%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU816^1 : 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 : n010.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 09:37:27 AM UTC 2026
% Result : Theorem 9.84s 2.82s
% Output : Refutation 9.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 98 ( 42 unt; 0 typ; 2 def)
% Number of atoms : 5815 (1539 equ; 0 cnn)
% Maximal formula atoms : 335 ( 59 avg)
% Number of connectives : 3145 ( 85 ~; 74 |;1046 &; 548 @)
% ( 9 <=>;1372 =>; 0 <=; 0 <~>)
% Maximal formula depth : 341 ( 27 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 698 ( 694 usr; 349 con; 0-6 aty)
% ( 11 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 173 ( 29 ^; 109 !; 35 ?; 173 :)
% 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_392,type,
stricttotalorderedByIn: $i > $o ).
thf(func_def_393,type,
wellorderedByIn: $i > $o ).
thf(func_def_394,type,
ordinal: $i > $o ).
thf(func_def_395,type,
limitOrdinal: $i > $o ).
thf(func_def_411,type,
sP0: $i > $o ).
thf(func_def_412,type,
sP1: $i > ( $i > $o ) > $o ).
thf(func_def_413,type,
sP2: $i > $i > ( $i > $o ) > $i > $o ).
thf(func_def_414,type,
sP3: ( $i > $o ) > $i > $o ).
thf(func_def_415,type,
sP4: ( $i > $o ) > $i > $o ).
thf(func_def_416,type,
sP5: $i > ( $i > $o ) > $o ).
thf(func_def_419,type,
sP8: $i > $i > $i > $o ).
thf(func_def_420,type,
sP9: $i > $i > $i > $o ).
thf(func_def_421,type,
sP10: ( $i > $o ) > $o ).
thf(func_def_422,type,
sP11: $i > $i > $i > $o ).
thf(func_def_423,type,
sP12: $i > ( $i > $i > $o ) > $i > $o ).
thf(func_def_424,type,
sP13: $i > ( $i > $i > $o ) > $i > $o ).
thf(func_def_426,type,
sP15: $i > $i > $i > $o ).
thf(func_def_428,type,
sP17: $i > $i > $o ).
thf(func_def_430,type,
sP19: $i > $i > $o > $i > $i > $i > $o ).
thf(func_def_431,type,
sP20: $i > ( $i > $o ) > $o ).
thf(func_def_433,type,
sP22: $i > $i > $i > $o ).
thf(func_def_434,type,
sP23: ( $i > $o ) > $i > $o ).
thf(func_def_435,type,
sP24: $i > ( $i > $o ) > $i > $i > $o ).
thf(func_def_436,type,
sP25: $i > ( $i > $o ) > $i > $o ).
thf(func_def_438,type,
sP27: ( $i > $o ) > $o ).
thf(func_def_439,type,
sP28: $i > $i > $i > $i > $o ).
thf(func_def_440,type,
sP29: $i > $i > $i > $o ).
thf(func_def_441,type,
sP30: $i > $i > $o ).
thf(func_def_444,type,
sP33: $i > ( $i > $o ) > $o ).
thf(func_def_446,type,
sP35: $i > $i > $i > $o ).
thf(func_def_448,type,
sP37: ( $i > $o ) > $i > $o ).
thf(func_def_449,type,
sP38: $i > ( $i > $o ) > $i > $o ).
thf(func_def_450,type,
sP39: $i > $i > $i > $i > $o ).
thf(func_def_451,type,
sP40: $i > $i > ( $i > $i ) > $o ).
thf(func_def_453,type,
sP42: $i > $i > $i > $i > $o ).
thf(func_def_454,type,
sP43: $i > $i > $i > $o ).
thf(func_def_456,type,
sP45: $i > $i > $o ).
thf(func_def_458,type,
sP47: ( $i > $o ) > $o ).
thf(func_def_459,type,
sP48: $i > ( $i > $i ) > $i > $o ).
thf(func_def_463,type,
sP52: $i > $i > $i > $o ).
thf(func_def_464,type,
sP53: $i > $i > $o ).
thf(func_def_465,type,
sP54: $i > $o ).
thf(func_def_466,type,
sP55: $i > $i > $o ).
thf(func_def_467,type,
sP56: $i > $i > $o ).
thf(func_def_468,type,
sP57: $i > $i > $o ).
thf(func_def_469,type,
sP58: $i > $i > $i > $o ).
thf(func_def_470,type,
sP59: ( $i > $o ) > $i > $o ).
thf(func_def_473,type,
sP62: $i > $i > $o > $o ).
thf(func_def_475,type,
sP64: $i > $o ).
thf(func_def_476,type,
sP65: $i > $o ).
thf(func_def_477,type,
sP66: $i > ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_478,type,
sP67: $i > $i > $i > $i > $o ).
thf(func_def_479,type,
sP68: $i > $i > $i > $i > $o ).
thf(func_def_480,type,
sP69: $i > ( $i > $i ) > $i > $o ).
thf(func_def_482,type,
sP71: ( $i > $o ) > $i > $o ).
thf(func_def_484,type,
sP73: $i > $i > ( $i > $i ) > $o ).
thf(func_def_487,type,
sP76: $i > $i > $i > $o ).
thf(func_def_488,type,
sP77: $i > $i > $i > $o ).
thf(func_def_489,type,
sP78: $o > $i > $i > $i > $o ).
thf(func_def_490,type,
sP79: $o > $i > $i > $i > $o ).
thf(func_def_491,type,
sP80: $i > ( $i > $i > $o ) > $i > $o ).
thf(func_def_492,type,
sP81: $i > ( $i > $i > $o ) > $o ).
thf(func_def_494,type,
sP83: ( $i > $o ) > $o ).
thf(func_def_495,type,
sP84: $i > $i > $o > $o ).
thf(func_def_498,type,
sP87: $i > $i > $i > $o ).
thf(func_def_499,type,
sP88: $o > $i > $i > $i > $o ).
thf(func_def_500,type,
sP89: $i > $i > $i > $i > $o ).
thf(func_def_501,type,
sP90: ( $i > $o ) > $o ).
thf(func_def_503,type,
sP92: $i > $i > $i > $i > $i > $o ).
thf(func_def_504,type,
sP93: $i > ( $i > $o ) > $o ).
thf(func_def_506,type,
sP95: ( $i > $i ) > $i > $i > $o ).
thf(func_def_509,type,
sP98: $i > $i > $o > $o ).
thf(func_def_510,type,
sP99: $i > $i > $i > $o ).
thf(func_def_511,type,
sP100: $i > $i > $o > $o ).
thf(func_def_512,type,
sP101: $i > $i > $i > $o ).
thf(func_def_513,type,
sP102: ( $i > $o ) > $i > $o ).
thf(func_def_514,type,
sP103: $i > ( $i > $o ) > $i > $o ).
thf(func_def_515,type,
sP104: $i > ( $i > $o ) > $o ).
thf(func_def_516,type,
sP105: ( $i > $o ) > $i > $o ).
thf(func_def_528,type,
sK117: $i > $o ).
thf(func_def_540,type,
sK129: $i > $i > $i ).
thf(func_def_541,type,
sK130: $i > $i ).
thf(func_def_544,type,
sK133: $i > $i > ( $i > $o ) > $i > $i ).
thf(func_def_545,type,
sK134: $i > $i > ( $i > $o ) > $i > $i ).
thf(func_def_546,type,
sK135: $i > ( $i > $o ) > $i ).
thf(func_def_550,type,
sK139: $i > $o ).
thf(func_def_579,type,
sK168: $i > $o ).
thf(func_def_592,type,
sK181: $i > $o ).
thf(func_def_637,type,
sK226: ( $i > $o ) > $i > $i ).
thf(func_def_638,type,
sK227: ( $i > $o ) > $i > $i ).
thf(func_def_639,type,
sK228: ( $i > $o ) > $i > $i ).
thf(func_def_640,type,
sK229: $i > $o ).
thf(func_def_681,type,
sK270: $i > $i > $o ).
thf(func_def_685,type,
sK274: $i > $o ).
thf(func_def_686,type,
sK275: ( $i > $o ) > $i > $i ).
thf(func_def_687,type,
sK276: $i > ( $i > $o ) > $i ).
thf(func_def_692,type,
sK281: $i > $i ).
thf(func_def_693,type,
sK282: ( $i > $i ) > $i > $i > $i ).
thf(func_def_721,type,
sK310: $i > $i > $i > $i ).
thf(func_def_722,type,
sK311: $i > $i > $i > $i ).
thf(func_def_723,type,
sK312: $i > $i > $i > $i ).
thf(func_def_724,type,
sK313: $i > $i > $i > $i ).
thf(func_def_734,type,
sK323: ( $i > $o ) > $i ).
thf(func_def_735,type,
sK324: $i > $o ).
thf(func_def_736,type,
sK325: $i > ( $i > $o ) > $i ).
thf(func_def_737,type,
sK326: ( $i > $o ) > $i ).
thf(func_def_738,type,
sK327: $i > $o ).
thf(func_def_739,type,
sK328: $i > $i > $o ).
thf(func_def_741,type,
sK330: $i > $o ).
thf(func_def_766,type,
sK355: $i > $i > $i > $i ).
thf(func_def_767,type,
sK356: $i > $i > $i > $i > $i ).
thf(func_def_771,type,
sK360: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_772,type,
sK361: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_773,type,
sK362: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_774,type,
sK363: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_777,type,
sK366: $i > $i > $o ).
thf(func_def_783,type,
sK372: $i > $i ).
thf(func_def_790,type,
sK379: $i > $i > $i > $i ).
thf(func_def_791,type,
sK380: $i > $i > $i > $i > $i ).
thf(func_def_797,type,
sK386: $i > $i > $i ).
thf(func_def_800,type,
sK389: $i > $i > $i ).
thf(func_def_801,type,
sK390: $i > $i > $o > $i > $i > $i > $i ).
thf(func_def_808,type,
sK397: $i > $o ).
thf(func_def_810,type,
sK399: $i > ( $i > $o ) > $i ).
thf(func_def_811,type,
sK400: $i > ( $i > $o ) > $i ).
thf(func_def_822,type,
sK411: $i > $i > $i > $i ).
thf(func_def_826,type,
sK415: $i > $o ).
thf(func_def_827,type,
sK416: $i > ( $i > $o ) > $i > $i > $i ).
thf(func_def_828,type,
sK417: $i > ( $i > $o ) > $i > $i > $i ).
thf(func_def_829,type,
sK418: ( $i > $o ) > $i > $i ).
thf(func_def_833,type,
sK422: $i > $o ).
thf(func_def_834,type,
sK423: $i > $o ).
thf(func_def_845,type,
sK434: $i > $i ).
thf(func_def_862,type,
sK451: $i > ( $i > $o ) > $i > $i ).
thf(func_def_863,type,
sK452: $i > $o ).
thf(func_def_884,type,
sK473: $i > $o ).
thf(func_def_888,type,
sK477: $i > $i ).
thf(func_def_890,type,
sK479: $i > ( $i > $i ) > $i > $i ).
thf(func_def_892,type,
sK481: $i > $o ).
thf(func_def_894,type,
sK483: ( $i > $o ) > $i ).
thf(func_def_895,type,
sK484: $i > ( $i > $o ) > $i ).
thf(func_def_896,type,
sK485: $i > $o ).
thf(func_def_901,type,
sK490: $i > $i ).
thf(func_def_911,type,
sK500: $i > $i > $o ).
thf(func_def_914,type,
sK503: $i > $o ).
thf(func_def_918,type,
sK507: $i > $i > $i > $i > $i ).
thf(func_def_919,type,
sK508: $i > $i > $i > $i > $i ).
thf(func_def_929,type,
sK518: $i > $i > $i > $i ).
thf(func_def_930,type,
sK519: $i > $i > $i > $i ).
thf(func_def_940,type,
sK529: $i > $i > $i ).
thf(func_def_941,type,
sK530: $i > $i > $i ).
thf(func_def_942,type,
sK531: $i > $o ).
thf(func_def_943,type,
sK532: $i > $o ).
thf(func_def_944,type,
sK533: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_945,type,
sK534: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_954,type,
sK543: $i > $o ).
thf(func_def_956,type,
sK545: $i > ( $i > $o ) > $i ).
thf(func_def_957,type,
sK546: $i > ( $i > $o ) > $i ).
thf(func_def_964,type,
sK553: $i > ( $i > $o ) > $i > $i ).
thf(func_def_965,type,
sK554: $i > ( $i > $o ) > $i > $i ).
thf(func_def_966,type,
sK555: ( $i > $o ) > $i > $i ).
thf(func_def_969,type,
sK558: $i > $o ).
thf(func_def_977,type,
sK566: $i > $i > $o ).
thf(func_def_979,type,
sK568: $i > $i > $i > $i > $i ).
thf(func_def_985,type,
sK574: $i > $i ).
thf(func_def_987,type,
sK576: $i > ( $i > $i ) > $i > $i ).
thf(func_def_988,type,
sK577: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1013,type,
sK602: $i > $i > $o ).
thf(func_def_1028,type,
sK617: $i > $i > $i > $i ).
thf(func_def_1029,type,
sK618: $i > $i > $i > $i > $i ).
thf(func_def_1030,type,
sK619: $i > $i > $i > $i > $i ).
thf(func_def_1031,type,
sK620: $i > $i > $i > $i > $i ).
thf(func_def_1040,type,
sK629: $i > $i > $i ).
thf(func_def_1059,type,
sK648: $i > $i > $i ).
thf(func_def_1067,type,
sK656: ( $i > $o ) > $i ).
thf(func_def_1068,type,
sK657: $i > ( $i > $o ) > $i ).
thf(func_def_1069,type,
sK658: $i > $o ).
thf(func_def_1076,type,
sK665: $i > $i ).
thf(func_def_1077,type,
sK666: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1082,type,
sK671: $i > $o ).
thf(func_def_1103,type,
sK692: $i > $o ).
thf(func_def_1104,type,
sK693: ( $i > $o ) > $i > $i ).
thf(func_def_1118,type,
sK707: $i > $i ).
thf(func_def_1120,type,
sK709: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1135,type,
sK724: $i > $i > $i ).
thf(func_def_1136,type,
sK725: $i > $i > $i ).
thf(func_def_1137,type,
sK726: $i > $i > $i ).
thf(func_def_1138,type,
sK727: $i > $i > $i ).
thf(func_def_1139,type,
sK728: $i > $i > $i ).
thf(func_def_1140,type,
sK729: $i > $i > $i ).
thf(func_def_1141,type,
sK730: $i > $i > $i ).
thf(func_def_1142,type,
sK731: $i > $i > $i > $i ).
thf(func_def_1143,type,
sK732: $i > $i ).
thf(func_def_1144,type,
sK733: $i > $i ).
thf(func_def_1145,type,
sK734: $i > $i ).
thf(func_def_1146,type,
sK735: $i > $i ).
thf(func_def_1147,type,
sK736: $i > $i > $i ).
thf(func_def_1148,type,
sK737: $i > $i > $i ).
thf(func_def_1149,type,
sK738: $i > $i > $i ).
thf(func_def_1150,type,
sK739: $i > $i > $i > $i ).
thf(func_def_1151,type,
sK740: $i > $i > $i > $i ).
thf(func_def_1153,type,
sK742: $i > $i ).
thf(func_def_1154,type,
sK743: $i > $i > $i > $i ).
thf(func_def_1160,type,
sK749: $i > $o ).
thf(func_def_1162,type,
sK751: $i > ( $i > $o ) > $i ).
thf(func_def_1163,type,
sK752: ( $i > $o ) > $i > $i ).
thf(func_def_1170,type,
sK759: $i > $i ).
thf(func_def_1172,type,
sK761: $i > $i ).
thf(func_def_1174,type,
sK763: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1180,type,
sK769: $i > $i > $o > $i ).
thf(func_def_1193,type,
sK782: $i > $i > $i ).
thf(func_def_1194,type,
sK783: $i > $i ).
thf(func_def_1195,type,
sK784: $i > $i ).
thf(func_def_1217,type,
sK806: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(func_def_1218,type,
sK807: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(func_def_1221,type,
sK810: $i > $o ).
thf(func_def_1222,type,
sK811: $i > $o ).
thf(func_def_1228,type,
sK817: $i > $i > $i > $i > $i ).
thf(func_def_1229,type,
sK818: $i > $i > $i > $i > $i ).
thf(func_def_1230,type,
sK819: $i > $i > $i > $i > $i ).
thf(func_def_1231,type,
sK820: $i > $i > $i > $i > $i ).
thf(func_def_1250,type,
sK839: $i > $i ).
thf(func_def_1251,type,
sK840: $i > $i ).
thf(func_def_1252,type,
sK841: ( $i > $i ) > $i > $i ).
thf(func_def_1253,type,
sK842: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1257,type,
sK846: $i > $o ).
thf(func_def_1258,type,
sK847: ( $i > $o ) > $i > $i ).
thf(func_def_1259,type,
sK848: ( $i > $o ) > $i > $i ).
thf(func_def_1273,type,
sK862: $i > $i ).
thf(func_def_1274,type,
sK863: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1275,type,
sK864: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1278,type,
sK867: $i > $i > $i ).
thf(func_def_1285,type,
sK874: $i > $i > $i > $i ).
thf(func_def_1286,type,
sK875: $i > $i > $i > $i ).
thf(func_def_1295,type,
sK884: $i > $i > $o ).
thf(func_def_1296,type,
sK885: ( $i > $i > $o ) > $i > $i ).
thf(func_def_1297,type,
sK886: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_1298,type,
sK887: $i > ( $i > $i > $o ) > $i ).
thf(func_def_1299,type,
sK888: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_1300,type,
sK889: ( $i > $o ) > $i ).
thf(func_def_1301,type,
sK890: ( $i > $o ) > $i ).
thf(func_def_1302,type,
sK891: $i > $o ).
thf(func_def_1318,type,
sK907: $i > $i ).
thf(func_def_1320,type,
sK909: $i > $i > $i > $i ).
thf(func_def_1321,type,
sK910: $i > $i > $i > $i ).
thf(func_def_1332,type,
sK921: $i > $i ).
thf(func_def_1345,type,
sK934: $i > $i > $i > $i > $o ).
thf(func_def_1367,type,
sK956: $i > ( $i > $o ) > $i ).
thf(func_def_1368,type,
sK957: ( $i > $o ) > $i ).
thf(func_def_1369,type,
sK958: $i > $o ).
thf(func_def_1377,type,
sK966: $i > $i > $i ).
thf(func_def_1394,type,
sK983: $i > $i > $i > $i > $i > $i ).
thf(func_def_1401,type,
sK990: $i > $o ).
thf(func_def_1402,type,
sK991: ( $i > $o ) > $i > $i ).
thf(func_def_1403,type,
sK992: $i > ( $i > $o ) > $i ).
thf(func_def_1404,type,
sK993: $i > $i ).
thf(func_def_1407,type,
sK996: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1408,type,
sK997: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1409,type,
sK998: $i > ( $i > $i ) > $i > $i > $i ).
thf(func_def_1428,type,
sK1017: $i > $i > $o ).
thf(func_def_1469,type,
sK1058: $i > $o ).
thf(func_def_1470,type,
sK1059: $i > $o ).
thf(func_def_1471,type,
sK1060: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1472,type,
sK1061: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1489,type,
sK1078: $i > $i > $o ).
thf(func_def_1492,type,
sK1081: $i > $o ).
thf(func_def_1494,type,
sK1083: $i > $i > $i > $o ).
thf(func_def_1506,type,
sK1095: $i > $i ).
thf(func_def_1508,type,
sK1097: $i > $i ).
thf(func_def_1511,type,
sK1100: $i > $i > $o ).
thf(func_def_1542,type,
sK1131: $i > $i > $i ).
thf(func_def_1550,type,
sK1139: $i > $o ).
thf(func_def_1567,type,
sK1156: $i > $o ).
thf(func_def_1571,type,
sK1160: $i > $i > $i > $o ).
thf(func_def_1572,type,
sK1161: $i > $i > $i > $i ).
thf(func_def_1578,type,
sK1167: $i > ( $i > $o ) > $i > $i ).
thf(func_def_1579,type,
sK1168: $i > ( $i > $o ) > $i > $i ).
thf(func_def_1580,type,
sK1169: ( $i > $o ) > $i > $i ).
thf(func_def_1583,type,
sK1172: $i > $o ).
thf(func_def_1589,type,
sK1178: ( $i > $o ) > $i > $i ).
thf(func_def_1590,type,
sK1179: ( $i > $o ) > $i > $i ).
thf(func_def_1591,type,
sK1180: $i > ( $i > $o ) > $i ).
thf(func_def_1593,type,
sK1182: $i > $o ).
thf(func_def_1594,type,
sK1183: $i > $i ).
thf(func_def_1597,type,
sK1186: $i > $i > ( $i > $i ) > $i ).
thf(func_def_1602,type,
sK1191: $i > $i ).
thf(func_def_1603,type,
sK1192: $i > $i ).
thf(func_def_1605,type,
sK1194: $i > $i ).
thf(func_def_1606,type,
sK1195: $i > $i ).
thf(func_def_1607,type,
sK1196: $i > $i ).
thf(func_def_1608,type,
ph1197:
!>[X0: $tType] : X0 ).
thf(f10494,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f9788,f10357,f10493]) ).
thf(f10493,plain,
spl1189_219,
inference(avatar_contradiction_clause,[status(thm)],[f10492]) ).
thf(f10492,plain,
( $false
| spl1189_219 ),
inference(trivial_inequality_removal,[status(thm)],[f10482]) ).
thf(f10482,plain,
( ( $false = $true )
| spl1189_219 ),
inference(backward_demodulation,[status(thm)],[f8933,f10428]) ).
thf(f10428,plain,
( ( ( in @ sK1190 @ sK980 )
= $false )
| spl1189_219 ),
inference(trivial_inequality_removal,[status(thm)],[f10419]) ).
thf(f10419,plain,
( ( ( in @ sK1190 @ sK980 )
= $false )
| ( $true != $true )
| spl1189_219 ),
inference(superposition,[status(thm)],[f9786,f7083]) ).
thf(f7083,plain,
! [X1: $i] :
( ( $true
= ( subset @ X1 @ sK980 ) )
| ( ( in @ X1 @ sK980 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f7082]) ).
thf(f7082,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK980 )
=> ( subset @ X1 @ sK980 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f7081]) ).
thf(f7081,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK980 )
=> ( subset @ Y0 @ sK980 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f7079]) ).
thf(f7079,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK980 )
=> ( subset @ Y0 @ sK980 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f7078]) ).
thf(f7078,plain,
( $true
= ( ( wellorderedByIn @ sK980 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK980 )
=> ( subset @ Y0 @ sK980 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f6528]) ).
thf(f6528,plain,
( $true
= ( ^ [Y0: $i] :
( ( wellorderedByIn @ Y0 )
& ( ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) )
@ Y0 ) )
@ sK980 ) ),
inference(definition_unfolding,[status(thm)],[f5201,f5551]) ).
thf(f5551,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( wellorderedByIn @ Y0 )
& ( ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f4899,f5320]) ).
thf(f5320,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f343]) ).
thf(f343,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f342]) ).
thf(f342,plain,
( ( ^ [X0: $i] :
! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) )
= transitiveset ),
inference(rectify,[status(thm)],[f331]) ).
thf(f331,axiom,
( ( ^ [X3: $i] :
! [X11: $i] :
( ( in @ X11 @ X3 )
=> ( subset @ X11 @ X3 ) ) )
= transitiveset ),
file('/export/starexec/sandbox/tmp/tmp.SkoTPvEhFx/DTF2THF_24321.p',transitiveset) ).
thf(f4899,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( wellorderedByIn @ Y0 )
& ( transitiveset @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f639]) ).
thf(f639,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( wellorderedByIn @ Y0 )
& ( transitiveset @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f638]) ).
thf(f638,plain,
( ( ^ [X0: $i] :
( ( transitiveset @ X0 )
& ( wellorderedByIn @ X0 ) ) )
= ordinal ),
inference(rectify,[status(thm)],[f338]) ).
thf(f338,axiom,
( ( ^ [X1: $i] :
( ( transitiveset @ X1 )
& ( wellorderedByIn @ X1 ) ) )
= ordinal ),
file('/export/starexec/sandbox/tmp/tmp.SkoTPvEhFx/DTF2THF_24321.p',ordinal) ).
thf(f5201,plain,
( ( ordinal @ sK980 )
= $true ),
inference(cnf_transformation,[status(thm)],[f3188]) ).
thf(f3188,plain,
( ( ex1I2 = $true )
& ( omega__Cong = $true )
& ( singletoninpowerset = $true )
& ( ksndsingleton = $true )
& ( woz13rule3 = $true )
& ( setminusILneg = $true )
& ( kfstpairEq = $true )
& ( woz1_1 = $true )
& ( exuEu = $true )
& ( subsetRefl = $true )
& ( peanoSinj = $true )
& ( image1I = $true )
& ( cartprodpairsurjEq = $true )
& ( binintersectSubset4 = $true )
& ( exuI3 = $true )
& ( secondinupair = $true )
& ( funcGraphProp1 = $true )
& ( binintersectSubset3 = $true )
& ( eqbreln = $true )
& ( sepInPowerset = $true )
& ( nonemptyE1 = $true )
& ( subsetI1 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( transitivesetOp1 = $true )
& ( apProp = $true )
& ( upairsetE = $true )
& ( setunionAx = $true )
& ( breln1unionI = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( foundationAx = $true )
& ( funcextLem = $true )
& ( setunionsingleton1 = $true )
& ( binunionTEcontra = $true )
& ( setadjoinIL = $true )
& ( binintersectSubset1 = $true )
& ( cartprodfstpairEq = $true )
& ( complementTE1 = $true )
& ( ( ordinal @ sK980 )
= $true )
& ( ( transitiveset @ ( binintersect @ sK980 @ sK981 ) )
!= $true )
& ( ( ordinal @ sK981 )
= $true )
& ( upairsetIR = $true )
& ( breln1compI = $true )
& ( exuE3u = $true )
& ( notdallE = $true )
& ( setukpairIR = $true )
& ( doubleComplementSub2 = $true )
& ( woz2A = $true )
& ( omegaSAx = $true )
& ( doubleComplementE1 = $true )
& ( dpsetconstrERa = $true )
& ( sepSubset = $true )
& ( contrasubsetT1 = $true )
& ( woz2Ex = $true )
& ( lam2lamEq = $true )
& ( cartprodpairin = $true )
& ( lamp = $true )
& ( cartprodsndpairEq = $true )
& ( ap2apEq2 = $true )
& ( singletonprop = $true )
& ( breln1unionE = $true )
& ( setextT = $true )
& ( omega0Ax = $true )
& ( doubleComplementI1 = $true )
& ( quantDeMorgan4 = $true )
& ( breln1unionEcases = $true )
& ( notdexE = $true )
& ( eqimpsubset2 = $true )
& ( setextAx = $true )
& ( image1Equiv = $true )
& ( ubforcartprodlem2 = $true )
& ( vacuousDall = $true )
& ( setminusIRneg = $true )
& ( breln1all2 = $true )
& ( replAx = $true )
& ( setminusSubset1 = $true )
& ( binunionIL = $true )
& ( setext = $true )
& ( contrasubsetT3 = $true )
& ( binunionLsub = $true )
& ( contrasubsetT = $true )
& ( setukpairinjL = $true )
& ( exuE2 = $true )
& ( iftrue = $true )
& ( setminusERneg = $true )
& ( woz2B = $true )
& ( setukpairinjR11 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( setminusSubset2 = $true )
& ( cartprodmempaircEq = $true )
& ( binintersectLsub = $true )
& ( funcImageSingleton = $true )
& ( bs114d = $true )
& ( binintersectER = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( dpsetconstrSub = $true )
& ( kpairsurjEq = $true )
& ( breln1invE = $true )
& ( eqinunit = $true )
& ( injFuncSetFuncInj = $true )
& ( demorgan2b = $true )
& ( cartprodfstin = $true )
& ( funcGraphProp4 = $true )
& ( ex1I = $true )
& ( ap2p = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( image1Ex = $true )
& ( exuI2 = $true )
& ( notinself = $true )
& ( emptyset__Cong = $true )
& ( binunionEcases = $true )
& ( dpsetconstrEL2 = $true )
& ( cartprodpairmemER = $true )
& ( lam2p = $true )
& ( inCongP = $true )
& ( setukpairinjR1 = $true )
& ( prop2setE = $true )
& ( binunionRsub = $true )
& ( ifSingleton = $true )
& ( inPowerset = $true )
& ( woz2W = $true )
& ( iffalseProp1 = $true )
& ( ex1E1 = $true )
& ( setunionE2 = $true )
& ( funcext = $true )
& ( singletonsubset = $true )
& ( uniqinunit = $true )
& ( woz13rule2 = $true )
& ( notinsingleton = $true )
& ( woz1_4 = $true )
& ( setminusI = $true )
& ( powersetsubset = $true )
& ( complementSubsetComplementIntersect = $true )
& ( powerset__Cong = $true )
& ( dpsetconstrI = $true )
& ( inIntersectImpInUnion = $true )
& ( woz1_2 = $true )
& ( surjFuncSetFuncSurj = $true )
& ( subsetE = $true )
& ( quantDeMorgan1 = $true )
& ( iftrueorfalse = $true )
& ( theeq = $true )
& ( cartprodmempair1 = $true )
& ( wellorderingAx = $true )
& ( quantDeMorgan2 = $true )
& ( demorgan2 = $true )
& ( powersetI = $true )
& ( funcGraphProp2 = $true )
& ( setukpairinjR12 = $true )
& ( symdiffI2 = $true )
& ( setukpairinjR2 = $true )
& ( subsetI2 = $true )
& ( subsetemptysetimpeq = $true )
& ( emptyI = $true )
& ( setukpairinjL2 = $true )
& ( beta1 = $true )
& ( surjCantorThm = $true )
& ( setminusEL = $true )
& ( demorgan2b2 = $true )
& ( notinemptyset = $true )
& ( powersetAx = $true )
& ( notinself2 = $true )
& ( powersetTI1 = $true )
& ( binintersectRsub = $true )
& ( subbreln = $true )
& ( upairsetIL = $true )
& ( subsetE2 = $true )
& ( kpairp = $true )
& ( doubleComplementSub1 = $true )
& ( notsubsetI = $true )
& ( binintersectEL = $true )
& ( setOfPairsIsBReln = $true )
& ( doubleComplementEq = $true )
& ( iffalse = $true )
& ( notequalI2 = $true )
& ( emptysetsubset = $true )
& ( upairequniteq = $true )
& ( dsetconstrI = $true )
& ( setunionE = $true )
& ( nonemptyImpWitness = $true )
& ( powersetE1 = $true )
& ( binunionIR = $true )
& ( binunionTIRcontra = $true )
& ( setadjoinIR = $true )
& ( demorgan2a1 = $true )
& ( noeltsimpempty = $true )
& ( funcext2 = $true )
& ( ifp = $true )
& ( breln1all1 = $true )
& ( nonemptyI1 = $true )
& ( surjFuncSetFuncIn = $true )
& ( injFuncInInjFuncSet = $true )
& ( setadjoinAx = $true )
& ( ap2apEq1 = $true )
& ( symdiffE = $true )
& ( binintersectSubset5 = $true )
& ( powersetTE1 = $true )
& ( woz1_3 = $true )
& ( funcGraphProp3 = $true )
& ( symdiffI1 = $true )
& ( kfstsingleton = $true )
& ( setminusLsub = $true )
& ( iftrueProp2 = $true )
& ( breln1compE = $true )
& ( setminusER = $true )
& ( ex1E2 = $true )
& ( beta2 = $true )
& ( eta2 = $true )
& ( upairsubunion = $true )
& ( exuE1 = $true )
& ( ubforcartprodlem3 = $true )
& ( theprop = $true )
& ( binunionE = $true )
& ( emptysetimpfalse = $true )
& ( complementTcontraSubset = $true )
& ( brelnall1 = $true )
& ( upairset2IR = $true )
& ( binintTransitive = $true )
& ( prop2setI = $true )
& ( funcinfuncset = $true )
& ( infuncsetfunc = $true )
& ( breln1compprop = $true )
& ( setunionTransitive = $true )
& ( woz13rule4 = $true )
& ( nonemptyI = $true )
& ( descrp = $true )
& ( ksndpairEq = $true )
& ( woz13rule0 = $true )
& ( setextsub = $true )
& ( breln1invprop = $true )
& ( symdiffIneg1 = $true )
& ( powersetI1 = $true )
& ( setukpairinjL1 = $true )
& ( setunionsingleton2 = $true )
& ( exuI1 = $true )
& ( omegaSclos = $true )
& ( breln1unionCommutes = $true )
& ( singletonsuniq = $true )
& ( iftrueProp1 = $true )
& ( powersetE = $true )
& ( subsetTrans = $true )
& ( setoftrueEq = $true )
& ( woz1_5 = $true )
& ( image1E = $true )
& ( emptyinPowerset = $true )
& ( breln1unionIR = $true )
& ( exu__Cong = $true )
& ( upairinpowunion = $true )
& ( emptyinunitempty = $true )
& ( contraSubsetComplement = $true )
& ( foundation2 = $true )
& ( emptyE1 = $true )
& ( dsetconstr__Cong = $true )
& ( singletoninpowunion = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( setunionI = $true )
& ( setadjoinSub2 = $true )
& ( setOfPairsIsBReln1 = $true )
& ( setukpairIL = $true )
& ( setbeta = $true )
& ( brelnall2 = $true )
& ( subset2powerset = $true )
& ( contrasubsetT2 = $true )
& ( setadjoinOr = $true )
& ( breln1SetBreln1 = $true )
& ( cartprodmempair = $true )
& ( lamProp = $true )
& ( subPowSU = $true )
& ( setadjoinSub = $true )
& ( binintersectT_lem = $true )
& ( setadjoin__Cong = $true )
& ( binintersectTELcontra = $true )
& ( emptysetAx = $true )
& ( transitivesetOp2 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( iffalseProp2 = $true )
& ( descr__Cong = $true )
& ( symdiffIneg2 = $true )
& ( demorgan1a = $true )
& ( breln1invI = $true )
& ( binintersectI = $true )
& ( demorgan1 = $true )
& ( leftInvIsSurj = $true )
& ( notequalI1 = $true )
& ( setminusT_lem = $true )
& ( peano0notS = $true )
& ( binunionT_lem = $true )
& ( complementImpComplementIntersect = $true )
& ( emptyInPowerset = $true )
& ( setunionsingleton = $true )
& ( demorgan2a = $true )
& ( eta1 = $true )
& ( eqimpsubset1 = $true )
& ( disjointsetsI1 = $true )
& ( binunionTILcontra = $true )
& ( subsetTI = $true )
& ( breln1unionIL = $true )
& ( singletonsswitch = $true )
& ( eqbreln1 = $true )
& ( quantDeMorgan3 = $true )
& ( dpsetconstrER = $true )
& ( setukpairinjR = $true )
& ( kpairiskpair = $true )
& ( emptysetE = $true )
& ( cartprodsndin = $true )
& ( setunion__Cong = $true )
& ( exuE3e = $true )
& ( setadjoinE = $true )
& ( complementTI1 = $true )
& ( omegaIndAx = $true )
& ( breln1compEex = $true )
& ( injFuncSetFuncIn = $true )
& ( prop2set2propI = $true )
& ( binintersectTERcontra = $true )
& ( complementTnotintersectT = $true )
& ( dpsetconstrEL1 = $true )
& ( subbreln1 = $true )
& ( image1Ex1 = $true )
& ( breln1unionprop = $true )
& ( complementT_lem = $true )
& ( app = $true )
& ( omegaSp = $true )
& ( upairset2E = $true )
& ( demorgan1b = $true )
& ( choice2fnsingleton = $true )
& ( ubforcartprodlem1 = $true )
& ( binunionTE = $true )
& ( powersetT_lem = $true )
& ( woz13rule1 = $true )
& ( demorgan2a2 = $true )
& ( binintersectSubset2 = $true )
& ( setminusELneg = $true )
& ( cartprodpairmemEL = $true )
& ( in__Cong = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK980,sK981])],[f1360,f3187,f3186]) ).
