
% 0.26/0.47 thf(powersetAx_type,type,
% 0.26/0.47 powersetAx: $o ).
% 0.26/0.47
% 0.26/0.47 thf(powersetAx,definition,
% 0.26/0.47 ( powersetAx
% 0.26/0.47 = ( ! [A: $i,B: $i] :
% 0.26/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.26/0.47 <=> ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ B )
% 0.26/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setunion_type,type,
% 0.26/0.47 setunion: $i > $i ).
% 0.26/0.47
% 0.26/0.47 thf(setunionAx_type,type,
% 0.26/0.47 setunionAx: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setunionAx,definition,
% 0.26/0.47 ( setunionAx
% 0.26/0.47 = ( ! [A: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.26/0.47 <=> ? [B: $i] :
% 0.26/0.47 ( ( in @ Xx @ B )
% 0.26/0.47 & ( in @ B @ A ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(omega_type,type,
% 0.26/0.47 omega: $i ).
% 0.26/0.47
% 0.26/0.47 thf(omega0Ax_type,type,
% 0.26/0.47 omega0Ax: $o ).
% 0.26/0.47
% 0.26/0.47 thf(omega0Ax,definition,
% 0.26/0.47 ( omega0Ax
% 0.26/0.47 = ( in @ emptyset @ omega ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(omegaSAx_type,type,
% 0.26/0.47 omegaSAx: $o ).
% 0.26/0.47
% 0.26/0.47 thf(omegaSAx,definition,
% 0.26/0.47 ( omegaSAx
% 0.26/0.47 = ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ omega )
% 0.26/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(omegaIndAx_type,type,
% 0.26/0.47 omegaIndAx: $o ).
% 0.26/0.47
% 0.26/0.47 thf(omegaIndAx,definition,
% 0.26/0.47 ( omegaIndAx
% 0.26/0.47 = ( ! [A: $i] :
% 0.26/0.47 ( ( ( in @ emptyset @ A )
% 0.26/0.47 & ! [Xx: $i] :
% 0.26/0.47 ( ( ( in @ Xx @ omega )
% 0.26/0.47 & ( in @ Xx @ A ) )
% 0.26/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.26/0.47 => ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ omega )
% 0.26/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(replAx_type,type,
% 0.26/0.47 replAx: $o ).
% 0.26/0.47
% 0.26/0.47 thf(replAx,definition,
% 0.26/0.47 ( replAx
% 0.26/0.47 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.26/0.47 ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( exu
% 0.26/0.47 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.26/0.47 => ? [B: $i] :
% 0.26/0.47 ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ B )
% 0.26/0.47 <=> ? [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ A )
% 0.26/0.47 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(foundationAx_type,type,
% 0.26/0.47 foundationAx: $o ).
% 0.26/0.47
% 0.26/0.47 thf(foundationAx,definition,
% 0.26/0.47 ( foundationAx
% 0.26/0.47 = ( ! [A: $i] :
% 0.26/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.26/0.47 => ? [B: $i] :
% 0.26/0.47 ( ( in @ B @ A )
% 0.26/0.47 & ~ ? [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ B )
% 0.26/0.47 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(wellorderingAx_type,type,
% 0.26/0.47 wellorderingAx: $o ).
% 0.26/0.47
% 0.26/0.47 thf(wellorderingAx,definition,
% 0.26/0.47 ( wellorderingAx
% 0.26/0.47 = ( ! [A: $i] :
% 0.26/0.47 ? [B: $i] :
% 0.26/0.47 ( ! [C: $i] :
% 0.26/0.47 ( ( in @ C @ B )
% 0.26/0.47 => ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ C )
% 0.26/0.47 => ( in @ Xx @ A ) ) )
% 0.26/0.47 & ! [Xx: $i,Xy: $i] :
% 0.26/0.47 ( ( ( in @ Xx @ A )
% 0.26/0.47 & ( in @ Xy @ A ) )
% 0.26/0.47 => ( ! [C: $i] :
% 0.26/0.47 ( ( in @ C @ B )
% 0.26/0.47 => ( ( in @ Xx @ C )
% 0.26/0.47 <=> ( in @ Xy @ C ) ) )
% 0.26/0.47 => ( Xx = Xy ) ) )
% 0.26/0.47 & ! [C: $i,D: $i] :
% 0.26/0.47 ( ( ( in @ C @ B )
% 0.26/0.47 & ( in @ D @ B ) )
% 0.26/0.47 => ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ C )
% 0.26/0.47 => ( in @ Xx @ D ) )
% 0.26/0.47 | ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ D )
% 0.26/0.47 => ( in @ Xx @ C ) ) ) )
% 0.26/0.47 & ! [C: $i] :
% 0.26/0.47 ( ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ C )
% 0.26/0.47 => ( in @ Xx @ A ) )
% 0.26/0.47 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.26/0.47 => ? [D: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ D @ B )
% 0.26/0.47 & ( in @ Xx @ C )
% 0.26/0.47 & ~ ? [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ D )
% 0.26/0.47 & ( in @ Xy @ C ) )
% 0.26/0.47 & ! [E: $i] :
% 0.26/0.47 ( ( in @ E @ B )
% 0.26/0.47 => ( ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ E )
% 0.26/0.47 => ( in @ Xy @ D ) )
% 0.26/0.47 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(descr_type,type,
% 0.26/0.47 descr: ( $i > $o ) > $i ).
% 0.26/0.47
% 0.26/0.47 thf(descrp_type,type,
% 0.26/0.47 descrp: $o ).
% 0.26/0.47
% 0.26/0.47 thf(descrp,definition,
% 0.26/0.47 ( descrp
% 0.26/0.47 = ( ! [Xphi: $i > $o] :
% 0.26/0.47 ( ( exu
% 0.26/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.26/0.47 => ( Xphi
% 0.26/0.47 @ ( descr
% 0.26/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(dsetconstr_type,type,
% 0.26/0.47 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.26/0.47
% 0.26/0.47 thf(dsetconstrI_type,type,
% 0.26/0.47 dsetconstrI: $o ).
% 0.26/0.47
% 0.26/0.47 thf(dsetconstrI,definition,
% 0.26/0.47 ( dsetconstrI
% 0.26/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( ( Xphi @ Xx )
% 0.26/0.47 => ( in @ Xx
% 0.26/0.47 @ ( dsetconstr @ A
% 0.26/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(dsetconstrEL_type,type,
% 0.26/0.47 dsetconstrEL: $o ).
% 0.26/0.47
% 0.26/0.47 thf(dsetconstrEL,definition,
% 0.26/0.47 ( dsetconstrEL
% 0.26/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx
% 0.26/0.47 @ ( dsetconstr @ A
% 0.26/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.26/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(dsetconstrER_type,type,
% 0.26/0.47 dsetconstrER: $o ).
% 0.26/0.47
% 0.26/0.47 thf(dsetconstrER,definition,
% 0.26/0.47 ( dsetconstrER
% 0.26/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx
% 0.26/0.47 @ ( dsetconstr @ A
% 0.26/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.26/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(exuE1_type,type,
% 0.26/0.47 exuE1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(exuE1,definition,
% 0.26/0.47 ( exuE1
% 0.26/0.47 = ( ! [Xphi: $i > $o] :
% 0.26/0.47 ( ( exu
% 0.26/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.26/0.47 => ? [Xx: $i] :
% 0.26/0.47 ( ( Xphi @ Xx )
% 0.26/0.47 & ! [Xy: $i] :
% 0.26/0.47 ( ( Xphi @ Xy )
% 0.26/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(prop2set_type,type,
% 0.26/0.47 prop2set: $o > $i ).
% 0.26/0.47
% 0.26/0.47 thf(prop2setE_type,type,
% 0.26/0.47 prop2setE: $o ).
% 0.26/0.47
% 0.26/0.47 thf(prop2setE,definition,
% 0.26/0.47 ( prop2setE
% 0.26/0.47 = ( ! [Xphi: $o,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.26/0.47 => Xphi ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(emptysetE_type,type,
% 0.26/0.47 emptysetE: $o ).
% 0.26/0.47
% 0.26/0.47 thf(emptysetE,definition,
% 0.26/0.47 ( emptysetE
% 0.26/0.47 = ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ emptyset )
% 0.26/0.47 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(emptysetimpfalse_type,type,
% 0.26/0.47 emptysetimpfalse: $o ).
% 0.26/0.47
% 0.26/0.47 thf(emptysetimpfalse,definition,
% 0.26/0.47 ( emptysetimpfalse
% 0.26/0.47 = ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ emptyset )
% 0.26/0.47 => $false ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(notinemptyset_type,type,
% 0.26/0.47 notinemptyset: $o ).
% 0.26/0.47
% 0.26/0.47 thf(notinemptyset,definition,
% 0.26/0.47 ( notinemptyset
% 0.26/0.47 = ( ! [Xx: $i] :
% 0.26/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(exuE3e_type,type,
% 0.26/0.47 exuE3e: $o ).
% 0.26/0.47
% 0.26/0.47 thf(exuE3e,definition,
% 0.26/0.47 ( exuE3e
% 0.26/0.47 = ( ! [Xphi: $i > $o] :
% 0.26/0.47 ( ( exu
% 0.26/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.26/0.47 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setext_type,type,
% 0.26/0.47 setext: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setext,definition,
% 0.26/0.47 ( setext
% 0.26/0.47 = ( ! [A: $i,B: $i] :
% 0.26/0.47 ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( in @ Xx @ B ) )
% 0.26/0.47 => ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ B )
% 0.26/0.47 => ( in @ Xx @ A ) )
% 0.26/0.47 => ( A = B ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(emptyI_type,type,
% 0.26/0.47 emptyI: $o ).
% 0.26/0.47
% 0.26/0.47 thf(emptyI,definition,
% 0.26/0.47 ( emptyI
% 0.26/0.47 = ( ! [A: $i] :
% 0.26/0.47 ( ! [Xx: $i] :
% 0.26/0.47 ~ ( in @ Xx @ A )
% 0.26/0.47 => ( A = emptyset ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(noeltsimpempty_type,type,
% 0.26/0.47 noeltsimpempty: $o ).
% 0.26/0.47
% 0.26/0.47 thf(noeltsimpempty,definition,
% 0.26/0.47 ( noeltsimpempty
% 0.26/0.47 = ( ! [A: $i] :
% 0.26/0.47 ( ! [Xx: $i] :
% 0.26/0.47 ~ ( in @ Xx @ A )
% 0.26/0.47 => ( A = emptyset ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setbeta_type,type,
% 0.26/0.47 setbeta: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setbeta,definition,
% 0.26/0.47 ( setbeta
% 0.26/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( ( in @ Xx
% 0.26/0.47 @ ( dsetconstr @ A
% 0.26/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.26/0.47 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(nonempty_type,type,
% 0.26/0.47 nonempty: $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(nonempty,definition,
% 0.26/0.47 ( nonempty
% 0.26/0.47 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(nonemptyE1_type,type,
% 0.26/0.47 nonemptyE1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(nonemptyE1,definition,
% 0.26/0.47 ( nonemptyE1
% 0.26/0.47 = ( ! [A: $i] :
% 0.26/0.47 ( ( nonempty @ A )
% 0.26/0.47 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(nonemptyI_type,type,
% 0.26/0.47 nonemptyI: $o ).
% 0.26/0.47
% 0.26/0.47 thf(nonemptyI,definition,
% 0.26/0.47 ( nonemptyI
% 0.26/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( ( Xphi @ Xx )
% 0.26/0.47 => ( nonempty
% 0.26/0.47 @ ( dsetconstr @ A
% 0.26/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(nonemptyI1_type,type,
% 0.26/0.47 nonemptyI1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(nonemptyI1,definition,
% 0.26/0.47 ( nonemptyI1
% 0.26/0.47 = ( ! [A: $i] :
% 0.26/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.26/0.47 => ( nonempty @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setadjoinIL_type,type,
% 0.26/0.47 setadjoinIL: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setadjoinIL,definition,
% 0.26/0.47 ( setadjoinIL
% 0.26/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(emptyinunitempty_type,type,
% 0.26/0.47 emptyinunitempty: $o ).
% 0.26/0.47
% 0.26/0.47 thf(emptyinunitempty,definition,
% 0.26/0.47 ( emptyinunitempty
% 0.26/0.47 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setadjoinIR_type,type,
% 0.26/0.47 setadjoinIR: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setadjoinIR,definition,
% 0.26/0.47 ( setadjoinIR
% 0.26/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ A )
% 0.26/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setadjoinE_type,type,
% 0.26/0.47 setadjoinE: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setadjoinE,definition,
% 0.26/0.47 ( setadjoinE
% 0.26/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.26/0.47 => ! [Xphi: $o] :
% 0.26/0.47 ( ( ( Xy = Xx )
% 0.26/0.47 => Xphi )
% 0.26/0.47 => ( ( ( in @ Xy @ A )
% 0.26/0.47 => Xphi )
% 0.26/0.47 => Xphi ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setadjoinOr_type,type,
% 0.26/0.47 setadjoinOr: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setadjoinOr,definition,
% 0.26/0.47 ( setadjoinOr
% 0.26/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.26/0.47 => ( ( Xy = Xx )
% 0.26/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setoftrueEq_type,type,
% 0.26/0.47 setoftrueEq: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setoftrueEq,definition,
% 0.26/0.47 ( setoftrueEq
% 0.26/0.47 = ( ! [A: $i] :
% 0.26/0.47 ( ( dsetconstr @ A
% 0.26/0.47 @ ^ [Xx: $i] : $true )
% 0.26/0.47 = A ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(powersetI_type,type,
% 0.26/0.47 powersetI: $o ).
% 0.26/0.47
% 0.26/0.47 thf(powersetI,definition,
% 0.26/0.47 ( powersetI
% 0.26/0.47 = ( ! [A: $i,B: $i] :
% 0.26/0.47 ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ B )
% 0.26/0.47 => ( in @ Xx @ A ) )
% 0.26/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(emptyinPowerset_type,type,
% 0.26/0.47 emptyinPowerset: $o ).
% 0.26/0.47
% 0.26/0.47 thf(emptyinPowerset,definition,
% 0.26/0.47 ( emptyinPowerset
% 0.26/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(emptyInPowerset_type,type,
% 0.26/0.47 emptyInPowerset: $o ).
% 0.26/0.47
% 0.26/0.47 thf(emptyInPowerset,definition,
% 0.26/0.47 ( emptyInPowerset
% 0.26/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(powersetE_type,type,
% 0.26/0.47 powersetE: $o ).
% 0.26/0.47
% 0.26/0.47 thf(powersetE,definition,
% 0.26/0.47 ( powersetE
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.26/0.47 => ( ( in @ Xx @ B )
% 0.26/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setunionI_type,type,
% 0.26/0.47 setunionI: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setunionI,definition,
% 0.26/0.47 ( setunionI
% 0.26/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.26/0.47 ( ( in @ Xx @ B )
% 0.26/0.47 => ( ( in @ B @ A )
% 0.26/0.47 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setunionE_type,type,
% 0.26/0.47 setunionE: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setunionE,definition,
% 0.26/0.47 ( setunionE
% 0.26/0.47 = ( ! [A: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.26/0.47 => ! [Xphi: $o] :
% 0.26/0.47 ( ! [B: $i] :
% 0.26/0.47 ( ( in @ Xx @ B )
% 0.26/0.47 => ( ( in @ B @ A )
% 0.26/0.47 => Xphi ) )
% 0.26/0.47 => Xphi ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(subPowSU_type,type,
% 0.26/0.47 subPowSU: $o ).
% 0.26/0.47
% 0.26/0.47 thf(subPowSU,definition,
% 0.26/0.47 ( subPowSU
% 0.26/0.47 = ( ! [A: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(exuE2_type,type,
% 0.26/0.47 exuE2: $o ).
% 0.26/0.47
% 0.26/0.47 thf(exuE2,definition,
% 0.26/0.47 ( exuE2
% 0.26/0.47 = ( ! [Xphi: $i > $o] :
% 0.26/0.47 ( ( exu
% 0.26/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.26/0.47 => ? [Xx: $i] :
% 0.26/0.47 ! [Xy: $i] :
% 0.26/0.47 ( ( Xphi @ Xy )
% 0.26/0.47 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(nonemptyImpWitness_type,type,
% 0.26/0.47 nonemptyImpWitness: $o ).
% 0.26/0.47
% 0.26/0.47 thf(nonemptyImpWitness,definition,
% 0.26/0.47 ( nonemptyImpWitness
% 0.26/0.47 = ( ! [A: $i] :
% 0.26/0.47 ( ( nonempty @ A )
% 0.26/0.47 => ? [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 & $true ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(uniqinunit_type,type,
% 0.26/0.47 uniqinunit: $o ).
% 0.26/0.47
% 0.26/0.47 thf(uniqinunit,definition,
% 0.26/0.47 ( uniqinunit
% 0.26/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.26/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.26/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(notinsingleton_type,type,
% 0.26/0.47 notinsingleton: $o ).
% 0.26/0.47
% 0.26/0.47 thf(notinsingleton,definition,
% 0.26/0.47 ( notinsingleton
% 0.26/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.26/0.47 ( ( Xx != Xy )
% 0.26/0.47 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(eqinunit_type,type,
% 0.26/0.47 eqinunit: $o ).
% 0.26/0.47
% 0.26/0.47 thf(eqinunit,definition,
% 0.26/0.47 ( eqinunit
% 0.26/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.26/0.47 ( ( Xx = Xy )
% 0.26/0.47 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(singletonsswitch_type,type,
% 0.26/0.47 singletonsswitch: $o ).
% 0.26/0.47
% 0.26/0.47 thf(singletonsswitch,definition,
% 0.26/0.47 ( singletonsswitch
% 0.26/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.26/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.26/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(upairsetE_type,type,
% 0.26/0.47 upairsetE: $o ).
% 0.26/0.47
% 0.26/0.47 thf(upairsetE,definition,
% 0.26/0.47 ( upairsetE
% 0.26/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.26/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.26/0.47 => ( ( Xz = Xx )
% 0.26/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(upairsetIL_type,type,
% 0.26/0.47 upairsetIL: $o ).
% 0.26/0.47
% 0.26/0.47 thf(upairsetIL,definition,
% 0.26/0.47 ( upairsetIL
% 0.26/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(upairsetIR_type,type,
% 0.26/0.47 upairsetIR: $o ).
% 0.26/0.47
% 0.26/0.47 thf(upairsetIR,definition,
% 0.26/0.47 ( upairsetIR
% 0.26/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(emptyE1_type,type,
% 0.26/0.47 emptyE1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(emptyE1,definition,
% 0.26/0.47 ( emptyE1
% 0.26/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.26/0.47 ( ? [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 & ( Xphi @ Xx ) )
% 0.26/0.47 => ( ( ( dsetconstr @ A
% 0.26/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.26/0.47 = emptyset )
% 0.26/0.47 => $false ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(vacuousDall_type,type,
% 0.26/0.47 vacuousDall: $o ).
% 0.26/0.47
% 0.26/0.47 thf(vacuousDall,definition,
% 0.26/0.47 ( vacuousDall
% 0.26/0.47 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ emptyset )
% 0.26/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(quantDeMorgan1_type,type,
% 0.26/0.47 quantDeMorgan1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(quantDeMorgan1,definition,
% 0.26/0.47 ( quantDeMorgan1
% 0.26/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.26/0.47 ( ~ ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( Xphi @ Xx ) )
% 0.26/0.47 => ? [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(quantDeMorgan2_type,type,
% 0.26/0.47 quantDeMorgan2: $o ).
% 0.26/0.47
% 0.26/0.47 thf(quantDeMorgan2,definition,
% 0.26/0.47 ( quantDeMorgan2
% 0.26/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.26/0.47 ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ~ ( Xphi @ Xx ) )
% 0.26/0.47 => ~ ? [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(quantDeMorgan3_type,type,
% 0.26/0.47 quantDeMorgan3: $o ).
% 0.26/0.47
% 0.26/0.47 thf(quantDeMorgan3,definition,
% 0.26/0.47 ( quantDeMorgan3
% 0.26/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.26/0.47 ( ~ ? [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 & ( Xphi @ Xx ) )
% 0.26/0.47 => ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(quantDeMorgan4_type,type,
% 0.26/0.47 quantDeMorgan4: $o ).
% 0.26/0.47
% 0.26/0.47 thf(quantDeMorgan4,definition,
% 0.26/0.47 ( quantDeMorgan4
% 0.26/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.26/0.47 ( ? [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 & ~ ( Xphi @ Xx ) )
% 0.26/0.47 => ~ ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(prop2setI_type,type,
% 0.26/0.47 prop2setI: $o ).
% 0.26/0.47
% 0.26/0.47 thf(prop2setI,definition,
% 0.26/0.47 ( prop2setI
% 0.26/0.47 = ( ! [Xphi: $o] :
% 0.26/0.47 ( Xphi
% 0.26/0.47 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(set2prop_type,type,
% 0.26/0.47 set2prop: $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(prop2set2propI_type,type,
% 0.26/0.47 prop2set2propI: $o ).
% 0.26/0.47
% 0.26/0.47 thf(prop2set2propI,definition,
% 0.26/0.47 ( prop2set2propI
% 0.26/0.47 = ( ! [Xphi: $o] :
% 0.26/0.47 ( Xphi
% 0.26/0.47 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(notdexE_type,type,
% 0.26/0.47 notdexE: $o ).
% 0.26/0.47
% 0.26/0.47 thf(notdexE,definition,
% 0.26/0.47 ( notdexE
% 0.26/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.26/0.47 ( ~ ? [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 & ( Xphi @ Xx ) )
% 0.26/0.47 => ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(notdallE_type,type,
% 0.26/0.47 notdallE: $o ).
% 0.26/0.47
% 0.26/0.47 thf(notdallE,definition,
% 0.26/0.47 ( notdallE
% 0.26/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.26/0.47 ( ~ ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( Xphi @ Xx ) )
% 0.26/0.47 => ? [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(exuI1_type,type,
% 0.26/0.47 exuI1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(exuI1,definition,
% 0.26/0.47 ( exuI1
% 0.26/0.47 = ( ! [Xphi: $i > $o] :
% 0.26/0.47 ( ? [Xx: $i] :
% 0.26/0.47 ( ( Xphi @ Xx )
% 0.26/0.47 & ! [Xy: $i] :
% 0.26/0.47 ( ( Xphi @ Xy )
% 0.26/0.47 => ( Xx = Xy ) ) )
% 0.26/0.47 => ( exu
% 0.26/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(exuI3_type,type,
% 0.26/0.47 exuI3: $o ).
% 0.26/0.47
% 0.26/0.47 thf(exuI3,definition,
% 0.26/0.47 ( exuI3
% 0.26/0.47 = ( ! [Xphi: $i > $o] :
% 0.26/0.47 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.26/0.47 => ( ! [Xx: $i,Xy: $i] :
% 0.26/0.47 ( ( Xphi @ Xx )
% 0.26/0.47 => ( ( Xphi @ Xy )
% 0.26/0.47 => ( Xx = Xy ) ) )
% 0.26/0.47 => ( exu
% 0.26/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(exuI2_type,type,
% 0.26/0.47 exuI2: $o ).
% 0.26/0.47
% 0.26/0.47 thf(exuI2,definition,
% 0.26/0.47 ( exuI2
% 0.26/0.47 = ( ! [Xphi: $i > $o] :
% 0.26/0.47 ( ? [Xx: $i] :
% 0.26/0.47 ! [Xy: $i] :
% 0.26/0.47 ( ( Xphi @ Xy )
% 0.26/0.47 <=> ( Xy = Xx ) )
% 0.26/0.47 => ( exu
% 0.26/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(inCongP_type,type,
% 0.26/0.47 inCongP: $o ).
% 0.26/0.47
% 0.26/0.47 thf(inCongP,definition,
% 0.26/0.47 ( inCongP
% 0.26/0.47 = ( ! [A: $i,B: $i] :
% 0.26/0.47 ( ( A = B )
% 0.26/0.47 => ! [Xx: $i,Xy: $i] :
% 0.26/0.47 ( ( Xx = Xy )
% 0.26/0.47 => ( ( in @ Xx @ A )
% 0.26/0.47 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(in__Cong_type,type,
% 0.26/0.47 in__Cong: $o ).
% 0.26/0.47
% 0.26/0.47 thf(in__Cong,definition,
% 0.26/0.47 ( in__Cong
% 0.26/0.47 = ( ! [A: $i,B: $i] :
% 0.26/0.47 ( ( A = B )
% 0.26/0.47 => ! [Xx: $i,Xy: $i] :
% 0.26/0.47 ( ( Xx = Xy )
% 0.26/0.47 => ( ( in @ Xx @ A )
% 0.26/0.47 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(exuE3u_type,type,
% 0.26/0.47 exuE3u: $o ).
% 0.26/0.47
% 0.26/0.47 thf(exuE3u,definition,
% 0.26/0.47 ( exuE3u
% 0.26/0.47 = ( ! [Xphi: $i > $o] :
% 0.26/0.47 ( ( exu
% 0.26/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.26/0.47 => ! [Xx: $i,Xy: $i] :
% 0.26/0.47 ( ( Xphi @ Xx )
% 0.26/0.47 => ( ( Xphi @ Xy )
% 0.26/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(exu__Cong_type,type,
% 0.26/0.47 exu__Cong: $o ).
% 0.26/0.47
% 0.26/0.47 thf(exu__Cong,definition,
% 0.26/0.47 ( exu__Cong
% 0.26/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.26/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.26/0.47 ( ( Xx = Xy )
% 0.26/0.47 => ( ( Xphi @ Xx )
% 0.26/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.26/0.47 => ( ( exu
% 0.26/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.26/0.47 <=> ( exu
% 0.26/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(emptyset__Cong_type,type,
% 0.26/0.47 emptyset__Cong: $o ).
% 0.26/0.47
% 0.26/0.47 thf(emptyset__Cong,definition,
% 0.26/0.47 ( emptyset__Cong
% 0.26/0.47 = ( emptyset = emptyset ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setadjoin__Cong_type,type,
% 0.26/0.47 setadjoin__Cong: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setadjoin__Cong,definition,
% 0.26/0.47 ( setadjoin__Cong
% 0.26/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.26/0.47 ( ( Xx = Xy )
% 0.26/0.47 => ! [Xz: $i,Xu: $i] :
% 0.26/0.47 ( ( Xz = Xu )
% 0.26/0.47 => ( ( setadjoin @ Xx @ Xz )
% 0.26/0.47 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(powerset__Cong_type,type,
% 0.26/0.47 powerset__Cong: $o ).
% 0.26/0.47
% 0.26/0.47 thf(powerset__Cong,definition,
% 0.26/0.47 ( powerset__Cong
% 0.26/0.47 = ( ! [A: $i,B: $i] :
% 0.26/0.47 ( ( A = B )
% 0.26/0.47 => ( ( powerset @ A )
% 0.26/0.47 = ( powerset @ B ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setunion__Cong_type,type,
% 0.26/0.47 setunion__Cong: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setunion__Cong,definition,
% 0.26/0.47 ( setunion__Cong
% 0.26/0.47 = ( ! [A: $i,B: $i] :
% 0.26/0.47 ( ( A = B )
% 0.26/0.47 => ( ( setunion @ A )
% 0.26/0.47 = ( setunion @ B ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(omega__Cong_type,type,
% 0.26/0.47 omega__Cong: $o ).
% 0.26/0.47
% 0.26/0.47 thf(omega__Cong,definition,
% 0.26/0.47 ( omega__Cong
% 0.26/0.47 = ( omega = omega ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(exuEu_type,type,
% 0.26/0.47 exuEu: $o ).
% 0.26/0.47
% 0.26/0.47 thf(exuEu,definition,
% 0.26/0.47 ( exuEu
% 0.26/0.47 = ( ! [Xphi: $i > $o] :
% 0.26/0.47 ( ( exu
% 0.26/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.26/0.47 => ! [Xx: $i,Xy: $i] :
% 0.26/0.47 ( ( Xphi @ Xx )
% 0.26/0.47 => ( ( Xphi @ Xy )
% 0.26/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(descr__Cong_type,type,
% 0.26/0.47 descr__Cong: $o ).
% 0.26/0.47
% 0.26/0.47 thf(descr__Cong,definition,
% 0.26/0.47 ( descr__Cong
% 0.26/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.26/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.26/0.47 ( ( Xx = Xy )
% 0.26/0.47 => ( ( Xphi @ Xx )
% 0.26/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.26/0.47 => ( ( exu
% 0.26/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.26/0.47 => ( ( exu
% 0.26/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.26/0.47 => ( ( descr
% 0.26/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.26/0.47 = ( descr
% 0.26/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(dsetconstr__Cong_type,type,
% 0.26/0.47 dsetconstr__Cong: $o ).
% 0.26/0.47
% 0.26/0.47 thf(dsetconstr__Cong,definition,
% 0.26/0.47 ( dsetconstr__Cong
% 0.26/0.47 = ( ! [A: $i,B: $i] :
% 0.26/0.47 ( ( A = B )
% 0.26/0.47 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.26/0.47 ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ B )
% 0.26/0.47 => ( ( Xx = Xy )
% 0.26/0.47 => ( ( Xphi @ Xx )
% 0.26/0.47 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.26/0.47 => ( ( dsetconstr @ A
% 0.26/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.26/0.47 = ( dsetconstr @ B
% 0.26/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(subset_type,type,
% 0.26/0.47 subset: $i > $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(disjoint_type,type,
% 0.26/0.47 disjoint: $i > $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(setsmeet_type,type,
% 0.26/0.47 setsmeet: $i > $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(subsetI1_type,type,
% 0.26/0.47 subsetI1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(subsetI1,definition,
% 0.26/0.47 ( subsetI1
% 0.26/0.47 = ( ! [A: $i,B: $i] :
% 0.26/0.47 ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( in @ Xx @ B ) )
% 0.26/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(eqimpsubset2_type,type,
% 0.26/0.47 eqimpsubset2: $o ).
% 0.26/0.47
% 0.26/0.47 thf(eqimpsubset2,definition,
% 0.26/0.47 ( eqimpsubset2
% 0.26/0.47 = ( ! [A: $i,B: $i] :
% 0.26/0.47 ( ( A = B )
% 0.26/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(eqimpsubset1_type,type,
% 0.26/0.47 eqimpsubset1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(eqimpsubset1,definition,
% 0.26/0.47 ( eqimpsubset1
% 0.26/0.47 = ( ! [A: $i,B: $i] :
% 0.26/0.47 ( ( A = B )
% 0.26/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(subsetI2_type,type,
% 0.26/0.47 subsetI2: $o ).
% 0.26/0.47
% 0.26/0.47 thf(subsetI2,definition,
% 0.26/0.47 ( subsetI2
% 0.26/0.47 = ( ! [A: $i,B: $i] :
% 0.26/0.47 ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( in @ Xx @ B ) )
% 0.26/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(emptysetsubset_type,type,
% 0.26/0.47 emptysetsubset: $o ).
% 0.26/0.47
% 0.26/0.47 thf(emptysetsubset,definition,
% 0.26/0.47 ( emptysetsubset
% 0.26/0.47 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(subsetE_type,type,
% 0.26/0.47 subsetE: $o ).
% 0.26/0.47
% 0.26/0.47 thf(subsetE,definition,
% 0.26/0.47 ( subsetE
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( subset @ A @ B )
% 0.26/0.47 => ( ( in @ Xx @ A )
% 0.26/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(subsetE2_type,type,
% 0.26/0.47 subsetE2: $o ).
% 0.26/0.47
% 0.26/0.47 thf(subsetE2,definition,
% 0.26/0.47 ( subsetE2
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( subset @ A @ B )
% 0.26/0.47 => ( ~ ( in @ Xx @ B )
% 0.26/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(notsubsetI_type,type,
% 0.26/0.47 notsubsetI: $o ).
% 0.26/0.47
% 0.26/0.47 thf(notsubsetI,definition,
% 0.26/0.47 ( notsubsetI
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( ~ ( in @ Xx @ B )
% 0.26/0.47 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(notequalI1_type,type,
% 0.26/0.47 notequalI1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(notequalI1,definition,
% 0.26/0.47 ( notequalI1
% 0.26/0.47 = ( ! [A: $i,B: $i] :
% 0.26/0.47 ( ~ ( subset @ A @ B )
% 0.26/0.47 => ( A != B ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(notequalI2_type,type,
% 0.26/0.47 notequalI2: $o ).
% 0.26/0.47
% 0.26/0.47 thf(notequalI2,definition,
% 0.26/0.47 ( notequalI2
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( ~ ( in @ Xx @ B )
% 0.26/0.47 => ( A != B ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(subsetRefl_type,type,
% 0.26/0.47 subsetRefl: $o ).
% 0.26/0.47
% 0.26/0.47 thf(subsetRefl,definition,
% 0.26/0.47 ( subsetRefl
% 0.26/0.47 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(subsetTrans_type,type,
% 0.26/0.47 subsetTrans: $o ).
% 0.26/0.47
% 0.26/0.47 thf(subsetTrans,definition,
% 0.26/0.47 ( subsetTrans
% 0.26/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.26/0.47 ( ( subset @ A @ B )
% 0.26/0.47 => ( ( subset @ B @ C )
% 0.26/0.47 => ( subset @ A @ C ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setadjoinSub_type,type,
% 0.26/0.47 setadjoinSub: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setadjoinSub,definition,
% 0.26/0.47 ( setadjoinSub
% 0.26/0.47 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setadjoinSub2_type,type,
% 0.26/0.47 setadjoinSub2: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setadjoinSub2,definition,
% 0.26/0.47 ( setadjoinSub2
% 0.26/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.26/0.47 ( ( subset @ A @ B )
% 0.26/0.47 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(subset2powerset_type,type,
% 0.26/0.47 subset2powerset: $o ).
% 0.26/0.47
% 0.26/0.47 thf(subset2powerset,definition,
% 0.26/0.47 ( subset2powerset
% 0.26/0.47 = ( ! [A: $i,B: $i] :
% 0.26/0.47 ( ( subset @ A @ B )
% 0.26/0.47 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setextsub_type,type,
% 0.26/0.47 setextsub: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setextsub,definition,
% 0.26/0.47 ( setextsub
% 0.26/0.47 = ( ! [A: $i,B: $i] :
% 0.26/0.47 ( ( subset @ A @ B )
% 0.26/0.47 => ( ( subset @ B @ A )
% 0.26/0.47 => ( A = B ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(subsetemptysetimpeq_type,type,
% 0.26/0.47 subsetemptysetimpeq: $o ).
% 0.26/0.47
% 0.26/0.47 thf(subsetemptysetimpeq,definition,
% 0.26/0.47 ( subsetemptysetimpeq
% 0.26/0.47 = ( ! [A: $i] :
% 0.26/0.47 ( ( subset @ A @ emptyset )
% 0.26/0.47 => ( A = emptyset ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(powersetI1_type,type,
% 0.26/0.47 powersetI1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(powersetI1,definition,
% 0.26/0.47 ( powersetI1
% 0.26/0.47 = ( ! [A: $i,B: $i] :
% 0.26/0.47 ( ( subset @ B @ A )
% 0.26/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(powersetE1_type,type,
% 0.26/0.47 powersetE1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(powersetE1,definition,
% 0.26/0.47 ( powersetE1
% 0.26/0.47 = ( ! [A: $i,B: $i] :
% 0.26/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.26/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(inPowerset_type,type,
% 0.26/0.47 inPowerset: $o ).
% 0.26/0.47
% 0.26/0.47 thf(inPowerset,definition,
% 0.26/0.47 ( inPowerset
% 0.26/0.47 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(powersetsubset_type,type,
% 0.26/0.47 powersetsubset: $o ).
% 0.26/0.47
% 0.26/0.47 thf(powersetsubset,definition,
% 0.26/0.47 ( powersetsubset
% 0.26/0.47 = ( ! [A: $i,B: $i] :
% 0.26/0.47 ( ( subset @ A @ B )
% 0.26/0.47 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(sepInPowerset_type,type,
% 0.26/0.47 sepInPowerset: $o ).
% 0.26/0.47
% 0.26/0.47 thf(sepInPowerset,definition,
% 0.26/0.47 ( sepInPowerset
% 0.26/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.26/0.47 ( in
% 0.26/0.47 @ ( dsetconstr @ A
% 0.26/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.26/0.47 @ ( powerset @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(sepSubset_type,type,
% 0.26/0.47 sepSubset: $o ).
% 0.26/0.47
% 0.26/0.47 thf(sepSubset,definition,
% 0.26/0.47 ( sepSubset
% 0.26/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.26/0.47 ( subset
% 0.26/0.47 @ ( dsetconstr @ A
% 0.26/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.26/0.47 @ A ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(binunion_type,type,
% 0.26/0.47 binunion: $i > $i > $i ).
% 0.26/0.47
% 0.26/0.47 thf(binunionIL_type,type,
% 0.26/0.47 binunionIL: $o ).
% 0.26/0.47
% 0.26/0.47 thf(binunionIL,definition,
% 0.26/0.47 ( binunionIL
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(upairset2IR_type,type,
% 0.26/0.47 upairset2IR: $o ).
% 0.26/0.47
% 0.26/0.47 thf(upairset2IR,definition,
% 0.26/0.47 ( upairset2IR
% 0.26/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(binunionIR_type,type,
% 0.26/0.47 binunionIR: $o ).
% 0.26/0.47
% 0.26/0.47 thf(binunionIR,definition,
% 0.26/0.47 ( binunionIR
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ B )
% 0.26/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(binunionEcases_type,type,
% 0.26/0.47 binunionEcases: $o ).
% 0.26/0.47
% 0.26/0.47 thf(binunionEcases,definition,
% 0.26/0.47 ( binunionEcases
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.26/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.26/0.47 => ( ( ( in @ Xx @ A )
% 0.26/0.47 => Xphi )
% 0.26/0.47 => ( ( ( in @ Xx @ B )
% 0.26/0.47 => Xphi )
% 0.26/0.47 => Xphi ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(binunionE_type,type,
% 0.26/0.47 binunionE: $o ).
% 0.26/0.47
% 0.26/0.47 thf(binunionE,definition,
% 0.26/0.47 ( binunionE
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.26/0.47 => ( ( in @ Xx @ A )
% 0.26/0.47 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(binunionLsub_type,type,
% 0.26/0.47 binunionLsub: $o ).
% 0.26/0.47
% 0.26/0.47 thf(binunionLsub,definition,
% 0.26/0.47 ( binunionLsub
% 0.26/0.47 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(binunionRsub_type,type,
% 0.26/0.47 binunionRsub: $o ).
% 0.26/0.47
% 0.26/0.47 thf(binunionRsub,definition,
% 0.26/0.47 ( binunionRsub
% 0.26/0.47 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(binintersect_type,type,
% 0.26/0.47 binintersect: $i > $i > $i ).
% 0.26/0.47
% 0.26/0.47 thf(binintersectI_type,type,
% 0.26/0.47 binintersectI: $o ).
% 0.26/0.47
% 0.26/0.47 thf(binintersectI,definition,
% 0.26/0.47 ( binintersectI
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( ( in @ Xx @ B )
% 0.26/0.47 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(binintersectSubset5_type,type,
% 0.26/0.47 binintersectSubset5: $o ).
% 0.26/0.47
% 0.26/0.47 thf(binintersectSubset5,definition,
% 0.26/0.47 ( binintersectSubset5
% 0.26/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.26/0.47 ( ( subset @ C @ A )
% 0.26/0.47 => ( ( subset @ C @ B )
% 0.26/0.47 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(binintersectEL_type,type,
% 0.26/0.47 binintersectEL: $o ).
% 0.26/0.47
% 0.26/0.47 thf(binintersectEL,definition,
% 0.26/0.47 ( binintersectEL
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.26/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(binintersectLsub_type,type,
% 0.26/0.47 binintersectLsub: $o ).
% 0.26/0.47
% 0.26/0.47 thf(binintersectLsub,definition,
% 0.26/0.47 ( binintersectLsub
% 0.26/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(binintersectSubset2_type,type,
% 0.26/0.47 binintersectSubset2: $o ).
% 0.26/0.47
% 0.26/0.47 thf(binintersectSubset2,definition,
% 0.26/0.47 ( binintersectSubset2
% 0.26/0.47 = ( ! [A: $i,B: $i] :
% 0.26/0.47 ( ( subset @ A @ B )
% 0.26/0.47 => ( ( binintersect @ A @ B )
% 0.26/0.47 = A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(binintersectSubset3_type,type,
% 0.26/0.47 binintersectSubset3: $o ).
% 0.26/0.47
% 0.26/0.47 thf(binintersectSubset3,definition,
% 0.26/0.47 ( binintersectSubset3
% 0.26/0.47 = ( ! [A: $i,B: $i] :
% 0.26/0.47 ( ( ( binintersect @ A @ B )
% 0.26/0.47 = B )
% 0.26/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(binintersectER_type,type,
% 0.26/0.47 binintersectER: $o ).
% 0.26/0.47
% 0.26/0.47 thf(binintersectER,definition,
% 0.26/0.47 ( binintersectER
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.26/0.47 => ( in @ Xx @ B ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(disjointsetsI1_type,type,
% 0.26/0.47 disjointsetsI1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(disjointsetsI1,definition,
% 0.26/0.47 ( disjointsetsI1
% 0.26/0.47 = ( ! [A: $i,B: $i] :
% 0.26/0.47 ( ~ ? [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 & ( in @ Xx @ B ) )
% 0.26/0.47 => ( ( binintersect @ A @ B )
% 0.26/0.47 = emptyset ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(binintersectRsub_type,type,
% 0.26/0.47 binintersectRsub: $o ).
% 0.26/0.47
% 0.26/0.47 thf(binintersectRsub,definition,
% 0.26/0.47 ( binintersectRsub
% 0.26/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(binintersectSubset4_type,type,
% 0.26/0.47 binintersectSubset4: $o ).
% 0.26/0.47
% 0.26/0.47 thf(binintersectSubset4,definition,
% 0.26/0.47 ( binintersectSubset4
% 0.26/0.47 = ( ! [A: $i,B: $i] :
% 0.26/0.47 ( ( subset @ B @ A )
% 0.26/0.47 => ( ( binintersect @ A @ B )
% 0.26/0.47 = B ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(binintersectSubset1_type,type,
% 0.26/0.47 binintersectSubset1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(binintersectSubset1,definition,
% 0.26/0.47 ( binintersectSubset1
% 0.26/0.47 = ( ! [A: $i,B: $i] :
% 0.26/0.47 ( ( ( binintersect @ A @ B )
% 0.26/0.47 = A )
% 0.26/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(bs114d_type,type,
% 0.26/0.47 bs114d: $o ).
% 0.26/0.47
% 0.26/0.47 thf(bs114d,definition,
% 0.26/0.47 ( bs114d
% 0.26/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.26/0.47 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.26/0.47 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(regular_type,type,
% 0.26/0.47 regular: $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(setminus_type,type,
% 0.26/0.47 setminus: $i > $i > $i ).
% 0.26/0.47
% 0.26/0.47 thf(setminusI_type,type,
% 0.26/0.47 setminusI: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setminusI,definition,
% 0.26/0.47 ( setminusI
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( ~ ( in @ Xx @ B )
% 0.26/0.47 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setminusEL_type,type,
% 0.26/0.47 setminusEL: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setminusEL,definition,
% 0.26/0.47 ( setminusEL
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.26/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setminusER_type,type,
% 0.26/0.47 setminusER: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setminusER,definition,
% 0.26/0.47 ( setminusER
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.26/0.47 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setminusSubset2_type,type,
% 0.26/0.47 setminusSubset2: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setminusSubset2,definition,
% 0.26/0.47 ( setminusSubset2
% 0.26/0.47 = ( ! [A: $i,B: $i] :
% 0.26/0.47 ( ( subset @ A @ B )
% 0.26/0.47 => ( ( setminus @ A @ B )
% 0.26/0.47 = emptyset ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setminusERneg_type,type,
% 0.26/0.47 setminusERneg: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setminusERneg,definition,
% 0.26/0.47 ( setminusERneg
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.26/0.47 => ( ( in @ Xx @ A )
% 0.26/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setminusELneg_type,type,
% 0.26/0.47 setminusELneg: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setminusELneg,definition,
% 0.26/0.47 ( setminusELneg
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.26/0.47 => ( ~ ( in @ Xx @ B )
% 0.26/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setminusILneg_type,type,
% 0.26/0.47 setminusILneg: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setminusILneg,definition,
% 0.26/0.47 ( setminusILneg
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ~ ( in @ Xx @ A )
% 0.26/0.47 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setminusIRneg_type,type,
% 0.26/0.47 setminusIRneg: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setminusIRneg,definition,
% 0.26/0.47 ( setminusIRneg
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ B )
% 0.26/0.47 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setminusLsub_type,type,
% 0.26/0.47 setminusLsub: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setminusLsub,definition,
% 0.26/0.47 ( setminusLsub
% 0.26/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setminusSubset1_type,type,
% 0.26/0.47 setminusSubset1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setminusSubset1,definition,
% 0.26/0.47 ( setminusSubset1
% 0.26/0.47 = ( ! [A: $i,B: $i] :
% 0.26/0.47 ( ( ( setminus @ A @ B )
% 0.26/0.47 = emptyset )
% 0.26/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(symdiff_type,type,
% 0.26/0.47 symdiff: $i > $i > $i ).
% 0.26/0.47
% 0.26/0.47 thf(symdiffE_type,type,
% 0.26/0.47 symdiffE: $o ).
% 0.26/0.47
% 0.26/0.47 thf(symdiffE,definition,
% 0.26/0.47 ( symdiffE
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.26/0.47 => ! [Xphi: $o] :
% 0.26/0.47 ( ( ( in @ Xx @ A )
% 0.26/0.47 => ( ~ ( in @ Xx @ B )
% 0.26/0.47 => Xphi ) )
% 0.26/0.47 => ( ( ~ ( in @ Xx @ A )
% 0.26/0.47 => ( ( in @ Xx @ B )
% 0.26/0.47 => Xphi ) )
% 0.26/0.47 => Xphi ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(symdiffI1_type,type,
% 0.26/0.47 symdiffI1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(symdiffI1,definition,
% 0.26/0.47 ( symdiffI1
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( ~ ( in @ Xx @ B )
% 0.26/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(symdiffI2_type,type,
% 0.26/0.47 symdiffI2: $o ).
% 0.26/0.47
% 0.26/0.47 thf(symdiffI2,definition,
% 0.26/0.47 ( symdiffI2
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ~ ( in @ Xx @ A )
% 0.26/0.47 => ( ( in @ Xx @ B )
% 0.26/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(symdiffIneg1_type,type,
% 0.26/0.47 symdiffIneg1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(symdiffIneg1,definition,
% 0.26/0.47 ( symdiffIneg1
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( ( in @ Xx @ B )
% 0.26/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(symdiffIneg2_type,type,
% 0.26/0.47 symdiffIneg2: $o ).
% 0.26/0.47
% 0.26/0.47 thf(symdiffIneg2,definition,
% 0.26/0.47 ( symdiffIneg2
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ~ ( in @ Xx @ A )
% 0.26/0.47 => ( ~ ( in @ Xx @ B )
% 0.26/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(iskpair_type,type,
% 0.26/0.47 iskpair: $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(secondinupair_type,type,
% 0.26/0.47 secondinupair: $o ).
% 0.26/0.47
% 0.26/0.47 thf(secondinupair,definition,
% 0.26/0.47 ( secondinupair
% 0.26/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setukpairIL_type,type,
% 0.26/0.47 setukpairIL: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setukpairIL,definition,
% 0.26/0.47 ( setukpairIL
% 0.26/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setukpairIR_type,type,
% 0.26/0.47 setukpairIR: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setukpairIR,definition,
% 0.26/0.47 ( setukpairIR
% 0.26/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(kpairiskpair_type,type,
% 0.26/0.47 kpairiskpair: $o ).
% 0.26/0.47
% 0.26/0.47 thf(kpairiskpair,definition,
% 0.26/0.47 ( kpairiskpair
% 0.26/0.47 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(kpair_type,type,
% 0.26/0.47 kpair: $i > $i > $i ).
% 0.26/0.47
% 0.26/0.47 thf(kpairp_type,type,
% 0.26/0.47 kpairp: $o ).
% 0.26/0.47
% 0.26/0.47 thf(kpairp,definition,
% 0.26/0.47 ( kpairp
% 0.26/0.47 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(cartprod_type,type,
% 0.26/0.47 cartprod: $i > $i > $i ).
% 0.26/0.47
% 0.26/0.47 thf(singletonsubset_type,type,
% 0.26/0.47 singletonsubset: $o ).
% 0.26/0.47
% 0.26/0.47 thf(singletonsubset,definition,
% 0.26/0.47 ( singletonsubset
% 0.26/0.47 = ( ! [A: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(singletoninpowerset_type,type,
% 0.26/0.47 singletoninpowerset: $o ).
% 0.26/0.47
% 0.26/0.47 thf(singletoninpowerset,definition,
% 0.26/0.47 ( singletoninpowerset
% 0.26/0.47 = ( ! [A: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(singletoninpowunion_type,type,
% 0.26/0.47 singletoninpowunion: $o ).
% 0.26/0.47
% 0.26/0.47 thf(singletoninpowunion,definition,
% 0.26/0.47 ( singletoninpowunion
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(upairset2E_type,type,
% 0.26/0.47 upairset2E: $o ).
% 0.26/0.47
% 0.26/0.47 thf(upairset2E,definition,
% 0.26/0.47 ( upairset2E
% 0.26/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.26/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.26/0.47 => ( ( Xz = Xx )
% 0.26/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(upairsubunion_type,type,
% 0.26/0.47 upairsubunion: $o ).
% 0.26/0.47
% 0.26/0.47 thf(upairsubunion,definition,
% 0.26/0.47 ( upairsubunion
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ B )
% 0.26/0.47 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(upairinpowunion_type,type,
% 0.26/0.47 upairinpowunion: $o ).
% 0.26/0.47
% 0.26/0.47 thf(upairinpowunion,definition,
% 0.26/0.47 ( upairinpowunion
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ B )
% 0.26/0.47 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(ubforcartprodlem1_type,type,
% 0.26/0.47 ubforcartprodlem1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(ubforcartprodlem1,definition,
% 0.26/0.47 ( ubforcartprodlem1
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ B )
% 0.26/0.47 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(ubforcartprodlem2_type,type,
% 0.26/0.47 ubforcartprodlem2: $o ).
% 0.26/0.47
% 0.26/0.47 thf(ubforcartprodlem2,definition,
% 0.26/0.47 ( ubforcartprodlem2
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ B )
% 0.26/0.47 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(ubforcartprodlem3_type,type,
% 0.26/0.47 ubforcartprodlem3: $o ).
% 0.26/0.47
% 0.26/0.47 thf(ubforcartprodlem3,definition,
% 0.26/0.47 ( ubforcartprodlem3
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ B )
% 0.26/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(cartprodpairin_type,type,
% 0.26/0.47 cartprodpairin: $o ).
% 0.26/0.47
% 0.26/0.47 thf(cartprodpairin,definition,
% 0.26/0.47 ( cartprodpairin
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ B )
% 0.26/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(cartprodmempair1_type,type,
% 0.26/0.47 cartprodmempair1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(cartprodmempair1,definition,
% 0.26/0.47 ( cartprodmempair1
% 0.26/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.26/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.26/0.47 => ? [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 & ? [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ B )
% 0.26/0.47 & ( Xu
% 0.26/0.47 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(cartprodmempair_type,type,
% 0.26/0.47 cartprodmempair: $o ).
% 0.26/0.47
% 0.26/0.47 thf(cartprodmempair,definition,
% 0.26/0.47 ( cartprodmempair
% 0.26/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.26/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.26/0.47 => ( iskpair @ Xu ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setunionE2_type,type,
% 0.26/0.47 setunionE2: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setunionE2,definition,
% 0.26/0.47 ( setunionE2
% 0.26/0.47 = ( ! [A: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.26/0.47 => ? [X: $i] :
% 0.26/0.47 ( ( in @ X @ A )
% 0.26/0.47 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setunionsingleton1_type,type,
% 0.26/0.47 setunionsingleton1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setunionsingleton1,definition,
% 0.26/0.47 ( setunionsingleton1
% 0.26/0.47 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setunionsingleton2_type,type,
% 0.26/0.47 setunionsingleton2: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setunionsingleton2,definition,
% 0.26/0.47 ( setunionsingleton2
% 0.26/0.47 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setunionsingleton_type,type,
% 0.26/0.47 setunionsingleton: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setunionsingleton,definition,
% 0.26/0.47 ( setunionsingleton
% 0.26/0.47 = ( ! [Xx: $i] :
% 0.26/0.47 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.26/0.47 = Xx ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(singleton_type,type,
% 0.26/0.47 singleton: $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(singletonprop_type,type,
% 0.26/0.47 singletonprop: $o ).
% 0.26/0.47
% 0.26/0.47 thf(singletonprop,definition,
% 0.26/0.47 ( singletonprop
% 0.26/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.26/0.47 ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ A )
% 0.26/0.47 => ( ( Xphi @ Xx )
% 0.26/0.47 => ( ( Xphi @ Xy )
% 0.26/0.47 => ( Xx = Xy ) ) ) ) )
% 0.26/0.47 => ( ? [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 & ( Xphi @ Xx ) )
% 0.26/0.47 => ( singleton
% 0.26/0.47 @ ( dsetconstr @ A
% 0.26/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(ex1_type,type,
% 0.26/0.47 ex1: $i > ( $i > $o ) > $o ).
% 0.26/0.47
% 0.26/0.47 thf(ex1E1_type,type,
% 0.26/0.47 ex1E1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(ex1E1,definition,
% 0.26/0.47 ( ex1E1
% 0.26/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.26/0.47 ( ( ex1 @ A
% 0.26/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.26/0.47 => ? [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(ex1I_type,type,
% 0.26/0.47 ex1I: $o ).
% 0.26/0.47
% 0.26/0.47 thf(ex1I,definition,
% 0.26/0.47 ( ex1I
% 0.26/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( ( Xphi @ Xx )
% 0.26/0.47 => ( ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ A )
% 0.26/0.47 => ( ( Xphi @ Xy )
% 0.26/0.47 => ( Xy = Xx ) ) )
% 0.26/0.47 => ( ex1 @ A
% 0.26/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(ex1I2_type,type,
% 0.26/0.47 ex1I2: $o ).
% 0.26/0.47
% 0.26/0.47 thf(ex1I2,definition,
% 0.26/0.47 ( ex1I2
% 0.26/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.26/0.47 ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ A )
% 0.26/0.47 => ( ( Xphi @ Xx )
% 0.26/0.47 => ( ( Xphi @ Xy )
% 0.26/0.47 => ( Xx = Xy ) ) ) ) )
% 0.26/0.47 => ( ? [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 & ( Xphi @ Xx ) )
% 0.26/0.47 => ( ex1 @ A
% 0.26/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(singletonsuniq_type,type,
% 0.26/0.47 singletonsuniq: $o ).
% 0.26/0.47
% 0.26/0.47 thf(singletonsuniq,definition,
% 0.26/0.47 ( singletonsuniq
% 0.26/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.26/0.47 ( ( ( setadjoin @ Xx @ emptyset )
% 0.26/0.47 = ( setadjoin @ Xy @ emptyset ) )
% 0.26/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(atmost1p_type,type,
% 0.26/0.47 atmost1p: $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(atleast2p_type,type,
% 0.26/0.47 atleast2p: $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(atmost2p_type,type,
% 0.26/0.47 atmost2p: $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(upairsetp_type,type,
% 0.26/0.47 upairsetp: $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(setukpairinjL1_type,type,
% 0.26/0.47 setukpairinjL1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setukpairinjL1,definition,
% 0.26/0.47 ( setukpairinjL1
% 0.26/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.26/0.47 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.26/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(kfstsingleton_type,type,
% 0.26/0.47 kfstsingleton: $o ).
% 0.26/0.47
% 0.26/0.47 thf(kfstsingleton,definition,
% 0.26/0.47 ( kfstsingleton
% 0.26/0.47 = ( ! [Xu: $i] :
% 0.26/0.47 ( ( iskpair @ Xu )
% 0.26/0.47 => ( singleton
% 0.26/0.47 @ ( dsetconstr @ ( setunion @ Xu )
% 0.26/0.47 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(theprop_type,type,
% 0.26/0.47 theprop: $o ).
% 0.26/0.47
% 0.26/0.47 thf(theprop,definition,
% 0.26/0.47 ( theprop
% 0.26/0.47 = ( ! [X: $i] :
% 0.26/0.47 ( ( singleton @ X )
% 0.26/0.47 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(kfst_type,type,
% 0.26/0.47 kfst: $i > $i ).
% 0.26/0.47
% 0.26/0.47 thf(kfstpairEq_type,type,
% 0.26/0.47 kfstpairEq: $o ).
% 0.26/0.47
% 0.26/0.47 thf(kfstpairEq,definition,
% 0.26/0.47 ( kfstpairEq
% 0.26/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.26/0.47 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.26/0.47 = Xx ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(cartprodfstin_type,type,
% 0.26/0.47 cartprodfstin: $o ).
% 0.26/0.47
% 0.26/0.47 thf(cartprodfstin,definition,
% 0.26/0.47 ( cartprodfstin
% 0.26/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.26/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.26/0.47 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setukpairinjL2_type,type,
% 0.26/0.47 setukpairinjL2: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setukpairinjL2,definition,
% 0.26/0.47 ( setukpairinjL2
% 0.26/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.26/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.26/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.26/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setukpairinjL_type,type,
% 0.26/0.47 setukpairinjL: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setukpairinjL,definition,
% 0.26/0.47 ( setukpairinjL
% 0.26/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.26/0.47 ( ( ( kpair @ Xx @ Xy )
% 0.26/0.47 = ( kpair @ Xz @ Xu ) )
% 0.26/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setukpairinjR11_type,type,
% 0.26/0.47 setukpairinjR11: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setukpairinjR11,definition,
% 0.26/0.47 ( setukpairinjR11
% 0.26/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.26/0.47 ( ( Xx = Xy )
% 0.26/0.47 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.26/0.47 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setukpairinjR12_type,type,
% 0.26/0.47 setukpairinjR12: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setukpairinjR12,definition,
% 0.26/0.47 ( setukpairinjR12
% 0.26/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.26/0.47 ( ( Xx = Xy )
% 0.26/0.47 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.26/0.47 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setukpairinjR1_type,type,
% 0.26/0.47 setukpairinjR1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setukpairinjR1,definition,
% 0.26/0.47 ( setukpairinjR1
% 0.26/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.26/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.26/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.26/0.47 => ( ( Xz = Xu )
% 0.26/0.47 => ( Xy = Xu ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(upairequniteq_type,type,
% 0.26/0.47 upairequniteq: $o ).
% 0.26/0.47
% 0.26/0.47 thf(upairequniteq,definition,
% 0.26/0.47 ( upairequniteq
% 0.26/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.26/0.47 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.26/0.47 = ( setadjoin @ Xz @ emptyset ) )
% 0.26/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setukpairinjR2_type,type,
% 0.26/0.47 setukpairinjR2: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setukpairinjR2,definition,
% 0.26/0.47 ( setukpairinjR2
% 0.26/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.26/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.26/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.26/0.47 => ( Xy = Xu ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setukpairinjR_type,type,
% 0.26/0.47 setukpairinjR: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setukpairinjR,definition,
% 0.26/0.47 ( setukpairinjR
% 0.26/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.26/0.47 ( ( ( kpair @ Xx @ Xy )
% 0.26/0.47 = ( kpair @ Xz @ Xu ) )
% 0.26/0.47 => ( Xy = Xu ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(ksndsingleton_type,type,
% 0.26/0.47 ksndsingleton: $o ).
% 0.26/0.47
% 0.26/0.47 thf(ksndsingleton,definition,
% 0.26/0.47 ( ksndsingleton
% 0.26/0.47 = ( ! [Xu: $i] :
% 0.26/0.47 ( ( iskpair @ Xu )
% 0.26/0.47 => ( singleton
% 0.26/0.47 @ ( dsetconstr @ ( setunion @ Xu )
% 0.26/0.47 @ ^ [Xx: $i] :
% 0.26/0.47 ( Xu
% 0.26/0.47 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(ksnd_type,type,
% 0.26/0.47 ksnd: $i > $i ).
% 0.26/0.47
% 0.26/0.47 thf(ksndpairEq_type,type,
% 0.26/0.47 ksndpairEq: $o ).
% 0.26/0.47
% 0.26/0.47 thf(ksndpairEq,definition,
% 0.26/0.47 ( ksndpairEq
% 0.26/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.26/0.47 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.26/0.47 = Xy ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(kpairsurjEq_type,type,
% 0.26/0.47 kpairsurjEq: $o ).
% 0.26/0.47
% 0.26/0.47 thf(kpairsurjEq,definition,
% 0.26/0.47 ( kpairsurjEq
% 0.26/0.47 = ( ! [Xu: $i] :
% 0.26/0.47 ( ( iskpair @ Xu )
% 0.26/0.47 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.26/0.47 = Xu ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(cartprodsndin_type,type,
% 0.26/0.47 cartprodsndin: $o ).
% 0.26/0.47
% 0.26/0.47 thf(cartprodsndin,definition,
% 0.26/0.47 ( cartprodsndin
% 0.26/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.26/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.26/0.47 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(cartprodpairmemEL_type,type,
% 0.26/0.47 cartprodpairmemEL: $o ).
% 0.26/0.47
% 0.26/0.47 thf(cartprodpairmemEL,definition,
% 0.26/0.47 ( cartprodpairmemEL
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.26/0.47 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.26/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(cartprodpairmemER_type,type,
% 0.26/0.47 cartprodpairmemER: $o ).
% 0.26/0.47
% 0.26/0.47 thf(cartprodpairmemER,definition,
% 0.26/0.47 ( cartprodpairmemER
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.26/0.47 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.26/0.47 => ( in @ Xy @ B ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(cartprodmempaircEq_type,type,
% 0.26/0.47 cartprodmempaircEq: $o ).
% 0.26/0.47
% 0.26/0.47 thf(cartprodmempaircEq,definition,
% 0.26/0.47 ( cartprodmempaircEq
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ B )
% 0.26/0.47 => ( ( kpair @ Xx @ Xy )
% 0.26/0.47 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(cartprodfstpairEq_type,type,
% 0.26/0.47 cartprodfstpairEq: $o ).
% 0.26/0.47
% 0.26/0.47 thf(cartprodfstpairEq,definition,
% 0.26/0.47 ( cartprodfstpairEq
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ B )
% 0.26/0.47 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.26/0.47 = Xx ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(cartprodsndpairEq_type,type,
% 0.26/0.47 cartprodsndpairEq: $o ).
% 0.26/0.47
% 0.26/0.47 thf(cartprodsndpairEq,definition,
% 0.26/0.47 ( cartprodsndpairEq
% 0.26/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ B )
% 0.26/0.47 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.26/0.47 = Xy ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(cartprodpairsurjEq_type,type,
% 0.26/0.47 cartprodpairsurjEq: $o ).
% 0.26/0.47
% 0.26/0.47 thf(cartprodpairsurjEq,definition,
% 0.26/0.47 ( cartprodpairsurjEq
% 0.26/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.26/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.26/0.47 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.26/0.47 = Xu ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(breln_type,type,
% 0.26/0.47 breln: $i > $i > $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(dpsetconstr_type,type,
% 0.26/0.47 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.26/0.47
% 0.26/0.47 thf(dpsetconstrI_type,type,
% 0.26/0.47 dpsetconstrI: $o ).
% 0.26/0.47
% 0.26/0.47 thf(dpsetconstrI,definition,
% 0.26/0.47 ( dpsetconstrI
% 0.26/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ B )
% 0.26/0.47 => ( ( Xphi @ Xx @ Xy )
% 0.26/0.47 => ( in @ ( kpair @ Xx @ Xy )
% 0.26/0.47 @ ( dpsetconstr @ A @ B
% 0.26/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(dpsetconstrSub_type,type,
% 0.26/0.47 dpsetconstrSub: $o ).
% 0.26/0.47
% 0.26/0.47 thf(dpsetconstrSub,definition,
% 0.26/0.47 ( dpsetconstrSub
% 0.26/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.26/0.47 ( subset
% 0.26/0.47 @ ( dpsetconstr @ A @ B
% 0.26/0.47 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.26/0.47 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(setOfPairsIsBReln_type,type,
% 0.26/0.47 setOfPairsIsBReln: $o ).
% 0.26/0.47
% 0.26/0.47 thf(setOfPairsIsBReln,definition,
% 0.26/0.47 ( setOfPairsIsBReln
% 0.26/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.26/0.47 ( breln @ A @ B
% 0.26/0.47 @ ( dpsetconstr @ A @ B
% 0.26/0.47 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(dpsetconstrERa_type,type,
% 0.26/0.47 dpsetconstrERa: $o ).
% 0.26/0.47
% 0.26/0.47 thf(dpsetconstrERa,definition,
% 0.26/0.47 ( dpsetconstrERa
% 0.26/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ B )
% 0.26/0.47 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.26/0.47 @ ( dpsetconstr @ A @ B
% 0.26/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.26/0.47 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(dpsetconstrEL1_type,type,
% 0.26/0.47 dpsetconstrEL1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(dpsetconstrEL1,definition,
% 0.26/0.47 ( dpsetconstrEL1
% 0.26/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.26/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.26/0.47 @ ( dpsetconstr @ A @ B
% 0.26/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.26/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(dpsetconstrEL2_type,type,
% 0.26/0.47 dpsetconstrEL2: $o ).
% 0.26/0.47
% 0.26/0.47 thf(dpsetconstrEL2,definition,
% 0.26/0.47 ( dpsetconstrEL2
% 0.26/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.26/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.26/0.47 @ ( dpsetconstr @ A @ B
% 0.26/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.26/0.47 => ( in @ Xy @ B ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(dpsetconstrER_type,type,
% 0.26/0.47 dpsetconstrER: $o ).
% 0.26/0.47
% 0.26/0.47 thf(dpsetconstrER,definition,
% 0.26/0.47 ( dpsetconstrER
% 0.26/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.26/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.26/0.47 @ ( dpsetconstr @ A @ B
% 0.26/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.26/0.47 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(func_type,type,
% 0.26/0.47 func: $i > $i > $i > $o ).
% 0.26/0.47
% 0.26/0.47 thf(funcSet_type,type,
% 0.26/0.47 funcSet: $i > $i > $i ).
% 0.26/0.47
% 0.26/0.47 thf(funcImageSingleton_type,type,
% 0.26/0.47 funcImageSingleton: $o ).
% 0.26/0.47
% 0.26/0.47 thf(funcImageSingleton,definition,
% 0.26/0.47 ( funcImageSingleton
% 0.26/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.26/0.47 ( ( func @ A @ B @ Xf )
% 0.26/0.47 => ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( singleton
% 0.26/0.47 @ ( dsetconstr @ B
% 0.26/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(apProp_type,type,
% 0.26/0.47 apProp: $o ).
% 0.26/0.47
% 0.26/0.47 thf(apProp,definition,
% 0.26/0.47 ( apProp
% 0.26/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.26/0.47 ( ( func @ A @ B @ Xf )
% 0.26/0.47 => ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( in
% 0.26/0.47 @ ( setunion
% 0.26/0.47 @ ( dsetconstr @ B
% 0.26/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.26/0.47 @ B ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(ap_type,type,
% 0.26/0.47 ap: $i > $i > $i > $i > $i ).
% 0.26/0.47
% 0.26/0.47 thf(app_type,type,
% 0.26/0.47 app: $o ).
% 0.26/0.47
% 0.26/0.47 thf(app,definition,
% 0.26/0.47 ( app
% 0.26/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.26/0.47 ( ( func @ A @ B @ Xf )
% 0.26/0.47 => ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(infuncsetfunc_type,type,
% 0.26/0.47 infuncsetfunc: $o ).
% 0.26/0.47
% 0.26/0.47 thf(infuncsetfunc,definition,
% 0.26/0.47 ( infuncsetfunc
% 0.26/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.26/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.26/0.47 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(ap2p_type,type,
% 0.26/0.47 ap2p: $o ).
% 0.26/0.47
% 0.26/0.47 thf(ap2p,definition,
% 0.26/0.47 ( ap2p
% 0.26/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.26/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.26/0.47 => ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(funcinfuncset_type,type,
% 0.26/0.47 funcinfuncset: $o ).
% 0.26/0.47
% 0.26/0.47 thf(funcinfuncset,definition,
% 0.26/0.47 ( funcinfuncset
% 0.26/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.26/0.47 ( ( func @ A @ B @ Xf )
% 0.26/0.47 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(lamProp_type,type,
% 0.26/0.47 lamProp: $o ).
% 0.26/0.47
% 0.26/0.47 thf(lamProp,definition,
% 0.26/0.47 ( lamProp
% 0.26/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.26/0.47 ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.26/0.47 => ( func @ A @ B
% 0.26/0.47 @ ( dpsetconstr @ A @ B
% 0.26/0.47 @ ^ [Xx: $i,Xy: $i] :
% 0.26/0.47 ( ( Xf @ Xx )
% 0.26/0.47 = Xy ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(lam_type,type,
% 0.26/0.47 lam: $i > $i > ( $i > $i ) > $i ).
% 0.26/0.47
% 0.26/0.47 thf(lamp_type,type,
% 0.26/0.47 lamp: $o ).
% 0.26/0.47
% 0.26/0.47 thf(lamp,definition,
% 0.26/0.47 ( lamp
% 0.26/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.26/0.47 ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.26/0.47 => ( func @ A @ B
% 0.26/0.47 @ ( lam @ A @ B
% 0.26/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(lam2p_type,type,
% 0.26/0.47 lam2p: $o ).
% 0.26/0.47
% 0.26/0.47 thf(lam2p,definition,
% 0.26/0.47 ( lam2p
% 0.26/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.26/0.47 ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.26/0.47 => ( in
% 0.26/0.47 @ ( lam @ A @ B
% 0.26/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.26/0.47 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(brelnall1_type,type,
% 0.26/0.47 brelnall1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(brelnall1,definition,
% 0.26/0.47 ( brelnall1
% 0.26/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.26/0.47 ( ( breln @ A @ B @ R )
% 0.26/0.47 => ! [Xphi: $i > $o] :
% 0.26/0.47 ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ B )
% 0.26/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.26/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.26/0.47 => ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ R )
% 0.26/0.47 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(brelnall2_type,type,
% 0.26/0.47 brelnall2: $o ).
% 0.26/0.47
% 0.26/0.47 thf(brelnall2,definition,
% 0.26/0.47 ( brelnall2
% 0.26/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.26/0.47 ( ( breln @ A @ B @ R )
% 0.26/0.47 => ! [Xphi: $i > $o] :
% 0.26/0.47 ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ B )
% 0.26/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.26/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.26/0.47 => ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ R )
% 0.26/0.47 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(ex1E2_type,type,
% 0.26/0.47 ex1E2: $o ).
% 0.26/0.47
% 0.26/0.47 thf(ex1E2,definition,
% 0.26/0.47 ( ex1E2
% 0.26/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.26/0.47 ( ( ex1 @ A
% 0.26/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.26/0.47 => ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ A )
% 0.26/0.47 => ( ( Xphi @ Xx )
% 0.26/0.47 => ( ( Xphi @ Xy )
% 0.26/0.47 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(funcGraphProp1_type,type,
% 0.26/0.47 funcGraphProp1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(funcGraphProp1,definition,
% 0.26/0.47 ( funcGraphProp1
% 0.26/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.26/0.47 ( ( func @ A @ B @ Xf )
% 0.26/0.47 => ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(funcGraphProp3_type,type,
% 0.26/0.47 funcGraphProp3: $o ).
% 0.26/0.47
% 0.26/0.47 thf(funcGraphProp3,definition,
% 0.26/0.47 ( funcGraphProp3
% 0.26/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.26/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.26/0.47 => ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(funcGraphProp2_type,type,
% 0.26/0.47 funcGraphProp2: $o ).
% 0.26/0.47
% 0.26/0.47 thf(funcGraphProp2,definition,
% 0.26/0.47 ( funcGraphProp2
% 0.26/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.26/0.47 ( ( func @ A @ B @ Xf )
% 0.26/0.47 => ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ B )
% 0.26/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.26/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.26/0.47 = Xy ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(funcextLem_type,type,
% 0.26/0.47 funcextLem: $o ).
% 0.26/0.47
% 0.26/0.47 thf(funcextLem,definition,
% 0.26/0.47 ( funcextLem
% 0.26/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.26/0.47 ( ( func @ A @ B @ Xf )
% 0.26/0.47 => ! [Xg: $i] :
% 0.26/0.47 ( ( func @ A @ B @ Xg )
% 0.26/0.47 => ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.26/0.47 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.26/0.47 => ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ B )
% 0.26/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 0.26/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(funcGraphProp4_type,type,
% 0.26/0.47 funcGraphProp4: $o ).
% 0.26/0.47
% 0.26/0.47 thf(funcGraphProp4,definition,
% 0.26/0.47 ( funcGraphProp4
% 0.26/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.26/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.26/0.47 => ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ B )
% 0.26/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.26/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.26/0.47 = Xy ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(subbreln_type,type,
% 0.26/0.47 subbreln: $o ).
% 0.26/0.47
% 0.26/0.47 thf(subbreln,definition,
% 0.26/0.47 ( subbreln
% 0.26/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.26/0.47 ( ( breln @ A @ B @ R )
% 0.26/0.47 => ! [S: $i] :
% 0.26/0.47 ( ( breln @ A @ B @ S )
% 0.26/0.47 => ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ B )
% 0.26/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.26/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.26/0.47 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(eqbreln_type,type,
% 0.26/0.47 eqbreln: $o ).
% 0.26/0.47
% 0.26/0.47 thf(eqbreln,definition,
% 0.26/0.47 ( eqbreln
% 0.26/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.26/0.47 ( ( breln @ A @ B @ R )
% 0.26/0.47 => ! [S: $i] :
% 0.26/0.47 ( ( breln @ A @ B @ S )
% 0.26/0.47 => ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ B )
% 0.26/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.26/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.26/0.47 => ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ B )
% 0.26/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.26/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.26/0.47 => ( R = S ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(funcext_type,type,
% 0.26/0.47 funcext: $o ).
% 0.26/0.47
% 0.26/0.47 thf(funcext,definition,
% 0.26/0.47 ( funcext
% 0.26/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.26/0.47 ( ( func @ A @ B @ Xf )
% 0.26/0.47 => ! [Xg: $i] :
% 0.26/0.47 ( ( func @ A @ B @ Xg )
% 0.26/0.47 => ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.26/0.47 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.26/0.47 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(funcext2_type,type,
% 0.26/0.47 funcext2: $o ).
% 0.26/0.47
% 0.26/0.47 thf(funcext2,definition,
% 0.26/0.47 ( funcext2
% 0.26/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.26/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.26/0.47 => ! [Xg: $i] :
% 0.26/0.47 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 0.26/0.47 => ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.26/0.47 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.26/0.47 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(ap2apEq1_type,type,
% 0.26/0.47 ap2apEq1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(ap2apEq1,definition,
% 0.26/0.47 ( ap2apEq1
% 0.26/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.26/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.26/0.47 => ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.26/0.47 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(ap2apEq2_type,type,
% 0.26/0.47 ap2apEq2: $o ).
% 0.26/0.47
% 0.26/0.47 thf(ap2apEq2,definition,
% 0.26/0.47 ( ap2apEq2
% 0.26/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.26/0.47 ( ( func @ A @ B @ Xf )
% 0.26/0.47 => ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.26/0.47 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(beta1_type,type,
% 0.26/0.47 beta1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(beta1,definition,
% 0.26/0.47 ( beta1
% 0.26/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.26/0.47 ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.26/0.47 => ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( ( ap @ A @ B
% 0.26/0.47 @ ( lam @ A @ B
% 0.26/0.47 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.26/0.47 @ Xx )
% 0.26/0.47 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(eta1_type,type,
% 0.26/0.47 eta1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(eta1,definition,
% 0.26/0.47 ( eta1
% 0.26/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.26/0.47 ( ( func @ A @ B @ Xf )
% 0.26/0.47 => ( ( lam @ A @ B
% 0.26/0.47 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.26/0.47 = Xf ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(lam2lamEq_type,type,
% 0.26/0.47 lam2lamEq: $o ).
% 0.26/0.47
% 0.26/0.47 thf(lam2lamEq,definition,
% 0.26/0.47 ( lam2lamEq
% 0.26/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.26/0.47 ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.26/0.47 => ( ( lam @ A @ B
% 0.26/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.26/0.47 = ( lam @ A @ B
% 0.26/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(beta2_type,type,
% 0.26/0.47 beta2: $o ).
% 0.26/0.47
% 0.26/0.47 thf(beta2,definition,
% 0.26/0.47 ( beta2
% 0.26/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.26/0.47 ( ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.26/0.47 => ! [Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ( ( ap @ A @ B
% 0.26/0.47 @ ( lam @ A @ B
% 0.26/0.47 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.26/0.47 @ Xx )
% 0.26/0.47 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(eta2_type,type,
% 0.26/0.47 eta2: $o ).
% 0.26/0.47
% 0.26/0.47 thf(eta2,definition,
% 0.26/0.47 ( eta2
% 0.26/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.26/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.26/0.47 => ( ( lam @ A @ B
% 0.26/0.47 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.26/0.47 = Xf ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(iffalseProp1_type,type,
% 0.26/0.47 iffalseProp1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(iffalseProp1,definition,
% 0.26/0.47 ( iffalseProp1
% 0.26/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ A )
% 0.26/0.47 => ( ~ Xphi
% 0.26/0.47 => ( in @ Xy
% 0.26/0.47 @ ( dsetconstr @ A
% 0.26/0.47 @ ^ [Xz: $i] :
% 0.26/0.47 ( ( Xphi
% 0.26/0.47 & ( Xz = Xx ) )
% 0.26/0.47 | ( ~ Xphi
% 0.26/0.47 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(iffalseProp2_type,type,
% 0.26/0.47 iffalseProp2: $o ).
% 0.26/0.47
% 0.26/0.47 thf(iffalseProp2,definition,
% 0.26/0.47 ( iffalseProp2
% 0.26/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ A )
% 0.26/0.47 => ( ~ Xphi
% 0.26/0.47 => ( ( dsetconstr @ A
% 0.26/0.47 @ ^ [Xz: $i] :
% 0.26/0.47 ( ( Xphi
% 0.26/0.47 & ( Xz = Xx ) )
% 0.26/0.47 | ( ~ Xphi
% 0.26/0.47 & ( Xz = Xy ) ) ) )
% 0.26/0.47 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(iftrueProp1_type,type,
% 0.26/0.47 iftrueProp1: $o ).
% 0.26/0.47
% 0.26/0.47 thf(iftrueProp1,definition,
% 0.26/0.47 ( iftrueProp1
% 0.26/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ A )
% 0.26/0.47 => ( Xphi
% 0.26/0.47 => ( in @ Xx
% 0.26/0.47 @ ( dsetconstr @ A
% 0.26/0.47 @ ^ [Xz: $i] :
% 0.26/0.47 ( ( Xphi
% 0.26/0.47 & ( Xz = Xx ) )
% 0.26/0.47 | ( ~ Xphi
% 0.26/0.47 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(iftrueProp2_type,type,
% 0.26/0.47 iftrueProp2: $o ).
% 0.26/0.47
% 0.26/0.47 thf(iftrueProp2,definition,
% 0.26/0.47 ( iftrueProp2
% 0.26/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ A )
% 0.26/0.47 => ( Xphi
% 0.26/0.47 => ( ( dsetconstr @ A
% 0.26/0.47 @ ^ [Xz: $i] :
% 0.26/0.47 ( ( Xphi
% 0.26/0.47 & ( Xz = Xx ) )
% 0.26/0.47 | ( ~ Xphi
% 0.26/0.47 & ( Xz = Xy ) ) ) )
% 0.26/0.47 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(ifSingleton_type,type,
% 0.26/0.47 ifSingleton: $o ).
% 0.26/0.47
% 0.26/0.47 thf(ifSingleton,definition,
% 0.26/0.47 ( ifSingleton
% 0.26/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.26/0.47 ( ( in @ Xx @ A )
% 0.26/0.47 => ! [Xy: $i] :
% 0.26/0.47 ( ( in @ Xy @ A )
% 0.26/0.47 => ( singleton
% 0.26/0.47 @ ( dsetconstr @ A
% 0.26/0.47 @ ^ [Xz: $i] :
% 0.26/0.47 ( ( Xphi
% 0.26/0.47 & ( Xz = Xx ) )
% 0.26/0.47 | ( ~ Xphi
% 0.26/0.47 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.26/0.47
% 0.26/0.47 thf(if_type,type,
% 0.26/0.47 if: $i > $o > $i > $i > $i ).
% 0.26/0.47
% 0.26/0.47 thf(ifp_type,type,
% 0.26/0.48 ifp: $o ).
% 0.26/0.48
% 0.26/0.48 thf(ifp,definition,
% 0.26/0.48 ( ifp
% 0.26/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ! [Xy: $i] :
% 0.26/0.48 ( ( in @ Xy @ A )
% 0.26/0.48 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(theeq_type,type,
% 0.26/0.48 theeq: $o ).
% 0.26/0.48
% 0.26/0.48 thf(theeq,definition,
% 0.26/0.48 ( theeq
% 0.26/0.48 = ( ! [X: $i] :
% 0.26/0.48 ( ( singleton @ X )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ X )
% 0.26/0.48 => ( ( setunion @ X )
% 0.26/0.48 = Xx ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(iftrue_type,type,
% 0.26/0.48 iftrue: $o ).
% 0.26/0.48
% 0.26/0.48 thf(iftrue,definition,
% 0.26/0.48 ( iftrue
% 0.26/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ! [Xy: $i] :
% 0.26/0.48 ( ( in @ Xy @ A )
% 0.26/0.48 => ( Xphi
% 0.26/0.48 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.26/0.48 = Xx ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(iffalse_type,type,
% 0.26/0.48 iffalse: $o ).
% 0.26/0.48
% 0.26/0.48 thf(iffalse,definition,
% 0.26/0.48 ( iffalse
% 0.26/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ! [Xy: $i] :
% 0.26/0.48 ( ( in @ Xy @ A )
% 0.26/0.48 => ( ~ Xphi
% 0.26/0.48 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.26/0.48 = Xy ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(iftrueorfalse_type,type,
% 0.26/0.48 iftrueorfalse: $o ).
% 0.26/0.48
% 0.26/0.48 thf(iftrueorfalse,definition,
% 0.26/0.48 ( iftrueorfalse
% 0.26/0.48 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ! [Xy: $i] :
% 0.26/0.48 ( ( in @ Xy @ A )
% 0.26/0.48 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(binintersectT_lem_type,type,
% 0.26/0.48 binintersectT_lem: $o ).
% 0.26/0.48
% 0.26/0.48 thf(binintersectT_lem,definition,
% 0.26/0.48 ( binintersectT_lem
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(binunionT_lem_type,type,
% 0.26/0.48 binunionT_lem: $o ).
% 0.26/0.48
% 0.26/0.48 thf(binunionT_lem,definition,
% 0.26/0.48 ( binunionT_lem
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(powersetT_lem_type,type,
% 0.26/0.48 powersetT_lem: $o ).
% 0.26/0.48
% 0.26/0.48 thf(powersetT_lem,definition,
% 0.26/0.48 ( powersetT_lem
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(setminusT_lem_type,type,
% 0.26/0.48 setminusT_lem: $o ).
% 0.26/0.48
% 0.26/0.48 thf(setminusT_lem,definition,
% 0.26/0.48 ( setminusT_lem
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(complementT_lem_type,type,
% 0.26/0.48 complementT_lem: $o ).
% 0.26/0.48
% 0.26/0.48 thf(complementT_lem,definition,
% 0.26/0.48 ( complementT_lem
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(setextT_type,type,
% 0.26/0.48 setextT: $o ).
% 0.26/0.48
% 0.26/0.48 thf(setextT,definition,
% 0.26/0.48 ( setextT
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ( ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ( in @ Xx @ X )
% 0.26/0.48 => ( in @ Xx @ Y ) ) )
% 0.26/0.48 => ( ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ( in @ Xx @ Y )
% 0.26/0.48 => ( in @ Xx @ X ) ) )
% 0.26/0.48 => ( X = Y ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(subsetTI_type,type,
% 0.26/0.48 subsetTI: $o ).
% 0.26/0.48
% 0.26/0.48 thf(subsetTI,definition,
% 0.26/0.48 ( subsetTI
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ( ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ( in @ Xx @ X )
% 0.26/0.48 => ( in @ Xx @ Y ) ) )
% 0.26/0.48 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(powersetTI1_type,type,
% 0.26/0.48 powersetTI1: $o ).
% 0.26/0.48
% 0.26/0.48 thf(powersetTI1,definition,
% 0.26/0.48 ( powersetTI1
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ( ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ( in @ Xx @ X )
% 0.26/0.48 => ( in @ Xx @ Y ) ) )
% 0.26/0.48 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(powersetTE1_type,type,
% 0.26/0.48 powersetTE1: $o ).
% 0.26/0.48
% 0.26/0.48 thf(powersetTE1,definition,
% 0.26/0.48 ( powersetTE1
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ( in @ X @ ( powerset @ Y ) )
% 0.26/0.48 => ( ( in @ Xx @ X )
% 0.26/0.48 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(complementTI1_type,type,
% 0.26/0.48 complementTI1: $o ).
% 0.26/0.48
% 0.26/0.48 thf(complementTI1,definition,
% 0.26/0.48 ( complementTI1
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ( in @ Xx @ X )
% 0.26/0.48 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(complementTE1_type,type,
% 0.26/0.48 complementTE1: $o ).
% 0.26/0.48
% 0.26/0.48 thf(complementTE1,definition,
% 0.26/0.48 ( complementTE1
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 0.26/0.48 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(binintersectTELcontra_type,type,
% 0.26/0.48 binintersectTELcontra: $o ).
% 0.26/0.48
% 0.26/0.48 thf(binintersectTELcontra,definition,
% 0.26/0.48 ( binintersectTELcontra
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ~ ( in @ Xx @ X )
% 0.26/0.48 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(binintersectTERcontra_type,type,
% 0.26/0.48 binintersectTERcontra: $o ).
% 0.26/0.48
% 0.26/0.48 thf(binintersectTERcontra,definition,
% 0.26/0.48 ( binintersectTERcontra
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ~ ( in @ Xx @ Y )
% 0.26/0.48 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(contrasubsetT_type,type,
% 0.26/0.48 contrasubsetT: $o ).
% 0.26/0.48
% 0.26/0.48 thf(contrasubsetT,definition,
% 0.26/0.48 ( contrasubsetT
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.26/0.48 => ( ( in @ Xx @ Y )
% 0.26/0.48 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(contrasubsetT1_type,type,
% 0.26/0.48 contrasubsetT1: $o ).
% 0.26/0.48
% 0.26/0.48 thf(contrasubsetT1,definition,
% 0.26/0.48 ( contrasubsetT1
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ( subset @ X @ Y )
% 0.26/0.48 => ( ~ ( in @ Xx @ Y )
% 0.26/0.48 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(contrasubsetT2_type,type,
% 0.26/0.48 contrasubsetT2: $o ).
% 0.26/0.48
% 0.26/0.48 thf(contrasubsetT2,definition,
% 0.26/0.48 ( contrasubsetT2
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ( ( subset @ X @ Y )
% 0.26/0.48 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(contrasubsetT3_type,type,
% 0.26/0.48 contrasubsetT3: $o ).
% 0.26/0.48
% 0.26/0.48 thf(contrasubsetT3,definition,
% 0.26/0.48 ( contrasubsetT3
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 0.26/0.48 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(doubleComplementI1_type,type,
% 0.26/0.48 doubleComplementI1: $o ).
% 0.26/0.48
% 0.26/0.48 thf(doubleComplementI1,definition,
% 0.26/0.48 ( doubleComplementI1
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ( in @ Xx @ X )
% 0.26/0.48 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(doubleComplementE1_type,type,
% 0.26/0.48 doubleComplementE1: $o ).
% 0.26/0.48
% 0.26/0.48 thf(doubleComplementE1,definition,
% 0.26/0.48 ( doubleComplementE1
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 0.26/0.48 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(doubleComplementSub1_type,type,
% 0.26/0.48 doubleComplementSub1: $o ).
% 0.26/0.48
% 0.26/0.48 thf(doubleComplementSub1,definition,
% 0.26/0.48 ( doubleComplementSub1
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(doubleComplementSub2_type,type,
% 0.26/0.48 doubleComplementSub2: $o ).
% 0.26/0.48
% 0.26/0.48 thf(doubleComplementSub2,definition,
% 0.26/0.48 ( doubleComplementSub2
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(doubleComplementEq_type,type,
% 0.26/0.48 doubleComplementEq: $o ).
% 0.26/0.48
% 0.26/0.48 thf(doubleComplementEq,definition,
% 0.26/0.48 ( doubleComplementEq
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ( X
% 0.26/0.48 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(complementTnotintersectT_type,type,
% 0.26/0.48 complementTnotintersectT: $o ).
% 0.26/0.48
% 0.26/0.48 thf(complementTnotintersectT,definition,
% 0.26/0.48 ( complementTnotintersectT
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.26/0.48 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(complementImpComplementIntersect_type,type,
% 0.26/0.48 complementImpComplementIntersect: $o ).
% 0.26/0.48
% 0.26/0.48 thf(complementImpComplementIntersect,definition,
% 0.26/0.48 ( complementImpComplementIntersect
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.26/0.48 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(complementSubsetComplementIntersect_type,type,
% 0.26/0.48 complementSubsetComplementIntersect: $o ).
% 0.26/0.48
% 0.26/0.48 thf(complementSubsetComplementIntersect,definition,
% 0.26/0.48 ( complementSubsetComplementIntersect
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(complementInPowersetComplementIntersect_type,type,
% 0.26/0.48 complementInPowersetComplementIntersect: $o ).
% 0.26/0.48
% 0.26/0.48 thf(complementInPowersetComplementIntersect,definition,
% 0.26/0.48 ( complementInPowersetComplementIntersect
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(contraSubsetComplement_type,type,
% 0.26/0.48 contraSubsetComplement: $o ).
% 0.26/0.48
% 0.26/0.48 thf(contraSubsetComplement,definition,
% 0.26/0.48 ( contraSubsetComplement
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ( in @ Xx @ Y )
% 0.26/0.48 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(complementTcontraSubset_type,type,
% 0.26/0.48 complementTcontraSubset: $o ).
% 0.26/0.48
% 0.26/0.48 thf(complementTcontraSubset,definition,
% 0.26/0.48 ( complementTcontraSubset
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.26/0.48 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(binunionTILcontra_type,type,
% 0.26/0.48 binunionTILcontra: $o ).
% 0.26/0.48
% 0.26/0.48 thf(binunionTILcontra,definition,
% 0.26/0.48 ( binunionTILcontra
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.26/0.48 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(binunionTIRcontra_type,type,
% 0.26/0.48 binunionTIRcontra: $o ).
% 0.26/0.48
% 0.26/0.48 thf(binunionTIRcontra,definition,
% 0.26/0.48 ( binunionTIRcontra
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.26/0.48 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(inIntersectImpInUnion_type,type,
% 0.26/0.48 inIntersectImpInUnion: $o ).
% 0.26/0.48
% 0.26/0.48 thf(inIntersectImpInUnion,definition,
% 0.26/0.48 ( inIntersectImpInUnion
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Z: $i] :
% 0.26/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.26/0.48 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(inIntersectImpInUnion2_type,type,
% 0.26/0.48 inIntersectImpInUnion2: $o ).
% 0.26/0.48
% 0.26/0.48 thf(inIntersectImpInUnion2,definition,
% 0.26/0.48 ( inIntersectImpInUnion2
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Z: $i] :
% 0.26/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.26/0.48 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(inIntersectImpInIntersectUnions_type,type,
% 0.26/0.48 inIntersectImpInIntersectUnions: $o ).
% 0.26/0.48
% 0.26/0.48 thf(inIntersectImpInIntersectUnions,definition,
% 0.26/0.48 ( inIntersectImpInIntersectUnions
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Z: $i] :
% 0.26/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.26/0.48 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(intersectInPowersetIntersectUnions_type,type,
% 0.26/0.48 intersectInPowersetIntersectUnions: $o ).
% 0.26/0.48
% 0.26/0.48 thf(intersectInPowersetIntersectUnions,definition,
% 0.26/0.48 ( intersectInPowersetIntersectUnions
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Z: $i] :
% 0.26/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.26/0.48 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(inComplementUnionImpNotIn1_type,type,
% 0.26/0.48 inComplementUnionImpNotIn1: $o ).
% 0.26/0.48
% 0.26/0.48 thf(inComplementUnionImpNotIn1,definition,
% 0.26/0.48 ( inComplementUnionImpNotIn1
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.26/0.48 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(inComplementUnionImpInComplement1_type,type,
% 0.26/0.48 inComplementUnionImpInComplement1: $o ).
% 0.26/0.48
% 0.26/0.48 thf(inComplementUnionImpInComplement1,definition,
% 0.26/0.48 ( inComplementUnionImpInComplement1
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.26/0.48 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(binunionTE_type,type,
% 0.26/0.48 binunionTE: $o ).
% 0.26/0.48
% 0.26/0.48 thf(binunionTE,definition,
% 0.26/0.48 ( binunionTE
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Xphi: $o,Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.26/0.48 => ( ( ( in @ Xx @ X )
% 0.26/0.48 => Xphi )
% 0.26/0.48 => ( ( ( in @ Xx @ Y )
% 0.26/0.48 => Xphi )
% 0.26/0.48 => Xphi ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(binunionTEcontra_type,type,
% 0.26/0.48 binunionTEcontra: $o ).
% 0.26/0.48
% 0.26/0.48 thf(binunionTEcontra,definition,
% 0.26/0.48 ( binunionTEcontra
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ~ ( in @ Xx @ X )
% 0.26/0.48 => ( ~ ( in @ Xx @ Y )
% 0.26/0.48 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(demorgan2a1_type,type,
% 0.26/0.48 demorgan2a1: $o ).
% 0.26/0.48
% 0.26/0.48 thf(demorgan2a1,definition,
% 0.26/0.48 ( demorgan2a1
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.26/0.48 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(complementUnionInPowersetComplement_type,type,
% 0.26/0.48 complementUnionInPowersetComplement: $o ).
% 0.26/0.48
% 0.26/0.48 thf(complementUnionInPowersetComplement,definition,
% 0.26/0.48 ( complementUnionInPowersetComplement
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(demorgan2a2_type,type,
% 0.26/0.48 demorgan2a2: $o ).
% 0.26/0.48
% 0.26/0.48 thf(demorgan2a2,definition,
% 0.26/0.48 ( demorgan2a2
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.26/0.48 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(demorgan1a_type,type,
% 0.26/0.48 demorgan1a: $o ).
% 0.26/0.48
% 0.26/0.48 thf(demorgan1a,definition,
% 0.26/0.48 ( demorgan1a
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 0.26/0.48 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(demorgan1b_type,type,
% 0.26/0.48 demorgan1b: $o ).
% 0.26/0.48
% 0.26/0.48 thf(demorgan1b,definition,
% 0.26/0.48 ( demorgan1b
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.26/0.48 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(demorgan1_type,type,
% 0.26/0.48 demorgan1: $o ).
% 0.26/0.48
% 0.26/0.48 thf(demorgan1,definition,
% 0.26/0.48 ( demorgan1
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 0.26/0.48 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(demorgan2a_type,type,
% 0.26/0.48 demorgan2a: $o ).
% 0.26/0.48
% 0.26/0.48 thf(demorgan2a,definition,
% 0.26/0.48 ( demorgan2a
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.26/0.48 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(demorgan2b2_type,type,
% 0.26/0.48 demorgan2b2: $o ).
% 0.26/0.48
% 0.26/0.48 thf(demorgan2b2,definition,
% 0.26/0.48 ( demorgan2b2
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.26/0.48 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 0.26/0.48 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(demorgan2b_type,type,
% 0.26/0.48 demorgan2b: $o ).
% 0.26/0.48
% 0.26/0.48 thf(demorgan2b,definition,
% 0.26/0.48 ( demorgan2b
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.26/0.48 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(demorgan2_type,type,
% 0.26/0.48 demorgan2: $o ).
% 0.26/0.48
% 0.26/0.48 thf(demorgan2,definition,
% 0.26/0.48 ( demorgan2
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 0.26/0.48 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(woz13rule0_type,type,
% 0.26/0.48 woz13rule0: $o ).
% 0.26/0.48
% 0.26/0.48 thf(woz13rule0,definition,
% 0.26/0.48 ( woz13rule0
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.26/0.48 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(woz13rule1_type,type,
% 0.26/0.48 woz13rule1: $o ).
% 0.26/0.48
% 0.26/0.48 thf(woz13rule1,definition,
% 0.26/0.48 ( woz13rule1
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Z: $i] :
% 0.26/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.26/0.48 => ( ( subset @ X @ Z )
% 0.26/0.48 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(woz13rule2_type,type,
% 0.26/0.48 woz13rule2: $o ).
% 0.26/0.48
% 0.26/0.48 thf(woz13rule2,definition,
% 0.26/0.48 ( woz13rule2
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Z: $i] :
% 0.26/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.26/0.48 => ( ( subset @ Y @ Z )
% 0.26/0.48 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(woz13rule3_type,type,
% 0.26/0.48 woz13rule3: $o ).
% 0.26/0.48
% 0.26/0.48 thf(woz13rule3,definition,
% 0.26/0.48 ( woz13rule3
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Z: $i] :
% 0.26/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.26/0.48 => ( ( subset @ X @ Y )
% 0.26/0.48 => ( ( subset @ X @ Z )
% 0.26/0.48 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(woz13rule4_type,type,
% 0.26/0.48 woz13rule4: $o ).
% 0.26/0.48
% 0.26/0.48 thf(woz13rule4,definition,
% 0.26/0.48 ( woz13rule4
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Z: $i] :
% 0.26/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.26/0.48 => ! [W: $i] :
% 0.26/0.48 ( ( in @ W @ ( powerset @ A ) )
% 0.26/0.48 => ( ( subset @ X @ Z )
% 0.26/0.48 => ( ( subset @ Y @ W )
% 0.26/0.48 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(woz1_1_type,type,
% 0.26/0.48 woz1_1: $o ).
% 0.26/0.48
% 0.26/0.48 thf(woz1_1,definition,
% 0.26/0.48 ( woz1_1
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(woz1_2_type,type,
% 0.26/0.48 woz1_2: $o ).
% 0.26/0.48
% 0.26/0.48 thf(woz1_2,definition,
% 0.26/0.48 ( woz1_2
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Z: $i] :
% 0.26/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.26/0.48 => ! [W: $i] :
% 0.26/0.48 ( ( in @ W @ ( powerset @ A ) )
% 0.26/0.48 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 0.26/0.48 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(woz1_3_type,type,
% 0.26/0.48 woz1_3: $o ).
% 0.26/0.48
% 0.26/0.48 thf(woz1_3,definition,
% 0.26/0.48 ( woz1_3
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ! [Z: $i] :
% 0.26/0.48 ( ( in @ Z @ ( powerset @ A ) )
% 0.26/0.48 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(woz1_4_type,type,
% 0.26/0.48 woz1_4: $o ).
% 0.26/0.48
% 0.26/0.48 thf(woz1_4,definition,
% 0.26/0.48 ( woz1_4
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.26/0.48 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(woz1_5_type,type,
% 0.26/0.48 woz1_5: $o ).
% 0.26/0.48
% 0.26/0.48 thf(woz1_5,definition,
% 0.26/0.48 ( woz1_5
% 0.26/0.48 = ( ! [A: $i,X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ ( powerset @ A ) )
% 0.26/0.48 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(breln1_type,type,
% 0.26/0.48 breln1: $i > $i > $o ).
% 0.26/0.48
% 0.26/0.48 thf(breln1all2_type,type,
% 0.26/0.48 breln1all2: $o ).
% 0.26/0.48
% 0.26/0.48 thf(breln1all2,definition,
% 0.26/0.48 ( breln1all2
% 0.26/0.48 = ( ! [A: $i,R: $i] :
% 0.26/0.48 ( ( breln1 @ A @ R )
% 0.26/0.48 => ! [Xphi: $i > $o] :
% 0.26/0.48 ( ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ! [Xy: $i] :
% 0.26/0.48 ( ( in @ Xy @ A )
% 0.26/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.26/0.48 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ R )
% 0.26/0.48 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(breln1Set_type,type,
% 0.26/0.48 breln1Set: $i > $i ).
% 0.26/0.48
% 0.26/0.48 thf(breln1SetBreln1_type,type,
% 0.26/0.48 breln1SetBreln1: $o ).
% 0.26/0.48
% 0.26/0.48 thf(breln1SetBreln1,definition,
% 0.26/0.48 ( breln1SetBreln1
% 0.26/0.48 = ( ! [A: $i,R: $i] :
% 0.26/0.48 ( ( in @ R @ ( breln1Set @ A ) )
% 0.26/0.48 => ( breln1 @ A @ R ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(transitive_type,type,
% 0.26/0.48 transitive: $i > $i > $o ).
% 0.26/0.48
% 0.26/0.48 thf(antisymmetric_type,type,
% 0.26/0.48 antisymmetric: $i > $i > $o ).
% 0.26/0.48
% 0.26/0.48 thf(reflexive_type,type,
% 0.26/0.48 reflexive: $i > $i > $o ).
% 0.26/0.48
% 0.26/0.48 thf(refltransitive_type,type,
% 0.26/0.48 refltransitive: $i > $i > $o ).
% 0.26/0.48
% 0.26/0.48 thf(refllinearorder_type,type,
% 0.26/0.48 refllinearorder: $i > $i > $o ).
% 0.26/0.48
% 0.26/0.48 thf(reflwellordering_type,type,
% 0.26/0.48 reflwellordering: $i > $i > $o ).
% 0.26/0.48
% 0.26/0.48 thf(choice2fnsingleton_type,type,
% 0.26/0.48 choice2fnsingleton: $o ).
% 0.26/0.48
% 0.26/0.48 thf(choice2fnsingleton,definition,
% 0.26/0.48 ( choice2fnsingleton
% 0.26/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.26/0.48 ( ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ? [Xy: $i] :
% 0.26/0.48 ( ( in @ Xy @ B )
% 0.26/0.48 & ( Xphi @ Xx @ Xy ) ) )
% 0.26/0.48 => ! [R: $i] :
% 0.26/0.48 ( ( in @ R @ ( breln1Set @ B ) )
% 0.26/0.48 => ( ( reflwellordering @ B @ R )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( singleton
% 0.26/0.48 @ ( dsetconstr @ B
% 0.26/0.48 @ ^ [Xy: $i] :
% 0.26/0.48 ( ( Xphi @ Xx @ Xy )
% 0.26/0.48 & ! [Xz: $i] :
% 0.26/0.48 ( ( in @ Xz @ B )
% 0.26/0.48 => ( ( Xphi @ Xx @ Xz )
% 0.26/0.48 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(setOfPairsIsBReln1_type,type,
% 0.26/0.48 setOfPairsIsBReln1: $o ).
% 0.26/0.48
% 0.26/0.48 thf(setOfPairsIsBReln1,definition,
% 0.26/0.48 ( setOfPairsIsBReln1
% 0.26/0.48 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 0.26/0.48 ( breln1 @ A
% 0.26/0.48 @ ( dpsetconstr @ A @ A
% 0.26/0.48 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(breln1all1_type,type,
% 0.26/0.48 breln1all1: $o ).
% 0.26/0.48
% 0.26/0.48 thf(breln1all1,definition,
% 0.26/0.48 ( breln1all1
% 0.26/0.48 = ( ! [A: $i,R: $i] :
% 0.26/0.48 ( ( breln1 @ A @ R )
% 0.26/0.48 => ! [Xphi: $i > $o] :
% 0.26/0.48 ( ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ! [Xy: $i] :
% 0.26/0.48 ( ( in @ Xy @ A )
% 0.26/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.26/0.48 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ R )
% 0.26/0.48 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(subbreln1_type,type,
% 0.26/0.48 subbreln1: $o ).
% 0.26/0.48
% 0.26/0.48 thf(subbreln1,definition,
% 0.26/0.48 ( subbreln1
% 0.26/0.48 = ( ! [A: $i,R: $i] :
% 0.26/0.48 ( ( breln1 @ A @ R )
% 0.26/0.48 => ! [S: $i] :
% 0.26/0.48 ( ( breln1 @ A @ S )
% 0.26/0.48 => ( ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ! [Xy: $i] :
% 0.26/0.48 ( ( in @ Xy @ A )
% 0.26/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.26/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.26/0.48 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(eqbreln1_type,type,
% 0.26/0.48 eqbreln1: $o ).
% 0.26/0.48
% 0.26/0.48 thf(eqbreln1,definition,
% 0.26/0.48 ( eqbreln1
% 0.26/0.48 = ( ! [A: $i,R: $i] :
% 0.26/0.48 ( ( breln1 @ A @ R )
% 0.26/0.48 => ! [S: $i] :
% 0.26/0.48 ( ( breln1 @ A @ S )
% 0.26/0.48 => ( ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ! [Xy: $i] :
% 0.26/0.48 ( ( in @ Xy @ A )
% 0.26/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.26/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.26/0.48 => ( ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ! [Xy: $i] :
% 0.26/0.48 ( ( in @ Xy @ A )
% 0.26/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.26/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.26/0.48 => ( R = S ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(breln1invset_type,type,
% 0.26/0.48 breln1invset: $i > $i > $i ).
% 0.26/0.48
% 0.26/0.48 thf(breln1invprop_type,type,
% 0.26/0.48 breln1invprop: $o ).
% 0.26/0.48
% 0.26/0.48 thf(breln1invprop,definition,
% 0.26/0.48 ( breln1invprop
% 0.26/0.48 = ( ! [A: $i,R: $i] :
% 0.26/0.48 ( ( breln1 @ A @ R )
% 0.26/0.48 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(breln1invI_type,type,
% 0.26/0.48 breln1invI: $o ).
% 0.26/0.48
% 0.26/0.48 thf(breln1invI,definition,
% 0.26/0.48 ( breln1invI
% 0.26/0.48 = ( ! [A: $i,R: $i] :
% 0.26/0.48 ( ( breln1 @ A @ R )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ! [Xy: $i] :
% 0.26/0.48 ( ( in @ Xy @ A )
% 0.26/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.26/0.48 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(breln1invE_type,type,
% 0.26/0.48 breln1invE: $o ).
% 0.26/0.48
% 0.26/0.48 thf(breln1invE,definition,
% 0.26/0.48 ( breln1invE
% 0.26/0.48 = ( ! [A: $i,R: $i] :
% 0.26/0.48 ( ( breln1 @ A @ R )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ! [Xy: $i] :
% 0.26/0.48 ( ( in @ Xy @ A )
% 0.26/0.48 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 0.26/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(breln1compset_type,type,
% 0.26/0.48 breln1compset: $i > $i > $i > $i ).
% 0.26/0.48
% 0.26/0.48 thf(breln1compprop_type,type,
% 0.26/0.48 breln1compprop: $o ).
% 0.26/0.48
% 0.26/0.48 thf(breln1compprop,definition,
% 0.26/0.48 ( breln1compprop
% 0.26/0.48 = ( ! [A: $i,R: $i] :
% 0.26/0.48 ( ( breln1 @ A @ R )
% 0.26/0.48 => ! [S: $i] :
% 0.26/0.48 ( ( breln1 @ A @ S )
% 0.26/0.48 => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(breln1compI_type,type,
% 0.26/0.48 breln1compI: $o ).
% 0.26/0.48
% 0.26/0.48 thf(breln1compI,definition,
% 0.26/0.48 ( breln1compI
% 0.26/0.48 = ( ! [A: $i,R: $i] :
% 0.26/0.48 ( ( breln1 @ A @ R )
% 0.26/0.48 => ! [S: $i] :
% 0.26/0.48 ( ( breln1 @ A @ S )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ! [Xy: $i] :
% 0.26/0.48 ( ( in @ Xy @ A )
% 0.26/0.48 => ! [Xz: $i] :
% 0.26/0.48 ( ( in @ Xz @ A )
% 0.26/0.48 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.26/0.48 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 0.26/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(breln1compE_type,type,
% 0.26/0.48 breln1compE: $o ).
% 0.26/0.48
% 0.26/0.48 thf(breln1compE,definition,
% 0.26/0.48 ( breln1compE
% 0.26/0.48 = ( ! [A: $i,R: $i] :
% 0.26/0.48 ( ( breln1 @ A @ R )
% 0.26/0.48 => ! [S: $i] :
% 0.26/0.48 ( ( breln1 @ A @ S )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ! [Xy: $i] :
% 0.26/0.48 ( ( in @ Xy @ A )
% 0.26/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 0.26/0.48 => ? [Xz: $i] :
% 0.26/0.48 ( ( in @ Xz @ A )
% 0.26/0.48 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.26/0.48 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(breln1compEex_type,type,
% 0.26/0.48 breln1compEex: $o ).
% 0.26/0.48
% 0.26/0.48 thf(breln1compEex,definition,
% 0.26/0.48 ( breln1compEex
% 0.26/0.48 = ( ! [A: $i,R: $i] :
% 0.26/0.48 ( ( breln1 @ A @ R )
% 0.26/0.48 => ! [S: $i] :
% 0.26/0.48 ( ( breln1 @ A @ S )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ! [Xy: $i] :
% 0.26/0.48 ( ( in @ Xy @ A )
% 0.26/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 0.26/0.48 => ! [Xphi: $o] :
% 0.26/0.48 ( ! [Xz: $i] :
% 0.26/0.48 ( ( in @ Xz @ A )
% 0.26/0.48 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.26/0.48 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 0.26/0.48 => Xphi ) ) )
% 0.26/0.48 => Xphi ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(breln1unionprop_type,type,
% 0.26/0.48 breln1unionprop: $o ).
% 0.26/0.48
% 0.26/0.48 thf(breln1unionprop,definition,
% 0.26/0.48 ( breln1unionprop
% 0.26/0.48 = ( ! [A: $i,R: $i] :
% 0.26/0.48 ( ( breln1 @ A @ R )
% 0.26/0.48 => ! [S: $i] :
% 0.26/0.48 ( ( breln1 @ A @ S )
% 0.26/0.48 => ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(breln1unionIL_type,type,
% 0.26/0.48 breln1unionIL: $o ).
% 0.26/0.48
% 0.26/0.48 thf(breln1unionIL,definition,
% 0.26/0.48 ( breln1unionIL
% 0.26/0.48 = ( ! [A: $i,R: $i] :
% 0.26/0.48 ( ( breln1 @ A @ R )
% 0.26/0.48 => ! [S: $i] :
% 0.26/0.48 ( ( breln1 @ A @ S )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ! [Xy: $i] :
% 0.26/0.48 ( ( in @ Xy @ A )
% 0.26/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.26/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(breln1unionIR_type,type,
% 0.26/0.48 breln1unionIR: $o ).
% 0.26/0.48
% 0.26/0.48 thf(breln1unionIR,definition,
% 0.26/0.48 ( breln1unionIR
% 0.26/0.48 = ( ! [A: $i,R: $i] :
% 0.26/0.48 ( ( breln1 @ A @ R )
% 0.26/0.48 => ! [S: $i] :
% 0.26/0.48 ( ( breln1 @ A @ S )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ! [Xy: $i] :
% 0.26/0.48 ( ( in @ Xy @ A )
% 0.26/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.26/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(breln1unionI_type,type,
% 0.26/0.48 breln1unionI: $o ).
% 0.26/0.48
% 0.26/0.48 thf(breln1unionI,definition,
% 0.26/0.48 ( breln1unionI
% 0.26/0.48 = ( ! [A: $i,R: $i] :
% 0.26/0.48 ( ( breln1 @ A @ R )
% 0.26/0.48 => ! [S: $i] :
% 0.26/0.48 ( ( breln1 @ A @ S )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ! [Xy: $i] :
% 0.26/0.48 ( ( in @ Xy @ A )
% 0.26/0.48 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.26/0.48 | ( in @ ( kpair @ Xx @ Xy ) @ S ) )
% 0.26/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(breln1unionE_type,type,
% 0.26/0.48 breln1unionE: $o ).
% 0.26/0.48
% 0.26/0.48 thf(breln1unionE,definition,
% 0.26/0.48 ( breln1unionE
% 0.26/0.48 = ( ! [A: $i,R: $i] :
% 0.26/0.48 ( ( breln1 @ A @ R )
% 0.26/0.48 => ! [S: $i] :
% 0.26/0.48 ( ( breln1 @ A @ S )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ! [Xy: $i] :
% 0.26/0.48 ( ( in @ Xy @ A )
% 0.26/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 0.26/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.26/0.48 | ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(breln1unionEcases_type,type,
% 0.26/0.48 breln1unionEcases: $o ).
% 0.26/0.48
% 0.26/0.48 thf(breln1unionEcases,definition,
% 0.26/0.48 ( breln1unionEcases
% 0.26/0.48 = ( ! [A: $i,R: $i] :
% 0.26/0.48 ( ( breln1 @ A @ R )
% 0.26/0.48 => ! [S: $i] :
% 0.26/0.48 ( ( breln1 @ A @ S )
% 0.26/0.48 => ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ! [Xy: $i] :
% 0.26/0.48 ( ( in @ Xy @ A )
% 0.26/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 0.26/0.48 => ! [Xphi: $o] :
% 0.26/0.48 ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.26/0.48 => Xphi )
% 0.26/0.48 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.26/0.48 => Xphi )
% 0.26/0.48 => Xphi ) ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(breln1unionCommutes_type,type,
% 0.26/0.48 breln1unionCommutes: $o ).