thf(f3186,plain,
( ? [X0: $i] :
( ( $true
= ( ordinal @ X0 ) )
& ? [X1: $i] :
( ( $true
!= ( transitiveset @ ( binintersect @ X0 @ X1 ) ) )
& ( $true
= ( ordinal @ X1 ) ) ) )
=> ( ( ( ordinal @ sK980 )
= $true )
& ? [X1: $i] :
( ( ( transitiveset @ ( binintersect @ sK980 @ X1 ) )
!= $true )
& ( $true
= ( ordinal @ X1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f3187,plain,
( ? [X1: $i] :
( ( ( transitiveset @ ( binintersect @ sK980 @ X1 ) )
!= $true )
& ( $true
= ( ordinal @ X1 ) ) )
=> ( ( ( transitiveset @ ( binintersect @ sK980 @ sK981 ) )
!= $true )
& ( ( ordinal @ sK981 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1360,plain,
( ( ex1I2 = $true )
& ( omega__Cong = $true )
& ( singletoninpowerset = $true )
& ( ksndsingleton = $true )
& ( woz13rule3 = $true )
& ( setminusILneg = $true )
& ( kfstpairEq = $true )
& ( woz1_1 = $true )
& ( exuEu = $true )
& ( subsetRefl = $true )
& ( peanoSinj = $true )
& ( image1I = $true )
& ( cartprodpairsurjEq = $true )
& ( binintersectSubset4 = $true )
& ( exuI3 = $true )
& ( secondinupair = $true )
& ( funcGraphProp1 = $true )
& ( binintersectSubset3 = $true )
& ( eqbreln = $true )
& ( sepInPowerset = $true )
& ( nonemptyE1 = $true )
& ( subsetI1 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( transitivesetOp1 = $true )
& ( apProp = $true )
& ( upairsetE = $true )
& ( setunionAx = $true )
& ( breln1unionI = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( foundationAx = $true )
& ( funcextLem = $true )
& ( setunionsingleton1 = $true )
& ( binunionTEcontra = $true )
& ( setadjoinIL = $true )
& ( binintersectSubset1 = $true )
& ( cartprodfstpairEq = $true )
& ( complementTE1 = $true )
& ? [X0: $i] :
( ( $true
= ( ordinal @ X0 ) )
& ? [X1: $i] :
( ( $true
!= ( transitiveset @ ( binintersect @ X0 @ X1 ) ) )
& ( $true
= ( ordinal @ X1 ) ) ) )
& ( upairsetIR = $true )
& ( breln1compI = $true )
& ( exuE3u = $true )
& ( notdallE = $true )
& ( setukpairIR = $true )
& ( doubleComplementSub2 = $true )
& ( woz2A = $true )
& ( omegaSAx = $true )
& ( doubleComplementE1 = $true )
& ( dpsetconstrERa = $true )
& ( sepSubset = $true )
& ( contrasubsetT1 = $true )
& ( woz2Ex = $true )
& ( lam2lamEq = $true )
& ( cartprodpairin = $true )
& ( lamp = $true )
& ( cartprodsndpairEq = $true )
& ( ap2apEq2 = $true )
& ( singletonprop = $true )
& ( breln1unionE = $true )
& ( setextT = $true )
& ( omega0Ax = $true )
& ( doubleComplementI1 = $true )
& ( quantDeMorgan4 = $true )
& ( breln1unionEcases = $true )
& ( notdexE = $true )
& ( eqimpsubset2 = $true )
& ( setextAx = $true )
& ( image1Equiv = $true )
& ( ubforcartprodlem2 = $true )
& ( vacuousDall = $true )
& ( setminusIRneg = $true )
& ( breln1all2 = $true )
& ( replAx = $true )
& ( setminusSubset1 = $true )
& ( binunionIL = $true )
& ( setext = $true )
& ( contrasubsetT3 = $true )
& ( binunionLsub = $true )
& ( contrasubsetT = $true )
& ( setukpairinjL = $true )
& ( exuE2 = $true )
& ( iftrue = $true )
& ( setminusERneg = $true )
& ( woz2B = $true )
& ( setukpairinjR11 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( setminusSubset2 = $true )
& ( cartprodmempaircEq = $true )
& ( binintersectLsub = $true )
& ( funcImageSingleton = $true )
& ( bs114d = $true )
& ( binintersectER = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( dpsetconstrSub = $true )
& ( kpairsurjEq = $true )
& ( breln1invE = $true )
& ( eqinunit = $true )
& ( injFuncSetFuncInj = $true )
& ( demorgan2b = $true )
& ( cartprodfstin = $true )
& ( funcGraphProp4 = $true )
& ( ex1I = $true )
& ( ap2p = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( image1Ex = $true )
& ( exuI2 = $true )
& ( notinself = $true )
& ( emptyset__Cong = $true )
& ( binunionEcases = $true )
& ( dpsetconstrEL2 = $true )
& ( cartprodpairmemER = $true )
& ( lam2p = $true )
& ( inCongP = $true )
& ( setukpairinjR1 = $true )
& ( prop2setE = $true )
& ( binunionRsub = $true )
& ( ifSingleton = $true )
& ( inPowerset = $true )
& ( woz2W = $true )
& ( iffalseProp1 = $true )
& ( ex1E1 = $true )
& ( setunionE2 = $true )
& ( funcext = $true )
& ( singletonsubset = $true )
& ( uniqinunit = $true )
& ( woz13rule2 = $true )
& ( notinsingleton = $true )
& ( woz1_4 = $true )
& ( setminusI = $true )
& ( powersetsubset = $true )
& ( complementSubsetComplementIntersect = $true )
& ( powerset__Cong = $true )
& ( dpsetconstrI = $true )
& ( inIntersectImpInUnion = $true )
& ( woz1_2 = $true )
& ( surjFuncSetFuncSurj = $true )
& ( subsetE = $true )
& ( quantDeMorgan1 = $true )
& ( iftrueorfalse = $true )
& ( theeq = $true )
& ( cartprodmempair1 = $true )
& ( wellorderingAx = $true )
& ( quantDeMorgan2 = $true )
& ( demorgan2 = $true )
& ( powersetI = $true )
& ( funcGraphProp2 = $true )
& ( setukpairinjR12 = $true )
& ( symdiffI2 = $true )
& ( setukpairinjR2 = $true )
& ( subsetI2 = $true )
& ( subsetemptysetimpeq = $true )
& ( emptyI = $true )
& ( setukpairinjL2 = $true )
& ( beta1 = $true )
& ( surjCantorThm = $true )
& ( setminusEL = $true )
& ( demorgan2b2 = $true )
& ( notinemptyset = $true )
& ( powersetAx = $true )
& ( notinself2 = $true )
& ( powersetTI1 = $true )
& ( binintersectRsub = $true )
& ( subbreln = $true )
& ( upairsetIL = $true )
& ( subsetE2 = $true )
& ( kpairp = $true )
& ( doubleComplementSub1 = $true )
& ( notsubsetI = $true )
& ( binintersectEL = $true )
& ( setOfPairsIsBReln = $true )
& ( doubleComplementEq = $true )
& ( iffalse = $true )
& ( notequalI2 = $true )
& ( emptysetsubset = $true )
& ( upairequniteq = $true )
& ( dsetconstrI = $true )
& ( setunionE = $true )
& ( nonemptyImpWitness = $true )
& ( powersetE1 = $true )
& ( binunionIR = $true )
& ( binunionTIRcontra = $true )
& ( setadjoinIR = $true )
& ( demorgan2a1 = $true )
& ( noeltsimpempty = $true )
& ( funcext2 = $true )
& ( ifp = $true )
& ( breln1all1 = $true )
& ( nonemptyI1 = $true )
& ( surjFuncSetFuncIn = $true )
& ( injFuncInInjFuncSet = $true )
& ( setadjoinAx = $true )
& ( ap2apEq1 = $true )
& ( symdiffE = $true )
& ( binintersectSubset5 = $true )
& ( powersetTE1 = $true )
& ( woz1_3 = $true )
& ( funcGraphProp3 = $true )
& ( symdiffI1 = $true )
& ( kfstsingleton = $true )
& ( setminusLsub = $true )
& ( iftrueProp2 = $true )
& ( breln1compE = $true )
& ( setminusER = $true )
& ( ex1E2 = $true )
& ( beta2 = $true )
& ( eta2 = $true )
& ( upairsubunion = $true )
& ( exuE1 = $true )
& ( ubforcartprodlem3 = $true )
& ( theprop = $true )
& ( binunionE = $true )
& ( emptysetimpfalse = $true )
& ( complementTcontraSubset = $true )
& ( brelnall1 = $true )
& ( upairset2IR = $true )
& ( binintTransitive = $true )
& ( prop2setI = $true )
& ( funcinfuncset = $true )
& ( infuncsetfunc = $true )
& ( breln1compprop = $true )
& ( setunionTransitive = $true )
& ( woz13rule4 = $true )
& ( nonemptyI = $true )
& ( descrp = $true )
& ( ksndpairEq = $true )
& ( woz13rule0 = $true )
& ( setextsub = $true )
& ( breln1invprop = $true )
& ( symdiffIneg1 = $true )
& ( powersetI1 = $true )
& ( setukpairinjL1 = $true )
& ( setunionsingleton2 = $true )
& ( exuI1 = $true )
& ( omegaSclos = $true )
& ( breln1unionCommutes = $true )
& ( singletonsuniq = $true )
& ( iftrueProp1 = $true )
& ( powersetE = $true )
& ( subsetTrans = $true )
& ( setoftrueEq = $true )
& ( woz1_5 = $true )
& ( image1E = $true )
& ( emptyinPowerset = $true )
& ( breln1unionIR = $true )
& ( exu__Cong = $true )
& ( upairinpowunion = $true )
& ( emptyinunitempty = $true )
& ( contraSubsetComplement = $true )
& ( foundation2 = $true )
& ( emptyE1 = $true )
& ( dsetconstr__Cong = $true )
& ( singletoninpowunion = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( setunionI = $true )
& ( setadjoinSub2 = $true )
& ( setOfPairsIsBReln1 = $true )
& ( setukpairIL = $true )
& ( setbeta = $true )
& ( brelnall2 = $true )
& ( subset2powerset = $true )
& ( contrasubsetT2 = $true )
& ( setadjoinOr = $true )
& ( breln1SetBreln1 = $true )
& ( cartprodmempair = $true )
& ( lamProp = $true )
& ( subPowSU = $true )
& ( setadjoinSub = $true )
& ( binintersectT_lem = $true )
& ( setadjoin__Cong = $true )
& ( binintersectTELcontra = $true )
& ( emptysetAx = $true )
& ( transitivesetOp2 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( iffalseProp2 = $true )
& ( descr__Cong = $true )
& ( symdiffIneg2 = $true )
& ( demorgan1a = $true )
& ( breln1invI = $true )
& ( binintersectI = $true )
& ( demorgan1 = $true )
& ( leftInvIsSurj = $true )
& ( notequalI1 = $true )
& ( setminusT_lem = $true )
& ( peano0notS = $true )
& ( binunionT_lem = $true )
& ( complementImpComplementIntersect = $true )
& ( emptyInPowerset = $true )
& ( setunionsingleton = $true )
& ( demorgan2a = $true )
& ( eta1 = $true )
& ( eqimpsubset1 = $true )
& ( disjointsetsI1 = $true )
& ( binunionTILcontra = $true )
& ( subsetTI = $true )
& ( breln1unionIL = $true )
& ( singletonsswitch = $true )
& ( eqbreln1 = $true )
& ( quantDeMorgan3 = $true )
& ( dpsetconstrER = $true )
& ( setukpairinjR = $true )
& ( kpairiskpair = $true )
& ( emptysetE = $true )
& ( cartprodsndin = $true )
& ( setunion__Cong = $true )
& ( exuE3e = $true )
& ( setadjoinE = $true )
& ( complementTI1 = $true )
& ( omegaIndAx = $true )
& ( breln1compEex = $true )
& ( injFuncSetFuncIn = $true )
& ( prop2set2propI = $true )
& ( binintersectTERcontra = $true )
& ( complementTnotintersectT = $true )
& ( dpsetconstrEL1 = $true )
& ( subbreln1 = $true )
& ( image1Ex1 = $true )
& ( breln1unionprop = $true )
& ( complementT_lem = $true )
& ( app = $true )
& ( omegaSp = $true )
& ( upairset2E = $true )
& ( demorgan1b = $true )
& ( choice2fnsingleton = $true )
& ( ubforcartprodlem1 = $true )
& ( binunionTE = $true )
& ( powersetT_lem = $true )
& ( woz13rule1 = $true )
& ( demorgan2a2 = $true )
& ( binintersectSubset2 = $true )
& ( setminusELneg = $true )
& ( cartprodpairmemEL = $true )
& ( in__Cong = $true ) ),
inference(flattening,[status(thm)],[f1359]) ).
thf(f1359,plain,
( ? [X0: $i] :
( ( $true
= ( ordinal @ X0 ) )
& ? [X1: $i] :
( ( $true
!= ( transitiveset @ ( binintersect @ X0 @ X1 ) ) )
& ( $true
= ( ordinal @ X1 ) ) ) )
& ( setunionTransitive = $true )
& ( transitivesetOp2 = $true )
& ( 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)],[f971]) ).
thf(f971,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 )
=> ( ( transitivesetOp2 = $true )
=> ( ( setunionTransitive = $true )
=> ! [X0: $i] :
( ( $true
= ( ordinal @ X0 ) )
=> ! [X1: $i] :
( ( $true
= ( ordinal @ X1 ) )
=> ( $true
= ( transitiveset @ ( binintersect @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f970]) ).
thf(f970,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
=> ( transitivesetOp2
=> ( setunionTransitive
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i] :
( ( ordinal @ X1 )
=> ( transitiveset @ ( binintersect @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f340]) ).
thf(f340,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
=> ( transitivesetOp2
=> ( setunionTransitive
=> ! [X11: $i] :
( ( ordinal @ X11 )
=> ! [X16: $i] :
( ( ordinal @ X16 )
=> ( transitiveset @ ( binintersect @ X11 @ X16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f339]) ).
thf(f339,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
=> ( transitivesetOp2
=> ( setunionTransitive
=> ! [X11: $i] :
( ( ordinal @ X11 )
=> ! [X16: $i] :
( ( ordinal @ X16 )
=> ( transitiveset @ ( binintersect @ X11 @ X16 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SkoTPvEhFx/DTF2THF_24321.p',ordinalMinLem1) ).
thf(f9786,plain,
( ( ( subset @ sK1190 @ sK980 )
!= $true )
| spl1189_219 ),
inference(avatar_component_clause,[status(thm)],[f9785]) ).
thf(f9785,definition,
( spl1189_219
<=> ( ( subset @ sK1190 @ sK980 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1189_219])],[avatar_definition]) ).
thf(f8933,plain,
( ( in @ sK1190 @ sK980 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f8925]) ).
thf(f8925,plain,
( ( ( in @ sK1190 @ sK980 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f7304,f6846]) ).
thf(f6846,plain,
( $true
= ( in @ sK1190 @ ( binintersect @ sK980 @ sK981 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f6844]) ).
thf(f6844,plain,
( $false
= ( ( in @ sK1190 @ ( binintersect @ sK980 @ sK981 ) )
=> ( subset @ sK1190 @ ( binintersect @ sK980 @ sK981 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f6843]) ).
thf(f6843,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( binintersect @ sK980 @ sK981 ) )
=> ( subset @ Y0 @ ( binintersect @ sK980 @ sK981 ) ) )
@ sK1190 ) ),
inference(sigma_clausification,[status(thm)],[f6842]) ).
thf(f6842,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( binintersect @ sK980 @ sK981 ) )
=> ( subset @ Y0 @ ( binintersect @ sK980 @ sK981 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f6529]) ).
thf(f6529,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) )
@ ( binintersect @ sK980 @ sK981 ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f5200,f5320]) ).
thf(f5200,plain,
( ( transitiveset @ ( binintersect @ sK980 @ sK981 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f3188]) ).
thf(f7304,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( binintersect @ X5 @ X4 ) ) )
| ( $true
= ( in @ X3 @ X5 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f5774]) ).
thf(f5774,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( binintersect @ X5 @ X4 ) ) )
| ( $true != $true )
| ( $true
= ( in @ X3 @ X5 ) ) ),
inference(definition_unfolding,[status(thm)],[f3803,f5069]) ).
thf(f5069,plain,
binintersectEL = $true,
inference(cnf_transformation,[status(thm)],[f3188]) ).
thf(f3803,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( binintersect @ X5 @ X4 ) ) )
| ( $true
= ( in @ X3 @ X5 ) )
| ( binintersectEL != $true ) ),
inference(cnf_transformation,[status(thm)],[f1960]) ).
thf(f1960,plain,
( ( ( binintersectEL = $true )
| ( ( $true
= ( in @ sK288 @ ( binintersect @ sK290 @ sK289 ) ) )
& ( $true
!= ( in @ sK288 @ sK290 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( binintersect @ X5 @ X4 ) ) )
| ( $true
= ( in @ X3 @ X5 ) ) )
| ( binintersectEL != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK288,sK289,sK290])],[f1958,f1959]) ).
thf(f1959,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( binintersect @ X2 @ X1 ) ) )
& ( $true
!= ( in @ X0 @ X2 ) ) )
=> ( ( $true
= ( in @ sK288 @ ( binintersect @ sK290 @ sK289 ) ) )
& ( $true
!= ( in @ sK288 @ sK290 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1958,plain,
( ( ( binintersectEL = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( binintersect @ X2 @ X1 ) ) )
& ( $true
!= ( in @ X0 @ X2 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( binintersect @ X5 @ X4 ) ) )
| ( $true
= ( in @ X3 @ X5 ) ) )
| ( binintersectEL != $true ) ) ),
inference(rectify,[status(thm)],[f1957]) ).
thf(f1957,plain,
( ( ( binintersectEL = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( binintersect @ X2 @ X1 ) ) )
& ( $true
!= ( in @ X0 @ X2 ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ ( binintersect @ X2 @ X1 ) ) )
| ( $true
= ( in @ X0 @ X2 ) ) )
| ( binintersectEL != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f1277]) ).
thf(f1277,plain,
( ( binintersectEL = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ ( binintersect @ X2 @ X1 ) ) )
| ( $true
= ( in @ X0 @ X2 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f789]) ).
thf(f789,plain,
( ( binintersectEL = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( binintersect @ X2 @ X1 ) ) )
=> ( $true
= ( in @ X0 @ X2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f788]) ).
thf(f788,plain,
( binintersectEL
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( binintersect @ X2 @ X1 ) )
=> ( in @ X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f110]) ).
thf(f110,axiom,
( binintersectEL
= ( ! [X1: $i,X4: $i,X3: $i] :
( ( in @ X1 @ ( binintersect @ X3 @ X4 ) )
=> ( in @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SkoTPvEhFx/DTF2THF_24321.p',binintersectEL) ).
thf(f10357,plain,
spl1189_218,
inference(avatar_contradiction_clause,[status(thm)],[f10356]) ).
thf(f10356,plain,
( $false
| spl1189_218 ),
inference(trivial_inequality_removal,[status(thm)],[f10346]) ).
thf(f10346,plain,
( ( $false = $true )
| spl1189_218 ),
inference(backward_demodulation,[status(thm)],[f8876,f10323]) ).
thf(f10323,plain,
( ( ( in @ sK1190 @ sK981 )
= $false )
| spl1189_218 ),
inference(trivial_inequality_removal,[status(thm)],[f10317]) ).
thf(f10317,plain,
( ( ( in @ sK1190 @ sK981 )
= $false )
| ( $true != $true )
| spl1189_218 ),
inference(superposition,[status(thm)],[f9783,f7141]) ).
thf(f7141,plain,
! [X1: $i] :
( ( $true
= ( subset @ X1 @ sK981 ) )
| ( $false
= ( in @ X1 @ sK981 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f7140]) ).
thf(f7140,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ sK981 )
=> ( subset @ X1 @ sK981 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f7139]) ).
thf(f7139,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK981 )
=> ( subset @ Y0 @ sK981 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f7137]) ).
thf(f7137,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK981 )
=> ( subset @ Y0 @ sK981 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f7136]) ).
thf(f7136,plain,
( ( ( wellorderedByIn @ sK981 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK981 )
=> ( subset @ Y0 @ sK981 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f6530]) ).
thf(f6530,plain,
( ( ^ [Y0: $i] :
( ( wellorderedByIn @ Y0 )
& ( ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) )
@ Y0 ) )
@ sK981 )
= $true ),
inference(definition_unfolding,[status(thm)],[f5199,f5551]) ).
thf(f5199,plain,
( ( ordinal @ sK981 )
= $true ),
inference(cnf_transformation,[status(thm)],[f3188]) ).
thf(f9783,plain,
( ( $true
!= ( subset @ sK1190 @ sK981 ) )
| spl1189_218 ),
inference(avatar_component_clause,[status(thm)],[f9782]) ).
thf(f9782,definition,
( spl1189_218
<=> ( $true
= ( subset @ sK1190 @ sK981 ) ) ),
introduced(definition,[new_symbols(naming,[spl1189_218])],[avatar_definition]) ).
thf(f8876,plain,
( ( in @ sK1190 @ sK981 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f8870]) ).
thf(f8870,plain,
( ( ( in @ sK1190 @ sK981 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f7072,f6846]) ).
thf(f7072,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( binintersect @ X3 @ X4 ) )
!= $true )
| ( ( in @ X5 @ X4 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f6218]) ).
thf(f6218,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( ( in @ X5 @ ( binintersect @ X3 @ X4 ) )
!= $true )
| ( ( in @ X5 @ X4 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f4426,f5146]) ).
thf(f5146,plain,
binintersectER = $true,
inference(cnf_transformation,[status(thm)],[f3188]) ).
thf(f4426,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
| ( ( in @ X5 @ ( binintersect @ X3 @ X4 ) )
!= $true )
| ( binintersectER != $true ) ),
inference(cnf_transformation,[status(thm)],[f2660]) ).
thf(f2660,plain,
( ( ( binintersectER = $true )
| ( ( ( in @ sK696 @ sK695 )
!= $true )
& ( $true
= ( in @ sK696 @ ( binintersect @ sK694 @ sK695 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
| ( ( in @ X5 @ ( binintersect @ X3 @ X4 ) )
!= $true ) )
| ( binintersectER != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK694,sK695,sK696])],[f2658,f2659]) ).
thf(f2659,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
& ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true ) )
=> ( ( ( in @ sK696 @ sK695 )
!= $true )
& ( $true
= ( in @ sK696 @ ( binintersect @ sK694 @ sK695 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2658,plain,
( ( ( binintersectER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
& ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X4 )
= $true )
| ( ( in @ X5 @ ( binintersect @ X3 @ X4 ) )
!= $true ) )
| ( binintersectER != $true ) ) ),
inference(rectify,[status(thm)],[f2657]) ).
thf(f2657,plain,
( ( ( binintersectER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
& ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
| ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
!= $true ) )
| ( binintersectER != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f1204]) ).
thf(f1204,plain,
( ( binintersectER = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
| ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f903]) ).
thf(f903,plain,
( ( binintersectER = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true )
=> ( $true
= ( in @ X2 @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f902]) ).
thf(f902,plain,
( binintersectER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f114]) ).
thf(f114,axiom,
( binintersectER
= ( ! [X3: $i,X4: $i,X1: $i] :
( ( in @ X1 @ ( binintersect @ X3 @ X4 ) )
=> ( in @ X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SkoTPvEhFx/DTF2THF_24321.p',binintersectER) ).
thf(f9788,plain,
( ~ spl1189_218
| ~ spl1189_219 ),
inference(avatar_split_clause,[status(thm)],[f9777,f9785,f9782]) ).
thf(f9777,plain,
( ( $true
!= ( subset @ sK1190 @ sK981 ) )
| ( ( subset @ sK1190 @ sK980 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f9772]) ).
thf(f9772,plain,
( ( $true
!= ( subset @ sK1190 @ sK981 ) )
| ( ( subset @ sK1190 @ sK980 )
!= $true )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f6845,f6933]) ).
thf(f6933,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ ( binintersect @ X0 @ X2 ) ) )
| ( $true
!= ( subset @ X1 @ X0 ) )
| ( ( subset @ X1 @ X2 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f5765]) ).
thf(f5765,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ ( binintersect @ X0 @ X2 ) ) )
| ( ( subset @ X1 @ X2 )
!= $true )
| ( $true
!= ( subset @ X1 @ X0 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f3799,f5044]) ).
thf(f5044,plain,
binintersectSubset5 = $true,
inference(cnf_transformation,[status(thm)],[f3188]) ).
thf(f3799,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X1 @ X2 )
!= $true )
| ( $true
= ( subset @ X1 @ ( binintersect @ X0 @ X2 ) ) )
| ( $true
!= ( subset @ X1 @ X0 ) )
| ( binintersectSubset5 != $true ) ),
inference(cnf_transformation,[status(thm)],[f1952]) ).
thf(f1952,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X2 )
!= $true )
| ( $true
= ( subset @ X1 @ ( binintersect @ X0 @ X2 ) ) )
| ( $true
!= ( subset @ X1 @ X0 ) ) )
| ( binintersectSubset5 != $true ) )
& ( ( binintersectSubset5 = $true )
| ( ( $true
= ( subset @ sK284 @ sK285 ) )
& ( $true
!= ( subset @ sK284 @ ( binintersect @ sK283 @ sK285 ) ) )
& ( $true
= ( subset @ sK284 @ sK283 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK283,sK284,sK285])],[f1950,f1951]) ).
thf(f1951,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X4 @ X5 )
= $true )
& ( ( subset @ X4 @ ( binintersect @ X3 @ X5 ) )
!= $true )
& ( ( subset @ X4 @ X3 )
= $true ) )
=> ( ( $true
= ( subset @ sK284 @ sK285 ) )
& ( $true
!= ( subset @ sK284 @ ( binintersect @ sK283 @ sK285 ) ) )
& ( $true
= ( subset @ sK284 @ sK283 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1950,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X2 )
!= $true )
| ( $true
= ( subset @ X1 @ ( binintersect @ X0 @ X2 ) ) )
| ( $true
!= ( subset @ X1 @ X0 ) ) )
| ( binintersectSubset5 != $true ) )
& ( ( binintersectSubset5 = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X4 @ X5 )
= $true )
& ( ( subset @ X4 @ ( binintersect @ X3 @ X5 ) )
!= $true )
& ( ( subset @ X4 @ X3 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f1949]) ).
thf(f1949,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X2 )
!= $true )
| ( $true
= ( subset @ X1 @ ( binintersect @ X0 @ X2 ) ) )
| ( $true
!= ( subset @ X1 @ X0 ) ) )
| ( binintersectSubset5 != $true ) )
& ( ( binintersectSubset5 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X2 )
= $true )
& ( $true
!= ( subset @ X1 @ ( binintersect @ X0 @ X2 ) ) )
& ( $true
= ( subset @ X1 @ X0 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f1102]) ).
thf(f1102,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X2 )
!= $true )
| ( $true
= ( subset @ X1 @ ( binintersect @ X0 @ X2 ) ) )
| ( $true
!= ( subset @ X1 @ X0 ) ) )
<=> ( binintersectSubset5 = $true ) ),
inference(flattening,[status(thm)],[f1101]) ).
thf(f1101,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( subset @ X1 @ ( binintersect @ X0 @ X2 ) ) )
| ( ( subset @ X1 @ X2 )
!= $true )
| ( $true
!= ( subset @ X1 @ X0 ) ) )
<=> ( binintersectSubset5 = $true ) ),
inference(ennf_transformation,[status(thm)],[f551]) ).
thf(f551,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
=> ( ( ( subset @ X1 @ X2 )
= $true )
=> ( $true
= ( subset @ X1 @ ( binintersect @ X0 @ X2 ) ) ) ) )
<=> ( binintersectSubset5 = $true ) ),
inference(fool_elimination,[status(thm)],[f550]) ).
thf(f550,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
=> ( ( subset @ X1 @ X2 )
=> ( subset @ X1 @ ( binintersect @ X0 @ X2 ) ) ) )
= binintersectSubset5 ),
inference(rectify,[status(thm)],[f109]) ).
thf(f109,axiom,
! [X3: $i,X5: $i,X4: $i] :
( ( ( subset @ X5 @ X3 )
=> ( ( subset @ X5 @ X4 )
=> ( subset @ X5 @ ( binintersect @ X3 @ X4 ) ) ) )
= binintersectSubset5 ),
file('/export/starexec/sandbox/tmp/tmp.SkoTPvEhFx/DTF2THF_24321.p',binintersectSubset5) ).
thf(f6845,plain,
( ( subset @ sK1190 @ ( binintersect @ sK980 @ sK981 ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f6844]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU816^1 : 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
% 0.16/0.33 % Computer : n010.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:34:33 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SEU816^1 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.46 % Domain : Set Theory
% 0.29/0.46 % Problem : Ordinals
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English : (! X:i.ordinal X -> (! Y:i.ordinal Y ->
% 0.29/0.46 % transitiveset (binintersect X Y)))
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.29/0.46 % Source : [Bro08]
% 0.29/0.46 % Names : ZFC318g [Bro08]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % 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, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0, 1.00 v3.7.0
% 0.29/0.46 % Syntax : Number of formulae : 734 ( 338 unt; 395 typ; 338 def)
% 0.29/0.46 % Number of atoms : 2088 ( 485 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 335 ( 6 avg)
% 0.29/0.46 % Number of connectives : 4530 ( 78 ~; 17 |; 60 &;3286 @)
% 0.29/0.46 % ( 17 <=>;1072 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 340 ( 2 avg)
% 0.29/0.46 % Number of types : 2 ( 0 usr)
% 0.29/0.46 % Number of type conns : 194 ( 194 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 398 ( 395 usr; 336 con; 0-4 aty)
% 0.29/0.46 % Number of variables : 1176 ( 79 ^;1052 !; 45 ?;1176 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : http://mathgate.info/detsetitem.php?id=512
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(in_type,type,
% 0.29/0.46 in: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(exu_type,type,
% 0.29/0.46 exu: ( $i > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(exu,definition,
% 0.29/0.46 ( exu
% 0.29/0.46 = ( ^ [Xphi: $i > $o] :
% 0.29/0.46 ? [Xx: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 & ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setextAx_type,type,
% 0.29/0.46 setextAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setextAx,definition,
% 0.29/0.46 ( setextAx
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 <=> ( in @ Xx @ B ) )
% 0.29/0.46 => ( A = B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyset_type,type,
% 0.29/0.46 emptyset: $i ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetAx_type,type,
% 0.29/0.46 emptysetAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetAx,definition,
% 0.29/0.46 ( emptysetAx
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoin_type,type,
% 0.29/0.46 setadjoin: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinAx_type,type,
% 0.29/0.46 setadjoinAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinAx,definition,
% 0.29/0.46 ( setadjoinAx
% 0.29/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.46 <=> ( ( Xy = Xx )
% 0.29/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powerset_type,type,
% 0.29/0.46 powerset: $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(powersetAx_type,type,
% 0.29/0.46 powersetAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetAx,definition,
% 0.29/0.46 ( powersetAx
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.46 <=> ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunion_type,type,
% 0.29/0.46 setunion: $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(setunionAx_type,type,
% 0.29/0.46 setunionAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionAx,definition,
% 0.29/0.46 ( setunionAx
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.46 <=> ? [B: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omega_type,type,
% 0.29/0.46 omega: $i ).
% 0.29/0.46
% 0.29/0.46 thf(omega0Ax_type,type,
% 0.29/0.46 omega0Ax: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omega0Ax,definition,
% 0.29/0.46 ( omega0Ax
% 0.29/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omegaSAx_type,type,
% 0.29/0.46 omegaSAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omegaSAx,definition,
% 0.29/0.46 ( omegaSAx
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ omega )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omegaIndAx_type,type,
% 0.29/0.46 omegaIndAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omegaIndAx,definition,
% 0.29/0.46 ( omegaIndAx
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( ( in @ emptyset @ A )
% 0.29/0.46 & ! [Xx: $i] :
% 0.29/0.46 ( ( ( in @ Xx @ omega )
% 0.29/0.46 & ( in @ Xx @ A ) )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ omega )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(replAx_type,type,
% 0.29/0.46 replAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(replAx,definition,
% 0.29/0.46 ( replAx
% 0.29/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( exu
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.29/0.46 => ? [B: $i] :
% 0.29/0.46 ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 <=> ? [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(foundationAx_type,type,
% 0.29/0.46 foundationAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(foundationAx,definition,
% 0.29/0.46 ( foundationAx
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.29/0.46 => ? [B: $i] :
% 0.29/0.46 ( ( in @ B @ A )
% 0.29/0.46 & ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(wellorderingAx_type,type,
% 0.29/0.46 wellorderingAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(wellorderingAx,definition,
% 0.29/0.46 ( wellorderingAx
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ? [B: $i] :
% 0.29/0.46 ( ! [C: $i] :
% 0.29/0.46 ( ( in @ C @ B )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ C )
% 0.29/0.46 => ( in @ Xx @ A ) ) )
% 0.29/0.46 & ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( ( in @ Xx @ A )
% 0.29/0.46 & ( in @ Xy @ A ) )
% 0.29/0.46 => ( ! [C: $i] :
% 0.29/0.46 ( ( in @ C @ B )
% 0.29/0.46 => ( ( in @ Xx @ C )
% 0.29/0.46 <=> ( in @ Xy @ C ) ) )
% 0.29/0.46 => ( Xx = Xy ) ) )
% 0.29/0.46 & ! [C: $i,D: $i] :
% 0.29/0.46 ( ( ( in @ C @ B )
% 0.29/0.46 & ( in @ D @ B ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ C )
% 0.29/0.46 => ( in @ Xx @ D ) )
% 0.29/0.46 | ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ D )
% 0.29/0.46 => ( in @ Xx @ C ) ) ) )
% 0.29/0.46 & ! [C: $i] :
% 0.29/0.46 ( ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ C )
% 0.29/0.46 => ( in @ Xx @ A ) )
% 0.29/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.29/0.46 => ? [D: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ D @ B )
% 0.29/0.46 & ( in @ Xx @ C )
% 0.29/0.46 & ~ ? [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ D )
% 0.29/0.46 & ( in @ Xy @ C ) )
% 0.29/0.46 & ! [E: $i] :
% 0.29/0.46 ( ( in @ E @ B )
% 0.29/0.46 => ( ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ E )
% 0.29/0.46 => ( in @ Xy @ D ) )
% 0.29/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(descr_type,type,
% 0.29/0.46 descr: ( $i > $o ) > $i ).
% 0.29/0.46
% 0.29/0.46 thf(descrp_type,type,
% 0.29/0.46 descrp: $o ).
% 0.29/0.46
% 0.29/0.46 thf(descrp,definition,
% 0.29/0.46 ( descrp
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ( Xphi
% 0.29/0.46 @ ( descr
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstr_type,type,
% 0.29/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrI_type,type,
% 0.29/0.46 dsetconstrI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrI,definition,
% 0.29/0.46 ( dsetconstrI
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrEL_type,type,
% 0.29/0.46 dsetconstrEL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrEL,definition,
% 0.29/0.46 ( dsetconstrEL
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrER_type,type,
% 0.29/0.46 dsetconstrER: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrER,definition,
% 0.29/0.46 ( dsetconstrER
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE1_type,type,
% 0.29/0.46 exuE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE1,definition,
% 0.29/0.46 ( exuE1
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 & ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(prop2set_type,type,
% 0.29/0.46 prop2set: $o > $i ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setE_type,type,
% 0.29/0.46 prop2setE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setE,definition,
% 0.29/0.46 ( prop2setE
% 0.29/0.46 = ( ! [Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.29/0.46 => Xphi ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetE_type,type,
% 0.29/0.46 emptysetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetE,definition,
% 0.29/0.46 ( emptysetE
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ emptyset )
% 0.29/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetimpfalse_type,type,
% 0.29/0.46 emptysetimpfalse: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetimpfalse,definition,
% 0.29/0.46 ( emptysetimpfalse
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ emptyset )
% 0.29/0.46 => $false ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notinemptyset_type,type,
% 0.29/0.46 notinemptyset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notinemptyset,definition,
% 0.29/0.46 ( notinemptyset
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3e_type,type,
% 0.29/0.46 exuE3e: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3e,definition,
% 0.29/0.46 ( exuE3e
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setext_type,type,
% 0.29/0.46 setext: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setext,definition,
% 0.29/0.46 ( setext
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) )
% 0.29/0.46 => ( A = B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyI_type,type,
% 0.29/0.46 emptyI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyI,definition,
% 0.29/0.46 ( emptyI
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ A )
% 0.29/0.46 => ( A = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(noeltsimpempty_type,type,
% 0.29/0.46 noeltsimpempty: $o ).
% 0.29/0.46
% 0.29/0.46 thf(noeltsimpempty,definition,
% 0.29/0.46 ( noeltsimpempty
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ A )
% 0.29/0.46 => ( A = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setbeta_type,type,
% 0.29/0.46 setbeta: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setbeta,definition,
% 0.29/0.46 ( setbeta
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonempty_type,type,
% 0.29/0.46 nonempty: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonempty,definition,
% 0.29/0.46 ( nonempty
% 0.29/0.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyE1_type,type,
% 0.29/0.46 nonemptyE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyE1,definition,
% 0.29/0.46 ( nonemptyE1
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( nonempty @ A )
% 0.29/0.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI_type,type,
% 0.29/0.46 nonemptyI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI,definition,
% 0.29/0.46 ( nonemptyI
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( nonempty
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI1_type,type,
% 0.29/0.46 nonemptyI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI1,definition,
% 0.29/0.46 ( nonemptyI1
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.29/0.46 => ( nonempty @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIL_type,type,
% 0.29/0.46 setadjoinIL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIL,definition,
% 0.29/0.46 ( setadjoinIL
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinunitempty_type,type,
% 0.29/0.46 emptyinunitempty: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinunitempty,definition,
% 0.29/0.46 ( emptyinunitempty
% 0.29/0.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIR_type,type,
% 0.29/0.46 setadjoinIR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIR,definition,
% 0.29/0.46 ( setadjoinIR
% 0.29/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinE_type,type,
% 0.29/0.46 setadjoinE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinE,definition,
% 0.29/0.46 ( setadjoinE
% 0.29/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.46 => ! [Xphi: $o] :
% 0.29/0.46 ( ( ( Xy = Xx )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => ( ( ( in @ Xy @ A )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinOr_type,type,
% 0.29/0.46 setadjoinOr: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinOr,definition,
% 0.29/0.46 ( setadjoinOr
% 0.29/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.46 => ( ( Xy = Xx )
% 0.29/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setoftrueEq_type,type,
% 0.29/0.46 setoftrueEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setoftrueEq,definition,
% 0.29/0.46 ( setoftrueEq
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : $true )
% 0.29/0.46 = A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI_type,type,
% 0.29/0.46 powersetI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI,definition,
% 0.29/0.46 ( powersetI
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) )
% 0.29/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinPowerset_type,type,
% 0.29/0.46 emptyinPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinPowerset,definition,
% 0.29/0.46 ( emptyinPowerset
% 0.29/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyInPowerset_type,type,
% 0.29/0.46 emptyInPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyInPowerset,definition,
% 0.29/0.46 ( emptyInPowerset
% 0.29/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE_type,type,
% 0.29/0.46 powersetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE,definition,
% 0.29/0.46 ( powersetE
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionI_type,type,
% 0.29/0.46 setunionI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionI,definition,
% 0.29/0.46 ( setunionI
% 0.29/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( ( in @ B @ A )
% 0.29/0.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionE_type,type,
% 0.29/0.46 setunionE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionE,definition,
% 0.29/0.46 ( setunionE
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.46 => ! [Xphi: $o] :
% 0.29/0.46 ( ! [B: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( ( in @ B @ A )
% 0.29/0.46 => Xphi ) )
% 0.29/0.46 => Xphi ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subPowSU_type,type,
% 0.29/0.46 subPowSU: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subPowSU,definition,
% 0.29/0.46 ( subPowSU
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE2_type,type,
% 0.29/0.46 exuE2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE2,definition,
% 0.29/0.46 ( exuE2
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyImpWitness_type,type,
% 0.29/0.46 nonemptyImpWitness: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyImpWitness,definition,
% 0.29/0.46 ( nonemptyImpWitness
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( nonempty @ A )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & $true ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(uniqinunit_type,type,
% 0.29/0.46 uniqinunit: $o ).