% 0.26/0.48
% 0.26/0.48 thf(breln1unionCommutes,definition,
% 0.26/0.48 ( breln1unionCommutes
% 0.26/0.48 = ( ! [A: $i,R: $i] :
% 0.26/0.48 ( ( breln1 @ A @ R )
% 0.26/0.48 => ! [S: $i] :
% 0.26/0.48 ( ( breln1 @ A @ S )
% 0.26/0.48 => ( ( binunion @ R @ S )
% 0.26/0.48 = ( binunion @ S @ R ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(woz2Ex_type,type,
% 0.26/0.48 woz2Ex: $o ).
% 0.26/0.48
% 0.26/0.48 thf(woz2Ex,definition,
% 0.26/0.48 ( woz2Ex
% 0.26/0.48 = ( ! [A: $i,R: $i] :
% 0.26/0.48 ( ( breln1 @ A @ R )
% 0.26/0.48 => ( R
% 0.26/0.48 = ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(woz2W_type,type,
% 0.26/0.48 woz2W: $o ).
% 0.26/0.48
% 0.26/0.48 thf(woz2W,definition,
% 0.26/0.48 ( woz2W
% 0.26/0.48 = ( ! [A: $i,R: $i] :
% 0.26/0.48 ( ( breln1 @ A @ R )
% 0.26/0.48 => ! [S: $i] :
% 0.26/0.48 ( ( breln1 @ A @ S )
% 0.26/0.48 => ( ( breln1invset @ A @ ( breln1compset @ A @ R @ S ) )
% 0.26/0.48 = ( breln1compset @ A @ ( breln1invset @ A @ S ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(woz2A_type,type,
% 0.26/0.48 woz2A: $o ).
% 0.26/0.48
% 0.26/0.48 thf(woz2A,definition,
% 0.26/0.48 ( woz2A
% 0.26/0.48 = ( ! [A: $i,R: $i] :
% 0.26/0.48 ( ( breln1 @ A @ R )
% 0.26/0.48 => ! [S: $i] :
% 0.26/0.48 ( ( breln1 @ A @ S )
% 0.26/0.48 => ! [T: $i] :
% 0.26/0.48 ( ( breln1 @ A @ T )
% 0.26/0.48 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 0.26/0.48 = ( binunion @ ( breln1compset @ A @ R @ T ) @ ( breln1compset @ A @ S @ T ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(woz2B_type,type,
% 0.26/0.48 woz2B: $o ).
% 0.26/0.48
% 0.26/0.48 thf(woz2B,definition,
% 0.26/0.48 ( woz2B
% 0.26/0.48 = ( ! [A: $i,R: $i] :
% 0.26/0.48 ( ( breln1 @ A @ R )
% 0.26/0.48 => ! [S: $i] :
% 0.26/0.48 ( ( breln1 @ A @ S )
% 0.26/0.48 => ! [T: $i] :
% 0.26/0.48 ( ( breln1 @ A @ T )
% 0.26/0.48 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 0.26/0.48 = ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ S ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(image1Ex_type,type,
% 0.26/0.48 image1Ex: $o ).
% 0.26/0.48
% 0.26/0.48 thf(image1Ex,definition,
% 0.26/0.48 ( image1Ex
% 0.26/0.48 = ( ! [A: $i,Xf: $i > $i] :
% 0.26/0.48 ? [B: $i] :
% 0.26/0.48 ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ B )
% 0.26/0.48 <=> ? [Xy: $i] :
% 0.26/0.48 ( ( in @ Xy @ A )
% 0.26/0.48 & ( Xx
% 0.26/0.48 = ( Xf @ Xy ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(image1Ex1_type,type,
% 0.26/0.48 image1Ex1: $o ).
% 0.26/0.48
% 0.26/0.48 thf(image1Ex1,definition,
% 0.26/0.48 ( image1Ex1
% 0.26/0.48 = ( ! [A: $i,Xf: $i > $i] :
% 0.26/0.48 ( exu
% 0.26/0.48 @ ^ [B: $i] :
% 0.26/0.48 ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ B )
% 0.26/0.48 <=> ? [Xy: $i] :
% 0.26/0.48 ( ( in @ Xy @ A )
% 0.26/0.48 & ( Xx
% 0.26/0.48 = ( Xf @ Xy ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(image1_type,type,
% 0.26/0.48 image1: $i > ( $i > $i ) > $i ).
% 0.26/0.48
% 0.26/0.48 thf(image1Equiv_type,type,
% 0.26/0.48 image1Equiv: $o ).
% 0.26/0.48
% 0.26/0.48 thf(image1Equiv,definition,
% 0.26/0.48 ( image1Equiv
% 0.26/0.48 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 0.26/0.48 ( ( in @ Xx
% 0.26/0.48 @ ( image1 @ A
% 0.26/0.48 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 0.26/0.48 <=> ? [Xy: $i] :
% 0.26/0.48 ( ( in @ Xy @ A )
% 0.26/0.48 & ( Xx
% 0.26/0.48 = ( Xf @ Xy ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(image1E_type,type,
% 0.26/0.48 image1E: $o ).
% 0.26/0.48
% 0.26/0.48 thf(image1E,definition,
% 0.26/0.48 ( image1E
% 0.26/0.48 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 0.26/0.48 ( ( in @ Xx
% 0.26/0.48 @ ( image1 @ A
% 0.26/0.48 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 0.26/0.48 => ? [Xy: $i] :
% 0.26/0.48 ( ( in @ Xy @ A )
% 0.26/0.48 & ( Xx
% 0.26/0.48 = ( Xf @ Xy ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(image1I_type,type,
% 0.26/0.48 image1I: $o ).
% 0.26/0.48
% 0.26/0.48 thf(image1I,definition,
% 0.26/0.48 ( image1I
% 0.26/0.48 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 0.26/0.48 ( ? [Xy: $i] :
% 0.26/0.48 ( ( in @ Xy @ A )
% 0.26/0.48 & ( Xx
% 0.26/0.48 = ( Xf @ Xy ) ) )
% 0.26/0.48 => ( in @ Xx
% 0.26/0.48 @ ( image1 @ A
% 0.26/0.48 @ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(injective_type,type,
% 0.26/0.48 injective: $i > $i > $i > $o ).
% 0.26/0.48
% 0.26/0.48 thf(injFuncSet_type,type,
% 0.26/0.48 injFuncSet: $i > $i > $i ).
% 0.26/0.48
% 0.26/0.48 thf(injFuncInInjFuncSet_type,type,
% 0.26/0.48 injFuncInInjFuncSet: $o ).
% 0.26/0.48
% 0.26/0.48 thf(injFuncInInjFuncSet,definition,
% 0.26/0.48 ( injFuncInInjFuncSet
% 0.26/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.26/0.48 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.26/0.48 => ( ( injective @ A @ B @ Xf )
% 0.26/0.48 => ( in @ Xf @ ( injFuncSet @ A @ B ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(injFuncSetFuncIn_type,type,
% 0.26/0.48 injFuncSetFuncIn: $o ).
% 0.26/0.48
% 0.26/0.48 thf(injFuncSetFuncIn,definition,
% 0.26/0.48 ( injFuncSetFuncIn
% 0.26/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.26/0.48 ( ( in @ Xf @ ( injFuncSet @ A @ B ) )
% 0.26/0.48 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(injFuncSetFuncInj_type,type,
% 0.26/0.48 injFuncSetFuncInj: $o ).
% 0.26/0.48
% 0.26/0.48 thf(injFuncSetFuncInj,definition,
% 0.26/0.48 ( injFuncSetFuncInj
% 0.26/0.48 = ( ! [Xx: $i,Xy: $i,Xf: $i] :
% 0.26/0.48 ( ( in @ Xf @ ( injFuncSet @ Xx @ Xy ) )
% 0.26/0.48 => ( injective @ Xx @ Xy @ Xf ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(surjective_type,type,
% 0.26/0.48 surjective: $i > $i > $i > $o ).
% 0.26/0.48
% 0.26/0.48 thf(surjFuncSet_type,type,
% 0.26/0.48 surjFuncSet: $i > $i > $i ).
% 0.26/0.48
% 0.26/0.48 thf(surjFuncSetFuncIn_type,type,
% 0.26/0.48 surjFuncSetFuncIn: $o ).
% 0.26/0.48
% 0.26/0.48 thf(surjFuncSetFuncIn,definition,
% 0.26/0.48 ( surjFuncSetFuncIn
% 0.26/0.48 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.26/0.48 ( ( in @ Xf @ ( surjFuncSet @ A @ B ) )
% 0.26/0.48 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(surjFuncSetFuncSurj_type,type,
% 0.26/0.48 surjFuncSetFuncSurj: $o ).
% 0.26/0.48
% 0.26/0.48 thf(surjFuncSetFuncSurj,definition,
% 0.26/0.48 ( surjFuncSetFuncSurj
% 0.26/0.48 = ( ! [Xx: $i,Xy: $i,Xf: $i] :
% 0.26/0.48 ( ( in @ Xf @ ( surjFuncSet @ Xx @ Xy ) )
% 0.26/0.48 => ( surjective @ Xx @ Xy @ Xf ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(leftInvIsSurj_type,type,
% 0.26/0.48 leftInvIsSurj: $o ).
% 0.26/0.48
% 0.26/0.48 thf(leftInvIsSurj,definition,
% 0.26/0.48 ( leftInvIsSurj
% 0.26/0.48 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.26/0.48 ( ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.26/0.48 => ! [Xg: $i] :
% 0.26/0.48 ( ( in @ Xg @ ( funcSet @ B @ A ) )
% 0.26/0.48 => ( ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ( ( ap @ B @ A @ Xg @ ( Xf @ Xx ) )
% 0.26/0.48 = Xx ) )
% 0.26/0.48 => ( surjective @ B @ A @ Xg ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(surjCantorThm_type,type,
% 0.26/0.48 surjCantorThm: $o ).
% 0.26/0.48
% 0.26/0.48 thf(surjCantorThm,definition,
% 0.26/0.48 ( surjCantorThm
% 0.26/0.48 = ( ! [A: $i,Xf: $i] :
% 0.26/0.48 ( ( in @ Xf @ ( funcSet @ A @ ( powerset @ A ) ) )
% 0.26/0.48 => ~ ( surjective @ A @ ( powerset @ A ) @ Xf ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(foundation2_type,type,
% 0.26/0.48 foundation2: $o ).
% 0.26/0.48
% 0.26/0.48 thf(foundation2,definition,
% 0.26/0.48 ( foundation2
% 0.26/0.48 = ( ! [A: $i] :
% 0.26/0.48 ( ( nonempty @ A )
% 0.26/0.48 => ? [X: $i] :
% 0.26/0.48 ( ( in @ X @ A )
% 0.26/0.48 & ( ( binintersect @ X @ A )
% 0.26/0.48 = emptyset ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(notinself_type,type,
% 0.26/0.48 notinself: $o ).
% 0.26/0.48
% 0.26/0.48 thf(notinself,definition,
% 0.26/0.48 ( notinself
% 0.26/0.48 = ( ! [A: $i] :
% 0.26/0.48 ~ ( in @ A @ A ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(notinself2_type,type,
% 0.26/0.48 notinself2: $o ).
% 0.26/0.48
% 0.26/0.48 thf(notinself2,definition,
% 0.26/0.48 ( notinself2
% 0.26/0.48 = ( ! [A: $i,B: $i] :
% 0.26/0.48 ( ( in @ A @ B )
% 0.26/0.48 => ~ ( in @ B @ A ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(omegaS_type,type,
% 0.26/0.48 omegaS: $i > $i ).
% 0.26/0.48
% 0.26/0.48 thf(omegaSp_type,type,
% 0.26/0.48 omegaSp: $o ).
% 0.26/0.48
% 0.26/0.48 thf(omegaSp,definition,
% 0.26/0.48 ( omegaSp
% 0.26/0.48 = ( ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ omega )
% 0.26/0.48 => ( in @ ( omegaS @ Xx ) @ omega ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(omegaSclos_type,type,
% 0.26/0.48 omegaSclos: $o ).
% 0.26/0.48
% 0.26/0.48 thf(omegaSclos,definition,
% 0.26/0.48 ( omegaSclos
% 0.26/0.48 = ( ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ omega )
% 0.26/0.48 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(peano0notS_type,type,
% 0.26/0.48 peano0notS: $o ).
% 0.26/0.48
% 0.26/0.48 thf(peano0notS,definition,
% 0.26/0.48 ( peano0notS
% 0.26/0.48 = ( ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ omega )
% 0.26/0.48 => ( ( omegaS @ Xx )
% 0.26/0.48 != emptyset ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(peano3_type,type,
% 0.26/0.48 peano3: $i > $i > $i > $o ).
% 0.26/0.48
% 0.26/0.48 thf(peano4_type,type,
% 0.26/0.48 peano4: $i > $i > $i > $o ).
% 0.26/0.48
% 0.26/0.48 thf(peano5_type,type,
% 0.26/0.48 peano5: $i > $i > $i > $o ).
% 0.26/0.48
% 0.26/0.48 thf(peanoSinj_type,type,
% 0.26/0.48 peanoSinj: $o ).
% 0.26/0.48
% 0.26/0.48 thf(peanoSinj,definition,
% 0.26/0.48 ( peanoSinj
% 0.26/0.48 = ( ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ omega )
% 0.26/0.48 => ! [Xy: $i] :
% 0.26/0.48 ( ( in @ Xy @ omega )
% 0.26/0.48 => ( ( ( omegaS @ Xx )
% 0.26/0.48 = ( omegaS @ Xy ) )
% 0.26/0.48 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(peano_type,type,
% 0.26/0.48 peano: $i > $i > $i > $o ).
% 0.26/0.48
% 0.26/0.48 thf(transitiveset_type,type,
% 0.26/0.48 transitiveset: $i > $o ).
% 0.26/0.48
% 0.26/0.48 thf(transitiveset,definition,
% 0.26/0.48 ( transitiveset
% 0.26/0.48 = ( ^ [A: $i] :
% 0.26/0.48 ! [X: $i] :
% 0.26/0.48 ( ( in @ X @ A )
% 0.26/0.48 => ( subset @ X @ A ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(transitivesetOp1_type,type,
% 0.26/0.48 transitivesetOp1: $o ).
% 0.26/0.48
% 0.26/0.48 thf(transitivesetOp1,definition,
% 0.26/0.48 ( transitivesetOp1
% 0.26/0.48 = ( ! [X: $i] :
% 0.26/0.48 ( ( transitiveset @ X )
% 0.26/0.48 => ! [A: $i] :
% 0.26/0.48 ( ( in @ A @ X )
% 0.26/0.48 => ( subset @ A @ X ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(binintTransitive_type,type,
% 0.26/0.48 binintTransitive: $o ).
% 0.26/0.48
% 0.26/0.48 thf(binintTransitive,definition,
% 0.26/0.48 ( binintTransitive
% 0.26/0.48 = ( ! [X: $i] :
% 0.26/0.48 ( ( transitiveset @ X )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( transitiveset @ Y )
% 0.26/0.48 => ( transitiveset @ ( binintersect @ X @ Y ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(transitivesetOp2,conjecture,
% 0.26/0.48 ( setextAx
% 0.26/0.48 => ( emptysetAx
% 0.26/0.48 => ( setadjoinAx
% 0.26/0.48 => ( powersetAx
% 0.26/0.48 => ( setunionAx
% 0.26/0.48 => ( omega0Ax
% 0.26/0.48 => ( omegaSAx
% 0.26/0.48 => ( omegaIndAx
% 0.26/0.48 => ( replAx
% 0.26/0.48 => ( foundationAx
% 0.26/0.48 => ( wellorderingAx
% 0.26/0.48 => ( descrp
% 0.26/0.48 => ( dsetconstrI
% 0.26/0.48 => ( dsetconstrEL
% 0.26/0.48 => ( dsetconstrER
% 0.26/0.48 => ( exuE1
% 0.26/0.48 => ( prop2setE
% 0.26/0.48 => ( emptysetE
% 0.26/0.48 => ( emptysetimpfalse
% 0.26/0.48 => ( notinemptyset
% 0.26/0.48 => ( exuE3e
% 0.26/0.48 => ( setext
% 0.26/0.48 => ( emptyI
% 0.26/0.48 => ( noeltsimpempty
% 0.26/0.48 => ( setbeta
% 0.26/0.48 => ( nonemptyE1
% 0.26/0.48 => ( nonemptyI
% 0.26/0.48 => ( nonemptyI1
% 0.26/0.48 => ( setadjoinIL
% 0.26/0.48 => ( emptyinunitempty
% 0.26/0.48 => ( setadjoinIR
% 0.26/0.48 => ( setadjoinE
% 0.26/0.48 => ( setadjoinOr
% 0.26/0.48 => ( setoftrueEq
% 0.26/0.48 => ( powersetI
% 0.26/0.48 => ( emptyinPowerset
% 0.26/0.48 => ( emptyInPowerset
% 0.26/0.48 => ( powersetE
% 0.26/0.48 => ( setunionI
% 0.26/0.48 => ( setunionE
% 0.26/0.48 => ( subPowSU
% 0.26/0.48 => ( exuE2
% 0.26/0.48 => ( nonemptyImpWitness
% 0.26/0.48 => ( uniqinunit
% 0.26/0.48 => ( notinsingleton
% 0.26/0.48 => ( eqinunit
% 0.26/0.48 => ( singletonsswitch
% 0.26/0.48 => ( upairsetE
% 0.26/0.48 => ( upairsetIL
% 0.26/0.48 => ( upairsetIR
% 0.26/0.48 => ( emptyE1
% 0.26/0.48 => ( vacuousDall
% 0.26/0.48 => ( quantDeMorgan1
% 0.26/0.48 => ( quantDeMorgan2
% 0.26/0.48 => ( quantDeMorgan3
% 0.26/0.48 => ( quantDeMorgan4
% 0.26/0.48 => ( prop2setI
% 0.26/0.48 => ( prop2set2propI
% 0.26/0.48 => ( notdexE
% 0.26/0.48 => ( notdallE
% 0.26/0.48 => ( exuI1
% 0.26/0.48 => ( exuI3
% 0.26/0.48 => ( exuI2
% 0.26/0.48 => ( inCongP
% 0.26/0.48 => ( in__Cong
% 0.26/0.48 => ( exuE3u
% 0.26/0.48 => ( exu__Cong
% 0.26/0.48 => ( emptyset__Cong
% 0.26/0.48 => ( setadjoin__Cong
% 0.26/0.48 => ( powerset__Cong
% 0.26/0.48 => ( setunion__Cong
% 0.26/0.48 => ( omega__Cong
% 0.26/0.48 => ( exuEu
% 0.26/0.48 => ( descr__Cong
% 0.26/0.48 => ( dsetconstr__Cong
% 0.26/0.48 => ( subsetI1
% 0.26/0.48 => ( eqimpsubset2
% 0.26/0.48 => ( eqimpsubset1
% 0.26/0.48 => ( subsetI2
% 0.26/0.48 => ( emptysetsubset
% 0.26/0.48 => ( subsetE
% 0.26/0.48 => ( subsetE2
% 0.26/0.48 => ( notsubsetI
% 0.26/0.48 => ( notequalI1
% 0.26/0.48 => ( notequalI2
% 0.26/0.48 => ( subsetRefl
% 0.26/0.48 => ( subsetTrans
% 0.26/0.48 => ( setadjoinSub
% 0.26/0.48 => ( setadjoinSub2
% 0.26/0.48 => ( subset2powerset
% 0.26/0.48 => ( setextsub
% 0.26/0.48 => ( subsetemptysetimpeq
% 0.26/0.48 => ( powersetI1
% 0.26/0.48 => ( powersetE1
% 0.26/0.48 => ( inPowerset
% 0.26/0.48 => ( powersetsubset
% 0.26/0.48 => ( sepInPowerset
% 0.26/0.48 => ( sepSubset
% 0.26/0.48 => ( binunionIL
% 0.26/0.48 => ( upairset2IR
% 0.26/0.48 => ( binunionIR
% 0.26/0.48 => ( binunionEcases
% 0.26/0.48 => ( binunionE
% 0.26/0.48 => ( binunionLsub
% 0.26/0.48 => ( binunionRsub
% 0.26/0.48 => ( binintersectI
% 0.26/0.48 => ( binintersectSubset5
% 0.26/0.48 => ( binintersectEL
% 0.26/0.48 => ( binintersectLsub
% 0.26/0.48 => ( binintersectSubset2
% 0.26/0.48 => ( binintersectSubset3
% 0.26/0.48 => ( binintersectER
% 0.26/0.48 => ( disjointsetsI1
% 0.26/0.48 => ( binintersectRsub
% 0.26/0.48 => ( binintersectSubset4
% 0.26/0.48 => ( binintersectSubset1
% 0.26/0.48 => ( bs114d
% 0.26/0.48 => ( setminusI
% 0.26/0.48 => ( setminusEL
% 0.26/0.48 => ( setminusER
% 0.26/0.48 => ( setminusSubset2
% 0.26/0.48 => ( setminusERneg
% 0.26/0.48 => ( setminusELneg
% 0.26/0.48 => ( setminusILneg
% 0.26/0.48 => ( setminusIRneg
% 0.26/0.48 => ( setminusLsub
% 0.26/0.48 => ( setminusSubset1
% 0.26/0.48 => ( symdiffE
% 0.26/0.48 => ( symdiffI1
% 0.26/0.48 => ( symdiffI2
% 0.26/0.48 => ( symdiffIneg1
% 0.26/0.48 => ( symdiffIneg2
% 0.26/0.48 => ( secondinupair
% 0.26/0.48 => ( setukpairIL
% 0.26/0.48 => ( setukpairIR
% 0.26/0.48 => ( kpairiskpair
% 0.26/0.48 => ( kpairp
% 0.26/0.48 => ( singletonsubset
% 0.26/0.48 => ( singletoninpowerset
% 0.26/0.48 => ( singletoninpowunion
% 0.26/0.48 => ( upairset2E
% 0.26/0.48 => ( upairsubunion
% 0.26/0.48 => ( upairinpowunion
% 0.26/0.48 => ( ubforcartprodlem1
% 0.26/0.48 => ( ubforcartprodlem2
% 0.26/0.48 => ( ubforcartprodlem3
% 0.26/0.48 => ( cartprodpairin
% 0.26/0.48 => ( cartprodmempair1
% 0.26/0.48 => ( cartprodmempair
% 0.26/0.48 => ( setunionE2
% 0.26/0.48 => ( setunionsingleton1
% 0.26/0.48 => ( setunionsingleton2
% 0.26/0.48 => ( setunionsingleton
% 0.26/0.48 => ( singletonprop
% 0.26/0.48 => ( ex1E1
% 0.26/0.48 => ( ex1I
% 0.26/0.48 => ( ex1I2
% 0.26/0.48 => ( singletonsuniq
% 0.26/0.48 => ( setukpairinjL1
% 0.26/0.48 => ( kfstsingleton
% 0.26/0.48 => ( theprop
% 0.26/0.48 => ( kfstpairEq
% 0.26/0.48 => ( cartprodfstin
% 0.26/0.48 => ( setukpairinjL2
% 0.26/0.48 => ( setukpairinjL
% 0.26/0.48 => ( setukpairinjR11
% 0.26/0.48 => ( setukpairinjR12
% 0.26/0.48 => ( setukpairinjR1
% 0.26/0.48 => ( upairequniteq
% 0.26/0.48 => ( setukpairinjR2
% 0.26/0.48 => ( setukpairinjR
% 0.26/0.48 => ( ksndsingleton
% 0.26/0.48 => ( ksndpairEq
% 0.26/0.48 => ( kpairsurjEq
% 0.26/0.48 => ( cartprodsndin
% 0.26/0.48 => ( cartprodpairmemEL
% 0.26/0.48 => ( cartprodpairmemER
% 0.26/0.48 => ( cartprodmempaircEq
% 0.26/0.48 => ( cartprodfstpairEq
% 0.26/0.48 => ( cartprodsndpairEq
% 0.26/0.48 => ( cartprodpairsurjEq
% 0.26/0.48 => ( dpsetconstrI
% 0.26/0.48 => ( dpsetconstrSub
% 0.26/0.48 => ( setOfPairsIsBReln
% 0.26/0.48 => ( dpsetconstrERa
% 0.26/0.48 => ( dpsetconstrEL1
% 0.26/0.48 => ( dpsetconstrEL2
% 0.26/0.48 => ( dpsetconstrER
% 0.26/0.48 => ( funcImageSingleton
% 0.26/0.48 => ( apProp
% 0.26/0.48 => ( app
% 0.26/0.48 => ( infuncsetfunc
% 0.26/0.48 => ( ap2p
% 0.26/0.48 => ( funcinfuncset
% 0.26/0.48 => ( lamProp
% 0.26/0.48 => ( lamp
% 0.26/0.48 => ( lam2p
% 0.26/0.48 => ( brelnall1
% 0.26/0.48 => ( brelnall2
% 0.26/0.48 => ( ex1E2
% 0.26/0.48 => ( funcGraphProp1
% 0.26/0.48 => ( funcGraphProp3
% 0.26/0.48 => ( funcGraphProp2
% 0.26/0.48 => ( funcextLem
% 0.26/0.48 => ( funcGraphProp4
% 0.26/0.48 => ( subbreln
% 0.26/0.48 => ( eqbreln
% 0.26/0.48 => ( funcext
% 0.26/0.48 => ( funcext2
% 0.26/0.48 => ( ap2apEq1
% 0.26/0.48 => ( ap2apEq2
% 0.26/0.48 => ( beta1
% 0.26/0.48 => ( eta1
% 0.26/0.48 => ( lam2lamEq
% 0.26/0.48 => ( beta2
% 0.26/0.48 => ( eta2
% 0.26/0.48 => ( iffalseProp1
% 0.26/0.48 => ( iffalseProp2
% 0.26/0.48 => ( iftrueProp1
% 0.26/0.48 => ( iftrueProp2
% 0.26/0.48 => ( ifSingleton
% 0.26/0.48 => ( ifp
% 0.26/0.48 => ( theeq
% 0.26/0.48 => ( iftrue
% 0.26/0.48 => ( iffalse
% 0.26/0.48 => ( iftrueorfalse
% 0.26/0.48 => ( binintersectT_lem
% 0.26/0.48 => ( binunionT_lem
% 0.26/0.48 => ( powersetT_lem
% 0.26/0.48 => ( setminusT_lem
% 0.26/0.48 => ( complementT_lem
% 0.26/0.48 => ( setextT
% 0.26/0.48 => ( subsetTI
% 0.26/0.48 => ( powersetTI1
% 0.26/0.48 => ( powersetTE1
% 0.26/0.48 => ( complementTI1
% 0.26/0.48 => ( complementTE1
% 0.26/0.48 => ( binintersectTELcontra
% 0.26/0.48 => ( binintersectTERcontra
% 0.26/0.48 => ( contrasubsetT
% 0.26/0.48 => ( contrasubsetT1
% 0.26/0.48 => ( contrasubsetT2
% 0.26/0.48 => ( contrasubsetT3
% 0.26/0.48 => ( doubleComplementI1
% 0.26/0.48 => ( doubleComplementE1
% 0.26/0.48 => ( doubleComplementSub1
% 0.26/0.48 => ( doubleComplementSub2
% 0.26/0.48 => ( doubleComplementEq
% 0.26/0.48 => ( complementTnotintersectT
% 0.26/0.48 => ( complementImpComplementIntersect
% 0.26/0.48 => ( complementSubsetComplementIntersect
% 0.26/0.48 => ( complementInPowersetComplementIntersect
% 0.26/0.48 => ( contraSubsetComplement
% 0.26/0.48 => ( complementTcontraSubset
% 0.26/0.48 => ( binunionTILcontra
% 0.26/0.48 => ( binunionTIRcontra
% 0.26/0.48 => ( inIntersectImpInUnion
% 0.26/0.48 => ( inIntersectImpInUnion2
% 0.26/0.48 => ( inIntersectImpInIntersectUnions
% 0.26/0.48 => ( intersectInPowersetIntersectUnions
% 0.26/0.48 => ( inComplementUnionImpNotIn1
% 0.26/0.48 => ( inComplementUnionImpInComplement1
% 0.26/0.48 => ( binunionTE
% 0.26/0.48 => ( binunionTEcontra
% 0.26/0.48 => ( demorgan2a1
% 0.26/0.48 => ( complementUnionInPowersetComplement
% 0.26/0.48 => ( demorgan2a2
% 0.26/0.48 => ( demorgan1a
% 0.26/0.48 => ( demorgan1b
% 0.26/0.48 => ( demorgan1
% 0.26/0.48 => ( demorgan2a
% 0.26/0.48 => ( demorgan2b2
% 0.26/0.48 => ( demorgan2b
% 0.26/0.48 => ( demorgan2
% 0.26/0.48 => ( woz13rule0
% 0.26/0.48 => ( woz13rule1
% 0.26/0.48 => ( woz13rule2
% 0.26/0.48 => ( woz13rule3
% 0.26/0.48 => ( woz13rule4
% 0.26/0.48 => ( woz1_1
% 0.26/0.48 => ( woz1_2
% 0.26/0.48 => ( woz1_3
% 0.26/0.48 => ( woz1_4
% 0.26/0.48 => ( woz1_5
% 0.26/0.48 => ( breln1all2
% 0.26/0.48 => ( breln1SetBreln1
% 0.26/0.48 => ( choice2fnsingleton
% 0.26/0.48 => ( setOfPairsIsBReln1
% 0.26/0.48 => ( breln1all1
% 0.26/0.48 => ( subbreln1
% 0.26/0.48 => ( eqbreln1
% 0.26/0.48 => ( breln1invprop
% 0.26/0.48 => ( breln1invI
% 0.26/0.48 => ( breln1invE
% 0.26/0.48 => ( breln1compprop
% 0.26/0.48 => ( breln1compI
% 0.26/0.48 => ( breln1compE
% 0.26/0.48 => ( breln1compEex
% 0.26/0.48 => ( breln1unionprop
% 0.26/0.48 => ( breln1unionIL
% 0.26/0.48 => ( breln1unionIR
% 0.26/0.48 => ( breln1unionI
% 0.26/0.48 => ( breln1unionE
% 0.26/0.48 => ( breln1unionEcases
% 0.26/0.48 => ( breln1unionCommutes
% 0.26/0.48 => ( woz2Ex
% 0.26/0.48 => ( woz2W
% 0.26/0.48 => ( woz2A
% 0.26/0.48 => ( woz2B
% 0.26/0.48 => ( image1Ex
% 0.26/0.48 => ( image1Ex1
% 0.26/0.48 => ( image1Equiv
% 0.26/0.48 => ( image1E
% 0.26/0.48 => ( image1I
% 0.26/0.48 => ( injFuncInInjFuncSet
% 0.26/0.48 => ( injFuncSetFuncIn
% 0.26/0.48 => ( injFuncSetFuncInj
% 0.26/0.48 => ( surjFuncSetFuncIn
% 0.26/0.48 => ( surjFuncSetFuncSurj
% 0.26/0.48 => ( leftInvIsSurj
% 0.26/0.48 => ( surjCantorThm
% 0.26/0.48 => ( foundation2
% 0.26/0.48 => ( notinself
% 0.26/0.48 => ( notinself2
% 0.26/0.48 => ( omegaSp
% 0.26/0.48 => ( omegaSclos
% 0.26/0.48 => ( peano0notS
% 0.26/0.48 => ( peanoSinj
% 0.26/0.48 => ( transitivesetOp1
% 0.26/0.48 => ( binintTransitive
% 0.26/0.48 => ! [X: $i] :
% 0.26/0.48 ( ( transitiveset @ X )
% 0.26/0.48 => ! [A: $i,Xx: $i] :
% 0.26/0.48 ( ( in @ A @ X )
% 0.26/0.48 => ( ( in @ Xx @ A )
% 0.26/0.48 => ( in @ Xx @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 %------------------------------------------------------------------------------
% 0.26/0.48 ------------------------
% 3.03/1.56 ---- Embedded in THF ---
% 3.03/1.56 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.03/1.56 %%% Generated on Tue Feb 24 12:35:04 EST 2026
% 3.03/1.56 %%% using '$$dhol' embedding, version 1.3.0.
% 3.03/1.56 %%% Logic specification used:
% 3.03/1.56 %%% thf(spec, logic, $$dhol).
% 3.03/1.56
% 3.03/1.56 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.zuy6gBFKOi/DTF2DTF17963.p
% See solution above
% 3.03/1.56 ------------------------
% 3.11/1.64 ---- Cleaned THF ---
% 3.11/1.64 thf(in_type,type,
% 3.11/1.64 in: $i > $i > $o ).
% 3.11/1.64
% 3.11/1.64 thf(exu_type,type,
% 3.11/1.64 exu: ( $i > $o ) > $o ).
% 3.11/1.64
% 3.11/1.64 thf(exu,definition,
% 3.11/1.64 ( exu
% 3.11/1.64 = ( ^ [Xphi: $i > $o] :
% 3.11/1.64 ? [Xx: $i] :
% 3.11/1.64 ( ( Xphi @ Xx )
% 3.11/1.64 & ! [Xy: $i] :
% 3.11/1.64 ( ( Xphi @ Xy )
% 3.11/1.64 => ( Xx = Xy ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(setextAx_type,type,
% 3.11/1.64 setextAx: $o ).
% 3.11/1.64
% 3.11/1.64 thf(setextAx,definition,
% 3.11/1.64 ( setextAx
% 3.11/1.64 = ( ! [A: $i,B: $i] :
% 3.11/1.64 ( ! [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ A )
% 3.11/1.64 <=> ( in @ Xx @ B ) )
% 3.11/1.64 => ( A = B ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(emptyset_type,type,
% 3.11/1.64 emptyset: $i ).
% 3.11/1.64
% 3.11/1.64 thf(emptysetAx_type,type,
% 3.11/1.64 emptysetAx: $o ).
% 3.11/1.64
% 3.11/1.64 thf(emptysetAx,definition,
% 3.11/1.64 ( emptysetAx
% 3.11/1.64 = ( ! [Xx: $i] :
% 3.11/1.64 ~ ( in @ Xx @ emptyset ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(setadjoin_type,type,
% 3.11/1.64 setadjoin: $i > $i > $i ).
% 3.11/1.64
% 3.11/1.64 thf(setadjoinAx_type,type,
% 3.11/1.64 setadjoinAx: $o ).
% 3.11/1.64
% 3.11/1.64 thf(setadjoinAx,definition,
% 3.11/1.64 ( setadjoinAx
% 3.11/1.64 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.11/1.64 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.11/1.64 <=> ( ( Xy = Xx )
% 3.11/1.64 | ( in @ Xy @ A ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(powerset_type,type,
% 3.11/1.64 powerset: $i > $i ).
% 3.11/1.64
% 3.11/1.64 thf(powersetAx_type,type,
% 3.11/1.64 powersetAx: $o ).
% 3.11/1.64
% 3.11/1.64 thf(powersetAx,definition,
% 3.11/1.64 ( powersetAx
% 3.11/1.64 = ( ! [A: $i,B: $i] :
% 3.11/1.64 ( ( in @ B @ ( powerset @ A ) )
% 3.11/1.64 <=> ! [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ B )
% 3.11/1.64 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(setunion_type,type,
% 3.11/1.64 setunion: $i > $i ).
% 3.11/1.64
% 3.11/1.64 thf(setunionAx_type,type,
% 3.11/1.64 setunionAx: $o ).
% 3.11/1.64
% 3.11/1.64 thf(setunionAx,definition,
% 3.11/1.64 ( setunionAx
% 3.11/1.64 = ( ! [A: $i,Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ ( setunion @ A ) )
% 3.11/1.64 <=> ? [B: $i] :
% 3.11/1.64 ( ( in @ Xx @ B )
% 3.11/1.64 & ( in @ B @ A ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(omega_type,type,
% 3.11/1.64 omega: $i ).
% 3.11/1.64
% 3.11/1.64 thf(omega0Ax_type,type,
% 3.11/1.64 omega0Ax: $o ).
% 3.11/1.64
% 3.11/1.64 thf(omega0Ax,definition,
% 3.11/1.64 ( omega0Ax
% 3.11/1.64 = ( in @ emptyset @ omega ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(omegaSAx_type,type,
% 3.11/1.64 omegaSAx: $o ).
% 3.11/1.64
% 3.11/1.64 thf(omegaSAx,definition,
% 3.11/1.64 ( omegaSAx
% 3.11/1.64 = ( ! [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ omega )
% 3.11/1.64 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(omegaIndAx_type,type,
% 3.11/1.64 omegaIndAx: $o ).
% 3.11/1.64
% 3.11/1.64 thf(omegaIndAx,definition,
% 3.11/1.64 ( omegaIndAx
% 3.11/1.64 = ( ! [A: $i] :
% 3.11/1.64 ( ( ( in @ emptyset @ A )
% 3.11/1.64 & ! [Xx: $i] :
% 3.11/1.64 ( ( ( in @ Xx @ omega )
% 3.11/1.64 & ( in @ Xx @ A ) )
% 3.11/1.64 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 3.11/1.64 => ! [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ omega )
% 3.11/1.64 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(replAx_type,type,
% 3.11/1.64 replAx: $o ).
% 3.11/1.64
% 3.11/1.64 thf(replAx,definition,
% 3.11/1.64 ( replAx
% 3.11/1.64 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 3.11/1.64 ( ! [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ A )
% 3.11/1.64 => ( exu
% 3.11/1.64 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 3.11/1.64 => ? [B: $i] :
% 3.11/1.64 ! [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ B )
% 3.11/1.64 <=> ? [Xy: $i] :
% 3.11/1.64 ( ( in @ Xy @ A )
% 3.11/1.64 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(foundationAx_type,type,
% 3.11/1.64 foundationAx: $o ).
% 3.11/1.64
% 3.11/1.64 thf(foundationAx,definition,
% 3.11/1.64 ( foundationAx
% 3.11/1.64 = ( ! [A: $i] :
% 3.11/1.64 ( ? [Xx: $i] : ( in @ Xx @ A )
% 3.11/1.64 => ? [B: $i] :
% 3.11/1.64 ( ( in @ B @ A )
% 3.11/1.64 & ~ ? [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ B )
% 3.11/1.64 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(wellorderingAx_type,type,
% 3.11/1.64 wellorderingAx: $o ).
% 3.11/1.64
% 3.11/1.64 thf(wellorderingAx,definition,
% 3.11/1.64 ( wellorderingAx
% 3.11/1.64 = ( ! [A: $i] :
% 3.11/1.64 ? [B: $i] :
% 3.11/1.64 ( ! [C: $i] :
% 3.11/1.64 ( ( in @ C @ B )
% 3.11/1.64 => ! [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ C )
% 3.11/1.64 => ( in @ Xx @ A ) ) )
% 3.11/1.64 & ! [Xx: $i,Xy: $i] :
% 3.11/1.64 ( ( ( in @ Xx @ A )
% 3.11/1.64 & ( in @ Xy @ A ) )
% 3.11/1.64 => ( ! [C: $i] :
% 3.11/1.64 ( ( in @ C @ B )
% 3.11/1.64 => ( ( in @ Xx @ C )
% 3.11/1.64 <=> ( in @ Xy @ C ) ) )
% 3.11/1.64 => ( Xx = Xy ) ) )
% 3.11/1.64 & ! [C: $i,D: $i] :
% 3.11/1.64 ( ( ( in @ C @ B )
% 3.11/1.64 & ( in @ D @ B ) )
% 3.11/1.64 => ( ! [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ C )
% 3.11/1.64 => ( in @ Xx @ D ) )
% 3.11/1.64 | ! [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ D )
% 3.11/1.64 => ( in @ Xx @ C ) ) ) )
% 3.11/1.64 & ! [C: $i] :
% 3.11/1.64 ( ( ! [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ C )
% 3.11/1.64 => ( in @ Xx @ A ) )
% 3.11/1.64 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 3.11/1.64 => ? [D: $i,Xx: $i] :
% 3.11/1.64 ( ( in @ D @ B )
% 3.11/1.64 & ( in @ Xx @ C )
% 3.11/1.64 & ~ ? [Xy: $i] :
% 3.11/1.64 ( ( in @ Xy @ D )
% 3.11/1.64 & ( in @ Xy @ C ) )
% 3.11/1.64 & ! [E: $i] :
% 3.11/1.64 ( ( in @ E @ B )
% 3.11/1.64 => ( ! [Xy: $i] :
% 3.11/1.64 ( ( in @ Xy @ E )
% 3.11/1.64 => ( in @ Xy @ D ) )
% 3.11/1.64 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(descr_type,type,
% 3.11/1.64 descr: ( $i > $o ) > $i ).
% 3.11/1.64
% 3.11/1.64 thf(descrp_type,type,
% 3.11/1.64 descrp: $o ).
% 3.11/1.64
% 3.11/1.64 thf(descrp,definition,
% 3.11/1.64 ( descrp
% 3.11/1.64 = ( ! [Xphi: $i > $o] :
% 3.11/1.64 ( ( exu
% 3.11/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.11/1.64 => ( Xphi
% 3.11/1.64 @ ( descr
% 3.11/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(dsetconstr_type,type,
% 3.11/1.64 dsetconstr: $i > ( $i > $o ) > $i ).
% 3.11/1.64
% 3.11/1.64 thf(dsetconstrI_type,type,
% 3.11/1.64 dsetconstrI: $o ).
% 3.11/1.64
% 3.11/1.64 thf(dsetconstrI,definition,
% 3.11/1.64 ( dsetconstrI
% 3.11/1.64 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ A )
% 3.11/1.64 => ( ( Xphi @ Xx )
% 3.11/1.64 => ( in @ Xx
% 3.11/1.64 @ ( dsetconstr @ A
% 3.11/1.64 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(dsetconstrEL_type,type,
% 3.11/1.64 dsetconstrEL: $o ).
% 3.11/1.64
% 3.11/1.64 thf(dsetconstrEL,definition,
% 3.11/1.64 ( dsetconstrEL
% 3.11/1.64 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.11/1.64 ( ( in @ Xx
% 3.11/1.64 @ ( dsetconstr @ A
% 3.11/1.64 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.11/1.64 => ( in @ Xx @ A ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(dsetconstrER_type,type,
% 3.11/1.64 dsetconstrER: $o ).
% 3.11/1.64
% 3.11/1.64 thf(dsetconstrER,definition,
% 3.11/1.64 ( dsetconstrER
% 3.11/1.64 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.11/1.64 ( ( in @ Xx
% 3.11/1.64 @ ( dsetconstr @ A
% 3.11/1.64 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.11/1.64 => ( Xphi @ Xx ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(exuE1_type,type,
% 3.11/1.64 exuE1: $o ).
% 3.11/1.64
% 3.11/1.64 thf(exuE1,definition,
% 3.11/1.64 ( exuE1
% 3.11/1.64 = ( ! [Xphi: $i > $o] :
% 3.11/1.64 ( ( exu
% 3.11/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.11/1.64 => ? [Xx: $i] :
% 3.11/1.64 ( ( Xphi @ Xx )
% 3.11/1.64 & ! [Xy: $i] :
% 3.11/1.64 ( ( Xphi @ Xy )
% 3.11/1.64 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(prop2set_type,type,
% 3.11/1.64 prop2set: $o > $i ).
% 3.11/1.64
% 3.11/1.64 thf(prop2setE_type,type,
% 3.11/1.64 prop2setE: $o ).
% 3.11/1.64
% 3.11/1.64 thf(prop2setE,definition,
% 3.11/1.64 ( prop2setE
% 3.11/1.64 = ( ! [Xphi: $o,Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 3.11/1.64 => Xphi ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(emptysetE_type,type,
% 3.11/1.64 emptysetE: $o ).
% 3.11/1.64
% 3.11/1.64 thf(emptysetE,definition,
% 3.11/1.64 ( emptysetE
% 3.11/1.64 = ( ! [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ emptyset )
% 3.11/1.64 => ! [Xphi: $o] : Xphi ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(emptysetimpfalse_type,type,
% 3.11/1.64 emptysetimpfalse: $o ).
% 3.11/1.64
% 3.11/1.64 thf(emptysetimpfalse,definition,
% 3.11/1.64 ( emptysetimpfalse
% 3.11/1.64 = ( ! [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ emptyset )
% 3.11/1.64 => $false ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(notinemptyset_type,type,
% 3.11/1.64 notinemptyset: $o ).
% 3.11/1.64
% 3.11/1.64 thf(notinemptyset,definition,
% 3.11/1.64 ( notinemptyset
% 3.11/1.64 = ( ! [Xx: $i] :
% 3.11/1.64 ~ ( in @ Xx @ emptyset ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(exuE3e_type,type,
% 3.11/1.64 exuE3e: $o ).
% 3.11/1.64
% 3.11/1.64 thf(exuE3e,definition,
% 3.11/1.64 ( exuE3e
% 3.11/1.64 = ( ! [Xphi: $i > $o] :
% 3.11/1.64 ( ( exu
% 3.11/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.11/1.64 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(setext_type,type,
% 3.11/1.64 setext: $o ).
% 3.11/1.64
% 3.11/1.64 thf(setext,definition,
% 3.11/1.64 ( setext
% 3.11/1.64 = ( ! [A: $i,B: $i] :
% 3.11/1.64 ( ! [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ A )
% 3.11/1.64 => ( in @ Xx @ B ) )
% 3.11/1.64 => ( ! [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ B )
% 3.11/1.64 => ( in @ Xx @ A ) )
% 3.11/1.64 => ( A = B ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(emptyI_type,type,
% 3.11/1.64 emptyI: $o ).
% 3.11/1.64
% 3.11/1.64 thf(emptyI,definition,
% 3.11/1.64 ( emptyI
% 3.11/1.64 = ( ! [A: $i] :
% 3.11/1.64 ( ! [Xx: $i] :
% 3.11/1.64 ~ ( in @ Xx @ A )
% 3.11/1.64 => ( A = emptyset ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(noeltsimpempty_type,type,
% 3.11/1.64 noeltsimpempty: $o ).
% 3.11/1.64
% 3.11/1.64 thf(noeltsimpempty,definition,
% 3.11/1.64 ( noeltsimpempty
% 3.11/1.64 = ( ! [A: $i] :
% 3.11/1.64 ( ! [Xx: $i] :
% 3.11/1.64 ~ ( in @ Xx @ A )
% 3.11/1.64 => ( A = emptyset ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(setbeta_type,type,
% 3.11/1.64 setbeta: $o ).
% 3.11/1.64
% 3.11/1.64 thf(setbeta,definition,
% 3.11/1.64 ( setbeta
% 3.11/1.64 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ A )
% 3.11/1.64 => ( ( in @ Xx
% 3.11/1.64 @ ( dsetconstr @ A
% 3.11/1.64 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.11/1.64 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(nonempty_type,type,
% 3.11/1.64 nonempty: $i > $o ).
% 3.11/1.64
% 3.11/1.64 thf(nonempty,definition,
% 3.11/1.64 ( nonempty
% 3.11/1.64 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(nonemptyE1_type,type,
% 3.11/1.64 nonemptyE1: $o ).
% 3.11/1.64
% 3.11/1.64 thf(nonemptyE1,definition,
% 3.11/1.64 ( nonemptyE1
% 3.11/1.64 = ( ! [A: $i] :
% 3.11/1.64 ( ( nonempty @ A )
% 3.11/1.64 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(nonemptyI_type,type,
% 3.11/1.64 nonemptyI: $o ).
% 3.11/1.64
% 3.11/1.64 thf(nonemptyI,definition,
% 3.11/1.64 ( nonemptyI
% 3.11/1.64 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ A )
% 3.11/1.64 => ( ( Xphi @ Xx )
% 3.11/1.64 => ( nonempty
% 3.11/1.64 @ ( dsetconstr @ A
% 3.11/1.64 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(nonemptyI1_type,type,
% 3.11/1.64 nonemptyI1: $o ).
% 3.11/1.64
% 3.11/1.64 thf(nonemptyI1,definition,
% 3.11/1.64 ( nonemptyI1
% 3.11/1.64 = ( ! [A: $i] :
% 3.11/1.64 ( ? [Xx: $i] : ( in @ Xx @ A )
% 3.11/1.64 => ( nonempty @ A ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(setadjoinIL_type,type,
% 3.11/1.64 setadjoinIL: $o ).
% 3.11/1.64
% 3.11/1.64 thf(setadjoinIL,definition,
% 3.11/1.64 ( setadjoinIL
% 3.11/1.64 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(emptyinunitempty_type,type,
% 3.11/1.64 emptyinunitempty: $o ).
% 3.11/1.64
% 3.11/1.64 thf(emptyinunitempty,definition,
% 3.11/1.64 ( emptyinunitempty
% 3.11/1.64 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(setadjoinIR_type,type,
% 3.11/1.64 setadjoinIR: $o ).
% 3.11/1.64
% 3.11/1.64 thf(setadjoinIR,definition,
% 3.11/1.64 ( setadjoinIR
% 3.11/1.64 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.11/1.64 ( ( in @ Xy @ A )
% 3.11/1.64 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(setadjoinE_type,type,
% 3.11/1.64 setadjoinE: $o ).
% 3.11/1.64
% 3.11/1.64 thf(setadjoinE,definition,
% 3.11/1.64 ( setadjoinE
% 3.11/1.64 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.11/1.64 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.11/1.64 => ! [Xphi: $o] :
% 3.11/1.64 ( ( ( Xy = Xx )
% 3.11/1.64 => Xphi )
% 3.11/1.64 => ( ( ( in @ Xy @ A )
% 3.11/1.64 => Xphi )
% 3.11/1.64 => Xphi ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(setadjoinOr_type,type,
% 3.11/1.64 setadjoinOr: $o ).
% 3.11/1.64
% 3.11/1.64 thf(setadjoinOr,definition,
% 3.11/1.64 ( setadjoinOr
% 3.11/1.64 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.11/1.64 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.11/1.64 => ( ( Xy = Xx )
% 3.11/1.64 | ( in @ Xy @ A ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(setoftrueEq_type,type,
% 3.11/1.64 setoftrueEq: $o ).
% 3.11/1.64
% 3.11/1.64 thf(setoftrueEq,definition,
% 3.11/1.64 ( setoftrueEq
% 3.11/1.64 = ( ! [A: $i] :
% 3.11/1.64 ( ( dsetconstr @ A
% 3.11/1.64 @ ^ [Xx: $i] : $true )
% 3.11/1.64 = A ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(powersetI_type,type,
% 3.11/1.64 powersetI: $o ).
% 3.11/1.64
% 3.11/1.64 thf(powersetI,definition,
% 3.11/1.64 ( powersetI
% 3.11/1.64 = ( ! [A: $i,B: $i] :
% 3.11/1.64 ( ! [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ B )
% 3.11/1.64 => ( in @ Xx @ A ) )
% 3.11/1.64 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(emptyinPowerset_type,type,
% 3.11/1.64 emptyinPowerset: $o ).
% 3.11/1.64
% 3.11/1.64 thf(emptyinPowerset,definition,
% 3.11/1.64 ( emptyinPowerset
% 3.11/1.64 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(emptyInPowerset_type,type,
% 3.11/1.64 emptyInPowerset: $o ).
% 3.11/1.64
% 3.11/1.64 thf(emptyInPowerset,definition,
% 3.11/1.64 ( emptyInPowerset
% 3.11/1.64 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(powersetE_type,type,
% 3.11/1.64 powersetE: $o ).
% 3.11/1.64
% 3.11/1.64 thf(powersetE,definition,
% 3.11/1.64 ( powersetE
% 3.11/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.64 ( ( in @ B @ ( powerset @ A ) )
% 3.11/1.64 => ( ( in @ Xx @ B )
% 3.11/1.64 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(setunionI_type,type,
% 3.11/1.64 setunionI: $o ).
% 3.11/1.64
% 3.11/1.64 thf(setunionI,definition,
% 3.11/1.64 ( setunionI
% 3.11/1.64 = ( ! [A: $i,Xx: $i,B: $i] :
% 3.11/1.64 ( ( in @ Xx @ B )
% 3.11/1.64 => ( ( in @ B @ A )
% 3.11/1.64 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(setunionE_type,type,
% 3.11/1.64 setunionE: $o ).
% 3.11/1.64
% 3.11/1.64 thf(setunionE,definition,
% 3.11/1.64 ( setunionE
% 3.11/1.64 = ( ! [A: $i,Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ ( setunion @ A ) )
% 3.11/1.64 => ! [Xphi: $o] :
% 3.11/1.64 ( ! [B: $i] :
% 3.11/1.64 ( ( in @ Xx @ B )
% 3.11/1.64 => ( ( in @ B @ A )
% 3.11/1.64 => Xphi ) )
% 3.11/1.64 => Xphi ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(subPowSU_type,type,
% 3.11/1.64 subPowSU: $o ).
% 3.11/1.64
% 3.11/1.64 thf(subPowSU,definition,
% 3.11/1.64 ( subPowSU
% 3.11/1.64 = ( ! [A: $i,Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ A )
% 3.11/1.64 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(exuE2_type,type,
% 3.11/1.64 exuE2: $o ).
% 3.11/1.64
% 3.11/1.64 thf(exuE2,definition,
% 3.11/1.64 ( exuE2
% 3.11/1.64 = ( ! [Xphi: $i > $o] :
% 3.11/1.64 ( ( exu
% 3.11/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.11/1.64 => ? [Xx: $i] :
% 3.11/1.64 ! [Xy: $i] :
% 3.11/1.64 ( ( Xphi @ Xy )
% 3.11/1.64 <=> ( Xy = Xx ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(nonemptyImpWitness_type,type,
% 3.11/1.64 nonemptyImpWitness: $o ).
% 3.11/1.64
% 3.11/1.64 thf(nonemptyImpWitness,definition,
% 3.11/1.64 ( nonemptyImpWitness
% 3.11/1.64 = ( ! [A: $i] :
% 3.11/1.64 ( ( nonempty @ A )
% 3.11/1.64 => ? [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ A )
% 3.11/1.64 & $true ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(uniqinunit_type,type,
% 3.11/1.64 uniqinunit: $o ).
% 3.11/1.64
% 3.11/1.64 thf(uniqinunit,definition,
% 3.11/1.64 ( uniqinunit
% 3.11/1.64 = ( ! [Xx: $i,Xy: $i] :
% 3.11/1.64 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.11/1.64 => ( Xx = Xy ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(notinsingleton_type,type,
% 3.11/1.64 notinsingleton: $o ).
% 3.11/1.64
% 3.11/1.64 thf(notinsingleton,definition,
% 3.11/1.64 ( notinsingleton
% 3.11/1.64 = ( ! [Xx: $i,Xy: $i] :
% 3.11/1.64 ( ( Xx != Xy )
% 3.11/1.64 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(eqinunit_type,type,
% 3.11/1.64 eqinunit: $o ).
% 3.11/1.64
% 3.11/1.64 thf(eqinunit,definition,
% 3.11/1.64 ( eqinunit
% 3.11/1.64 = ( ! [Xx: $i,Xy: $i] :
% 3.11/1.64 ( ( Xx = Xy )
% 3.11/1.64 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(singletonsswitch_type,type,
% 3.11/1.64 singletonsswitch: $o ).
% 3.11/1.64
% 3.11/1.64 thf(singletonsswitch,definition,
% 3.11/1.64 ( singletonsswitch
% 3.11/1.64 = ( ! [Xx: $i,Xy: $i] :
% 3.11/1.64 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.11/1.64 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(upairsetE_type,type,
% 3.11/1.64 upairsetE: $o ).
% 3.11/1.64
% 3.11/1.64 thf(upairsetE,definition,
% 3.11/1.64 ( upairsetE
% 3.11/1.64 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.11/1.64 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 3.11/1.64 => ( ( Xz = Xx )
% 3.11/1.64 | ( Xz = Xy ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(upairsetIL_type,type,
% 3.11/1.64 upairsetIL: $o ).
% 3.11/1.64
% 3.11/1.64 thf(upairsetIL,definition,
% 3.11/1.64 ( upairsetIL
% 3.11/1.64 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(upairsetIR_type,type,
% 3.11/1.64 upairsetIR: $o ).
% 3.11/1.64
% 3.11/1.64 thf(upairsetIR,definition,
% 3.11/1.64 ( upairsetIR
% 3.11/1.64 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(emptyE1_type,type,
% 3.11/1.64 emptyE1: $o ).
% 3.11/1.64
% 3.11/1.64 thf(emptyE1,definition,
% 3.11/1.64 ( emptyE1
% 3.11/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 3.11/1.64 ( ? [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ A )
% 3.11/1.64 & ( Xphi @ Xx ) )
% 3.11/1.64 => ( ( ( dsetconstr @ A
% 3.11/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.11/1.64 = emptyset )
% 3.11/1.64 => $false ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(vacuousDall_type,type,
% 3.11/1.64 vacuousDall: $o ).
% 3.11/1.64
% 3.11/1.64 thf(vacuousDall,definition,
% 3.11/1.64 ( vacuousDall
% 3.11/1.64 = ( ! [Xphi: $i > $o,Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ emptyset )
% 3.11/1.64 => ( Xphi @ Xx ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(quantDeMorgan1_type,type,
% 3.11/1.64 quantDeMorgan1: $o ).
% 3.11/1.64
% 3.11/1.64 thf(quantDeMorgan1,definition,
% 3.11/1.64 ( quantDeMorgan1
% 3.11/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 3.11/1.64 ( ~ ! [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ A )
% 3.11/1.64 => ( Xphi @ Xx ) )
% 3.11/1.64 => ? [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ A )
% 3.11/1.64 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(quantDeMorgan2_type,type,
% 3.11/1.64 quantDeMorgan2: $o ).
% 3.11/1.64
% 3.11/1.64 thf(quantDeMorgan2,definition,
% 3.11/1.64 ( quantDeMorgan2
% 3.11/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 3.11/1.64 ( ! [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ A )
% 3.11/1.64 => ~ ( Xphi @ Xx ) )
% 3.11/1.64 => ~ ? [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ A )
% 3.11/1.64 & ( Xphi @ Xx ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(quantDeMorgan3_type,type,
% 3.11/1.64 quantDeMorgan3: $o ).
% 3.11/1.64
% 3.11/1.64 thf(quantDeMorgan3,definition,
% 3.11/1.64 ( quantDeMorgan3
% 3.11/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 3.11/1.64 ( ~ ? [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ A )
% 3.11/1.64 & ( Xphi @ Xx ) )
% 3.11/1.64 => ! [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ A )
% 3.11/1.64 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(quantDeMorgan4_type,type,
% 3.11/1.64 quantDeMorgan4: $o ).
% 3.11/1.64
% 3.11/1.64 thf(quantDeMorgan4,definition,
% 3.11/1.64 ( quantDeMorgan4
% 3.11/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 3.11/1.64 ( ? [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ A )
% 3.11/1.64 & ~ ( Xphi @ Xx ) )
% 3.11/1.64 => ~ ! [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ A )
% 3.11/1.64 => ( Xphi @ Xx ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(prop2setI_type,type,
% 3.11/1.64 prop2setI: $o ).
% 3.11/1.64
% 3.11/1.64 thf(prop2setI,definition,
% 3.11/1.64 ( prop2setI
% 3.11/1.64 = ( ! [Xphi: $o] :
% 3.11/1.64 ( Xphi
% 3.11/1.64 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(set2prop_type,type,
% 3.11/1.64 set2prop: $i > $o ).
% 3.11/1.64
% 3.11/1.64 thf(prop2set2propI_type,type,
% 3.11/1.64 prop2set2propI: $o ).
% 3.11/1.64
% 3.11/1.64 thf(prop2set2propI,definition,
% 3.11/1.64 ( prop2set2propI
% 3.11/1.64 = ( ! [Xphi: $o] :
% 3.11/1.64 ( Xphi
% 3.11/1.64 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(notdexE_type,type,
% 3.11/1.64 notdexE: $o ).
% 3.11/1.64
% 3.11/1.64 thf(notdexE,definition,
% 3.11/1.64 ( notdexE
% 3.11/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 3.11/1.64 ( ~ ? [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ A )
% 3.11/1.64 & ( Xphi @ Xx ) )
% 3.11/1.64 => ! [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ A )
% 3.11/1.64 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(notdallE_type,type,
% 3.11/1.64 notdallE: $o ).
% 3.11/1.64
% 3.11/1.64 thf(notdallE,definition,
% 3.11/1.64 ( notdallE
% 3.11/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 3.11/1.64 ( ~ ! [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ A )
% 3.11/1.64 => ( Xphi @ Xx ) )
% 3.11/1.64 => ? [Xx: $i] :
% 3.11/1.64 ( ( in @ Xx @ A )
% 3.11/1.64 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(exuI1_type,type,
% 3.11/1.64 exuI1: $o ).
% 3.11/1.64
% 3.11/1.64 thf(exuI1,definition,
% 3.11/1.64 ( exuI1
% 3.11/1.64 = ( ! [Xphi: $i > $o] :
% 3.11/1.64 ( ? [Xx: $i] :
% 3.11/1.64 ( ( Xphi @ Xx )
% 3.11/1.64 & ! [Xy: $i] :
% 3.11/1.64 ( ( Xphi @ Xy )
% 3.11/1.64 => ( Xx = Xy ) ) )
% 3.11/1.64 => ( exu
% 3.11/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(exuI3_type,type,
% 3.11/1.64 exuI3: $o ).
% 3.11/1.64
% 3.11/1.64 thf(exuI3,definition,
% 3.11/1.64 ( exuI3
% 3.11/1.64 = ( ! [Xphi: $i > $o] :
% 3.11/1.64 ( ? [Xx: $i] : ( Xphi @ Xx )
% 3.11/1.64 => ( ! [Xx: $i,Xy: $i] :
% 3.11/1.64 ( ( Xphi @ Xx )
% 3.11/1.64 => ( ( Xphi @ Xy )
% 3.11/1.64 => ( Xx = Xy ) ) )
% 3.11/1.64 => ( exu
% 3.11/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(exuI2_type,type,
% 3.11/1.64 exuI2: $o ).
% 3.11/1.64
% 3.11/1.64 thf(exuI2,definition,
% 3.11/1.64 ( exuI2
% 3.11/1.64 = ( ! [Xphi: $i > $o] :
% 3.11/1.64 ( ? [Xx: $i] :
% 3.11/1.64 ! [Xy: $i] :
% 3.11/1.64 ( ( Xphi @ Xy )
% 3.11/1.64 <=> ( Xy = Xx ) )
% 3.11/1.64 => ( exu
% 3.11/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(inCongP_type,type,
% 3.11/1.64 inCongP: $o ).
% 3.11/1.64
% 3.11/1.64 thf(inCongP,definition,
% 3.11/1.64 ( inCongP
% 3.11/1.64 = ( ! [A: $i,B: $i] :
% 3.11/1.64 ( ( A = B )
% 3.11/1.64 => ! [Xx: $i,Xy: $i] :
% 3.11/1.64 ( ( Xx = Xy )
% 3.11/1.64 => ( ( in @ Xx @ A )
% 3.11/1.64 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(in__Cong_type,type,
% 3.11/1.64 in__Cong: $o ).
% 3.11/1.64
% 3.11/1.64 thf(in__Cong,definition,
% 3.11/1.64 ( in__Cong
% 3.11/1.64 = ( ! [A: $i,B: $i] :
% 3.11/1.64 ( ( A = B )
% 3.11/1.64 => ! [Xx: $i,Xy: $i] :
% 3.11/1.64 ( ( Xx = Xy )
% 3.11/1.64 => ( ( in @ Xx @ A )
% 3.11/1.64 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(exuE3u_type,type,
% 3.11/1.64 exuE3u: $o ).
% 3.11/1.64
% 3.11/1.64 thf(exuE3u,definition,
% 3.11/1.64 ( exuE3u
% 3.11/1.64 = ( ! [Xphi: $i > $o] :
% 3.11/1.64 ( ( exu
% 3.11/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.11/1.64 => ! [Xx: $i,Xy: $i] :
% 3.11/1.64 ( ( Xphi @ Xx )
% 3.11/1.64 => ( ( Xphi @ Xy )
% 3.11/1.64 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(exu__Cong_type,type,
% 3.11/1.64 exu__Cong: $o ).
% 3.11/1.64
% 3.11/1.64 thf(exu__Cong,definition,
% 3.11/1.64 ( exu__Cong
% 3.11/1.64 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.11/1.64 ( ! [Xx: $i,Xy: $i] :
% 3.11/1.64 ( ( Xx = Xy )
% 3.11/1.64 => ( ( Xphi @ Xx )
% 3.11/1.64 <=> ( Xpsi @ Xy ) ) )
% 3.11/1.64 => ( ( exu
% 3.11/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.11/1.64 <=> ( exu
% 3.11/1.64 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(emptyset__Cong_type,type,
% 3.11/1.64 emptyset__Cong: $o ).
% 3.11/1.64
% 3.11/1.64 thf(emptyset__Cong,definition,
% 3.11/1.64 ( emptyset__Cong
% 3.11/1.64 = ( emptyset = emptyset ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(setadjoin__Cong_type,type,
% 3.11/1.64 setadjoin__Cong: $o ).
% 3.11/1.64
% 3.11/1.64 thf(setadjoin__Cong,definition,
% 3.11/1.64 ( setadjoin__Cong
% 3.11/1.64 = ( ! [Xx: $i,Xy: $i] :
% 3.11/1.64 ( ( Xx = Xy )
% 3.11/1.64 => ! [Xz: $i,Xu: $i] :
% 3.11/1.64 ( ( Xz = Xu )
% 3.11/1.64 => ( ( setadjoin @ Xx @ Xz )
% 3.11/1.64 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(powerset__Cong_type,type,
% 3.11/1.64 powerset__Cong: $o ).
% 3.11/1.64
% 3.11/1.64 thf(powerset__Cong,definition,
% 3.11/1.64 ( powerset__Cong
% 3.11/1.64 = ( ! [A: $i,B: $i] :
% 3.11/1.64 ( ( A = B )
% 3.11/1.64 => ( ( powerset @ A )
% 3.11/1.64 = ( powerset @ B ) ) ) ) ) ).
% 3.11/1.64
% 3.11/1.64 thf(setunion__Cong_type,type,
% 3.11/1.64 setunion__Cong: $o ).
% 3.11/1.64
% 3.11/1.64 thf(setunion__Cong,definition,
% 3.11/1.64 ( setunion__Cong
% 3.11/1.64 = ( ! [A: $i,B: $i] :
% 3.11/1.64 ( ( A = B )
% 3.11/1.64 => ( ( setunion @ A )
% 3.11/1.65 = ( setunion @ B ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(omega__Cong_type,type,
% 3.11/1.65 omega__Cong: $o ).
% 3.11/1.65
% 3.11/1.65 thf(omega__Cong,definition,
% 3.11/1.65 ( omega__Cong
% 3.11/1.65 = ( omega = omega ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(exuEu_type,type,
% 3.11/1.65 exuEu: $o ).
% 3.11/1.65
% 3.11/1.65 thf(exuEu,definition,
% 3.11/1.65 ( exuEu
% 3.11/1.65 = ( ! [Xphi: $i > $o] :
% 3.11/1.65 ( ( exu
% 3.11/1.65 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.11/1.65 => ! [Xx: $i,Xy: $i] :
% 3.11/1.65 ( ( Xphi @ Xx )
% 3.11/1.65 => ( ( Xphi @ Xy )
% 3.11/1.65 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(descr__Cong_type,type,
% 3.11/1.65 descr__Cong: $o ).
% 3.11/1.65
% 3.11/1.65 thf(descr__Cong,definition,
% 3.11/1.65 ( descr__Cong
% 3.11/1.65 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.11/1.65 ( ! [Xx: $i,Xy: $i] :
% 3.11/1.65 ( ( Xx = Xy )
% 3.11/1.65 => ( ( Xphi @ Xx )
% 3.11/1.65 <=> ( Xpsi @ Xy ) ) )
% 3.11/1.65 => ( ( exu
% 3.11/1.65 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.11/1.65 => ( ( exu
% 3.11/1.65 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 3.11/1.65 => ( ( descr
% 3.11/1.65 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.11/1.65 = ( descr
% 3.11/1.65 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(dsetconstr__Cong_type,type,
% 3.11/1.65 dsetconstr__Cong: $o ).
% 3.11/1.65
% 3.11/1.65 thf(dsetconstr__Cong,definition,
% 3.11/1.65 ( dsetconstr__Cong
% 3.11/1.65 = ( ! [A: $i,B: $i] :
% 3.11/1.65 ( ( A = B )
% 3.11/1.65 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.11/1.65 ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ B )
% 3.11/1.65 => ( ( Xx = Xy )
% 3.11/1.65 => ( ( Xphi @ Xx )
% 3.11/1.65 <=> ( Xpsi @ Xy ) ) ) ) )
% 3.11/1.65 => ( ( dsetconstr @ A
% 3.11/1.65 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.11/1.65 = ( dsetconstr @ B
% 3.11/1.65 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(subset_type,type,
% 3.11/1.65 subset: $i > $i > $o ).
% 3.11/1.65
% 3.11/1.65 thf(disjoint_type,type,
% 3.11/1.65 disjoint: $i > $i > $o ).
% 3.11/1.65
% 3.11/1.65 thf(setsmeet_type,type,
% 3.11/1.65 setsmeet: $i > $i > $o ).
% 3.11/1.65
% 3.11/1.65 thf(subsetI1_type,type,
% 3.11/1.65 subsetI1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(subsetI1,definition,
% 3.11/1.65 ( subsetI1
% 3.11/1.65 = ( ! [A: $i,B: $i] :
% 3.11/1.65 ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( in @ Xx @ B ) )
% 3.11/1.65 => ( subset @ A @ B ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(eqimpsubset2_type,type,
% 3.11/1.65 eqimpsubset2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(eqimpsubset2,definition,
% 3.11/1.65 ( eqimpsubset2
% 3.11/1.65 = ( ! [A: $i,B: $i] :
% 3.11/1.65 ( ( A = B )
% 3.11/1.65 => ( subset @ B @ A ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(eqimpsubset1_type,type,
% 3.11/1.65 eqimpsubset1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(eqimpsubset1,definition,
% 3.11/1.65 ( eqimpsubset1
% 3.11/1.65 = ( ! [A: $i,B: $i] :
% 3.11/1.65 ( ( A = B )
% 3.11/1.65 => ( subset @ A @ B ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(subsetI2_type,type,
% 3.11/1.65 subsetI2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(subsetI2,definition,
% 3.11/1.65 ( subsetI2
% 3.11/1.65 = ( ! [A: $i,B: $i] :
% 3.11/1.65 ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( in @ Xx @ B ) )
% 3.11/1.65 => ( subset @ A @ B ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(emptysetsubset_type,type,
% 3.11/1.65 emptysetsubset: $o ).
% 3.11/1.65
% 3.11/1.65 thf(emptysetsubset,definition,
% 3.11/1.65 ( emptysetsubset
% 3.11/1.65 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(subsetE_type,type,
% 3.11/1.65 subsetE: $o ).
% 3.11/1.65
% 3.11/1.65 thf(subsetE,definition,
% 3.11/1.65 ( subsetE
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ( subset @ A @ B )
% 3.11/1.65 => ( ( in @ Xx @ A )
% 3.11/1.65 => ( in @ Xx @ B ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(subsetE2_type,type,
% 3.11/1.65 subsetE2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(subsetE2,definition,
% 3.11/1.65 ( subsetE2
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ( subset @ A @ B )
% 3.11/1.65 => ( ~ ( in @ Xx @ B )
% 3.11/1.65 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(notsubsetI_type,type,
% 3.11/1.65 notsubsetI: $o ).
% 3.11/1.65
% 3.11/1.65 thf(notsubsetI,definition,
% 3.11/1.65 ( notsubsetI
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ~ ( in @ Xx @ B )
% 3.11/1.65 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(notequalI1_type,type,
% 3.11/1.65 notequalI1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(notequalI1,definition,
% 3.11/1.65 ( notequalI1
% 3.11/1.65 = ( ! [A: $i,B: $i] :
% 3.11/1.65 ( ~ ( subset @ A @ B )
% 3.11/1.65 => ( A != B ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(notequalI2_type,type,
% 3.11/1.65 notequalI2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(notequalI2,definition,
% 3.11/1.65 ( notequalI2
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ~ ( in @ Xx @ B )
% 3.11/1.65 => ( A != B ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(subsetRefl_type,type,
% 3.11/1.65 subsetRefl: $o ).
% 3.11/1.65
% 3.11/1.65 thf(subsetRefl,definition,
% 3.11/1.65 ( subsetRefl
% 3.11/1.65 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(subsetTrans_type,type,
% 3.11/1.65 subsetTrans: $o ).
% 3.11/1.65
% 3.11/1.65 thf(subsetTrans,definition,
% 3.11/1.65 ( subsetTrans
% 3.11/1.65 = ( ! [A: $i,B: $i,C: $i] :
% 3.11/1.65 ( ( subset @ A @ B )
% 3.11/1.65 => ( ( subset @ B @ C )
% 3.11/1.65 => ( subset @ A @ C ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(setadjoinSub_type,type,
% 3.11/1.65 setadjoinSub: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setadjoinSub,definition,
% 3.11/1.65 ( setadjoinSub
% 3.11/1.65 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(setadjoinSub2_type,type,
% 3.11/1.65 setadjoinSub2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setadjoinSub2,definition,
% 3.11/1.65 ( setadjoinSub2
% 3.11/1.65 = ( ! [A: $i,Xx: $i,B: $i] :
% 3.11/1.65 ( ( subset @ A @ B )
% 3.11/1.65 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(subset2powerset_type,type,
% 3.11/1.65 subset2powerset: $o ).
% 3.11/1.65
% 3.11/1.65 thf(subset2powerset,definition,
% 3.11/1.65 ( subset2powerset
% 3.11/1.65 = ( ! [A: $i,B: $i] :
% 3.11/1.65 ( ( subset @ A @ B )
% 3.11/1.65 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(setextsub_type,type,
% 3.11/1.65 setextsub: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setextsub,definition,
% 3.11/1.65 ( setextsub
% 3.11/1.65 = ( ! [A: $i,B: $i] :
% 3.11/1.65 ( ( subset @ A @ B )
% 3.11/1.65 => ( ( subset @ B @ A )
% 3.11/1.65 => ( A = B ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(subsetemptysetimpeq_type,type,
% 3.11/1.65 subsetemptysetimpeq: $o ).
% 3.11/1.65
% 3.11/1.65 thf(subsetemptysetimpeq,definition,
% 3.11/1.65 ( subsetemptysetimpeq
% 3.11/1.65 = ( ! [A: $i] :
% 3.11/1.65 ( ( subset @ A @ emptyset )
% 3.11/1.65 => ( A = emptyset ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(powersetI1_type,type,
% 3.11/1.65 powersetI1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(powersetI1,definition,
% 3.11/1.65 ( powersetI1
% 3.11/1.65 = ( ! [A: $i,B: $i] :
% 3.11/1.65 ( ( subset @ B @ A )
% 3.11/1.65 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(powersetE1_type,type,
% 3.11/1.65 powersetE1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(powersetE1,definition,
% 3.11/1.65 ( powersetE1
% 3.11/1.65 = ( ! [A: $i,B: $i] :
% 3.11/1.65 ( ( in @ B @ ( powerset @ A ) )
% 3.11/1.65 => ( subset @ B @ A ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(inPowerset_type,type,
% 3.11/1.65 inPowerset: $o ).
% 3.11/1.65
% 3.11/1.65 thf(inPowerset,definition,
% 3.11/1.65 ( inPowerset
% 3.11/1.65 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(powersetsubset_type,type,
% 3.11/1.65 powersetsubset: $o ).
% 3.11/1.65
% 3.11/1.65 thf(powersetsubset,definition,
% 3.11/1.65 ( powersetsubset
% 3.11/1.65 = ( ! [A: $i,B: $i] :
% 3.11/1.65 ( ( subset @ A @ B )
% 3.11/1.65 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(sepInPowerset_type,type,
% 3.11/1.65 sepInPowerset: $o ).
% 3.11/1.65
% 3.11/1.65 thf(sepInPowerset,definition,
% 3.11/1.65 ( sepInPowerset
% 3.11/1.65 = ( ! [A: $i,Xphi: $i > $o] :
% 3.11/1.65 ( in
% 3.11/1.65 @ ( dsetconstr @ A
% 3.11/1.65 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.11/1.65 @ ( powerset @ A ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(sepSubset_type,type,
% 3.11/1.65 sepSubset: $o ).
% 3.11/1.65
% 3.11/1.65 thf(sepSubset,definition,
% 3.11/1.65 ( sepSubset
% 3.11/1.65 = ( ! [A: $i,Xphi: $i > $o] :
% 3.11/1.65 ( subset
% 3.11/1.65 @ ( dsetconstr @ A
% 3.11/1.65 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.11/1.65 @ A ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(binunion_type,type,
% 3.11/1.65 binunion: $i > $i > $i ).
% 3.11/1.65
% 3.11/1.65 thf(binunionIL_type,type,
% 3.11/1.65 binunionIL: $o ).
% 3.11/1.65
% 3.11/1.65 thf(binunionIL,definition,
% 3.11/1.65 ( binunionIL
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(upairset2IR_type,type,
% 3.11/1.65 upairset2IR: $o ).
% 3.11/1.65
% 3.11/1.65 thf(upairset2IR,definition,
% 3.11/1.65 ( upairset2IR
% 3.11/1.65 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(binunionIR_type,type,
% 3.11/1.65 binunionIR: $o ).
% 3.11/1.65
% 3.11/1.65 thf(binunionIR,definition,
% 3.11/1.65 ( binunionIR
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ B )
% 3.11/1.65 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(binunionEcases_type,type,
% 3.11/1.65 binunionEcases: $o ).
% 3.11/1.65
% 3.11/1.65 thf(binunionEcases,definition,
% 3.11/1.65 ( binunionEcases
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 3.11/1.65 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 3.11/1.65 => ( ( ( in @ Xx @ A )
% 3.11/1.65 => Xphi )
% 3.11/1.65 => ( ( ( in @ Xx @ B )
% 3.11/1.65 => Xphi )
% 3.11/1.65 => Xphi ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(binunionE_type,type,
% 3.11/1.65 binunionE: $o ).
% 3.11/1.65
% 3.11/1.65 thf(binunionE,definition,
% 3.11/1.65 ( binunionE
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 3.11/1.65 => ( ( in @ Xx @ A )
% 3.11/1.65 | ( in @ Xx @ B ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(binunionLsub_type,type,
% 3.11/1.65 binunionLsub: $o ).
% 3.11/1.65
% 3.11/1.65 thf(binunionLsub,definition,
% 3.11/1.65 ( binunionLsub
% 3.11/1.65 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(binunionRsub_type,type,
% 3.11/1.65 binunionRsub: $o ).
% 3.11/1.65
% 3.11/1.65 thf(binunionRsub,definition,
% 3.11/1.65 ( binunionRsub
% 3.11/1.65 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(binintersect_type,type,
% 3.11/1.65 binintersect: $i > $i > $i ).
% 3.11/1.65
% 3.11/1.65 thf(binintersectI_type,type,
% 3.11/1.65 binintersectI: $o ).
% 3.11/1.65
% 3.11/1.65 thf(binintersectI,definition,
% 3.11/1.65 ( binintersectI
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( in @ Xx @ B )
% 3.11/1.65 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(binintersectSubset5_type,type,
% 3.11/1.65 binintersectSubset5: $o ).
% 3.11/1.65
% 3.11/1.65 thf(binintersectSubset5,definition,
% 3.11/1.65 ( binintersectSubset5
% 3.11/1.65 = ( ! [A: $i,B: $i,C: $i] :
% 3.11/1.65 ( ( subset @ C @ A )
% 3.11/1.65 => ( ( subset @ C @ B )
% 3.11/1.65 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(binintersectEL_type,type,
% 3.11/1.65 binintersectEL: $o ).
% 3.11/1.65
% 3.11/1.65 thf(binintersectEL,definition,
% 3.11/1.65 ( binintersectEL
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 3.11/1.65 => ( in @ Xx @ A ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(binintersectLsub_type,type,
% 3.11/1.65 binintersectLsub: $o ).
% 3.11/1.65
% 3.11/1.65 thf(binintersectLsub,definition,
% 3.11/1.65 ( binintersectLsub
% 3.11/1.65 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(binintersectSubset2_type,type,
% 3.11/1.65 binintersectSubset2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(binintersectSubset2,definition,
% 3.11/1.65 ( binintersectSubset2
% 3.11/1.65 = ( ! [A: $i,B: $i] :
% 3.11/1.65 ( ( subset @ A @ B )
% 3.11/1.65 => ( ( binintersect @ A @ B )
% 3.11/1.65 = A ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(binintersectSubset3_type,type,
% 3.11/1.65 binintersectSubset3: $o ).
% 3.11/1.65
% 3.11/1.65 thf(binintersectSubset3,definition,
% 3.11/1.65 ( binintersectSubset3
% 3.11/1.65 = ( ! [A: $i,B: $i] :
% 3.11/1.65 ( ( ( binintersect @ A @ B )
% 3.11/1.65 = B )
% 3.11/1.65 => ( subset @ B @ A ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(binintersectER_type,type,
% 3.11/1.65 binintersectER: $o ).
% 3.11/1.65
% 3.11/1.65 thf(binintersectER,definition,
% 3.11/1.65 ( binintersectER
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 3.11/1.65 => ( in @ Xx @ B ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(disjointsetsI1_type,type,
% 3.11/1.65 disjointsetsI1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(disjointsetsI1,definition,
% 3.11/1.65 ( disjointsetsI1
% 3.11/1.65 = ( ! [A: $i,B: $i] :
% 3.11/1.65 ( ~ ? [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 & ( in @ Xx @ B ) )
% 3.11/1.65 => ( ( binintersect @ A @ B )
% 3.11/1.65 = emptyset ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(binintersectRsub_type,type,
% 3.11/1.65 binintersectRsub: $o ).
% 3.11/1.65
% 3.11/1.65 thf(binintersectRsub,definition,
% 3.11/1.65 ( binintersectRsub
% 3.11/1.65 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(binintersectSubset4_type,type,
% 3.11/1.65 binintersectSubset4: $o ).
% 3.11/1.65
% 3.11/1.65 thf(binintersectSubset4,definition,
% 3.11/1.65 ( binintersectSubset4
% 3.11/1.65 = ( ! [A: $i,B: $i] :
% 3.11/1.65 ( ( subset @ B @ A )
% 3.11/1.65 => ( ( binintersect @ A @ B )
% 3.11/1.65 = B ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(binintersectSubset1_type,type,
% 3.11/1.65 binintersectSubset1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(binintersectSubset1,definition,
% 3.11/1.65 ( binintersectSubset1
% 3.11/1.65 = ( ! [A: $i,B: $i] :
% 3.11/1.65 ( ( ( binintersect @ A @ B )
% 3.11/1.65 = A )
% 3.11/1.65 => ( subset @ A @ B ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(bs114d_type,type,
% 3.11/1.65 bs114d: $o ).
% 3.11/1.65
% 3.11/1.65 thf(bs114d,definition,
% 3.11/1.65 ( bs114d
% 3.11/1.65 = ( ! [A: $i,B: $i,C: $i] :
% 3.11/1.65 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 3.11/1.65 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(regular_type,type,
% 3.11/1.65 regular: $i > $o ).
% 3.11/1.65
% 3.11/1.65 thf(setminus_type,type,
% 3.11/1.65 setminus: $i > $i > $i ).
% 3.11/1.65
% 3.11/1.65 thf(setminusI_type,type,
% 3.11/1.65 setminusI: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setminusI,definition,
% 3.11/1.65 ( setminusI
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ~ ( in @ Xx @ B )
% 3.11/1.65 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(setminusEL_type,type,
% 3.11/1.65 setminusEL: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setminusEL,definition,
% 3.11/1.65 ( setminusEL
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 3.11/1.65 => ( in @ Xx @ A ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(setminusER_type,type,
% 3.11/1.65 setminusER: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setminusER,definition,
% 3.11/1.65 ( setminusER
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 3.11/1.65 => ~ ( in @ Xx @ B ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(setminusSubset2_type,type,
% 3.11/1.65 setminusSubset2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setminusSubset2,definition,
% 3.11/1.65 ( setminusSubset2
% 3.11/1.65 = ( ! [A: $i,B: $i] :
% 3.11/1.65 ( ( subset @ A @ B )
% 3.11/1.65 => ( ( setminus @ A @ B )
% 3.11/1.65 = emptyset ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(setminusERneg_type,type,
% 3.11/1.65 setminusERneg: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setminusERneg,definition,
% 3.11/1.65 ( setminusERneg
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 3.11/1.65 => ( ( in @ Xx @ A )
% 3.11/1.65 => ( in @ Xx @ B ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(setminusELneg_type,type,
% 3.11/1.65 setminusELneg: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setminusELneg,definition,
% 3.11/1.65 ( setminusELneg
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 3.11/1.65 => ( ~ ( in @ Xx @ B )
% 3.11/1.65 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(setminusILneg_type,type,
% 3.11/1.65 setminusILneg: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setminusILneg,definition,
% 3.11/1.65 ( setminusILneg
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ~ ( in @ Xx @ A )
% 3.11/1.65 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(setminusIRneg_type,type,
% 3.11/1.65 setminusIRneg: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setminusIRneg,definition,
% 3.11/1.65 ( setminusIRneg
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ B )
% 3.11/1.65 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(setminusLsub_type,type,
% 3.11/1.65 setminusLsub: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setminusLsub,definition,
% 3.11/1.65 ( setminusLsub
% 3.11/1.65 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(setminusSubset1_type,type,
% 3.11/1.65 setminusSubset1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setminusSubset1,definition,
% 3.11/1.65 ( setminusSubset1
% 3.11/1.65 = ( ! [A: $i,B: $i] :
% 3.11/1.65 ( ( ( setminus @ A @ B )
% 3.11/1.65 = emptyset )
% 3.11/1.65 => ( subset @ A @ B ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(symdiff_type,type,
% 3.11/1.65 symdiff: $i > $i > $i ).
% 3.11/1.65
% 3.11/1.65 thf(symdiffE_type,type,
% 3.11/1.65 symdiffE: $o ).
% 3.11/1.65
% 3.11/1.65 thf(symdiffE,definition,
% 3.11/1.65 ( symdiffE
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 3.11/1.65 => ! [Xphi: $o] :
% 3.11/1.65 ( ( ( in @ Xx @ A )
% 3.11/1.65 => ( ~ ( in @ Xx @ B )
% 3.11/1.65 => Xphi ) )
% 3.11/1.65 => ( ( ~ ( in @ Xx @ A )
% 3.11/1.65 => ( ( in @ Xx @ B )
% 3.11/1.65 => Xphi ) )
% 3.11/1.65 => Xphi ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(symdiffI1_type,type,
% 3.11/1.65 symdiffI1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(symdiffI1,definition,
% 3.11/1.65 ( symdiffI1
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ~ ( in @ Xx @ B )
% 3.11/1.65 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(symdiffI2_type,type,
% 3.11/1.65 symdiffI2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(symdiffI2,definition,
% 3.11/1.65 ( symdiffI2
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ~ ( in @ Xx @ A )
% 3.11/1.65 => ( ( in @ Xx @ B )
% 3.11/1.65 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(symdiffIneg1_type,type,
% 3.11/1.65 symdiffIneg1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(symdiffIneg1,definition,
% 3.11/1.65 ( symdiffIneg1
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( in @ Xx @ B )
% 3.11/1.65 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(symdiffIneg2_type,type,
% 3.11/1.65 symdiffIneg2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(symdiffIneg2,definition,
% 3.11/1.65 ( symdiffIneg2
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ~ ( in @ Xx @ A )
% 3.11/1.65 => ( ~ ( in @ Xx @ B )
% 3.11/1.65 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(iskpair_type,type,
% 3.11/1.65 iskpair: $i > $o ).
% 3.11/1.65
% 3.11/1.65 thf(secondinupair_type,type,
% 3.11/1.65 secondinupair: $o ).
% 3.11/1.65
% 3.11/1.65 thf(secondinupair,definition,
% 3.11/1.65 ( secondinupair
% 3.11/1.65 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(setukpairIL_type,type,
% 3.11/1.65 setukpairIL: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setukpairIL,definition,
% 3.11/1.65 ( setukpairIL
% 3.11/1.65 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(setukpairIR_type,type,
% 3.11/1.65 setukpairIR: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setukpairIR,definition,
% 3.11/1.65 ( setukpairIR
% 3.11/1.65 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(kpairiskpair_type,type,
% 3.11/1.65 kpairiskpair: $o ).
% 3.11/1.65
% 3.11/1.65 thf(kpairiskpair,definition,
% 3.11/1.65 ( kpairiskpair
% 3.11/1.65 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(kpair_type,type,
% 3.11/1.65 kpair: $i > $i > $i ).
% 3.11/1.65
% 3.11/1.65 thf(kpairp_type,type,
% 3.11/1.65 kpairp: $o ).
% 3.11/1.65
% 3.11/1.65 thf(kpairp,definition,
% 3.11/1.65 ( kpairp
% 3.11/1.65 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(cartprod_type,type,
% 3.11/1.65 cartprod: $i > $i > $i ).
% 3.11/1.65
% 3.11/1.65 thf(singletonsubset_type,type,
% 3.11/1.65 singletonsubset: $o ).
% 3.11/1.65
% 3.11/1.65 thf(singletonsubset,definition,
% 3.11/1.65 ( singletonsubset
% 3.11/1.65 = ( ! [A: $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(singletoninpowerset_type,type,
% 3.11/1.65 singletoninpowerset: $o ).
% 3.11/1.65
% 3.11/1.65 thf(singletoninpowerset,definition,
% 3.11/1.65 ( singletoninpowerset
% 3.11/1.65 = ( ! [A: $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(singletoninpowunion_type,type,
% 3.11/1.65 singletoninpowunion: $o ).
% 3.11/1.65
% 3.11/1.65 thf(singletoninpowunion,definition,
% 3.11/1.65 ( singletoninpowunion
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(upairset2E_type,type,
% 3.11/1.65 upairset2E: $o ).
% 3.11/1.65
% 3.11/1.65 thf(upairset2E,definition,
% 3.11/1.65 ( upairset2E
% 3.11/1.65 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.11/1.65 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 3.11/1.65 => ( ( Xz = Xx )
% 3.11/1.65 | ( Xz = Xy ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(upairsubunion_type,type,
% 3.11/1.65 upairsubunion: $o ).
% 3.11/1.65
% 3.11/1.65 thf(upairsubunion,definition,
% 3.11/1.65 ( upairsubunion
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ B )
% 3.11/1.65 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(upairinpowunion_type,type,
% 3.11/1.65 upairinpowunion: $o ).
% 3.11/1.65
% 3.11/1.65 thf(upairinpowunion,definition,
% 3.11/1.65 ( upairinpowunion
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ B )
% 3.11/1.65 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(ubforcartprodlem1_type,type,
% 3.11/1.65 ubforcartprodlem1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(ubforcartprodlem1,definition,
% 3.11/1.65 ( ubforcartprodlem1
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ B )
% 3.11/1.65 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(ubforcartprodlem2_type,type,
% 3.11/1.65 ubforcartprodlem2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(ubforcartprodlem2,definition,
% 3.11/1.65 ( ubforcartprodlem2
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ B )
% 3.11/1.65 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(ubforcartprodlem3_type,type,
% 3.11/1.65 ubforcartprodlem3: $o ).
% 3.11/1.65
% 3.11/1.65 thf(ubforcartprodlem3,definition,
% 3.11/1.65 ( ubforcartprodlem3
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ B )
% 3.11/1.65 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(cartprodpairin_type,type,
% 3.11/1.65 cartprodpairin: $o ).
% 3.11/1.65
% 3.11/1.65 thf(cartprodpairin,definition,
% 3.11/1.65 ( cartprodpairin
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ B )
% 3.11/1.65 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(cartprodmempair1_type,type,
% 3.11/1.65 cartprodmempair1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(cartprodmempair1,definition,
% 3.11/1.65 ( cartprodmempair1
% 3.11/1.65 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.11/1.65 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.11/1.65 => ? [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 & ? [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ B )
% 3.11/1.65 & ( Xu
% 3.11/1.65 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(cartprodmempair_type,type,
% 3.11/1.65 cartprodmempair: $o ).
% 3.11/1.65
% 3.11/1.65 thf(cartprodmempair,definition,
% 3.11/1.65 ( cartprodmempair
% 3.11/1.65 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.11/1.65 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.11/1.65 => ( iskpair @ Xu ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(setunionE2_type,type,
% 3.11/1.65 setunionE2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setunionE2,definition,
% 3.11/1.65 ( setunionE2
% 3.11/1.65 = ( ! [A: $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ ( setunion @ A ) )
% 3.11/1.65 => ? [X: $i] :
% 3.11/1.65 ( ( in @ X @ A )
% 3.11/1.65 & ( in @ Xx @ X ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(setunionsingleton1_type,type,
% 3.11/1.65 setunionsingleton1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setunionsingleton1,definition,
% 3.11/1.65 ( setunionsingleton1
% 3.11/1.65 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(setunionsingleton2_type,type,
% 3.11/1.65 setunionsingleton2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setunionsingleton2,definition,
% 3.11/1.65 ( setunionsingleton2
% 3.11/1.65 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(setunionsingleton_type,type,
% 3.11/1.65 setunionsingleton: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setunionsingleton,definition,
% 3.11/1.65 ( setunionsingleton
% 3.11/1.65 = ( ! [Xx: $i] :
% 3.11/1.65 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 3.11/1.65 = Xx ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(singleton_type,type,
% 3.11/1.65 singleton: $i > $o ).
% 3.11/1.65
% 3.11/1.65 thf(singletonprop_type,type,
% 3.11/1.65 singletonprop: $o ).
% 3.11/1.65
% 3.11/1.65 thf(singletonprop,definition,
% 3.11/1.65 ( singletonprop
% 3.11/1.65 = ( ! [A: $i,Xphi: $i > $o] :
% 3.11/1.65 ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 => ( ( Xphi @ Xx )
% 3.11/1.65 => ( ( Xphi @ Xy )
% 3.11/1.65 => ( Xx = Xy ) ) ) ) )
% 3.11/1.65 => ( ? [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 & ( Xphi @ Xx ) )
% 3.11/1.65 => ( singleton
% 3.11/1.65 @ ( dsetconstr @ A
% 3.11/1.65 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(ex1_type,type,
% 3.11/1.65 ex1: $i > ( $i > $o ) > $o ).
% 3.11/1.65
% 3.11/1.65 thf(ex1E1_type,type,
% 3.11/1.65 ex1E1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(ex1E1,definition,
% 3.11/1.65 ( ex1E1
% 3.11/1.65 = ( ! [A: $i,Xphi: $i > $o] :
% 3.11/1.65 ( ( ex1 @ A
% 3.11/1.65 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.11/1.65 => ? [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 & ( Xphi @ Xx ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(ex1I_type,type,
% 3.11/1.65 ex1I: $o ).
% 3.11/1.65
% 3.11/1.65 thf(ex1I,definition,
% 3.11/1.65 ( ex1I
% 3.11/1.65 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( Xphi @ Xx )
% 3.11/1.65 => ( ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 => ( ( Xphi @ Xy )
% 3.11/1.65 => ( Xy = Xx ) ) )
% 3.11/1.65 => ( ex1 @ A
% 3.11/1.65 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(ex1I2_type,type,
% 3.11/1.65 ex1I2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(ex1I2,definition,
% 3.11/1.65 ( ex1I2
% 3.11/1.65 = ( ! [A: $i,Xphi: $i > $o] :
% 3.11/1.65 ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 => ( ( Xphi @ Xx )
% 3.11/1.65 => ( ( Xphi @ Xy )
% 3.11/1.65 => ( Xx = Xy ) ) ) ) )
% 3.11/1.65 => ( ? [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 & ( Xphi @ Xx ) )
% 3.11/1.65 => ( ex1 @ A
% 3.11/1.65 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(singletonsuniq_type,type,
% 3.11/1.65 singletonsuniq: $o ).
% 3.11/1.65
% 3.11/1.65 thf(singletonsuniq,definition,
% 3.11/1.65 ( singletonsuniq
% 3.11/1.65 = ( ! [Xx: $i,Xy: $i] :
% 3.11/1.65 ( ( ( setadjoin @ Xx @ emptyset )
% 3.11/1.65 = ( setadjoin @ Xy @ emptyset ) )
% 3.11/1.65 => ( Xx = Xy ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(atmost1p_type,type,
% 3.11/1.65 atmost1p: $i > $o ).
% 3.11/1.65
% 3.11/1.65 thf(atleast2p_type,type,
% 3.11/1.65 atleast2p: $i > $o ).
% 3.11/1.65
% 3.11/1.65 thf(atmost2p_type,type,
% 3.11/1.65 atmost2p: $i > $o ).
% 3.11/1.65
% 3.11/1.65 thf(upairsetp_type,type,
% 3.11/1.65 upairsetp: $i > $o ).
% 3.11/1.65
% 3.11/1.65 thf(setukpairinjL1_type,type,
% 3.11/1.65 setukpairinjL1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setukpairinjL1,definition,
% 3.11/1.65 ( setukpairinjL1
% 3.11/1.65 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.11/1.65 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 3.11/1.65 => ( Xx = Xz ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(kfstsingleton_type,type,
% 3.11/1.65 kfstsingleton: $o ).
% 3.11/1.65
% 3.11/1.65 thf(kfstsingleton,definition,
% 3.11/1.65 ( kfstsingleton
% 3.11/1.65 = ( ! [Xu: $i] :
% 3.11/1.65 ( ( iskpair @ Xu )
% 3.11/1.65 => ( singleton
% 3.11/1.65 @ ( dsetconstr @ ( setunion @ Xu )
% 3.11/1.65 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(theprop_type,type,
% 3.11/1.65 theprop: $o ).
% 3.11/1.65
% 3.11/1.65 thf(theprop,definition,
% 3.11/1.65 ( theprop
% 3.11/1.65 = ( ! [X: $i] :
% 3.11/1.65 ( ( singleton @ X )
% 3.11/1.65 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(kfst_type,type,
% 3.11/1.65 kfst: $i > $i ).
% 3.11/1.65
% 3.11/1.65 thf(kfstpairEq_type,type,
% 3.11/1.65 kfstpairEq: $o ).
% 3.11/1.65
% 3.11/1.65 thf(kfstpairEq,definition,
% 3.11/1.65 ( kfstpairEq
% 3.11/1.65 = ( ! [Xx: $i,Xy: $i] :
% 3.11/1.65 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 3.11/1.65 = Xx ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(cartprodfstin_type,type,
% 3.11/1.65 cartprodfstin: $o ).
% 3.11/1.65
% 3.11/1.65 thf(cartprodfstin,definition,
% 3.11/1.65 ( cartprodfstin
% 3.11/1.65 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.11/1.65 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.11/1.65 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(setukpairinjL2_type,type,
% 3.11/1.65 setukpairinjL2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setukpairinjL2,definition,
% 3.11/1.65 ( setukpairinjL2
% 3.11/1.65 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.11/1.65 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.11/1.65 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.11/1.65 => ( Xx = Xz ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(setukpairinjL_type,type,
% 3.11/1.65 setukpairinjL: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setukpairinjL,definition,
% 3.11/1.65 ( setukpairinjL
% 3.11/1.65 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.11/1.65 ( ( ( kpair @ Xx @ Xy )
% 3.11/1.65 = ( kpair @ Xz @ Xu ) )
% 3.11/1.65 => ( Xx = Xz ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(setukpairinjR11_type,type,
% 3.11/1.65 setukpairinjR11: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setukpairinjR11,definition,
% 3.11/1.65 ( setukpairinjR11
% 3.11/1.65 = ( ! [Xx: $i,Xy: $i] :
% 3.11/1.65 ( ( Xx = Xy )
% 3.11/1.65 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.11/1.65 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(setukpairinjR12_type,type,
% 3.11/1.65 setukpairinjR12: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setukpairinjR12,definition,
% 3.11/1.65 ( setukpairinjR12
% 3.11/1.65 = ( ! [Xx: $i,Xy: $i] :
% 3.11/1.65 ( ( Xx = Xy )
% 3.11/1.65 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.11/1.65 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(setukpairinjR1_type,type,
% 3.11/1.65 setukpairinjR1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setukpairinjR1,definition,
% 3.11/1.65 ( setukpairinjR1
% 3.11/1.65 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.11/1.65 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.11/1.65 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.11/1.65 => ( ( Xz = Xu )
% 3.11/1.65 => ( Xy = Xu ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(upairequniteq_type,type,
% 3.11/1.65 upairequniteq: $o ).
% 3.11/1.65
% 3.11/1.65 thf(upairequniteq,definition,
% 3.11/1.65 ( upairequniteq
% 3.11/1.65 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.11/1.65 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.11/1.65 = ( setadjoin @ Xz @ emptyset ) )
% 3.11/1.65 => ( Xx = Xy ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(setukpairinjR2_type,type,
% 3.11/1.65 setukpairinjR2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setukpairinjR2,definition,
% 3.11/1.65 ( setukpairinjR2
% 3.11/1.65 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.11/1.65 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.11/1.65 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.11/1.65 => ( Xy = Xu ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(setukpairinjR_type,type,
% 3.11/1.65 setukpairinjR: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setukpairinjR,definition,
% 3.11/1.65 ( setukpairinjR
% 3.11/1.65 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.11/1.65 ( ( ( kpair @ Xx @ Xy )
% 3.11/1.65 = ( kpair @ Xz @ Xu ) )
% 3.11/1.65 => ( Xy = Xu ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(ksndsingleton_type,type,
% 3.11/1.65 ksndsingleton: $o ).
% 3.11/1.65
% 3.11/1.65 thf(ksndsingleton,definition,
% 3.11/1.65 ( ksndsingleton
% 3.11/1.65 = ( ! [Xu: $i] :
% 3.11/1.65 ( ( iskpair @ Xu )
% 3.11/1.65 => ( singleton
% 3.11/1.65 @ ( dsetconstr @ ( setunion @ Xu )
% 3.11/1.65 @ ^ [Xx: $i] :
% 3.11/1.65 ( Xu
% 3.11/1.65 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(ksnd_type,type,
% 3.11/1.65 ksnd: $i > $i ).
% 3.11/1.65
% 3.11/1.65 thf(ksndpairEq_type,type,
% 3.11/1.65 ksndpairEq: $o ).
% 3.11/1.65
% 3.11/1.65 thf(ksndpairEq,definition,
% 3.11/1.65 ( ksndpairEq
% 3.11/1.65 = ( ! [Xx: $i,Xy: $i] :
% 3.11/1.65 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 3.11/1.65 = Xy ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(kpairsurjEq_type,type,
% 3.11/1.65 kpairsurjEq: $o ).
% 3.11/1.65
% 3.11/1.65 thf(kpairsurjEq,definition,
% 3.11/1.65 ( kpairsurjEq
% 3.11/1.65 = ( ! [Xu: $i] :
% 3.11/1.65 ( ( iskpair @ Xu )
% 3.11/1.65 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 3.11/1.65 = Xu ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(cartprodsndin_type,type,
% 3.11/1.65 cartprodsndin: $o ).
% 3.11/1.65
% 3.11/1.65 thf(cartprodsndin,definition,
% 3.11/1.65 ( cartprodsndin
% 3.11/1.65 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.11/1.65 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.11/1.65 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(cartprodpairmemEL_type,type,
% 3.11/1.65 cartprodpairmemEL: $o ).
% 3.11/1.65
% 3.11/1.65 thf(cartprodpairmemEL,definition,
% 3.11/1.65 ( cartprodpairmemEL
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 3.11/1.65 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 3.11/1.65 => ( in @ Xx @ A ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(cartprodpairmemER_type,type,
% 3.11/1.65 cartprodpairmemER: $o ).
% 3.11/1.65
% 3.11/1.65 thf(cartprodpairmemER,definition,
% 3.11/1.65 ( cartprodpairmemER
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 3.11/1.65 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 3.11/1.65 => ( in @ Xy @ B ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(cartprodmempaircEq_type,type,
% 3.11/1.65 cartprodmempaircEq: $o ).
% 3.11/1.65
% 3.11/1.65 thf(cartprodmempaircEq,definition,
% 3.11/1.65 ( cartprodmempaircEq
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ B )
% 3.11/1.65 => ( ( kpair @ Xx @ Xy )
% 3.11/1.65 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(cartprodfstpairEq_type,type,
% 3.11/1.65 cartprodfstpairEq: $o ).
% 3.11/1.65
% 3.11/1.65 thf(cartprodfstpairEq,definition,
% 3.11/1.65 ( cartprodfstpairEq
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ B )
% 3.11/1.65 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 3.11/1.65 = Xx ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(cartprodsndpairEq_type,type,
% 3.11/1.65 cartprodsndpairEq: $o ).
% 3.11/1.65
% 3.11/1.65 thf(cartprodsndpairEq,definition,
% 3.11/1.65 ( cartprodsndpairEq
% 3.11/1.65 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ B )
% 3.11/1.65 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 3.11/1.65 = Xy ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(cartprodpairsurjEq_type,type,
% 3.11/1.65 cartprodpairsurjEq: $o ).
% 3.11/1.65
% 3.11/1.65 thf(cartprodpairsurjEq,definition,
% 3.11/1.65 ( cartprodpairsurjEq
% 3.11/1.65 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.11/1.65 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.11/1.65 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 3.11/1.65 = Xu ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(breln_type,type,
% 3.11/1.65 breln: $i > $i > $i > $o ).
% 3.11/1.65
% 3.11/1.65 thf(dpsetconstr_type,type,
% 3.11/1.65 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 3.11/1.65
% 3.11/1.65 thf(dpsetconstrI_type,type,
% 3.11/1.65 dpsetconstrI: $o ).
% 3.11/1.65
% 3.11/1.65 thf(dpsetconstrI,definition,
% 3.11/1.65 ( dpsetconstrI
% 3.11/1.65 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ B )
% 3.11/1.65 => ( ( Xphi @ Xx @ Xy )
% 3.11/1.65 => ( in @ ( kpair @ Xx @ Xy )
% 3.11/1.65 @ ( dpsetconstr @ A @ B
% 3.11/1.65 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(dpsetconstrSub_type,type,
% 3.11/1.65 dpsetconstrSub: $o ).
% 3.11/1.65
% 3.11/1.65 thf(dpsetconstrSub,definition,
% 3.11/1.65 ( dpsetconstrSub
% 3.11/1.65 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.11/1.65 ( subset
% 3.11/1.65 @ ( dpsetconstr @ A @ B
% 3.11/1.65 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 3.11/1.65 @ ( cartprod @ A @ B ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(setOfPairsIsBReln_type,type,
% 3.11/1.65 setOfPairsIsBReln: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setOfPairsIsBReln,definition,
% 3.11/1.65 ( setOfPairsIsBReln
% 3.11/1.65 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.11/1.65 ( breln @ A @ B
% 3.11/1.65 @ ( dpsetconstr @ A @ B
% 3.11/1.65 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(dpsetconstrERa_type,type,
% 3.11/1.65 dpsetconstrERa: $o ).
% 3.11/1.65
% 3.11/1.65 thf(dpsetconstrERa,definition,
% 3.11/1.65 ( dpsetconstrERa
% 3.11/1.65 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ B )
% 3.11/1.65 => ( ( in @ ( kpair @ Xx @ Xy )
% 3.11/1.65 @ ( dpsetconstr @ A @ B
% 3.11/1.65 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.11/1.65 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(dpsetconstrEL1_type,type,
% 3.11/1.65 dpsetconstrEL1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(dpsetconstrEL1,definition,
% 3.11/1.65 ( dpsetconstrEL1
% 3.11/1.65 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.11/1.65 ( ( in @ ( kpair @ Xx @ Xy )
% 3.11/1.65 @ ( dpsetconstr @ A @ B
% 3.11/1.65 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.11/1.65 => ( in @ Xx @ A ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(dpsetconstrEL2_type,type,
% 3.11/1.65 dpsetconstrEL2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(dpsetconstrEL2,definition,
% 3.11/1.65 ( dpsetconstrEL2
% 3.11/1.65 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.11/1.65 ( ( in @ ( kpair @ Xx @ Xy )
% 3.11/1.65 @ ( dpsetconstr @ A @ B
% 3.11/1.65 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.11/1.65 => ( in @ Xy @ B ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(dpsetconstrER_type,type,
% 3.11/1.65 dpsetconstrER: $o ).
% 3.11/1.65
% 3.11/1.65 thf(dpsetconstrER,definition,
% 3.11/1.65 ( dpsetconstrER
% 3.11/1.65 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.11/1.65 ( ( in @ ( kpair @ Xx @ Xy )
% 3.11/1.65 @ ( dpsetconstr @ A @ B
% 3.11/1.65 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.11/1.65 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(func_type,type,
% 3.11/1.65 func: $i > $i > $i > $o ).
% 3.11/1.65
% 3.11/1.65 thf(funcSet_type,type,
% 3.11/1.65 funcSet: $i > $i > $i ).
% 3.11/1.65
% 3.11/1.65 thf(funcImageSingleton_type,type,
% 3.11/1.65 funcImageSingleton: $o ).
% 3.11/1.65
% 3.11/1.65 thf(funcImageSingleton,definition,
% 3.11/1.65 ( funcImageSingleton
% 3.11/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.11/1.65 ( ( func @ A @ B @ Xf )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( singleton
% 3.11/1.65 @ ( dsetconstr @ B
% 3.11/1.65 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(apProp_type,type,
% 3.11/1.65 apProp: $o ).
% 3.11/1.65
% 3.11/1.65 thf(apProp,definition,
% 3.11/1.65 ( apProp
% 3.11/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.11/1.65 ( ( func @ A @ B @ Xf )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( in
% 3.11/1.65 @ ( setunion
% 3.11/1.65 @ ( dsetconstr @ B
% 3.11/1.65 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 3.11/1.65 @ B ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(ap_type,type,
% 3.11/1.65 ap: $i > $i > $i > $i > $i ).
% 3.11/1.65
% 3.11/1.65 thf(app_type,type,
% 3.11/1.65 app: $o ).
% 3.11/1.65
% 3.11/1.65 thf(app,definition,
% 3.11/1.65 ( app
% 3.11/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.11/1.65 ( ( func @ A @ B @ Xf )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(infuncsetfunc_type,type,
% 3.11/1.65 infuncsetfunc: $o ).
% 3.11/1.65
% 3.11/1.65 thf(infuncsetfunc,definition,
% 3.11/1.65 ( infuncsetfunc
% 3.11/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.11/1.65 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.11/1.65 => ( func @ A @ B @ Xf ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(ap2p_type,type,
% 3.11/1.65 ap2p: $o ).
% 3.11/1.65
% 3.11/1.65 thf(ap2p,definition,
% 3.11/1.65 ( ap2p
% 3.11/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.11/1.65 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(funcinfuncset_type,type,
% 3.11/1.65 funcinfuncset: $o ).
% 3.11/1.65
% 3.11/1.65 thf(funcinfuncset,definition,
% 3.11/1.65 ( funcinfuncset
% 3.11/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.11/1.65 ( ( func @ A @ B @ Xf )
% 3.11/1.65 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(lamProp_type,type,
% 3.11/1.65 lamProp: $o ).
% 3.11/1.65
% 3.11/1.65 thf(lamProp,definition,
% 3.11/1.65 ( lamProp
% 3.11/1.65 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.11/1.65 ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.11/1.65 => ( func @ A @ B
% 3.11/1.65 @ ( dpsetconstr @ A @ B
% 3.11/1.65 @ ^ [Xx: $i,Xy: $i] :
% 3.11/1.65 ( ( Xf @ Xx )
% 3.11/1.65 = Xy ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(lam_type,type,
% 3.11/1.65 lam: $i > $i > ( $i > $i ) > $i ).
% 3.11/1.65
% 3.11/1.65 thf(lamp_type,type,
% 3.11/1.65 lamp: $o ).
% 3.11/1.65
% 3.11/1.65 thf(lamp,definition,
% 3.11/1.65 ( lamp
% 3.11/1.65 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.11/1.65 ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.11/1.65 => ( func @ A @ B
% 3.11/1.65 @ ( lam @ A @ B
% 3.11/1.65 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(lam2p_type,type,
% 3.11/1.65 lam2p: $o ).