% 0.29/0.46
% 0.29/0.46 thf(uniqinunit,definition,
% 0.29/0.46 ( uniqinunit
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notinsingleton_type,type,
% 0.29/0.46 notinsingleton: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notinsingleton,definition,
% 0.29/0.46 ( notinsingleton
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx != Xy )
% 0.29/0.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eqinunit_type,type,
% 0.29/0.46 eqinunit: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eqinunit,definition,
% 0.29/0.46 ( eqinunit
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsswitch_type,type,
% 0.29/0.46 singletonsswitch: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsswitch,definition,
% 0.29/0.46 ( singletonsswitch
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetE_type,type,
% 0.29/0.46 upairsetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetE,definition,
% 0.29/0.46 ( upairsetE
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.29/0.46 => ( ( Xz = Xx )
% 0.29/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetIL_type,type,
% 0.29/0.46 upairsetIL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetIL,definition,
% 0.29/0.46 ( upairsetIL
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetIR_type,type,
% 0.29/0.46 upairsetIR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetIR,definition,
% 0.29/0.46 ( upairsetIR
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyE1_type,type,
% 0.29/0.46 emptyE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyE1,definition,
% 0.29/0.46 ( emptyE1
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ( ( ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 = emptyset )
% 0.29/0.46 => $false ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(vacuousDall_type,type,
% 0.29/0.46 vacuousDall: $o ).
% 0.29/0.46
% 0.29/0.46 thf(vacuousDall,definition,
% 0.29/0.46 ( vacuousDall
% 0.29/0.46 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ emptyset )
% 0.29/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan1_type,type,
% 0.29/0.46 quantDeMorgan1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan1,definition,
% 0.29/0.46 ( quantDeMorgan1
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ~ ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan2_type,type,
% 0.29/0.46 quantDeMorgan2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan2,definition,
% 0.29/0.46 ( quantDeMorgan2
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ~ ( Xphi @ Xx ) )
% 0.29/0.46 => ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan3_type,type,
% 0.29/0.46 quantDeMorgan3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan3,definition,
% 0.29/0.46 ( quantDeMorgan3
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan4_type,type,
% 0.29/0.46 quantDeMorgan4: $o ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan4,definition,
% 0.29/0.46 ( quantDeMorgan4
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ~ ( Xphi @ Xx ) )
% 0.29/0.46 => ~ ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setI_type,type,
% 0.29/0.46 prop2setI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setI,definition,
% 0.29/0.46 ( prop2setI
% 0.29/0.46 = ( ! [Xphi: $o] :
% 0.29/0.46 ( Xphi
% 0.29/0.46 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(set2prop_type,type,
% 0.29/0.46 set2prop: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(prop2set2propI_type,type,
% 0.29/0.46 prop2set2propI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(prop2set2propI,definition,
% 0.29/0.46 ( prop2set2propI
% 0.29/0.46 = ( ! [Xphi: $o] :
% 0.29/0.46 ( Xphi
% 0.29/0.46 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notdexE_type,type,
% 0.29/0.46 notdexE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notdexE,definition,
% 0.29/0.46 ( notdexE
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notdallE_type,type,
% 0.29/0.46 notdallE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notdallE,definition,
% 0.29/0.46 ( notdallE
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ~ ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuI1_type,type,
% 0.29/0.46 exuI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuI1,definition,
% 0.29/0.46 ( exuI1
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 & ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) )
% 0.29/0.46 => ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuI3_type,type,
% 0.29/0.46 exuI3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuI3,definition,
% 0.29/0.46 ( exuI3
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.29/0.46 => ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) )
% 0.29/0.46 => ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuI2_type,type,
% 0.29/0.46 exuI2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuI2,definition,
% 0.29/0.46 ( exuI2
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] :
% 0.29/0.46 ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 <=> ( Xy = Xx ) )
% 0.29/0.46 => ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(inCongP_type,type,
% 0.29/0.46 inCongP: $o ).
% 0.29/0.46
% 0.29/0.46 thf(inCongP,definition,
% 0.29/0.46 ( inCongP
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(in__Cong_type,type,
% 0.29/0.46 in__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(in__Cong,definition,
% 0.29/0.46 ( in__Cong
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3u_type,type,
% 0.29/0.46 exuE3u: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3u,definition,
% 0.29/0.46 ( exuE3u
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exu__Cong_type,type,
% 0.29/0.46 exu__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exu__Cong,definition,
% 0.29/0.46 ( exu__Cong
% 0.29/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.29/0.46 => ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 <=> ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyset__Cong_type,type,
% 0.29/0.46 emptyset__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyset__Cong,definition,
% 0.29/0.46 ( emptyset__Cong
% 0.29/0.46 = ( emptyset = emptyset ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoin__Cong_type,type,
% 0.29/0.46 setadjoin__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoin__Cong,definition,
% 0.29/0.46 ( setadjoin__Cong
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ! [Xz: $i,Xu: $i] :
% 0.29/0.46 ( ( Xz = Xu )
% 0.29/0.46 => ( ( setadjoin @ Xx @ Xz )
% 0.29/0.46 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powerset__Cong_type,type,
% 0.29/0.46 powerset__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powerset__Cong,definition,
% 0.29/0.46 ( powerset__Cong
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ( ( powerset @ A )
% 0.29/0.46 = ( powerset @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunion__Cong_type,type,
% 0.29/0.46 setunion__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunion__Cong,definition,
% 0.29/0.46 ( setunion__Cong
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ( ( setunion @ A )
% 0.29/0.46 = ( setunion @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omega__Cong_type,type,
% 0.29/0.46 omega__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omega__Cong,definition,
% 0.29/0.46 ( omega__Cong
% 0.29/0.46 = ( omega = omega ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuEu_type,type,
% 0.29/0.46 exuEu: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuEu,definition,
% 0.29/0.46 ( exuEu
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(descr__Cong_type,type,
% 0.29/0.46 descr__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(descr__Cong,definition,
% 0.29/0.46 ( descr__Cong
% 0.29/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.29/0.46 => ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.29/0.46 => ( ( descr
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 = ( descr
% 0.29/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstr__Cong_type,type,
% 0.29/0.46 dsetconstr__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstr__Cong,definition,
% 0.29/0.46 ( dsetconstr__Cong
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( Xx = Xy )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.29/0.46 => ( ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 = ( dsetconstr @ B
% 0.29/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subset_type,type,
% 0.29/0.46 subset: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(disjoint_type,type,
% 0.29/0.46 disjoint: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(setsmeet_type,type,
% 0.29/0.46 setsmeet: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI1_type,type,
% 0.29/0.46 subsetI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI1,definition,
% 0.29/0.46 ( subsetI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eqimpsubset2_type,type,
% 0.29/0.46 eqimpsubset2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eqimpsubset2,definition,
% 0.29/0.46 ( eqimpsubset2
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eqimpsubset1_type,type,
% 0.29/0.46 eqimpsubset1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eqimpsubset1,definition,
% 0.29/0.46 ( eqimpsubset1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI2_type,type,
% 0.29/0.46 subsetI2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI2,definition,
% 0.29/0.46 ( subsetI2
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetsubset_type,type,
% 0.29/0.46 emptysetsubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetsubset,definition,
% 0.29/0.46 ( emptysetsubset
% 0.29/0.46 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE_type,type,
% 0.29/0.46 subsetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE,definition,
% 0.29/0.46 ( subsetE
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE2_type,type,
% 0.29/0.46 subsetE2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE2,definition,
% 0.29/0.46 ( subsetE2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notsubsetI_type,type,
% 0.29/0.46 notsubsetI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notsubsetI,definition,
% 0.29/0.46 ( notsubsetI
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notequalI1_type,type,
% 0.29/0.46 notequalI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notequalI1,definition,
% 0.29/0.46 ( notequalI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ~ ( subset @ A @ B )
% 0.29/0.46 => ( A != B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notequalI2_type,type,
% 0.29/0.46 notequalI2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notequalI2,definition,
% 0.29/0.46 ( notequalI2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ( A != B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetRefl_type,type,
% 0.29/0.46 subsetRefl: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetRefl,definition,
% 0.29/0.46 ( subsetRefl
% 0.29/0.46 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetTrans_type,type,
% 0.29/0.46 subsetTrans: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetTrans,definition,
% 0.29/0.46 ( subsetTrans
% 0.29/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( subset @ B @ C )
% 0.29/0.46 => ( subset @ A @ C ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinSub_type,type,
% 0.29/0.46 setadjoinSub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinSub,definition,
% 0.29/0.46 ( setadjoinSub
% 0.29/0.46 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinSub2_type,type,
% 0.29/0.46 setadjoinSub2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinSub2,definition,
% 0.29/0.46 ( setadjoinSub2
% 0.29/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subset2powerset_type,type,
% 0.29/0.46 subset2powerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subset2powerset,definition,
% 0.29/0.46 ( subset2powerset
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setextsub_type,type,
% 0.29/0.46 setextsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setextsub,definition,
% 0.29/0.46 ( setextsub
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( subset @ B @ A )
% 0.29/0.46 => ( A = B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetemptysetimpeq_type,type,
% 0.29/0.46 subsetemptysetimpeq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetemptysetimpeq,definition,
% 0.29/0.46 ( subsetemptysetimpeq
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( subset @ A @ emptyset )
% 0.29/0.46 => ( A = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI1_type,type,
% 0.29/0.46 powersetI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI1,definition,
% 0.29/0.46 ( powersetI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ B @ A )
% 0.29/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE1_type,type,
% 0.29/0.46 powersetE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE1,definition,
% 0.29/0.46 ( powersetE1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(inPowerset_type,type,
% 0.29/0.46 inPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(inPowerset,definition,
% 0.29/0.46 ( inPowerset
% 0.29/0.46 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetsubset_type,type,
% 0.29/0.46 powersetsubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetsubset,definition,
% 0.29/0.46 ( powersetsubset
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sepInPowerset_type,type,
% 0.29/0.46 sepInPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(sepInPowerset,definition,
% 0.29/0.46 ( sepInPowerset
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( in
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sepSubset_type,type,
% 0.29/0.46 sepSubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(sepSubset,definition,
% 0.29/0.46 ( sepSubset
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( subset
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunion_type,type,
% 0.29/0.46 binunion: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(binunionIL_type,type,
% 0.29/0.46 binunionIL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionIL,definition,
% 0.29/0.46 ( binunionIL
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairset2IR_type,type,
% 0.29/0.46 upairset2IR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairset2IR,definition,
% 0.29/0.46 ( upairset2IR
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionIR_type,type,
% 0.29/0.46 binunionIR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionIR,definition,
% 0.29/0.46 ( binunionIR
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionEcases_type,type,
% 0.29/0.46 binunionEcases: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionEcases,definition,
% 0.29/0.46 ( binunionEcases
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.29/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.29/0.46 => ( ( ( in @ Xx @ A )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => ( ( ( in @ Xx @ B )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionE_type,type,
% 0.29/0.46 binunionE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionE,definition,
% 0.29/0.46 ( binunionE
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionLsub_type,type,
% 0.29/0.46 binunionLsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionLsub,definition,
% 0.29/0.46 ( binunionLsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionRsub_type,type,
% 0.29/0.46 binunionRsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionRsub,definition,
% 0.29/0.46 ( binunionRsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersect_type,type,
% 0.29/0.46 binintersect: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectI_type,type,
% 0.29/0.46 binintersectI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectI,definition,
% 0.29/0.46 ( binintersectI
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset5_type,type,
% 0.29/0.46 binintersectSubset5: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset5,definition,
% 0.29/0.46 ( binintersectSubset5
% 0.29/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.46 ( ( subset @ C @ A )
% 0.29/0.46 => ( ( subset @ C @ B )
% 0.29/0.46 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectEL_type,type,
% 0.29/0.46 binintersectEL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectEL,definition,
% 0.29/0.46 ( binintersectEL
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectLsub_type,type,
% 0.29/0.46 binintersectLsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectLsub,definition,
% 0.29/0.46 ( binintersectLsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset2_type,type,
% 0.29/0.46 binintersectSubset2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset2,definition,
% 0.29/0.46 ( binintersectSubset2
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( binintersect @ A @ B )
% 0.29/0.46 = A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset3_type,type,
% 0.29/0.46 binintersectSubset3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset3,definition,
% 0.29/0.46 ( binintersectSubset3
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( ( binintersect @ A @ B )
% 0.29/0.46 = B )
% 0.29/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectER_type,type,
% 0.29/0.46 binintersectER: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectER,definition,
% 0.29/0.46 ( binintersectER
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.29/0.46 => ( in @ Xx @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(disjointsetsI1_type,type,
% 0.29/0.46 disjointsetsI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(disjointsetsI1,definition,
% 0.29/0.46 ( disjointsetsI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( in @ Xx @ B ) )
% 0.29/0.46 => ( ( binintersect @ A @ B )
% 0.29/0.46 = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectRsub_type,type,
% 0.29/0.46 binintersectRsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectRsub,definition,
% 0.29/0.46 ( binintersectRsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset4_type,type,
% 0.29/0.46 binintersectSubset4: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset4,definition,
% 0.29/0.46 ( binintersectSubset4
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ B @ A )
% 0.29/0.46 => ( ( binintersect @ A @ B )
% 0.29/0.46 = B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset1_type,type,
% 0.29/0.46 binintersectSubset1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset1,definition,
% 0.29/0.46 ( binintersectSubset1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( ( binintersect @ A @ B )
% 0.29/0.46 = A )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(bs114d_type,type,
% 0.29/0.46 bs114d: $o ).
% 0.29/0.46
% 0.29/0.46 thf(bs114d,definition,
% 0.29/0.46 ( bs114d
% 0.29/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.46 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.29/0.46 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(regular_type,type,
% 0.29/0.46 regular: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminus_type,type,
% 0.29/0.46 setminus: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(setminusI_type,type,
% 0.29/0.46 setminusI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusI,definition,
% 0.29/0.46 ( setminusI
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusEL_type,type,
% 0.29/0.46 setminusEL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusEL,definition,
% 0.29/0.46 ( setminusEL
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusER_type,type,
% 0.29/0.46 setminusER: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusER,definition,
% 0.29/0.46 ( setminusER
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.46 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusSubset2_type,type,
% 0.29/0.46 setminusSubset2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusSubset2,definition,
% 0.29/0.46 ( setminusSubset2
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( setminus @ A @ B )
% 0.29/0.46 = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusERneg_type,type,
% 0.29/0.46 setminusERneg: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusERneg,definition,
% 0.29/0.46 ( setminusERneg
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusELneg_type,type,
% 0.29/0.46 setminusELneg: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusELneg,definition,
% 0.29/0.46 ( setminusELneg
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusILneg_type,type,
% 0.29/0.46 setminusILneg: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusILneg,definition,
% 0.29/0.46 ( setminusILneg
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ A )
% 0.29/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusIRneg_type,type,
% 0.29/0.46 setminusIRneg: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusIRneg,definition,
% 0.29/0.46 ( setminusIRneg
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusLsub_type,type,
% 0.29/0.46 setminusLsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusLsub,definition,
% 0.29/0.46 ( setminusLsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusSubset1_type,type,
% 0.29/0.46 setminusSubset1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusSubset1,definition,
% 0.29/0.46 ( setminusSubset1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( ( setminus @ A @ B )
% 0.29/0.46 = emptyset )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiff_type,type,
% 0.29/0.46 symdiff: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffE_type,type,
% 0.29/0.46 symdiffE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffE,definition,
% 0.29/0.46 ( symdiffE
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.29/0.46 => ! [Xphi: $o] :
% 0.29/0.46 ( ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => Xphi ) )
% 0.29/0.46 => ( ( ~ ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => Xphi ) )
% 0.29/0.46 => Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffI1_type,type,
% 0.29/0.46 symdiffI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffI1,definition,
% 0.29/0.46 ( symdiffI1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffI2_type,type,
% 0.29/0.46 symdiffI2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffI2,definition,
% 0.29/0.46 ( symdiffI2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffIneg1_type,type,
% 0.29/0.46 symdiffIneg1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffIneg1,definition,
% 0.29/0.46 ( symdiffIneg1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffIneg2_type,type,
% 0.29/0.46 symdiffIneg2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffIneg2,definition,
% 0.29/0.46 ( symdiffIneg2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(iskpair_type,type,
% 0.29/0.46 iskpair: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(secondinupair_type,type,
% 0.29/0.46 secondinupair: $o ).
% 0.29/0.46
% 0.29/0.46 thf(secondinupair,definition,
% 0.29/0.46 ( secondinupair
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairIL_type,type,
% 0.29/0.46 setukpairIL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairIL,definition,
% 0.29/0.46 ( setukpairIL
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairIR_type,type,
% 0.29/0.46 setukpairIR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairIR,definition,
% 0.29/0.46 ( setukpairIR
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(kpairiskpair_type,type,
% 0.29/0.46 kpairiskpair: $o ).
% 0.29/0.46
% 0.29/0.46 thf(kpairiskpair,definition,
% 0.29/0.46 ( kpairiskpair
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(kpair_type,type,
% 0.29/0.46 kpair: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(kpairp_type,type,
% 0.29/0.46 kpairp: $o ).
% 0.29/0.46
% 0.29/0.46 thf(kpairp,definition,
% 0.29/0.46 ( kpairp
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprod_type,type,
% 0.29/0.46 cartprod: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsubset_type,type,
% 0.29/0.46 singletonsubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsubset,definition,
% 0.29/0.46 ( singletonsubset
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singletoninpowerset_type,type,
% 0.29/0.46 singletoninpowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletoninpowerset,definition,
% 0.29/0.46 ( singletoninpowerset
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singletoninpowunion_type,type,
% 0.29/0.46 singletoninpowunion: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletoninpowunion,definition,
% 0.29/0.46 ( singletoninpowunion
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairset2E_type,type,
% 0.29/0.46 upairset2E: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairset2E,definition,
% 0.29/0.46 ( upairset2E
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.29/0.46 => ( ( Xz = Xx )
% 0.29/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairsubunion_type,type,
% 0.29/0.46 upairsubunion: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsubunion,definition,
% 0.29/0.46 ( upairsubunion
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairinpowunion_type,type,
% 0.29/0.46 upairinpowunion: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairinpowunion,definition,
% 0.29/0.46 ( upairinpowunion
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem1_type,type,
% 0.29/0.46 ubforcartprodlem1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem1,definition,
% 0.29/0.46 ( ubforcartprodlem1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem2_type,type,
% 0.29/0.46 ubforcartprodlem2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem2,definition,
% 0.29/0.46 ( ubforcartprodlem2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem3_type,type,
% 0.29/0.46 ubforcartprodlem3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem3,definition,
% 0.29/0.46 ( ubforcartprodlem3
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodpairin_type,type,
% 0.29/0.46 cartprodpairin: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodpairin,definition,
% 0.29/0.46 ( cartprodpairin
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodmempair1_type,type,
% 0.29/0.46 cartprodmempair1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodmempair1,definition,
% 0.29/0.46 ( cartprodmempair1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ? [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 & ( Xu
% 0.29/0.46 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodmempair_type,type,
% 0.29/0.46 cartprodmempair: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodmempair,definition,
% 0.29/0.46 ( cartprodmempair
% 0.29/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.46 => ( iskpair @ Xu ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionE2_type,type,
% 0.29/0.46 setunionE2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionE2,definition,
% 0.29/0.46 ( setunionE2
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.46 => ? [X: $i] :
% 0.29/0.46 ( ( in @ X @ A )
% 0.29/0.46 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton1_type,type,
% 0.29/0.46 setunionsingleton1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton1,definition,
% 0.29/0.46 ( setunionsingleton1
% 0.29/0.46 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton2_type,type,
% 0.29/0.46 setunionsingleton2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton2,definition,
% 0.29/0.46 ( setunionsingleton2
% 0.29/0.46 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton_type,type,
% 0.29/0.46 setunionsingleton: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton,definition,
% 0.29/0.46 ( setunionsingleton
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.29/0.46 = Xx ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singleton_type,type,
% 0.29/0.46 singleton: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletonprop_type,type,
% 0.29/0.46 singletonprop: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletonprop,definition,
% 0.29/0.46 ( singletonprop
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) )
% 0.29/0.46 => ( ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ( singleton
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ex1_type,type,
% 0.29/0.46 ex1: $i > ( $i > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(ex1E1_type,type,
% 0.29/0.46 ex1E1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ex1E1,definition,
% 0.29/0.46 ( ex1E1
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ( ex1 @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ex1I_type,type,
% 0.29/0.46 ex1I: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ex1I,definition,
% 0.29/0.46 ( ex1I
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xy = Xx ) ) )
% 0.29/0.46 => ( ex1 @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ex1I2_type,type,
% 0.29/0.46 ex1I2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ex1I2,definition,
% 0.29/0.46 ( ex1I2
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) )
% 0.29/0.46 => ( ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ( ex1 @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsuniq_type,type,
% 0.29/0.46 singletonsuniq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsuniq,definition,
% 0.29/0.46 ( singletonsuniq
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( ( setadjoin @ Xx @ emptyset )
% 0.29/0.46 = ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(atmost1p_type,type,
% 0.29/0.46 atmost1p: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(atleast2p_type,type,
% 0.29/0.46 atleast2p: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(atmost2p_type,type,
% 0.29/0.46 atmost2p: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetp_type,type,
% 0.29/0.46 upairsetp: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjL1_type,type,
% 0.29/0.46 setukpairinjL1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjL1,definition,
% 0.29/0.46 ( setukpairinjL1
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.46 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.29/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(kfstsingleton_type,type,
% 0.29/0.46 kfstsingleton: $o ).
% 0.29/0.46
% 0.29/0.46 thf(kfstsingleton,definition,
% 0.29/0.46 ( kfstsingleton
% 0.29/0.46 = ( ! [Xu: $i] :
% 0.29/0.46 ( ( iskpair @ Xu )
% 0.29/0.46 => ( singleton
% 0.29/0.46 @ ( dsetconstr @ ( setunion @ Xu )
% 0.29/0.46 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(theprop_type,type,
% 0.29/0.46 theprop: $o ).
% 0.29/0.46
% 0.29/0.46 thf(theprop,definition,
% 0.29/0.46 ( theprop
% 0.29/0.46 = ( ! [X: $i] :
% 0.29/0.46 ( ( singleton @ X )
% 0.29/0.46 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(kfst_type,type,
% 0.29/0.46 kfst: $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(kfstpairEq_type,type,
% 0.29/0.46 kfstpairEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(kfstpairEq,definition,
% 0.29/0.46 ( kfstpairEq
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.29/0.46 = Xx ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodfstin_type,type,
% 0.29/0.46 cartprodfstin: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodfstin,definition,
% 0.29/0.46 ( cartprodfstin
% 0.29/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.46 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjL2_type,type,
% 0.29/0.46 setukpairinjL2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjL2,definition,
% 0.29/0.46 ( setukpairinjL2
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.46 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.29/0.46 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.29/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjL_type,type,
% 0.29/0.46 setukpairinjL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjL,definition,
% 0.29/0.46 ( setukpairinjL
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.46 ( ( ( kpair @ Xx @ Xy )
% 0.29/0.46 = ( kpair @ Xz @ Xu ) )
% 0.29/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR11_type,type,
% 0.29/0.46 setukpairinjR11: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR11,definition,
% 0.29/0.46 ( setukpairinjR11
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR12_type,type,
% 0.29/0.46 setukpairinjR12: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR12,definition,
% 0.29/0.46 ( setukpairinjR12
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.29/0.46 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR1_type,type,
% 0.29/0.46 setukpairinjR1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR1,definition,
% 0.29/0.46 ( setukpairinjR1
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.46 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.29/0.46 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.29/0.46 => ( ( Xz = Xu )
% 0.29/0.46 => ( Xy = Xu ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairequniteq_type,type,
% 0.29/0.46 upairequniteq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairequniteq,definition,
% 0.29/0.46 ( upairequniteq
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.46 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.46 = ( setadjoin @ Xz @ emptyset ) )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR2_type,type,
% 0.29/0.46 setukpairinjR2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR2,definition,
% 0.29/0.46 ( setukpairinjR2
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.46 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.29/0.46 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.29/0.46 => ( Xy = Xu ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR_type,type,
% 0.29/0.46 setukpairinjR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR,definition,
% 0.29/0.46 ( setukpairinjR
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.46 ( ( ( kpair @ Xx @ Xy )
% 0.29/0.46 = ( kpair @ Xz @ Xu ) )
% 0.29/0.46 => ( Xy = Xu ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ksndsingleton_type,type,
% 0.29/0.46 ksndsingleton: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ksndsingleton,definition,
% 0.29/0.46 ( ksndsingleton
% 0.29/0.46 = ( ! [Xu: $i] :
% 0.29/0.46 ( ( iskpair @ Xu )
% 0.29/0.46 => ( singleton
% 0.29/0.46 @ ( dsetconstr @ ( setunion @ Xu )
% 0.29/0.46 @ ^ [Xx: $i] :
% 0.29/0.46 ( Xu
% 0.29/0.46 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ksnd_type,type,
% 0.29/0.46 ksnd: $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(ksndpairEq_type,type,
% 0.29/0.46 ksndpairEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ksndpairEq,definition,
% 0.29/0.46 ( ksndpairEq
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.29/0.46 = Xy ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(kpairsurjEq_type,type,
% 0.29/0.46 kpairsurjEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(kpairsurjEq,definition,
% 0.29/0.46 ( kpairsurjEq
% 0.29/0.46 = ( ! [Xu: $i] :
% 0.29/0.46 ( ( iskpair @ Xu )
% 0.29/0.46 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.29/0.46 = Xu ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodsndin_type,type,
% 0.29/0.46 cartprodsndin: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodsndin,definition,
% 0.29/0.46 ( cartprodsndin
% 0.29/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.46 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodpairmemEL_type,type,
% 0.29/0.46 cartprodpairmemEL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodpairmemEL,definition,
% 0.29/0.46 ( cartprodpairmemEL
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodpairmemER_type,type,
% 0.29/0.46 cartprodpairmemER: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodpairmemER,definition,
% 0.29/0.46 ( cartprodpairmemER
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.29/0.46 => ( in @ Xy @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodmempaircEq_type,type,
% 0.29/0.46 cartprodmempaircEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodmempaircEq,definition,
% 0.29/0.46 ( cartprodmempaircEq
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( kpair @ Xx @ Xy )
% 0.29/0.46 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodfstpairEq_type,type,
% 0.29/0.46 cartprodfstpairEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodfstpairEq,definition,
% 0.29/0.46 ( cartprodfstpairEq
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.29/0.46 = Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodsndpairEq_type,type,
% 0.29/0.46 cartprodsndpairEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodsndpairEq,definition,
% 0.29/0.46 ( cartprodsndpairEq
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.29/0.46 = Xy ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodpairsurjEq_type,type,
% 0.29/0.46 cartprodpairsurjEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodpairsurjEq,definition,
% 0.29/0.46 ( cartprodpairsurjEq
% 0.29/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.46 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.29/0.46 = Xu ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(breln_type,type,
% 0.29/0.46 breln: $i > $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstr_type,type,
% 0.29/0.46 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrI_type,type,
% 0.29/0.46 dpsetconstrI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrI,definition,
% 0.29/0.46 ( dpsetconstrI
% 0.29/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( Xphi @ Xx @ Xy )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.46 @ ( dpsetconstr @ A @ B
% 0.29/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrSub_type,type,
% 0.29/0.46 dpsetconstrSub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrSub,definition,
% 0.29/0.46 ( dpsetconstrSub
% 0.29/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.29/0.46 ( subset
% 0.29/0.46 @ ( dpsetconstr @ A @ B
% 0.29/0.46 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.29/0.46 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setOfPairsIsBReln_type,type,
% 0.29/0.46 setOfPairsIsBReln: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setOfPairsIsBReln,definition,
% 0.29/0.46 ( setOfPairsIsBReln
% 0.29/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.29/0.46 ( breln @ A @ B
% 0.29/0.46 @ ( dpsetconstr @ A @ B
% 0.29/0.46 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrERa_type,type,
% 0.29/0.46 dpsetconstrERa: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrERa,definition,
% 0.29/0.46 ( dpsetconstrERa
% 0.29/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.46 @ ( dpsetconstr @ A @ B
% 0.29/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.29/0.46 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrEL1_type,type,
% 0.29/0.46 dpsetconstrEL1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrEL1,definition,
% 0.29/0.46 ( dpsetconstrEL1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.46 @ ( dpsetconstr @ A @ B
% 0.29/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrEL2_type,type,
% 0.29/0.46 dpsetconstrEL2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrEL2,definition,
% 0.29/0.46 ( dpsetconstrEL2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.46 @ ( dpsetconstr @ A @ B
% 0.29/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.29/0.46 => ( in @ Xy @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrER_type,type,
% 0.29/0.46 dpsetconstrER: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrER,definition,
% 0.29/0.46 ( dpsetconstrER
% 0.29/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.46 @ ( dpsetconstr @ A @ B
% 0.29/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.29/0.46 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(func_type,type,
% 0.29/0.46 func: $i > $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcSet_type,type,
% 0.29/0.46 funcSet: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(funcImageSingleton_type,type,
% 0.29/0.46 funcImageSingleton: $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcImageSingleton,definition,
% 0.29/0.46 ( funcImageSingleton
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( singleton
% 0.29/0.46 @ ( dsetconstr @ B
% 0.29/0.46 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(apProp_type,type,
% 0.29/0.46 apProp: $o ).
% 0.29/0.46
% 0.29/0.46 thf(apProp,definition,
% 0.29/0.46 ( apProp
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in
% 0.29/0.46 @ ( setunion
% 0.29/0.46 @ ( dsetconstr @ B
% 0.29/0.46 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.29/0.46 @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ap_type,type,
% 0.29/0.46 ap: $i > $i > $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(app_type,type,
% 0.29/0.46 app: $o ).
% 0.29/0.46
% 0.29/0.46 thf(app,definition,
% 0.29/0.46 ( app
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(infuncsetfunc_type,type,
% 0.29/0.46 infuncsetfunc: $o ).
% 0.29/0.46
% 0.29/0.46 thf(infuncsetfunc,definition,
% 0.29/0.46 ( infuncsetfunc
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.46 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ap2p_type,type,
% 0.29/0.46 ap2p: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ap2p,definition,
% 0.29/0.46 ( ap2p
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(funcinfuncset_type,type,
% 0.29/0.46 funcinfuncset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcinfuncset,definition,
% 0.29/0.46 ( funcinfuncset
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(lamProp_type,type,
% 0.29/0.46 lamProp: $o ).
% 0.29/0.46
% 0.29/0.46 thf(lamProp,definition,
% 0.29/0.46 ( lamProp
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.46 => ( func @ A @ B
% 0.29/0.46 @ ( dpsetconstr @ A @ B
% 0.29/0.46 @ ^ [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xf @ Xx )
% 0.29/0.46 = Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(lam_type,type,
% 0.29/0.46 lam: $i > $i > ( $i > $i ) > $i ).
% 0.29/0.46
% 0.29/0.46 thf(lamp_type,type,
% 0.29/0.46 lamp: $o ).
% 0.29/0.46
% 0.29/0.46 thf(lamp,definition,
% 0.29/0.46 ( lamp
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.46 => ( func @ A @ B
% 0.29/0.46 @ ( lam @ A @ B
% 0.29/0.46 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(lam2p_type,type,
% 0.29/0.46 lam2p: $o ).
% 0.29/0.46
% 0.29/0.46 thf(lam2p,definition,
% 0.29/0.46 ( lam2p
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.46 => ( in
% 0.29/0.46 @ ( lam @ A @ B
% 0.29/0.46 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.29/0.46 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(brelnall1_type,type,
% 0.29/0.46 brelnall1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(brelnall1,definition,
% 0.29/0.46 ( brelnall1
% 0.29/0.46 = ( ! [A: $i,B: $i,R: $i] :
% 0.29/0.46 ( ( breln @ A @ B @ R )
% 0.29/0.46 => ! [Xphi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.46 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ R )
% 0.29/0.46 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(brelnall2_type,type,
% 0.29/0.46 brelnall2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(brelnall2,definition,
% 0.29/0.46 ( brelnall2
% 0.29/0.46 = ( ! [A: $i,B: $i,R: $i] :
% 0.29/0.46 ( ( breln @ A @ B @ R )
% 0.29/0.46 => ! [Xphi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.46 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ R )
% 0.29/0.46 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ex1E2_type,type,
% 0.29/0.46 ex1E2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ex1E2,definition,
% 0.29/0.46 ( ex1E2
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ( ex1 @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(funcGraphProp1_type,type,
% 0.29/0.46 funcGraphProp1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcGraphProp1,definition,
% 0.29/0.46 ( funcGraphProp1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(funcGraphProp3_type,type,
% 0.29/0.46 funcGraphProp3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcGraphProp3,definition,
% 0.29/0.46 ( funcGraphProp3
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(funcGraphProp2_type,type,
% 0.29/0.46 funcGraphProp2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcGraphProp2,definition,
% 0.29/0.46 ( funcGraphProp2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.29/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.46 = Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(funcextLem_type,type,
% 0.29/0.46 funcextLem: $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcextLem,definition,
% 0.29/0.46 ( funcextLem
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ! [Xg: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xg )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.46 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(funcGraphProp4_type,type,
% 0.29/0.46 funcGraphProp4: $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcGraphProp4,definition,
% 0.29/0.46 ( funcGraphProp4
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.29/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.46 = Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subbreln_type,type,
% 0.29/0.46 subbreln: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subbreln,definition,
% 0.29/0.46 ( subbreln
% 0.29/0.46 = ( ! [A: $i,B: $i,R: $i] :
% 0.29/0.46 ( ( breln @ A @ B @ R )
% 0.29/0.46 => ! [S: $i] :
% 0.29/0.46 ( ( breln @ A @ B @ S )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.29/0.46 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eqbreln_type,type,
% 0.29/0.46 eqbreln: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eqbreln,definition,
% 0.29/0.46 ( eqbreln
% 0.29/0.46 = ( ! [A: $i,B: $i,R: $i] :
% 0.29/0.46 ( ( breln @ A @ B @ R )
% 0.29/0.46 => ! [S: $i] :
% 0.29/0.46 ( ( breln @ A @ B @ S )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.29/0.46 => ( R = S ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(funcext_type,type,
% 0.29/0.46 funcext: $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcext,definition,
% 0.29/0.46 ( funcext
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ! [Xg: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xg )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.46 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.29/0.46 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(funcext2_type,type,
% 0.29/0.46 funcext2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcext2,definition,
% 0.29/0.46 ( funcext2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.46 => ! [Xg: $i] :
% 0.29/0.46 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.46 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.29/0.46 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ap2apEq1_type,type,
% 0.29/0.46 ap2apEq1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ap2apEq1,definition,
% 0.29/0.46 ( ap2apEq1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.46 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ap2apEq2_type,type,
% 0.29/0.46 ap2apEq2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ap2apEq2,definition,
% 0.29/0.46 ( ap2apEq2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.46 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(beta1_type,type,
% 0.29/0.46 beta1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(beta1,definition,
% 0.29/0.46 ( beta1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( ap @ A @ B
% 0.29/0.46 @ ( lam @ A @ B
% 0.29/0.46 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.29/0.46 @ Xx )
% 0.29/0.46 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eta1_type,type,
% 0.29/0.46 eta1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eta1,definition,
% 0.29/0.46 ( eta1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ( ( lam @ A @ B
% 0.29/0.46 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.29/0.46 = Xf ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(lam2lamEq_type,type,
% 0.29/0.46 lam2lamEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(lam2lamEq,definition,
% 0.29/0.46 ( lam2lamEq
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.46 => ( ( lam @ A @ B
% 0.29/0.46 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.29/0.46 = ( lam @ A @ B
% 0.29/0.46 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(beta2_type,type,
% 0.29/0.46 beta2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(beta2,definition,
% 0.29/0.46 ( beta2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( ap @ A @ B
% 0.29/0.46 @ ( lam @ A @ B
% 0.29/0.46 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.29/0.46 @ Xx )
% 0.29/0.46 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eta2_type,type,
% 0.29/0.46 eta2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eta2,definition,
% 0.29/0.46 ( eta2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.46 => ( ( lam @ A @ B
% 0.29/0.46 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.29/0.46 = Xf ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(iffalseProp1_type,type,
% 0.29/0.46 iffalseProp1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(iffalseProp1,definition,
% 0.29/0.46 ( iffalseProp1
% 0.29/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( ~ Xphi
% 0.29/0.46 => ( in @ Xy
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xz: $i] :
% 0.29/0.46 ( ( Xphi
% 0.29/0.46 & ( Xz = Xx ) )
% 0.29/0.46 | ( ~ Xphi
% 0.29/0.46 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(iffalseProp2_type,type,
% 0.29/0.46 iffalseProp2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(iffalseProp2,definition,
% 0.29/0.46 ( iffalseProp2
% 0.29/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( ~ Xphi
% 0.29/0.46 => ( ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xz: $i] :
% 0.29/0.46 ( ( Xphi
% 0.29/0.46 & ( Xz = Xx ) )
% 0.29/0.46 | ( ~ Xphi
% 0.29/0.46 & ( Xz = Xy ) ) ) )
% 0.29/0.46 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(iftrueProp1_type,type,
% 0.29/0.46 iftrueProp1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(iftrueProp1,definition,
% 0.29/0.46 ( iftrueProp1
% 0.29/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( Xphi
% 0.29/0.46 => ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xz: $i] :
% 0.29/0.46 ( ( Xphi
% 0.29/0.46 & ( Xz = Xx ) )
% 0.29/0.46 | ( ~ Xphi
% 0.29/0.46 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(iftrueProp2_type,type,
% 0.29/0.46 iftrueProp2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(iftrueProp2,definition,
% 0.29/0.46 ( iftrueProp2
% 0.29/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( Xphi
% 0.29/0.46 => ( ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xz: $i] :
% 0.29/0.46 ( ( Xphi
% 0.29/0.46 & ( Xz = Xx ) )
% 0.29/0.46 | ( ~ Xphi
% 0.29/0.46 & ( Xz = Xy ) ) ) )
% 0.29/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ifSingleton_type,type,
% 0.29/0.46 ifSingleton: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ifSingleton,definition,
% 0.29/0.46 ( ifSingleton
% 0.29/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( singleton
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xz: $i] :
% 0.29/0.46 ( ( Xphi
% 0.29/0.46 & ( Xz = Xx ) )
% 0.29/0.46 | ( ~ Xphi
% 0.29/0.46 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(if_type,type,
% 0.29/0.46 if: $i > $o > $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(ifp_type,type,
% 0.29/0.46 ifp: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ifp,definition,
% 0.29/0.46 ( ifp
% 0.29/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(theeq_type,type,
% 0.29/0.46 theeq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(theeq,definition,
% 0.29/0.46 ( theeq
% 0.29/0.46 = ( ! [X: $i] :
% 0.29/0.46 ( ( singleton @ X )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ X )
% 0.29/0.46 => ( ( setunion @ X )
% 0.29/0.46 = Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(iftrue_type,type,
% 0.29/0.46 iftrue: $o ).