% 3.11/1.65
% 3.11/1.65 thf(lam2p,definition,
% 3.11/1.65 ( lam2p
% 3.11/1.65 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.11/1.65 ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.11/1.65 => ( in
% 3.11/1.65 @ ( lam @ A @ B
% 3.11/1.65 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 3.11/1.65 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(brelnall1_type,type,
% 3.11/1.65 brelnall1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(brelnall1,definition,
% 3.11/1.65 ( brelnall1
% 3.11/1.65 = ( ! [A: $i,B: $i,R: $i] :
% 3.11/1.65 ( ( breln @ A @ B @ R )
% 3.11/1.65 => ! [Xphi: $i > $o] :
% 3.11/1.65 ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ B )
% 3.11/1.65 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.11/1.65 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ R )
% 3.11/1.65 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(brelnall2_type,type,
% 3.11/1.65 brelnall2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(brelnall2,definition,
% 3.11/1.65 ( brelnall2
% 3.11/1.65 = ( ! [A: $i,B: $i,R: $i] :
% 3.11/1.65 ( ( breln @ A @ B @ R )
% 3.11/1.65 => ! [Xphi: $i > $o] :
% 3.11/1.65 ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ B )
% 3.11/1.65 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.11/1.65 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ R )
% 3.11/1.65 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(ex1E2_type,type,
% 3.11/1.65 ex1E2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(ex1E2,definition,
% 3.11/1.65 ( ex1E2
% 3.11/1.65 = ( ! [A: $i,Xphi: $i > $o] :
% 3.11/1.65 ( ( ex1 @ A
% 3.11/1.65 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 => ( ( Xphi @ Xx )
% 3.11/1.65 => ( ( Xphi @ Xy )
% 3.11/1.65 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(funcGraphProp1_type,type,
% 3.11/1.65 funcGraphProp1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(funcGraphProp1,definition,
% 3.11/1.65 ( funcGraphProp1
% 3.11/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.11/1.65 ( ( func @ A @ B @ Xf )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(funcGraphProp3_type,type,
% 3.11/1.65 funcGraphProp3: $o ).
% 3.11/1.65
% 3.11/1.65 thf(funcGraphProp3,definition,
% 3.11/1.65 ( funcGraphProp3
% 3.11/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.11/1.65 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(funcGraphProp2_type,type,
% 3.11/1.65 funcGraphProp2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(funcGraphProp2,definition,
% 3.11/1.65 ( funcGraphProp2
% 3.11/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.11/1.65 ( ( func @ A @ B @ Xf )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ B )
% 3.11/1.65 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 3.11/1.65 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.11/1.65 = Xy ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(funcextLem_type,type,
% 3.11/1.65 funcextLem: $o ).
% 3.11/1.65
% 3.11/1.65 thf(funcextLem,definition,
% 3.11/1.65 ( funcextLem
% 3.11/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.11/1.65 ( ( func @ A @ B @ Xf )
% 3.11/1.65 => ! [Xg: $i] :
% 3.11/1.65 ( ( func @ A @ B @ Xg )
% 3.11/1.65 => ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.11/1.65 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ B )
% 3.11/1.65 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 3.11/1.65 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(funcGraphProp4_type,type,
% 3.11/1.65 funcGraphProp4: $o ).
% 3.11/1.65
% 3.11/1.65 thf(funcGraphProp4,definition,
% 3.11/1.65 ( funcGraphProp4
% 3.11/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.11/1.65 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ B )
% 3.11/1.65 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 3.11/1.65 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.11/1.65 = Xy ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(subbreln_type,type,
% 3.11/1.65 subbreln: $o ).
% 3.11/1.65
% 3.11/1.65 thf(subbreln,definition,
% 3.11/1.65 ( subbreln
% 3.11/1.65 = ( ! [A: $i,B: $i,R: $i] :
% 3.11/1.65 ( ( breln @ A @ B @ R )
% 3.11/1.65 => ! [S: $i] :
% 3.11/1.65 ( ( breln @ A @ B @ S )
% 3.11/1.65 => ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ B )
% 3.11/1.65 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.11/1.65 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.11/1.65 => ( subset @ R @ S ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(eqbreln_type,type,
% 3.11/1.65 eqbreln: $o ).
% 3.11/1.65
% 3.11/1.65 thf(eqbreln,definition,
% 3.11/1.65 ( eqbreln
% 3.11/1.65 = ( ! [A: $i,B: $i,R: $i] :
% 3.11/1.65 ( ( breln @ A @ B @ R )
% 3.11/1.65 => ! [S: $i] :
% 3.11/1.65 ( ( breln @ A @ B @ S )
% 3.11/1.65 => ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ B )
% 3.11/1.65 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.11/1.65 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.11/1.65 => ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ B )
% 3.11/1.65 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.11/1.65 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 3.11/1.65 => ( R = S ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(funcext_type,type,
% 3.11/1.65 funcext: $o ).
% 3.11/1.65
% 3.11/1.65 thf(funcext,definition,
% 3.11/1.65 ( funcext
% 3.11/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.11/1.65 ( ( func @ A @ B @ Xf )
% 3.11/1.65 => ! [Xg: $i] :
% 3.11/1.65 ( ( func @ A @ B @ Xg )
% 3.11/1.65 => ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.11/1.65 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.11/1.65 => ( Xf = Xg ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(funcext2_type,type,
% 3.11/1.65 funcext2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(funcext2,definition,
% 3.11/1.65 ( funcext2
% 3.11/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.11/1.65 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.11/1.65 => ! [Xg: $i] :
% 3.11/1.65 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 3.11/1.65 => ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.11/1.65 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.11/1.65 => ( Xf = Xg ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(ap2apEq1_type,type,
% 3.11/1.65 ap2apEq1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(ap2apEq1,definition,
% 3.11/1.65 ( ap2apEq1
% 3.11/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.11/1.65 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.11/1.65 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(ap2apEq2_type,type,
% 3.11/1.65 ap2apEq2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(ap2apEq2,definition,
% 3.11/1.65 ( ap2apEq2
% 3.11/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.11/1.65 ( ( func @ A @ B @ Xf )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.11/1.65 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(beta1_type,type,
% 3.11/1.65 beta1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(beta1,definition,
% 3.11/1.65 ( beta1
% 3.11/1.65 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.11/1.65 ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( ap @ A @ B
% 3.11/1.65 @ ( lam @ A @ B
% 3.11/1.65 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 3.11/1.65 @ Xx )
% 3.11/1.65 = ( Xf @ Xx ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(eta1_type,type,
% 3.11/1.65 eta1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(eta1,definition,
% 3.11/1.65 ( eta1
% 3.11/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.11/1.65 ( ( func @ A @ B @ Xf )
% 3.11/1.65 => ( ( lam @ A @ B
% 3.11/1.65 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 3.11/1.65 = Xf ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(lam2lamEq_type,type,
% 3.11/1.65 lam2lamEq: $o ).
% 3.11/1.65
% 3.11/1.65 thf(lam2lamEq,definition,
% 3.11/1.65 ( lam2lamEq
% 3.11/1.65 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.11/1.65 ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.11/1.65 => ( ( lam @ A @ B
% 3.11/1.65 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 3.11/1.65 = ( lam @ A @ B
% 3.11/1.65 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(beta2_type,type,
% 3.11/1.65 beta2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(beta2,definition,
% 3.11/1.65 ( beta2
% 3.11/1.65 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.11/1.65 ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( ap @ A @ B
% 3.11/1.65 @ ( lam @ A @ B
% 3.11/1.65 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 3.11/1.65 @ Xx )
% 3.11/1.65 = ( Xf @ Xx ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(eta2_type,type,
% 3.11/1.65 eta2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(eta2,definition,
% 3.11/1.65 ( eta2
% 3.11/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.11/1.65 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.11/1.65 => ( ( lam @ A @ B
% 3.11/1.65 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 3.11/1.65 = Xf ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(iffalseProp1_type,type,
% 3.11/1.65 iffalseProp1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(iffalseProp1,definition,
% 3.11/1.65 ( iffalseProp1
% 3.11/1.65 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 => ( ~ Xphi
% 3.11/1.65 => ( in @ Xy
% 3.11/1.65 @ ( dsetconstr @ A
% 3.11/1.65 @ ^ [Xz: $i] :
% 3.11/1.65 ( ( Xphi
% 3.11/1.65 & ( Xz = Xx ) )
% 3.11/1.65 | ( ~ Xphi
% 3.11/1.65 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(iffalseProp2_type,type,
% 3.11/1.65 iffalseProp2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(iffalseProp2,definition,
% 3.11/1.65 ( iffalseProp2
% 3.11/1.65 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 => ( ~ Xphi
% 3.11/1.65 => ( ( dsetconstr @ A
% 3.11/1.65 @ ^ [Xz: $i] :
% 3.11/1.65 ( ( Xphi
% 3.11/1.65 & ( Xz = Xx ) )
% 3.11/1.65 | ( ~ Xphi
% 3.11/1.65 & ( Xz = Xy ) ) ) )
% 3.11/1.65 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(iftrueProp1_type,type,
% 3.11/1.65 iftrueProp1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(iftrueProp1,definition,
% 3.11/1.65 ( iftrueProp1
% 3.11/1.65 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 => ( Xphi
% 3.11/1.65 => ( in @ Xx
% 3.11/1.65 @ ( dsetconstr @ A
% 3.11/1.65 @ ^ [Xz: $i] :
% 3.11/1.65 ( ( Xphi
% 3.11/1.65 & ( Xz = Xx ) )
% 3.11/1.65 | ( ~ Xphi
% 3.11/1.65 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(iftrueProp2_type,type,
% 3.11/1.65 iftrueProp2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(iftrueProp2,definition,
% 3.11/1.65 ( iftrueProp2
% 3.11/1.65 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 => ( Xphi
% 3.11/1.65 => ( ( dsetconstr @ A
% 3.11/1.65 @ ^ [Xz: $i] :
% 3.11/1.65 ( ( Xphi
% 3.11/1.65 & ( Xz = Xx ) )
% 3.11/1.65 | ( ~ Xphi
% 3.11/1.65 & ( Xz = Xy ) ) ) )
% 3.11/1.65 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(ifSingleton_type,type,
% 3.11/1.65 ifSingleton: $o ).
% 3.11/1.65
% 3.11/1.65 thf(ifSingleton,definition,
% 3.11/1.65 ( ifSingleton
% 3.11/1.65 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 => ( singleton
% 3.11/1.65 @ ( dsetconstr @ A
% 3.11/1.65 @ ^ [Xz: $i] :
% 3.11/1.65 ( ( Xphi
% 3.11/1.65 & ( Xz = Xx ) )
% 3.11/1.65 | ( ~ Xphi
% 3.11/1.65 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(if_type,type,
% 3.11/1.65 if: $i > $o > $i > $i > $i ).
% 3.11/1.65
% 3.11/1.65 thf(ifp_type,type,
% 3.11/1.65 ifp: $o ).
% 3.11/1.65
% 3.11/1.65 thf(ifp,definition,
% 3.11/1.65 ( ifp
% 3.11/1.65 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(theeq_type,type,
% 3.11/1.65 theeq: $o ).
% 3.11/1.65
% 3.11/1.65 thf(theeq,definition,
% 3.11/1.65 ( theeq
% 3.11/1.65 = ( ! [X: $i] :
% 3.11/1.65 ( ( singleton @ X )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ X )
% 3.11/1.65 => ( ( setunion @ X )
% 3.11/1.65 = Xx ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(iftrue_type,type,
% 3.11/1.65 iftrue: $o ).
% 3.11/1.65
% 3.11/1.65 thf(iftrue,definition,
% 3.11/1.65 ( iftrue
% 3.11/1.65 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 => ( Xphi
% 3.11/1.65 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 3.11/1.65 = Xx ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(iffalse_type,type,
% 3.11/1.65 iffalse: $o ).
% 3.11/1.65
% 3.11/1.65 thf(iffalse,definition,
% 3.11/1.65 ( iffalse
% 3.11/1.65 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 => ( ~ Xphi
% 3.11/1.65 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 3.11/1.65 = Xy ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(iftrueorfalse_type,type,
% 3.11/1.65 iftrueorfalse: $o ).
% 3.11/1.65
% 3.11/1.65 thf(iftrueorfalse,definition,
% 3.11/1.65 ( iftrueorfalse
% 3.11/1.65 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(binintersectT_lem_type,type,
% 3.11/1.65 binintersectT_lem: $o ).
% 3.11/1.65
% 3.11/1.65 thf(binintersectT_lem,definition,
% 3.11/1.65 ( binintersectT_lem
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(binunionT_lem_type,type,
% 3.11/1.65 binunionT_lem: $o ).
% 3.11/1.65
% 3.11/1.65 thf(binunionT_lem,definition,
% 3.11/1.65 ( binunionT_lem
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(powersetT_lem_type,type,
% 3.11/1.65 powersetT_lem: $o ).
% 3.11/1.65
% 3.11/1.65 thf(powersetT_lem,definition,
% 3.11/1.65 ( powersetT_lem
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(setminusT_lem_type,type,
% 3.11/1.65 setminusT_lem: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setminusT_lem,definition,
% 3.11/1.65 ( setminusT_lem
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(complementT_lem_type,type,
% 3.11/1.65 complementT_lem: $o ).
% 3.11/1.65
% 3.11/1.65 thf(complementT_lem,definition,
% 3.11/1.65 ( complementT_lem
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(setextT_type,type,
% 3.11/1.65 setextT: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setextT,definition,
% 3.11/1.65 ( setextT
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( in @ Xx @ X )
% 3.11/1.65 => ( in @ Xx @ Y ) ) )
% 3.11/1.65 => ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( in @ Xx @ Y )
% 3.11/1.65 => ( in @ Xx @ X ) ) )
% 3.11/1.65 => ( X = Y ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(subsetTI_type,type,
% 3.11/1.65 subsetTI: $o ).
% 3.11/1.65
% 3.11/1.65 thf(subsetTI,definition,
% 3.11/1.65 ( subsetTI
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( in @ Xx @ X )
% 3.11/1.65 => ( in @ Xx @ Y ) ) )
% 3.11/1.65 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(powersetTI1_type,type,
% 3.11/1.65 powersetTI1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(powersetTI1,definition,
% 3.11/1.65 ( powersetTI1
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( in @ Xx @ X )
% 3.11/1.65 => ( in @ Xx @ Y ) ) )
% 3.11/1.65 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(powersetTE1_type,type,
% 3.11/1.65 powersetTE1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(powersetTE1,definition,
% 3.11/1.65 ( powersetTE1
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( in @ X @ ( powerset @ Y ) )
% 3.11/1.65 => ( ( in @ Xx @ X )
% 3.11/1.65 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(complementTI1_type,type,
% 3.11/1.65 complementTI1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(complementTI1,definition,
% 3.11/1.65 ( complementTI1
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( in @ Xx @ X )
% 3.11/1.65 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(complementTE1_type,type,
% 3.11/1.65 complementTE1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(complementTE1,definition,
% 3.11/1.65 ( complementTE1
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 3.11/1.65 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(binintersectTELcontra_type,type,
% 3.11/1.65 binintersectTELcontra: $o ).
% 3.11/1.65
% 3.11/1.65 thf(binintersectTELcontra,definition,
% 3.11/1.65 ( binintersectTELcontra
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ~ ( in @ Xx @ X )
% 3.11/1.65 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(binintersectTERcontra_type,type,
% 3.11/1.65 binintersectTERcontra: $o ).
% 3.11/1.65
% 3.11/1.65 thf(binintersectTERcontra,definition,
% 3.11/1.65 ( binintersectTERcontra
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ~ ( in @ Xx @ Y )
% 3.11/1.65 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(contrasubsetT_type,type,
% 3.11/1.65 contrasubsetT: $o ).
% 3.11/1.65
% 3.11/1.65 thf(contrasubsetT,definition,
% 3.11/1.65 ( contrasubsetT
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.11/1.65 => ( ( in @ Xx @ Y )
% 3.11/1.65 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(contrasubsetT1_type,type,
% 3.11/1.65 contrasubsetT1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(contrasubsetT1,definition,
% 3.11/1.65 ( contrasubsetT1
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( subset @ X @ Y )
% 3.11/1.65 => ( ~ ( in @ Xx @ Y )
% 3.11/1.65 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(contrasubsetT2_type,type,
% 3.11/1.65 contrasubsetT2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(contrasubsetT2,definition,
% 3.11/1.65 ( contrasubsetT2
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ( ( subset @ X @ Y )
% 3.11/1.65 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(contrasubsetT3_type,type,
% 3.11/1.65 contrasubsetT3: $o ).
% 3.11/1.65
% 3.11/1.65 thf(contrasubsetT3,definition,
% 3.11/1.65 ( contrasubsetT3
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 3.11/1.65 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(doubleComplementI1_type,type,
% 3.11/1.65 doubleComplementI1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(doubleComplementI1,definition,
% 3.11/1.65 ( doubleComplementI1
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( in @ Xx @ X )
% 3.11/1.65 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(doubleComplementE1_type,type,
% 3.11/1.65 doubleComplementE1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(doubleComplementE1,definition,
% 3.11/1.65 ( doubleComplementE1
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 3.11/1.65 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(doubleComplementSub1_type,type,
% 3.11/1.65 doubleComplementSub1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(doubleComplementSub1,definition,
% 3.11/1.65 ( doubleComplementSub1
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(doubleComplementSub2_type,type,
% 3.11/1.65 doubleComplementSub2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(doubleComplementSub2,definition,
% 3.11/1.65 ( doubleComplementSub2
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(doubleComplementEq_type,type,
% 3.11/1.65 doubleComplementEq: $o ).
% 3.11/1.65
% 3.11/1.65 thf(doubleComplementEq,definition,
% 3.11/1.65 ( doubleComplementEq
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ( X
% 3.11/1.65 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(complementTnotintersectT_type,type,
% 3.11/1.65 complementTnotintersectT: $o ).
% 3.11/1.65
% 3.11/1.65 thf(complementTnotintersectT,definition,
% 3.11/1.65 ( complementTnotintersectT
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.11/1.65 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(complementImpComplementIntersect_type,type,
% 3.11/1.65 complementImpComplementIntersect: $o ).
% 3.11/1.65
% 3.11/1.65 thf(complementImpComplementIntersect,definition,
% 3.11/1.65 ( complementImpComplementIntersect
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.11/1.65 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(complementSubsetComplementIntersect_type,type,
% 3.11/1.65 complementSubsetComplementIntersect: $o ).
% 3.11/1.65
% 3.11/1.65 thf(complementSubsetComplementIntersect,definition,
% 3.11/1.65 ( complementSubsetComplementIntersect
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(complementInPowersetComplementIntersect_type,type,
% 3.11/1.65 complementInPowersetComplementIntersect: $o ).
% 3.11/1.65
% 3.11/1.65 thf(complementInPowersetComplementIntersect,definition,
% 3.11/1.65 ( complementInPowersetComplementIntersect
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(contraSubsetComplement_type,type,
% 3.11/1.65 contraSubsetComplement: $o ).
% 3.11/1.65
% 3.11/1.65 thf(contraSubsetComplement,definition,
% 3.11/1.65 ( contraSubsetComplement
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( in @ Xx @ Y )
% 3.11/1.65 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(complementTcontraSubset_type,type,
% 3.11/1.65 complementTcontraSubset: $o ).
% 3.11/1.65
% 3.11/1.65 thf(complementTcontraSubset,definition,
% 3.11/1.65 ( complementTcontraSubset
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.11/1.65 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(binunionTILcontra_type,type,
% 3.11/1.65 binunionTILcontra: $o ).
% 3.11/1.65
% 3.11/1.65 thf(binunionTILcontra,definition,
% 3.11/1.65 ( binunionTILcontra
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.11/1.65 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(binunionTIRcontra_type,type,
% 3.11/1.65 binunionTIRcontra: $o ).
% 3.11/1.65
% 3.11/1.65 thf(binunionTIRcontra,definition,
% 3.11/1.65 ( binunionTIRcontra
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.11/1.65 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(inIntersectImpInUnion_type,type,
% 3.11/1.65 inIntersectImpInUnion: $o ).
% 3.11/1.65
% 3.11/1.65 thf(inIntersectImpInUnion,definition,
% 3.11/1.65 ( inIntersectImpInUnion
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Z: $i] :
% 3.11/1.65 ( ( in @ Z @ ( powerset @ A ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.11/1.65 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(inIntersectImpInUnion2_type,type,
% 3.11/1.65 inIntersectImpInUnion2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(inIntersectImpInUnion2,definition,
% 3.11/1.65 ( inIntersectImpInUnion2
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Z: $i] :
% 3.11/1.65 ( ( in @ Z @ ( powerset @ A ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.11/1.65 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(inIntersectImpInIntersectUnions_type,type,
% 3.11/1.65 inIntersectImpInIntersectUnions: $o ).
% 3.11/1.65
% 3.11/1.65 thf(inIntersectImpInIntersectUnions,definition,
% 3.11/1.65 ( inIntersectImpInIntersectUnions
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Z: $i] :
% 3.11/1.65 ( ( in @ Z @ ( powerset @ A ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.11/1.65 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(intersectInPowersetIntersectUnions_type,type,
% 3.11/1.65 intersectInPowersetIntersectUnions: $o ).
% 3.11/1.65
% 3.11/1.65 thf(intersectInPowersetIntersectUnions,definition,
% 3.11/1.65 ( intersectInPowersetIntersectUnions
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Z: $i] :
% 3.11/1.65 ( ( in @ Z @ ( powerset @ A ) )
% 3.11/1.65 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(inComplementUnionImpNotIn1_type,type,
% 3.11/1.65 inComplementUnionImpNotIn1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(inComplementUnionImpNotIn1,definition,
% 3.11/1.65 ( inComplementUnionImpNotIn1
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.11/1.65 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(inComplementUnionImpInComplement1_type,type,
% 3.11/1.65 inComplementUnionImpInComplement1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(inComplementUnionImpInComplement1,definition,
% 3.11/1.65 ( inComplementUnionImpInComplement1
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.11/1.65 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(binunionTE_type,type,
% 3.11/1.65 binunionTE: $o ).
% 3.11/1.65
% 3.11/1.65 thf(binunionTE,definition,
% 3.11/1.65 ( binunionTE
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Xphi: $o,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.11/1.65 => ( ( ( in @ Xx @ X )
% 3.11/1.65 => Xphi )
% 3.11/1.65 => ( ( ( in @ Xx @ Y )
% 3.11/1.65 => Xphi )
% 3.11/1.65 => Xphi ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(binunionTEcontra_type,type,
% 3.11/1.65 binunionTEcontra: $o ).
% 3.11/1.65
% 3.11/1.65 thf(binunionTEcontra,definition,
% 3.11/1.65 ( binunionTEcontra
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ~ ( in @ Xx @ X )
% 3.11/1.65 => ( ~ ( in @ Xx @ Y )
% 3.11/1.65 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(demorgan2a1_type,type,
% 3.11/1.65 demorgan2a1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(demorgan2a1,definition,
% 3.11/1.65 ( demorgan2a1
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.11/1.65 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(complementUnionInPowersetComplement_type,type,
% 3.11/1.65 complementUnionInPowersetComplement: $o ).
% 3.11/1.65
% 3.11/1.65 thf(complementUnionInPowersetComplement,definition,
% 3.11/1.65 ( complementUnionInPowersetComplement
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(demorgan2a2_type,type,
% 3.11/1.65 demorgan2a2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(demorgan2a2,definition,
% 3.11/1.65 ( demorgan2a2
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.11/1.65 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(demorgan1a_type,type,
% 3.11/1.65 demorgan1a: $o ).
% 3.11/1.65
% 3.11/1.65 thf(demorgan1a,definition,
% 3.11/1.65 ( demorgan1a
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 3.11/1.65 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(demorgan1b_type,type,
% 3.11/1.65 demorgan1b: $o ).
% 3.11/1.65
% 3.11/1.65 thf(demorgan1b,definition,
% 3.11/1.65 ( demorgan1b
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 3.11/1.65 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(demorgan1_type,type,
% 3.11/1.65 demorgan1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(demorgan1,definition,
% 3.11/1.65 ( demorgan1
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 3.11/1.65 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(demorgan2a_type,type,
% 3.11/1.65 demorgan2a: $o ).
% 3.11/1.65
% 3.11/1.65 thf(demorgan2a,definition,
% 3.11/1.65 ( demorgan2a
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.11/1.65 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(demorgan2b2_type,type,
% 3.11/1.65 demorgan2b2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(demorgan2b2,definition,
% 3.11/1.65 ( demorgan2b2
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.11/1.65 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 3.11/1.65 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(demorgan2b_type,type,
% 3.11/1.65 demorgan2b: $o ).
% 3.11/1.65
% 3.11/1.65 thf(demorgan2b,definition,
% 3.11/1.65 ( demorgan2b
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 3.11/1.65 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(demorgan2_type,type,
% 3.11/1.65 demorgan2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(demorgan2,definition,
% 3.11/1.65 ( demorgan2
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 3.11/1.65 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(woz13rule0_type,type,
% 3.11/1.65 woz13rule0: $o ).
% 3.11/1.65
% 3.11/1.65 thf(woz13rule0,definition,
% 3.11/1.65 ( woz13rule0
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.11/1.65 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(woz13rule1_type,type,
% 3.11/1.65 woz13rule1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(woz13rule1,definition,
% 3.11/1.65 ( woz13rule1
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Z: $i] :
% 3.11/1.65 ( ( in @ Z @ ( powerset @ A ) )
% 3.11/1.65 => ( ( subset @ X @ Z )
% 3.11/1.65 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(woz13rule2_type,type,
% 3.11/1.65 woz13rule2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(woz13rule2,definition,
% 3.11/1.65 ( woz13rule2
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Z: $i] :
% 3.11/1.65 ( ( in @ Z @ ( powerset @ A ) )
% 3.11/1.65 => ( ( subset @ Y @ Z )
% 3.11/1.65 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(woz13rule3_type,type,
% 3.11/1.65 woz13rule3: $o ).
% 3.11/1.65
% 3.11/1.65 thf(woz13rule3,definition,
% 3.11/1.65 ( woz13rule3
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Z: $i] :
% 3.11/1.65 ( ( in @ Z @ ( powerset @ A ) )
% 3.11/1.65 => ( ( subset @ X @ Y )
% 3.11/1.65 => ( ( subset @ X @ Z )
% 3.11/1.65 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(woz13rule4_type,type,
% 3.11/1.65 woz13rule4: $o ).
% 3.11/1.65
% 3.11/1.65 thf(woz13rule4,definition,
% 3.11/1.65 ( woz13rule4
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Z: $i] :
% 3.11/1.65 ( ( in @ Z @ ( powerset @ A ) )
% 3.11/1.65 => ! [W: $i] :
% 3.11/1.65 ( ( in @ W @ ( powerset @ A ) )
% 3.11/1.65 => ( ( subset @ X @ Z )
% 3.11/1.65 => ( ( subset @ Y @ W )
% 3.11/1.65 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(woz1_1_type,type,
% 3.11/1.65 woz1_1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(woz1_1,definition,
% 3.11/1.65 ( woz1_1
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(woz1_2_type,type,
% 3.11/1.65 woz1_2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(woz1_2,definition,
% 3.11/1.65 ( woz1_2
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Z: $i] :
% 3.11/1.65 ( ( in @ Z @ ( powerset @ A ) )
% 3.11/1.65 => ! [W: $i] :
% 3.11/1.65 ( ( in @ W @ ( powerset @ A ) )
% 3.11/1.65 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 3.11/1.65 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(woz1_3_type,type,
% 3.11/1.65 woz1_3: $o ).
% 3.11/1.65
% 3.11/1.65 thf(woz1_3,definition,
% 3.11/1.65 ( woz1_3
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ! [Z: $i] :
% 3.11/1.65 ( ( in @ Z @ ( powerset @ A ) )
% 3.11/1.65 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(woz1_4_type,type,
% 3.11/1.65 woz1_4: $o ).
% 3.11/1.65
% 3.11/1.65 thf(woz1_4,definition,
% 3.11/1.65 ( woz1_4
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.11/1.65 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(woz1_5_type,type,
% 3.11/1.65 woz1_5: $o ).
% 3.11/1.65
% 3.11/1.65 thf(woz1_5,definition,
% 3.11/1.65 ( woz1_5
% 3.11/1.65 = ( ! [A: $i,X: $i] :
% 3.11/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.11/1.65 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(breln1_type,type,
% 3.11/1.65 breln1: $i > $i > $o ).
% 3.11/1.65
% 3.11/1.65 thf(breln1all2_type,type,
% 3.11/1.65 breln1all2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(breln1all2,definition,
% 3.11/1.65 ( breln1all2
% 3.11/1.65 = ( ! [A: $i,R: $i] :
% 3.11/1.65 ( ( breln1 @ A @ R )
% 3.11/1.65 => ! [Xphi: $i > $o] :
% 3.11/1.65 ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.11/1.65 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ R )
% 3.11/1.65 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(breln1Set_type,type,
% 3.11/1.65 breln1Set: $i > $i ).
% 3.11/1.65
% 3.11/1.65 thf(breln1SetBreln1_type,type,
% 3.11/1.65 breln1SetBreln1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(breln1SetBreln1,definition,
% 3.11/1.65 ( breln1SetBreln1
% 3.11/1.65 = ( ! [A: $i,R: $i] :
% 3.11/1.65 ( ( in @ R @ ( breln1Set @ A ) )
% 3.11/1.65 => ( breln1 @ A @ R ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(transitive_type,type,
% 3.11/1.65 transitive: $i > $i > $o ).
% 3.11/1.65
% 3.11/1.65 thf(antisymmetric_type,type,
% 3.11/1.65 antisymmetric: $i > $i > $o ).
% 3.11/1.65
% 3.11/1.65 thf(reflexive_type,type,
% 3.11/1.65 reflexive: $i > $i > $o ).
% 3.11/1.65
% 3.11/1.65 thf(refltransitive_type,type,
% 3.11/1.65 refltransitive: $i > $i > $o ).
% 3.11/1.65
% 3.11/1.65 thf(refllinearorder_type,type,
% 3.11/1.65 refllinearorder: $i > $i > $o ).
% 3.11/1.65
% 3.11/1.65 thf(reflwellordering_type,type,
% 3.11/1.65 reflwellordering: $i > $i > $o ).
% 3.11/1.65
% 3.11/1.65 thf(choice2fnsingleton_type,type,
% 3.11/1.65 choice2fnsingleton: $o ).
% 3.11/1.65
% 3.11/1.65 thf(choice2fnsingleton,definition,
% 3.11/1.65 ( choice2fnsingleton
% 3.11/1.65 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.11/1.65 ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ? [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ B )
% 3.11/1.65 & ( Xphi @ Xx @ Xy ) ) )
% 3.11/1.65 => ! [R: $i] :
% 3.11/1.65 ( ( in @ R @ ( breln1Set @ B ) )
% 3.11/1.65 => ( ( reflwellordering @ B @ R )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( singleton
% 3.11/1.65 @ ( dsetconstr @ B
% 3.11/1.65 @ ^ [Xy: $i] :
% 3.11/1.65 ( ( Xphi @ Xx @ Xy )
% 3.11/1.65 & ! [Xz: $i] :
% 3.11/1.65 ( ( in @ Xz @ B )
% 3.11/1.65 => ( ( Xphi @ Xx @ Xz )
% 3.11/1.65 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(setOfPairsIsBReln1_type,type,
% 3.11/1.65 setOfPairsIsBReln1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(setOfPairsIsBReln1,definition,
% 3.11/1.65 ( setOfPairsIsBReln1
% 3.11/1.65 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 3.11/1.65 ( breln1 @ A
% 3.11/1.65 @ ( dpsetconstr @ A @ A
% 3.11/1.65 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(breln1all1_type,type,
% 3.11/1.65 breln1all1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(breln1all1,definition,
% 3.11/1.65 ( breln1all1
% 3.11/1.65 = ( ! [A: $i,R: $i] :
% 3.11/1.65 ( ( breln1 @ A @ R )
% 3.11/1.65 => ! [Xphi: $i > $o] :
% 3.11/1.65 ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.11/1.65 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ R )
% 3.11/1.65 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(subbreln1_type,type,
% 3.11/1.65 subbreln1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(subbreln1,definition,
% 3.11/1.65 ( subbreln1
% 3.11/1.65 = ( ! [A: $i,R: $i] :
% 3.11/1.65 ( ( breln1 @ A @ R )
% 3.11/1.65 => ! [S: $i] :
% 3.11/1.65 ( ( breln1 @ A @ S )
% 3.11/1.65 => ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.11/1.65 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.11/1.65 => ( subset @ R @ S ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(eqbreln1_type,type,
% 3.11/1.65 eqbreln1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(eqbreln1,definition,
% 3.11/1.65 ( eqbreln1
% 3.11/1.65 = ( ! [A: $i,R: $i] :
% 3.11/1.65 ( ( breln1 @ A @ R )
% 3.11/1.65 => ! [S: $i] :
% 3.11/1.65 ( ( breln1 @ A @ S )
% 3.11/1.65 => ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.11/1.65 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.11/1.65 => ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.11/1.65 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 3.11/1.65 => ( R = S ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(breln1invset_type,type,
% 3.11/1.65 breln1invset: $i > $i > $i ).
% 3.11/1.65
% 3.11/1.65 thf(breln1invprop_type,type,
% 3.11/1.65 breln1invprop: $o ).
% 3.11/1.65
% 3.11/1.65 thf(breln1invprop,definition,
% 3.11/1.65 ( breln1invprop
% 3.11/1.65 = ( ! [A: $i,R: $i] :
% 3.11/1.65 ( ( breln1 @ A @ R )
% 3.11/1.65 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(breln1invI_type,type,
% 3.11/1.65 breln1invI: $o ).
% 3.11/1.65
% 3.11/1.65 thf(breln1invI,definition,
% 3.11/1.65 ( breln1invI
% 3.11/1.65 = ( ! [A: $i,R: $i] :
% 3.11/1.65 ( ( breln1 @ A @ R )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.11/1.65 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(breln1invE_type,type,
% 3.11/1.65 breln1invE: $o ).
% 3.11/1.65
% 3.11/1.65 thf(breln1invE,definition,
% 3.11/1.65 ( breln1invE
% 3.11/1.65 = ( ! [A: $i,R: $i] :
% 3.11/1.65 ( ( breln1 @ A @ R )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 3.11/1.65 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(breln1compset_type,type,
% 3.11/1.65 breln1compset: $i > $i > $i > $i ).
% 3.11/1.65
% 3.11/1.65 thf(breln1compprop_type,type,
% 3.11/1.65 breln1compprop: $o ).
% 3.11/1.65
% 3.11/1.65 thf(breln1compprop,definition,
% 3.11/1.65 ( breln1compprop
% 3.11/1.65 = ( ! [A: $i,R: $i] :
% 3.11/1.65 ( ( breln1 @ A @ R )
% 3.11/1.65 => ! [S: $i] :
% 3.11/1.65 ( ( breln1 @ A @ S )
% 3.11/1.65 => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(breln1compI_type,type,
% 3.11/1.65 breln1compI: $o ).
% 3.11/1.65
% 3.11/1.65 thf(breln1compI,definition,
% 3.11/1.65 ( breln1compI
% 3.11/1.65 = ( ! [A: $i,R: $i] :
% 3.11/1.65 ( ( breln1 @ A @ R )
% 3.11/1.65 => ! [S: $i] :
% 3.11/1.65 ( ( breln1 @ A @ S )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 => ! [Xz: $i] :
% 3.11/1.65 ( ( in @ Xz @ A )
% 3.11/1.65 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 3.11/1.65 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 3.11/1.65 => ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(breln1compE_type,type,
% 3.11/1.65 breln1compE: $o ).
% 3.11/1.65
% 3.11/1.65 thf(breln1compE,definition,
% 3.11/1.65 ( breln1compE
% 3.11/1.65 = ( ! [A: $i,R: $i] :
% 3.11/1.65 ( ( breln1 @ A @ R )
% 3.11/1.65 => ! [S: $i] :
% 3.11/1.65 ( ( breln1 @ A @ S )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 3.11/1.65 => ? [Xz: $i] :
% 3.11/1.65 ( ( in @ Xz @ A )
% 3.11/1.65 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 3.11/1.65 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(breln1compEex_type,type,
% 3.11/1.65 breln1compEex: $o ).
% 3.11/1.65
% 3.11/1.65 thf(breln1compEex,definition,
% 3.11/1.65 ( breln1compEex
% 3.11/1.65 = ( ! [A: $i,R: $i] :
% 3.11/1.65 ( ( breln1 @ A @ R )
% 3.11/1.65 => ! [S: $i] :
% 3.11/1.65 ( ( breln1 @ A @ S )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 3.11/1.65 => ! [Xphi: $o] :
% 3.11/1.65 ( ! [Xz: $i] :
% 3.11/1.65 ( ( in @ Xz @ A )
% 3.11/1.65 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 3.11/1.65 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 3.11/1.65 => Xphi ) ) )
% 3.11/1.65 => Xphi ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(breln1unionprop_type,type,
% 3.11/1.65 breln1unionprop: $o ).
% 3.11/1.65
% 3.11/1.65 thf(breln1unionprop,definition,
% 3.11/1.65 ( breln1unionprop
% 3.11/1.65 = ( ! [A: $i,R: $i] :
% 3.11/1.65 ( ( breln1 @ A @ R )
% 3.11/1.65 => ! [S: $i] :
% 3.11/1.65 ( ( breln1 @ A @ S )
% 3.11/1.65 => ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(breln1unionIL_type,type,
% 3.11/1.65 breln1unionIL: $o ).
% 3.11/1.65
% 3.11/1.65 thf(breln1unionIL,definition,
% 3.11/1.65 ( breln1unionIL
% 3.11/1.65 = ( ! [A: $i,R: $i] :
% 3.11/1.65 ( ( breln1 @ A @ R )
% 3.11/1.65 => ! [S: $i] :
% 3.11/1.65 ( ( breln1 @ A @ S )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.11/1.65 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(breln1unionIR_type,type,
% 3.11/1.65 breln1unionIR: $o ).
% 3.11/1.65
% 3.11/1.65 thf(breln1unionIR,definition,
% 3.11/1.65 ( breln1unionIR
% 3.11/1.65 = ( ! [A: $i,R: $i] :
% 3.11/1.65 ( ( breln1 @ A @ R )
% 3.11/1.65 => ! [S: $i] :
% 3.11/1.65 ( ( breln1 @ A @ S )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.11/1.65 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(breln1unionI_type,type,
% 3.11/1.65 breln1unionI: $o ).
% 3.11/1.65
% 3.11/1.65 thf(breln1unionI,definition,
% 3.11/1.65 ( breln1unionI
% 3.11/1.65 = ( ! [A: $i,R: $i] :
% 3.11/1.65 ( ( breln1 @ A @ R )
% 3.11/1.65 => ! [S: $i] :
% 3.11/1.65 ( ( breln1 @ A @ S )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.11/1.65 | ( in @ ( kpair @ Xx @ Xy ) @ S ) )
% 3.11/1.65 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(breln1unionE_type,type,
% 3.11/1.65 breln1unionE: $o ).
% 3.11/1.65
% 3.11/1.65 thf(breln1unionE,definition,
% 3.11/1.65 ( breln1unionE
% 3.11/1.65 = ( ! [A: $i,R: $i] :
% 3.11/1.65 ( ( breln1 @ A @ R )
% 3.11/1.65 => ! [S: $i] :
% 3.11/1.65 ( ( breln1 @ A @ S )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 3.11/1.65 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.11/1.65 | ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(breln1unionEcases_type,type,
% 3.11/1.65 breln1unionEcases: $o ).
% 3.11/1.65
% 3.11/1.65 thf(breln1unionEcases,definition,
% 3.11/1.65 ( breln1unionEcases
% 3.11/1.65 = ( ! [A: $i,R: $i] :
% 3.11/1.65 ( ( breln1 @ A @ R )
% 3.11/1.65 => ! [S: $i] :
% 3.11/1.65 ( ( breln1 @ A @ S )
% 3.11/1.65 => ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 3.11/1.65 => ! [Xphi: $o] :
% 3.11/1.65 ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.11/1.65 => Xphi )
% 3.11/1.65 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.11/1.65 => Xphi )
% 3.11/1.65 => Xphi ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(breln1unionCommutes_type,type,
% 3.11/1.65 breln1unionCommutes: $o ).
% 3.11/1.65
% 3.11/1.65 thf(breln1unionCommutes,definition,
% 3.11/1.65 ( breln1unionCommutes
% 3.11/1.65 = ( ! [A: $i,R: $i] :
% 3.11/1.65 ( ( breln1 @ A @ R )
% 3.11/1.65 => ! [S: $i] :
% 3.11/1.65 ( ( breln1 @ A @ S )
% 3.11/1.65 => ( ( binunion @ R @ S )
% 3.11/1.65 = ( binunion @ S @ R ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(woz2Ex_type,type,
% 3.11/1.65 woz2Ex: $o ).
% 3.11/1.65
% 3.11/1.65 thf(woz2Ex,definition,
% 3.11/1.65 ( woz2Ex
% 3.11/1.65 = ( ! [A: $i,R: $i] :
% 3.11/1.65 ( ( breln1 @ A @ R )
% 3.11/1.65 => ( R
% 3.11/1.65 = ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(woz2W_type,type,
% 3.11/1.65 woz2W: $o ).
% 3.11/1.65
% 3.11/1.65 thf(woz2W,definition,
% 3.11/1.65 ( woz2W
% 3.11/1.65 = ( ! [A: $i,R: $i] :
% 3.11/1.65 ( ( breln1 @ A @ R )
% 3.11/1.65 => ! [S: $i] :
% 3.11/1.65 ( ( breln1 @ A @ S )
% 3.11/1.65 => ( ( breln1invset @ A @ ( breln1compset @ A @ R @ S ) )
% 3.11/1.65 = ( breln1compset @ A @ ( breln1invset @ A @ S ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(woz2A_type,type,
% 3.11/1.65 woz2A: $o ).
% 3.11/1.65
% 3.11/1.65 thf(woz2A,definition,
% 3.11/1.65 ( woz2A
% 3.11/1.65 = ( ! [A: $i,R: $i] :
% 3.11/1.65 ( ( breln1 @ A @ R )
% 3.11/1.65 => ! [S: $i] :
% 3.11/1.65 ( ( breln1 @ A @ S )
% 3.11/1.65 => ! [T: $i] :
% 3.11/1.65 ( ( breln1 @ A @ T )
% 3.11/1.65 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 3.11/1.65 = ( binunion @ ( breln1compset @ A @ R @ T ) @ ( breln1compset @ A @ S @ T ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(woz2B_type,type,
% 3.11/1.65 woz2B: $o ).
% 3.11/1.65
% 3.11/1.65 thf(woz2B,definition,
% 3.11/1.65 ( woz2B
% 3.11/1.65 = ( ! [A: $i,R: $i] :
% 3.11/1.65 ( ( breln1 @ A @ R )
% 3.11/1.65 => ! [S: $i] :
% 3.11/1.65 ( ( breln1 @ A @ S )
% 3.11/1.65 => ! [T: $i] :
% 3.11/1.65 ( ( breln1 @ A @ T )
% 3.11/1.65 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 3.11/1.65 = ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ S ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(image1Ex_type,type,
% 3.11/1.65 image1Ex: $o ).
% 3.11/1.65
% 3.11/1.65 thf(image1Ex,definition,
% 3.11/1.65 ( image1Ex
% 3.11/1.65 = ( ! [A: $i,Xf: $i > $i] :
% 3.11/1.65 ? [B: $i] :
% 3.11/1.65 ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ B )
% 3.11/1.65 <=> ? [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 & ( Xx
% 3.11/1.65 = ( Xf @ Xy ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(image1Ex1_type,type,
% 3.11/1.65 image1Ex1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(image1Ex1,definition,
% 3.11/1.65 ( image1Ex1
% 3.11/1.65 = ( ! [A: $i,Xf: $i > $i] :
% 3.11/1.65 ( exu
% 3.11/1.65 @ ^ [B: $i] :
% 3.11/1.65 ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ B )
% 3.11/1.65 <=> ? [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 & ( Xx
% 3.11/1.65 = ( Xf @ Xy ) ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(image1_type,type,
% 3.11/1.65 image1: $i > ( $i > $i ) > $i ).
% 3.11/1.65
% 3.11/1.65 thf(image1Equiv_type,type,
% 3.11/1.65 image1Equiv: $o ).
% 3.11/1.65
% 3.11/1.65 thf(image1Equiv,definition,
% 3.11/1.65 ( image1Equiv
% 3.11/1.65 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx
% 3.11/1.65 @ ( image1 @ A
% 3.11/1.65 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 3.11/1.65 <=> ? [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 & ( Xx
% 3.11/1.65 = ( Xf @ Xy ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(image1E_type,type,
% 3.11/1.65 image1E: $o ).
% 3.11/1.65
% 3.11/1.65 thf(image1E,definition,
% 3.11/1.65 ( image1E
% 3.11/1.65 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 3.11/1.65 ( ( in @ Xx
% 3.11/1.65 @ ( image1 @ A
% 3.11/1.65 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 3.11/1.65 => ? [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 & ( Xx
% 3.11/1.65 = ( Xf @ Xy ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(image1I_type,type,
% 3.11/1.65 image1I: $o ).
% 3.11/1.65
% 3.11/1.65 thf(image1I,definition,
% 3.11/1.65 ( image1I
% 3.11/1.65 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 3.11/1.65 ( ? [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ A )
% 3.11/1.65 & ( Xx
% 3.11/1.65 = ( Xf @ Xy ) ) )
% 3.11/1.65 => ( in @ Xx
% 3.11/1.65 @ ( image1 @ A
% 3.11/1.65 @ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(injective_type,type,
% 3.11/1.65 injective: $i > $i > $i > $o ).
% 3.11/1.65
% 3.11/1.65 thf(injFuncSet_type,type,
% 3.11/1.65 injFuncSet: $i > $i > $i ).
% 3.11/1.65
% 3.11/1.65 thf(injFuncInInjFuncSet_type,type,
% 3.11/1.65 injFuncInInjFuncSet: $o ).
% 3.11/1.65
% 3.11/1.65 thf(injFuncInInjFuncSet,definition,
% 3.11/1.65 ( injFuncInInjFuncSet
% 3.11/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.11/1.65 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.11/1.65 => ( ( injective @ A @ B @ Xf )
% 3.11/1.65 => ( in @ Xf @ ( injFuncSet @ A @ B ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(injFuncSetFuncIn_type,type,
% 3.11/1.65 injFuncSetFuncIn: $o ).
% 3.11/1.65
% 3.11/1.65 thf(injFuncSetFuncIn,definition,
% 3.11/1.65 ( injFuncSetFuncIn
% 3.11/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.11/1.65 ( ( in @ Xf @ ( injFuncSet @ A @ B ) )
% 3.11/1.65 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(injFuncSetFuncInj_type,type,
% 3.11/1.65 injFuncSetFuncInj: $o ).
% 3.11/1.65
% 3.11/1.65 thf(injFuncSetFuncInj,definition,
% 3.11/1.65 ( injFuncSetFuncInj
% 3.11/1.65 = ( ! [Xx: $i,Xy: $i,Xf: $i] :
% 3.11/1.65 ( ( in @ Xf @ ( injFuncSet @ Xx @ Xy ) )
% 3.11/1.65 => ( injective @ Xx @ Xy @ Xf ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(surjective_type,type,
% 3.11/1.65 surjective: $i > $i > $i > $o ).
% 3.11/1.65
% 3.11/1.65 thf(surjFuncSet_type,type,
% 3.11/1.65 surjFuncSet: $i > $i > $i ).
% 3.11/1.65
% 3.11/1.65 thf(surjFuncSetFuncIn_type,type,
% 3.11/1.65 surjFuncSetFuncIn: $o ).
% 3.11/1.65
% 3.11/1.65 thf(surjFuncSetFuncIn,definition,
% 3.11/1.65 ( surjFuncSetFuncIn
% 3.11/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.11/1.65 ( ( in @ Xf @ ( surjFuncSet @ A @ B ) )
% 3.11/1.65 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(surjFuncSetFuncSurj_type,type,
% 3.11/1.65 surjFuncSetFuncSurj: $o ).
% 3.11/1.65
% 3.11/1.65 thf(surjFuncSetFuncSurj,definition,
% 3.11/1.65 ( surjFuncSetFuncSurj
% 3.11/1.65 = ( ! [Xx: $i,Xy: $i,Xf: $i] :
% 3.11/1.65 ( ( in @ Xf @ ( surjFuncSet @ Xx @ Xy ) )
% 3.11/1.65 => ( surjective @ Xx @ Xy @ Xf ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(leftInvIsSurj_type,type,
% 3.11/1.65 leftInvIsSurj: $o ).
% 3.11/1.65
% 3.11/1.65 thf(leftInvIsSurj,definition,
% 3.11/1.65 ( leftInvIsSurj
% 3.11/1.65 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.11/1.65 ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.11/1.65 => ! [Xg: $i] :
% 3.11/1.65 ( ( in @ Xg @ ( funcSet @ B @ A ) )
% 3.11/1.65 => ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ A )
% 3.11/1.65 => ( ( ap @ B @ A @ Xg @ ( Xf @ Xx ) )
% 3.11/1.65 = Xx ) )
% 3.11/1.65 => ( surjective @ B @ A @ Xg ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(surjCantorThm_type,type,
% 3.11/1.65 surjCantorThm: $o ).
% 3.11/1.65
% 3.11/1.65 thf(surjCantorThm,definition,
% 3.11/1.65 ( surjCantorThm
% 3.11/1.65 = ( ! [A: $i,Xf: $i] :
% 3.11/1.65 ( ( in @ Xf @ ( funcSet @ A @ ( powerset @ A ) ) )
% 3.11/1.65 => ~ ( surjective @ A @ ( powerset @ A ) @ Xf ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(foundation2_type,type,
% 3.11/1.65 foundation2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(foundation2,definition,
% 3.11/1.65 ( foundation2
% 3.11/1.65 = ( ! [A: $i] :
% 3.11/1.65 ( ( nonempty @ A )
% 3.11/1.65 => ? [X: $i] :
% 3.11/1.65 ( ( in @ X @ A )
% 3.11/1.65 & ( ( binintersect @ X @ A )
% 3.11/1.65 = emptyset ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(notinself_type,type,
% 3.11/1.65 notinself: $o ).
% 3.11/1.65
% 3.11/1.65 thf(notinself,definition,
% 3.11/1.65 ( notinself
% 3.11/1.65 = ( ! [A: $i] :
% 3.11/1.65 ~ ( in @ A @ A ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(notinself2_type,type,
% 3.11/1.65 notinself2: $o ).
% 3.11/1.65
% 3.11/1.65 thf(notinself2,definition,
% 3.11/1.65 ( notinself2
% 3.11/1.65 = ( ! [A: $i,B: $i] :
% 3.11/1.65 ( ( in @ A @ B )
% 3.11/1.65 => ~ ( in @ B @ A ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(omegaS_type,type,
% 3.11/1.65 omegaS: $i > $i ).
% 3.11/1.65
% 3.11/1.65 thf(omegaSp_type,type,
% 3.11/1.65 omegaSp: $o ).
% 3.11/1.65
% 3.11/1.65 thf(omegaSp,definition,
% 3.11/1.65 ( omegaSp
% 3.11/1.65 = ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ omega )
% 3.11/1.65 => ( in @ ( omegaS @ Xx ) @ omega ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(omegaSclos_type,type,
% 3.11/1.65 omegaSclos: $o ).
% 3.11/1.65
% 3.11/1.65 thf(omegaSclos,definition,
% 3.11/1.65 ( omegaSclos
% 3.11/1.65 = ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ omega )
% 3.11/1.65 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(peano0notS_type,type,
% 3.11/1.65 peano0notS: $o ).
% 3.11/1.65
% 3.11/1.65 thf(peano0notS,definition,
% 3.11/1.65 ( peano0notS
% 3.11/1.65 = ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ omega )
% 3.11/1.65 => ( ( omegaS @ Xx )
% 3.11/1.65 != emptyset ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(peano3_type,type,
% 3.11/1.65 peano3: $i > $i > $i > $o ).
% 3.11/1.65
% 3.11/1.65 thf(peano4_type,type,
% 3.11/1.65 peano4: $i > $i > $i > $o ).
% 3.11/1.65
% 3.11/1.65 thf(peano5_type,type,
% 3.11/1.65 peano5: $i > $i > $i > $o ).
% 3.11/1.65
% 3.11/1.65 thf(peanoSinj_type,type,
% 3.11/1.65 peanoSinj: $o ).
% 3.11/1.65
% 3.11/1.65 thf(peanoSinj,definition,
% 3.11/1.65 ( peanoSinj
% 3.11/1.65 = ( ! [Xx: $i] :
% 3.11/1.65 ( ( in @ Xx @ omega )
% 3.11/1.65 => ! [Xy: $i] :
% 3.11/1.65 ( ( in @ Xy @ omega )
% 3.11/1.65 => ( ( ( omegaS @ Xx )
% 3.11/1.65 = ( omegaS @ Xy ) )
% 3.11/1.65 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(peano_type,type,
% 3.11/1.65 peano: $i > $i > $i > $o ).
% 3.11/1.65
% 3.11/1.65 thf(transitiveset_type,type,
% 3.11/1.65 transitiveset: $i > $o ).
% 3.11/1.65
% 3.11/1.65 thf(transitiveset,definition,
% 3.11/1.65 ( transitiveset
% 3.11/1.65 = ( ^ [A: $i] :
% 3.11/1.65 ! [X: $i] :
% 3.11/1.65 ( ( in @ X @ A )
% 3.11/1.65 => ( subset @ X @ A ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(transitivesetOp1_type,type,
% 3.11/1.65 transitivesetOp1: $o ).
% 3.11/1.65
% 3.11/1.65 thf(transitivesetOp1,definition,
% 3.11/1.65 ( transitivesetOp1
% 3.11/1.65 = ( ! [X: $i] :
% 3.11/1.65 ( ( transitiveset @ X )
% 3.11/1.65 => ! [A: $i] :
% 3.11/1.65 ( ( in @ A @ X )
% 3.11/1.65 => ( subset @ A @ X ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(binintTransitive_type,type,
% 3.11/1.65 binintTransitive: $o ).
% 3.11/1.65
% 3.11/1.65 thf(binintTransitive,definition,
% 3.11/1.65 ( binintTransitive
% 3.11/1.65 = ( ! [X: $i] :
% 3.11/1.65 ( ( transitiveset @ X )
% 3.11/1.65 => ! [Y: $i] :
% 3.11/1.65 ( ( transitiveset @ Y )
% 3.11/1.65 => ( transitiveset @ ( binintersect @ X @ Y ) ) ) ) ) ) ).