% 0.29/0.46
% 0.29/0.46 thf(iftrue,definition,
% 0.29/0.46 ( iftrue
% 0.29/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( Xphi
% 0.29/0.46 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.29/0.46 = Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(iffalse_type,type,
% 0.29/0.46 iffalse: $o ).
% 0.29/0.46
% 0.29/0.46 thf(iffalse,definition,
% 0.29/0.46 ( iffalse
% 0.29/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( ~ Xphi
% 0.29/0.46 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.29/0.46 = Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(iftrueorfalse_type,type,
% 0.29/0.46 iftrueorfalse: $o ).
% 0.29/0.46
% 0.29/0.46 thf(iftrueorfalse,definition,
% 0.29/0.46 ( iftrueorfalse
% 0.29/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectT_lem_type,type,
% 0.29/0.46 binintersectT_lem: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectT_lem,definition,
% 0.29/0.46 ( binintersectT_lem
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionT_lem_type,type,
% 0.29/0.46 binunionT_lem: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionT_lem,definition,
% 0.29/0.46 ( binunionT_lem
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetT_lem_type,type,
% 0.29/0.46 powersetT_lem: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetT_lem,definition,
% 0.29/0.46 ( powersetT_lem
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusT_lem_type,type,
% 0.29/0.46 setminusT_lem: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusT_lem,definition,
% 0.29/0.46 ( setminusT_lem
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(complementT_lem_type,type,
% 0.29/0.46 complementT_lem: $o ).
% 0.29/0.46
% 0.29/0.46 thf(complementT_lem,definition,
% 0.29/0.46 ( complementT_lem
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setextT_type,type,
% 0.29/0.46 setextT: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setextT,definition,
% 0.29/0.46 ( setextT
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ X )
% 0.29/0.46 => ( in @ Xx @ Y ) ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ Y )
% 0.29/0.46 => ( in @ Xx @ X ) ) )
% 0.29/0.46 => ( X = Y ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetTI_type,type,
% 0.29/0.46 subsetTI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetTI,definition,
% 0.29/0.46 ( subsetTI
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ X )
% 0.29/0.46 => ( in @ Xx @ Y ) ) )
% 0.29/0.46 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetTI1_type,type,
% 0.29/0.46 powersetTI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetTI1,definition,
% 0.29/0.46 ( powersetTI1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ X )
% 0.29/0.46 => ( in @ Xx @ Y ) ) )
% 0.29/0.46 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetTE1_type,type,
% 0.29/0.46 powersetTE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetTE1,definition,
% 0.29/0.46 ( powersetTE1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ X @ ( powerset @ Y ) )
% 0.29/0.46 => ( ( in @ Xx @ X )
% 0.29/0.46 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(complementTI1_type,type,
% 0.29/0.46 complementTI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(complementTI1,definition,
% 0.29/0.46 ( complementTI1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ X )
% 0.29/0.46 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(complementTE1_type,type,
% 0.29/0.46 complementTE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(complementTE1,definition,
% 0.29/0.46 ( complementTE1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 0.29/0.46 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectTELcontra_type,type,
% 0.29/0.46 binintersectTELcontra: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectTELcontra,definition,
% 0.29/0.46 ( binintersectTELcontra
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ X )
% 0.29/0.46 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectTERcontra_type,type,
% 0.29/0.46 binintersectTERcontra: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectTERcontra,definition,
% 0.29/0.46 ( binintersectTERcontra
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ Y )
% 0.29/0.46 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(contrasubsetT_type,type,
% 0.29/0.46 contrasubsetT: $o ).
% 0.29/0.46
% 0.29/0.46 thf(contrasubsetT,definition,
% 0.29/0.46 ( contrasubsetT
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.29/0.46 => ( ( in @ Xx @ Y )
% 0.29/0.46 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(contrasubsetT1_type,type,
% 0.29/0.46 contrasubsetT1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(contrasubsetT1,definition,
% 0.29/0.46 ( contrasubsetT1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( subset @ X @ Y )
% 0.29/0.46 => ( ~ ( in @ Xx @ Y )
% 0.29/0.46 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(contrasubsetT2_type,type,
% 0.29/0.46 contrasubsetT2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(contrasubsetT2,definition,
% 0.29/0.46 ( contrasubsetT2
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( ( subset @ X @ Y )
% 0.29/0.46 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(contrasubsetT3_type,type,
% 0.29/0.46 contrasubsetT3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(contrasubsetT3,definition,
% 0.29/0.46 ( contrasubsetT3
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 0.29/0.46 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementI1_type,type,
% 0.29/0.46 doubleComplementI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementI1,definition,
% 0.29/0.46 ( doubleComplementI1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ X )
% 0.29/0.46 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementE1_type,type,
% 0.29/0.46 doubleComplementE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementE1,definition,
% 0.29/0.46 ( doubleComplementE1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 0.29/0.46 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementSub1_type,type,
% 0.29/0.46 doubleComplementSub1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementSub1,definition,
% 0.29/0.46 ( doubleComplementSub1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementSub2_type,type,
% 0.29/0.46 doubleComplementSub2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementSub2,definition,
% 0.29/0.46 ( doubleComplementSub2
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementEq_type,type,
% 0.29/0.46 doubleComplementEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementEq,definition,
% 0.29/0.46 ( doubleComplementEq
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ( X
% 0.29/0.46 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(complementTnotintersectT_type,type,
% 0.29/0.46 complementTnotintersectT: $o ).
% 0.29/0.46
% 0.29/0.46 thf(complementTnotintersectT,definition,
% 0.29/0.46 ( complementTnotintersectT
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.29/0.46 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(complementImpComplementIntersect_type,type,
% 0.29/0.46 complementImpComplementIntersect: $o ).
% 0.29/0.46
% 0.29/0.46 thf(complementImpComplementIntersect,definition,
% 0.29/0.46 ( complementImpComplementIntersect
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.29/0.46 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(complementSubsetComplementIntersect_type,type,
% 0.29/0.46 complementSubsetComplementIntersect: $o ).
% 0.29/0.46
% 0.29/0.46 thf(complementSubsetComplementIntersect,definition,
% 0.29/0.46 ( complementSubsetComplementIntersect
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(complementInPowersetComplementIntersect_type,type,
% 0.29/0.46 complementInPowersetComplementIntersect: $o ).
% 0.29/0.46
% 0.29/0.46 thf(complementInPowersetComplementIntersect,definition,
% 0.29/0.46 ( complementInPowersetComplementIntersect
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(contraSubsetComplement_type,type,
% 0.29/0.46 contraSubsetComplement: $o ).
% 0.29/0.46
% 0.29/0.46 thf(contraSubsetComplement,definition,
% 0.29/0.46 ( contraSubsetComplement
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ Y )
% 0.29/0.46 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(complementTcontraSubset_type,type,
% 0.29/0.46 complementTcontraSubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(complementTcontraSubset,definition,
% 0.29/0.46 ( complementTcontraSubset
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.29/0.46 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionTILcontra_type,type,
% 0.29/0.46 binunionTILcontra: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionTILcontra,definition,
% 0.29/0.46 ( binunionTILcontra
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.29/0.46 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionTIRcontra_type,type,
% 0.29/0.46 binunionTIRcontra: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionTIRcontra,definition,
% 0.29/0.46 ( binunionTIRcontra
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.29/0.46 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(inIntersectImpInUnion_type,type,
% 0.29/0.46 inIntersectImpInUnion: $o ).
% 0.29/0.46
% 0.29/0.46 thf(inIntersectImpInUnion,definition,
% 0.29/0.46 ( inIntersectImpInUnion
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Z: $i] :
% 0.29/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.29/0.46 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(inIntersectImpInUnion2_type,type,
% 0.29/0.46 inIntersectImpInUnion2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(inIntersectImpInUnion2,definition,
% 0.29/0.46 ( inIntersectImpInUnion2
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Z: $i] :
% 0.29/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.29/0.46 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(inIntersectImpInIntersectUnions_type,type,
% 0.29/0.46 inIntersectImpInIntersectUnions: $o ).
% 0.29/0.46
% 0.29/0.46 thf(inIntersectImpInIntersectUnions,definition,
% 0.29/0.46 ( inIntersectImpInIntersectUnions
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Z: $i] :
% 0.29/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.29/0.46 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(intersectInPowersetIntersectUnions_type,type,
% 0.29/0.46 intersectInPowersetIntersectUnions: $o ).
% 0.29/0.46
% 0.29/0.46 thf(intersectInPowersetIntersectUnions,definition,
% 0.29/0.46 ( intersectInPowersetIntersectUnions
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Z: $i] :
% 0.29/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.46 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(inComplementUnionImpNotIn1_type,type,
% 0.29/0.46 inComplementUnionImpNotIn1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(inComplementUnionImpNotIn1,definition,
% 0.29/0.46 ( inComplementUnionImpNotIn1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.29/0.46 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(inComplementUnionImpInComplement1_type,type,
% 0.29/0.46 inComplementUnionImpInComplement1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(inComplementUnionImpInComplement1,definition,
% 0.29/0.46 ( inComplementUnionImpInComplement1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.29/0.46 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionTE_type,type,
% 0.29/0.46 binunionTE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionTE,definition,
% 0.29/0.46 ( binunionTE
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.29/0.46 => ( ( ( in @ Xx @ X )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => ( ( ( in @ Xx @ Y )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => Xphi ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionTEcontra_type,type,
% 0.29/0.47 binunionTEcontra: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binunionTEcontra,definition,
% 0.29/0.47 ( binunionTEcontra
% 0.29/0.47 = ( ! [A: $i,X: $i] :
% 0.29/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.47 => ! [Y: $i] :
% 0.29/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ~ ( in @ Xx @ X )
% 0.29/0.47 => ( ~ ( in @ Xx @ Y )
% 0.29/0.47 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(demorgan2a1_type,type,
% 0.29/0.47 demorgan2a1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(demorgan2a1,definition,
% 0.29/0.47 ( demorgan2a1
% 0.29/0.47 = ( ! [A: $i,X: $i] :
% 0.29/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.47 => ! [Y: $i] :
% 0.29/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.29/0.47 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(complementUnionInPowersetComplement_type,type,
% 0.29/0.47 complementUnionInPowersetComplement: $o ).
% 0.29/0.47
% 0.29/0.47 thf(complementUnionInPowersetComplement,definition,
% 0.29/0.47 ( complementUnionInPowersetComplement
% 0.29/0.47 = ( ! [A: $i,X: $i] :
% 0.29/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.47 => ! [Y: $i] :
% 0.29/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.47 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(demorgan2a2_type,type,
% 0.29/0.47 demorgan2a2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(demorgan2a2,definition,
% 0.29/0.47 ( demorgan2a2
% 0.29/0.47 = ( ! [A: $i,X: $i] :
% 0.29/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.47 => ! [Y: $i] :
% 0.29/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.29/0.47 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(demorgan1a_type,type,
% 0.29/0.47 demorgan1a: $o ).
% 0.29/0.47
% 0.29/0.47 thf(demorgan1a,definition,
% 0.29/0.47 ( demorgan1a
% 0.29/0.47 = ( ! [A: $i,X: $i] :
% 0.29/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.47 => ! [Y: $i] :
% 0.29/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 0.29/0.47 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(demorgan1b_type,type,
% 0.29/0.47 demorgan1b: $o ).
% 0.29/0.47
% 0.29/0.47 thf(demorgan1b,definition,
% 0.29/0.47 ( demorgan1b
% 0.29/0.47 = ( ! [A: $i,X: $i] :
% 0.29/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.47 => ! [Y: $i] :
% 0.29/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.29/0.47 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(demorgan1_type,type,
% 0.29/0.47 demorgan1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(demorgan1,definition,
% 0.29/0.47 ( demorgan1
% 0.29/0.47 = ( ! [A: $i,X: $i] :
% 0.29/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.47 => ! [Y: $i] :
% 0.29/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.47 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 0.29/0.47 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(demorgan2a_type,type,
% 0.29/0.47 demorgan2a: $o ).
% 0.29/0.47
% 0.29/0.47 thf(demorgan2a,definition,
% 0.29/0.47 ( demorgan2a
% 0.29/0.47 = ( ! [A: $i,X: $i] :
% 0.29/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.47 => ! [Y: $i] :
% 0.29/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.29/0.47 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(demorgan2b2_type,type,
% 0.29/0.47 demorgan2b2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(demorgan2b2,definition,
% 0.29/0.47 ( demorgan2b2
% 0.29/0.47 = ( ! [A: $i,X: $i] :
% 0.29/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.47 => ! [Y: $i] :
% 0.29/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.29/0.47 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 0.29/0.47 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(demorgan2b_type,type,
% 0.29/0.47 demorgan2b: $o ).
% 0.29/0.47
% 0.29/0.47 thf(demorgan2b,definition,
% 0.29/0.47 ( demorgan2b
% 0.29/0.47 = ( ! [A: $i,X: $i] :
% 0.29/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.47 => ! [Y: $i] :
% 0.29/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.29/0.47 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(demorgan2_type,type,
% 0.29/0.47 demorgan2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(demorgan2,definition,
% 0.29/0.47 ( demorgan2
% 0.29/0.47 = ( ! [A: $i,X: $i] :
% 0.29/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.47 => ! [Y: $i] :
% 0.29/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.47 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 0.29/0.47 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(woz13rule0_type,type,
% 0.29/0.47 woz13rule0: $o ).
% 0.29/0.47
% 0.29/0.47 thf(woz13rule0,definition,
% 0.29/0.47 ( woz13rule0
% 0.29/0.47 = ( ! [A: $i,X: $i] :
% 0.29/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.47 => ! [Y: $i] :
% 0.29/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.29/0.47 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(woz13rule1_type,type,
% 0.29/0.47 woz13rule1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(woz13rule1,definition,
% 0.29/0.47 ( woz13rule1
% 0.29/0.47 = ( ! [A: $i,X: $i] :
% 0.29/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.47 => ! [Y: $i] :
% 0.29/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.47 => ! [Z: $i] :
% 0.29/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.47 => ( ( subset @ X @ Z )
% 0.29/0.47 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(woz13rule2_type,type,
% 0.29/0.47 woz13rule2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(woz13rule2,definition,
% 0.29/0.47 ( woz13rule2
% 0.29/0.47 = ( ! [A: $i,X: $i] :
% 0.29/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.47 => ! [Y: $i] :
% 0.29/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.47 => ! [Z: $i] :
% 0.29/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.47 => ( ( subset @ Y @ Z )
% 0.29/0.47 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(woz13rule3_type,type,
% 0.29/0.47 woz13rule3: $o ).
% 0.29/0.47
% 0.29/0.47 thf(woz13rule3,definition,
% 0.29/0.47 ( woz13rule3
% 0.29/0.47 = ( ! [A: $i,X: $i] :
% 0.29/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.47 => ! [Y: $i] :
% 0.29/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.47 => ! [Z: $i] :
% 0.29/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.47 => ( ( subset @ X @ Y )
% 0.29/0.47 => ( ( subset @ X @ Z )
% 0.29/0.47 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(woz13rule4_type,type,
% 0.29/0.47 woz13rule4: $o ).
% 0.29/0.47
% 0.29/0.47 thf(woz13rule4,definition,
% 0.29/0.47 ( woz13rule4
% 0.29/0.47 = ( ! [A: $i,X: $i] :
% 0.29/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.47 => ! [Y: $i] :
% 0.29/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.47 => ! [Z: $i] :
% 0.29/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.47 => ! [W: $i] :
% 0.29/0.47 ( ( in @ W @ ( powerset @ A ) )
% 0.29/0.47 => ( ( subset @ X @ Z )
% 0.29/0.47 => ( ( subset @ Y @ W )
% 0.29/0.47 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(woz1_1_type,type,
% 0.29/0.47 woz1_1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(woz1_1,definition,
% 0.29/0.47 ( woz1_1
% 0.29/0.47 = ( ! [A: $i,X: $i] :
% 0.29/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.47 => ! [Y: $i] :
% 0.29/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.47 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(woz1_2_type,type,
% 0.29/0.47 woz1_2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(woz1_2,definition,
% 0.29/0.47 ( woz1_2
% 0.29/0.47 = ( ! [A: $i,X: $i] :
% 0.29/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.47 => ! [Y: $i] :
% 0.29/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.47 => ! [Z: $i] :
% 0.29/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.47 => ! [W: $i] :
% 0.29/0.47 ( ( in @ W @ ( powerset @ A ) )
% 0.29/0.47 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 0.29/0.47 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(woz1_3_type,type,
% 0.29/0.47 woz1_3: $o ).
% 0.29/0.47
% 0.29/0.47 thf(woz1_3,definition,
% 0.29/0.47 ( woz1_3
% 0.29/0.47 = ( ! [A: $i,X: $i] :
% 0.29/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.47 => ! [Y: $i] :
% 0.29/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.47 => ! [Z: $i] :
% 0.29/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.47 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(woz1_4_type,type,
% 0.29/0.47 woz1_4: $o ).
% 0.29/0.47
% 0.29/0.47 thf(woz1_4,definition,
% 0.29/0.47 ( woz1_4
% 0.29/0.47 = ( ! [A: $i,X: $i] :
% 0.29/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.47 => ! [Y: $i] :
% 0.29/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.47 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.29/0.47 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(woz1_5_type,type,
% 0.29/0.47 woz1_5: $o ).
% 0.29/0.47
% 0.29/0.47 thf(woz1_5,definition,
% 0.29/0.47 ( woz1_5
% 0.29/0.47 = ( ! [A: $i,X: $i] :
% 0.29/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.47 => ! [Y: $i] :
% 0.29/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.47 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(breln1_type,type,
% 0.29/0.47 breln1: $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(breln1all2_type,type,
% 0.29/0.47 breln1all2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(breln1all2,definition,
% 0.29/0.47 ( breln1all2
% 0.29/0.47 = ( ! [A: $i,R: $i] :
% 0.29/0.47 ( ( breln1 @ A @ R )
% 0.29/0.47 => ! [Xphi: $i > $o] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ R )
% 0.29/0.47 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(breln1Set_type,type,
% 0.29/0.47 breln1Set: $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(breln1SetBreln1_type,type,
% 0.29/0.47 breln1SetBreln1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(breln1SetBreln1,definition,
% 0.29/0.47 ( breln1SetBreln1
% 0.29/0.47 = ( ! [A: $i,R: $i] :
% 0.29/0.47 ( ( in @ R @ ( breln1Set @ A ) )
% 0.29/0.47 => ( breln1 @ A @ R ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(transitive_type,type,
% 0.29/0.47 transitive: $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(antisymmetric_type,type,
% 0.29/0.47 antisymmetric: $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(reflexive_type,type,
% 0.29/0.47 reflexive: $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(refltransitive_type,type,
% 0.29/0.47 refltransitive: $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(refllinearorder_type,type,
% 0.29/0.47 refllinearorder: $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(reflwellordering_type,type,
% 0.29/0.47 reflwellordering: $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(choice2fnsingleton_type,type,
% 0.29/0.47 choice2fnsingleton: $o ).
% 0.29/0.47
% 0.29/0.47 thf(choice2fnsingleton,definition,
% 0.29/0.47 ( choice2fnsingleton
% 0.29/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ? [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 & ( Xphi @ Xx @ Xy ) ) )
% 0.29/0.47 => ! [R: $i] :
% 0.29/0.47 ( ( in @ R @ ( breln1Set @ B ) )
% 0.29/0.47 => ( ( reflwellordering @ B @ R )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( singleton
% 0.29/0.47 @ ( dsetconstr @ B
% 0.29/0.47 @ ^ [Xy: $i] :
% 0.29/0.47 ( ( Xphi @ Xx @ Xy )
% 0.29/0.47 & ! [Xz: $i] :
% 0.29/0.47 ( ( in @ Xz @ B )
% 0.29/0.47 => ( ( Xphi @ Xx @ Xz )
% 0.29/0.47 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setOfPairsIsBReln1_type,type,
% 0.29/0.47 setOfPairsIsBReln1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setOfPairsIsBReln1,definition,
% 0.29/0.47 ( setOfPairsIsBReln1
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 0.29/0.47 ( breln1 @ A
% 0.29/0.47 @ ( dpsetconstr @ A @ A
% 0.29/0.47 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(breln1all1_type,type,
% 0.29/0.47 breln1all1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(breln1all1,definition,
% 0.29/0.47 ( breln1all1
% 0.29/0.47 = ( ! [A: $i,R: $i] :
% 0.29/0.47 ( ( breln1 @ A @ R )
% 0.29/0.47 => ! [Xphi: $i > $o] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ R )
% 0.29/0.47 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subbreln1_type,type,
% 0.29/0.47 subbreln1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subbreln1,definition,
% 0.29/0.47 ( subbreln1
% 0.29/0.47 = ( ! [A: $i,R: $i] :
% 0.29/0.47 ( ( breln1 @ A @ R )
% 0.29/0.47 => ! [S: $i] :
% 0.29/0.47 ( ( breln1 @ A @ S )
% 0.29/0.47 => ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.29/0.47 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(eqbreln1_type,type,
% 0.29/0.47 eqbreln1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(eqbreln1,definition,
% 0.29/0.47 ( eqbreln1
% 0.29/0.47 = ( ! [A: $i,R: $i] :
% 0.29/0.47 ( ( breln1 @ A @ R )
% 0.29/0.47 => ! [S: $i] :
% 0.29/0.47 ( ( breln1 @ A @ S )
% 0.29/0.47 => ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.29/0.47 => ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.29/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.29/0.47 => ( R = S ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(breln1invset_type,type,
% 0.29/0.47 breln1invset: $i > $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(breln1invprop_type,type,
% 0.29/0.47 breln1invprop: $o ).
% 0.29/0.47
% 0.29/0.47 thf(breln1invprop,definition,
% 0.29/0.47 ( breln1invprop
% 0.29/0.47 = ( ! [A: $i,R: $i] :
% 0.29/0.47 ( ( breln1 @ A @ R )
% 0.29/0.47 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(breln1invI_type,type,
% 0.29/0.47 breln1invI: $o ).
% 0.29/0.47
% 0.29/0.47 thf(breln1invI,definition,
% 0.29/0.47 ( breln1invI
% 0.29/0.47 = ( ! [A: $i,R: $i] :
% 0.29/0.47 ( ( breln1 @ A @ R )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.47 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(breln1invE_type,type,
% 0.29/0.47 breln1invE: $o ).
% 0.29/0.47
% 0.29/0.47 thf(breln1invE,definition,
% 0.29/0.47 ( breln1invE
% 0.29/0.47 = ( ! [A: $i,R: $i] :
% 0.29/0.47 ( ( breln1 @ A @ R )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 0.29/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(breln1compset_type,type,
% 0.29/0.47 breln1compset: $i > $i > $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(breln1compprop_type,type,
% 0.29/0.47 breln1compprop: $o ).
% 0.29/0.47
% 0.29/0.47 thf(breln1compprop,definition,
% 0.29/0.47 ( breln1compprop
% 0.29/0.47 = ( ! [A: $i,R: $i] :
% 0.29/0.47 ( ( breln1 @ A @ R )
% 0.29/0.47 => ! [S: $i] :
% 0.29/0.47 ( ( breln1 @ A @ S )
% 0.29/0.47 => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(breln1compI_type,type,
% 0.29/0.47 breln1compI: $o ).
% 0.29/0.47
% 0.29/0.47 thf(breln1compI,definition,
% 0.29/0.47 ( breln1compI
% 0.29/0.47 = ( ! [A: $i,R: $i] :
% 0.29/0.47 ( ( breln1 @ A @ R )
% 0.29/0.47 => ! [S: $i] :
% 0.29/0.47 ( ( breln1 @ A @ S )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 => ! [Xz: $i] :
% 0.29/0.47 ( ( in @ Xz @ A )
% 0.29/0.47 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.29/0.47 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 0.29/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(breln1compE_type,type,
% 0.29/0.47 breln1compE: $o ).
% 0.29/0.47
% 0.29/0.47 thf(breln1compE,definition,
% 0.29/0.47 ( breln1compE
% 0.29/0.47 = ( ! [A: $i,R: $i] :
% 0.29/0.47 ( ( breln1 @ A @ R )
% 0.29/0.47 => ! [S: $i] :
% 0.29/0.47 ( ( breln1 @ A @ S )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 0.29/0.47 => ? [Xz: $i] :
% 0.29/0.47 ( ( in @ Xz @ A )
% 0.29/0.47 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.29/0.47 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(breln1compEex_type,type,
% 0.29/0.47 breln1compEex: $o ).
% 0.29/0.47
% 0.29/0.47 thf(breln1compEex,definition,
% 0.29/0.47 ( breln1compEex
% 0.29/0.47 = ( ! [A: $i,R: $i] :
% 0.29/0.47 ( ( breln1 @ A @ R )
% 0.29/0.47 => ! [S: $i] :
% 0.29/0.47 ( ( breln1 @ A @ S )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 0.29/0.47 => ! [Xphi: $o] :
% 0.29/0.47 ( ! [Xz: $i] :
% 0.29/0.47 ( ( in @ Xz @ A )
% 0.29/0.47 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.29/0.47 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 0.29/0.47 => Xphi ) ) )
% 0.29/0.47 => Xphi ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(breln1unionprop_type,type,
% 0.29/0.47 breln1unionprop: $o ).
% 0.29/0.47
% 0.29/0.47 thf(breln1unionprop,definition,
% 0.29/0.47 ( breln1unionprop
% 0.29/0.47 = ( ! [A: $i,R: $i] :
% 0.29/0.47 ( ( breln1 @ A @ R )
% 0.29/0.47 => ! [S: $i] :
% 0.29/0.47 ( ( breln1 @ A @ S )
% 0.29/0.47 => ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(breln1unionIL_type,type,
% 0.29/0.47 breln1unionIL: $o ).
% 0.29/0.47
% 0.29/0.47 thf(breln1unionIL,definition,
% 0.29/0.47 ( breln1unionIL
% 0.29/0.47 = ( ! [A: $i,R: $i] :
% 0.29/0.47 ( ( breln1 @ A @ R )
% 0.29/0.47 => ! [S: $i] :
% 0.29/0.47 ( ( breln1 @ A @ S )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(breln1unionIR_type,type,
% 0.29/0.47 breln1unionIR: $o ).
% 0.29/0.47
% 0.29/0.47 thf(breln1unionIR,definition,
% 0.29/0.47 ( breln1unionIR
% 0.29/0.47 = ( ! [A: $i,R: $i] :
% 0.29/0.47 ( ( breln1 @ A @ R )
% 0.29/0.47 => ! [S: $i] :
% 0.29/0.47 ( ( breln1 @ A @ S )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.29/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(breln1unionI_type,type,
% 0.29/0.47 breln1unionI: $o ).
% 0.29/0.47
% 0.29/0.47 thf(breln1unionI,definition,
% 0.29/0.47 ( breln1unionI
% 0.29/0.47 = ( ! [A: $i,R: $i] :
% 0.29/0.47 ( ( breln1 @ A @ R )
% 0.29/0.47 => ! [S: $i] :
% 0.29/0.47 ( ( breln1 @ A @ S )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.47 | ( in @ ( kpair @ Xx @ Xy ) @ S ) )
% 0.29/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(breln1unionE_type,type,
% 0.29/0.47 breln1unionE: $o ).
% 0.29/0.47
% 0.29/0.47 thf(breln1unionE,definition,
% 0.29/0.47 ( breln1unionE
% 0.29/0.47 = ( ! [A: $i,R: $i] :
% 0.29/0.47 ( ( breln1 @ A @ R )
% 0.29/0.47 => ! [S: $i] :
% 0.29/0.47 ( ( breln1 @ A @ S )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 0.29/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.47 | ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(breln1unionEcases_type,type,
% 0.29/0.47 breln1unionEcases: $o ).
% 0.29/0.47
% 0.29/0.47 thf(breln1unionEcases,definition,
% 0.29/0.47 ( breln1unionEcases
% 0.29/0.47 = ( ! [A: $i,R: $i] :
% 0.29/0.47 ( ( breln1 @ A @ R )
% 0.29/0.47 => ! [S: $i] :
% 0.29/0.47 ( ( breln1 @ A @ S )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 0.29/0.47 => ! [Xphi: $o] :
% 0.29/0.47 ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.47 => Xphi )
% 0.29/0.47 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.29/0.47 => Xphi )
% 0.29/0.47 => Xphi ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(breln1unionCommutes_type,type,
% 0.29/0.47 breln1unionCommutes: $o ).
% 0.29/0.47
% 0.29/0.47 thf(breln1unionCommutes,definition,
% 0.29/0.47 ( breln1unionCommutes
% 0.29/0.47 = ( ! [A: $i,R: $i] :
% 0.29/0.47 ( ( breln1 @ A @ R )
% 0.29/0.47 => ! [S: $i] :
% 0.29/0.47 ( ( breln1 @ A @ S )
% 0.29/0.47 => ( ( binunion @ R @ S )
% 0.29/0.47 = ( binunion @ S @ R ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(woz2Ex_type,type,
% 0.29/0.47 woz2Ex: $o ).
% 0.29/0.47
% 0.29/0.47 thf(woz2Ex,definition,
% 0.29/0.47 ( woz2Ex
% 0.29/0.47 = ( ! [A: $i,R: $i] :
% 0.29/0.47 ( ( breln1 @ A @ R )
% 0.29/0.47 => ( R
% 0.29/0.47 = ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(woz2W_type,type,
% 0.29/0.47 woz2W: $o ).
% 0.29/0.47
% 0.29/0.47 thf(woz2W,definition,
% 0.29/0.47 ( woz2W
% 0.29/0.47 = ( ! [A: $i,R: $i] :
% 0.29/0.47 ( ( breln1 @ A @ R )
% 0.29/0.47 => ! [S: $i] :
% 0.29/0.47 ( ( breln1 @ A @ S )
% 0.29/0.47 => ( ( breln1invset @ A @ ( breln1compset @ A @ R @ S ) )
% 0.29/0.47 = ( breln1compset @ A @ ( breln1invset @ A @ S ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(woz2A_type,type,
% 0.29/0.47 woz2A: $o ).
% 0.29/0.47
% 0.29/0.47 thf(woz2A,definition,
% 0.29/0.47 ( woz2A
% 0.29/0.47 = ( ! [A: $i,R: $i] :
% 0.29/0.47 ( ( breln1 @ A @ R )
% 0.29/0.47 => ! [S: $i] :
% 0.29/0.47 ( ( breln1 @ A @ S )
% 0.29/0.47 => ! [T: $i] :
% 0.29/0.47 ( ( breln1 @ A @ T )
% 0.29/0.47 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 0.29/0.47 = ( binunion @ ( breln1compset @ A @ R @ T ) @ ( breln1compset @ A @ S @ T ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(woz2B_type,type,
% 0.29/0.47 woz2B: $o ).
% 0.29/0.47
% 0.29/0.47 thf(woz2B,definition,
% 0.29/0.47 ( woz2B
% 0.29/0.47 = ( ! [A: $i,R: $i] :
% 0.29/0.47 ( ( breln1 @ A @ R )
% 0.29/0.47 => ! [S: $i] :
% 0.29/0.47 ( ( breln1 @ A @ S )
% 0.29/0.47 => ! [T: $i] :
% 0.29/0.47 ( ( breln1 @ A @ T )
% 0.29/0.47 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 0.29/0.47 = ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ S ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(image1Ex_type,type,
% 0.29/0.47 image1Ex: $o ).
% 0.29/0.47
% 0.29/0.47 thf(image1Ex,definition,
% 0.29/0.47 ( image1Ex
% 0.29/0.47 = ( ! [A: $i,Xf: $i > $i] :
% 0.29/0.47 ? [B: $i] :
% 0.29/0.47 ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ B )
% 0.29/0.47 <=> ? [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 & ( Xx
% 0.29/0.47 = ( Xf @ Xy ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(image1Ex1_type,type,
% 0.29/0.47 image1Ex1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(image1Ex1,definition,
% 0.29/0.47 ( image1Ex1
% 0.29/0.47 = ( ! [A: $i,Xf: $i > $i] :
% 0.29/0.47 ( exu
% 0.29/0.47 @ ^ [B: $i] :
% 0.29/0.47 ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ B )
% 0.29/0.47 <=> ? [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 & ( Xx
% 0.29/0.47 = ( Xf @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(image1_type,type,
% 0.29/0.47 image1: $i > ( $i > $i ) > $i ).
% 0.29/0.47
% 0.29/0.47 thf(image1Equiv_type,type,
% 0.29/0.47 image1Equiv: $o ).
% 0.29/0.47
% 0.29/0.47 thf(image1Equiv,definition,
% 0.29/0.47 ( image1Equiv
% 0.29/0.47 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx
% 0.29/0.47 @ ( image1 @ A
% 0.29/0.47 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 0.29/0.47 <=> ? [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 & ( Xx
% 0.29/0.47 = ( Xf @ Xy ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(image1E_type,type,
% 0.29/0.47 image1E: $o ).
% 0.29/0.47
% 0.29/0.47 thf(image1E,definition,
% 0.29/0.47 ( image1E
% 0.29/0.47 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx
% 0.29/0.47 @ ( image1 @ A
% 0.29/0.47 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 0.29/0.47 => ? [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 & ( Xx
% 0.29/0.47 = ( Xf @ Xy ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(image1I_type,type,
% 0.29/0.47 image1I: $o ).
% 0.29/0.47
% 0.29/0.47 thf(image1I,definition,
% 0.29/0.47 ( image1I
% 0.29/0.47 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 0.29/0.47 ( ? [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 & ( Xx
% 0.29/0.47 = ( Xf @ Xy ) ) )
% 0.29/0.47 => ( in @ Xx
% 0.29/0.47 @ ( image1 @ A
% 0.29/0.47 @ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(injective_type,type,
% 0.29/0.47 injective: $i > $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(injFuncSet_type,type,
% 0.29/0.47 injFuncSet: $i > $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(injFuncInInjFuncSet_type,type,
% 0.29/0.47 injFuncInInjFuncSet: $o ).
% 0.29/0.47
% 0.29/0.47 thf(injFuncInInjFuncSet,definition,
% 0.29/0.47 ( injFuncInInjFuncSet
% 0.29/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.47 => ( ( injective @ A @ B @ Xf )
% 0.29/0.47 => ( in @ Xf @ ( injFuncSet @ A @ B ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(injFuncSetFuncIn_type,type,
% 0.29/0.47 injFuncSetFuncIn: $o ).
% 0.29/0.47
% 0.29/0.47 thf(injFuncSetFuncIn,definition,
% 0.29/0.47 ( injFuncSetFuncIn
% 0.29/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.47 ( ( in @ Xf @ ( injFuncSet @ A @ B ) )
% 0.29/0.47 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(injFuncSetFuncInj_type,type,
% 0.29/0.47 injFuncSetFuncInj: $o ).
% 0.29/0.47
% 0.29/0.47 thf(injFuncSetFuncInj,definition,
% 0.29/0.47 ( injFuncSetFuncInj
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i,Xf: $i] :
% 0.29/0.47 ( ( in @ Xf @ ( injFuncSet @ Xx @ Xy ) )
% 0.29/0.47 => ( injective @ Xx @ Xy @ Xf ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(surjective_type,type,
% 0.29/0.47 surjective: $i > $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(surjFuncSet_type,type,
% 0.29/0.47 surjFuncSet: $i > $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(surjFuncSetFuncIn_type,type,
% 0.29/0.47 surjFuncSetFuncIn: $o ).
% 0.29/0.47
% 0.29/0.47 thf(surjFuncSetFuncIn,definition,
% 0.29/0.47 ( surjFuncSetFuncIn
% 0.29/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.47 ( ( in @ Xf @ ( surjFuncSet @ A @ B ) )
% 0.29/0.47 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(surjFuncSetFuncSurj_type,type,
% 0.29/0.47 surjFuncSetFuncSurj: $o ).
% 0.29/0.47
% 0.29/0.47 thf(surjFuncSetFuncSurj,definition,
% 0.29/0.47 ( surjFuncSetFuncSurj
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i,Xf: $i] :
% 0.29/0.47 ( ( in @ Xf @ ( surjFuncSet @ Xx @ Xy ) )
% 0.29/0.47 => ( surjective @ Xx @ Xy @ Xf ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(leftInvIsSurj_type,type,
% 0.29/0.47 leftInvIsSurj: $o ).
% 0.29/0.47
% 0.29/0.47 thf(leftInvIsSurj,definition,
% 0.29/0.47 ( leftInvIsSurj
% 0.29/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.47 => ! [Xg: $i] :
% 0.29/0.47 ( ( in @ Xg @ ( funcSet @ B @ A ) )
% 0.29/0.47 => ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ( ap @ B @ A @ Xg @ ( Xf @ Xx ) )
% 0.29/0.47 = Xx ) )
% 0.29/0.47 => ( surjective @ B @ A @ Xg ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(surjCantorThm_type,type,
% 0.29/0.47 surjCantorThm: $o ).
% 0.29/0.47
% 0.29/0.47 thf(surjCantorThm,definition,
% 0.29/0.47 ( surjCantorThm
% 0.29/0.47 = ( ! [A: $i,Xf: $i] :
% 0.29/0.47 ( ( in @ Xf @ ( funcSet @ A @ ( powerset @ A ) ) )
% 0.29/0.47 => ~ ( surjective @ A @ ( powerset @ A ) @ Xf ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(foundation2_type,type,
% 0.29/0.47 foundation2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(foundation2,definition,
% 0.29/0.47 ( foundation2
% 0.29/0.47 = ( ! [A: $i] :
% 0.29/0.47 ( ( nonempty @ A )
% 0.29/0.47 => ? [X: $i] :
% 0.29/0.47 ( ( in @ X @ A )
% 0.29/0.47 & ( ( binintersect @ X @ A )
% 0.29/0.47 = emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(notinself_type,type,
% 0.29/0.47 notinself: $o ).
% 0.29/0.47
% 0.29/0.47 thf(notinself,definition,
% 0.29/0.47 ( notinself
% 0.29/0.47 = ( ! [A: $i] :
% 0.29/0.47 ~ ( in @ A @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(notinself2_type,type,
% 0.29/0.47 notinself2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(notinself2,definition,
% 0.29/0.47 ( notinself2
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( in @ A @ B )
% 0.29/0.47 => ~ ( in @ B @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(omegaS_type,type,
% 0.29/0.47 omegaS: $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(omegaSp_type,type,
% 0.29/0.47 omegaSp: $o ).
% 0.29/0.47
% 0.29/0.47 thf(omegaSp,definition,
% 0.29/0.47 ( omegaSp
% 0.29/0.47 = ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ omega )
% 0.29/0.47 => ( in @ ( omegaS @ Xx ) @ omega ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(omegaSclos_type,type,
% 0.29/0.47 omegaSclos: $o ).
% 0.29/0.47
% 0.29/0.47 thf(omegaSclos,definition,
% 0.29/0.47 ( omegaSclos
% 0.29/0.47 = ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ omega )
% 0.29/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(peano0notS_type,type,
% 0.29/0.47 peano0notS: $o ).
% 0.29/0.47
% 0.29/0.47 thf(peano0notS,definition,
% 0.29/0.47 ( peano0notS
% 0.29/0.47 = ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ omega )
% 0.29/0.47 => ( ( omegaS @ Xx )
% 0.29/0.47 != emptyset ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(peano3_type,type,
% 0.29/0.47 peano3: $i > $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(peano4_type,type,
% 0.29/0.47 peano4: $i > $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(peano5_type,type,
% 0.29/0.47 peano5: $i > $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(peanoSinj_type,type,
% 0.29/0.47 peanoSinj: $o ).
% 0.29/0.47
% 0.29/0.47 thf(peanoSinj,definition,
% 0.29/0.47 ( peanoSinj
% 0.29/0.47 = ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ omega )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ omega )
% 0.29/0.47 => ( ( ( omegaS @ Xx )
% 0.29/0.47 = ( omegaS @ Xy ) )
% 0.29/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(peano_type,type,
% 0.29/0.47 peano: $i > $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(transitiveset_type,type,
% 0.29/0.47 transitiveset: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(transitiveset,definition,
% 0.29/0.47 ( transitiveset
% 0.29/0.47 = ( ^ [A: $i] :
% 0.29/0.47 ! [X: $i] :
% 0.29/0.47 ( ( in @ X @ A )
% 0.29/0.47 => ( subset @ X @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(transitivesetOp1_type,type,
% 0.29/0.47 transitivesetOp1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(transitivesetOp1,definition,
% 0.29/0.47 ( transitivesetOp1
% 0.29/0.47 = ( ! [X: $i] :
% 0.29/0.47 ( ( transitiveset @ X )
% 0.29/0.47 => ! [A: $i] :
% 0.29/0.47 ( ( in @ A @ X )
% 0.29/0.47 => ( subset @ A @ X ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binintTransitive_type,type,
% 0.29/0.47 binintTransitive: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binintTransitive,definition,
% 0.29/0.47 ( binintTransitive
% 0.29/0.47 = ( ! [X: $i] :
% 0.29/0.47 ( ( transitiveset @ X )
% 0.29/0.47 => ! [Y: $i] :
% 0.29/0.47 ( ( transitiveset @ Y )
% 0.29/0.47 => ( transitiveset @ ( binintersect @ X @ Y ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(transitivesetOp2_type,type,
% 0.29/0.47 transitivesetOp2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(transitivesetOp2,definition,
% 0.29/0.47 ( transitivesetOp2
% 0.29/0.47 = ( ! [X: $i] :
% 0.29/0.47 ( ( transitiveset @ X )
% 0.29/0.47 => ! [A: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ A @ X )
% 0.29/0.47 => ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setunionTransitive_type,type,
% 0.29/0.47 setunionTransitive: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setunionTransitive,definition,
% 0.29/0.47 ( setunionTransitive
% 0.29/0.47 = ( ! [X: $i] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ X )
% 0.29/0.47 => ( transitiveset @ Xx ) )
% 0.29/0.47 => ( transitiveset @ ( setunion @ X ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(stricttotalorderedByIn_type,type,
% 0.29/0.47 stricttotalorderedByIn: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(stricttotalorderedByIn,definition,
% 0.29/0.47 ( stricttotalorderedByIn
% 0.29/0.47 = ( ^ [A: $i] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [X: $i] :
% 0.29/0.47 ( ( in @ X @ A )
% 0.29/0.47 => ! [Y: $i] :
% 0.29/0.47 ( ( in @ Y @ A )
% 0.29/0.47 => ( ( ( in @ Xx @ X )
% 0.29/0.47 & ( in @ X @ Y ) )
% 0.29/0.47 => ( in @ Xx @ Y ) ) ) ) )
% 0.29/0.47 & ! [X: $i] :
% 0.29/0.47 ( ( in @ X @ A )
% 0.29/0.47 => ! [Y: $i] :
% 0.29/0.47 ( ( in @ Y @ A )
% 0.29/0.47 => ( ( X = Y )
% 0.29/0.47 | ( in @ X @ Y )
% 0.29/0.47 | ( in @ Y @ X ) ) ) )
% 0.29/0.47 & ! [X: $i] :
% 0.29/0.47 ( ( in @ X @ A )
% 0.29/0.47 => ~ ( in @ X @ X ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(wellorderedByIn_type,type,
% 0.29/0.47 wellorderedByIn: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(wellorderedByIn,definition,
% 0.29/0.47 ( wellorderedByIn
% 0.29/0.47 = ( ^ [A: $i] :
% 0.29/0.47 ( ( stricttotalorderedByIn @ A )
% 0.29/0.47 & ! [X: $i] :
% 0.29/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.47 => ( ( nonempty @ X )
% 0.29/0.47 => ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ X )
% 0.29/0.47 & ! [Y: $i] :
% 0.29/0.47 ( ( in @ Y @ X )
% 0.29/0.47 => ( ( Xx = Y )
% 0.29/0.47 | ( in @ Xx @ Y ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(ordinal_type,type,
% 0.29/0.47 ordinal: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(ordinal,definition,
% 0.29/0.47 ( ordinal
% 0.29/0.47 = ( ^ [Xx: $i] :
% 0.29/0.47 ( ( transitiveset @ Xx )
% 0.29/0.47 & ( wellorderedByIn @ Xx ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(limitOrdinal_type,type,
% 0.29/0.47 limitOrdinal: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(ordinalMinLem1,conjecture,
% 0.29/0.47 ( setextAx
% 0.29/0.47 => ( emptysetAx
% 0.29/0.47 => ( setadjoinAx
% 0.29/0.47 => ( powersetAx
% 0.29/0.47 => ( setunionAx
% 0.29/0.47 => ( omega0Ax
% 0.29/0.47 => ( omegaSAx
% 0.29/0.47 => ( omegaIndAx
% 0.29/0.47 => ( replAx
% 0.29/0.47 => ( foundationAx
% 0.29/0.47 => ( wellorderingAx
% 0.29/0.47 => ( descrp
% 0.29/0.47 => ( dsetconstrI
% 0.29/0.47 => ( dsetconstrEL
% 0.29/0.47 => ( dsetconstrER
% 0.29/0.47 => ( exuE1
% 0.29/0.47 => ( prop2setE
% 0.29/0.47 => ( emptysetE
% 0.29/0.47 => ( emptysetimpfalse
% 0.29/0.47 => ( notinemptyset
% 0.29/0.47 => ( exuE3e
% 0.29/0.47 => ( setext
% 0.29/0.47 => ( emptyI
% 0.29/0.47 => ( noeltsimpempty
% 0.29/0.47 => ( setbeta
% 0.29/0.47 => ( nonemptyE1
% 0.29/0.47 => ( nonemptyI
% 0.29/0.47 => ( nonemptyI1
% 0.29/0.47 => ( setadjoinIL
% 0.29/0.47 => ( emptyinunitempty
% 0.29/0.47 => ( setadjoinIR
% 0.29/0.47 => ( setadjoinE
% 0.29/0.47 => ( setadjoinOr
% 0.29/0.47 => ( setoftrueEq
% 0.29/0.47 => ( powersetI
% 0.29/0.47 => ( emptyinPowerset
% 0.29/0.47 => ( emptyInPowerset
% 0.29/0.47 => ( powersetE
% 0.29/0.47 => ( setunionI
% 0.29/0.47 => ( setunionE
% 0.29/0.47 => ( subPowSU
% 0.29/0.47 => ( exuE2
% 0.29/0.47 => ( nonemptyImpWitness
% 0.29/0.47 => ( uniqinunit
% 0.29/0.47 => ( notinsingleton
% 0.29/0.47 => ( eqinunit
% 0.29/0.47 => ( singletonsswitch
% 0.29/0.47 => ( upairsetE
% 0.29/0.47 => ( upairsetIL
% 0.29/0.47 => ( upairsetIR
% 0.29/0.47 => ( emptyE1
% 0.29/0.47 => ( vacuousDall
% 0.29/0.47 => ( quantDeMorgan1
% 0.29/0.47 => ( quantDeMorgan2
% 0.29/0.47 => ( quantDeMorgan3
% 0.29/0.47 => ( quantDeMorgan4
% 0.29/0.47 => ( prop2setI
% 0.29/0.47 => ( prop2set2propI
% 0.29/0.47 => ( notdexE
% 0.29/0.47 => ( notdallE
% 0.29/0.47 => ( exuI1
% 0.29/0.47 => ( exuI3
% 0.29/0.47 => ( exuI2
% 0.29/0.47 => ( inCongP
% 0.29/0.47 => ( in__Cong
% 0.29/0.47 => ( exuE3u
% 0.29/0.47 => ( exu__Cong
% 0.29/0.47 => ( emptyset__Cong
% 0.29/0.47 => ( setadjoin__Cong
% 0.29/0.47 => ( powerset__Cong
% 0.29/0.47 => ( setunion__Cong
% 0.29/0.47 => ( omega__Cong
% 0.29/0.47 => ( exuEu
% 0.29/0.47 => ( descr__Cong
% 0.29/0.47 => ( dsetconstr__Cong
% 0.29/0.47 => ( subsetI1
% 0.29/0.47 => ( eqimpsubset2
% 0.29/0.47 => ( eqimpsubset1
% 0.29/0.47 => ( subsetI2
% 0.29/0.47 => ( emptysetsubset
% 0.29/0.47 => ( subsetE
% 0.29/0.47 => ( subsetE2
% 0.29/0.47 => ( notsubsetI
% 0.29/0.47 => ( notequalI1
% 0.29/0.47 => ( notequalI2
% 0.29/0.47 => ( subsetRefl
% 0.29/0.47 => ( subsetTrans
% 0.29/0.47 => ( setadjoinSub
% 0.29/0.47 => ( setadjoinSub2
% 0.29/0.47 => ( subset2powerset
% 0.29/0.47 => ( setextsub
% 0.29/0.47 => ( subsetemptysetimpeq
% 0.29/0.47 => ( powersetI1
% 0.29/0.47 => ( powersetE1
% 0.29/0.47 => ( inPowerset
% 0.29/0.47 => ( powersetsubset
% 0.29/0.47 => ( sepInPowerset
% 0.29/0.47 => ( sepSubset
% 0.29/0.47 => ( binunionIL
% 0.29/0.47 => ( upairset2IR
% 0.29/0.47 => ( binunionIR
% 0.29/0.47 => ( binunionEcases
% 0.29/0.47 => ( binunionE
% 0.29/0.47 => ( binunionLsub
% 0.29/0.47 => ( binunionRsub
% 0.29/0.47 => ( binintersectI
% 0.29/0.47 => ( binintersectSubset5
% 0.29/0.47 => ( binintersectEL
% 0.29/0.47 => ( binintersectLsub
% 0.29/0.47 => ( binintersectSubset2
% 0.29/0.47 => ( binintersectSubset3
% 0.29/0.47 => ( binintersectER
% 0.29/0.47 => ( disjointsetsI1
% 0.29/0.47 => ( binintersectRsub
% 0.29/0.47 => ( binintersectSubset4
% 0.29/0.47 => ( binintersectSubset1
% 0.29/0.47 => ( bs114d
% 0.29/0.47 => ( setminusI
% 0.29/0.47 => ( setminusEL
% 0.29/0.47 => ( setminusER
% 0.29/0.47 => ( setminusSubset2
% 0.29/0.47 => ( setminusERneg
% 0.29/0.47 => ( setminusELneg
% 0.29/0.47 => ( setminusILneg
% 0.29/0.47 => ( setminusIRneg
% 0.29/0.47 => ( setminusLsub
% 0.29/0.47 => ( setminusSubset1
% 0.29/0.47 => ( symdiffE
% 0.29/0.47 => ( symdiffI1
% 0.29/0.47 => ( symdiffI2
% 0.29/0.47 => ( symdiffIneg1
% 0.29/0.47 => ( symdiffIneg2
% 0.29/0.47 => ( secondinupair
% 0.29/0.47 => ( setukpairIL
% 0.29/0.47 => ( setukpairIR
% 0.29/0.47 => ( kpairiskpair
% 0.29/0.47 => ( kpairp
% 0.29/0.47 => ( singletonsubset
% 0.29/0.47 => ( singletoninpowerset
% 0.29/0.47 => ( singletoninpowunion
% 0.29/0.47 => ( upairset2E
% 0.29/0.47 => ( upairsubunion
% 0.29/0.47 => ( upairinpowunion
% 0.29/0.47 => ( ubforcartprodlem1
% 0.29/0.47 => ( ubforcartprodlem2
% 0.29/0.47 => ( ubforcartprodlem3
% 0.29/0.47 => ( cartprodpairin
% 0.29/0.47 => ( cartprodmempair1
% 0.29/0.47 => ( cartprodmempair
% 0.29/0.47 => ( setunionE2
% 0.29/0.47 => ( setunionsingleton1
% 0.29/0.47 => ( setunionsingleton2
% 0.29/0.47 => ( setunionsingleton
% 0.29/0.47 => ( singletonprop
% 0.29/0.47 => ( ex1E1
% 0.29/0.47 => ( ex1I
% 0.29/0.47 => ( ex1I2
% 0.29/0.47 => ( singletonsuniq
% 0.29/0.47 => ( setukpairinjL1
% 0.29/0.47 => ( kfstsingleton
% 0.29/0.47 => ( theprop
% 0.29/0.47 => ( kfstpairEq
% 0.29/0.47 => ( cartprodfstin
% 0.29/0.47 => ( setukpairinjL2
% 0.29/0.47 => ( setukpairinjL
% 0.29/0.47 => ( setukpairinjR11
% 0.29/0.47 => ( setukpairinjR12
% 0.29/0.47 => ( setukpairinjR1
% 0.29/0.47 => ( upairequniteq
% 0.29/0.47 => ( setukpairinjR2
% 0.29/0.47 => ( setukpairinjR
% 0.29/0.47 => ( ksndsingleton
% 0.29/0.47 => ( ksndpairEq
% 0.29/0.47 => ( kpairsurjEq
% 0.29/0.47 => ( cartprodsndin
% 0.29/0.47 => ( cartprodpairmemEL
% 0.29/0.47 => ( cartprodpairmemER
% 0.29/0.47 => ( cartprodmempaircEq
% 0.29/0.47 => ( cartprodfstpairEq
% 0.29/0.47 => ( cartprodsndpairEq
% 0.29/0.47 => ( cartprodpairsurjEq
% 0.29/0.47 => ( dpsetconstrI
% 0.29/0.47 => ( dpsetconstrSub
% 0.29/0.47 => ( setOfPairsIsBReln
% 0.29/0.47 => ( dpsetconstrERa
% 0.29/0.47 => ( dpsetconstrEL1
% 0.29/0.47 => ( dpsetconstrEL2
% 0.29/0.47 => ( dpsetconstrER
% 0.29/0.47 => ( funcImageSingleton
% 0.29/0.47 => ( apProp
% 0.29/0.47 => ( app
% 0.29/0.47 => ( infuncsetfunc
% 0.29/0.47 => ( ap2p
% 0.29/0.47 => ( funcinfuncset
% 0.29/0.47 => ( lamProp
% 0.29/0.47 => ( lamp
% 0.29/0.47 => ( lam2p
% 0.29/0.47 => ( brelnall1
% 0.29/0.47 => ( brelnall2
% 0.29/0.47 => ( ex1E2
% 0.29/0.47 => ( funcGraphProp1
% 0.29/0.47 => ( funcGraphProp3
% 0.29/0.47 => ( funcGraphProp2
% 0.29/0.47 => ( funcextLem
% 0.29/0.47 => ( funcGraphProp4
% 0.29/0.47 => ( subbreln
% 0.29/0.47 => ( eqbreln
% 0.29/0.47 => ( funcext
% 0.29/0.47 => ( funcext2
% 0.29/0.47 => ( ap2apEq1
% 0.29/0.47 => ( ap2apEq2
% 0.29/0.47 => ( beta1
% 0.29/0.47 => ( eta1
% 0.29/0.47 => ( lam2lamEq
% 0.29/0.47 => ( beta2
% 0.29/0.47 => ( eta2
% 0.29/0.47 => ( iffalseProp1
% 0.29/0.47 => ( iffalseProp2
% 0.29/0.47 => ( iftrueProp1
% 0.29/0.47 => ( iftrueProp2
% 0.29/0.47 => ( ifSingleton
% 0.29/0.47 => ( ifp
% 0.29/0.47 => ( theeq
% 0.29/0.47 => ( iftrue
% 0.29/0.47 => ( iffalse
% 0.29/0.47 => ( iftrueorfalse
% 0.29/0.47 => ( binintersectT_lem
% 0.29/0.47 => ( binunionT_lem
% 0.29/0.47 => ( powersetT_lem
% 0.29/0.47 => ( setminusT_lem
% 0.29/0.47 => ( complementT_lem
% 0.29/0.47 => ( setextT
% 0.29/0.47 => ( subsetTI
% 0.29/0.47 => ( powersetTI1
% 0.29/0.47 => ( powersetTE1
% 0.29/0.47 => ( complementTI1
% 0.29/0.47 => ( complementTE1
% 0.29/0.47 => ( binintersectTELcontra
% 0.29/0.47 => ( binintersectTERcontra
% 0.29/0.47 => ( contrasubsetT
% 0.29/0.47 => ( contrasubsetT1
% 0.29/0.47 => ( contrasubsetT2
% 0.29/0.47 => ( contrasubsetT3
% 0.29/0.47 => ( doubleComplementI1
% 0.29/0.47 => ( doubleComplementE1
% 0.29/0.47 => ( doubleComplementSub1
% 0.29/0.47 => ( doubleComplementSub2
% 0.29/0.47 => ( doubleComplementEq
% 0.29/0.47 => ( complementTnotintersectT
% 0.29/0.47 => ( complementImpComplementIntersect
% 0.29/0.47 => ( complementSubsetComplementIntersect
% 0.29/0.47 => ( complementInPowersetComplementIntersect
% 0.29/0.47 => ( contraSubsetComplement
% 0.29/0.47 => ( complementTcontraSubset
% 0.29/0.47 => ( binunionTILcontra
% 0.29/0.47 => ( binunionTIRcontra
% 0.29/0.47 => ( inIntersectImpInUnion
% 0.29/0.47 => ( inIntersectImpInUnion2
% 0.29/0.47 => ( inIntersectImpInIntersectUnions
% 0.29/0.47 => ( intersectInPowersetIntersectUnions
% 0.29/0.47 => ( inComplementUnionImpNotIn1
% 0.29/0.47 => ( inComplementUnionImpInComplement1
% 0.29/0.47 => ( binunionTE
% 0.29/0.47 => ( binunionTEcontra
% 0.29/0.47 => ( demorgan2a1
% 0.29/0.47 => ( complementUnionInPowersetComplement
% 0.29/0.47 => ( demorgan2a2
% 0.29/0.47 => ( demorgan1a
% 0.29/0.47 => ( demorgan1b
% 0.29/0.47 => ( demorgan1
% 0.29/0.47 => ( demorgan2a
% 0.29/0.47 => ( demorgan2b2
% 0.29/0.47 => ( demorgan2b
% 0.29/0.47 => ( demorgan2
% 0.29/0.47 => ( woz13rule0
% 0.29/0.47 => ( woz13rule1
% 0.29/0.47 => ( woz13rule2
% 0.29/0.47 => ( woz13rule3
% 0.29/0.47 => ( woz13rule4
% 0.29/0.47 => ( woz1_1
% 0.29/0.47 => ( woz1_2
% 0.29/0.47 => ( woz1_3
% 0.29/0.47 => ( woz1_4
% 0.29/0.47 => ( woz1_5
% 0.29/0.47 => ( breln1all2
% 0.29/0.47 => ( breln1SetBreln1
% 0.29/0.47 => ( choice2fnsingleton
% 0.29/0.47 => ( setOfPairsIsBReln1
% 0.29/0.47 => ( breln1all1
% 0.29/0.47 => ( subbreln1
% 0.29/0.47 => ( eqbreln1
% 0.29/0.47 => ( breln1invprop
% 0.29/0.47 => ( breln1invI
% 0.29/0.47 => ( breln1invE
% 0.29/0.47 => ( breln1compprop
% 0.29/0.47 => ( breln1compI
% 0.29/0.47 => ( breln1compE
% 0.29/0.47 => ( breln1compEex
% 0.29/0.47 => ( breln1unionprop
% 0.29/0.47 => ( breln1unionIL
% 0.29/0.47 => ( breln1unionIR
% 0.29/0.47 => ( breln1unionI
% 0.29/0.47 => ( breln1unionE
% 0.29/0.47 => ( breln1unionEcases
% 0.29/0.47 => ( breln1unionCommutes
% 0.29/0.47 => ( woz2Ex
% 0.29/0.47 => ( woz2W
% 0.29/0.47 => ( woz2A
% 0.29/0.47 => ( woz2B
% 0.29/0.47 => ( image1Ex
% 0.29/0.47 => ( image1Ex1
% 0.29/0.47 => ( image1Equiv
% 0.29/0.47 => ( image1E
% 0.29/0.47 => ( image1I
% 0.29/0.47 => ( injFuncInInjFuncSet
% 0.29/0.47 => ( injFuncSetFuncIn
% 0.29/0.47 => ( injFuncSetFuncInj
% 0.29/0.47 => ( surjFuncSetFuncIn
% 0.29/0.47 => ( surjFuncSetFuncSurj
% 0.29/0.47 => ( leftInvIsSurj
% 0.29/0.47 => ( surjCantorThm
% 0.29/0.47 => ( foundation2
% 0.29/0.47 => ( notinself
% 0.29/0.47 => ( notinself2
% 0.29/0.47 => ( omegaSp
% 0.29/0.47 => ( omegaSclos
% 0.29/0.47 => ( peano0notS
% 0.29/0.47 => ( peanoSinj
% 0.29/0.47 => ( transitivesetOp1
% 0.29/0.47 => ( binintTransitive
% 0.29/0.47 => ( transitivesetOp2
% 0.29/0.47 => ( setunionTransitive
% 0.29/0.47 => ! [X: $i] :
% 0.29/0.47 ( ( ordinal @ X )
% 0.29/0.47 => ! [Y: $i] :
% 0.29/0.47 ( ( ordinal @ Y )
% 0.29/0.47 => ( transitiveset @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 ------------------------
% 3.01/1.52 ---- Embedded in THF ---
% 3.01/1.52 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.01/1.52 %%% Generated on Tue Feb 24 12:34:34 EST 2026
% 3.01/1.52 %%% using '$$dhol' embedding, version 1.3.0.
% 3.01/1.52 %%% Logic specification used:
% 3.01/1.52 %%% thf(spec, logic, $$dhol).
% 3.01/1.52
% 3.01/1.52 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.SkoTPvEhFx/DTF2DTF24321.p
% See solution above
% 3.01/1.53 ------------------------
% 3.07/1.60 ---- Cleaned THF ---
% 3.07/1.60 thf(in_type,type,
% 3.07/1.60 in: $i > $i > $o ).
% 3.07/1.60
% 3.07/1.60 thf(exu_type,type,
% 3.07/1.60 exu: ( $i > $o ) > $o ).
% 3.07/1.60
% 3.07/1.60 thf(exu,definition,
% 3.07/1.60 ( exu
% 3.07/1.60 = ( ^ [Xphi: $i > $o] :
% 3.07/1.60 ? [Xx: $i] :
% 3.07/1.60 ( ( Xphi @ Xx )
% 3.07/1.60 & ! [Xy: $i] :
% 3.07/1.60 ( ( Xphi @ Xy )
% 3.07/1.60 => ( Xx = Xy ) ) ) ) ) ).
% 3.07/1.60
% 3.07/1.60 thf(setextAx_type,type,
% 3.07/1.60 setextAx: $o ).
% 3.07/1.60
% 3.07/1.60 thf(setextAx,definition,
% 3.07/1.60 ( setextAx
% 3.07/1.60 = ( ! [A: $i,B: $i] :
% 3.07/1.60 ( ! [Xx: $i] :
% 3.07/1.60 ( ( in @ Xx @ A )
% 3.07/1.60 <=> ( in @ Xx @ B ) )
% 3.07/1.60 => ( A = B ) ) ) ) ).
% 3.07/1.60
% 3.07/1.60 thf(emptyset_type,type,
% 3.07/1.60 emptyset: $i ).
% 3.07/1.60
% 3.07/1.60 thf(emptysetAx_type,type,
% 3.07/1.60 emptysetAx: $o ).
% 3.07/1.60
% 3.07/1.60 thf(emptysetAx,definition,
% 3.07/1.60 ( emptysetAx
% 3.07/1.60 = ( ! [Xx: $i] :
% 3.07/1.60 ~ ( in @ Xx @ emptyset ) ) ) ).
% 3.07/1.60
% 3.07/1.60 thf(setadjoin_type,type,
% 3.07/1.60 setadjoin: $i > $i > $i ).
% 3.07/1.60
% 3.07/1.60 thf(setadjoinAx_type,type,
% 3.07/1.60 setadjoinAx: $o ).
% 3.07/1.60
% 3.07/1.60 thf(setadjoinAx,definition,
% 3.07/1.60 ( setadjoinAx
% 3.07/1.60 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.07/1.60 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.07/1.60 <=> ( ( Xy = Xx )
% 3.07/1.60 | ( in @ Xy @ A ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(powerset_type,type,
% 3.07/1.61 powerset: $i > $i ).
% 3.07/1.61
% 3.07/1.61 thf(powersetAx_type,type,
% 3.07/1.61 powersetAx: $o ).
% 3.07/1.61
% 3.07/1.61 thf(powersetAx,definition,
% 3.07/1.61 ( powersetAx
% 3.07/1.61 = ( ! [A: $i,B: $i] :
% 3.07/1.61 ( ( in @ B @ ( powerset @ A ) )
% 3.07/1.61 <=> ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ B )
% 3.07/1.61 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setunion_type,type,
% 3.07/1.61 setunion: $i > $i ).
% 3.07/1.61
% 3.07/1.61 thf(setunionAx_type,type,
% 3.07/1.61 setunionAx: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setunionAx,definition,
% 3.07/1.61 ( setunionAx
% 3.07/1.61 = ( ! [A: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ ( setunion @ A ) )
% 3.07/1.61 <=> ? [B: $i] :
% 3.07/1.61 ( ( in @ Xx @ B )
% 3.07/1.61 & ( in @ B @ A ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(omega_type,type,
% 3.07/1.61 omega: $i ).
% 3.07/1.61
% 3.07/1.61 thf(omega0Ax_type,type,
% 3.07/1.61 omega0Ax: $o ).
% 3.07/1.61
% 3.07/1.61 thf(omega0Ax,definition,
% 3.07/1.61 ( omega0Ax
% 3.07/1.61 = ( in @ emptyset @ omega ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(omegaSAx_type,type,
% 3.07/1.61 omegaSAx: $o ).
% 3.07/1.61
% 3.07/1.61 thf(omegaSAx,definition,
% 3.07/1.61 ( omegaSAx
% 3.07/1.61 = ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ omega )
% 3.07/1.61 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(omegaIndAx_type,type,
% 3.07/1.61 omegaIndAx: $o ).
% 3.07/1.61
% 3.07/1.61 thf(omegaIndAx,definition,
% 3.07/1.61 ( omegaIndAx
% 3.07/1.61 = ( ! [A: $i] :
% 3.07/1.61 ( ( ( in @ emptyset @ A )
% 3.07/1.61 & ! [Xx: $i] :
% 3.07/1.61 ( ( ( in @ Xx @ omega )
% 3.07/1.61 & ( in @ Xx @ A ) )
% 3.07/1.61 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ omega )
% 3.07/1.61 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(replAx_type,type,
% 3.07/1.61 replAx: $o ).
% 3.07/1.61
% 3.07/1.61 thf(replAx,definition,
% 3.07/1.61 ( replAx
% 3.07/1.61 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 3.07/1.61 ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( exu
% 3.07/1.61 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 3.07/1.61 => ? [B: $i] :
% 3.07/1.61 ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ B )
% 3.07/1.61 <=> ? [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(foundationAx_type,type,
% 3.07/1.61 foundationAx: $o ).
% 3.07/1.61
% 3.07/1.61 thf(foundationAx,definition,
% 3.07/1.61 ( foundationAx
% 3.07/1.61 = ( ! [A: $i] :
% 3.07/1.61 ( ? [Xx: $i] : ( in @ Xx @ A )
% 3.07/1.61 => ? [B: $i] :
% 3.07/1.61 ( ( in @ B @ A )
% 3.07/1.61 & ~ ? [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ B )
% 3.07/1.61 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(wellorderingAx_type,type,
% 3.07/1.61 wellorderingAx: $o ).
% 3.07/1.61
% 3.07/1.61 thf(wellorderingAx,definition,
% 3.07/1.61 ( wellorderingAx
% 3.07/1.61 = ( ! [A: $i] :
% 3.07/1.61 ? [B: $i] :
% 3.07/1.61 ( ! [C: $i] :
% 3.07/1.61 ( ( in @ C @ B )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ C )
% 3.07/1.61 => ( in @ Xx @ A ) ) )
% 3.07/1.61 & ! [Xx: $i,Xy: $i] :
% 3.07/1.61 ( ( ( in @ Xx @ A )
% 3.07/1.61 & ( in @ Xy @ A ) )
% 3.07/1.61 => ( ! [C: $i] :
% 3.07/1.61 ( ( in @ C @ B )
% 3.07/1.61 => ( ( in @ Xx @ C )
% 3.07/1.61 <=> ( in @ Xy @ C ) ) )
% 3.07/1.61 => ( Xx = Xy ) ) )
% 3.07/1.61 & ! [C: $i,D: $i] :
% 3.07/1.61 ( ( ( in @ C @ B )
% 3.07/1.61 & ( in @ D @ B ) )
% 3.07/1.61 => ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ C )
% 3.07/1.61 => ( in @ Xx @ D ) )
% 3.07/1.61 | ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ D )
% 3.07/1.61 => ( in @ Xx @ C ) ) ) )
% 3.07/1.61 & ! [C: $i] :
% 3.07/1.61 ( ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ C )
% 3.07/1.61 => ( in @ Xx @ A ) )
% 3.07/1.61 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 3.07/1.61 => ? [D: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ D @ B )
% 3.07/1.61 & ( in @ Xx @ C )
% 3.07/1.61 & ~ ? [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ D )
% 3.07/1.61 & ( in @ Xy @ C ) )
% 3.07/1.61 & ! [E: $i] :
% 3.07/1.61 ( ( in @ E @ B )
% 3.07/1.61 => ( ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ E )
% 3.07/1.61 => ( in @ Xy @ D ) )
% 3.07/1.61 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(descr_type,type,
% 3.07/1.61 descr: ( $i > $o ) > $i ).
% 3.07/1.61
% 3.07/1.61 thf(descrp_type,type,
% 3.07/1.61 descrp: $o ).
% 3.07/1.61
% 3.07/1.61 thf(descrp,definition,
% 3.07/1.61 ( descrp
% 3.07/1.61 = ( ! [Xphi: $i > $o] :
% 3.07/1.61 ( ( exu
% 3.07/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.07/1.61 => ( Xphi
% 3.07/1.61 @ ( descr
% 3.07/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(dsetconstr_type,type,
% 3.07/1.61 dsetconstr: $i > ( $i > $o ) > $i ).
% 3.07/1.61
% 3.07/1.61 thf(dsetconstrI_type,type,
% 3.07/1.61 dsetconstrI: $o ).
% 3.07/1.61
% 3.07/1.61 thf(dsetconstrI,definition,
% 3.07/1.61 ( dsetconstrI
% 3.07/1.61 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( Xphi @ Xx )
% 3.07/1.61 => ( in @ Xx
% 3.07/1.61 @ ( dsetconstr @ A
% 3.07/1.61 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(dsetconstrEL_type,type,
% 3.07/1.61 dsetconstrEL: $o ).
% 3.07/1.61
% 3.07/1.61 thf(dsetconstrEL,definition,
% 3.07/1.61 ( dsetconstrEL
% 3.07/1.61 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx
% 3.07/1.61 @ ( dsetconstr @ A
% 3.07/1.61 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.07/1.61 => ( in @ Xx @ A ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(dsetconstrER_type,type,
% 3.07/1.61 dsetconstrER: $o ).
% 3.07/1.61
% 3.07/1.61 thf(dsetconstrER,definition,
% 3.07/1.61 ( dsetconstrER
% 3.07/1.61 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx
% 3.07/1.61 @ ( dsetconstr @ A
% 3.07/1.61 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.07/1.61 => ( Xphi @ Xx ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(exuE1_type,type,
% 3.07/1.61 exuE1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(exuE1,definition,
% 3.07/1.61 ( exuE1
% 3.07/1.61 = ( ! [Xphi: $i > $o] :
% 3.07/1.61 ( ( exu
% 3.07/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.07/1.61 => ? [Xx: $i] :
% 3.07/1.61 ( ( Xphi @ Xx )
% 3.07/1.61 & ! [Xy: $i] :
% 3.07/1.61 ( ( Xphi @ Xy )
% 3.07/1.61 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(prop2set_type,type,
% 3.07/1.61 prop2set: $o > $i ).
% 3.07/1.61
% 3.07/1.61 thf(prop2setE_type,type,
% 3.07/1.61 prop2setE: $o ).
% 3.07/1.61
% 3.07/1.61 thf(prop2setE,definition,
% 3.07/1.61 ( prop2setE
% 3.07/1.61 = ( ! [Xphi: $o,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 3.07/1.61 => Xphi ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(emptysetE_type,type,
% 3.07/1.61 emptysetE: $o ).
% 3.07/1.61
% 3.07/1.61 thf(emptysetE,definition,
% 3.07/1.61 ( emptysetE
% 3.07/1.61 = ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ emptyset )
% 3.07/1.61 => ! [Xphi: $o] : Xphi ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(emptysetimpfalse_type,type,
% 3.07/1.61 emptysetimpfalse: $o ).
% 3.07/1.61
% 3.07/1.61 thf(emptysetimpfalse,definition,
% 3.07/1.61 ( emptysetimpfalse
% 3.07/1.61 = ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ emptyset )
% 3.07/1.61 => $false ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(notinemptyset_type,type,
% 3.07/1.61 notinemptyset: $o ).
% 3.07/1.61
% 3.07/1.61 thf(notinemptyset,definition,
% 3.07/1.61 ( notinemptyset
% 3.07/1.61 = ( ! [Xx: $i] :
% 3.07/1.61 ~ ( in @ Xx @ emptyset ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(exuE3e_type,type,
% 3.07/1.61 exuE3e: $o ).
% 3.07/1.61
% 3.07/1.61 thf(exuE3e,definition,
% 3.07/1.61 ( exuE3e
% 3.07/1.61 = ( ! [Xphi: $i > $o] :
% 3.07/1.61 ( ( exu
% 3.07/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.07/1.61 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setext_type,type,
% 3.07/1.61 setext: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setext,definition,
% 3.07/1.61 ( setext
% 3.07/1.61 = ( ! [A: $i,B: $i] :
% 3.07/1.61 ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( in @ Xx @ B ) )
% 3.07/1.61 => ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ B )
% 3.07/1.61 => ( in @ Xx @ A ) )
% 3.07/1.61 => ( A = B ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(emptyI_type,type,
% 3.07/1.61 emptyI: $o ).