% 3.11/1.65
% 3.11/1.65 thf(transitivesetOp2,conjecture,
% 3.11/1.65 ( setextAx
% 3.11/1.65 => ( emptysetAx
% 3.11/1.65 => ( setadjoinAx
% 3.11/1.65 => ( powersetAx
% 3.11/1.65 => ( setunionAx
% 3.11/1.65 => ( omega0Ax
% 3.11/1.65 => ( omegaSAx
% 3.11/1.65 => ( omegaIndAx
% 3.11/1.65 => ( replAx
% 3.11/1.65 => ( foundationAx
% 3.11/1.65 => ( wellorderingAx
% 3.11/1.65 => ( descrp
% 3.11/1.65 => ( dsetconstrI
% 3.11/1.65 => ( dsetconstrEL
% 3.11/1.65 => ( dsetconstrER
% 3.11/1.65 => ( exuE1
% 3.11/1.65 => ( prop2setE
% 3.11/1.65 => ( emptysetE
% 3.11/1.65 => ( emptysetimpfalse
% 3.11/1.65 => ( notinemptyset
% 3.11/1.65 => ( exuE3e
% 3.11/1.65 => ( setext
% 3.11/1.65 => ( emptyI
% 3.11/1.65 => ( noeltsimpempty
% 3.11/1.65 => ( setbeta
% 3.11/1.65 => ( nonemptyE1
% 3.11/1.65 => ( nonemptyI
% 3.11/1.65 => ( nonemptyI1
% 3.11/1.65 => ( setadjoinIL
% 3.11/1.65 => ( emptyinunitempty
% 3.11/1.65 => ( setadjoinIR
% 3.11/1.65 => ( setadjoinE
% 3.11/1.65 => ( setadjoinOr
% 3.11/1.65 => ( setoftrueEq
% 3.11/1.65 => ( powersetI
% 3.11/1.65 => ( emptyinPowerset
% 3.11/1.65 => ( emptyInPowerset
% 3.11/1.65 => ( powersetE
% 3.11/1.65 => ( setunionI
% 3.11/1.65 => ( setunionE
% 3.11/1.65 => ( subPowSU
% 3.11/1.65 => ( exuE2
% 3.11/1.65 => ( nonemptyImpWitness
% 3.11/1.65 => ( uniqinunit
% 3.11/1.65 => ( notinsingleton
% 3.11/1.65 => ( eqinunit
% 3.11/1.65 => ( singletonsswitch
% 3.11/1.65 => ( upairsetE
% 3.11/1.65 => ( upairsetIL
% 3.11/1.65 => ( upairsetIR
% 3.11/1.65 => ( emptyE1
% 3.11/1.65 => ( vacuousDall
% 3.11/1.65 => ( quantDeMorgan1
% 3.11/1.65 => ( quantDeMorgan2
% 3.11/1.65 => ( quantDeMorgan3
% 3.11/1.65 => ( quantDeMorgan4
% 3.11/1.65 => ( prop2setI
% 3.11/1.65 => ( prop2set2propI
% 3.11/1.65 => ( notdexE
% 3.11/1.65 => ( notdallE
% 3.11/1.65 => ( exuI1
% 3.11/1.65 => ( exuI3
% 3.11/1.65 => ( exuI2
% 3.11/1.65 => ( inCongP
% 3.11/1.65 => ( in__Cong
% 3.11/1.65 => ( exuE3u
% 3.11/1.65 => ( exu__Cong
% 3.11/1.65 => ( emptyset__Cong
% 3.11/1.65 => ( setadjoin__Cong
% 3.11/1.65 => ( powerset__Cong
% 3.11/1.65 => ( setunion__Cong
% 3.11/1.65 => ( omega__Cong
% 3.11/1.65 => ( exuEu
% 3.11/1.65 => ( descr__Cong
% 3.11/1.65 => ( dsetconstr__Cong
% 3.11/1.65 => ( subsetI1
% 3.11/1.65 => ( eqimpsubset2
% 3.11/1.65 => ( eqimpsubset1
% 3.11/1.65 => ( subsetI2
% 3.11/1.65 => ( emptysetsubset
% 3.11/1.65 => ( subsetE
% 3.11/1.65 => ( subsetE2
% 3.11/1.65 => ( notsubsetI
% 3.11/1.65 => ( notequalI1
% 3.11/1.65 => ( notequalI2
% 3.11/1.65 => ( subsetRefl
% 3.11/1.65 => ( subsetTrans
% 3.11/1.65 => ( setadjoinSub
% 3.11/1.65 => ( setadjoinSub2
% 3.11/1.65 => ( subset2powerset
% 3.11/1.65 => ( setextsub
% 3.11/1.65 => ( subsetemptysetimpeq
% 3.11/1.65 => ( powersetI1
% 3.11/1.65 => ( powersetE1
% 3.11/1.65 => ( inPowerset
% 3.11/1.65 => ( powersetsubset
% 3.11/1.65 => ( sepInPowerset
% 3.11/1.65 => ( sepSubset
% 3.11/1.65 => ( binunionIL
% 3.11/1.65 => ( upairset2IR
% 3.11/1.65 => ( binunionIR
% 3.11/1.65 => ( binunionEcases
% 3.11/1.65 => ( binunionE
% 3.11/1.65 => ( binunionLsub
% 3.11/1.65 => ( binunionRsub
% 3.11/1.65 => ( binintersectI
% 3.11/1.65 => ( binintersectSubset5
% 3.11/1.65 => ( binintersectEL
% 3.11/1.65 => ( binintersectLsub
% 3.11/1.65 => ( binintersectSubset2
% 3.11/1.65 => ( binintersectSubset3
% 3.11/1.65 => ( binintersectER
% 3.11/1.65 => ( disjointsetsI1
% 3.11/1.65 => ( binintersectRsub
% 3.11/1.65 => ( binintersectSubset4
% 3.11/1.65 => ( binintersectSubset1
% 3.11/1.65 => ( bs114d
% 3.11/1.65 => ( setminusI
% 3.11/1.65 => ( setminusEL
% 3.11/1.65 => ( setminusER
% 3.11/1.65 => ( setminusSubset2
% 3.11/1.65 => ( setminusERneg
% 3.11/1.65 => ( setminusELneg
% 3.11/1.65 => ( setminusILneg
% 3.11/1.65 => ( setminusIRneg
% 3.11/1.65 => ( setminusLsub
% 3.11/1.65 => ( setminusSubset1
% 3.11/1.65 => ( symdiffE
% 3.11/1.65 => ( symdiffI1
% 3.11/1.65 => ( symdiffI2
% 3.11/1.65 => ( symdiffIneg1
% 3.11/1.65 => ( symdiffIneg2
% 3.11/1.65 => ( secondinupair
% 3.11/1.65 => ( setukpairIL
% 3.11/1.65 => ( setukpairIR
% 3.11/1.65 => ( kpairiskpair
% 3.11/1.65 => ( kpairp
% 3.11/1.65 => ( singletonsubset
% 3.11/1.65 => ( singletoninpowerset
% 3.11/1.65 => ( singletoninpowunion
% 3.11/1.65 => ( upairset2E
% 3.11/1.65 => ( upairsubunion
% 3.11/1.65 => ( upairinpowunion
% 3.11/1.65 => ( ubforcartprodlem1
% 3.11/1.65 => ( ubforcartprodlem2
% 3.11/1.65 => ( ubforcartprodlem3
% 3.11/1.65 => ( cartprodpairin
% 3.11/1.65 => ( cartprodmempair1
% 3.11/1.65 => ( cartprodmempair
% 3.11/1.65 => ( setunionE2
% 3.11/1.65 => ( setunionsingleton1
% 3.11/1.65 => ( setunionsingleton2
% 3.11/1.65 => ( setunionsingleton
% 3.11/1.65 => ( singletonprop
% 3.11/1.65 => ( ex1E1
% 3.11/1.65 => ( ex1I
% 3.11/1.65 => ( ex1I2
% 3.11/1.65 => ( singletonsuniq
% 3.11/1.65 => ( setukpairinjL1
% 3.11/1.65 => ( kfstsingleton
% 3.11/1.65 => ( theprop
% 3.11/1.65 => ( kfstpairEq
% 3.11/1.65 => ( cartprodfstin
% 3.11/1.65 => ( setukpairinjL2
% 3.11/1.65 => ( setukpairinjL
% 3.11/1.65 => ( setukpairinjR11
% 3.11/1.65 => ( setukpairinjR12
% 3.11/1.65 => ( setukpairinjR1
% 3.11/1.65 => ( upairequniteq
% 3.11/1.65 => ( setukpairinjR2
% 3.11/1.65 => ( setukpairinjR
% 3.11/1.65 => ( ksndsingleton
% 3.11/1.65 => ( ksndpairEq
% 3.11/1.65 => ( kpairsurjEq
% 3.11/1.65 => ( cartprodsndin
% 3.11/1.65 => ( cartprodpairmemEL
% 3.11/1.65 => ( cartprodpairmemER
% 3.11/1.65 => ( cartprodmempaircEq
% 3.11/1.65 => ( cartprodfstpairEq
% 3.11/1.65 => ( cartprodsndpairEq
% 3.11/1.65 => ( cartprodpairsurjEq
% 3.11/1.65 => ( dpsetconstrI
% 3.11/1.65 => ( dpsetconstrSub
% 3.11/1.65 => ( setOfPairsIsBReln
% 3.11/1.65 => ( dpsetconstrERa
% 3.11/1.65 => ( dpsetconstrEL1
% 3.11/1.65 => ( dpsetconstrEL2
% 3.11/1.65 => ( dpsetconstrER
% 3.11/1.65 => ( funcImageSingleton
% 3.11/1.65 => ( apProp
% 3.11/1.65 => ( app
% 3.11/1.65 => ( infuncsetfunc
% 3.11/1.65 => ( ap2p
% 3.11/1.65 => ( funcinfuncset
% 3.11/1.65 => ( lamProp
% 3.11/1.65 => ( lamp
% 3.11/1.65 => ( lam2p
% 3.11/1.65 => ( brelnall1
% 3.11/1.65 => ( brelnall2
% 3.11/1.65 => ( ex1E2
% 3.11/1.65 => ( funcGraphProp1
% 3.11/1.65 => ( funcGraphProp3
% 3.11/1.65 => ( funcGraphProp2
% 3.11/1.65 => ( funcextLem
% 3.11/1.65 => ( funcGraphProp4
% 3.11/1.65 => ( subbreln
% 3.11/1.65 => ( eqbreln
% 3.11/1.65 => ( funcext
% 3.11/1.65 => ( funcext2
% 3.11/1.65 => ( ap2apEq1
% 3.11/1.65 => ( ap2apEq2
% 3.11/1.65 => ( beta1
% 3.11/1.65 => ( eta1
% 3.11/1.65 => ( lam2lamEq
% 3.11/1.65 => ( beta2
% 3.11/1.65 => ( eta2
% 3.11/1.65 => ( iffalseProp1
% 3.11/1.65 => ( iffalseProp2
% 3.11/1.65 => ( iftrueProp1
% 3.11/1.65 => ( iftrueProp2
% 3.11/1.65 => ( ifSingleton
% 3.11/1.65 => ( ifp
% 3.11/1.65 => ( theeq
% 3.11/1.65 => ( iftrue
% 3.11/1.65 => ( iffalse
% 3.11/1.65 => ( iftrueorfalse
% 3.11/1.65 => ( binintersectT_lem
% 3.11/1.65 => ( binunionT_lem
% 3.11/1.65 => ( powersetT_lem
% 3.11/1.65 => ( setminusT_lem
% 3.11/1.65 => ( complementT_lem
% 3.11/1.65 => ( setextT
% 3.11/1.65 => ( subsetTI
% 3.11/1.65 => ( powersetTI1
% 3.11/1.65 => ( powersetTE1
% 3.11/1.65 => ( complementTI1
% 3.11/1.65 => ( complementTE1
% 3.11/1.65 => ( binintersectTELcontra
% 3.11/1.65 => ( binintersectTERcontra
% 3.11/1.65 => ( contrasubsetT
% 3.11/1.65 => ( contrasubsetT1
% 3.11/1.65 => ( contrasubsetT2
% 3.11/1.65 => ( contrasubsetT3
% 3.11/1.65 => ( doubleComplementI1
% 3.11/1.65 => ( doubleComplementE1
% 3.11/1.65 => ( doubleComplementSub1
% 3.11/1.65 => ( doubleComplementSub2
% 3.11/1.65 => ( doubleComplementEq
% 3.11/1.65 => ( complementTnotintersectT
% 3.11/1.65 => ( complementImpComplementIntersect
% 3.11/1.65 => ( complementSubsetComplementIntersect
% 3.11/1.65 => ( complementInPowersetComplementIntersect
% 3.11/1.65 => ( contraSubsetComplement
% 3.11/1.65 => ( complementTcontraSubset
% 3.11/1.65 => ( binunionTILcontra
% 3.11/1.65 => ( binunionTIRcontra
% 3.11/1.65 => ( inIntersectImpInUnion
% 3.11/1.65 => ( inIntersectImpInUnion2
% 3.11/1.65 => ( inIntersectImpInIntersectUnions
% 3.11/1.65 => ( intersectInPowersetIntersectUnions
% 3.11/1.65 => ( inComplementUnionImpNotIn1
% 3.11/1.65 => ( inComplementUnionImpInComplement1
% 3.11/1.65 => ( binunionTE
% 3.11/1.65 => ( binunionTEcontra
% 3.11/1.65 => ( demorgan2a1
% 3.11/1.65 => ( complementUnionInPowersetComplement
% 3.11/1.65 => ( demorgan2a2
% 3.11/1.65 => ( demorgan1a
% 3.11/1.65 => ( demorgan1b
% 3.11/1.65 => ( demorgan1
% 3.11/1.65 => ( demorgan2a
% 3.11/1.65 => ( demorgan2b2
% 3.11/1.65 => ( demorgan2b
% 3.11/1.65 => ( demorgan2
% 3.11/1.65 => ( woz13rule0
% 3.11/1.65 => ( woz13rule1
% 3.11/1.65 => ( woz13rule2
% 3.11/1.65 => ( woz13rule3
% 3.11/1.65 => ( woz13rule4
% 3.11/1.65 => ( woz1_1
% 3.11/1.65 => ( woz1_2
% 3.11/1.65 => ( woz1_3
% 3.11/1.65 => ( woz1_4
% 3.11/1.65 => ( woz1_5
% 3.11/1.65 => ( breln1all2
% 3.11/1.65 => ( breln1SetBreln1
% 3.11/1.65 => ( choice2fnsingleton
% 3.11/1.65 => ( setOfPairsIsBReln1
% 3.11/1.65 => ( breln1all1
% 3.11/1.65 => ( subbreln1
% 3.11/1.65 => ( eqbreln1
% 3.11/1.65 => ( breln1invprop
% 3.11/1.65 => ( breln1invI
% 3.11/1.65 => ( breln1invE
% 3.11/1.65 => ( breln1compprop
% 3.11/1.65 => ( breln1compI
% 3.11/1.65 => ( breln1compE
% 3.11/1.65 => ( breln1compEex
% 3.11/1.65 => ( breln1unionprop
% 3.11/1.65 => ( breln1unionIL
% 3.11/1.65 => ( breln1unionIR
% 3.11/1.65 => ( breln1unionI
% 3.11/1.65 => ( breln1unionE
% 3.11/1.65 => ( breln1unionEcases
% 3.11/1.65 => ( breln1unionCommutes
% 3.11/1.65 => ( woz2Ex
% 3.11/1.65 => ( woz2W
% 3.11/1.65 => ( woz2A
% 3.11/1.65 => ( woz2B
% 3.11/1.65 => ( image1Ex
% 3.11/1.65 => ( image1Ex1
% 3.11/1.65 => ( image1Equiv
% 3.11/1.65 => ( image1E
% 3.11/1.65 => ( image1I
% 3.11/1.65 => ( injFuncInInjFuncSet
% 3.11/1.65 => ( injFuncSetFuncIn
% 3.11/1.65 => ( injFuncSetFuncInj
% 3.11/1.65 => ( surjFuncSetFuncIn
% 3.11/1.65 => ( surjFuncSetFuncSurj
% 3.11/1.65 => ( leftInvIsSurj
% 3.11/1.65 => ( surjCantorThm
% 3.11/1.65 => ( foundation2
% 3.11/1.65 => ( notinself
% 3.11/1.65 => ( notinself2
% 3.11/1.65 => ( omegaSp
% 3.11/1.65 => ( omegaSclos
% 3.11/1.65 => ( peano0notS
% 3.11/1.65 => ( peanoSinj
% 3.11/1.65 => ( transitivesetOp1
% 3.11/1.65 => ( binintTransitive
% 3.11/1.65 => ! [X: $i] :
% 3.11/1.65 ( ( transitiveset @ X )
% 3.11/1.65 => ! [A: $i,Xx: $i] :
% 3.11/1.65 ( ( in @ A @ X )
% 3.11/1.65 => ( ( in @ Xx @ A )
% 3.11/1.65 => ( in @ Xx @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.11/1.65 ------------------------
% 3.11/1.68 % (18200)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17963 for (2999ds/183Mi)
% 3.11/1.69 % (18201)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_17963 for (2999ds/4Mi)
% 3.11/1.69 % (18203)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17963 for (2999ds/2Mi)
% 3.11/1.69 % (18206)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17963 for (2999ds/18Mi)
% 3.11/1.69 % (18203)Instruction limit reached!
% 3.11/1.69 % (18203)------------------------------
% 3.11/1.69 % (18203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.69 % (18203)Termination reason: Unknown
% 3.11/1.69 % (18203)Termination phase: shuffling
% 3.11/1.69
% 3.11/1.69 % (18203)Memory used [KB]: 1663
% 3.11/1.69 % (18203)Time elapsed: 0.003 s
% 3.11/1.69 % (18203)Instructions burned: 3 (million)
% 3.11/1.69 % (18203)------------------------------
% 3.11/1.69 % (18203)------------------------------
% 3.11/1.69 % (18202)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_17963 for (2999ds/27Mi)
% 3.11/1.69 % (18204)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_17963 for (2999ds/2Mi)
% 3.11/1.69 % (18205)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_17963 for (2999ds/275Mi)
% 3.11/1.69 % (18201)Instruction limit reached!
% 3.11/1.69 % (18201)------------------------------
% 3.11/1.69 % (18201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.69 % (18201)Termination reason: Unknown
% 3.11/1.69 % (18201)Termination phase: shuffling
% 3.11/1.69
% 3.11/1.69 % (18201)Memory used [KB]: 1663
% 3.11/1.69 % (18201)Time elapsed: 0.004 s
% 3.11/1.69 % (18201)Instructions burned: 5 (million)
% 3.11/1.69 % (18201)------------------------------
% 3.11/1.69 % (18201)------------------------------
% 3.11/1.69 % (18204)Instruction limit reached!
% 3.11/1.69 % (18204)------------------------------
% 3.11/1.69 % (18204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.11/1.69 % (18204)Termination reason: Unknown
% 3.11/1.69 % (18204)Termination phase: shuffling
% 3.11/1.69
% 3.11/1.69 % (18204)Memory used [KB]: 1663
% 3.11/1.69 % (18204)Time elapsed: 0.002 s
% 3.11/1.69 % (18204)Instructions burned: 2 (million)
% 3.11/1.69 % (18204)------------------------------
% 3.11/1.69 % (18204)------------------------------
% 3.20/1.70 % (18206)Instruction limit reached!
% 3.20/1.70 % (18206)------------------------------
% 3.20/1.70 % (18206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.70 % (18206)Termination reason: Unknown
% 3.20/1.70 % (18206)Termination phase: shuffling
% 3.20/1.70
% 3.20/1.70 % (18206)Memory used [KB]: 1918
% 3.20/1.70 % (18206)Time elapsed: 0.011 s
% 3.20/1.70 % (18206)Instructions burned: 18 (million)
% 3.20/1.70 % (18206)------------------------------
% 3.20/1.70 % (18206)------------------------------
% 3.20/1.70 % (18202)Instruction limit reached!
% 3.20/1.70 % (18202)------------------------------
% 3.20/1.70 % (18202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.70 % (18202)Termination reason: Unknown
% 3.20/1.70 % (18202)Termination phase: shuffling
% 3.20/1.70
% 3.20/1.70 % (18202)Memory used [KB]: 2174
% 3.20/1.70 % (18202)Time elapsed: 0.014 s
% 3.20/1.70 % (18202)Instructions burned: 28 (million)
% 3.20/1.70 % (18202)------------------------------
% 3.20/1.70 % (18202)------------------------------
% 3.20/1.71 % (18208)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_17963 for (2999ds/3Mi)
% 3.20/1.71 % (18210)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_17963 for (2999ds/15Mi)
% 3.20/1.71 % (18208)Instruction limit reached!
% 3.20/1.71 % (18208)------------------------------
% 3.20/1.71 % (18208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.71 % (18208)Termination reason: Unknown
% 3.20/1.71 % (18208)Termination phase: shuffling
% 3.20/1.71
% 3.20/1.71 % (18208)Memory used [KB]: 1663
% 3.20/1.71 % (18208)Time elapsed: 0.004 s
% 3.20/1.71 % (18208)Instructions burned: 4 (million)
% 3.20/1.71 % (18208)------------------------------
% 3.20/1.71 % (18208)------------------------------
% 3.20/1.71 % (18209)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_17963 for (2999ds/37Mi)
% 3.20/1.71 % (18213)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_17963 for (2999ds/3Mi)
% 3.20/1.71 % (18210)Instruction limit reached!
% 3.20/1.71 % (18210)------------------------------
% 3.20/1.71 % (18210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.71 % (18210)Termination reason: Unknown
% 3.20/1.71 % (18210)Termination phase: shuffling
% 3.20/1.71
% 3.20/1.71 % (18210)Memory used [KB]: 1918
% 3.20/1.71 % (18210)Time elapsed: 0.009 s
% 3.20/1.71 % (18210)Instructions burned: 15 (million)
% 3.20/1.71 % (18210)------------------------------
% 3.20/1.71 % (18210)------------------------------
% 3.20/1.71 % (18213)Instruction limit reached!
% 3.20/1.71 % (18213)------------------------------
% 3.20/1.71 % (18213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.71 % (18213)Termination reason: Unknown
% 3.20/1.71 % (18213)Termination phase: shuffling
% 3.20/1.71
% 3.20/1.71 % (18213)Memory used [KB]: 1663
% 3.20/1.71 % (18213)Time elapsed: 0.003 s
% 3.20/1.71 % (18213)Instructions burned: 3 (million)
% 3.20/1.71 % (18213)------------------------------
% 3.20/1.71 % (18213)------------------------------
% 3.20/1.72 % (18214)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_17963 for (2999ds/1041Mi)
% 3.20/1.72 % (18215)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_17963 for (2999ds/7Mi)
% 3.20/1.73 % (18215)Instruction limit reached!
% 3.20/1.73 % (18215)------------------------------
% 3.20/1.73 % (18215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.73 % (18215)Termination reason: Unknown
% 3.20/1.73 % (18215)Termination phase: shuffling
% 3.20/1.73
% 3.20/1.73 % (18209)Instruction limit reached!
% 3.20/1.73 % (18209)------------------------------
% 3.20/1.73 % (18209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.73 % (18209)Termination reason: Unknown
% 3.20/1.73 % (18209)Termination phase: shuffling
% 3.20/1.73
% 3.20/1.73 % (18209)Memory used [KB]: 2430
% 3.20/1.73 % (18209)Time elapsed: 0.021 s
% 3.20/1.73 % (18209)Instructions burned: 38 (million)
% 3.20/1.73 % (18209)------------------------------
% 3.20/1.73 % (18209)------------------------------
% 3.20/1.73 % (18215)Memory used [KB]: 1663
% 3.20/1.73 % (18215)Time elapsed: 0.005 s
% 3.20/1.73 % (18215)Instructions burned: 7 (million)
% 3.20/1.73 % (18215)------------------------------
% 3.20/1.73 % (18215)------------------------------
% 3.20/1.73 % (18200)Instruction limit reached!
% 3.20/1.73 % (18200)------------------------------
% 3.20/1.73 % (18200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.73 % (18200)Termination reason: Unknown
% 3.20/1.73 % (18200)Termination phase: Property scanning
% 3.20/1.73
% 3.20/1.73 % (18200)Memory used [KB]: 3198
% 3.20/1.73 % (18200)Time elapsed: 0.049 s
% 3.20/1.73 % (18200)Instructions burned: 185 (million)
% 3.20/1.73 % (18200)------------------------------
% 3.20/1.73 % (18200)------------------------------
% 3.20/1.73 % (18216)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_17963 for (2999ds/16Mi)
% 3.20/1.73 % (18217)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_17963 for (2999ds/3Mi)
% 3.20/1.73 % (18217)Instruction limit reached!
% 3.20/1.73 % (18217)------------------------------
% 3.20/1.73 % (18217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.73 % (18217)Termination reason: Unknown
% 3.20/1.73 % (18217)Termination phase: shuffling
% 3.20/1.73
% 3.20/1.73 % (18217)Memory used [KB]: 1663
% 3.20/1.73 % (18217)Time elapsed: 0.003 s
% 3.20/1.73 % (18217)Instructions burned: 3 (million)
% 3.20/1.73 % (18217)------------------------------
% 3.20/1.73 % (18217)------------------------------
% 3.20/1.74 % (18216)Instruction limit reached!
% 3.20/1.74 % (18216)------------------------------
% 3.20/1.74 % (18216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.74 % (18216)Termination reason: Unknown
% 3.20/1.74 % (18216)Termination phase: shuffling
% 3.20/1.74
% 3.20/1.74 % (18216)Memory used [KB]: 1918
% 3.20/1.74 % (18216)Time elapsed: 0.009 s
% 3.20/1.74 % (18216)Instructions burned: 16 (million)
% 3.20/1.74 % (18216)------------------------------
% 3.20/1.74 % (18216)------------------------------
% 3.20/1.74 % (18221)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_17963 for (2999ds/3Mi)
% 3.20/1.74 % (18221)Instruction limit reached!
% 3.20/1.74 % (18221)------------------------------
% 3.20/1.74 % (18221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.74 % (18221)Termination reason: Unknown
% 3.20/1.74 % (18221)Termination phase: shuffling
% 3.20/1.74
% 3.20/1.74 % (18221)Memory used [KB]: 1663
% 3.20/1.74 % (18221)Time elapsed: 0.003 s
% 3.20/1.74 % (18221)Instructions burned: 4 (million)
% 3.20/1.74 % (18221)------------------------------
% 3.20/1.74 % (18221)------------------------------
% 3.20/1.74 % (18220)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_17963 for (2999ds/7Mi)
% 3.20/1.74 % (18219)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_17963 for (2999ds/3Mi)
% 3.20/1.75 % (18219)Instruction limit reached!
% 3.20/1.75 % (18219)------------------------------
% 3.20/1.75 % (18219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.75 % (18219)Termination reason: Unknown
% 3.20/1.75 % (18219)Termination phase: shuffling
% 3.20/1.75
% 3.20/1.75 % (18219)Memory used [KB]: 1663
% 3.20/1.75 % (18219)Time elapsed: 0.004 s
% 3.20/1.75 % (18219)Instructions burned: 4 (million)
% 3.20/1.75 % (18219)------------------------------
% 3.20/1.75 % (18219)------------------------------
% 3.20/1.75 % (18220)Instruction limit reached!
% 3.20/1.75 % (18220)------------------------------
% 3.20/1.75 % (18220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.75 % (18220)Termination reason: Unknown
% 3.20/1.75 % (18220)Termination phase: shuffling
% 3.20/1.75
% 3.20/1.75 % (18220)Memory used [KB]: 1663
% 3.20/1.75 % (18220)Time elapsed: 0.005 s
% 3.20/1.75 % (18220)Instructions burned: 7 (million)
% 3.20/1.75 % (18220)------------------------------
% 3.20/1.75 % (18220)------------------------------
% 3.20/1.75 % (18223)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_17963 for (2999ds/18Mi)
% 3.20/1.75 % (18222)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_17963 for (2999ds/4Mi)
% 3.20/1.75 % (18222)Instruction limit reached!
% 3.20/1.75 % (18222)------------------------------
% 3.20/1.75 % (18222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.75 % (18222)Termination reason: Unknown
% 3.20/1.75 % (18222)Termination phase: shuffling
% 3.20/1.75
% 3.20/1.75 % (18222)Memory used [KB]: 1663
% 3.20/1.75 % (18222)Time elapsed: 0.004 s
% 3.20/1.75 % (18222)Instructions burned: 5 (million)
% 3.20/1.75 % (18222)------------------------------
% 3.20/1.75 % (18222)------------------------------
% 3.20/1.75 % (18223)Instruction limit reached!
% 3.20/1.75 % (18223)------------------------------
% 3.20/1.75 % (18223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.75 % (18223)Termination reason: Unknown
% 3.20/1.75 % (18223)Termination phase: shuffling
% 3.20/1.75
% 3.20/1.75 % (18223)Memory used [KB]: 1918
% 3.20/1.75 % (18223)Time elapsed: 0.007 s
% 3.20/1.75 % (18223)Instructions burned: 21 (million)
% 3.20/1.75 % (18223)------------------------------
% 3.20/1.75 % (18223)------------------------------
% 3.20/1.76 % (18224)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_17963 for (2999ds/710Mi)
% 3.20/1.76 % (18228)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_17963 for (2999ds/5Mi)
% 3.20/1.76 % (18226)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_17963 for (2999ds/902Mi)
% 3.20/1.76 % (18225)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_17963 for (2999ds/6Mi)
% 3.20/1.76 % (18228)Instruction limit reached!
% 3.20/1.76 % (18228)------------------------------
% 3.20/1.76 % (18228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.76 % (18228)Termination reason: Unknown
% 3.20/1.76 % (18228)Termination phase: shuffling
% 3.20/1.76
% 3.20/1.76 % (18228)Memory used [KB]: 1663
% 3.20/1.76 % (18228)Time elapsed: 0.003 s
% 3.20/1.76 % (18228)Instructions burned: 7 (million)
% 3.20/1.76 % (18228)------------------------------
% 3.20/1.76 % (18228)------------------------------
% 3.20/1.77 % (18227)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_17963 for (2999ds/21Mi)
% 3.20/1.77 % (18225)Instruction limit reached!
% 3.20/1.77 % (18225)------------------------------
% 3.20/1.77 % (18225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.77 % (18225)Termination reason: Unknown
% 3.20/1.77 % (18225)Termination phase: shuffling
% 3.20/1.77
% 3.20/1.77 % (18225)Memory used [KB]: 1663
% 3.20/1.77 % (18225)Time elapsed: 0.005 s
% 3.20/1.77 % (18225)Instructions burned: 7 (million)
% 3.20/1.77 % (18225)------------------------------
% 3.20/1.77 % (18225)------------------------------
% 3.20/1.77 % (18230)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_17963 for (2998ds/6Mi)
% 3.20/1.78 % (18230)Instruction limit reached!
% 3.20/1.78 % (18230)------------------------------
% 3.20/1.78 % (18230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.78 % (18230)Termination reason: Unknown
% 3.20/1.78 % (18230)Termination phase: shuffling
% 3.20/1.78
% 3.20/1.78 % (18230)Memory used [KB]: 1663
% 3.20/1.78 % (18230)Time elapsed: 0.003 s
% 3.20/1.78 % (18230)Instructions burned: 6 (million)
% 3.20/1.78 % (18230)------------------------------
% 3.20/1.78 % (18230)------------------------------
% 3.20/1.78 % (18227)Instruction limit reached!
% 3.20/1.78 % (18227)------------------------------
% 3.20/1.78 % (18227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.78 % (18227)Termination reason: Unknown
% 3.20/1.78 % (18227)Termination phase: shuffling
% 3.20/1.78
% 3.20/1.78 % (18227)Memory used [KB]: 1918
% 3.20/1.78 % (18227)Time elapsed: 0.011 s
% 3.20/1.78 % (18227)Instructions burned: 21 (million)
% 3.20/1.78 % (18227)------------------------------
% 3.20/1.78 % (18227)------------------------------
% 3.20/1.79 % (18232)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_17963 for (2998ds/377Mi)
% 3.20/1.79 % (18233)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_17963 for (2998ds/779Mi)
% 3.20/1.79 % (18234)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_17963 for (2998ds/19Mi)
% 3.20/1.80 % (18234)Instruction limit reached!
% 3.20/1.80 % (18234)------------------------------
% 3.20/1.80 % (18234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.80 % (18234)Termination reason: Unknown
% 3.20/1.80 % (18234)Termination phase: shuffling
% 3.20/1.80
% 3.20/1.80 % (18234)Memory used [KB]: 1918
% 3.20/1.80 % (18234)Time elapsed: 0.011 s
% 3.20/1.80 % (18234)Instructions burned: 21 (million)
% 3.20/1.80 % (18234)------------------------------
% 3.20/1.80 % (18234)------------------------------
% 3.20/1.82 % (18235)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_17963 for (2998ds/879Mi)
% 3.20/1.82 % (18205)Instruction limit reached!
% 3.20/1.82 % (18205)------------------------------
% 3.20/1.82 % (18205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.82 % (18205)Termination reason: Unknown
% 3.20/1.82 % (18205)Termination phase: Property scanning
% 3.20/1.82
% 3.20/1.82 % (18205)Memory used [KB]: 6012
% 3.20/1.82 % (18205)Time elapsed: 0.131 s
% 3.20/1.82 % (18205)Instructions burned: 276 (million)
% 3.20/1.82 % (18205)------------------------------
% 3.20/1.82 % (18205)------------------------------
% 3.20/1.84 % (18237)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_17963 for (2998ds/17Mi)
% 3.20/1.84 % (18237)Instruction limit reached!
% 3.20/1.84 % (18237)------------------------------
% 3.20/1.84 % (18237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.84 % (18237)Termination reason: Unknown
% 3.20/1.84 % (18237)Termination phase: shuffling
% 3.20/1.84
% 3.20/1.84 % (18237)Memory used [KB]: 1918
% 3.20/1.84 % (18237)Time elapsed: 0.010 s
% 3.20/1.84 % (18237)Instructions burned: 17 (million)
% 3.20/1.84 % (18237)------------------------------
% 3.20/1.84 % (18237)------------------------------
% 3.20/1.86 % (18239)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_17963 for (2998ds/3Mi)
% 3.20/1.86 % (18239)Instruction limit reached!
% 3.20/1.86 % (18239)------------------------------
% 3.20/1.86 % (18239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.86 % (18239)Termination reason: Unknown
% 3.20/1.86 % (18239)Termination phase: shuffling
% 3.20/1.86
% 3.20/1.86 % (18239)Memory used [KB]: 1663
% 3.20/1.86 % (18239)Time elapsed: 0.004 s
% 3.20/1.86 % (18239)Instructions burned: 4 (million)
% 3.20/1.86 % (18239)------------------------------
% 3.20/1.86 % (18239)------------------------------
% 3.20/1.88 % (18243)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_17963 for (2998ds/30Mi)
% 3.20/1.89 % (18243)Instruction limit reached!
% 3.20/1.89 % (18243)------------------------------
% 3.20/1.89 % (18243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.89 % (18243)Termination reason: Unknown
% 3.20/1.89 % (18243)Termination phase: shuffling
% 3.20/1.89
% 3.20/1.89 % (18243)Memory used [KB]: 2302
% 3.20/1.89 % (18243)Time elapsed: 0.016 s
% 3.20/1.89 % (18243)Instructions burned: 31 (million)
% 3.20/1.89 % (18243)------------------------------
% 3.20/1.89 % (18243)------------------------------
% 3.20/1.90 % (18247)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_17963 for (2997ds/127Mi)
% 3.20/1.94 % (18247)Instruction limit reached!
% 3.20/1.94 % (18247)------------------------------
% 3.20/1.94 % (18247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.94 % (18247)Termination reason: Unknown
% 3.20/1.94 % (18247)Termination phase: Property scanning
% 3.20/1.94
% 3.20/1.94 % (18247)Memory used [KB]: 3070
% 3.20/1.94 % (18247)Time elapsed: 0.035 s
% 3.20/1.94 % (18247)Instructions burned: 130 (million)
% 3.20/1.94 % (18247)------------------------------
% 3.20/1.94 % (18247)------------------------------
% 3.20/1.94 % (18232)Instruction limit reached!
% 3.20/1.94 % (18232)------------------------------
% 3.20/1.94 % (18232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.94 % (18232)Termination reason: Unknown
% 3.20/1.94 % (18232)Termination phase: Saturation
% 3.20/1.94
% 3.20/1.94 % (18232)Memory used [KB]: 9466
% 3.20/1.94 % (18232)Time elapsed: 0.159 s
% 3.20/1.94 % (18232)Instructions burned: 377 (million)
% 3.20/1.94 % (18232)------------------------------
% 3.20/1.94 % (18232)------------------------------
% 3.20/1.95 % (18253)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_17963 for (2997ds/100Mi)
% 3.20/1.96 % (18254)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_17963 for (2997ds/3Mi)
% 3.20/1.96 % (18254)Instruction limit reached!
% 3.20/1.96 % (18254)------------------------------
% 3.20/1.96 % (18254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.96 % (18254)Termination reason: Unknown
% 3.20/1.96 % (18254)Termination phase: shuffling
% 3.20/1.96
% 3.20/1.96 % (18254)Memory used [KB]: 1663
% 3.20/1.96 % (18254)Time elapsed: 0.003 s
% 3.20/1.96 % (18254)Instructions burned: 3 (million)
% 3.20/1.96 % (18254)------------------------------
% 3.20/1.96 % (18254)------------------------------
% 3.20/1.97 % (18253)Instruction limit reached!
% 3.20/1.97 % (18253)------------------------------
% 3.20/1.97 % (18253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.97 % (18253)Termination reason: Unknown
% 3.20/1.97 % (18253)Termination phase: Preprocessing 3
% 3.20/1.97
% 3.20/1.97 % (18253)Memory used [KB]: 2942
% 3.20/1.97 % (18253)Time elapsed: 0.028 s
% 3.20/1.97 % (18253)Instructions burned: 103 (million)
% 3.20/1.97 % (18253)------------------------------
% 3.20/1.97 % (18253)------------------------------
% 3.20/1.98 % (18257)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_17963 for (2997ds/20Mi)
% 3.20/1.98 % (18260)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_17963 for (2996ds/86Mi)
% 3.20/1.99 % (18257)Instruction limit reached!
% 3.20/1.99 % (18257)------------------------------
% 3.20/1.99 % (18257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.99 % (18257)Termination reason: Unknown
% 3.20/1.99 % (18257)Termination phase: shuffling
% 3.20/1.99
% 3.20/1.99 % (18257)Memory used [KB]: 1918
% 3.20/1.99 % (18257)Time elapsed: 0.012 s
% 3.20/1.99 % (18257)Instructions burned: 21 (million)
% 3.20/1.99 % (18257)------------------------------
% 3.20/1.99 % (18257)------------------------------
% 3.20/2.00 % (18262)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_17963 for (2996ds/107Mi)
% 3.20/2.01 % (18260)Instruction limit reached!
% 3.20/2.01 % (18260)------------------------------
% 3.20/2.01 % (18260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/2.01 % (18260)Termination reason: Unknown
% 3.20/2.01 % (18260)Termination phase: Property scanning
% 3.20/2.01
% 3.20/2.01 % (18260)Memory used [KB]: 2814
% 3.20/2.01 % (18260)Time elapsed: 0.025 s
% 3.20/2.01 % (18260)Instructions burned: 89 (million)
% 3.20/2.01 % (18260)------------------------------
% 3.20/2.01 % (18260)------------------------------
% 5.51/2.02 % (18264)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_17963 for (2996ds/39Mi)
% 5.51/2.03 % (18262)Instruction limit reached!
% 5.51/2.03 % (18262)------------------------------
% 5.51/2.03 % (18262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.51/2.03 % (18262)Termination reason: Unknown
% 5.51/2.03 % (18262)Termination phase: SInE selection
% 5.51/2.03
% 5.51/2.03 % (18262)Memory used [KB]: 2814
% 5.51/2.03 % (18262)Time elapsed: 0.030 s
% 5.51/2.03 % (18262)Instructions burned: 110 (million)
% 5.51/2.03 % (18262)------------------------------
% 5.51/2.03 % (18262)------------------------------
% 5.51/2.03 % (18264)Instruction limit reached!
% 5.51/2.03 % (18264)------------------------------
% 5.51/2.03 % (18264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.51/2.03 % (18264)Termination reason: Unknown
% 5.51/2.03 % (18264)Termination phase: shuffling
% 5.51/2.03
% 5.51/2.03 % (18264)Memory used [KB]: 2430
% 5.51/2.03 % (18264)Time elapsed: 0.012 s
% 5.51/2.03 % (18264)Instructions burned: 40 (million)
% 5.51/2.03 % (18264)------------------------------
% 5.51/2.03 % (18264)------------------------------
% 5.51/2.04 % (18265)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_17963 for (2996ds/448Mi)
% 5.51/2.04 % (18233)Instruction limit reached!
% 5.51/2.04 % (18233)------------------------------
% 5.51/2.04 % (18233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.51/2.04 % (18233)Termination reason: Unknown
% 5.51/2.04 % (18233)Termination phase: Saturation
% 5.51/2.04
% 5.51/2.04 % (18233)Memory used [KB]: 8059
% 5.51/2.04 % (18233)Time elapsed: 0.251 s
% 5.51/2.04 % (18233)Instructions burned: 781 (million)
% 5.51/2.04 % (18233)------------------------------
% 5.51/2.04 % (18233)------------------------------
% 5.51/2.04 % (18266)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_17963 for (2996ds/46Mi)
% 5.51/2.05 % (18267)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_17963 for (2996ds/98Mi)
% 5.51/2.05 % (18266)Instruction limit reached!
% 5.51/2.05 % (18266)------------------------------
% 5.51/2.05 % (18266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.51/2.05 % (18266)Termination reason: Unknown
% 5.51/2.05 % (18266)Termination phase: shuffling
% 5.51/2.05
% 5.51/2.05 % (18266)Memory used [KB]: 2558
% 5.51/2.05 % (18266)Time elapsed: 0.014 s
% 5.51/2.05 % (18266)Instructions burned: 47 (million)
% 5.51/2.05 % (18266)------------------------------
% 5.51/2.05 % (18266)------------------------------
% 5.51/2.06 % (18224)Instruction limit reached!
% 5.51/2.06 % (18224)------------------------------
% 5.51/2.06 % (18224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.51/2.06 % (18224)Termination reason: Unknown
% 5.51/2.06 % (18224)Termination phase: Saturation
% 5.51/2.06
% 5.51/2.06 % (18224)Memory used [KB]: 11897
% 5.51/2.06 % (18224)Time elapsed: 0.304 s
% 5.51/2.06 % (18224)Instructions burned: 712 (million)
% 5.51/2.06 % (18224)------------------------------
% 5.51/2.06 % (18224)------------------------------
% 5.51/2.06 % (18268)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_17963 for (2996ds/507Mi)
% 5.51/2.07 % (18269)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_17963 for (2995ds/149Mi)
% 5.51/2.07 % (18267)Instruction limit reached!
% 5.51/2.07 % (18267)------------------------------
% 5.51/2.07 % (18267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.51/2.07 % (18267)Termination reason: Unknown
% 5.51/2.07 % (18267)Termination phase: Property scanning
% 5.51/2.07
% 5.51/2.07 % (18267)Memory used [KB]: 2814
% 5.51/2.07 % (18267)Time elapsed: 0.027 s
% 5.51/2.07 % (18267)Instructions burned: 101 (million)
% 5.51/2.07 % (18267)------------------------------
% 5.51/2.07 % (18267)------------------------------
% 5.51/2.08 % (18270)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_17963 for (2995ds/39Mi)
% 5.51/2.08 % (18214)Instruction limit reached!
% 5.51/2.08 % (18214)------------------------------
% 5.51/2.08 % (18214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.51/2.08 % (18214)Termination reason: Unknown
% 5.51/2.08 % (18214)Termination phase: Saturation
% 5.51/2.08
% 5.51/2.08 % (18214)Memory used [KB]: 18933
% 5.51/2.08 % (18214)Time elapsed: 0.365 s
% 5.51/2.08 % (18214)Instructions burned: 1044 (million)
% 5.51/2.08 % (18214)------------------------------
% 5.51/2.08 % (18214)------------------------------
% 5.51/2.09 % (18270)Instruction limit reached!
% 5.51/2.09 % (18270)------------------------------
% 5.51/2.09 % (18270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.51/2.09 % (18270)Termination reason: Unknown
% 5.51/2.09 % (18270)Termination phase: shuffling
% 5.51/2.09
% 5.51/2.09 % (18270)Memory used [KB]: 2430
% 5.51/2.09 % (18270)Time elapsed: 0.012 s
% 5.51/2.09 % (18270)Instructions burned: 40 (million)
% 5.51/2.09 % (18270)------------------------------
% 5.51/2.09 % (18270)------------------------------
% 5.51/2.09 % (18271)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_17963 for (2995ds/6Mi)
% 5.51/2.10 % (18271)Instruction limit reached!
% 5.51/2.10 % (18271)------------------------------
% 5.51/2.10 % (18271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.51/2.10 % (18271)Termination reason: Unknown
% 5.51/2.10 % (18271)Termination phase: shuffling
% 5.51/2.10
% 5.51/2.10 % (18271)Memory used [KB]: 1791
% 5.51/2.10 % (18271)Time elapsed: 0.004 s
% 5.51/2.10 % (18271)Instructions burned: 9 (million)
% 5.51/2.10 % (18271)------------------------------
% 5.51/2.10 % (18271)------------------------------
% 5.51/2.10 % (18272)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_17963 for (2995ds/1087Mi)
% 5.51/2.11 % (18273)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_17963 for (2995ds/47Mi)
% 5.51/2.11 % (18269)Instruction limit reached!
% 5.51/2.11 % (18269)------------------------------
% 5.51/2.11 % (18269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.51/2.11 % (18269)Termination reason: Unknown
% 5.51/2.11 % (18269)Termination phase: Function definition elimination
% 5.51/2.11
% 5.51/2.11 % (18269)Memory used [KB]: 3070
% 5.51/2.11 % (18269)Time elapsed: 0.040 s
% 5.51/2.11 % (18269)Instructions burned: 149 (million)
% 5.51/2.11 % (18269)------------------------------
% 5.51/2.11 % (18269)------------------------------
% 6.08/2.12 % (18273)Instruction limit reached!
% 6.08/2.12 % (18273)------------------------------
% 6.08/2.12 % (18273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.12 % (18273)Termination reason: Unknown
% 6.08/2.12 % (18273)Termination phase: shuffling
% 6.08/2.12
% 6.08/2.12 % (18273)Memory used [KB]: 2430
% 6.08/2.12 % (18273)Time elapsed: 0.014 s
% 6.08/2.12 % (18273)Instructions burned: 47 (million)
% 6.08/2.12 % (18273)------------------------------
% 6.08/2.12 % (18273)------------------------------
% 6.08/2.12 % (18274)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_17963 for (2995ds/44Mi)
% 6.08/2.12 % (18226)Instruction limit reached!
% 6.08/2.12 % (18226)------------------------------
% 6.08/2.12 % (18226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.12 % (18226)Termination reason: Unknown
% 6.08/2.12 % (18226)Termination phase: Saturation
% 6.08/2.12
% 6.08/2.12 % (18226)Memory used [KB]: 13304
% 6.08/2.12 % (18226)Time elapsed: 0.359 s
% 6.08/2.12 % (18226)Instructions burned: 903 (million)
% 6.08/2.12 % (18226)------------------------------
% 6.08/2.12 % (18226)------------------------------
% 6.08/2.13 % (18279)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_17963 for (2995ds/432Mi)
% 6.08/2.13 % (18235)Instruction limit reached!
% 6.08/2.13 % (18235)------------------------------
% 6.08/2.13 % (18235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.13 % (18235)Termination reason: Unknown
% 6.08/2.13 % (18235)Termination phase: Saturation
% 6.08/2.13
% 6.08/2.13 % (18235)Memory used [KB]: 10746
% 6.08/2.13 % (18235)Time elapsed: 0.313 s
% 6.08/2.13 % (18235)Instructions burned: 880 (million)
% 6.08/2.13 % (18235)------------------------------
% 6.08/2.13 % (18235)------------------------------
% 6.08/2.13 % (18274)Instruction limit reached!
% 6.08/2.13 % (18274)------------------------------
% 6.08/2.13 % (18274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.13 % (18274)Termination reason: Unknown
% 6.08/2.13 % (18274)Termination phase: shuffling
% 6.08/2.13
% 6.08/2.13 % (18274)Memory used [KB]: 2430
% 6.08/2.13 % (18274)Time elapsed: 0.014 s
% 6.08/2.13 % (18274)Instructions burned: 46 (million)
% 6.08/2.13 % (18274)------------------------------
% 6.08/2.13 % (18274)------------------------------
% 6.08/2.13 % (18281)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_17963 for (2995ds/62Mi)
% 6.08/2.14 % (18286)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_17963 for (2995ds/31Mi)
% 6.08/2.14 % (18288)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_17963 for (2995ds/96Mi)
% 6.08/2.14 % (18265)Instruction limit reached!
% 6.08/2.14 % (18265)------------------------------
% 6.08/2.14 % (18265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.14 % (18265)Termination reason: Unknown
% 6.08/2.14 % (18265)Termination phase: Saturation
% 6.08/2.14
% 6.08/2.14 % (18265)Memory used [KB]: 7931
% 6.08/2.14 % (18265)Time elapsed: 0.111 s
% 6.08/2.14 % (18265)Instructions burned: 448 (million)
% 6.08/2.14 % (18265)------------------------------
% 6.08/2.14 % (18265)------------------------------
% 6.08/2.15 % (18281)Instruction limit reached!
% 6.08/2.15 % (18281)------------------------------
% 6.08/2.15 % (18281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.15 % (18281)Termination reason: Unknown
% 6.08/2.15 % (18281)Termination phase: shuffling
% 6.08/2.15
% 6.08/2.15 % (18281)Memory used [KB]: 2814
% 6.08/2.15 % (18281)Time elapsed: 0.018 s
% 6.08/2.15 % (18281)Instructions burned: 63 (million)
% 6.08/2.15 % (18281)------------------------------
% 6.08/2.15 % (18281)------------------------------
% 6.08/2.15 % (18286)Instruction limit reached!
% 6.08/2.15 % (18286)------------------------------
% 6.08/2.15 % (18286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.15 % (18286)Termination reason: Unknown
% 6.08/2.15 % (18286)Termination phase: shuffling
% 6.08/2.15
% 6.08/2.15 % (18286)Memory used [KB]: 2302
% 6.08/2.15 % (18286)Time elapsed: 0.010 s
% 6.08/2.15 % (18286)Instructions burned: 32 (million)
% 6.08/2.15 % (18286)------------------------------
% 6.08/2.15 % (18286)------------------------------
% 6.08/2.15 % (18295)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_17963 for (2995ds/453Mi)
% 6.08/2.16 % (18298)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_17963 for (2995ds/71Mi)
% 6.08/2.16 % (18299)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_17963 for (2995ds/83Mi)
% 6.08/2.17 % (18288)Instruction limit reached!
% 6.08/2.17 % (18288)------------------------------
% 6.08/2.17 % (18288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.17 % (18288)Termination reason: Unknown
% 6.08/2.17 % (18288)Termination phase: Property scanning
% 6.08/2.17
% 6.08/2.17 % (18288)Memory used [KB]: 2814
% 6.08/2.17 % (18288)Time elapsed: 0.027 s
% 6.08/2.17 % (18288)Instructions burned: 98 (million)
% 6.08/2.17 % (18288)------------------------------
% 6.08/2.17 % (18288)------------------------------
% 6.08/2.18 % (18307)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_17963 for (2994ds/11Mi)
% 6.08/2.18 % (18298)Instruction limit reached!
% 6.08/2.18 % (18298)------------------------------
% 6.08/2.18 % (18298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.18 % (18298)Termination reason: Unknown
% 6.08/2.18 % (18298)Termination phase: Property scanning
% 6.08/2.18
% 6.08/2.18 % (18298)Memory used [KB]: 2814
% 6.08/2.18 % (18298)Time elapsed: 0.021 s
% 6.08/2.18 % (18298)Instructions burned: 72 (million)
% 6.08/2.18 % (18298)------------------------------
% 6.08/2.18 % (18298)------------------------------
% 6.08/2.18 % (18307)Instruction limit reached!
% 6.08/2.18 % (18307)------------------------------
% 6.08/2.18 % (18307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.18 % (18307)Termination reason: Unknown
% 6.08/2.18 % (18307)Termination phase: shuffling
% 6.08/2.18
% 6.08/2.18 % (18307)Memory used [KB]: 1791
% 6.08/2.18 % (18307)Time elapsed: 0.005 s
% 6.08/2.18 % (18307)Instructions burned: 12 (million)
% 6.08/2.18 % (18307)------------------------------
% 6.08/2.18 % (18307)------------------------------
% 6.08/2.18 % (18299)Instruction limit reached!
% 6.08/2.18 % (18299)------------------------------
% 6.08/2.18 % (18299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.18 % (18299)Termination reason: Unknown
% 6.08/2.18 % (18299)Termination phase: Property scanning
% 6.08/2.18
% 6.08/2.18 % (18299)Memory used [KB]: 2814
% 6.08/2.18 % (18299)Time elapsed: 0.024 s
% 6.08/2.18 % (18299)Instructions burned: 85 (million)
% 6.08/2.18 % (18299)------------------------------
% 6.08/2.18 % (18299)------------------------------
% 6.08/2.19 % (18314)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_17963 for (2994ds/41Mi)
% 6.08/2.19 % (18317)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_17963 for (2994ds/6Mi)
% 6.08/2.19 % (18318)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_17963 for (2994ds/150Mi)
% 6.08/2.19 % (18317)Instruction limit reached!
% 6.08/2.19 % (18317)------------------------------
% 6.08/2.19 % (18317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.08/2.19 % (18317)Termination reason: Unknown
% 6.08/2.19 % (18317)Termination phase: shuffling
% 6.08/2.19
% 6.08/2.19 % (18317)Memory used [KB]: 1663
% 6.08/2.19 % (18317)Time elapsed: 0.003 s
% 6.08/2.19 % (18317)Instructions burned: 6 (million)
% 6.08/2.19 % (18317)------------------------------
% 6.08/2.19 % (18317)------------------------------
% 6.46/2.20 % (18314)Instruction limit reached!
% 6.46/2.20 % (18314)------------------------------
% 6.46/2.20 % (18314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.46/2.20 % (18314)Termination reason: Unknown
% 6.46/2.20 % (18314)Termination phase: shuffling
% 6.46/2.20
% 6.46/2.20 % (18314)Memory used [KB]: 2430
% 6.46/2.20 % (18314)Time elapsed: 0.012 s
% 6.46/2.20 % (18314)Instructions burned: 41 (million)
% 6.46/2.20 % (18314)------------------------------
% 6.46/2.20 % (18314)------------------------------
% 6.46/2.20 % (18325)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_17963 for (2994ds/343Mi)
% 6.46/2.20 % (18268)Instruction limit reached!
% 6.46/2.20 % (18268)------------------------------
% 6.46/2.20 % (18268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.46/2.20 % (18268)Termination reason: Unknown
% 6.46/2.20 % (18268)Termination phase: Saturation
% 6.46/2.20
% 6.46/2.20 % (18268)Memory used [KB]: 8443
% 6.46/2.20 % (18268)Time elapsed: 0.145 s
% 6.46/2.20 % (18268)Instructions burned: 509 (million)
% 6.46/2.20 % (18268)------------------------------
% 6.46/2.20 % (18268)------------------------------
% 6.46/2.21 % (18327)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_17963 for (2994ds/109Mi)
% 6.46/2.21 % (18330)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_17963 for (2994ds/253Mi)
% 6.46/2.23 % (18318)Instruction limit reached!
% 6.46/2.23 % (18318)------------------------------
% 6.46/2.23 % (18318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.46/2.23 % (18318)Termination reason: Unknown
% 6.46/2.24 % (18318)Termination phase: Preprocessing 3
% 6.46/2.24
% 6.46/2.24 % (18318)Memory used [KB]: 5373
% 6.46/2.24 % (18318)Time elapsed: 0.046 s
% 6.46/2.24 % (18318)Instructions burned: 153 (million)
% 6.46/2.24 % (18318)------------------------------
% 6.46/2.24 % (18318)------------------------------
% 6.46/2.24 % (18279)Instruction limit reached!
% 6.46/2.24 % (18279)------------------------------
% 6.46/2.24 % (18279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.46/2.24 % (18279)Termination reason: Unknown
% 6.46/2.24 % (18279)Termination phase: Saturation
% 6.46/2.24
% 6.46/2.24 % (18279)Memory used [KB]: 3454
% 6.46/2.24 % (18279)Time elapsed: 0.109 s
% 6.46/2.24 % (18279)Instructions burned: 433 (million)
% 6.46/2.24 % (18279)------------------------------
% 6.46/2.24 % (18279)------------------------------
% 6.46/2.24 % (18327)Instruction limit reached!
% 6.46/2.24 % (18327)------------------------------
% 6.46/2.24 % (18327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.46/2.24 % (18327)Termination reason: Unknown
% 6.46/2.24 % (18327)Termination phase: SInE selection
% 6.46/2.24
% 6.46/2.24 % (18327)Memory used [KB]: 2814
% 6.46/2.24 % (18327)Time elapsed: 0.030 s
% 6.46/2.24 % (18327)Instructions burned: 112 (million)
% 6.46/2.24 % (18327)------------------------------
% 6.46/2.24 % (18327)------------------------------
% 6.46/2.25 % (18344)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_17963 for (2994ds/140Mi)
% 6.46/2.25 % (18345)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_17963 for (2994ds/614Mi)
% 6.46/2.25 % (18346)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_17963 for (2994ds/202Mi)
% 6.46/2.27 % (18295)Instruction limit reached!
% 6.46/2.27 % (18295)------------------------------
% 6.46/2.27 % (18295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.46/2.27 % (18295)Termination reason: Unknown
% 6.46/2.27 % (18295)Termination phase: Saturation
% 6.46/2.27
% 6.46/2.27 % (18295)Memory used [KB]: 7931
% 6.46/2.27 % (18295)Time elapsed: 0.114 s
% 6.46/2.27 % (18295)Instructions burned: 454 (million)
% 6.46/2.27 % (18295)------------------------------
% 6.46/2.27 % (18295)------------------------------
% 6.46/2.28 % (18358)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_17963 for (2994ds/339Mi)
% 6.46/2.28 % (18344)Instruction limit reached!
% 6.46/2.28 % (18344)------------------------------
% 6.46/2.28 % (18344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.46/2.28 % (18344)Termination reason: Unknown
% 6.46/2.28 % (18344)Termination phase: Property scanning
% 6.46/2.28
% 6.46/2.28 % (18344)Memory used [KB]: 3070
% 6.46/2.28 % (18344)Time elapsed: 0.038 s
% 6.46/2.28 % (18344)Instructions burned: 140 (million)
% 6.46/2.28 % (18344)------------------------------
% 6.46/2.28 % (18344)------------------------------
% 6.46/2.28 % (18330)Instruction limit reached!