% 3.07/1.61
% 3.07/1.61 thf(emptyI,definition,
% 3.07/1.61 ( emptyI
% 3.07/1.61 = ( ! [A: $i] :
% 3.07/1.61 ( ! [Xx: $i] :
% 3.07/1.61 ~ ( in @ Xx @ A )
% 3.07/1.61 => ( A = emptyset ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(noeltsimpempty_type,type,
% 3.07/1.61 noeltsimpempty: $o ).
% 3.07/1.61
% 3.07/1.61 thf(noeltsimpempty,definition,
% 3.07/1.61 ( noeltsimpempty
% 3.07/1.61 = ( ! [A: $i] :
% 3.07/1.61 ( ! [Xx: $i] :
% 3.07/1.61 ~ ( in @ Xx @ A )
% 3.07/1.61 => ( A = emptyset ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setbeta_type,type,
% 3.07/1.61 setbeta: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setbeta,definition,
% 3.07/1.61 ( setbeta
% 3.07/1.61 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( in @ Xx
% 3.07/1.61 @ ( dsetconstr @ A
% 3.07/1.61 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.07/1.61 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(nonempty_type,type,
% 3.07/1.61 nonempty: $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(nonempty,definition,
% 3.07/1.61 ( nonempty
% 3.07/1.61 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(nonemptyE1_type,type,
% 3.07/1.61 nonemptyE1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(nonemptyE1,definition,
% 3.07/1.61 ( nonemptyE1
% 3.07/1.61 = ( ! [A: $i] :
% 3.07/1.61 ( ( nonempty @ A )
% 3.07/1.61 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(nonemptyI_type,type,
% 3.07/1.61 nonemptyI: $o ).
% 3.07/1.61
% 3.07/1.61 thf(nonemptyI,definition,
% 3.07/1.61 ( nonemptyI
% 3.07/1.61 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( Xphi @ Xx )
% 3.07/1.61 => ( nonempty
% 3.07/1.61 @ ( dsetconstr @ A
% 3.07/1.61 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(nonemptyI1_type,type,
% 3.07/1.61 nonemptyI1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(nonemptyI1,definition,
% 3.07/1.61 ( nonemptyI1
% 3.07/1.61 = ( ! [A: $i] :
% 3.07/1.61 ( ? [Xx: $i] : ( in @ Xx @ A )
% 3.07/1.61 => ( nonempty @ A ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setadjoinIL_type,type,
% 3.07/1.61 setadjoinIL: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setadjoinIL,definition,
% 3.07/1.61 ( setadjoinIL
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(emptyinunitempty_type,type,
% 3.07/1.61 emptyinunitempty: $o ).
% 3.07/1.61
% 3.07/1.61 thf(emptyinunitempty,definition,
% 3.07/1.61 ( emptyinunitempty
% 3.07/1.61 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setadjoinIR_type,type,
% 3.07/1.61 setadjoinIR: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setadjoinIR,definition,
% 3.07/1.61 ( setadjoinIR
% 3.07/1.61 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setadjoinE_type,type,
% 3.07/1.61 setadjoinE: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setadjoinE,definition,
% 3.07/1.61 ( setadjoinE
% 3.07/1.61 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.07/1.61 => ! [Xphi: $o] :
% 3.07/1.61 ( ( ( Xy = Xx )
% 3.07/1.61 => Xphi )
% 3.07/1.61 => ( ( ( in @ Xy @ A )
% 3.07/1.61 => Xphi )
% 3.07/1.61 => Xphi ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setadjoinOr_type,type,
% 3.07/1.61 setadjoinOr: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setadjoinOr,definition,
% 3.07/1.61 ( setadjoinOr
% 3.07/1.61 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.07/1.61 => ( ( Xy = Xx )
% 3.07/1.61 | ( in @ Xy @ A ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setoftrueEq_type,type,
% 3.07/1.61 setoftrueEq: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setoftrueEq,definition,
% 3.07/1.61 ( setoftrueEq
% 3.07/1.61 = ( ! [A: $i] :
% 3.07/1.61 ( ( dsetconstr @ A
% 3.07/1.61 @ ^ [Xx: $i] : $true )
% 3.07/1.61 = A ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(powersetI_type,type,
% 3.07/1.61 powersetI: $o ).
% 3.07/1.61
% 3.07/1.61 thf(powersetI,definition,
% 3.07/1.61 ( powersetI
% 3.07/1.61 = ( ! [A: $i,B: $i] :
% 3.07/1.61 ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ B )
% 3.07/1.61 => ( in @ Xx @ A ) )
% 3.07/1.61 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(emptyinPowerset_type,type,
% 3.07/1.61 emptyinPowerset: $o ).
% 3.07/1.61
% 3.07/1.61 thf(emptyinPowerset,definition,
% 3.07/1.61 ( emptyinPowerset
% 3.07/1.61 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(emptyInPowerset_type,type,
% 3.07/1.61 emptyInPowerset: $o ).
% 3.07/1.61
% 3.07/1.61 thf(emptyInPowerset,definition,
% 3.07/1.61 ( emptyInPowerset
% 3.07/1.61 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(powersetE_type,type,
% 3.07/1.61 powersetE: $o ).
% 3.07/1.61
% 3.07/1.61 thf(powersetE,definition,
% 3.07/1.61 ( powersetE
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ B @ ( powerset @ A ) )
% 3.07/1.61 => ( ( in @ Xx @ B )
% 3.07/1.61 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setunionI_type,type,
% 3.07/1.61 setunionI: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setunionI,definition,
% 3.07/1.61 ( setunionI
% 3.07/1.61 = ( ! [A: $i,Xx: $i,B: $i] :
% 3.07/1.61 ( ( in @ Xx @ B )
% 3.07/1.61 => ( ( in @ B @ A )
% 3.07/1.61 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setunionE_type,type,
% 3.07/1.61 setunionE: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setunionE,definition,
% 3.07/1.61 ( setunionE
% 3.07/1.61 = ( ! [A: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ ( setunion @ A ) )
% 3.07/1.61 => ! [Xphi: $o] :
% 3.07/1.61 ( ! [B: $i] :
% 3.07/1.61 ( ( in @ Xx @ B )
% 3.07/1.61 => ( ( in @ B @ A )
% 3.07/1.61 => Xphi ) )
% 3.07/1.61 => Xphi ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(subPowSU_type,type,
% 3.07/1.61 subPowSU: $o ).
% 3.07/1.61
% 3.07/1.61 thf(subPowSU,definition,
% 3.07/1.61 ( subPowSU
% 3.07/1.61 = ( ! [A: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(exuE2_type,type,
% 3.07/1.61 exuE2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(exuE2,definition,
% 3.07/1.61 ( exuE2
% 3.07/1.61 = ( ! [Xphi: $i > $o] :
% 3.07/1.61 ( ( exu
% 3.07/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.07/1.61 => ? [Xx: $i] :
% 3.07/1.61 ! [Xy: $i] :
% 3.07/1.61 ( ( Xphi @ Xy )
% 3.07/1.61 <=> ( Xy = Xx ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(nonemptyImpWitness_type,type,
% 3.07/1.61 nonemptyImpWitness: $o ).
% 3.07/1.61
% 3.07/1.61 thf(nonemptyImpWitness,definition,
% 3.07/1.61 ( nonemptyImpWitness
% 3.07/1.61 = ( ! [A: $i] :
% 3.07/1.61 ( ( nonempty @ A )
% 3.07/1.61 => ? [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 & $true ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(uniqinunit_type,type,
% 3.07/1.61 uniqinunit: $o ).
% 3.07/1.61
% 3.07/1.61 thf(uniqinunit,definition,
% 3.07/1.61 ( uniqinunit
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i] :
% 3.07/1.61 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.07/1.61 => ( Xx = Xy ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(notinsingleton_type,type,
% 3.07/1.61 notinsingleton: $o ).
% 3.07/1.61
% 3.07/1.61 thf(notinsingleton,definition,
% 3.07/1.61 ( notinsingleton
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i] :
% 3.07/1.61 ( ( Xx != Xy )
% 3.07/1.61 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(eqinunit_type,type,
% 3.07/1.61 eqinunit: $o ).
% 3.07/1.61
% 3.07/1.61 thf(eqinunit,definition,
% 3.07/1.61 ( eqinunit
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i] :
% 3.07/1.61 ( ( Xx = Xy )
% 3.07/1.61 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(singletonsswitch_type,type,
% 3.07/1.61 singletonsswitch: $o ).
% 3.07/1.61
% 3.07/1.61 thf(singletonsswitch,definition,
% 3.07/1.61 ( singletonsswitch
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i] :
% 3.07/1.61 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.07/1.61 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(upairsetE_type,type,
% 3.07/1.61 upairsetE: $o ).
% 3.07/1.61
% 3.07/1.61 thf(upairsetE,definition,
% 3.07/1.61 ( upairsetE
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.07/1.61 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 3.07/1.61 => ( ( Xz = Xx )
% 3.07/1.61 | ( Xz = Xy ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(upairsetIL_type,type,
% 3.07/1.61 upairsetIL: $o ).
% 3.07/1.61
% 3.07/1.61 thf(upairsetIL,definition,
% 3.07/1.61 ( upairsetIL
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(upairsetIR_type,type,
% 3.07/1.61 upairsetIR: $o ).
% 3.07/1.61
% 3.07/1.61 thf(upairsetIR,definition,
% 3.07/1.61 ( upairsetIR
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(emptyE1_type,type,
% 3.07/1.61 emptyE1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(emptyE1,definition,
% 3.07/1.61 ( emptyE1
% 3.07/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 3.07/1.61 ( ? [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 & ( Xphi @ Xx ) )
% 3.07/1.61 => ( ( ( dsetconstr @ A
% 3.07/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.07/1.61 = emptyset )
% 3.07/1.61 => $false ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(vacuousDall_type,type,
% 3.07/1.61 vacuousDall: $o ).
% 3.07/1.61
% 3.07/1.61 thf(vacuousDall,definition,
% 3.07/1.61 ( vacuousDall
% 3.07/1.61 = ( ! [Xphi: $i > $o,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ emptyset )
% 3.07/1.61 => ( Xphi @ Xx ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(quantDeMorgan1_type,type,
% 3.07/1.61 quantDeMorgan1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(quantDeMorgan1,definition,
% 3.07/1.61 ( quantDeMorgan1
% 3.07/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 3.07/1.61 ( ~ ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( Xphi @ Xx ) )
% 3.07/1.61 => ? [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(quantDeMorgan2_type,type,
% 3.07/1.61 quantDeMorgan2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(quantDeMorgan2,definition,
% 3.07/1.61 ( quantDeMorgan2
% 3.07/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 3.07/1.61 ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ~ ( Xphi @ Xx ) )
% 3.07/1.61 => ~ ? [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 & ( Xphi @ Xx ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(quantDeMorgan3_type,type,
% 3.07/1.61 quantDeMorgan3: $o ).
% 3.07/1.61
% 3.07/1.61 thf(quantDeMorgan3,definition,
% 3.07/1.61 ( quantDeMorgan3
% 3.07/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 3.07/1.61 ( ~ ? [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 & ( Xphi @ Xx ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(quantDeMorgan4_type,type,
% 3.07/1.61 quantDeMorgan4: $o ).
% 3.07/1.61
% 3.07/1.61 thf(quantDeMorgan4,definition,
% 3.07/1.61 ( quantDeMorgan4
% 3.07/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 3.07/1.61 ( ? [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 & ~ ( Xphi @ Xx ) )
% 3.07/1.61 => ~ ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( Xphi @ Xx ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(prop2setI_type,type,
% 3.07/1.61 prop2setI: $o ).
% 3.07/1.61
% 3.07/1.61 thf(prop2setI,definition,
% 3.07/1.61 ( prop2setI
% 3.07/1.61 = ( ! [Xphi: $o] :
% 3.07/1.61 ( Xphi
% 3.07/1.61 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(set2prop_type,type,
% 3.07/1.61 set2prop: $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(prop2set2propI_type,type,
% 3.07/1.61 prop2set2propI: $o ).
% 3.07/1.61
% 3.07/1.61 thf(prop2set2propI,definition,
% 3.07/1.61 ( prop2set2propI
% 3.07/1.61 = ( ! [Xphi: $o] :
% 3.07/1.61 ( Xphi
% 3.07/1.61 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(notdexE_type,type,
% 3.07/1.61 notdexE: $o ).
% 3.07/1.61
% 3.07/1.61 thf(notdexE,definition,
% 3.07/1.61 ( notdexE
% 3.07/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 3.07/1.61 ( ~ ? [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 & ( Xphi @ Xx ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(notdallE_type,type,
% 3.07/1.61 notdallE: $o ).
% 3.07/1.61
% 3.07/1.61 thf(notdallE,definition,
% 3.07/1.61 ( notdallE
% 3.07/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 3.07/1.61 ( ~ ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( Xphi @ Xx ) )
% 3.07/1.61 => ? [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(exuI1_type,type,
% 3.07/1.61 exuI1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(exuI1,definition,
% 3.07/1.61 ( exuI1
% 3.07/1.61 = ( ! [Xphi: $i > $o] :
% 3.07/1.61 ( ? [Xx: $i] :
% 3.07/1.61 ( ( Xphi @ Xx )
% 3.07/1.61 & ! [Xy: $i] :
% 3.07/1.61 ( ( Xphi @ Xy )
% 3.07/1.61 => ( Xx = Xy ) ) )
% 3.07/1.61 => ( exu
% 3.07/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(exuI3_type,type,
% 3.07/1.61 exuI3: $o ).
% 3.07/1.61
% 3.07/1.61 thf(exuI3,definition,
% 3.07/1.61 ( exuI3
% 3.07/1.61 = ( ! [Xphi: $i > $o] :
% 3.07/1.61 ( ? [Xx: $i] : ( Xphi @ Xx )
% 3.07/1.61 => ( ! [Xx: $i,Xy: $i] :
% 3.07/1.61 ( ( Xphi @ Xx )
% 3.07/1.61 => ( ( Xphi @ Xy )
% 3.07/1.61 => ( Xx = Xy ) ) )
% 3.07/1.61 => ( exu
% 3.07/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(exuI2_type,type,
% 3.07/1.61 exuI2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(exuI2,definition,
% 3.07/1.61 ( exuI2
% 3.07/1.61 = ( ! [Xphi: $i > $o] :
% 3.07/1.61 ( ? [Xx: $i] :
% 3.07/1.61 ! [Xy: $i] :
% 3.07/1.61 ( ( Xphi @ Xy )
% 3.07/1.61 <=> ( Xy = Xx ) )
% 3.07/1.61 => ( exu
% 3.07/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(inCongP_type,type,
% 3.07/1.61 inCongP: $o ).
% 3.07/1.61
% 3.07/1.61 thf(inCongP,definition,
% 3.07/1.61 ( inCongP
% 3.07/1.61 = ( ! [A: $i,B: $i] :
% 3.07/1.61 ( ( A = B )
% 3.07/1.61 => ! [Xx: $i,Xy: $i] :
% 3.07/1.61 ( ( Xx = Xy )
% 3.07/1.61 => ( ( in @ Xx @ A )
% 3.07/1.61 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(in__Cong_type,type,
% 3.07/1.61 in__Cong: $o ).
% 3.07/1.61
% 3.07/1.61 thf(in__Cong,definition,
% 3.07/1.61 ( in__Cong
% 3.07/1.61 = ( ! [A: $i,B: $i] :
% 3.07/1.61 ( ( A = B )
% 3.07/1.61 => ! [Xx: $i,Xy: $i] :
% 3.07/1.61 ( ( Xx = Xy )
% 3.07/1.61 => ( ( in @ Xx @ A )
% 3.07/1.61 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(exuE3u_type,type,
% 3.07/1.61 exuE3u: $o ).
% 3.07/1.61
% 3.07/1.61 thf(exuE3u,definition,
% 3.07/1.61 ( exuE3u
% 3.07/1.61 = ( ! [Xphi: $i > $o] :
% 3.07/1.61 ( ( exu
% 3.07/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.07/1.61 => ! [Xx: $i,Xy: $i] :
% 3.07/1.61 ( ( Xphi @ Xx )
% 3.07/1.61 => ( ( Xphi @ Xy )
% 3.07/1.61 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(exu__Cong_type,type,
% 3.07/1.61 exu__Cong: $o ).
% 3.07/1.61
% 3.07/1.61 thf(exu__Cong,definition,
% 3.07/1.61 ( exu__Cong
% 3.07/1.61 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.07/1.61 ( ! [Xx: $i,Xy: $i] :
% 3.07/1.61 ( ( Xx = Xy )
% 3.07/1.61 => ( ( Xphi @ Xx )
% 3.07/1.61 <=> ( Xpsi @ Xy ) ) )
% 3.07/1.61 => ( ( exu
% 3.07/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.07/1.61 <=> ( exu
% 3.07/1.61 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(emptyset__Cong_type,type,
% 3.07/1.61 emptyset__Cong: $o ).
% 3.07/1.61
% 3.07/1.61 thf(emptyset__Cong,definition,
% 3.07/1.61 ( emptyset__Cong
% 3.07/1.61 = ( emptyset = emptyset ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setadjoin__Cong_type,type,
% 3.07/1.61 setadjoin__Cong: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setadjoin__Cong,definition,
% 3.07/1.61 ( setadjoin__Cong
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i] :
% 3.07/1.61 ( ( Xx = Xy )
% 3.07/1.61 => ! [Xz: $i,Xu: $i] :
% 3.07/1.61 ( ( Xz = Xu )
% 3.07/1.61 => ( ( setadjoin @ Xx @ Xz )
% 3.07/1.61 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(powerset__Cong_type,type,
% 3.07/1.61 powerset__Cong: $o ).
% 3.07/1.61
% 3.07/1.61 thf(powerset__Cong,definition,
% 3.07/1.61 ( powerset__Cong
% 3.07/1.61 = ( ! [A: $i,B: $i] :
% 3.07/1.61 ( ( A = B )
% 3.07/1.61 => ( ( powerset @ A )
% 3.07/1.61 = ( powerset @ B ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setunion__Cong_type,type,
% 3.07/1.61 setunion__Cong: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setunion__Cong,definition,
% 3.07/1.61 ( setunion__Cong
% 3.07/1.61 = ( ! [A: $i,B: $i] :
% 3.07/1.61 ( ( A = B )
% 3.07/1.61 => ( ( setunion @ A )
% 3.07/1.61 = ( setunion @ B ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(omega__Cong_type,type,
% 3.07/1.61 omega__Cong: $o ).
% 3.07/1.61
% 3.07/1.61 thf(omega__Cong,definition,
% 3.07/1.61 ( omega__Cong
% 3.07/1.61 = ( omega = omega ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(exuEu_type,type,
% 3.07/1.61 exuEu: $o ).
% 3.07/1.61
% 3.07/1.61 thf(exuEu,definition,
% 3.07/1.61 ( exuEu
% 3.07/1.61 = ( ! [Xphi: $i > $o] :
% 3.07/1.61 ( ( exu
% 3.07/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.07/1.61 => ! [Xx: $i,Xy: $i] :
% 3.07/1.61 ( ( Xphi @ Xx )
% 3.07/1.61 => ( ( Xphi @ Xy )
% 3.07/1.61 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(descr__Cong_type,type,
% 3.07/1.61 descr__Cong: $o ).
% 3.07/1.61
% 3.07/1.61 thf(descr__Cong,definition,
% 3.07/1.61 ( descr__Cong
% 3.07/1.61 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.07/1.61 ( ! [Xx: $i,Xy: $i] :
% 3.07/1.61 ( ( Xx = Xy )
% 3.07/1.61 => ( ( Xphi @ Xx )
% 3.07/1.61 <=> ( Xpsi @ Xy ) ) )
% 3.07/1.61 => ( ( exu
% 3.07/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.07/1.61 => ( ( exu
% 3.07/1.61 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 3.07/1.61 => ( ( descr
% 3.07/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.07/1.61 = ( descr
% 3.07/1.61 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(dsetconstr__Cong_type,type,
% 3.07/1.61 dsetconstr__Cong: $o ).
% 3.07/1.61
% 3.07/1.61 thf(dsetconstr__Cong,definition,
% 3.07/1.61 ( dsetconstr__Cong
% 3.07/1.61 = ( ! [A: $i,B: $i] :
% 3.07/1.61 ( ( A = B )
% 3.07/1.61 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.07/1.61 ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ B )
% 3.07/1.61 => ( ( Xx = Xy )
% 3.07/1.61 => ( ( Xphi @ Xx )
% 3.07/1.61 <=> ( Xpsi @ Xy ) ) ) ) )
% 3.07/1.61 => ( ( dsetconstr @ A
% 3.07/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.07/1.61 = ( dsetconstr @ B
% 3.07/1.61 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(subset_type,type,
% 3.07/1.61 subset: $i > $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(disjoint_type,type,
% 3.07/1.61 disjoint: $i > $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(setsmeet_type,type,
% 3.07/1.61 setsmeet: $i > $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(subsetI1_type,type,
% 3.07/1.61 subsetI1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(subsetI1,definition,
% 3.07/1.61 ( subsetI1
% 3.07/1.61 = ( ! [A: $i,B: $i] :
% 3.07/1.61 ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( in @ Xx @ B ) )
% 3.07/1.61 => ( subset @ A @ B ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(eqimpsubset2_type,type,
% 3.07/1.61 eqimpsubset2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(eqimpsubset2,definition,
% 3.07/1.61 ( eqimpsubset2
% 3.07/1.61 = ( ! [A: $i,B: $i] :
% 3.07/1.61 ( ( A = B )
% 3.07/1.61 => ( subset @ B @ A ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(eqimpsubset1_type,type,
% 3.07/1.61 eqimpsubset1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(eqimpsubset1,definition,
% 3.07/1.61 ( eqimpsubset1
% 3.07/1.61 = ( ! [A: $i,B: $i] :
% 3.07/1.61 ( ( A = B )
% 3.07/1.61 => ( subset @ A @ B ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(subsetI2_type,type,
% 3.07/1.61 subsetI2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(subsetI2,definition,
% 3.07/1.61 ( subsetI2
% 3.07/1.61 = ( ! [A: $i,B: $i] :
% 3.07/1.61 ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( in @ Xx @ B ) )
% 3.07/1.61 => ( subset @ A @ B ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(emptysetsubset_type,type,
% 3.07/1.61 emptysetsubset: $o ).
% 3.07/1.61
% 3.07/1.61 thf(emptysetsubset,definition,
% 3.07/1.61 ( emptysetsubset
% 3.07/1.61 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(subsetE_type,type,
% 3.07/1.61 subsetE: $o ).
% 3.07/1.61
% 3.07/1.61 thf(subsetE,definition,
% 3.07/1.61 ( subsetE
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ( subset @ A @ B )
% 3.07/1.61 => ( ( in @ Xx @ A )
% 3.07/1.61 => ( in @ Xx @ B ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(subsetE2_type,type,
% 3.07/1.61 subsetE2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(subsetE2,definition,
% 3.07/1.61 ( subsetE2
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ( subset @ A @ B )
% 3.07/1.61 => ( ~ ( in @ Xx @ B )
% 3.07/1.61 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(notsubsetI_type,type,
% 3.07/1.61 notsubsetI: $o ).
% 3.07/1.61
% 3.07/1.61 thf(notsubsetI,definition,
% 3.07/1.61 ( notsubsetI
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ~ ( in @ Xx @ B )
% 3.07/1.61 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(notequalI1_type,type,
% 3.07/1.61 notequalI1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(notequalI1,definition,
% 3.07/1.61 ( notequalI1
% 3.07/1.61 = ( ! [A: $i,B: $i] :
% 3.07/1.61 ( ~ ( subset @ A @ B )
% 3.07/1.61 => ( A != B ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(notequalI2_type,type,
% 3.07/1.61 notequalI2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(notequalI2,definition,
% 3.07/1.61 ( notequalI2
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ~ ( in @ Xx @ B )
% 3.07/1.61 => ( A != B ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(subsetRefl_type,type,
% 3.07/1.61 subsetRefl: $o ).
% 3.07/1.61
% 3.07/1.61 thf(subsetRefl,definition,
% 3.07/1.61 ( subsetRefl
% 3.07/1.61 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(subsetTrans_type,type,
% 3.07/1.61 subsetTrans: $o ).
% 3.07/1.61
% 3.07/1.61 thf(subsetTrans,definition,
% 3.07/1.61 ( subsetTrans
% 3.07/1.61 = ( ! [A: $i,B: $i,C: $i] :
% 3.07/1.61 ( ( subset @ A @ B )
% 3.07/1.61 => ( ( subset @ B @ C )
% 3.07/1.61 => ( subset @ A @ C ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setadjoinSub_type,type,
% 3.07/1.61 setadjoinSub: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setadjoinSub,definition,
% 3.07/1.61 ( setadjoinSub
% 3.07/1.61 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setadjoinSub2_type,type,
% 3.07/1.61 setadjoinSub2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setadjoinSub2,definition,
% 3.07/1.61 ( setadjoinSub2
% 3.07/1.61 = ( ! [A: $i,Xx: $i,B: $i] :
% 3.07/1.61 ( ( subset @ A @ B )
% 3.07/1.61 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(subset2powerset_type,type,
% 3.07/1.61 subset2powerset: $o ).
% 3.07/1.61
% 3.07/1.61 thf(subset2powerset,definition,
% 3.07/1.61 ( subset2powerset
% 3.07/1.61 = ( ! [A: $i,B: $i] :
% 3.07/1.61 ( ( subset @ A @ B )
% 3.07/1.61 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setextsub_type,type,
% 3.07/1.61 setextsub: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setextsub,definition,
% 3.07/1.61 ( setextsub
% 3.07/1.61 = ( ! [A: $i,B: $i] :
% 3.07/1.61 ( ( subset @ A @ B )
% 3.07/1.61 => ( ( subset @ B @ A )
% 3.07/1.61 => ( A = B ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(subsetemptysetimpeq_type,type,
% 3.07/1.61 subsetemptysetimpeq: $o ).
% 3.07/1.61
% 3.07/1.61 thf(subsetemptysetimpeq,definition,
% 3.07/1.61 ( subsetemptysetimpeq
% 3.07/1.61 = ( ! [A: $i] :
% 3.07/1.61 ( ( subset @ A @ emptyset )
% 3.07/1.61 => ( A = emptyset ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(powersetI1_type,type,
% 3.07/1.61 powersetI1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(powersetI1,definition,
% 3.07/1.61 ( powersetI1
% 3.07/1.61 = ( ! [A: $i,B: $i] :
% 3.07/1.61 ( ( subset @ B @ A )
% 3.07/1.61 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(powersetE1_type,type,
% 3.07/1.61 powersetE1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(powersetE1,definition,
% 3.07/1.61 ( powersetE1
% 3.07/1.61 = ( ! [A: $i,B: $i] :
% 3.07/1.61 ( ( in @ B @ ( powerset @ A ) )
% 3.07/1.61 => ( subset @ B @ A ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(inPowerset_type,type,
% 3.07/1.61 inPowerset: $o ).
% 3.07/1.61
% 3.07/1.61 thf(inPowerset,definition,
% 3.07/1.61 ( inPowerset
% 3.07/1.61 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(powersetsubset_type,type,
% 3.07/1.61 powersetsubset: $o ).
% 3.07/1.61
% 3.07/1.61 thf(powersetsubset,definition,
% 3.07/1.61 ( powersetsubset
% 3.07/1.61 = ( ! [A: $i,B: $i] :
% 3.07/1.61 ( ( subset @ A @ B )
% 3.07/1.61 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(sepInPowerset_type,type,
% 3.07/1.61 sepInPowerset: $o ).
% 3.07/1.61
% 3.07/1.61 thf(sepInPowerset,definition,
% 3.07/1.61 ( sepInPowerset
% 3.07/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 3.07/1.61 ( in
% 3.07/1.61 @ ( dsetconstr @ A
% 3.07/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.07/1.61 @ ( powerset @ A ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(sepSubset_type,type,
% 3.07/1.61 sepSubset: $o ).
% 3.07/1.61
% 3.07/1.61 thf(sepSubset,definition,
% 3.07/1.61 ( sepSubset
% 3.07/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 3.07/1.61 ( subset
% 3.07/1.61 @ ( dsetconstr @ A
% 3.07/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.07/1.61 @ A ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(binunion_type,type,
% 3.07/1.61 binunion: $i > $i > $i ).
% 3.07/1.61
% 3.07/1.61 thf(binunionIL_type,type,
% 3.07/1.61 binunionIL: $o ).
% 3.07/1.61
% 3.07/1.61 thf(binunionIL,definition,
% 3.07/1.61 ( binunionIL
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(upairset2IR_type,type,
% 3.07/1.61 upairset2IR: $o ).
% 3.07/1.61
% 3.07/1.61 thf(upairset2IR,definition,
% 3.07/1.61 ( upairset2IR
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(binunionIR_type,type,
% 3.07/1.61 binunionIR: $o ).
% 3.07/1.61
% 3.07/1.61 thf(binunionIR,definition,
% 3.07/1.61 ( binunionIR
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ B )
% 3.07/1.61 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(binunionEcases_type,type,
% 3.07/1.61 binunionEcases: $o ).
% 3.07/1.61
% 3.07/1.61 thf(binunionEcases,definition,
% 3.07/1.61 ( binunionEcases
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 3.07/1.61 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 3.07/1.61 => ( ( ( in @ Xx @ A )
% 3.07/1.61 => Xphi )
% 3.07/1.61 => ( ( ( in @ Xx @ B )
% 3.07/1.61 => Xphi )
% 3.07/1.61 => Xphi ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(binunionE_type,type,
% 3.07/1.61 binunionE: $o ).
% 3.07/1.61
% 3.07/1.61 thf(binunionE,definition,
% 3.07/1.61 ( binunionE
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 3.07/1.61 => ( ( in @ Xx @ A )
% 3.07/1.61 | ( in @ Xx @ B ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(binunionLsub_type,type,
% 3.07/1.61 binunionLsub: $o ).
% 3.07/1.61
% 3.07/1.61 thf(binunionLsub,definition,
% 3.07/1.61 ( binunionLsub
% 3.07/1.61 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(binunionRsub_type,type,
% 3.07/1.61 binunionRsub: $o ).
% 3.07/1.61
% 3.07/1.61 thf(binunionRsub,definition,
% 3.07/1.61 ( binunionRsub
% 3.07/1.61 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(binintersect_type,type,
% 3.07/1.61 binintersect: $i > $i > $i ).
% 3.07/1.61
% 3.07/1.61 thf(binintersectI_type,type,
% 3.07/1.61 binintersectI: $o ).
% 3.07/1.61
% 3.07/1.61 thf(binintersectI,definition,
% 3.07/1.61 ( binintersectI
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( in @ Xx @ B )
% 3.07/1.61 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(binintersectSubset5_type,type,
% 3.07/1.61 binintersectSubset5: $o ).
% 3.07/1.61
% 3.07/1.61 thf(binintersectSubset5,definition,
% 3.07/1.61 ( binintersectSubset5
% 3.07/1.61 = ( ! [A: $i,B: $i,C: $i] :
% 3.07/1.61 ( ( subset @ C @ A )
% 3.07/1.61 => ( ( subset @ C @ B )
% 3.07/1.61 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(binintersectEL_type,type,
% 3.07/1.61 binintersectEL: $o ).
% 3.07/1.61
% 3.07/1.61 thf(binintersectEL,definition,
% 3.07/1.61 ( binintersectEL
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 3.07/1.61 => ( in @ Xx @ A ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(binintersectLsub_type,type,
% 3.07/1.61 binintersectLsub: $o ).
% 3.07/1.61
% 3.07/1.61 thf(binintersectLsub,definition,
% 3.07/1.61 ( binintersectLsub
% 3.07/1.61 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(binintersectSubset2_type,type,
% 3.07/1.61 binintersectSubset2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(binintersectSubset2,definition,
% 3.07/1.61 ( binintersectSubset2
% 3.07/1.61 = ( ! [A: $i,B: $i] :
% 3.07/1.61 ( ( subset @ A @ B )
% 3.07/1.61 => ( ( binintersect @ A @ B )
% 3.07/1.61 = A ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(binintersectSubset3_type,type,
% 3.07/1.61 binintersectSubset3: $o ).
% 3.07/1.61
% 3.07/1.61 thf(binintersectSubset3,definition,
% 3.07/1.61 ( binintersectSubset3
% 3.07/1.61 = ( ! [A: $i,B: $i] :
% 3.07/1.61 ( ( ( binintersect @ A @ B )
% 3.07/1.61 = B )
% 3.07/1.61 => ( subset @ B @ A ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(binintersectER_type,type,
% 3.07/1.61 binintersectER: $o ).
% 3.07/1.61
% 3.07/1.61 thf(binintersectER,definition,
% 3.07/1.61 ( binintersectER
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 3.07/1.61 => ( in @ Xx @ B ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(disjointsetsI1_type,type,
% 3.07/1.61 disjointsetsI1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(disjointsetsI1,definition,
% 3.07/1.61 ( disjointsetsI1
% 3.07/1.61 = ( ! [A: $i,B: $i] :
% 3.07/1.61 ( ~ ? [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 & ( in @ Xx @ B ) )
% 3.07/1.61 => ( ( binintersect @ A @ B )
% 3.07/1.61 = emptyset ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(binintersectRsub_type,type,
% 3.07/1.61 binintersectRsub: $o ).
% 3.07/1.61
% 3.07/1.61 thf(binintersectRsub,definition,
% 3.07/1.61 ( binintersectRsub
% 3.07/1.61 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(binintersectSubset4_type,type,
% 3.07/1.61 binintersectSubset4: $o ).
% 3.07/1.61
% 3.07/1.61 thf(binintersectSubset4,definition,
% 3.07/1.61 ( binintersectSubset4
% 3.07/1.61 = ( ! [A: $i,B: $i] :
% 3.07/1.61 ( ( subset @ B @ A )
% 3.07/1.61 => ( ( binintersect @ A @ B )
% 3.07/1.61 = B ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(binintersectSubset1_type,type,
% 3.07/1.61 binintersectSubset1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(binintersectSubset1,definition,
% 3.07/1.61 ( binintersectSubset1
% 3.07/1.61 = ( ! [A: $i,B: $i] :
% 3.07/1.61 ( ( ( binintersect @ A @ B )
% 3.07/1.61 = A )
% 3.07/1.61 => ( subset @ A @ B ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(bs114d_type,type,
% 3.07/1.61 bs114d: $o ).
% 3.07/1.61
% 3.07/1.61 thf(bs114d,definition,
% 3.07/1.61 ( bs114d
% 3.07/1.61 = ( ! [A: $i,B: $i,C: $i] :
% 3.07/1.61 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 3.07/1.61 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(regular_type,type,
% 3.07/1.61 regular: $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(setminus_type,type,
% 3.07/1.61 setminus: $i > $i > $i ).
% 3.07/1.61
% 3.07/1.61 thf(setminusI_type,type,
% 3.07/1.61 setminusI: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setminusI,definition,
% 3.07/1.61 ( setminusI
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ~ ( in @ Xx @ B )
% 3.07/1.61 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setminusEL_type,type,
% 3.07/1.61 setminusEL: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setminusEL,definition,
% 3.07/1.61 ( setminusEL
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 3.07/1.61 => ( in @ Xx @ A ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setminusER_type,type,
% 3.07/1.61 setminusER: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setminusER,definition,
% 3.07/1.61 ( setminusER
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 3.07/1.61 => ~ ( in @ Xx @ B ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setminusSubset2_type,type,
% 3.07/1.61 setminusSubset2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setminusSubset2,definition,
% 3.07/1.61 ( setminusSubset2
% 3.07/1.61 = ( ! [A: $i,B: $i] :
% 3.07/1.61 ( ( subset @ A @ B )
% 3.07/1.61 => ( ( setminus @ A @ B )
% 3.07/1.61 = emptyset ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setminusERneg_type,type,
% 3.07/1.61 setminusERneg: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setminusERneg,definition,
% 3.07/1.61 ( setminusERneg
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 3.07/1.61 => ( ( in @ Xx @ A )
% 3.07/1.61 => ( in @ Xx @ B ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setminusELneg_type,type,
% 3.07/1.61 setminusELneg: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setminusELneg,definition,
% 3.07/1.61 ( setminusELneg
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 3.07/1.61 => ( ~ ( in @ Xx @ B )
% 3.07/1.61 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setminusILneg_type,type,
% 3.07/1.61 setminusILneg: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setminusILneg,definition,
% 3.07/1.61 ( setminusILneg
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ~ ( in @ Xx @ A )
% 3.07/1.61 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setminusIRneg_type,type,
% 3.07/1.61 setminusIRneg: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setminusIRneg,definition,
% 3.07/1.61 ( setminusIRneg
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ B )
% 3.07/1.61 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setminusLsub_type,type,
% 3.07/1.61 setminusLsub: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setminusLsub,definition,
% 3.07/1.61 ( setminusLsub
% 3.07/1.61 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setminusSubset1_type,type,
% 3.07/1.61 setminusSubset1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setminusSubset1,definition,
% 3.07/1.61 ( setminusSubset1
% 3.07/1.61 = ( ! [A: $i,B: $i] :
% 3.07/1.61 ( ( ( setminus @ A @ B )
% 3.07/1.61 = emptyset )
% 3.07/1.61 => ( subset @ A @ B ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(symdiff_type,type,
% 3.07/1.61 symdiff: $i > $i > $i ).
% 3.07/1.61
% 3.07/1.61 thf(symdiffE_type,type,
% 3.07/1.61 symdiffE: $o ).