% 6.46/2.28 % (18330)------------------------------
% 6.46/2.28 % (18330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.46/2.28 % (18330)Termination reason: Unknown
% 6.46/2.28 % (18330)Termination phase: Property scanning
% 6.46/2.28
% 6.46/2.28 % (18330)Memory used [KB]: 6012
% 6.46/2.28 % (18330)Time elapsed: 0.072 s
% 6.46/2.28 % (18330)Instructions burned: 254 (million)
% 6.46/2.28 % (18330)------------------------------
% 6.46/2.28 % (18330)------------------------------
% 6.46/2.29 % (18325)Instruction limit reached!
% 6.46/2.29 % (18325)------------------------------
% 6.46/2.29 % (18325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.46/2.29 % (18325)Termination reason: Unknown
% 6.46/2.29 % (18325)Termination phase: Saturation
% 6.46/2.29
% 6.46/2.29 % (18325)Memory used [KB]: 8443
% 6.46/2.29 % (18325)Time elapsed: 0.092 s
% 6.46/2.29 % (18325)Instructions burned: 344 (million)
% 6.46/2.29 % (18325)------------------------------
% 6.46/2.29 % (18325)------------------------------
% 6.46/2.29 % (18361)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_17963 for (2993ds/283Mi)
% 6.46/2.29 % (18365)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_17963 for (2993ds/134Mi)
% 7.19/2.30 % (18372)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_17963 for (2993ds/298Mi)
% 7.19/2.30 % (18346)Instruction limit reached!
% 7.19/2.30 % (18346)------------------------------
% 7.19/2.30 % (18346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.19/2.30 % (18346)Termination reason: Unknown
% 7.19/2.30 % (18346)Termination phase: Property scanning
% 7.19/2.30
% 7.19/2.30 % (18346)Memory used [KB]: 5756
% 7.19/2.30 % (18346)Time elapsed: 0.059 s
% 7.19/2.30 % (18346)Instructions burned: 204 (million)
% 7.19/2.30 % (18346)------------------------------
% 7.19/2.30 % (18346)------------------------------
% 7.19/2.31 % (18380)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_17963 for (2993ds/192Mi)
% 7.19/2.33 % (18365)Instruction limit reached!
% 7.19/2.33 % (18365)------------------------------
% 7.19/2.33 % (18365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.19/2.33 % (18365)Termination reason: Unknown
% 7.19/2.33 % (18365)Termination phase: Property scanning
% 7.19/2.33
% 7.19/2.33 % (18365)Memory used [KB]: 3070
% 7.19/2.33 % (18365)Time elapsed: 0.037 s
% 7.19/2.33 % (18365)Instructions burned: 136 (million)
% 7.19/2.33 % (18365)------------------------------
% 7.19/2.33 % (18365)------------------------------
% 7.19/2.34 % (18391)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_17963 for (2993ds/258Mi)
% 7.19/2.36 % (18361)Instruction limit reached!
% 7.19/2.36 % (18361)------------------------------
% 7.19/2.36 % (18361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.19/2.36 % (18361)Termination reason: Unknown
% 7.19/2.36 % (18361)Termination phase: Saturation
% 7.19/2.36
% 7.19/2.36 % (18361)Memory used [KB]: 7803
% 7.19/2.36 % (18361)Time elapsed: 0.072 s
% 7.19/2.36 % (18361)Instructions burned: 284 (million)
% 7.19/2.36 % (18361)------------------------------
% 7.19/2.36 % (18361)------------------------------
% 7.19/2.36 % (18380)Instruction limit reached!
% 7.19/2.36 % (18380)------------------------------
% 7.19/2.36 % (18380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.19/2.36 % (18380)Termination reason: Unknown
% 7.19/2.36 % (18380)Termination phase: Property scanning
% 7.19/2.36
% 7.19/2.36 % (18380)Memory used [KB]: 3198
% 7.19/2.36 % (18380)Time elapsed: 0.051 s
% 7.19/2.36 % (18380)Instructions burned: 194 (million)
% 7.19/2.36 % (18380)------------------------------
% 7.19/2.36 % (18380)------------------------------
% 7.19/2.37 % (18358)Instruction limit reached!
% 7.19/2.37 % (18358)------------------------------
% 7.19/2.37 % (18358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.19/2.37 % (18358)Termination reason: Unknown
% 7.19/2.37 % (18358)Termination phase: Saturation
% 7.19/2.37
% 7.19/2.37 % (18358)Memory used [KB]: 8059
% 7.19/2.37 % (18358)Time elapsed: 0.092 s
% 7.19/2.37 % (18358)Instructions burned: 340 (million)
% 7.19/2.37 % (18358)------------------------------
% 7.19/2.37 % (18358)------------------------------
% 7.19/2.37 % (18408)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_17963 for (2993ds/90Mi)
% 7.19/2.37 % (18409)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_17963 for (2993ds/231Mi)
% 7.19/2.38 % (18372)Instruction limit reached!
% 7.19/2.38 % (18372)------------------------------
% 7.19/2.38 % (18372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.19/2.38 % (18372)Termination reason: Unknown
% 7.19/2.38 % (18372)Termination phase: Saturation
% 7.19/2.38
% 7.19/2.38 % (18372)Memory used [KB]: 7803
% 7.19/2.38 % (18372)Time elapsed: 0.076 s
% 7.19/2.38 % (18372)Instructions burned: 300 (million)
% 7.19/2.38 % (18372)------------------------------
% 7.19/2.38 % (18372)------------------------------
% 7.19/2.38 % (18410)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_17963 for (2993ds/458Mi)
% 7.19/2.39 % (18416)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_17963 for (2992ds/31Mi)
% 7.19/2.40 % (18416)Instruction limit reached!
% 7.19/2.40 % (18416)------------------------------
% 7.19/2.40 % (18416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.19/2.40 % (18416)Termination reason: Unknown
% 7.19/2.40 % (18416)Termination phase: shuffling
% 7.19/2.40
% 7.19/2.40 % (18416)Memory used [KB]: 2302
% 7.19/2.40 % (18416)Time elapsed: 0.011 s
% 7.19/2.40 % (18416)Instructions burned: 33 (million)
% 7.19/2.40 % (18416)------------------------------
% 7.19/2.40 % (18416)------------------------------
% 7.66/2.40 % (18408)Instruction limit reached!
% 7.66/2.40 % (18408)------------------------------
% 7.66/2.40 % (18408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.66/2.40 % (18408)Termination reason: Unknown
% 7.66/2.40 % (18408)Termination phase: Property scanning
% 7.66/2.40
% 7.66/2.40 % (18408)Memory used [KB]: 2814
% 7.66/2.40 % (18408)Time elapsed: 0.026 s
% 7.66/2.40 % (18408)Instructions burned: 91 (million)
% 7.66/2.40 % (18408)------------------------------
% 7.66/2.40 % (18408)------------------------------
% 7.66/2.41 % (18427)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_17963 for (2992ds/297Mi)
% 7.66/2.41 % (18429)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_17963 for (2992ds/987Mi)
% 7.66/2.41 % (18391)Instruction limit reached!
% 7.66/2.41 % (18391)------------------------------
% 7.66/2.41 % (18391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.66/2.41 % (18391)Termination reason: Unknown
% 7.66/2.41 % (18391)Termination phase: Saturation
% 7.66/2.41
% 7.66/2.41 % (18391)Memory used [KB]: 8059
% 7.66/2.41 % (18391)Time elapsed: 0.069 s
% 7.66/2.41 % (18391)Instructions burned: 258 (million)
% 7.66/2.41 % (18391)------------------------------
% 7.66/2.41 % (18391)------------------------------
% 7.66/2.42 % (18434)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_17963 for (2992ds/182Mi)
% 7.66/2.42 % (18345)Instruction limit reached!
% 7.66/2.42 % (18345)------------------------------
% 7.66/2.42 % (18345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.66/2.42 % (18345)Termination reason: Unknown
% 7.66/2.42 % (18345)Termination phase: Saturation
% 7.66/2.42
% 7.66/2.42 % (18345)Memory used [KB]: 10490
% 7.66/2.42 % (18345)Time elapsed: 0.176 s
% 7.66/2.42 % (18345)Instructions burned: 617 (million)
% 7.66/2.42 % (18345)------------------------------
% 7.66/2.42 % (18345)------------------------------
% 7.66/2.43 % (18443)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_17963 for (2992ds/182Mi)
% 7.66/2.43 % (18409)Instruction limit reached!
% 7.66/2.43 % (18409)------------------------------
% 7.66/2.43 % (18409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.66/2.43 % (18409)Termination reason: Unknown
% 7.66/2.43 % (18409)Termination phase: Property scanning
% 7.66/2.43
% 7.66/2.43 % (18409)Memory used [KB]: 4349
% 7.66/2.43 % (18409)Time elapsed: 0.062 s
% 7.66/2.43 % (18409)Instructions burned: 231 (million)
% 7.66/2.43 % (18409)------------------------------
% 7.66/2.43 % (18409)------------------------------
% 7.66/2.44 % (18272)Instruction limit reached!
% 7.66/2.44 % (18272)------------------------------
% 7.66/2.44 % (18272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.66/2.44 % (18272)Termination reason: Unknown
% 7.66/2.44 % (18272)Termination phase: Saturation
% 7.66/2.44
% 7.66/2.44 % (18272)Memory used [KB]: 13048
% 7.66/2.44 % (18272)Time elapsed: 0.342 s
% 7.66/2.44 % (18272)Instructions burned: 1088 (million)
% 7.66/2.44 % (18272)------------------------------
% 7.66/2.44 % (18272)------------------------------
% 7.66/2.44 % (18447)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_17963 for (2992ds/154Mi)
% 7.66/2.45 % (18452)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_17963 for (2992ds/79Mi)
% 7.66/2.46 % (18434)Instruction limit reached!
% 7.66/2.46 % (18434)------------------------------
% 7.66/2.46 % (18434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.66/2.46 % (18434)Termination reason: Unknown
% 7.66/2.46 % (18434)Termination phase: Property scanning
% 7.66/2.46
% 7.66/2.46 % (18434)Memory used [KB]: 3070
% 7.66/2.46 % (18434)Time elapsed: 0.048 s
% 7.66/2.46 % (18434)Instructions burned: 185 (million)
% 7.66/2.46 % (18434)------------------------------
% 7.66/2.46 % (18434)------------------------------
% 7.66/2.47 % (18452)Instruction limit reached!
% 7.66/2.47 % (18452)------------------------------
% 7.66/2.47 % (18452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.66/2.47 % (18452)Termination reason: Unknown
% 7.66/2.47 % (18452)Termination phase: Property scanning
% 7.66/2.47
% 7.66/2.47 % (18452)Memory used [KB]: 2814
% 7.66/2.47 % (18452)Time elapsed: 0.023 s
% 7.66/2.47 % (18452)Instructions burned: 80 (million)
% 7.66/2.47 % (18452)------------------------------
% 7.66/2.47 % (18452)------------------------------
% 7.66/2.47 % (18459)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_17963 for (2991ds/216Mi)
% 7.66/2.48 % (18427)Instruction limit reached!
% 7.66/2.48 % (18427)------------------------------
% 7.66/2.48 % (18427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.66/2.48 % (18427)Termination reason: Unknown
% 7.66/2.48 % (18427)Termination phase: Saturation
% 7.66/2.48
% 7.66/2.48 % (18427)Memory used [KB]: 7803
% 7.66/2.48 % (18427)Time elapsed: 0.077 s
% 7.66/2.48 % (18427)Instructions burned: 297 (million)
% 7.66/2.48 % (18427)------------------------------
% 7.66/2.48 % (18427)------------------------------
% 7.66/2.48 % (18447)Instruction limit reached!
% 7.66/2.48 % (18447)------------------------------
% 7.66/2.48 % (18447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.66/2.48 % (18447)Termination reason: Unknown
% 7.66/2.48 % (18447)Termination phase: Function definition elimination
% 7.66/2.48
% 7.66/2.48 % (18447)Memory used [KB]: 2942
% 7.66/2.48 % (18447)Time elapsed: 0.041 s
% 7.66/2.48 % (18447)Instructions burned: 155 (million)
% 7.66/2.48 % (18447)------------------------------
% 7.66/2.48 % (18447)------------------------------
% 7.66/2.48 % (18463)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_17963 for (2991ds/114Mi)
% 7.66/2.48 % (18443)Instruction limit reached!
% 7.66/2.48 % (18443)------------------------------
% 7.66/2.48 % (18443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.66/2.48 % (18443)Termination reason: Unknown
% 7.66/2.48 % (18443)Termination phase: Property scanning
% 7.66/2.48
% 7.66/2.49 % (18443)Memory used [KB]: 5756
% 7.66/2.49 % (18443)Time elapsed: 0.056 s
% 7.66/2.49 % (18443)Instructions burned: 185 (million)
% 7.66/2.49 % (18443)------------------------------
% 7.66/2.49 % (18443)------------------------------
% 7.66/2.49 % (18468)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_17963 for (2991ds/922Mi)
% 7.66/2.49 % (18470)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_17963 for (2991ds/182Mi)
% 7.66/2.50 % (18472)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_17963 for (2991ds/164Mi)
% 8.67/2.50 % (18410)Instruction limit reached!
% 8.67/2.50 % (18410)------------------------------
% 8.67/2.50 % (18410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.67/2.50 % (18410)Termination reason: Unknown
% 8.67/2.50 % (18410)Termination phase: Saturation
% 8.67/2.50
% 8.67/2.50 % (18410)Memory used [KB]: 9722
% 8.67/2.50 % (18410)Time elapsed: 0.123 s
% 8.67/2.50 % (18410)Instructions burned: 459 (million)
% 8.67/2.50 % (18410)------------------------------
% 8.67/2.50 % (18410)------------------------------
% 8.67/2.51 % (18479)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_17963 for (2991ds/50Mi)
% 8.67/2.51 % (18463)Instruction limit reached!
% 8.67/2.51 % (18463)------------------------------
% 8.67/2.51 % (18463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.67/2.51 % (18463)Termination reason: Unknown
% 8.67/2.51 % (18463)Termination phase: Property scanning
% 8.67/2.51
% 8.67/2.51 % (18463)Memory used [KB]: 3070
% 8.67/2.51 % (18463)Time elapsed: 0.032 s
% 8.67/2.51 % (18463)Instructions burned: 115 (million)
% 8.67/2.51 % (18463)------------------------------
% 8.67/2.51 % (18463)------------------------------
% 8.67/2.52 % (18479)Instruction limit reached!
% 8.67/2.52 % (18479)------------------------------
% 8.67/2.52 % (18479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.67/2.52 % (18479)Termination reason: Unknown
% 8.67/2.52 % (18479)Termination phase: shuffling
% 8.67/2.52
% 8.67/2.52 % (18479)Memory used [KB]: 2558
% 8.67/2.52 % (18479)Time elapsed: 0.015 s
% 8.67/2.52 % (18479)Instructions burned: 51 (million)
% 8.67/2.52 % (18479)------------------------------
% 8.67/2.52 % (18479)------------------------------
% 8.67/2.52 % (18484)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_17963 for (2991ds/368Mi)
% 8.67/2.53 % (18459)Instruction limit reached!
% 8.67/2.53 % (18459)------------------------------
% 8.67/2.53 % (18459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.67/2.53 % (18459)Termination reason: Unknown
% 8.67/2.53 % (18459)Termination phase: Property scanning
% 8.67/2.53
% 8.67/2.53 % (18459)Memory used [KB]: 3326
% 8.67/2.53 % (18459)Time elapsed: 0.056 s
% 8.67/2.53 % (18459)Instructions burned: 218 (million)
% 8.67/2.53 % (18459)------------------------------
% 8.67/2.53 % (18459)------------------------------
% 8.67/2.53 % (18487)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_17963 for (2991ds/1021Mi)
% 8.67/2.54 % (18472)Instruction limit reached!
% 8.67/2.54 % (18472)------------------------------
% 8.67/2.54 % (18472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.67/2.54 % (18472)Termination reason: Unknown
% 8.67/2.54 % (18472)Termination phase: Property scanning
% 8.67/2.54
% 8.67/2.54 % (18472)Memory used [KB]: 3070
% 8.67/2.54 % (18472)Time elapsed: 0.044 s
% 8.67/2.54 % (18472)Instructions burned: 167 (million)
% 8.67/2.54 % (18472)------------------------------
% 8.67/2.54 % (18472)------------------------------
% 8.67/2.54 % (18490)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_17963 for (2991ds/267Mi)
% 8.67/2.54 % (18470)Instruction limit reached!
% 8.67/2.54 % (18470)------------------------------
% 8.67/2.54 % (18470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.67/2.54 % (18470)Termination reason: Unknown
% 8.67/2.54 % (18470)Termination phase: Property scanning
% 8.67/2.54
% 8.67/2.54 % (18470)Memory used [KB]: 3198
% 8.67/2.54 % (18470)Time elapsed: 0.048 s
% 8.67/2.54 % (18470)Instructions burned: 185 (million)
% 8.67/2.54 % (18470)------------------------------
% 8.67/2.54 % (18470)------------------------------
% 8.67/2.55 % (18492)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_17963 for (2991ds/204Mi)
% 8.67/2.55 % (18493)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_17963 for (2991ds/26Mi)
% 8.67/2.56 % (18493)Instruction limit reached!
% 8.67/2.56 % (18493)------------------------------
% 8.67/2.56 % (18493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.67/2.56 % (18493)Termination reason: Unknown
% 8.67/2.56 % (18493)Termination phase: shuffling
% 8.67/2.56
% 8.67/2.56 % (18493)Memory used [KB]: 2302
% 8.67/2.56 % (18493)Time elapsed: 0.009 s
% 8.67/2.56 % (18493)Instructions burned: 29 (million)
% 8.67/2.56 % (18493)------------------------------
% 8.67/2.56 % (18493)------------------------------
% 8.67/2.57 % (18501)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_17963 for (2991ds/53Mi)
% 8.67/2.58 % (18501)Instruction limit reached!
% 8.67/2.58 % (18501)------------------------------
% 8.67/2.58 % (18501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.67/2.58 % (18501)Termination reason: Unknown
% 8.67/2.58 % (18501)Termination phase: shuffling
% 8.67/2.58
% 8.67/2.58 % (18501)Memory used [KB]: 2686
% 8.67/2.58 % (18501)Time elapsed: 0.016 s
% 8.67/2.58 % (18501)Instructions burned: 56 (million)
% 8.67/2.58 % (18501)------------------------------
% 8.67/2.58 % (18501)------------------------------
% 8.67/2.59 % (18510)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_17963 for (2990ds/4436Mi)
% 9.07/2.60 % (18492)Instruction limit reached!
% 9.07/2.60 % (18492)------------------------------
% 9.07/2.60 % (18492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.07/2.60 % (18492)Termination reason: Unknown
% 9.07/2.60 % (18492)Termination phase: Property scanning
% 9.07/2.60
% 9.07/2.60 % (18492)Memory used [KB]: 3198
% 9.07/2.60 % (18492)Time elapsed: 0.053 s
% 9.07/2.60 % (18492)Instructions burned: 207 (million)
% 9.07/2.60 % (18492)------------------------------
% 9.07/2.60 % (18492)------------------------------
% 9.07/2.61 % (18490)Instruction limit reached!
% 9.07/2.61 % (18490)------------------------------
% 9.07/2.61 % (18490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.07/2.61 % (18490)Termination reason: Unknown
% 9.07/2.61 % (18490)Termination phase: Saturation
% 9.07/2.61
% 9.07/2.61 % (18490)Memory used [KB]: 7803
% 9.07/2.61 % (18490)Time elapsed: 0.068 s
% 9.07/2.61 % (18490)Instructions burned: 269 (million)
% 9.07/2.61 % (18490)------------------------------
% 9.07/2.61 % (18490)------------------------------
% 9.07/2.61 % (18517)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_17963 for (2990ds/1539Mi)
% 9.07/2.62 % (18521)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_17963 for (2990ds/408Mi)
% 9.07/2.62 % (18484)Instruction limit reached!
% 9.07/2.62 % (18484)------------------------------
% 9.07/2.62 % (18484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.07/2.62 % (18484)Termination reason: Unknown
% 9.07/2.62 % (18484)Termination phase: Saturation
% 9.07/2.62
% 9.07/2.62 % (18484)Memory used [KB]: 9466
% 9.07/2.62 % (18484)Time elapsed: 0.099 s
% 9.07/2.62 % (18484)Instructions burned: 369 (million)
% 9.07/2.62 % (18484)------------------------------
% 9.07/2.62 % (18484)------------------------------
% 9.07/2.63 % (18533)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_17963 for (2990ds/5205Mi)
% 9.07/2.66 % (18429)Instruction limit reached!
% 9.07/2.66 % (18429)------------------------------
% 9.07/2.66 % (18429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.07/2.66 % (18429)Termination reason: Unknown
% 9.07/2.66 % (18429)Termination phase: Saturation
% 9.07/2.66
% 9.07/2.66 % (18429)Memory used [KB]: 12920
% 9.07/2.66 % (18429)Time elapsed: 0.273 s
% 9.07/2.66 % (18429)Instructions burned: 990 (million)
% 9.07/2.66 % (18429)------------------------------
% 9.07/2.66 % (18429)------------------------------
% 9.07/2.67 % (18550)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_17963 for (2990ds/1913Mi)
% 9.57/2.74 % (18521)Instruction limit reached!
% 9.57/2.74 % (18521)------------------------------
% 9.57/2.74 % (18521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.57/2.74 % (18521)Termination reason: Unknown
% 9.57/2.74 % (18521)Termination phase: Saturation
% 9.57/2.74
% 9.57/2.74 % (18521)Memory used [KB]: 11897
% 9.57/2.74 % (18521)Time elapsed: 0.125 s
% 9.57/2.74 % (18521)Instructions burned: 411 (million)
% 9.57/2.74 % (18521)------------------------------
% 9.57/2.74 % (18521)------------------------------
% 9.57/2.75 % (18556)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_17963 for (2989ds/4350Mi)
% 9.57/2.78 % (18468)Instruction limit reached!
% 9.57/2.78 % (18468)------------------------------
% 9.57/2.78 % (18468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.57/2.78 % (18468)Termination reason: Unknown
% 9.57/2.78 % (18468)Termination phase: Saturation
% 9.57/2.78
% 9.57/2.78 % (18468)Memory used [KB]: 13048
% 9.57/2.78 % (18468)Time elapsed: 0.291 s
% 9.57/2.78 % (18468)Instructions burned: 923 (million)
% 9.57/2.78 % (18468)------------------------------
% 9.57/2.78 % (18468)------------------------------
% 9.57/2.79 % (18557)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_17963 for (2988ds/68Mi)
% 10.02/2.81 % (18557)Instruction limit reached!
% 10.02/2.81 % (18557)------------------------------
% 10.02/2.81 % (18557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.02/2.81 % (18557)Termination reason: Unknown
% 10.02/2.81 % (18557)Termination phase: Property scanning
% 10.02/2.81
% 10.02/2.81 % (18557)Memory used [KB]: 2814
% 10.02/2.81 % (18557)Time elapsed: 0.020 s
% 10.02/2.81 % (18557)Instructions burned: 69 (million)
% 10.02/2.81 % (18557)------------------------------
% 10.02/2.81 % (18557)------------------------------
% 10.02/2.82 % (18558)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_17963 for (2988ds/358Mi)
% 10.02/2.85 % (18487)Instruction limit reached!
% 10.02/2.85 % (18487)------------------------------
% 10.02/2.85 % (18487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.02/2.85 % (18487)Termination reason: Unknown
% 10.02/2.85 % (18487)Termination phase: Saturation
% 10.02/2.85
% 10.02/2.85 % (18487)Memory used [KB]: 13432
% 10.02/2.85 % (18487)Time elapsed: 0.320 s
% 10.02/2.85 % (18487)Instructions burned: 1023 (million)
% 10.02/2.85 % (18487)------------------------------
% 10.02/2.85 % (18487)------------------------------
% 10.02/2.86 % (18559)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_17963 for (2988ds/31Mi)
% 10.02/2.87 % (18559)Instruction limit reached!
% 10.02/2.87 % (18559)------------------------------
% 10.02/2.87 % (18559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.02/2.87 % (18559)Termination reason: Unknown
% 10.02/2.87 % (18559)Termination phase: shuffling
% 10.02/2.87
% 10.02/2.87 % (18559)Memory used [KB]: 2302
% 10.02/2.87 % (18559)Time elapsed: 0.010 s
% 10.02/2.87 % (18559)Instructions burned: 32 (million)
% 10.02/2.87 % (18559)------------------------------
% 10.02/2.87 % (18559)------------------------------
% 10.02/2.88 % (18560)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_17963 for (2987ds/279Mi)
% 10.40/2.91 % (18558)Instruction limit reached!
% 10.40/2.91 % (18558)------------------------------
% 10.40/2.91 % (18558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.40/2.91 % (18558)Termination reason: Unknown
% 10.40/2.91 % (18558)Termination phase: Saturation
% 10.40/2.91
% 10.40/2.91 % (18558)Memory used [KB]: 8443
% 10.40/2.91 % (18558)Time elapsed: 0.094 s
% 10.40/2.91 % (18558)Instructions burned: 359 (million)
% 10.40/2.91 % (18558)------------------------------
% 10.40/2.91 % (18558)------------------------------
% 10.40/2.92 % (18561)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_17963 for (2987ds/258Mi)
% 10.40/2.95 % (18560)Instruction limit reached!
% 10.40/2.95 % (18560)------------------------------
% 10.40/2.95 % (18560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.40/2.95 % (18560)Termination reason: Unknown
% 10.40/2.95 % (18560)Termination phase: Saturation
% 10.40/2.95
% 10.40/2.95 % (18560)Memory used [KB]: 7803
% 10.40/2.95 % (18560)Time elapsed: 0.072 s
% 10.40/2.95 % (18560)Instructions burned: 283 (million)
% 10.40/2.95 % (18560)------------------------------
% 10.40/2.95 % (18560)------------------------------
% 10.40/2.96 % (18562)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_17963 for (2987ds/26Mi)
% 10.40/2.97 % (18562)Instruction limit reached!
% 10.40/2.97 % (18562)------------------------------
% 10.40/2.97 % (18562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.40/2.97 % (18562)Termination reason: Unknown
% 10.40/2.97 % (18562)Termination phase: shuffling
% 10.40/2.97
% 10.40/2.97 % (18562)Memory used [KB]: 2046
% 10.40/2.97 % (18562)Time elapsed: 0.008 s
% 10.40/2.97 % (18562)Instructions burned: 26 (million)
% 10.40/2.97 % (18562)------------------------------
% 10.40/2.97 % (18562)------------------------------
% 10.40/2.98 % (18563)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_17963 for (2987ds/995Mi)
% 10.40/2.99 % (18561)Instruction limit reached!
% 10.40/2.99 % (18561)------------------------------
% 10.40/2.99 % (18561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.40/2.99 % (18561)Termination reason: Unknown
% 10.40/2.99 % (18561)Termination phase: Saturation
% 10.40/2.99
% 10.40/2.99 % (18561)Memory used [KB]: 8315
% 10.40/2.99 % (18561)Time elapsed: 0.069 s
% 10.40/2.99 % (18561)Instructions burned: 258 (million)
% 10.40/2.99 % (18561)------------------------------
% 10.40/2.99 % (18561)------------------------------
% 10.40/3.00 % (18564)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_17963 for (2986ds/373Mi)
% 12.62/3.07 % (18517)Instruction limit reached!
% 12.62/3.07 % (18517)------------------------------
% 12.62/3.07 % (18517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.62/3.07 % (18517)Termination reason: Unknown
% 12.62/3.07 % (18517)Termination phase: Saturation
% 12.62/3.07
% 12.62/3.07 % (18517)Memory used [KB]: 11001
% 12.62/3.07 % (18517)Time elapsed: 0.467 s
% 12.62/3.08 % (18517)Instructions burned: 1539 (million)
% 12.62/3.08 % (18517)------------------------------
% 12.62/3.08 % (18517)------------------------------
% 12.62/3.09 % (18565)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_17963 for (2985ds/253Mi)
% 12.62/3.10 % (18564)Instruction limit reached!
% 12.62/3.10 % (18564)------------------------------
% 12.62/3.10 % (18564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.62/3.10 % (18564)Termination reason: Unknown
% 12.62/3.10 % (18564)Termination phase: Saturation
% 12.62/3.10
% 12.62/3.10 % (18564)Memory used [KB]: 9466
% 12.62/3.10 % (18564)Time elapsed: 0.102 s
% 12.62/3.10 % (18564)Instructions burned: 376 (million)
% 12.62/3.10 % (18564)------------------------------
% 12.62/3.10 % (18564)------------------------------
% 12.62/3.11 % (18566)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_17963 for (2985ds/832Mi)
% 13.29/3.15 % (18565)Instruction limit reached!
% 13.29/3.15 % (18565)------------------------------
% 13.29/3.15 % (18565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.29/3.15 % (18565)Termination reason: Unknown
% 13.29/3.15 % (18565)Termination phase: Saturation
% 13.29/3.15
% 13.29/3.15 % (18565)Memory used [KB]: 7803
% 13.29/3.15 % (18565)Time elapsed: 0.066 s
% 13.29/3.15 % (18565)Instructions burned: 255 (million)
% 13.29/3.15 % (18565)------------------------------
% 13.29/3.15 % (18565)------------------------------
% 13.29/3.16 % (18567)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_17963 for (2985ds/668Mi)
% 13.72/3.24 % (18563)Instruction limit reached!
% 13.72/3.24 % (18563)------------------------------
% 13.72/3.24 % (18563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.72/3.24 % (18563)Termination reason: Unknown
% 13.72/3.24 % (18563)Termination phase: Saturation
% 13.72/3.24
% 13.72/3.24 % (18563)Memory used [KB]: 17398
% 13.72/3.24 % (18563)Time elapsed: 0.260 s
% 13.72/3.24 % (18563)Instructions burned: 995 (million)
% 13.72/3.24 % (18563)------------------------------
% 13.72/3.24 % (18563)------------------------------
% 13.72/3.25 % (18568)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_17963 for (2984ds/40Mi)
% 13.72/3.25 % (18510)First to succeed.
% 13.72/3.25 % (18550)Instruction limit reached!
% 13.72/3.25 % (18550)------------------------------
% 13.72/3.25 % (18550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.72/3.25 % (18550)Termination reason: Unknown
% 13.72/3.25 % (18550)Termination phase: Saturation
% 13.72/3.25
% 13.72/3.25 % (18550)Memory used [KB]: 6780
% 13.72/3.25 % (18550)Time elapsed: 0.587 s
% 13.72/3.25 % (18550)Instructions burned: 1913 (million)
% 13.72/3.25 % (18550)------------------------------
% 13.72/3.25 % (18550)------------------------------
% 13.72/3.26 % (18510)Refutation found. Thanks to Tanya!
% 13.72/3.26 % SZS status Theorem for DTF2THF_17963
% 13.72/3.26 % SZS output start Proof for DTF2THF_17963
% 13.72/3.26 thf(func_def_0, type, in: $i > $i > $o).
% 13.72/3.26 thf(func_def_1, type, exu: ($i > $o) > $o).
% 13.72/3.26 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 13.72/3.26 thf(func_def_8, type, powerset: $i > $i).
% 13.72/3.26 thf(func_def_10, type, setunion: $i > $i).
% 13.72/3.26 thf(func_def_19, type, descr: ($i > $o) > $i).
% 13.72/3.26 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 13.72/3.26 thf(func_def_26, type, prop2set: $o > $i).
% 13.72/3.26 thf(func_def_36, type, nonempty: $i > $o).
% 13.72/3.26 thf(func_def_69, type, set2prop: $i > $o).
% 13.72/3.26 thf(func_def_88, type, subset: $i > $i > $o).
% 13.72/3.26 thf(func_def_89, type, disjoint: $i > $i > $o).
% 13.72/3.26 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 13.72/3.26 thf(func_def_114, type, binunion: $i > $i > $i).
% 13.72/3.26 thf(func_def_122, type, binintersect: $i > $i > $i).
% 13.72/3.26 thf(func_def_135, type, regular: $i > $o).
% 13.72/3.26 thf(func_def_136, type, setminus: $i > $i > $i).
% 13.72/3.26 thf(func_def_147, type, symdiff: $i > $i > $i).
% 13.72/3.26 thf(func_def_153, type, iskpair: $i > $o).
% 13.72/3.26 thf(func_def_158, type, kpair: $i > $i > $i).
% 13.72/3.26 thf(func_def_160, type, cartprod: $i > $i > $i).
% 13.72/3.26 thf(func_def_177, type, singleton: $i > $o).
% 13.72/3.26 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 13.72/3.26 thf(func_def_184, type, atmost1p: $i > $o).
% 13.72/3.26 thf(func_def_185, type, atleast2p: $i > $o).
% 13.72/3.26 thf(func_def_186, type, atmost2p: $i > $o).
% 13.72/3.26 thf(func_def_187, type, upairsetp: $i > $o).
% 13.72/3.26 thf(func_def_191, type, kfst: $i > $i).
% 13.72/3.26 thf(func_def_203, type, ksnd: $i > $i).
% 13.72/3.26 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 13.72/3.26 thf(func_def_222, type, func: $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_223, type, funcSet: $i > $i > $i).
% 13.72/3.26 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 13.72/3.26 thf(func_def_259, type, if: $i > $o > $i > $i > $i).
% 13.72/3.26 thf(func_def_323, type, breln1: $i > $i > $o).
% 13.72/3.26 thf(func_def_325, type, breln1Set: $i > $i).
% 13.72/3.26 thf(func_def_327, type, transitive: $i > $i > $o).
% 13.72/3.26 thf(func_def_328, type, antisymmetric: $i > $i > $o).
% 13.72/3.26 thf(func_def_329, type, reflexive: $i > $i > $o).
% 13.72/3.26 thf(func_def_330, type, refltransitive: $i > $i > $o).
% 13.72/3.26 thf(func_def_331, type, refllinearorder: $i > $i > $o).
% 13.72/3.26 thf(func_def_332, type, reflwellordering: $i > $i > $o).
% 13.72/3.26 thf(func_def_338, type, breln1invset: $i > $i > $i).
% 13.72/3.26 thf(func_def_342, type, breln1compset: $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_360, type, image1: $i > ($i > $i) > $i).
% 13.72/3.26 thf(func_def_364, type, injective: $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_365, type, injFuncSet: $i > $i > $i).
% 13.72/3.26 thf(func_def_369, type, surjective: $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_370, type, surjFuncSet: $i > $i > $i).
% 13.72/3.26 thf(func_def_378, type, omegaS: $i > $i).
% 13.72/3.26 thf(func_def_382, type, peano3: $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_383, type, peano4: $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_384, type, peano5: $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_386, type, peano: $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_387, type, transitiveset: $i > $o).
% 13.72/3.26 thf(func_def_405, type, sP1: $i > $i > $o > $o).
% 13.72/3.26 thf(func_def_406, type, sP2: ($i > $i) > $i > $i > $o).
% 13.72/3.26 thf(func_def_408, type, sP4: $o > $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_409, type, sP5: $i > $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_411, type, sP7: ($i > $o) > $i > $i > $o).
% 13.72/3.26 thf(func_def_413, type, sP9: $i > ($i > $o) > $o).
% 13.72/3.26 thf(func_def_415, type, sP11: $i > ($i > $o) > $o).
% 13.72/3.26 thf(func_def_417, type, sP13: $o > $i > $i > $o).
% 13.72/3.26 thf(func_def_419, type, sP15: $i > $i > $o).
% 13.72/3.26 thf(func_def_424, type, sP20: $i > $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_425, type, sP21: $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_426, type, sP22: $o > $i > $i > $o).
% 13.72/3.26 thf(func_def_427, type, sP23: $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_428, type, sP24: $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_429, type, sP25: $i > ($i > $o) > $o).
% 13.72/3.26 thf(func_def_431, type, sP27: ($i > $o) > $i > $o).
% 13.72/3.26 thf(func_def_433, type, sP29: $i > $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_434, type, sP30: $i > $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_435, type, sP31: $i > ($i > $o) > $o).
% 13.72/3.26 thf(func_def_436, type, sP32: ($i > $o) > $i > $o).
% 13.72/3.26 thf(func_def_437, type, sP33: ($i > $i > $o) > $i > $i > $o).
% 13.72/3.26 thf(func_def_438, type, sP34: ($i > $i > $o) > $i > $o).
% 13.72/3.26 thf(func_def_443, type, sP39: $i > $o).
% 13.72/3.26 thf(func_def_444, type, sP40: $i > $o).
% 13.72/3.26 thf(func_def_445, type, sP41: $i > $i > $o).
% 13.72/3.26 thf(func_def_448, type, sP44: $i > $i > $o > $o).
% 13.72/3.26 thf(func_def_449, type, sP45: $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_450, type, sP46: $i > ($i > $i) > $i > $o).
% 13.72/3.26 thf(func_def_452, type, sP48: $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_453, type, sP49: $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_454, type, sP50: ($i > $o) > $i > $o).
% 13.72/3.26 thf(func_def_455, type, sP51: ($i > $o) > $i > $o).
% 13.72/3.26 thf(func_def_456, type, sP52: $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_457, type, sP53: $i > ($i > $i > $o) > $i > $o).
% 13.72/3.26 thf(func_def_458, type, sP54: ($i > $i > $o) > $i > $i > $o).
% 13.72/3.26 thf(func_def_459, type, sP55: ($i > $o) > $o).
% 13.72/3.26 thf(func_def_460, type, sP56: ($i > $o) > $i > $o).
% 13.72/3.26 thf(func_def_461, type, sP57: $i > ($i > $o) > $i > $i > $o).
% 13.72/3.26 thf(func_def_462, type, sP58: ($i > $o) > $o).
% 13.72/3.26 thf(func_def_463, type, sP59: $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_464, type, sP60: $i > $o).
% 13.72/3.26 thf(func_def_465, type, sP61: ($i > $o) > $i > $o).
% 13.72/3.26 thf(func_def_466, type, sP62: ($i > $o) > $i > $i > $o).
% 13.72/3.26 thf(func_def_467, type, sP63: $i > ($i > $o) > ($i > $o) > $i > $o).
% 13.72/3.26 thf(func_def_468, type, sP64: $i > $i > $o).
% 13.72/3.26 thf(func_def_470, type, sP66: ($i > $o) > $i > $o).
% 13.72/3.26 thf(func_def_473, type, sP69: $i > ($i > $i) > $i > $o).
% 13.72/3.26 thf(func_def_475, type, sP71: $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_476, type, sP72: $i > $i > $o).
% 13.72/3.26 thf(func_def_477, type, sP73: $i > $i > $o).
% 13.72/3.26 thf(func_def_478, type, sP74: $i > $i > $o).
% 13.72/3.26 thf(func_def_479, type, sP75: $i > $i > $o).
% 13.72/3.26 thf(func_def_480, type, sP76: $i > $o).
% 13.72/3.26 thf(func_def_481, type, sP77: $i > $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_482, type, sP78: $i > ($i > $i) > $i > $o).
% 13.72/3.26 thf(func_def_484, type, sP80: ($i > $o) > $o).
% 13.72/3.26 thf(func_def_485, type, sP81: ($i > $i) > $i > $i > $o).
% 13.72/3.26 thf(func_def_487, type, sP83: $i > $i > $i > $i > $o > $i > $o).
% 13.72/3.26 thf(func_def_488, type, sP84: $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_490, type, sP86: $i > ($i > $o) > $o).
% 13.72/3.26 thf(func_def_492, type, sP88: ($i > $o) > $o).
% 13.72/3.26 thf(func_def_495, type, sP91: ($i > $o) > $i > $o).
% 13.72/3.26 thf(func_def_496, type, sP92: ($i > $o) > $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_497, type, sP93: $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_498, type, sP94: $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_499, type, sP95: $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_500, type, sP96: $i > $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_501, type, sP97: $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_502, type, sP98: $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_503, type, sP99: $i > $o > $i > $i > $o).
% 13.72/3.26 thf(func_def_504, type, sP100: $o > $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_505, type, sP101: $i > ($i > $o) > $o).
% 13.72/3.26 thf(func_def_506, type, sP102: $i > $i > ($i > $o) > $o).
% 13.72/3.26 thf(func_def_508, type, sP104: ($i > $o) > $o).
% 13.72/3.26 thf(func_def_509, type, sP105: $i > $i > $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_514, type, sK110: $i > $i > $i).
% 13.72/3.26 thf(func_def_515, type, sK111: $i > $o).
% 13.72/3.26 thf(func_def_528, type, sK124: $i > $i > $o > $i).
% 13.72/3.26 thf(func_def_537, type, sK133: $i > $o).
% 13.72/3.26 thf(func_def_555, type, sK151: $i > $o).
% 13.72/3.26 thf(func_def_558, type, sK154: $i > $i).
% 13.72/3.26 thf(func_def_561, type, sK157: $i > $i > ($i > $i) > $i).
% 13.72/3.26 thf(func_def_562, type, sK158: ($i > $i) > $i > $i > $i).
% 13.72/3.26 thf(func_def_563, type, sK159: $i > ($i > $i) > $i > $i > $i).
% 13.72/3.26 thf(func_def_565, type, sK161: $i > $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_572, type, sK168: $i > $i).
% 13.72/3.26 thf(func_def_599, type, sK195: $i > $o).
% 13.72/3.26 thf(func_def_600, type, sK196: $i > $o).
% 13.72/3.26 thf(func_def_601, type, sK197: ($i > $o) > ($i > $o) > $i).
% 13.72/3.26 thf(func_def_602, type, sK198: ($i > $o) > ($i > $o) > $i).
% 13.72/3.26 thf(func_def_621, type, sK217: ($i > $o) > $i > $i > $i).
% 13.72/3.26 thf(func_def_622, type, sK218: $i > $o).
% 13.72/3.26 thf(func_def_627, type, sK223: $i > $i).
% 13.72/3.26 thf(func_def_629, type, sK225: $i > ($i > $i) > $i > $i).
% 13.72/3.26 thf(func_def_633, type, sK229: $i > $o).
% 13.72/3.26 thf(func_def_635, type, sK231: $i > ($i > $o) > $i).
% 13.72/3.26 thf(func_def_636, type, sK232: $i > ($i > $o) > $i).
% 13.72/3.26 thf(func_def_641, type, sK237: $i > $o).
% 13.72/3.26 thf(func_def_650, type, sK246: $i > $o).
% 13.72/3.26 thf(func_def_652, type, sK248: $i > ($i > $o) > $i).
% 13.72/3.26 thf(func_def_653, type, sK249: $i > ($i > $o) > $i).
% 13.72/3.26 thf(func_def_679, type, sK275: $i > $i > $i).
% 13.72/3.26 thf(func_def_685, type, sK281: $i > $i > $i).
% 13.72/3.26 thf(func_def_693, type, sK289: $i > $i).
% 13.72/3.26 thf(func_def_730, type, sK326: $i > $o).
% 13.72/3.26 thf(func_def_731, type, sK327: ($i > $o) > $i > $i).
% 13.72/3.26 thf(func_def_732, type, sK328: $i > $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_739, type, sK335: $i > $i > $o).
% 13.72/3.26 thf(func_def_747, type, sK343: $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_748, type, sK344: $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_752, type, sK348: $i > $i > $i).
% 13.72/3.26 thf(func_def_755, type, sK351: $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_759, type, sK355: $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_766, type, sK362: $i > $o).
% 13.72/3.26 thf(func_def_768, type, sK364: $i > ($i > $o) > $i).
% 13.72/3.26 thf(func_def_769, type, sK365: $i > ($i > $o) > $i).
% 13.72/3.26 thf(func_def_778, type, sK374: $i > $o).
% 13.72/3.26 thf(func_def_780, type, sK376: $i > ($i > $o) > $i).
% 13.72/3.26 thf(func_def_781, type, sK377: ($i > $o) > $i > $i).
% 13.72/3.26 thf(func_def_786, type, sK382: $i > $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_787, type, sK383: $i > $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_788, type, sK384: $i > $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_789, type, sK385: $i > $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_797, type, sK393: $i > $o).
% 13.72/3.26 thf(func_def_798, type, sK394: ($i > $o) > $i).
% 13.72/3.26 thf(func_def_810, type, sK406: ($i > $o) > $i > $i).
% 13.72/3.26 thf(func_def_811, type, sK407: ($i > $o) > $i > $i).
% 13.72/3.26 thf(func_def_812, type, sK408: $i > ($i > $o) > $i).
% 13.72/3.26 thf(func_def_814, type, sK410: $i > $o).
% 13.72/3.26 thf(func_def_824, type, sK420: $i > $i > $o).
% 13.72/3.26 thf(func_def_842, type, sK438: $i > $i > $o).
% 13.72/3.26 thf(func_def_844, type, sK440: $i > ($i > $i > $o) > $i).
% 13.72/3.26 thf(func_def_845, type, sK441: $i > ($i > $i > $o) > $i > $i).
% 13.72/3.26 thf(func_def_846, type, sK442: ($i > $i > $o) > $i > $i).
% 13.72/3.26 thf(func_def_847, type, sK443: ($i > $i > $o) > $i > $i > $i).
% 13.72/3.26 thf(func_def_885, type, sK481: $i > $i).
% 13.72/3.26 thf(func_def_887, type, sK483: $i > ($i > $i) > $i > $i).
% 13.72/3.26 thf(func_def_894, type, sK490: $i > $o).
% 13.72/3.26 thf(func_def_912, type, sK508: $i > $i > $i).
% 13.72/3.26 thf(func_def_917, type, sK513: $i > $o).
% 13.72/3.26 thf(func_def_928, type, sK524: $i > $i).
% 13.72/3.26 thf(func_def_929, type, sK525: ($i > $i) > $i > $i > $i).
% 13.72/3.26 thf(func_def_938, type, sK534: $i > $i).
% 13.72/3.26 thf(func_def_939, type, sK535: $i > $i).
% 13.72/3.26 thf(func_def_950, type, sK546: $i > $i > $o).
% 13.72/3.26 thf(func_def_954, type, sK550: $i > $i > $i).
% 13.72/3.26 thf(func_def_960, type, sK556: $i > $i).
% 13.72/3.26 thf(func_def_962, type, sK558: $i > ($i > $i) > $i > $i).
% 13.72/3.26 thf(func_def_966, type, sK562: $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_967, type, sK563: $i > $i > $i > $o).
% 13.72/3.26 thf(func_def_975, type, sK571: $i > $i).
% 13.72/3.26 thf(func_def_976, type, sK572: ($i > $i) > $i > $i > $i).
% 13.72/3.26 thf(func_def_977, type, sK573: $i > ($i > $i) > $i > $i).
% 13.72/3.26 thf(func_def_982, type, sK578: $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_983, type, sK579: $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_991, type, sK587: ($i > $o) > $i > $i).
% 13.72/3.26 thf(func_def_992, type, sK588: ($i > $o) > $i > $i).
% 13.72/3.26 thf(func_def_993, type, sK589: ($i > $o) > $i > $i).
% 13.72/3.26 thf(func_def_994, type, sK590: $i > $o).
% 13.72/3.26 thf(func_def_1007, type, sK603: $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_1008, type, sK604: $i > $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_1012, type, sK608: $i > $o).
% 13.72/3.26 thf(func_def_1036, type, sK632: $i > ($i > $i > $o) > $i > $i).
% 13.72/3.26 thf(func_def_1037, type, sK633: ($i > $i > $o) > $i > $i > $i).
% 13.72/3.26 thf(func_def_1038, type, sK634: $i > ($i > $i > $o) > $i > $i).
% 13.72/3.26 thf(func_def_1039, type, sK635: $i > ($i > $i > $o) > $i > $i).
% 13.72/3.26 thf(func_def_1042, type, sK638: $i > $i > $o).
% 13.72/3.26 thf(func_def_1053, type, sK649: $i > $i).
% 13.72/3.26 thf(func_def_1058, type, sK654: $i > $o).
% 13.72/3.26 thf(func_def_1061, type, sK657: $i > ($i > $o) > $i).
% 13.72/3.26 thf(func_def_1062, type, sK658: ($i > $o) > $i).
% 13.72/3.26 thf(func_def_1063, type, sK659: $i > $o).
% 13.72/3.26 thf(func_def_1064, type, sK660: $i > ($i > $o) > $i > $i > $i).
% 13.72/3.26 thf(func_def_1065, type, sK661: $i > ($i > $o) > $i > $i > $i).
% 13.72/3.26 thf(func_def_1066, type, sK662: ($i > $o) > $i > $i).
% 13.72/3.26 thf(func_def_1070, type, sK666: $i > $o).
% 13.72/3.26 thf(func_def_1079, type, sK675: ($i > $o) > $i).
% 13.72/3.26 thf(func_def_1080, type, sK676: ($i > $o) > $i).
% 13.72/3.26 thf(func_def_1081, type, sK677: $i > $o).
% 13.72/3.26 thf(func_def_1097, type, sK693: $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_1102, type, sK698: $i > $i > $o).
% 13.72/3.26 thf(func_def_1109, type, sK705: $i > $i > $i).
% 13.72/3.26 thf(func_def_1110, type, sK706: $i > $i).
% 13.72/3.26 thf(func_def_1120, type, sK716: ($i > $o) > $i > $i > $i).
% 13.72/3.26 thf(func_def_1121, type, sK717: ($i > $o) > $i > $i > $i).
% 13.72/3.26 thf(func_def_1122, type, sK718: ($i > $o) > $i > $i).
% 13.72/3.26 thf(func_def_1125, type, sK721: $i > $o).
% 13.72/3.26 thf(func_def_1126, type, sK722: $i > ($i > $o) > ($i > $o) > $i > $i).
% 13.72/3.26 thf(func_def_1127, type, sK723: $i > ($i > $o) > ($i > $o) > $i > $i).
% 13.72/3.26 thf(func_def_1130, type, sK726: $i > $o).
% 13.72/3.26 thf(func_def_1131, type, sK727: $i > $o).
% 13.72/3.26 thf(func_def_1141, type, sK737: $i > $i > $i).
% 13.72/3.26 thf(func_def_1142, type, sK738: $i > $i > $i).
% 13.72/3.26 thf(func_def_1157, type, sK753: $i > $o).
% 13.72/3.26 thf(func_def_1158, type, sK754: ($i > $o) > $i > $i).
% 13.72/3.26 thf(func_def_1159, type, sK755: ($i > $o) > $i > $i).
% 13.72/3.26 thf(func_def_1162, type, sK758: $i > $i).
% 13.72/3.26 thf(func_def_1175, type, sK771: $i > $i).
% 13.72/3.26 thf(func_def_1179, type, sK775: $i > $o).
% 13.72/3.26 thf(func_def_1180, type, sK776: $i > $o).
% 13.72/3.26 thf(func_def_1181, type, sK777: ($i > $o) > ($i > $o) > $i).
% 13.72/3.26 thf(func_def_1182, type, sK778: ($i > $o) > ($i > $o) > $i).
% 13.72/3.26 thf(func_def_1183, type, sK779: $i > $i).
% 13.72/3.26 thf(func_def_1186, type, sK782: $i > ($i > $i) > $i > $i).
% 13.72/3.26 thf(func_def_1197, type, sK793: $i > $i).
% 13.72/3.26 thf(func_def_1198, type, sK794: $i > $i).
% 13.72/3.26 thf(func_def_1199, type, sK795: $i > $i).
% 13.72/3.26 thf(func_def_1200, type, sK796: $i > $i).
% 13.72/3.26 thf(func_def_1201, type, sK797: $i > $i > $i).
% 13.72/3.26 thf(func_def_1202, type, sK798: $i > $i > $i).
% 13.72/3.26 thf(func_def_1203, type, sK799: $i > $i > $i).
% 13.72/3.26 thf(func_def_1204, type, sK800: $i > $i > $i).
% 13.72/3.26 thf(func_def_1205, type, sK801: $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_1206, type, sK802: $i > $i > $i).
% 13.72/3.26 thf(func_def_1207, type, sK803: $i > $i > $i).
% 13.72/3.26 thf(func_def_1208, type, sK804: $i > $i > $i).
% 13.72/3.26 thf(func_def_1209, type, sK805: $i > $i > $i).
% 13.72/3.26 thf(func_def_1210, type, sK806: $i > $i > $i).
% 13.72/3.26 thf(func_def_1211, type, sK807: $i > $i > $i).
% 13.72/3.26 thf(func_def_1212, type, sK808: $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_1213, type, sK809: $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_1215, type, sK811: $i > $i).
% 13.72/3.26 thf(func_def_1216, type, sK812: $i > $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_1217, type, sK813: $i > $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_1223, type, sK819: $i > $i).
% 13.72/3.26 thf(func_def_1225, type, sK821: $i > ($i > $i) > $i > $i).
% 13.72/3.26 thf(func_def_1226, type, sK822: $i > ($i > $i) > $i > $i).
% 13.72/3.26 thf(func_def_1235, type, sK831: ($i > $o) > $i).
% 13.72/3.26 thf(func_def_1236, type, sK832: $i > ($i > $o) > $i).
% 13.72/3.26 thf(func_def_1237, type, sK833: $i > $o).
% 13.72/3.26 thf(func_def_1250, type, sK846: $i > $i > $o).
% 13.72/3.26 thf(func_def_1287, type, sK883: $i > $i).
% 13.72/3.26 thf(func_def_1289, type, sK885: $i > $i).
% 13.72/3.26 thf(func_def_1290, type, sK886: $i > ($i > $i) > $i).
% 13.72/3.26 thf(func_def_1291, type, sK887: ($i > $i) > $i > $i > $i).
% 13.72/3.26 thf(func_def_1305, type, sK901: $i > $i > $o).
% 13.72/3.26 thf(func_def_1308, type, sK904: $i > $i > $i > $i > $o > $i > $i).
% 13.72/3.26 thf(func_def_1322, type, sK918: $i > $i > $o).
% 13.72/3.26 thf(func_def_1336, type, sK932: $i > $o).
% 13.72/3.26 thf(func_def_1338, type, sK934: $i > ($i > $o) > $i).
% 13.72/3.26 thf(func_def_1339, type, sK935: $i > ($i > $o) > $i).
% 13.72/3.26 thf(func_def_1340, type, sK936: $i > ($i > $o) > $i).
% 13.72/3.26 thf(func_def_1341, type, sK937: ($i > $o) > $i).
% 13.72/3.26 thf(func_def_1342, type, sK938: $i > $o).
% 13.72/3.26 thf(func_def_1349, type, sK945: $i > $i).
% 13.72/3.26 thf(func_def_1352, type, sK948: $i > $i > ($i > $i) > $i).
% 13.72/3.26 thf(func_def_1359, type, sK955: $i > $o).
% 13.72/3.26 thf(func_def_1365, type, sK961: $i > $i > $o).
% 13.72/3.26 thf(func_def_1392, type, sK988: $i > $o).
% 13.72/3.26 thf(func_def_1398, type, sK994: $i > $i).
% 13.72/3.26 thf(func_def_1407, type, sK1003: $i > $i > $i).
% 13.72/3.26 thf(func_def_1413, type, sK1009: $i > $o).
% 13.72/3.26 thf(func_def_1420, type, sK1016: $i > $o).
% 13.72/3.26 thf(func_def_1438, type, sK1034: ($i > $o) > $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_1439, type, sK1035: ($i > $o) > $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_1440, type, sK1036: ($i > $o) > $i > $i).
% 13.72/3.26 thf(func_def_1444, type, sK1040: $i > $o).
% 13.72/3.26 thf(func_def_1477, type, sK1073: $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_1478, type, sK1074: $i > $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_1496, type, sK1092: $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_1497, type, sK1093: $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_1498, type, sK1094: $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_1499, type, sK1095: $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_1516, type, sK1112: $i > $i).
% 13.72/3.26 thf(func_def_1521, type, sK1117: $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_1522, type, sK1118: $i > $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_1523, type, sK1119: $i > $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_1524, type, sK1120: $i > $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_1539, type, sK1135: $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_1540, type, sK1136: $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_1556, type, sK1152: $i > $i > ($i > $o) > $i).
% 13.72/3.26 thf(func_def_1557, type, sK1153: $i > $i > ($i > $o) > $i).
% 13.72/3.26 thf(func_def_1558, type, sK1154: $i > ($i > $o) > $i).
% 13.72/3.26 thf(func_def_1561, type, sK1157: $i > $o).
% 13.72/3.26 thf(func_def_1571, type, sK1167: $i > $i > $i).
% 13.72/3.26 thf(func_def_1573, type, sK1169: ($i > $o) > $i).
% 13.72/3.26 thf(func_def_1574, type, sK1170: $i > ($i > $o) > $i).
% 13.72/3.26 thf(func_def_1575, type, sK1171: $i > $o).
% 13.72/3.26 thf(func_def_1579, type, sK1175: $i > $o).
% 13.72/3.26 thf(func_def_1582, type, sK1178: $i > $i > $i > $i > $i > $i).
% 13.72/3.26 thf(func_def_1589, type, sK1185: $i > $i).
% 13.72/3.26 thf(func_def_1590, type, sK1186: $i > $i).
% 13.72/3.26 thf(func_def_1591, type, sK1187: $i > $i).
% 13.72/3.26 thf(func_def_1592, type, ph1188: !>[X0: $tType]:(X0)).
% 13.72/3.26 thf(f12158,plain,(
% 13.72/3.26 $false),
% 13.72/3.26 inference(trivial_inequality_removal,[status(thm)],[f12145])).
% 13.72/3.26 thf(f12145,plain,(
% 13.72/3.26 ($true = $false)),
% 13.72/3.26 inference(backward_demodulation,[status(thm)],[f5042,f12120])).
% 13.72/3.26 thf(f12120,plain,(
% 13.72/3.26 ($false = (in @ sK1042 @ sK1041))),
% 13.72/3.26 inference(trivial_inequality_removal,[status(thm)],[f12113])).
% 13.72/3.26 thf(f12113,plain,(
% 13.72/3.26 ($true != $true) | ($false = (in @ sK1042 @ sK1041))),
% 13.72/3.26 inference(superposition,[status(thm)],[f12019,f6924])).
% 13.72/3.26 thf(f6924,plain,(
% 13.72/3.26 ( ! [X1 : $i] : (($true = (subset @ X1 @ sK1041)) | ($false = (in @ X1 @ sK1041))) )),
% 13.72/3.26 inference(binary_proxy_clausification,[status(thm)],[f6923])).
% 13.72/3.26 thf(f6923,plain,(
% 13.72/3.26 ( ! [X1 : $i] : ((((in @ X1 @ sK1041) => (subset @ X1 @ sK1041)) = $true)) )),
% 13.72/3.26 inference(beta_eta_normalization,[status(thm)],[f6922])).
% 13.72/3.26 thf(f6922,plain,(
% 13.72/3.26 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ sK1041) => (subset @ Y0 @ sK1041))) @ X1))) )),
% 13.72/3.26 inference(pi_clausification,[status(thm)],[f6921])).
% 13.72/3.26 thf(f6921,plain,(
% 13.72/3.26 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK1041) => (subset @ Y0 @ sK1041)))))),
% 13.72/3.26 inference(beta_eta_normalization,[status(thm)],[f6556])).
% 13.72/3.26 thf(f6556,plain,(
% 13.72/3.26 ($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))) @ sK1041))),
% 13.72/3.26 inference(definition_unfolding,[status(thm)],[f5044,f4246])).
% 13.72/3.26 thf(f4246,plain,(
% 13.72/3.26 (transitiveset = (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))))),
% 13.72/3.26 inference(cnf_transformation,[status(thm)],[f394])).
% 13.72/3.26 thf(f394,plain,(
% 13.72/3.26 (transitiveset = (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))))),
% 13.72/3.26 inference(fool_elimination,[status(thm)],[f393])).
% 13.72/3.26 thf(f393,plain,(
% 13.72/3.26 (transitiveset = (^[X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (subset @ X1 @ X0)))))),
% 13.72/3.26 inference(rectify,[status(thm)],[f331])).
% 13.72/3.26 thf(f331,axiom,(
% 13.72/3.26 (transitiveset = (^[X3 : $i] : (! [X11 : $i] : ((in @ X11 @ X3) => (subset @ X11 @ X3)))))),
% 13.72/3.26 file('/export/starexec/sandbox/tmp/tmp.zuy6gBFKOi/DTF2THF_17963.p',transitiveset)).
% 13.72/3.26 thf(f5044,plain,(
% 13.72/3.26 ((transitiveset @ sK1041) = $true)),
% 13.72/3.26 inference(cnf_transformation,[status(thm)],[f3260])).
% 13.72/3.26 thf(f3260,plain,(
% 13.72/3.26 (doubleComplementE1 = $true) & (iffalseProp1 = $true) & (powersetTE1 = $true) & (notinemptyset = $true) & (brelnall1 = $true) & (ubforcartprodlem1 = $true) & (dpsetconstrI = $true) & (breln1unionE = $true) & (woz1_4 = $true) & (subsetI2 = $true) & (funcGraphProp2 = $true) & (injFuncInInjFuncSet = $true) & (binunionTE = $true) & (disjointsetsI1 = $true) & (iftrueProp2 = $true) & (setukpairinjR = $true) & (emptysetsubset = $true) & (setunionAx = $true) & (leftInvIsSurj = $true) & (inComplementUnionImpInComplement1 = $true) & (binintersectSubset3 = $true) & (symdiffI1 = $true) & (surjCantorThm = $true) & (subsetI1 = $true) & (setukpairinjR2 = $true) & (setukpairinjL = $true) & (surjFuncSetFuncSurj = $true) & (funcinfuncset = $true) & (image1Ex1 = $true) & (breln1compprop = $true) & (setunionI = $true) & (cartprodpairmemEL = $true) & (cartprodmempair1 = $true) & (notinself = $true) & (setminusI = $true) & (setminusIRneg = $true) & (contraSubsetComplement = $true) & (emptyI = $true) & (peano0notS = $true) & (lam2p = $true) & (inCongP = $true) & (transitivesetOp1 = $true) & (nonemptyI = $true) & (woz13rule3 = $true) & (singletonsubset = $true) & (powersetE = $true) & (setadjoinSub = $true) & (notsubsetI = $true) & (prop2setI = $true) & (woz2B = $true) & (contrasubsetT1 = $true) & (vacuousDall = $true) & (cartprodmempaircEq = $true) & (quantDeMorgan1 = $true) & (contrasubsetT = $true) & (cartprodsndin = $true) & (funcext = $true) & (setminusER = $true) & (setukpairinjL1 = $true) & (image1I = $true) & (binintersectTELcontra = $true) & (funcGraphProp4 = $true) & (iffalse = $true) & (binintTransitive = $true) & (binintersectTERcontra = $true) & (binintersectEL = $true) & (funcGraphProp1 = $true) & (infuncsetfunc = $true) & (binintersectER = $true) & (complementImpComplementIntersect = $true) & (app = $true) & (setunionsingleton2 = $true) & (image1Equiv = $true) & (breln1unionIR = $true) & (wellorderingAx = $true) & (breln1unionI = $true) & (setukpairinjR11 = $true) & (breln1all1 = $true) & (upairset2IR = $true) & (emptyE1 = $true) & (binunionLsub = $true) & (subsetTrans = $true) & (setukpairinjR1 = $true) & (subbreln1 = $true) & (subsetE = $true) & (ap2apEq2 = $true) & (emptyset__Cong = $true) & (injFuncSetFuncInj = $true) & (binunionT_lem = $true) & (complementTI1 = $true) & (noeltsimpempty = $true) & (setextAx = $true) & (binintersectLsub = $true) & (kfstsingleton = $true) & (doubleComplementEq = $true) & (setextT = $true) & (subsetRefl = $true) & (foundation2 = $true) & (uniqinunit = $true) & (woz1_5 = $true) & (doubleComplementSub1 = $true) & (setminusSubset2 = $true) & (subsetemptysetimpeq = $true) & (dpsetconstrEL1 = $true) & (dpsetconstrEL2 = $true) & (setadjoin__Cong = $true) & (woz13rule0 = $true) & (emptysetimpfalse = $true) & (woz13rule1 = $true) & (dpsetconstrER = $true) & (quantDeMorgan4 = $true) & (beta1 = $true) & (complementTE1 = $true) & (dsetconstr__Cong = $true) & (injFuncSetFuncIn = $true) & (singletoninpowunion = $true) & (exuI2 = $true) & (notinself2 = $true) & (woz13rule2 = $true) & (demorgan1b = $true) & (subsetTI = $true) & (breln1compI = $true) & (eqbreln1 = $true) & (setext = $true) & (apProp = $true) & (exuE3e = $true) & (setadjoinSub2 = $true) & (setminusILneg = $true) & (kpairp = $true) & (eqbreln = $true) & (emptyinunitempty = $true) & (eta1 = $true) & (demorgan2a1 = $true) & (inComplementUnionImpNotIn1 = $true) & (woz13rule4 = $true) & (sepInPowerset = $true) & (binunionTEcontra = $true) & (powersetE1 = $true) & (in__Cong = $true) & (lam2lamEq = $true) & (surjFuncSetFuncIn = $true) & (setadjoinE = $true) & (exuE2 = $true) & (setOfPairsIsBReln1 = $true) & (ifSingleton = $true) & (exuI3 = $true) & (setadjoinIR = $true) & (setukpairinjL2 = $true) & (subPowSU = $true) & (singletoninpowerset = $true) & (omegaSclos = $true) & (demorgan2 = $true) & (eqimpsubset2 = $true) & (symdiffIneg2 = $true) & (binintersectSubset1 = $true) & (complementT_lem = $true) & (woz1_3 = $true) & (emptyinPowerset = $true) & (complementSubsetComplementIntersect = $true) & (powersetTI1 = $true) & (cartprodfstpairEq = $true) & (contrasubsetT2 = $true) & (upairinpowunion = $true) & (funcGraphProp3 = $true) & (demorgan2b2 = $true) & (funcext2 = $true) & (setadjoinAx = $true) & (cartprodmempair = $true) & (upairequniteq = $true) & (omegaIndAx = $true) & (setadjoinIL = $true) & (kpairsurjEq = $true) & (funcextLem = $true) & (iftrueProp1 = $true) & (demorgan1a = $true) & (emptysetE = $true) & (foundationAx = $true) & (theprop = $true) & (doubleComplementSub2 = $true) & (binunionE = $true) & (ksndsingleton = $true) & (dsetconstrEL = $true) & (kpairiskpair = $true) & (subbreln = $true) & (ex1I = $true) & (symdiffI2 = $true) & (setunionsingleton1 = $true) & (woz1_1 = $true) & (woz1_2 = $true) & (setextsub = $true) & (brelnall2 = $true) & (inIntersectImpInIntersectUnions = $true) & (complementInPowersetComplementIntersect = $true) & (binintersectRsub = $true) & (iftrue = $true) & (emptyInPowerset = $true) & (breln1unionprop = $true) & (binintersectSubset4 = $true) & (upairset2E = $true) & (subset2powerset = $true) & (dsetconstrI = $true) & (exu__Cong = $true) & (breln1compEex = $true) & (complementTcontraSubset = $true) & (omegaSAx = $true) & (setunion__Cong = $true) & (exuEu = $true) & (dsetconstrER = $true) & (image1E = $true) & (notequalI2 = $true) & (upairsetIR = $true) & (notinsingleton = $true) & (setminusT_lem = $true) & (breln1all2 = $true) & (notequalI1 = $true) & (breln1SetBreln1 = $true) & (powersetT_lem = $true) & (replAx = $true) & (binunionIR = $true) & (ap2p = $true) & (singletonsswitch = $true) & (binintersectSubset2 = $true) & (ifp = $true) & (prop2set2propI = $true) & (binintersectT_lem = $true) & (prop2setE = $true) & (setadjoinOr = $true) & (woz2Ex = $true) & (inIntersectImpInUnion = $true) & (subsetE2 = $true) & (binunionTILcontra = $true) & (omega__Cong = $true) & (breln1compE = $true) & (demorgan1 = $true) & (cartprodfstin = $true) & (ksndpairEq = $true) & (cartprodsndpairEq = $true) & (cartprodpairin = $true) & (contrasubsetT3 = $true) & (woz2A = $true) & (kfstpairEq = $true) & (cartprodpairmemER = $true) & (((transitiveset @ sK1041) = $true) & (($true = (in @ sK1043 @ sK1042)) & ($true = (in @ sK1042 @ sK1041)) & ((in @ sK1043 @ sK1041) != $true))) & (choice2fnsingleton = $true) & (funcImageSingleton = $true) & (setukpairinjR12 = $true) & (exuE3u = $true) & (singletonprop = $true) & (iftrueorfalse = $true) & (ex1E1 = $true) & (doubleComplementI1 = $true) & (eqimpsubset1 = $true) & (notdallE = $true) & (nonemptyI1 = $true) & (breln1invE = $true) & (breln1invprop = $true) & (sepSubset = $true) & (powersetI1 = $true) & (iffalseProp2 = $true) & (complementUnionInPowersetComplement = $true) & (quantDeMorgan2 = $true) & (nonemptyImpWitness = $true) & (bs114d = $true) & (inIntersectImpInUnion2 = $true) & (omegaSp = $true) & (ex1E2 = $true) & (setminusLsub = $true) & (setunionE = $true) & (eta2 = $true) & (breln1unionEcases = $true) & (powerset__Cong = $true) & (powersetAx = $true) & (upairsetIL = $true) & (setoftrueEq = $true) & (binunionRsub = $true) & (demorgan2b = $true) & (setbeta = $true) & (binunionIL = $true) & (dpsetconstrERa = $true) & (image1Ex = $true) & (secondinupair = $true) & (demorgan2a2 = $true) & (lamp = $true) & (cartprodpairsurjEq = $true) & (setminusERneg = $true) & (omega0Ax = $true) & (setukpairIR = $true) & (ubforcartprodlem3 = $true) & (exuI1 = $true) & (breln1unionIL = $true) & (binunionTIRcontra = $true) & (breln1invI = $true) & (eqinunit = $true) & (singletonsuniq = $true) & (upairsubunion = $true) & (binintersectI = $true) & (intersectInPowersetIntersectUnions = $true) & (symdiffE = $true) & (setukpairIL = $true) & (setminusEL = $true) & (ubforcartprodlem2 = $true) & (upairsetE = $true) & (quantDeMorgan3 = $true) & (powersetI = $true) & (lamProp = $true) & (binunionEcases = $true) & (dpsetconstrSub = $true) & (binintersectSubset5 = $true) & (descrp = $true) & (descr__Cong = $true) & (ex1I2 = $true) & (setminusELneg = $true) & (breln1unionCommutes = $true) & (theeq = $true) & (complementTnotintersectT = $true) & (beta2 = $true) & (setunionsingleton = $true) & (ap2apEq1 = $true) & (symdiffIneg1 = $true) & (emptysetAx = $true) & (notdexE = $true) & (nonemptyE1 = $true) & (demorgan2a = $true) & (setunionE2 = $true) & (setminusSubset1 = $true) & (inPowerset = $true) & (powersetsubset = $true) & (exuE1 = $true) & (woz2W = $true) & (setOfPairsIsBReln = $true) & (peanoSinj = $true)),
% 13.72/3.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1041,sK1042,sK1043])],[f1384,f3259,f3258])).
% 13.72/3.26 thf(f3258,plain,(
% 13.72/3.26 ? [X0 : $i] : (($true = (transitiveset @ X0)) & ? [X1 : $i,X2 : $i] : (($true = (in @ X2 @ X1)) & ($true = (in @ X1 @ X0)) & ($true != (in @ X2 @ X0)))) => (((transitiveset @ sK1041) = $true) & ? [X2 : $i,X1 : $i] : (($true = (in @ X2 @ X1)) & ($true = (in @ X1 @ sK1041)) & ($true != (in @ X2 @ sK1041))))),
% 13.72/3.26 introduced(definition,[],[choice_axiom])).
% 13.72/3.26 thf(f3259,plain,(
% 13.72/3.26 ? [X2 : $i,X1 : $i] : (($true = (in @ X2 @ X1)) & ($true = (in @ X1 @ sK1041)) & ($true != (in @ X2 @ sK1041))) => (($true = (in @ sK1043 @ sK1042)) & ($true = (in @ sK1042 @ sK1041)) & ((in @ sK1043 @ sK1041) != $true))),
% 13.72/3.26 introduced(definition,[],[choice_axiom])).
% 13.72/3.26 thf(f1384,plain,(
% 13.72/3.26 (doubleComplementE1 = $true) & (iffalseProp1 = $true) & (powersetTE1 = $true) & (notinemptyset = $true) & (brelnall1 = $true) & (ubforcartprodlem1 = $true) & (dpsetconstrI = $true) & (breln1unionE = $true) & (woz1_4 = $true) & (subsetI2 = $true) & (funcGraphProp2 = $true) & (injFuncInInjFuncSet = $true) & (binunionTE = $true) & (disjointsetsI1 = $true) & (iftrueProp2 = $true) & (setukpairinjR = $true) & (emptysetsubset = $true) & (setunionAx = $true) & (leftInvIsSurj = $true) & (inComplementUnionImpInComplement1 = $true) & (binintersectSubset3 = $true) & (symdiffI1 = $true) & (surjCantorThm = $true) & (subsetI1 = $true) & (setukpairinjR2 = $true) & (setukpairinjL = $true) & (surjFuncSetFuncSurj = $true) & (funcinfuncset = $true) & (image1Ex1 = $true) & (breln1compprop = $true) & (setunionI = $true) & (cartprodpairmemEL = $true) & (cartprodmempair1 = $true) & (notinself = $true) & (setminusI = $true) & (setminusIRneg = $true) & (contraSubsetComplement = $true) & (emptyI = $true) & (peano0notS = $true) & (lam2p = $true) & (inCongP = $true) & (transitivesetOp1 = $true) & (nonemptyI = $true) & (woz13rule3 = $true) & (singletonsubset = $true) & (powersetE = $true) & (setadjoinSub = $true) & (notsubsetI = $true) & (prop2setI = $true) & (woz2B = $true) & (contrasubsetT1 = $true) & (vacuousDall = $true) & (cartprodmempaircEq = $true) & (quantDeMorgan1 = $true) & (contrasubsetT = $true) & (cartprodsndin = $true) & (funcext = $true) & (setminusER = $true) & (setukpairinjL1 = $true) & (image1I = $true) & (binintersectTELcontra = $true) & (funcGraphProp4 = $true) & (iffalse = $true) & (binintTransitive = $true) & (binintersectTERcontra = $true) & (binintersectEL = $true) & (funcGraphProp1 = $true) & (infuncsetfunc = $true) & (binintersectER = $true) & (complementImpComplementIntersect = $true) & (app = $true) & (setunionsingleton2 = $true) & (image1Equiv = $true) & (breln1unionIR = $true) & (wellorderingAx = $true) & (breln1unionI = $true) & (setukpairinjR11 = $true) & (breln1all1 = $true) & (upairset2IR = $true) & (emptyE1 = $true) & (binunionLsub = $true) & (subsetTrans = $true) & (setukpairinjR1 = $true) & (subbreln1 = $true) & (subsetE = $true) & (ap2apEq2 = $true) & (emptyset__Cong = $true) & (injFuncSetFuncInj = $true) & (binunionT_lem = $true) & (complementTI1 = $true) & (noeltsimpempty = $true) & (setextAx = $true) & (binintersectLsub = $true) & (kfstsingleton = $true) & (doubleComplementEq = $true) & (setextT = $true) & (subsetRefl = $true) & (foundation2 = $true) & (uniqinunit = $true) & (woz1_5 = $true) & (doubleComplementSub1 = $true) & (setminusSubset2 = $true) & (subsetemptysetimpeq = $true) & (dpsetconstrEL1 = $true) & (dpsetconstrEL2 = $true) & (setadjoin__Cong = $true) & (woz13rule0 = $true) & (emptysetimpfalse = $true) & (woz13rule1 = $true) & (dpsetconstrER = $true) & (quantDeMorgan4 = $true) & (beta1 = $true) & (complementTE1 = $true) & (dsetconstr__Cong = $true) & (injFuncSetFuncIn = $true) & (singletoninpowunion = $true) & (exuI2 = $true) & (notinself2 = $true) & (woz13rule2 = $true) & (demorgan1b = $true) & (subsetTI = $true) & (breln1compI = $true) & (eqbreln1 = $true) & (setext = $true) & (apProp = $true) & (exuE3e = $true) & (setadjoinSub2 = $true) & (setminusILneg = $true) & (kpairp = $true) & (eqbreln = $true) & (emptyinunitempty = $true) & (eta1 = $true) & (demorgan2a1 = $true) & (inComplementUnionImpNotIn1 = $true) & (woz13rule4 = $true) & (sepInPowerset = $true) & (binunionTEcontra = $true) & (powersetE1 = $true) & (in__Cong = $true) & (lam2lamEq = $true) & (surjFuncSetFuncIn = $true) & (setadjoinE = $true) & (exuE2 = $true) & (setOfPairsIsBReln1 = $true) & (ifSingleton = $true) & (exuI3 = $true) & (setadjoinIR = $true) & (setukpairinjL2 = $true) & (subPowSU = $true) & (singletoninpowerset = $true) & (omegaSclos = $true) & (demorgan2 = $true) & (eqimpsubset2 = $true) & (symdiffIneg2 = $true) & (binintersectSubset1 = $true) & (complementT_lem = $true) & (woz1_3 = $true) & (emptyinPowerset = $true) & (complementSubsetComplementIntersect = $true) & (powersetTI1 = $true) & (cartprodfstpairEq = $true) & (contrasubsetT2 = $true) & (upairinpowunion = $true) & (funcGraphProp3 = $true) & (demorgan2b2 = $true) & (funcext2 = $true) & (setadjoinAx = $true) & (cartprodmempair = $true) & (upairequniteq = $true) & (omegaIndAx = $true) & (setadjoinIL = $true) & (kpairsurjEq = $true) & (funcextLem = $true) & (iftrueProp1 = $true) & (demorgan1a = $true) & (emptysetE = $true) & (foundationAx = $true) & (theprop = $true) & (doubleComplementSub2 = $true) & (binunionE = $true) & (ksndsingleton = $true) & (dsetconstrEL = $true) & (kpairiskpair = $true) & (subbreln = $true) & (ex1I = $true) & (symdiffI2 = $true) & (setunionsingleton1 = $true) & (woz1_1 = $true) & (woz1_2 = $true) & (setextsub = $true) & (brelnall2 = $true) & (inIntersectImpInIntersectUnions = $true) & (complementInPowersetComplementIntersect = $true) & (binintersectRsub = $true) & (iftrue = $true) & (emptyInPowerset = $true) & (breln1unionprop = $true) & (binintersectSubset4 = $true) & (upairset2E = $true) & (subset2powerset = $true) & (dsetconstrI = $true) & (exu__Cong = $true) & (breln1compEex = $true) & (complementTcontraSubset = $true) & (omegaSAx = $true) & (setunion__Cong = $true) & (exuEu = $true) & (dsetconstrER = $true) & (image1E = $true) & (notequalI2 = $true) & (upairsetIR = $true) & (notinsingleton = $true) & (setminusT_lem = $true) & (breln1all2 = $true) & (notequalI1 = $true) & (breln1SetBreln1 = $true) & (powersetT_lem = $true) & (replAx = $true) & (binunionIR = $true) & (ap2p = $true) & (singletonsswitch = $true) & (binintersectSubset2 = $true) & (ifp = $true) & (prop2set2propI = $true) & (binintersectT_lem = $true) & (prop2setE = $true) & (setadjoinOr = $true) & (woz2Ex = $true) & (inIntersectImpInUnion = $true) & (subsetE2 = $true) & (binunionTILcontra = $true) & (omega__Cong = $true) & (breln1compE = $true) & (demorgan1 = $true) & (cartprodfstin = $true) & (ksndpairEq = $true) & (cartprodsndpairEq = $true) & (cartprodpairin = $true) & (contrasubsetT3 = $true) & (woz2A = $true) & (kfstpairEq = $true) & (cartprodpairmemER = $true) & ? [X0 : $i] : (($true = (transitiveset @ X0)) & ? [X1 : $i,X2 : $i] : (($true = (in @ X2 @ X1)) & ($true = (in @ X1 @ X0)) & ($true != (in @ X2 @ X0)))) & (choice2fnsingleton = $true) & (funcImageSingleton = $true) & (setukpairinjR12 = $true) & (exuE3u = $true) & (singletonprop = $true) & (iftrueorfalse = $true) & (ex1E1 = $true) & (doubleComplementI1 = $true) & (eqimpsubset1 = $true) & (notdallE = $true) & (nonemptyI1 = $true) & (breln1invE = $true) & (breln1invprop = $true) & (sepSubset = $true) & (powersetI1 = $true) & (iffalseProp2 = $true) & (complementUnionInPowersetComplement = $true) & (quantDeMorgan2 = $true) & (nonemptyImpWitness = $true) & (bs114d = $true) & (inIntersectImpInUnion2 = $true) & (omegaSp = $true) & (ex1E2 = $true) & (setminusLsub = $true) & (setunionE = $true) & (eta2 = $true) & (breln1unionEcases = $true) & (powerset__Cong = $true) & (powersetAx = $true) & (upairsetIL = $true) & (setoftrueEq = $true) & (binunionRsub = $true) & (demorgan2b = $true) & (setbeta = $true) & (binunionIL = $true) & (dpsetconstrERa = $true) & (image1Ex = $true) & (secondinupair = $true) & (demorgan2a2 = $true) & (lamp = $true) & (cartprodpairsurjEq = $true) & (setminusERneg = $true) & (omega0Ax = $true) & (setukpairIR = $true) & (ubforcartprodlem3 = $true) & (exuI1 = $true) & (breln1unionIL = $true) & (binunionTIRcontra = $true) & (breln1invI = $true) & (eqinunit = $true) & (singletonsuniq = $true) & (upairsubunion = $true) & (binintersectI = $true) & (intersectInPowersetIntersectUnions = $true) & (symdiffE = $true) & (setukpairIL = $true) & (setminusEL = $true) & (ubforcartprodlem2 = $true) & (upairsetE = $true) & (quantDeMorgan3 = $true) & (powersetI = $true) & (lamProp = $true) & (binunionEcases = $true) & (dpsetconstrSub = $true) & (binintersectSubset5 = $true) & (descrp = $true) & (descr__Cong = $true) & (ex1I2 = $true) & (setminusELneg = $true) & (breln1unionCommutes = $true) & (theeq = $true) & (complementTnotintersectT = $true) & (beta2 = $true) & (setunionsingleton = $true) & (ap2apEq1 = $true) & (symdiffIneg1 = $true) & (emptysetAx = $true) & (notdexE = $true) & (nonemptyE1 = $true) & (demorgan2a = $true) & (setunionE2 = $true) & (setminusSubset1 = $true) & (inPowerset = $true) & (powersetsubset = $true) & (exuE1 = $true) & (woz2W = $true) & (setOfPairsIsBReln = $true) & (peanoSinj = $true)),
% 13.72/3.26 inference(flattening,[status(thm)],[f1383])).
% 13.72/3.26 thf(f1383,plain,(
% 13.72/3.26 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i] : (? [X1 : $i,X2 : $i] : ((($true != (in @ X2 @ X0)) & ($true = (in @ X2 @ X1))) & ($true = (in @ X1 @ X0))) & ($true = (transitiveset @ X0))) & (binintTransitive = $true)) & (transitivesetOp1 = $true)) & (peanoSinj = $true)) & (peano0notS = $true)) & (omegaSclos = $true)) & (omegaSp = $true)) & (notinself2 = $true)) & (notinself = $true)) & (foundation2 = $true)) & (surjCantorThm = $true)) & (leftInvIsSurj = $true)) & (surjFuncSetFuncSurj = $true)) & (surjFuncSetFuncIn = $true)) & (injFuncSetFuncInj = $true)) & (injFuncSetFuncIn = $true)) & (injFuncInInjFuncSet = $true)) & (image1I = $true)) & (image1E = $true)) & (image1Equiv = $true)) & (image1Ex1 = $true)) & (image1Ex = $true)) & (woz2B = $true)) & (woz2A = $true)) & (woz2W = $true)) & (woz2Ex = $true)) & (breln1unionCommutes = $true)) & (breln1unionEcases = $true)) & (breln1unionE = $true)) & (breln1unionI = $true)) & (breln1unionIR = $true)) & (breln1unionIL = $true)) & (breln1unionprop = $true)) & (breln1compEex = $true)) & (breln1compE = $true)) & (breln1compI = $true)) & (breln1compprop = $true)) & (breln1invE = $true)) & (breln1invI = $true)) & (breln1invprop = $true)) & (eqbreln1 = $true)) & (subbreln1 = $true)) & (breln1all1 = $true)) & (setOfPairsIsBReln1 = $true)) & (choice2fnsingleton = $true)) & (breln1SetBreln1 = $true)) & (breln1all2 = $true)) & (woz1_5 = $true)) & (woz1_4 = $true)) & (woz1_3 = $true)) & (woz1_2 = $true)) & (woz1_1 = $true)) & (woz13rule4 = $true)) & (woz13rule3 = $true)) & (woz13rule2 = $true)) & (woz13rule1 = $true)) & (woz13rule0 = $true)) & (demorgan2 = $true)) & (demorgan2b = $true)) & (demorgan2b2 = $true)) & (demorgan2a = $true)) & (demorgan1 = $true)) & (demorgan1b = $true)) & (demorgan1a = $true)) & (demorgan2a2 = $true)) & (complementUnionInPowersetComplement = $true)) & (demorgan2a1 = $true)) & (binunionTEcontra = $true)) & (binunionTE = $true)) & (inComplementUnionImpInComplement1 = $true)) & (inComplementUnionImpNotIn1 = $true)) & (intersectInPowersetIntersectUnions = $true)) & (inIntersectImpInIntersectUnions = $true)) & (inIntersectImpInUnion2 = $true)) & (inIntersectImpInUnion = $true)) & (binunionTIRcontra = $true)) & (binunionTILcontra = $true)) & (complementTcontraSubset = $true)) & (contraSubsetComplement = $true)) & (complementInPowersetComplementIntersect = $true)) & (complementSubsetComplementIntersect = $true)) & (complementImpComplementIntersect = $true)) & (complementTnotintersectT = $true)) & (doubleComplementEq = $true)) & (doubleComplementSub2 = $true)) & (doubleComplementSub1 = $true)) & (doubleComplementE1 = $true)) & (doubleComplementI1 = $true)) & (contrasubsetT3 = $true)) & (contrasubsetT2 = $true)) & (contrasubsetT1 = $true)) & (contrasubsetT = $true)) & (binintersectTERcontra = $true)) & (binintersectTELcontra = $true)) & (complementTE1 = $true)) & (complementTI1 = $true)) & (powersetTE1 = $true)) & (powersetTI1 = $true)) & (subsetTI = $true)) & (setextT = $true)) & (complementT_lem = $true)) & (setminusT_lem = $true)) & (powersetT_lem = $true)) & (binunionT_lem = $true)) & (binintersectT_lem = $true)) & (iftrueorfalse = $true)) & (iffalse = $true)) & (iftrue = $true)) & (theeq = $true)) & (ifp = $true)) & (ifSingleton = $true)) & (iftrueProp2 = $true)) & (iftrueProp1 = $true)) & (iffalseProp2 = $true)) & (iffalseProp1 = $true)) & (eta2 = $true)) & (beta2 = $true)) & (lam2lamEq = $true)) & (eta1 = $true)) & (beta1 = $true)) & (ap2apEq2 = $true)) & (ap2apEq1 = $true)) & (funcext2 = $true)) & (funcext = $true)) & (eqbreln = $true)) & (subbreln = $true)) & (funcGraphProp4 = $true)) & (funcextLem = $true)) & (funcGraphProp2 = $true)) & (funcGraphProp3 = $true)) & (funcGraphProp1 = $true)) & (ex1E2 = $true)) & (brelnall2 = $true)) & (brelnall1 = $true)) & (lam2p = $true)) & (lamp = $true)) & (lamProp = $true)) & (funcinfuncset = $true)) & (ap2p = $true)) & (infuncsetfunc = $true)) & (app = $true)) & (apProp = $true)) & (funcImageSingleton = $true)) & (dpsetconstrER = $true)) & (dpsetconstrEL2 = $true)) & (dpsetconstrEL1 = $true)) & (dpsetconstrERa = $true)) & (setOfPairsIsBReln = $true)) & (dpsetconstrSub = $true)) & (dpsetconstrI = $true)) & (cartprodpairsurjEq = $true)) & (cartprodsndpairEq = $true)) & (cartprodfstpairEq = $true)) & (cartprodmempaircEq = $true)) & (cartprodpairmemER = $true)) & (cartprodpairmemEL = $true)) & (cartprodsndin = $true)) & (kpairsurjEq = $true)) & (ksndpairEq = $true)) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (setukpairinjR2 = $true)) & (upairequniteq = $true)) & (setukpairinjR1 = $true)) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 13.72/3.26 inference(ennf_transformation,[status(thm)],[f368])).
% 13.72/3.26 thf(f368,plain,(
% 13.72/3.26 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ((upairequniteq = $true) => ((setukpairinjR2 = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ((ksndpairEq = $true) => ((kpairsurjEq = $true) => ((cartprodsndin = $true) => ((cartprodpairmemEL = $true) => ((cartprodpairmemER = $true) => ((cartprodmempaircEq = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ((cartprodpairsurjEq = $true) => ((dpsetconstrI = $true) => ((dpsetconstrSub = $true) => ((setOfPairsIsBReln = $true) => ((dpsetconstrERa = $true) => ((dpsetconstrEL1 = $true) => ((dpsetconstrEL2 = $true) => ((dpsetconstrER = $true) => ((funcImageSingleton = $true) => ((apProp = $true) => ((app = $true) => ((infuncsetfunc = $true) => ((ap2p = $true) => ((funcinfuncset = $true) => ((lamProp = $true) => ((lamp = $true) => ((lam2p = $true) => ((brelnall1 = $true) => ((brelnall2 = $true) => ((ex1E2 = $true) => ((funcGraphProp1 = $true) => ((funcGraphProp3 = $true) => ((funcGraphProp2 = $true) => ((funcextLem = $true) => ((funcGraphProp4 = $true) => ((subbreln = $true) => ((eqbreln = $true) => ((funcext = $true) => ((funcext2 = $true) => ((ap2apEq1 = $true) => ((ap2apEq2 = $true) => ((beta1 = $true) => ((eta1 = $true) => ((lam2lamEq = $true) => ((beta2 = $true) => ((eta2 = $true) => ((iffalseProp1 = $true) => ((iffalseProp2 = $true) => ((iftrueProp1 = $true) => ((iftrueProp2 = $true) => ((ifSingleton = $true) => ((ifp = $true) => ((theeq = $true) => ((iftrue = $true) => ((iffalse = $true) => ((iftrueorfalse = $true) => ((binintersectT_lem = $true) => ((binunionT_lem = $true) => ((powersetT_lem = $true) => ((setminusT_lem = $true) => ((complementT_lem = $true) => ((setextT = $true) => ((subsetTI = $true) => ((powersetTI1 = $true) => ((powersetTE1 = $true) => ((complementTI1 = $true) => ((complementTE1 = $true) => ((binintersectTELcontra = $true) => ((binintersectTERcontra = $true) => ((contrasubsetT = $true) => ((contrasubsetT1 = $true) => ((contrasubsetT2 = $true) => ((contrasubsetT3 = $true) => ((doubleComplementI1 = $true) => ((doubleComplementE1 = $true) => ((doubleComplementSub1 = $true) => ((doubleComplementSub2 = $true) => ((doubleComplementEq = $true) => ((complementTnotintersectT = $true) => ((complementImpComplementIntersect = $true) => ((complementSubsetComplementIntersect = $true) => ((complementInPowersetComplementIntersect = $true) => ((contraSubsetComplement = $true) => ((complementTcontraSubset = $true) => ((binunionTILcontra = $true) => ((binunionTIRcontra = $true) => ((inIntersectImpInUnion = $true) => ((inIntersectImpInUnion2 = $true) => ((inIntersectImpInIntersectUnions = $true) => ((intersectInPowersetIntersectUnions = $true) => ((inComplementUnionImpNotIn1 = $true) => ((inComplementUnionImpInComplement1 = $true) => ((binunionTE = $true) => ((binunionTEcontra = $true) => ((demorgan2a1 = $true) => ((complementUnionInPowersetComplement = $true) => ((demorgan2a2 = $true) => ((demorgan1a = $true) => ((demorgan1b = $true) => ((demorgan1 = $true) => ((demorgan2a = $true) => ((demorgan2b2 = $true) => ((demorgan2b = $true) => ((demorgan2 = $true) => ((woz13rule0 = $true) => ((woz13rule1 = $true) => ((woz13rule2 = $true) => ((woz13rule3 = $true) => ((woz13rule4 = $true) => ((woz1_1 = $true) => ((woz1_2 = $true) => ((woz1_3 = $true) => ((woz1_4 = $true) => ((woz1_5 = $true) => ((breln1all2 = $true) => ((breln1SetBreln1 = $true) => ((choice2fnsingleton = $true) => ((setOfPairsIsBReln1 = $true) => ((breln1all1 = $true) => ((subbreln1 = $true) => ((eqbreln1 = $true) => ((breln1invprop = $true) => ((breln1invI = $true) => ((breln1invE = $true) => ((breln1compprop = $true) => ((breln1compI = $true) => ((breln1compE = $true) => ((breln1compEex = $true) => ((breln1unionprop = $true) => ((breln1unionIL = $true) => ((breln1unionIR = $true) => ((breln1unionI = $true) => ((breln1unionE = $true) => ((breln1unionEcases = $true) => ((breln1unionCommutes = $true) => ((woz2Ex = $true) => ((woz2W = $true) => ((woz2A = $true) => ((woz2B = $true) => ((image1Ex = $true) => ((image1Ex1 = $true) => ((image1Equiv = $true) => ((image1E = $true) => ((image1I = $true) => ((injFuncInInjFuncSet = $true) => ((injFuncSetFuncIn = $true) => ((injFuncSetFuncInj = $true) => ((surjFuncSetFuncIn = $true) => ((surjFuncSetFuncSurj = $true) => ((leftInvIsSurj = $true) => ((surjCantorThm = $true) => ((foundation2 = $true) => ((notinself = $true) => ((notinself2 = $true) => ((omegaSp = $true) => ((omegaSclos = $true) => ((peano0notS = $true) => ((peanoSinj = $true) => ((transitivesetOp1 = $true) => ((binintTransitive = $true) => ! [X0 : $i] : (($true = (transitiveset @ X0)) => ! [X1 : $i,X2 : $i] : (($true = (in @ X1 @ X0)) => (($true = (in @ X2 @ X1)) => ($true = (in @ X2 @ X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 13.72/3.26 inference(fool_elimination,[status(thm)],[f367])).
% 13.72/3.26 thf(f367,plain,(
% 13.72/3.26 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (eqbreln1 => (breln1invprop => (breln1invI => (breln1invE => (breln1compprop => (breln1compI => (breln1compE => (breln1compEex => (breln1unionprop => (breln1unionIL => (breln1unionIR => (breln1unionI => (breln1unionE => (breln1unionEcases => (breln1unionCommutes => (woz2Ex => (woz2W => (woz2A => (woz2B => (image1Ex => (image1Ex1 => (image1Equiv => (image1E => (image1I => (injFuncInInjFuncSet => (injFuncSetFuncIn => (injFuncSetFuncInj => (surjFuncSetFuncIn => (surjFuncSetFuncSurj => (leftInvIsSurj => (surjCantorThm => (foundation2 => (notinself => (notinself2 => (omegaSp => (omegaSclos => (peano0notS => (peanoSinj => (transitivesetOp1 => (binintTransitive => ! [X0 : $i] : ((transitiveset @ X0) => ! [X1 : $i,X2 : $i] : ((in @ X1 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 13.72/3.26 inference(rectify,[status(thm)],[f335])).
% 13.72/3.26 thf(f335,negated_conjecture,(
% 13.72/3.26 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (eqbreln1 => (breln1invprop => (breln1invI => (breln1invE => (breln1compprop => (breln1compI => (breln1compE => (breln1compEex => (breln1unionprop => (breln1unionIL => (breln1unionIR => (breln1unionI => (breln1unionE => (breln1unionEcases => (breln1unionCommutes => (woz2Ex => (woz2W => (woz2A => (woz2B => (image1Ex => (image1Ex1 => (image1Equiv => (image1E => (image1I => (injFuncInInjFuncSet => (injFuncSetFuncIn => (injFuncSetFuncInj => (surjFuncSetFuncIn => (surjFuncSetFuncSurj => (leftInvIsSurj => (surjCantorThm => (foundation2 => (notinself => (notinself2 => (omegaSp => (omegaSclos => (peano0notS => (peanoSinj => (transitivesetOp1 => (binintTransitive => ! [X11 : $i] : ((transitiveset @ X11) => ! [X3 : $i,X1 : $i] : ((in @ X3 @ X11) => ((in @ X1 @ X3) => (in @ X1 @ X11))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 13.72/3.26 inference(negated_conjecture,[status(cth)],[f334])).
% 13.72/3.26 thf(f334,conjecture,(
% 13.72/3.26 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (eqbreln1 => (breln1invprop => (breln1invI => (breln1invE => (breln1compprop => (breln1compI => (breln1compE => (breln1compEex => (breln1unionprop => (breln1unionIL => (breln1unionIR => (breln1unionI => (breln1unionE => (breln1unionEcases => (breln1unionCommutes => (woz2Ex => (woz2W => (woz2A => (woz2B => (image1Ex => (image1Ex1 => (image1Equiv => (image1E => (image1I => (injFuncInInjFuncSet => (injFuncSetFuncIn => (injFuncSetFuncInj => (surjFuncSetFuncIn => (surjFuncSetFuncSurj => (leftInvIsSurj => (surjCantorThm => (foundation2 => (notinself => (notinself2 => (omegaSp => (omegaSclos => (peano0notS => (peanoSinj => (transitivesetOp1 => (binintTransitive => ! [X11 : $i] : ((transitiveset @ X11) => ! [X3 : $i,X1 : $i] : ((in @ X3 @ X11) => ((in @ X1 @ X3) => (in @ X1 @ X11)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 13.72/3.26 file('/export/starexec/sandbox/tmp/tmp.zuy6gBFKOi/DTF2THF_17963.p',transitivesetOp2)).
% 13.72/3.26 thf(f12019,plain,(
% 13.72/3.26 ((subset @ sK1042 @ sK1041) != $true)),
% 13.72/3.26 inference(trivial_inequality_removal,[status(thm)],[f12017])).
% 13.72/3.26 thf(f12017,plain,(
% 13.72/3.26 ((subset @ sK1042 @ sK1041) != $true) | (sK1042 != sK1042)),
% 13.72/3.26 inference(superposition,[status(thm)],[f11946,f6953])).
% 13.72/3.26 thf(f6953,plain,(
% 13.72/3.26 ( ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X1) | ($true != (subset @ X1 @ X0))) )),
% 13.72/3.26 inference(trivial_inequality_removal,[status(thm)],[f6139])).
% 13.72/3.26 thf(f6139,plain,(
% 13.72/3.26 ( ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X1) | ($true != $true) | ($true != (subset @ X1 @ X0))) )),
% 13.72/3.26 inference(definition_unfolding,[status(thm)],[f4393,f5089])).
% 13.72/3.26 thf(f5089,plain,(
% 13.72/3.26 (binintersectSubset4 = $true)),
% 13.72/3.26 inference(cnf_transformation,[status(thm)],[f3260])).
% 13.72/3.26 thf(f4393,plain,(
% 13.72/3.26 ( ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X1) | ($true != (subset @ X1 @ X0)) | (binintersectSubset4 != $true)) )),
% 13.72/3.26 inference(cnf_transformation,[status(thm)],[f2624])).
% 13.72/3.26 thf(f2624,plain,(
% 13.72/3.26 (! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X1) | ($true != (subset @ X1 @ X0))) | (binintersectSubset4 != $true)) & ((binintersectSubset4 = $true) | (((binintersect @ sK667 @ sK668) != sK668) & ($true = (subset @ sK668 @ sK667))))),
% 13.72/3.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK667,sK668])],[f2622,f2623])).
% 13.72/3.26 thf(f2623,plain,(
% 13.72/3.26 ? [X2 : $i,X3 : $i] : (((binintersect @ X2 @ X3) != X3) & ($true = (subset @ X3 @ X2))) => (((binintersect @ sK667 @ sK668) != sK668) & ($true = (subset @ sK668 @ sK667)))),
% 13.72/3.26 introduced(definition,[],[choice_axiom])).
% 13.72/3.26 thf(f2622,plain,(
% 13.72/3.26 (! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X1) | ($true != (subset @ X1 @ X0))) | (binintersectSubset4 != $true)) & ((binintersectSubset4 = $true) | ? [X2 : $i,X3 : $i] : (((binintersect @ X2 @ X3) != X3) & ($true = (subset @ X3 @ X2))))),
% 13.72/3.26 inference(rectify,[status(thm)],[f2621])).
% 13.72/3.26 thf(f2621,plain,(
% 13.72/3.26 (! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X1) | ($true != (subset @ X1 @ X0))) | (binintersectSubset4 != $true)) & ((binintersectSubset4 = $true) | ? [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) != X1) & ($true = (subset @ X1 @ X0))))),
% 13.72/3.26 inference(nnf_transformation,[status(thm)],[f1239])).
% 13.72/3.26 thf(f1239,plain,(
% 13.72/3.26 ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X1) | ($true != (subset @ X1 @ X0))) <=> (binintersectSubset4 = $true)),
% 13.72/3.26 inference(ennf_transformation,[status(thm)],[f944])).
% 13.72/3.26 thf(f944,plain,(
% 13.72/3.26 (binintersectSubset4 = $true) <=> ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) => ((binintersect @ X0 @ X1) = X1))),
% 13.72/3.26 inference(fool_elimination,[status(thm)],[f943])).
% 13.72/3.26 thf(f943,plain,(
% 13.72/3.26 (! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => ((binintersect @ X0 @ X1) = X1)) = binintersectSubset4)),
% 13.72/3.26 inference(rectify,[status(thm)],[f117])).
% 13.72/3.26 thf(f117,axiom,(
% 13.72/3.26 (! [X3 : $i,X4 : $i] : ((subset @ X4 @ X3) => ((binintersect @ X3 @ X4) = X4)) = binintersectSubset4)),
% 13.72/3.26 file('/export/starexec/sandbox/tmp/tmp.zuy6gBFKOi/DTF2THF_17963.p',binintersectSubset4)).
% 13.72/3.26 thf(f11946,plain,(
% 13.72/3.26 (sK1042 != (binintersect @ sK1041 @ sK1042))),
% 13.72/3.26 inference(trivial_inequality_removal,[status(thm)],[f11938])).
% 13.72/3.26 thf(f11938,plain,(
% 13.72/3.26 ($true != $true) | (sK1042 != (binintersect @ sK1041 @ sK1042))),
% 13.72/3.26 inference(superposition,[status(thm)],[f9724,f5043])).
% 13.72/3.26 thf(f5043,plain,(
% 13.72/3.26 ($true = (in @ sK1043 @ sK1042))),
% 13.72/3.26 inference(cnf_transformation,[status(thm)],[f3260])).
% 13.72/3.26 thf(f9724,plain,(
% 13.72/3.26 ( ! [X0 : $i] : (($true != (in @ sK1043 @ X0)) | ((binintersect @ sK1041 @ X0) != X0)) )),
% 13.72/3.26 inference(trivial_inequality_removal,[status(thm)],[f9721])).
% 13.72/3.26 thf(f9721,plain,(
% 13.72/3.26 ( ! [X0 : $i] : (($true != (in @ sK1043 @ X0)) | ((binintersect @ sK1041 @ X0) != X0) | ($true != $true)) )),
% 13.72/3.26 inference(superposition,[status(thm)],[f8878,f6900])).
% 13.72/3.26 thf(f6900,plain,(
% 13.72/3.26 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | ((binintersect @ X0 @ X1) != X1)) )),
% 13.72/3.26 inference(trivial_inequality_removal,[status(thm)],[f5712])).
% 13.72/3.26 thf(f5712,plain,(
% 13.72/3.26 ( ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) != X1) | ($true != $true) | ($true = (subset @ X1 @ X0))) )),
% 13.72/3.26 inference(definition_unfolding,[status(thm)],[f3801,f5266])).
% 13.72/3.26 thf(f5266,plain,(
% 13.72/3.26 (binintersectSubset3 = $true)),
% 13.72/3.26 inference(cnf_transformation,[status(thm)],[f3260])).
% 13.72/3.26 thf(f3801,plain,(
% 13.72/3.26 ( ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) != X1) | ($true = (subset @ X1 @ X0)) | (binintersectSubset3 != $true)) )),
% 13.72/3.26 inference(cnf_transformation,[status(thm)],[f1949])).
% 13.72/3.26 thf(f1949,plain,(
% 13.72/3.26 (! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) != X1) | ($true = (subset @ X1 @ X0))) | (binintersectSubset3 != $true)) & ((binintersectSubset3 = $true) | (((binintersect @ sK282 @ sK283) = sK283) & ((subset @ sK283 @ sK282) != $true)))),
% 13.72/3.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK282,sK283])],[f1947,f1948])).
% 13.72/3.26 thf(f1948,plain,(
% 13.72/3.26 ? [X2 : $i,X3 : $i] : (((binintersect @ X2 @ X3) = X3) & ($true != (subset @ X3 @ X2))) => (((binintersect @ sK282 @ sK283) = sK283) & ((subset @ sK283 @ sK282) != $true))),
% 13.72/3.26 introduced(definition,[],[choice_axiom])).
% 13.72/3.26 thf(f1947,plain,(
% 13.72/3.26 (! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) != X1) | ($true = (subset @ X1 @ X0))) | (binintersectSubset3 != $true)) & ((binintersectSubset3 = $true) | ? [X2 : $i,X3 : $i] : (((binintersect @ X2 @ X3) = X3) & ($true != (subset @ X3 @ X2))))),
% 13.72/3.26 inference(rectify,[status(thm)],[f1946])).
% 13.72/3.26 thf(f1946,plain,(
% 13.72/3.26 (! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) != X1) | ($true = (subset @ X1 @ X0))) | (binintersectSubset3 != $true)) & ((binintersectSubset3 = $true) | ? [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X1) & ($true != (subset @ X1 @ X0))))),
% 13.72/3.26 inference(nnf_transformation,[status(thm)],[f1152])).
% 13.72/3.26 thf(f1152,plain,(
% 13.72/3.26 ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) != X1) | ($true = (subset @ X1 @ X0))) <=> (binintersectSubset3 = $true)),
% 13.72/3.26 inference(ennf_transformation,[status(thm)],[f918])).
% 13.72/3.26 thf(f918,plain,(
% 13.72/3.26 ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X1) => ($true = (subset @ X1 @ X0))) <=> (binintersectSubset3 = $true)),
% 13.72/3.26 inference(fool_elimination,[status(thm)],[f917])).
% 13.72/3.26 thf(f917,plain,(
% 13.72/3.26 (! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X1) => (subset @ X1 @ X0)) = binintersectSubset3)),
% 13.72/3.26 inference(rectify,[status(thm)],[f113])).
% 13.72/3.26 thf(f113,axiom,(
% 13.72/3.26 (! [X3 : $i,X4 : $i] : (((binintersect @ X3 @ X4) = X4) => (subset @ X4 @ X3)) = binintersectSubset3)),
% 13.72/3.26 file('/export/starexec/sandbox/tmp/tmp.zuy6gBFKOi/DTF2THF_17963.p',binintersectSubset3)).
% 13.72/3.26 thf(f8878,plain,(
% 13.72/3.26 ( ! [X0 : $i] : (($true != (subset @ X0 @ sK1041)) | ($true != (in @ sK1043 @ X0))) )),
% 13.72/3.26 inference(trivial_inequality_removal,[status(thm)],[f8862])).
% 13.72/3.26 thf(f8862,plain,(
% 13.72/3.26 ( ! [X0 : $i] : (($true != $true) | ($true != (in @ sK1043 @ X0)) | ($true != (subset @ X0 @ sK1041))) )),
% 13.72/3.26 inference(superposition,[status(thm)],[f5041,f6851])).
% 13.72/3.26 thf(f6851,plain,(
% 13.72/3.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X0 @ X1)) | ($true != (in @ X0 @ X2)) | ($true != (subset @ X2 @ X1))) )),
% 13.72/3.26 inference(trivial_inequality_removal,[status(thm)],[f6264])).
% 13.72/3.26 thf(f6264,plain,(
% 13.72/3.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X0 @ X1)) | ($true != $true) | ($true != (subset @ X2 @ X1)) | ($true != (in @ X0 @ X2))) )),
% 13.72/3.26 inference(definition_unfolding,[status(thm)],[f4559,f5202])).
% 13.72/3.26 thf(f5202,plain,(
% 13.72/3.26 (subsetE = $true)),
% 13.72/3.26 inference(cnf_transformation,[status(thm)],[f3260])).
% 13.72/3.26 thf(f4559,plain,(
% 13.72/3.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X0 @ X1)) | ($true != (in @ X0 @ X2)) | ($true != (subset @ X2 @ X1)) | (subsetE != $true)) )),
% 13.72/3.26 inference(cnf_transformation,[status(thm)],[f2817])).
% 13.72/3.26 thf(f2817,plain,(
% 13.72/3.26 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X1)) | ($true != (in @ X0 @ X2)) | ($true != (subset @ X2 @ X1))) | (subsetE != $true)) & ((subsetE = $true) | (((in @ sK772 @ sK773) != $true) & ($true = (in @ sK772 @ sK774)) & ($true = (subset @ sK774 @ sK773))))),
% 13.72/3.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK772,sK773,sK774])],[f2815,f2816])).
% 13.72/3.26 thf(f2816,plain,(
% 13.72/3.26 ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) != $true) & ($true = (in @ X3 @ X5)) & ((subset @ X5 @ X4) = $true)) => (((in @ sK772 @ sK773) != $true) & ($true = (in @ sK772 @ sK774)) & ($true = (subset @ sK774 @ sK773)))),
% 13.72/3.26 introduced(definition,[],[choice_axiom])).
% 13.72/3.26 thf(f2815,plain,(
% 13.72/3.26 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X1)) | ($true != (in @ X0 @ X2)) | ($true != (subset @ X2 @ X1))) | (subsetE != $true)) & ((subsetE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) != $true) & ($true = (in @ X3 @ X5)) & ((subset @ X5 @ X4) = $true)))),
% 13.72/3.26 inference(rectify,[status(thm)],[f2814])).
% 13.72/3.26 thf(f2814,plain,(
% 13.72/3.26 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X1)) | ($true != (in @ X0 @ X2)) | ($true != (subset @ X2 @ X1))) | (subsetE != $true)) & ((subsetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X1)) & ($true = (in @ X0 @ X2)) & ($true = (subset @ X2 @ X1))))),
% 13.72/3.26 inference(nnf_transformation,[status(thm)],[f1256])).
% 13.72/3.26 thf(f1256,plain,(
% 13.72/3.26 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X1)) | ($true != (in @ X0 @ X2)) | ($true != (subset @ X2 @ X1))) <=> (subsetE = $true)),
% 13.72/3.26 inference(flattening,[status(thm)],[f1255])).
% 13.72/3.26 thf(f1255,plain,(
% 13.72/3.26 (subsetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((($true = (in @ X0 @ X1)) | ($true != (in @ X0 @ X2))) | ($true != (subset @ X2 @ X1)))),
% 13.72/3.26 inference(ennf_transformation,[status(thm)],[f938])).
% 13.72/3.26 thf(f938,plain,(
% 13.72/3.26 (subsetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (subset @ X2 @ X1)) => (($true = (in @ X0 @ X2)) => ($true = (in @ X0 @ X1))))),
% 13.72/3.26 inference(fool_elimination,[status(thm)],[f937])).
% 13.72/3.26 thf(f937,plain,(
% 13.72/3.26 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X2 @ X1) => ((in @ X0 @ X2) => (in @ X0 @ X1))) = subsetE)),
% 13.72/3.26 inference(rectify,[status(thm)],[f83])).
% 13.72/3.26 thf(f83,axiom,(
% 13.72/3.26 (! [X1 : $i,X4 : $i,X3 : $i] : ((subset @ X3 @ X4) => ((in @ X1 @ X3) => (in @ X1 @ X4))) = subsetE)),
% 13.72/3.26 file('/export/starexec/sandbox/tmp/tmp.zuy6gBFKOi/DTF2THF_17963.p',subsetE)).
% 13.72/3.26 thf(f5041,plain,(
% 13.72/3.26 ((in @ sK1043 @ sK1041) != $true)),
% 13.72/3.26 inference(cnf_transformation,[status(thm)],[f3260])).
% 13.72/3.26 thf(f5042,plain,(
% 13.72/3.26 ($true = (in @ sK1042 @ sK1041))),
% 13.72/3.26 inference(cnf_transformation,[status(thm)],[f3260])).
% 13.72/3.26 % SZS output end Proof for DTF2THF_17963
% 13.72/3.26 % (18510)------------------------------
% 13.72/3.26 % (18510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.72/3.26 % (18510)Termination reason: Refutation
% 13.72/3.26
% 13.72/3.26 % (18510)Memory used [KB]: 14328
% 13.72/3.26 % (18510)Time elapsed: 0.664 s
% 13.72/3.26 % (18510)Instructions burned: 2070 (million)
% 13.72/3.26 % (18510)------------------------------
% 13.72/3.26 % (18510)------------------------------
% 13.72/3.26 % (18198)Success in time 1.6 s
%------------------------------------------------------------------------------