% 3.07/1.61
% 3.07/1.61 thf(symdiffE,definition,
% 3.07/1.61 ( symdiffE
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 3.07/1.61 => ! [Xphi: $o] :
% 3.07/1.61 ( ( ( in @ Xx @ A )
% 3.07/1.61 => ( ~ ( in @ Xx @ B )
% 3.07/1.61 => Xphi ) )
% 3.07/1.61 => ( ( ~ ( in @ Xx @ A )
% 3.07/1.61 => ( ( in @ Xx @ B )
% 3.07/1.61 => Xphi ) )
% 3.07/1.61 => Xphi ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(symdiffI1_type,type,
% 3.07/1.61 symdiffI1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(symdiffI1,definition,
% 3.07/1.61 ( symdiffI1
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ~ ( in @ Xx @ B )
% 3.07/1.61 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(symdiffI2_type,type,
% 3.07/1.61 symdiffI2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(symdiffI2,definition,
% 3.07/1.61 ( symdiffI2
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ~ ( in @ Xx @ A )
% 3.07/1.61 => ( ( in @ Xx @ B )
% 3.07/1.61 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(symdiffIneg1_type,type,
% 3.07/1.61 symdiffIneg1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(symdiffIneg1,definition,
% 3.07/1.61 ( symdiffIneg1
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( in @ Xx @ B )
% 3.07/1.61 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(symdiffIneg2_type,type,
% 3.07/1.61 symdiffIneg2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(symdiffIneg2,definition,
% 3.07/1.61 ( symdiffIneg2
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ~ ( in @ Xx @ A )
% 3.07/1.61 => ( ~ ( in @ Xx @ B )
% 3.07/1.61 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(iskpair_type,type,
% 3.07/1.61 iskpair: $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(secondinupair_type,type,
% 3.07/1.61 secondinupair: $o ).
% 3.07/1.61
% 3.07/1.61 thf(secondinupair,definition,
% 3.07/1.61 ( secondinupair
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setukpairIL_type,type,
% 3.07/1.61 setukpairIL: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setukpairIL,definition,
% 3.07/1.61 ( setukpairIL
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setukpairIR_type,type,
% 3.07/1.61 setukpairIR: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setukpairIR,definition,
% 3.07/1.61 ( setukpairIR
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(kpairiskpair_type,type,
% 3.07/1.61 kpairiskpair: $o ).
% 3.07/1.61
% 3.07/1.61 thf(kpairiskpair,definition,
% 3.07/1.61 ( kpairiskpair
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(kpair_type,type,
% 3.07/1.61 kpair: $i > $i > $i ).
% 3.07/1.61
% 3.07/1.61 thf(kpairp_type,type,
% 3.07/1.61 kpairp: $o ).
% 3.07/1.61
% 3.07/1.61 thf(kpairp,definition,
% 3.07/1.61 ( kpairp
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(cartprod_type,type,
% 3.07/1.61 cartprod: $i > $i > $i ).
% 3.07/1.61
% 3.07/1.61 thf(singletonsubset_type,type,
% 3.07/1.61 singletonsubset: $o ).
% 3.07/1.61
% 3.07/1.61 thf(singletonsubset,definition,
% 3.07/1.61 ( singletonsubset
% 3.07/1.61 = ( ! [A: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(singletoninpowerset_type,type,
% 3.07/1.61 singletoninpowerset: $o ).
% 3.07/1.61
% 3.07/1.61 thf(singletoninpowerset,definition,
% 3.07/1.61 ( singletoninpowerset
% 3.07/1.61 = ( ! [A: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(singletoninpowunion_type,type,
% 3.07/1.61 singletoninpowunion: $o ).
% 3.07/1.61
% 3.07/1.61 thf(singletoninpowunion,definition,
% 3.07/1.61 ( singletoninpowunion
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(upairset2E_type,type,
% 3.07/1.61 upairset2E: $o ).
% 3.07/1.61
% 3.07/1.61 thf(upairset2E,definition,
% 3.07/1.61 ( upairset2E
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.07/1.61 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 3.07/1.61 => ( ( Xz = Xx )
% 3.07/1.61 | ( Xz = Xy ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(upairsubunion_type,type,
% 3.07/1.61 upairsubunion: $o ).
% 3.07/1.61
% 3.07/1.61 thf(upairsubunion,definition,
% 3.07/1.61 ( upairsubunion
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ B )
% 3.07/1.61 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(upairinpowunion_type,type,
% 3.07/1.61 upairinpowunion: $o ).
% 3.07/1.61
% 3.07/1.61 thf(upairinpowunion,definition,
% 3.07/1.61 ( upairinpowunion
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ B )
% 3.07/1.61 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(ubforcartprodlem1_type,type,
% 3.07/1.61 ubforcartprodlem1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(ubforcartprodlem1,definition,
% 3.07/1.61 ( ubforcartprodlem1
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ B )
% 3.07/1.61 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(ubforcartprodlem2_type,type,
% 3.07/1.61 ubforcartprodlem2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(ubforcartprodlem2,definition,
% 3.07/1.61 ( ubforcartprodlem2
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ B )
% 3.07/1.61 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(ubforcartprodlem3_type,type,
% 3.07/1.61 ubforcartprodlem3: $o ).
% 3.07/1.61
% 3.07/1.61 thf(ubforcartprodlem3,definition,
% 3.07/1.61 ( ubforcartprodlem3
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ B )
% 3.07/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(cartprodpairin_type,type,
% 3.07/1.61 cartprodpairin: $o ).
% 3.07/1.61
% 3.07/1.61 thf(cartprodpairin,definition,
% 3.07/1.61 ( cartprodpairin
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ B )
% 3.07/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(cartprodmempair1_type,type,
% 3.07/1.61 cartprodmempair1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(cartprodmempair1,definition,
% 3.07/1.61 ( cartprodmempair1
% 3.07/1.61 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.07/1.61 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.07/1.61 => ? [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 & ? [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ B )
% 3.07/1.61 & ( Xu
% 3.07/1.61 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(cartprodmempair_type,type,
% 3.07/1.61 cartprodmempair: $o ).
% 3.07/1.61
% 3.07/1.61 thf(cartprodmempair,definition,
% 3.07/1.61 ( cartprodmempair
% 3.07/1.61 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.07/1.61 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.07/1.61 => ( iskpair @ Xu ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setunionE2_type,type,
% 3.07/1.61 setunionE2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setunionE2,definition,
% 3.07/1.61 ( setunionE2
% 3.07/1.61 = ( ! [A: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ ( setunion @ A ) )
% 3.07/1.61 => ? [X: $i] :
% 3.07/1.61 ( ( in @ X @ A )
% 3.07/1.61 & ( in @ Xx @ X ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setunionsingleton1_type,type,
% 3.07/1.61 setunionsingleton1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setunionsingleton1,definition,
% 3.07/1.61 ( setunionsingleton1
% 3.07/1.61 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setunionsingleton2_type,type,
% 3.07/1.61 setunionsingleton2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setunionsingleton2,definition,
% 3.07/1.61 ( setunionsingleton2
% 3.07/1.61 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setunionsingleton_type,type,
% 3.07/1.61 setunionsingleton: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setunionsingleton,definition,
% 3.07/1.61 ( setunionsingleton
% 3.07/1.61 = ( ! [Xx: $i] :
% 3.07/1.61 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 3.07/1.61 = Xx ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(singleton_type,type,
% 3.07/1.61 singleton: $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(singletonprop_type,type,
% 3.07/1.61 singletonprop: $o ).
% 3.07/1.61
% 3.07/1.61 thf(singletonprop,definition,
% 3.07/1.61 ( singletonprop
% 3.07/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 3.07/1.61 ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 => ( ( Xphi @ Xx )
% 3.07/1.61 => ( ( Xphi @ Xy )
% 3.07/1.61 => ( Xx = Xy ) ) ) ) )
% 3.07/1.61 => ( ? [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 & ( Xphi @ Xx ) )
% 3.07/1.61 => ( singleton
% 3.07/1.61 @ ( dsetconstr @ A
% 3.07/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(ex1_type,type,
% 3.07/1.61 ex1: $i > ( $i > $o ) > $o ).
% 3.07/1.61
% 3.07/1.61 thf(ex1E1_type,type,
% 3.07/1.61 ex1E1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(ex1E1,definition,
% 3.07/1.61 ( ex1E1
% 3.07/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 3.07/1.61 ( ( ex1 @ A
% 3.07/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.07/1.61 => ? [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 & ( Xphi @ Xx ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(ex1I_type,type,
% 3.07/1.61 ex1I: $o ).
% 3.07/1.61
% 3.07/1.61 thf(ex1I,definition,
% 3.07/1.61 ( ex1I
% 3.07/1.61 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( Xphi @ Xx )
% 3.07/1.61 => ( ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 => ( ( Xphi @ Xy )
% 3.07/1.61 => ( Xy = Xx ) ) )
% 3.07/1.61 => ( ex1 @ A
% 3.07/1.61 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(ex1I2_type,type,
% 3.07/1.61 ex1I2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(ex1I2,definition,
% 3.07/1.61 ( ex1I2
% 3.07/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 3.07/1.61 ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 => ( ( Xphi @ Xx )
% 3.07/1.61 => ( ( Xphi @ Xy )
% 3.07/1.61 => ( Xx = Xy ) ) ) ) )
% 3.07/1.61 => ( ? [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 & ( Xphi @ Xx ) )
% 3.07/1.61 => ( ex1 @ A
% 3.07/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(singletonsuniq_type,type,
% 3.07/1.61 singletonsuniq: $o ).
% 3.07/1.61
% 3.07/1.61 thf(singletonsuniq,definition,
% 3.07/1.61 ( singletonsuniq
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i] :
% 3.07/1.61 ( ( ( setadjoin @ Xx @ emptyset )
% 3.07/1.61 = ( setadjoin @ Xy @ emptyset ) )
% 3.07/1.61 => ( Xx = Xy ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(atmost1p_type,type,
% 3.07/1.61 atmost1p: $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(atleast2p_type,type,
% 3.07/1.61 atleast2p: $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(atmost2p_type,type,
% 3.07/1.61 atmost2p: $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(upairsetp_type,type,
% 3.07/1.61 upairsetp: $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(setukpairinjL1_type,type,
% 3.07/1.61 setukpairinjL1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setukpairinjL1,definition,
% 3.07/1.61 ( setukpairinjL1
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.07/1.61 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 3.07/1.61 => ( Xx = Xz ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(kfstsingleton_type,type,
% 3.07/1.61 kfstsingleton: $o ).
% 3.07/1.61
% 3.07/1.61 thf(kfstsingleton,definition,
% 3.07/1.61 ( kfstsingleton
% 3.07/1.61 = ( ! [Xu: $i] :
% 3.07/1.61 ( ( iskpair @ Xu )
% 3.07/1.61 => ( singleton
% 3.07/1.61 @ ( dsetconstr @ ( setunion @ Xu )
% 3.07/1.61 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(theprop_type,type,
% 3.07/1.61 theprop: $o ).
% 3.07/1.61
% 3.07/1.61 thf(theprop,definition,
% 3.07/1.61 ( theprop
% 3.07/1.61 = ( ! [X: $i] :
% 3.07/1.61 ( ( singleton @ X )
% 3.07/1.61 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(kfst_type,type,
% 3.07/1.61 kfst: $i > $i ).
% 3.07/1.61
% 3.07/1.61 thf(kfstpairEq_type,type,
% 3.07/1.61 kfstpairEq: $o ).
% 3.07/1.61
% 3.07/1.61 thf(kfstpairEq,definition,
% 3.07/1.61 ( kfstpairEq
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i] :
% 3.07/1.61 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 3.07/1.61 = Xx ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(cartprodfstin_type,type,
% 3.07/1.61 cartprodfstin: $o ).
% 3.07/1.61
% 3.07/1.61 thf(cartprodfstin,definition,
% 3.07/1.61 ( cartprodfstin
% 3.07/1.61 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.07/1.61 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.07/1.61 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setukpairinjL2_type,type,
% 3.07/1.61 setukpairinjL2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setukpairinjL2,definition,
% 3.07/1.61 ( setukpairinjL2
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.07/1.61 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.07/1.61 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.07/1.61 => ( Xx = Xz ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setukpairinjL_type,type,
% 3.07/1.61 setukpairinjL: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setukpairinjL,definition,
% 3.07/1.61 ( setukpairinjL
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.07/1.61 ( ( ( kpair @ Xx @ Xy )
% 3.07/1.61 = ( kpair @ Xz @ Xu ) )
% 3.07/1.61 => ( Xx = Xz ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setukpairinjR11_type,type,
% 3.07/1.61 setukpairinjR11: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setukpairinjR11,definition,
% 3.07/1.61 ( setukpairinjR11
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i] :
% 3.07/1.61 ( ( Xx = Xy )
% 3.07/1.61 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.07/1.61 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setukpairinjR12_type,type,
% 3.07/1.61 setukpairinjR12: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setukpairinjR12,definition,
% 3.07/1.61 ( setukpairinjR12
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i] :
% 3.07/1.61 ( ( Xx = Xy )
% 3.07/1.61 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.07/1.61 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setukpairinjR1_type,type,
% 3.07/1.61 setukpairinjR1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setukpairinjR1,definition,
% 3.07/1.61 ( setukpairinjR1
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.07/1.61 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.07/1.61 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.07/1.61 => ( ( Xz = Xu )
% 3.07/1.61 => ( Xy = Xu ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(upairequniteq_type,type,
% 3.07/1.61 upairequniteq: $o ).
% 3.07/1.61
% 3.07/1.61 thf(upairequniteq,definition,
% 3.07/1.61 ( upairequniteq
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.07/1.61 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.07/1.61 = ( setadjoin @ Xz @ emptyset ) )
% 3.07/1.61 => ( Xx = Xy ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setukpairinjR2_type,type,
% 3.07/1.61 setukpairinjR2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setukpairinjR2,definition,
% 3.07/1.61 ( setukpairinjR2
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.07/1.61 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.07/1.61 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.07/1.61 => ( Xy = Xu ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setukpairinjR_type,type,
% 3.07/1.61 setukpairinjR: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setukpairinjR,definition,
% 3.07/1.61 ( setukpairinjR
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.07/1.61 ( ( ( kpair @ Xx @ Xy )
% 3.07/1.61 = ( kpair @ Xz @ Xu ) )
% 3.07/1.61 => ( Xy = Xu ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(ksndsingleton_type,type,
% 3.07/1.61 ksndsingleton: $o ).
% 3.07/1.61
% 3.07/1.61 thf(ksndsingleton,definition,
% 3.07/1.61 ( ksndsingleton
% 3.07/1.61 = ( ! [Xu: $i] :
% 3.07/1.61 ( ( iskpair @ Xu )
% 3.07/1.61 => ( singleton
% 3.07/1.61 @ ( dsetconstr @ ( setunion @ Xu )
% 3.07/1.61 @ ^ [Xx: $i] :
% 3.07/1.61 ( Xu
% 3.07/1.61 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(ksnd_type,type,
% 3.07/1.61 ksnd: $i > $i ).
% 3.07/1.61
% 3.07/1.61 thf(ksndpairEq_type,type,
% 3.07/1.61 ksndpairEq: $o ).
% 3.07/1.61
% 3.07/1.61 thf(ksndpairEq,definition,
% 3.07/1.61 ( ksndpairEq
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i] :
% 3.07/1.61 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 3.07/1.61 = Xy ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(kpairsurjEq_type,type,
% 3.07/1.61 kpairsurjEq: $o ).
% 3.07/1.61
% 3.07/1.61 thf(kpairsurjEq,definition,
% 3.07/1.61 ( kpairsurjEq
% 3.07/1.61 = ( ! [Xu: $i] :
% 3.07/1.61 ( ( iskpair @ Xu )
% 3.07/1.61 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 3.07/1.61 = Xu ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(cartprodsndin_type,type,
% 3.07/1.61 cartprodsndin: $o ).
% 3.07/1.61
% 3.07/1.61 thf(cartprodsndin,definition,
% 3.07/1.61 ( cartprodsndin
% 3.07/1.61 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.07/1.61 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.07/1.61 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(cartprodpairmemEL_type,type,
% 3.07/1.61 cartprodpairmemEL: $o ).
% 3.07/1.61
% 3.07/1.61 thf(cartprodpairmemEL,definition,
% 3.07/1.61 ( cartprodpairmemEL
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 3.07/1.61 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 3.07/1.61 => ( in @ Xx @ A ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(cartprodpairmemER_type,type,
% 3.07/1.61 cartprodpairmemER: $o ).
% 3.07/1.61
% 3.07/1.61 thf(cartprodpairmemER,definition,
% 3.07/1.61 ( cartprodpairmemER
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 3.07/1.61 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 3.07/1.61 => ( in @ Xy @ B ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(cartprodmempaircEq_type,type,
% 3.07/1.61 cartprodmempaircEq: $o ).
% 3.07/1.61
% 3.07/1.61 thf(cartprodmempaircEq,definition,
% 3.07/1.61 ( cartprodmempaircEq
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ B )
% 3.07/1.61 => ( ( kpair @ Xx @ Xy )
% 3.07/1.61 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(cartprodfstpairEq_type,type,
% 3.07/1.61 cartprodfstpairEq: $o ).
% 3.07/1.61
% 3.07/1.61 thf(cartprodfstpairEq,definition,
% 3.07/1.61 ( cartprodfstpairEq
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ B )
% 3.07/1.61 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 3.07/1.61 = Xx ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(cartprodsndpairEq_type,type,
% 3.07/1.61 cartprodsndpairEq: $o ).
% 3.07/1.61
% 3.07/1.61 thf(cartprodsndpairEq,definition,
% 3.07/1.61 ( cartprodsndpairEq
% 3.07/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ B )
% 3.07/1.61 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 3.07/1.61 = Xy ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(cartprodpairsurjEq_type,type,
% 3.07/1.61 cartprodpairsurjEq: $o ).
% 3.07/1.61
% 3.07/1.61 thf(cartprodpairsurjEq,definition,
% 3.07/1.61 ( cartprodpairsurjEq
% 3.07/1.61 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.07/1.61 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.07/1.61 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 3.07/1.61 = Xu ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(breln_type,type,
% 3.07/1.61 breln: $i > $i > $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(dpsetconstr_type,type,
% 3.07/1.61 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 3.07/1.61
% 3.07/1.61 thf(dpsetconstrI_type,type,
% 3.07/1.61 dpsetconstrI: $o ).
% 3.07/1.61
% 3.07/1.61 thf(dpsetconstrI,definition,
% 3.07/1.61 ( dpsetconstrI
% 3.07/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ B )
% 3.07/1.61 => ( ( Xphi @ Xx @ Xy )
% 3.07/1.61 => ( in @ ( kpair @ Xx @ Xy )
% 3.07/1.61 @ ( dpsetconstr @ A @ B
% 3.07/1.61 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(dpsetconstrSub_type,type,
% 3.07/1.61 dpsetconstrSub: $o ).
% 3.07/1.61
% 3.07/1.61 thf(dpsetconstrSub,definition,
% 3.07/1.61 ( dpsetconstrSub
% 3.07/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.07/1.61 ( subset
% 3.07/1.61 @ ( dpsetconstr @ A @ B
% 3.07/1.61 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 3.07/1.61 @ ( cartprod @ A @ B ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setOfPairsIsBReln_type,type,
% 3.07/1.61 setOfPairsIsBReln: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setOfPairsIsBReln,definition,
% 3.07/1.61 ( setOfPairsIsBReln
% 3.07/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.07/1.61 ( breln @ A @ B
% 3.07/1.61 @ ( dpsetconstr @ A @ B
% 3.07/1.61 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(dpsetconstrERa_type,type,
% 3.07/1.61 dpsetconstrERa: $o ).
% 3.07/1.61
% 3.07/1.61 thf(dpsetconstrERa,definition,
% 3.07/1.61 ( dpsetconstrERa
% 3.07/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ B )
% 3.07/1.61 => ( ( in @ ( kpair @ Xx @ Xy )
% 3.07/1.61 @ ( dpsetconstr @ A @ B
% 3.07/1.61 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.07/1.61 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(dpsetconstrEL1_type,type,
% 3.07/1.61 dpsetconstrEL1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(dpsetconstrEL1,definition,
% 3.07/1.61 ( dpsetconstrEL1
% 3.07/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.07/1.61 ( ( in @ ( kpair @ Xx @ Xy )
% 3.07/1.61 @ ( dpsetconstr @ A @ B
% 3.07/1.61 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.07/1.61 => ( in @ Xx @ A ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(dpsetconstrEL2_type,type,
% 3.07/1.61 dpsetconstrEL2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(dpsetconstrEL2,definition,
% 3.07/1.61 ( dpsetconstrEL2
% 3.07/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.07/1.61 ( ( in @ ( kpair @ Xx @ Xy )
% 3.07/1.61 @ ( dpsetconstr @ A @ B
% 3.07/1.61 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.07/1.61 => ( in @ Xy @ B ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(dpsetconstrER_type,type,
% 3.07/1.61 dpsetconstrER: $o ).
% 3.07/1.61
% 3.07/1.61 thf(dpsetconstrER,definition,
% 3.07/1.61 ( dpsetconstrER
% 3.07/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.07/1.61 ( ( in @ ( kpair @ Xx @ Xy )
% 3.07/1.61 @ ( dpsetconstr @ A @ B
% 3.07/1.61 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.07/1.61 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(func_type,type,
% 3.07/1.61 func: $i > $i > $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(funcSet_type,type,
% 3.07/1.61 funcSet: $i > $i > $i ).
% 3.07/1.61
% 3.07/1.61 thf(funcImageSingleton_type,type,
% 3.07/1.61 funcImageSingleton: $o ).
% 3.07/1.61
% 3.07/1.61 thf(funcImageSingleton,definition,
% 3.07/1.61 ( funcImageSingleton
% 3.07/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.07/1.61 ( ( func @ A @ B @ Xf )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( singleton
% 3.07/1.61 @ ( dsetconstr @ B
% 3.07/1.61 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(apProp_type,type,
% 3.07/1.61 apProp: $o ).
% 3.07/1.61
% 3.07/1.61 thf(apProp,definition,
% 3.07/1.61 ( apProp
% 3.07/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.07/1.61 ( ( func @ A @ B @ Xf )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( in
% 3.07/1.61 @ ( setunion
% 3.07/1.61 @ ( dsetconstr @ B
% 3.07/1.61 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 3.07/1.61 @ B ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(ap_type,type,
% 3.07/1.61 ap: $i > $i > $i > $i > $i ).
% 3.07/1.61
% 3.07/1.61 thf(app_type,type,
% 3.07/1.61 app: $o ).
% 3.07/1.61
% 3.07/1.61 thf(app,definition,
% 3.07/1.61 ( app
% 3.07/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.07/1.61 ( ( func @ A @ B @ Xf )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(infuncsetfunc_type,type,
% 3.07/1.61 infuncsetfunc: $o ).
% 3.07/1.61
% 3.07/1.61 thf(infuncsetfunc,definition,
% 3.07/1.61 ( infuncsetfunc
% 3.07/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.07/1.61 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.07/1.61 => ( func @ A @ B @ Xf ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(ap2p_type,type,
% 3.07/1.61 ap2p: $o ).
% 3.07/1.61
% 3.07/1.61 thf(ap2p,definition,
% 3.07/1.61 ( ap2p
% 3.07/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.07/1.61 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(funcinfuncset_type,type,
% 3.07/1.61 funcinfuncset: $o ).
% 3.07/1.61
% 3.07/1.61 thf(funcinfuncset,definition,
% 3.07/1.61 ( funcinfuncset
% 3.07/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.07/1.61 ( ( func @ A @ B @ Xf )
% 3.07/1.61 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(lamProp_type,type,
% 3.07/1.61 lamProp: $o ).
% 3.07/1.61
% 3.07/1.61 thf(lamProp,definition,
% 3.07/1.61 ( lamProp
% 3.07/1.61 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.07/1.61 ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.07/1.61 => ( func @ A @ B
% 3.07/1.61 @ ( dpsetconstr @ A @ B
% 3.07/1.61 @ ^ [Xx: $i,Xy: $i] :
% 3.07/1.61 ( ( Xf @ Xx )
% 3.07/1.61 = Xy ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(lam_type,type,
% 3.07/1.61 lam: $i > $i > ( $i > $i ) > $i ).
% 3.07/1.61
% 3.07/1.61 thf(lamp_type,type,
% 3.07/1.61 lamp: $o ).
% 3.07/1.61
% 3.07/1.61 thf(lamp,definition,
% 3.07/1.61 ( lamp
% 3.07/1.61 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.07/1.61 ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.07/1.61 => ( func @ A @ B
% 3.07/1.61 @ ( lam @ A @ B
% 3.07/1.61 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(lam2p_type,type,
% 3.07/1.61 lam2p: $o ).
% 3.07/1.61
% 3.07/1.61 thf(lam2p,definition,
% 3.07/1.61 ( lam2p
% 3.07/1.61 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.07/1.61 ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.07/1.61 => ( in
% 3.07/1.61 @ ( lam @ A @ B
% 3.07/1.61 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 3.07/1.61 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(brelnall1_type,type,
% 3.07/1.61 brelnall1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(brelnall1,definition,
% 3.07/1.61 ( brelnall1
% 3.07/1.61 = ( ! [A: $i,B: $i,R: $i] :
% 3.07/1.61 ( ( breln @ A @ B @ R )
% 3.07/1.61 => ! [Xphi: $i > $o] :
% 3.07/1.61 ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ B )
% 3.07/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.07/1.61 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ R )
% 3.07/1.61 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(brelnall2_type,type,
% 3.07/1.61 brelnall2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(brelnall2,definition,
% 3.07/1.61 ( brelnall2
% 3.07/1.61 = ( ! [A: $i,B: $i,R: $i] :
% 3.07/1.61 ( ( breln @ A @ B @ R )
% 3.07/1.61 => ! [Xphi: $i > $o] :
% 3.07/1.61 ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ B )
% 3.07/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.07/1.61 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ R )
% 3.07/1.61 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(ex1E2_type,type,
% 3.07/1.61 ex1E2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(ex1E2,definition,
% 3.07/1.61 ( ex1E2
% 3.07/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 3.07/1.61 ( ( ex1 @ A
% 3.07/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 => ( ( Xphi @ Xx )
% 3.07/1.61 => ( ( Xphi @ Xy )
% 3.07/1.61 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(funcGraphProp1_type,type,
% 3.07/1.61 funcGraphProp1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(funcGraphProp1,definition,
% 3.07/1.61 ( funcGraphProp1
% 3.07/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.07/1.61 ( ( func @ A @ B @ Xf )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(funcGraphProp3_type,type,
% 3.07/1.61 funcGraphProp3: $o ).
% 3.07/1.61
% 3.07/1.61 thf(funcGraphProp3,definition,
% 3.07/1.61 ( funcGraphProp3
% 3.07/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.07/1.61 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(funcGraphProp2_type,type,
% 3.07/1.61 funcGraphProp2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(funcGraphProp2,definition,
% 3.07/1.61 ( funcGraphProp2
% 3.07/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.07/1.61 ( ( func @ A @ B @ Xf )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ B )
% 3.07/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 3.07/1.61 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.07/1.61 = Xy ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(funcextLem_type,type,
% 3.07/1.61 funcextLem: $o ).
% 3.07/1.61
% 3.07/1.61 thf(funcextLem,definition,
% 3.07/1.61 ( funcextLem
% 3.07/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.07/1.61 ( ( func @ A @ B @ Xf )
% 3.07/1.61 => ! [Xg: $i] :
% 3.07/1.61 ( ( func @ A @ B @ Xg )
% 3.07/1.61 => ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.07/1.61 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ B )
% 3.07/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 3.07/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(funcGraphProp4_type,type,
% 3.07/1.61 funcGraphProp4: $o ).
% 3.07/1.61
% 3.07/1.61 thf(funcGraphProp4,definition,
% 3.07/1.61 ( funcGraphProp4
% 3.07/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.07/1.61 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ B )
% 3.07/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 3.07/1.61 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.07/1.61 = Xy ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(subbreln_type,type,
% 3.07/1.61 subbreln: $o ).
% 3.07/1.61
% 3.07/1.61 thf(subbreln,definition,
% 3.07/1.61 ( subbreln
% 3.07/1.61 = ( ! [A: $i,B: $i,R: $i] :
% 3.07/1.61 ( ( breln @ A @ B @ R )
% 3.07/1.61 => ! [S: $i] :
% 3.07/1.61 ( ( breln @ A @ B @ S )
% 3.07/1.61 => ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ B )
% 3.07/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.07/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.07/1.61 => ( subset @ R @ S ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(eqbreln_type,type,
% 3.07/1.61 eqbreln: $o ).
% 3.07/1.61
% 3.07/1.61 thf(eqbreln,definition,
% 3.07/1.61 ( eqbreln
% 3.07/1.61 = ( ! [A: $i,B: $i,R: $i] :
% 3.07/1.61 ( ( breln @ A @ B @ R )
% 3.07/1.61 => ! [S: $i] :
% 3.07/1.61 ( ( breln @ A @ B @ S )
% 3.07/1.61 => ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ B )
% 3.07/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.07/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.07/1.61 => ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ B )
% 3.07/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.07/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 3.07/1.61 => ( R = S ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(funcext_type,type,
% 3.07/1.61 funcext: $o ).
% 3.07/1.61
% 3.07/1.61 thf(funcext,definition,
% 3.07/1.61 ( funcext
% 3.07/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.07/1.61 ( ( func @ A @ B @ Xf )
% 3.07/1.61 => ! [Xg: $i] :
% 3.07/1.61 ( ( func @ A @ B @ Xg )
% 3.07/1.61 => ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.07/1.61 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.07/1.61 => ( Xf = Xg ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(funcext2_type,type,
% 3.07/1.61 funcext2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(funcext2,definition,
% 3.07/1.61 ( funcext2
% 3.07/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.07/1.61 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.07/1.61 => ! [Xg: $i] :
% 3.07/1.61 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 3.07/1.61 => ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.07/1.61 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.07/1.61 => ( Xf = Xg ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(ap2apEq1_type,type,
% 3.07/1.61 ap2apEq1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(ap2apEq1,definition,
% 3.07/1.61 ( ap2apEq1
% 3.07/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.07/1.61 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.07/1.61 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(ap2apEq2_type,type,
% 3.07/1.61 ap2apEq2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(ap2apEq2,definition,
% 3.07/1.61 ( ap2apEq2
% 3.07/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.07/1.61 ( ( func @ A @ B @ Xf )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.07/1.61 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(beta1_type,type,
% 3.07/1.61 beta1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(beta1,definition,
% 3.07/1.61 ( beta1
% 3.07/1.61 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.07/1.61 ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( ap @ A @ B
% 3.07/1.61 @ ( lam @ A @ B
% 3.07/1.61 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 3.07/1.61 @ Xx )
% 3.07/1.61 = ( Xf @ Xx ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(eta1_type,type,
% 3.07/1.61 eta1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(eta1,definition,
% 3.07/1.61 ( eta1
% 3.07/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.07/1.61 ( ( func @ A @ B @ Xf )
% 3.07/1.61 => ( ( lam @ A @ B
% 3.07/1.61 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 3.07/1.61 = Xf ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(lam2lamEq_type,type,
% 3.07/1.61 lam2lamEq: $o ).
% 3.07/1.61
% 3.07/1.61 thf(lam2lamEq,definition,
% 3.07/1.61 ( lam2lamEq
% 3.07/1.61 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.07/1.61 ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.07/1.61 => ( ( lam @ A @ B
% 3.07/1.61 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 3.07/1.61 = ( lam @ A @ B
% 3.07/1.61 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(beta2_type,type,
% 3.07/1.61 beta2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(beta2,definition,
% 3.07/1.61 ( beta2
% 3.07/1.61 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.07/1.61 ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( ap @ A @ B
% 3.07/1.61 @ ( lam @ A @ B
% 3.07/1.61 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 3.07/1.61 @ Xx )
% 3.07/1.61 = ( Xf @ Xx ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(eta2_type,type,
% 3.07/1.61 eta2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(eta2,definition,
% 3.07/1.61 ( eta2
% 3.07/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.07/1.61 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.07/1.61 => ( ( lam @ A @ B
% 3.07/1.61 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 3.07/1.61 = Xf ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(iffalseProp1_type,type,
% 3.07/1.61 iffalseProp1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(iffalseProp1,definition,
% 3.07/1.61 ( iffalseProp1
% 3.07/1.61 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 => ( ~ Xphi
% 3.07/1.61 => ( in @ Xy
% 3.07/1.61 @ ( dsetconstr @ A
% 3.07/1.61 @ ^ [Xz: $i] :
% 3.07/1.61 ( ( Xphi
% 3.07/1.61 & ( Xz = Xx ) )
% 3.07/1.61 | ( ~ Xphi
% 3.07/1.61 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(iffalseProp2_type,type,
% 3.07/1.61 iffalseProp2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(iffalseProp2,definition,
% 3.07/1.61 ( iffalseProp2
% 3.07/1.61 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 => ( ~ Xphi
% 3.07/1.61 => ( ( dsetconstr @ A
% 3.07/1.61 @ ^ [Xz: $i] :
% 3.07/1.61 ( ( Xphi
% 3.07/1.61 & ( Xz = Xx ) )
% 3.07/1.61 | ( ~ Xphi
% 3.07/1.61 & ( Xz = Xy ) ) ) )
% 3.07/1.61 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(iftrueProp1_type,type,
% 3.07/1.61 iftrueProp1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(iftrueProp1,definition,
% 3.07/1.61 ( iftrueProp1
% 3.07/1.61 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 => ( Xphi
% 3.07/1.61 => ( in @ Xx
% 3.07/1.61 @ ( dsetconstr @ A
% 3.07/1.61 @ ^ [Xz: $i] :
% 3.07/1.61 ( ( Xphi
% 3.07/1.61 & ( Xz = Xx ) )
% 3.07/1.61 | ( ~ Xphi
% 3.07/1.61 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(iftrueProp2_type,type,
% 3.07/1.61 iftrueProp2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(iftrueProp2,definition,
% 3.07/1.61 ( iftrueProp2
% 3.07/1.61 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 => ( Xphi
% 3.07/1.61 => ( ( dsetconstr @ A
% 3.07/1.61 @ ^ [Xz: $i] :
% 3.07/1.61 ( ( Xphi
% 3.07/1.61 & ( Xz = Xx ) )
% 3.07/1.61 | ( ~ Xphi
% 3.07/1.61 & ( Xz = Xy ) ) ) )
% 3.07/1.61 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(ifSingleton_type,type,
% 3.07/1.61 ifSingleton: $o ).
% 3.07/1.61
% 3.07/1.61 thf(ifSingleton,definition,
% 3.07/1.61 ( ifSingleton
% 3.07/1.61 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 => ( singleton
% 3.07/1.61 @ ( dsetconstr @ A
% 3.07/1.61 @ ^ [Xz: $i] :
% 3.07/1.61 ( ( Xphi
% 3.07/1.61 & ( Xz = Xx ) )
% 3.07/1.61 | ( ~ Xphi
% 3.07/1.61 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(if_type,type,
% 3.07/1.61 if: $i > $o > $i > $i > $i ).
% 3.07/1.61
% 3.07/1.61 thf(ifp_type,type,
% 3.07/1.61 ifp: $o ).
% 3.07/1.61
% 3.07/1.61 thf(ifp,definition,
% 3.07/1.61 ( ifp
% 3.07/1.61 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(theeq_type,type,
% 3.07/1.61 theeq: $o ).
% 3.07/1.61
% 3.07/1.61 thf(theeq,definition,
% 3.07/1.61 ( theeq
% 3.07/1.61 = ( ! [X: $i] :
% 3.07/1.61 ( ( singleton @ X )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ X )
% 3.07/1.61 => ( ( setunion @ X )
% 3.07/1.61 = Xx ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(iftrue_type,type,
% 3.07/1.61 iftrue: $o ).
% 3.07/1.61
% 3.07/1.61 thf(iftrue,definition,
% 3.07/1.61 ( iftrue
% 3.07/1.61 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 => ( Xphi
% 3.07/1.61 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 3.07/1.61 = Xx ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(iffalse_type,type,
% 3.07/1.61 iffalse: $o ).
% 3.07/1.61
% 3.07/1.61 thf(iffalse,definition,
% 3.07/1.61 ( iffalse
% 3.07/1.61 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 => ( ~ Xphi
% 3.07/1.61 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 3.07/1.61 = Xy ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(iftrueorfalse_type,type,
% 3.07/1.61 iftrueorfalse: $o ).
% 3.07/1.61
% 3.07/1.61 thf(iftrueorfalse,definition,
% 3.07/1.61 ( iftrueorfalse
% 3.07/1.61 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(binintersectT_lem_type,type,
% 3.07/1.61 binintersectT_lem: $o ).
% 3.07/1.61
% 3.07/1.61 thf(binintersectT_lem,definition,
% 3.07/1.61 ( binintersectT_lem
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(binunionT_lem_type,type,
% 3.07/1.61 binunionT_lem: $o ).
% 3.07/1.61
% 3.07/1.61 thf(binunionT_lem,definition,
% 3.07/1.61 ( binunionT_lem
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(powersetT_lem_type,type,
% 3.07/1.61 powersetT_lem: $o ).
% 3.07/1.61
% 3.07/1.61 thf(powersetT_lem,definition,
% 3.07/1.61 ( powersetT_lem
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setminusT_lem_type,type,
% 3.07/1.61 setminusT_lem: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setminusT_lem,definition,
% 3.07/1.61 ( setminusT_lem
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(complementT_lem_type,type,
% 3.07/1.61 complementT_lem: $o ).
% 3.07/1.61
% 3.07/1.61 thf(complementT_lem,definition,
% 3.07/1.61 ( complementT_lem
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setextT_type,type,
% 3.07/1.61 setextT: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setextT,definition,
% 3.07/1.61 ( setextT
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( in @ Xx @ X )
% 3.07/1.61 => ( in @ Xx @ Y ) ) )
% 3.07/1.61 => ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( in @ Xx @ Y )
% 3.07/1.61 => ( in @ Xx @ X ) ) )
% 3.07/1.61 => ( X = Y ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(subsetTI_type,type,
% 3.07/1.61 subsetTI: $o ).
% 3.07/1.61
% 3.07/1.61 thf(subsetTI,definition,
% 3.07/1.61 ( subsetTI
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( in @ Xx @ X )
% 3.07/1.61 => ( in @ Xx @ Y ) ) )
% 3.07/1.61 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(powersetTI1_type,type,
% 3.07/1.61 powersetTI1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(powersetTI1,definition,
% 3.07/1.61 ( powersetTI1
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( in @ Xx @ X )
% 3.07/1.61 => ( in @ Xx @ Y ) ) )
% 3.07/1.61 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(powersetTE1_type,type,
% 3.07/1.61 powersetTE1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(powersetTE1,definition,
% 3.07/1.61 ( powersetTE1
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( in @ X @ ( powerset @ Y ) )
% 3.07/1.61 => ( ( in @ Xx @ X )
% 3.07/1.61 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(complementTI1_type,type,
% 3.07/1.61 complementTI1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(complementTI1,definition,
% 3.07/1.61 ( complementTI1
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( in @ Xx @ X )
% 3.07/1.61 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(complementTE1_type,type,
% 3.07/1.61 complementTE1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(complementTE1,definition,
% 3.07/1.61 ( complementTE1
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 3.07/1.61 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(binintersectTELcontra_type,type,
% 3.07/1.61 binintersectTELcontra: $o ).
% 3.07/1.61
% 3.07/1.61 thf(binintersectTELcontra,definition,
% 3.07/1.61 ( binintersectTELcontra
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ~ ( in @ Xx @ X )
% 3.07/1.61 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(binintersectTERcontra_type,type,
% 3.07/1.61 binintersectTERcontra: $o ).
% 3.07/1.61
% 3.07/1.61 thf(binintersectTERcontra,definition,
% 3.07/1.61 ( binintersectTERcontra
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ~ ( in @ Xx @ Y )
% 3.07/1.61 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(contrasubsetT_type,type,
% 3.07/1.61 contrasubsetT: $o ).
% 3.07/1.61
% 3.07/1.61 thf(contrasubsetT,definition,
% 3.07/1.61 ( contrasubsetT
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.07/1.61 => ( ( in @ Xx @ Y )
% 3.07/1.61 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(contrasubsetT1_type,type,
% 3.07/1.61 contrasubsetT1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(contrasubsetT1,definition,
% 3.07/1.61 ( contrasubsetT1
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( subset @ X @ Y )
% 3.07/1.61 => ( ~ ( in @ Xx @ Y )
% 3.07/1.61 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(contrasubsetT2_type,type,
% 3.07/1.61 contrasubsetT2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(contrasubsetT2,definition,
% 3.07/1.61 ( contrasubsetT2
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ( ( subset @ X @ Y )
% 3.07/1.61 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(contrasubsetT3_type,type,
% 3.07/1.61 contrasubsetT3: $o ).
% 3.07/1.61
% 3.07/1.61 thf(contrasubsetT3,definition,
% 3.07/1.61 ( contrasubsetT3
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 3.07/1.61 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(doubleComplementI1_type,type,
% 3.07/1.61 doubleComplementI1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(doubleComplementI1,definition,
% 3.07/1.61 ( doubleComplementI1
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( in @ Xx @ X )
% 3.07/1.61 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(doubleComplementE1_type,type,
% 3.07/1.61 doubleComplementE1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(doubleComplementE1,definition,
% 3.07/1.61 ( doubleComplementE1
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 3.07/1.61 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(doubleComplementSub1_type,type,
% 3.07/1.61 doubleComplementSub1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(doubleComplementSub1,definition,
% 3.07/1.61 ( doubleComplementSub1
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(doubleComplementSub2_type,type,
% 3.07/1.61 doubleComplementSub2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(doubleComplementSub2,definition,
% 3.07/1.61 ( doubleComplementSub2
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(doubleComplementEq_type,type,
% 3.07/1.61 doubleComplementEq: $o ).
% 3.07/1.61
% 3.07/1.61 thf(doubleComplementEq,definition,
% 3.07/1.61 ( doubleComplementEq
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ( X
% 3.07/1.61 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(complementTnotintersectT_type,type,
% 3.07/1.61 complementTnotintersectT: $o ).
% 3.07/1.61
% 3.07/1.61 thf(complementTnotintersectT,definition,
% 3.07/1.61 ( complementTnotintersectT
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.07/1.61 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(complementImpComplementIntersect_type,type,
% 3.07/1.61 complementImpComplementIntersect: $o ).
% 3.07/1.61
% 3.07/1.61 thf(complementImpComplementIntersect,definition,
% 3.07/1.61 ( complementImpComplementIntersect
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.07/1.61 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(complementSubsetComplementIntersect_type,type,
% 3.07/1.61 complementSubsetComplementIntersect: $o ).
% 3.07/1.61
% 3.07/1.61 thf(complementSubsetComplementIntersect,definition,
% 3.07/1.61 ( complementSubsetComplementIntersect
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(complementInPowersetComplementIntersect_type,type,
% 3.07/1.61 complementInPowersetComplementIntersect: $o ).
% 3.07/1.61
% 3.07/1.61 thf(complementInPowersetComplementIntersect,definition,
% 3.07/1.61 ( complementInPowersetComplementIntersect
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(contraSubsetComplement_type,type,
% 3.07/1.61 contraSubsetComplement: $o ).
% 3.07/1.61
% 3.07/1.61 thf(contraSubsetComplement,definition,
% 3.07/1.61 ( contraSubsetComplement
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( in @ Xx @ Y )
% 3.07/1.61 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(complementTcontraSubset_type,type,
% 3.07/1.61 complementTcontraSubset: $o ).
% 3.07/1.61
% 3.07/1.61 thf(complementTcontraSubset,definition,
% 3.07/1.61 ( complementTcontraSubset
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.07/1.61 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(binunionTILcontra_type,type,
% 3.07/1.61 binunionTILcontra: $o ).
% 3.07/1.61
% 3.07/1.61 thf(binunionTILcontra,definition,
% 3.07/1.61 ( binunionTILcontra
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.07/1.61 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(binunionTIRcontra_type,type,
% 3.07/1.61 binunionTIRcontra: $o ).
% 3.07/1.61
% 3.07/1.61 thf(binunionTIRcontra,definition,
% 3.07/1.61 ( binunionTIRcontra
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.07/1.61 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(inIntersectImpInUnion_type,type,
% 3.07/1.61 inIntersectImpInUnion: $o ).
% 3.07/1.61
% 3.07/1.61 thf(inIntersectImpInUnion,definition,
% 3.07/1.61 ( inIntersectImpInUnion
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Z: $i] :
% 3.07/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.07/1.61 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(inIntersectImpInUnion2_type,type,
% 3.07/1.61 inIntersectImpInUnion2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(inIntersectImpInUnion2,definition,
% 3.07/1.61 ( inIntersectImpInUnion2
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Z: $i] :
% 3.07/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.07/1.61 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(inIntersectImpInIntersectUnions_type,type,
% 3.07/1.61 inIntersectImpInIntersectUnions: $o ).
% 3.07/1.61
% 3.07/1.61 thf(inIntersectImpInIntersectUnions,definition,
% 3.07/1.61 ( inIntersectImpInIntersectUnions
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Z: $i] :
% 3.07/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.07/1.61 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(intersectInPowersetIntersectUnions_type,type,
% 3.07/1.61 intersectInPowersetIntersectUnions: $o ).
% 3.07/1.61
% 3.07/1.61 thf(intersectInPowersetIntersectUnions,definition,
% 3.07/1.61 ( intersectInPowersetIntersectUnions
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Z: $i] :
% 3.07/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 3.07/1.61 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(inComplementUnionImpNotIn1_type,type,
% 3.07/1.61 inComplementUnionImpNotIn1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(inComplementUnionImpNotIn1,definition,
% 3.07/1.61 ( inComplementUnionImpNotIn1
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.07/1.61 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(inComplementUnionImpInComplement1_type,type,
% 3.07/1.61 inComplementUnionImpInComplement1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(inComplementUnionImpInComplement1,definition,
% 3.07/1.61 ( inComplementUnionImpInComplement1
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.07/1.61 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(binunionTE_type,type,
% 3.07/1.61 binunionTE: $o ).
% 3.07/1.61
% 3.07/1.61 thf(binunionTE,definition,
% 3.07/1.61 ( binunionTE
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Xphi: $o,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.07/1.61 => ( ( ( in @ Xx @ X )
% 3.07/1.61 => Xphi )
% 3.07/1.61 => ( ( ( in @ Xx @ Y )
% 3.07/1.61 => Xphi )
% 3.07/1.61 => Xphi ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(binunionTEcontra_type,type,
% 3.07/1.61 binunionTEcontra: $o ).
% 3.07/1.61
% 3.07/1.61 thf(binunionTEcontra,definition,
% 3.07/1.61 ( binunionTEcontra
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ~ ( in @ Xx @ X )
% 3.07/1.61 => ( ~ ( in @ Xx @ Y )
% 3.07/1.61 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(demorgan2a1_type,type,
% 3.07/1.61 demorgan2a1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(demorgan2a1,definition,
% 3.07/1.61 ( demorgan2a1
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.07/1.61 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(complementUnionInPowersetComplement_type,type,
% 3.07/1.61 complementUnionInPowersetComplement: $o ).
% 3.07/1.61
% 3.07/1.61 thf(complementUnionInPowersetComplement,definition,
% 3.07/1.61 ( complementUnionInPowersetComplement
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(demorgan2a2_type,type,
% 3.07/1.61 demorgan2a2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(demorgan2a2,definition,
% 3.07/1.61 ( demorgan2a2
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.07/1.61 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(demorgan1a_type,type,
% 3.07/1.61 demorgan1a: $o ).
% 3.07/1.61
% 3.07/1.61 thf(demorgan1a,definition,
% 3.07/1.61 ( demorgan1a
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 3.07/1.61 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(demorgan1b_type,type,
% 3.07/1.61 demorgan1b: $o ).
% 3.07/1.61
% 3.07/1.61 thf(demorgan1b,definition,
% 3.07/1.61 ( demorgan1b
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 3.07/1.61 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(demorgan1_type,type,
% 3.07/1.61 demorgan1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(demorgan1,definition,
% 3.07/1.61 ( demorgan1
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 3.07/1.61 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(demorgan2a_type,type,
% 3.07/1.61 demorgan2a: $o ).
% 3.07/1.61
% 3.07/1.61 thf(demorgan2a,definition,
% 3.07/1.61 ( demorgan2a
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.07/1.61 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(demorgan2b2_type,type,
% 3.07/1.61 demorgan2b2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(demorgan2b2,definition,
% 3.07/1.61 ( demorgan2b2
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.07/1.61 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 3.07/1.61 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(demorgan2b_type,type,
% 3.07/1.61 demorgan2b: $o ).
% 3.07/1.61
% 3.07/1.61 thf(demorgan2b,definition,
% 3.07/1.61 ( demorgan2b
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 3.07/1.61 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(demorgan2_type,type,
% 3.07/1.61 demorgan2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(demorgan2,definition,
% 3.07/1.61 ( demorgan2
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 3.07/1.61 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(woz13rule0_type,type,
% 3.07/1.61 woz13rule0: $o ).
% 3.07/1.61
% 3.07/1.61 thf(woz13rule0,definition,
% 3.07/1.61 ( woz13rule0
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.07/1.61 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(woz13rule1_type,type,
% 3.07/1.61 woz13rule1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(woz13rule1,definition,
% 3.07/1.61 ( woz13rule1
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Z: $i] :
% 3.07/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 3.07/1.61 => ( ( subset @ X @ Z )
% 3.07/1.61 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(woz13rule2_type,type,
% 3.07/1.61 woz13rule2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(woz13rule2,definition,
% 3.07/1.61 ( woz13rule2
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Z: $i] :
% 3.07/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 3.07/1.61 => ( ( subset @ Y @ Z )
% 3.07/1.61 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(woz13rule3_type,type,
% 3.07/1.61 woz13rule3: $o ).
% 3.07/1.61
% 3.07/1.61 thf(woz13rule3,definition,
% 3.07/1.61 ( woz13rule3
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Z: $i] :
% 3.07/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 3.07/1.61 => ( ( subset @ X @ Y )
% 3.07/1.61 => ( ( subset @ X @ Z )
% 3.07/1.61 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(woz13rule4_type,type,
% 3.07/1.61 woz13rule4: $o ).
% 3.07/1.61
% 3.07/1.61 thf(woz13rule4,definition,
% 3.07/1.61 ( woz13rule4
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Z: $i] :
% 3.07/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 3.07/1.61 => ! [W: $i] :
% 3.07/1.61 ( ( in @ W @ ( powerset @ A ) )
% 3.07/1.61 => ( ( subset @ X @ Z )
% 3.07/1.61 => ( ( subset @ Y @ W )
% 3.07/1.61 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(woz1_1_type,type,
% 3.07/1.61 woz1_1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(woz1_1,definition,
% 3.07/1.61 ( woz1_1
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(woz1_2_type,type,
% 3.07/1.61 woz1_2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(woz1_2,definition,
% 3.07/1.61 ( woz1_2
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Z: $i] :
% 3.07/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 3.07/1.61 => ! [W: $i] :
% 3.07/1.61 ( ( in @ W @ ( powerset @ A ) )
% 3.07/1.61 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 3.07/1.61 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(woz1_3_type,type,
% 3.07/1.61 woz1_3: $o ).
% 3.07/1.61
% 3.07/1.61 thf(woz1_3,definition,
% 3.07/1.61 ( woz1_3
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ! [Z: $i] :
% 3.07/1.61 ( ( in @ Z @ ( powerset @ A ) )
% 3.07/1.61 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(woz1_4_type,type,
% 3.07/1.61 woz1_4: $o ).
% 3.07/1.61
% 3.07/1.61 thf(woz1_4,definition,
% 3.07/1.61 ( woz1_4
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.07/1.61 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(woz1_5_type,type,
% 3.07/1.61 woz1_5: $o ).
% 3.07/1.61
% 3.07/1.61 thf(woz1_5,definition,
% 3.07/1.61 ( woz1_5
% 3.07/1.61 = ( ! [A: $i,X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ ( powerset @ A ) )
% 3.07/1.61 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(breln1_type,type,
% 3.07/1.61 breln1: $i > $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(breln1all2_type,type,
% 3.07/1.61 breln1all2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(breln1all2,definition,
% 3.07/1.61 ( breln1all2
% 3.07/1.61 = ( ! [A: $i,R: $i] :
% 3.07/1.61 ( ( breln1 @ A @ R )
% 3.07/1.61 => ! [Xphi: $i > $o] :
% 3.07/1.61 ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.07/1.61 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ R )
% 3.07/1.61 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(breln1Set_type,type,
% 3.07/1.61 breln1Set: $i > $i ).
% 3.07/1.61
% 3.07/1.61 thf(breln1SetBreln1_type,type,
% 3.07/1.61 breln1SetBreln1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(breln1SetBreln1,definition,
% 3.07/1.61 ( breln1SetBreln1
% 3.07/1.61 = ( ! [A: $i,R: $i] :
% 3.07/1.61 ( ( in @ R @ ( breln1Set @ A ) )
% 3.07/1.61 => ( breln1 @ A @ R ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(transitive_type,type,
% 3.07/1.61 transitive: $i > $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(antisymmetric_type,type,
% 3.07/1.61 antisymmetric: $i > $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(reflexive_type,type,
% 3.07/1.61 reflexive: $i > $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(refltransitive_type,type,
% 3.07/1.61 refltransitive: $i > $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(refllinearorder_type,type,
% 3.07/1.61 refllinearorder: $i > $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(reflwellordering_type,type,
% 3.07/1.61 reflwellordering: $i > $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(choice2fnsingleton_type,type,
% 3.07/1.61 choice2fnsingleton: $o ).
% 3.07/1.61
% 3.07/1.61 thf(choice2fnsingleton,definition,
% 3.07/1.61 ( choice2fnsingleton
% 3.07/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.07/1.61 ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ? [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ B )
% 3.07/1.61 & ( Xphi @ Xx @ Xy ) ) )
% 3.07/1.61 => ! [R: $i] :
% 3.07/1.61 ( ( in @ R @ ( breln1Set @ B ) )
% 3.07/1.61 => ( ( reflwellordering @ B @ R )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( singleton
% 3.07/1.61 @ ( dsetconstr @ B
% 3.07/1.61 @ ^ [Xy: $i] :
% 3.07/1.61 ( ( Xphi @ Xx @ Xy )
% 3.07/1.61 & ! [Xz: $i] :
% 3.07/1.61 ( ( in @ Xz @ B )
% 3.07/1.61 => ( ( Xphi @ Xx @ Xz )
% 3.07/1.61 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setOfPairsIsBReln1_type,type,
% 3.07/1.61 setOfPairsIsBReln1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setOfPairsIsBReln1,definition,
% 3.07/1.61 ( setOfPairsIsBReln1
% 3.07/1.61 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 3.07/1.61 ( breln1 @ A
% 3.07/1.61 @ ( dpsetconstr @ A @ A
% 3.07/1.61 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(breln1all1_type,type,
% 3.07/1.61 breln1all1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(breln1all1,definition,
% 3.07/1.61 ( breln1all1
% 3.07/1.61 = ( ! [A: $i,R: $i] :
% 3.07/1.61 ( ( breln1 @ A @ R )
% 3.07/1.61 => ! [Xphi: $i > $o] :
% 3.07/1.61 ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.07/1.61 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ R )
% 3.07/1.61 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(subbreln1_type,type,
% 3.07/1.61 subbreln1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(subbreln1,definition,
% 3.07/1.61 ( subbreln1
% 3.07/1.61 = ( ! [A: $i,R: $i] :
% 3.07/1.61 ( ( breln1 @ A @ R )
% 3.07/1.61 => ! [S: $i] :
% 3.07/1.61 ( ( breln1 @ A @ S )
% 3.07/1.61 => ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.07/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.07/1.61 => ( subset @ R @ S ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(eqbreln1_type,type,
% 3.07/1.61 eqbreln1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(eqbreln1,definition,
% 3.07/1.61 ( eqbreln1
% 3.07/1.61 = ( ! [A: $i,R: $i] :
% 3.07/1.61 ( ( breln1 @ A @ R )
% 3.07/1.61 => ! [S: $i] :
% 3.07/1.61 ( ( breln1 @ A @ S )
% 3.07/1.61 => ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.07/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.07/1.61 => ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.07/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 3.07/1.61 => ( R = S ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(breln1invset_type,type,
% 3.07/1.61 breln1invset: $i > $i > $i ).
% 3.07/1.61
% 3.07/1.61 thf(breln1invprop_type,type,
% 3.07/1.61 breln1invprop: $o ).
% 3.07/1.61
% 3.07/1.61 thf(breln1invprop,definition,
% 3.07/1.61 ( breln1invprop
% 3.07/1.61 = ( ! [A: $i,R: $i] :
% 3.07/1.61 ( ( breln1 @ A @ R )
% 3.07/1.61 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(breln1invI_type,type,
% 3.07/1.61 breln1invI: $o ).
% 3.07/1.61
% 3.07/1.61 thf(breln1invI,definition,
% 3.07/1.61 ( breln1invI
% 3.07/1.61 = ( ! [A: $i,R: $i] :
% 3.07/1.61 ( ( breln1 @ A @ R )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.07/1.61 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(breln1invE_type,type,
% 3.07/1.61 breln1invE: $o ).
% 3.07/1.61
% 3.07/1.61 thf(breln1invE,definition,
% 3.07/1.61 ( breln1invE
% 3.07/1.61 = ( ! [A: $i,R: $i] :
% 3.07/1.61 ( ( breln1 @ A @ R )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 3.07/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(breln1compset_type,type,
% 3.07/1.61 breln1compset: $i > $i > $i > $i ).
% 3.07/1.61
% 3.07/1.61 thf(breln1compprop_type,type,
% 3.07/1.61 breln1compprop: $o ).
% 3.07/1.61
% 3.07/1.61 thf(breln1compprop,definition,
% 3.07/1.61 ( breln1compprop
% 3.07/1.61 = ( ! [A: $i,R: $i] :
% 3.07/1.61 ( ( breln1 @ A @ R )
% 3.07/1.61 => ! [S: $i] :
% 3.07/1.61 ( ( breln1 @ A @ S )
% 3.07/1.61 => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(breln1compI_type,type,
% 3.07/1.61 breln1compI: $o ).
% 3.07/1.61
% 3.07/1.61 thf(breln1compI,definition,
% 3.07/1.61 ( breln1compI
% 3.07/1.61 = ( ! [A: $i,R: $i] :
% 3.07/1.61 ( ( breln1 @ A @ R )
% 3.07/1.61 => ! [S: $i] :
% 3.07/1.61 ( ( breln1 @ A @ S )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 => ! [Xz: $i] :
% 3.07/1.61 ( ( in @ Xz @ A )
% 3.07/1.61 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 3.07/1.61 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 3.07/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(breln1compE_type,type,
% 3.07/1.61 breln1compE: $o ).
% 3.07/1.61
% 3.07/1.61 thf(breln1compE,definition,
% 3.07/1.61 ( breln1compE
% 3.07/1.61 = ( ! [A: $i,R: $i] :
% 3.07/1.61 ( ( breln1 @ A @ R )
% 3.07/1.61 => ! [S: $i] :
% 3.07/1.61 ( ( breln1 @ A @ S )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 3.07/1.61 => ? [Xz: $i] :
% 3.07/1.61 ( ( in @ Xz @ A )
% 3.07/1.61 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 3.07/1.61 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(breln1compEex_type,type,
% 3.07/1.61 breln1compEex: $o ).
% 3.07/1.61
% 3.07/1.61 thf(breln1compEex,definition,
% 3.07/1.61 ( breln1compEex
% 3.07/1.61 = ( ! [A: $i,R: $i] :
% 3.07/1.61 ( ( breln1 @ A @ R )
% 3.07/1.61 => ! [S: $i] :
% 3.07/1.61 ( ( breln1 @ A @ S )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 3.07/1.61 => ! [Xphi: $o] :
% 3.07/1.61 ( ! [Xz: $i] :
% 3.07/1.61 ( ( in @ Xz @ A )
% 3.07/1.61 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 3.07/1.61 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 3.07/1.61 => Xphi ) ) )
% 3.07/1.61 => Xphi ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(breln1unionprop_type,type,
% 3.07/1.61 breln1unionprop: $o ).
% 3.07/1.61
% 3.07/1.61 thf(breln1unionprop,definition,
% 3.07/1.61 ( breln1unionprop
% 3.07/1.61 = ( ! [A: $i,R: $i] :
% 3.07/1.61 ( ( breln1 @ A @ R )
% 3.07/1.61 => ! [S: $i] :
% 3.07/1.61 ( ( breln1 @ A @ S )
% 3.07/1.61 => ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(breln1unionIL_type,type,
% 3.07/1.61 breln1unionIL: $o ).
% 3.07/1.61
% 3.07/1.61 thf(breln1unionIL,definition,
% 3.07/1.61 ( breln1unionIL
% 3.07/1.61 = ( ! [A: $i,R: $i] :
% 3.07/1.61 ( ( breln1 @ A @ R )
% 3.07/1.61 => ! [S: $i] :
% 3.07/1.61 ( ( breln1 @ A @ S )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.07/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(breln1unionIR_type,type,
% 3.07/1.61 breln1unionIR: $o ).
% 3.07/1.61
% 3.07/1.61 thf(breln1unionIR,definition,
% 3.07/1.61 ( breln1unionIR
% 3.07/1.61 = ( ! [A: $i,R: $i] :
% 3.07/1.61 ( ( breln1 @ A @ R )
% 3.07/1.61 => ! [S: $i] :
% 3.07/1.61 ( ( breln1 @ A @ S )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.07/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(breln1unionI_type,type,
% 3.07/1.61 breln1unionI: $o ).
% 3.07/1.61
% 3.07/1.61 thf(breln1unionI,definition,
% 3.07/1.61 ( breln1unionI
% 3.07/1.61 = ( ! [A: $i,R: $i] :
% 3.07/1.61 ( ( breln1 @ A @ R )
% 3.07/1.61 => ! [S: $i] :
% 3.07/1.61 ( ( breln1 @ A @ S )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.07/1.61 | ( in @ ( kpair @ Xx @ Xy ) @ S ) )
% 3.07/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(breln1unionE_type,type,
% 3.07/1.61 breln1unionE: $o ).
% 3.07/1.61
% 3.07/1.61 thf(breln1unionE,definition,
% 3.07/1.61 ( breln1unionE
% 3.07/1.61 = ( ! [A: $i,R: $i] :
% 3.07/1.61 ( ( breln1 @ A @ R )
% 3.07/1.61 => ! [S: $i] :
% 3.07/1.61 ( ( breln1 @ A @ S )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 3.07/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.07/1.61 | ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(breln1unionEcases_type,type,
% 3.07/1.61 breln1unionEcases: $o ).
% 3.07/1.61
% 3.07/1.61 thf(breln1unionEcases,definition,
% 3.07/1.61 ( breln1unionEcases
% 3.07/1.61 = ( ! [A: $i,R: $i] :
% 3.07/1.61 ( ( breln1 @ A @ R )
% 3.07/1.61 => ! [S: $i] :
% 3.07/1.61 ( ( breln1 @ A @ S )
% 3.07/1.61 => ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 3.07/1.61 => ! [Xphi: $o] :
% 3.07/1.61 ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.07/1.61 => Xphi )
% 3.07/1.61 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.07/1.61 => Xphi )
% 3.07/1.61 => Xphi ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(breln1unionCommutes_type,type,
% 3.07/1.61 breln1unionCommutes: $o ).
% 3.07/1.61
% 3.07/1.61 thf(breln1unionCommutes,definition,
% 3.07/1.61 ( breln1unionCommutes
% 3.07/1.61 = ( ! [A: $i,R: $i] :
% 3.07/1.61 ( ( breln1 @ A @ R )
% 3.07/1.61 => ! [S: $i] :
% 3.07/1.61 ( ( breln1 @ A @ S )
% 3.07/1.61 => ( ( binunion @ R @ S )
% 3.07/1.61 = ( binunion @ S @ R ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(woz2Ex_type,type,
% 3.07/1.61 woz2Ex: $o ).
% 3.07/1.61
% 3.07/1.61 thf(woz2Ex,definition,
% 3.07/1.61 ( woz2Ex
% 3.07/1.61 = ( ! [A: $i,R: $i] :
% 3.07/1.61 ( ( breln1 @ A @ R )
% 3.07/1.61 => ( R
% 3.07/1.61 = ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(woz2W_type,type,
% 3.07/1.61 woz2W: $o ).
% 3.07/1.61
% 3.07/1.61 thf(woz2W,definition,
% 3.07/1.61 ( woz2W
% 3.07/1.61 = ( ! [A: $i,R: $i] :
% 3.07/1.61 ( ( breln1 @ A @ R )
% 3.07/1.61 => ! [S: $i] :
% 3.07/1.61 ( ( breln1 @ A @ S )
% 3.07/1.61 => ( ( breln1invset @ A @ ( breln1compset @ A @ R @ S ) )
% 3.07/1.61 = ( breln1compset @ A @ ( breln1invset @ A @ S ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(woz2A_type,type,
% 3.07/1.61 woz2A: $o ).
% 3.07/1.61
% 3.07/1.61 thf(woz2A,definition,
% 3.07/1.61 ( woz2A
% 3.07/1.61 = ( ! [A: $i,R: $i] :
% 3.07/1.61 ( ( breln1 @ A @ R )
% 3.07/1.61 => ! [S: $i] :
% 3.07/1.61 ( ( breln1 @ A @ S )
% 3.07/1.61 => ! [T: $i] :
% 3.07/1.61 ( ( breln1 @ A @ T )
% 3.07/1.61 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 3.07/1.61 = ( binunion @ ( breln1compset @ A @ R @ T ) @ ( breln1compset @ A @ S @ T ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(woz2B_type,type,
% 3.07/1.61 woz2B: $o ).
% 3.07/1.61
% 3.07/1.61 thf(woz2B,definition,
% 3.07/1.61 ( woz2B
% 3.07/1.61 = ( ! [A: $i,R: $i] :
% 3.07/1.61 ( ( breln1 @ A @ R )
% 3.07/1.61 => ! [S: $i] :
% 3.07/1.61 ( ( breln1 @ A @ S )
% 3.07/1.61 => ! [T: $i] :
% 3.07/1.61 ( ( breln1 @ A @ T )
% 3.07/1.61 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 3.07/1.61 = ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ S ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(image1Ex_type,type,
% 3.07/1.61 image1Ex: $o ).
% 3.07/1.61
% 3.07/1.61 thf(image1Ex,definition,
% 3.07/1.61 ( image1Ex
% 3.07/1.61 = ( ! [A: $i,Xf: $i > $i] :
% 3.07/1.61 ? [B: $i] :
% 3.07/1.61 ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ B )
% 3.07/1.61 <=> ? [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 & ( Xx
% 3.07/1.61 = ( Xf @ Xy ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(image1Ex1_type,type,
% 3.07/1.61 image1Ex1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(image1Ex1,definition,
% 3.07/1.61 ( image1Ex1
% 3.07/1.61 = ( ! [A: $i,Xf: $i > $i] :
% 3.07/1.61 ( exu
% 3.07/1.61 @ ^ [B: $i] :
% 3.07/1.61 ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ B )
% 3.07/1.61 <=> ? [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 & ( Xx
% 3.07/1.61 = ( Xf @ Xy ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(image1_type,type,
% 3.07/1.61 image1: $i > ( $i > $i ) > $i ).
% 3.07/1.61
% 3.07/1.61 thf(image1Equiv_type,type,
% 3.07/1.61 image1Equiv: $o ).
% 3.07/1.61
% 3.07/1.61 thf(image1Equiv,definition,
% 3.07/1.61 ( image1Equiv
% 3.07/1.61 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx
% 3.07/1.61 @ ( image1 @ A
% 3.07/1.61 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 3.07/1.61 <=> ? [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 & ( Xx
% 3.07/1.61 = ( Xf @ Xy ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(image1E_type,type,
% 3.07/1.61 image1E: $o ).
% 3.07/1.61
% 3.07/1.61 thf(image1E,definition,
% 3.07/1.61 ( image1E
% 3.07/1.61 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 3.07/1.61 ( ( in @ Xx
% 3.07/1.61 @ ( image1 @ A
% 3.07/1.61 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 3.07/1.61 => ? [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 & ( Xx
% 3.07/1.61 = ( Xf @ Xy ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(image1I_type,type,
% 3.07/1.61 image1I: $o ).
% 3.07/1.61
% 3.07/1.61 thf(image1I,definition,
% 3.07/1.61 ( image1I
% 3.07/1.61 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 3.07/1.61 ( ? [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ A )
% 3.07/1.61 & ( Xx
% 3.07/1.61 = ( Xf @ Xy ) ) )
% 3.07/1.61 => ( in @ Xx
% 3.07/1.61 @ ( image1 @ A
% 3.07/1.61 @ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(injective_type,type,
% 3.07/1.61 injective: $i > $i > $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(injFuncSet_type,type,
% 3.07/1.61 injFuncSet: $i > $i > $i ).
% 3.07/1.61
% 3.07/1.61 thf(injFuncInInjFuncSet_type,type,
% 3.07/1.61 injFuncInInjFuncSet: $o ).
% 3.07/1.61
% 3.07/1.61 thf(injFuncInInjFuncSet,definition,
% 3.07/1.61 ( injFuncInInjFuncSet
% 3.07/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.07/1.61 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.07/1.61 => ( ( injective @ A @ B @ Xf )
% 3.07/1.61 => ( in @ Xf @ ( injFuncSet @ A @ B ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(injFuncSetFuncIn_type,type,
% 3.07/1.61 injFuncSetFuncIn: $o ).
% 3.07/1.61
% 3.07/1.61 thf(injFuncSetFuncIn,definition,
% 3.07/1.61 ( injFuncSetFuncIn
% 3.07/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.07/1.61 ( ( in @ Xf @ ( injFuncSet @ A @ B ) )
% 3.07/1.61 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(injFuncSetFuncInj_type,type,
% 3.07/1.61 injFuncSetFuncInj: $o ).
% 3.07/1.61
% 3.07/1.61 thf(injFuncSetFuncInj,definition,
% 3.07/1.61 ( injFuncSetFuncInj
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i,Xf: $i] :
% 3.07/1.61 ( ( in @ Xf @ ( injFuncSet @ Xx @ Xy ) )
% 3.07/1.61 => ( injective @ Xx @ Xy @ Xf ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(surjective_type,type,
% 3.07/1.61 surjective: $i > $i > $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(surjFuncSet_type,type,
% 3.07/1.61 surjFuncSet: $i > $i > $i ).
% 3.07/1.61
% 3.07/1.61 thf(surjFuncSetFuncIn_type,type,
% 3.07/1.61 surjFuncSetFuncIn: $o ).
% 3.07/1.61
% 3.07/1.61 thf(surjFuncSetFuncIn,definition,
% 3.07/1.61 ( surjFuncSetFuncIn
% 3.07/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.07/1.61 ( ( in @ Xf @ ( surjFuncSet @ A @ B ) )
% 3.07/1.61 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(surjFuncSetFuncSurj_type,type,
% 3.07/1.61 surjFuncSetFuncSurj: $o ).
% 3.07/1.61
% 3.07/1.61 thf(surjFuncSetFuncSurj,definition,
% 3.07/1.61 ( surjFuncSetFuncSurj
% 3.07/1.61 = ( ! [Xx: $i,Xy: $i,Xf: $i] :
% 3.07/1.61 ( ( in @ Xf @ ( surjFuncSet @ Xx @ Xy ) )
% 3.07/1.61 => ( surjective @ Xx @ Xy @ Xf ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(leftInvIsSurj_type,type,
% 3.07/1.61 leftInvIsSurj: $o ).
% 3.07/1.61
% 3.07/1.61 thf(leftInvIsSurj,definition,
% 3.07/1.61 ( leftInvIsSurj
% 3.07/1.61 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.07/1.61 ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.07/1.61 => ! [Xg: $i] :
% 3.07/1.61 ( ( in @ Xg @ ( funcSet @ B @ A ) )
% 3.07/1.61 => ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ( ( ap @ B @ A @ Xg @ ( Xf @ Xx ) )
% 3.07/1.61 = Xx ) )
% 3.07/1.61 => ( surjective @ B @ A @ Xg ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(surjCantorThm_type,type,
% 3.07/1.61 surjCantorThm: $o ).
% 3.07/1.61
% 3.07/1.61 thf(surjCantorThm,definition,
% 3.07/1.61 ( surjCantorThm
% 3.07/1.61 = ( ! [A: $i,Xf: $i] :
% 3.07/1.61 ( ( in @ Xf @ ( funcSet @ A @ ( powerset @ A ) ) )
% 3.07/1.61 => ~ ( surjective @ A @ ( powerset @ A ) @ Xf ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(foundation2_type,type,
% 3.07/1.61 foundation2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(foundation2,definition,
% 3.07/1.61 ( foundation2
% 3.07/1.61 = ( ! [A: $i] :
% 3.07/1.61 ( ( nonempty @ A )
% 3.07/1.61 => ? [X: $i] :
% 3.07/1.61 ( ( in @ X @ A )
% 3.07/1.61 & ( ( binintersect @ X @ A )
% 3.07/1.61 = emptyset ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(notinself_type,type,
% 3.07/1.61 notinself: $o ).
% 3.07/1.61
% 3.07/1.61 thf(notinself,definition,
% 3.07/1.61 ( notinself
% 3.07/1.61 = ( ! [A: $i] :
% 3.07/1.61 ~ ( in @ A @ A ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(notinself2_type,type,
% 3.07/1.61 notinself2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(notinself2,definition,
% 3.07/1.61 ( notinself2
% 3.07/1.61 = ( ! [A: $i,B: $i] :
% 3.07/1.61 ( ( in @ A @ B )
% 3.07/1.61 => ~ ( in @ B @ A ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(omegaS_type,type,
% 3.07/1.61 omegaS: $i > $i ).
% 3.07/1.61
% 3.07/1.61 thf(omegaSp_type,type,
% 3.07/1.61 omegaSp: $o ).
% 3.07/1.61
% 3.07/1.61 thf(omegaSp,definition,
% 3.07/1.61 ( omegaSp
% 3.07/1.61 = ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ omega )
% 3.07/1.61 => ( in @ ( omegaS @ Xx ) @ omega ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(omegaSclos_type,type,
% 3.07/1.61 omegaSclos: $o ).
% 3.07/1.61
% 3.07/1.61 thf(omegaSclos,definition,
% 3.07/1.61 ( omegaSclos
% 3.07/1.61 = ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ omega )
% 3.07/1.61 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(peano0notS_type,type,
% 3.07/1.61 peano0notS: $o ).
% 3.07/1.61
% 3.07/1.61 thf(peano0notS,definition,
% 3.07/1.61 ( peano0notS
% 3.07/1.61 = ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ omega )
% 3.07/1.61 => ( ( omegaS @ Xx )
% 3.07/1.61 != emptyset ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(peano3_type,type,
% 3.07/1.61 peano3: $i > $i > $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(peano4_type,type,
% 3.07/1.61 peano4: $i > $i > $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(peano5_type,type,
% 3.07/1.61 peano5: $i > $i > $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(peanoSinj_type,type,
% 3.07/1.61 peanoSinj: $o ).
% 3.07/1.61
% 3.07/1.61 thf(peanoSinj,definition,
% 3.07/1.61 ( peanoSinj
% 3.07/1.61 = ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ omega )
% 3.07/1.61 => ! [Xy: $i] :
% 3.07/1.61 ( ( in @ Xy @ omega )
% 3.07/1.61 => ( ( ( omegaS @ Xx )
% 3.07/1.61 = ( omegaS @ Xy ) )
% 3.07/1.61 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(peano_type,type,
% 3.07/1.61 peano: $i > $i > $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(transitiveset_type,type,
% 3.07/1.61 transitiveset: $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(transitiveset,definition,
% 3.07/1.61 ( transitiveset
% 3.07/1.61 = ( ^ [A: $i] :
% 3.07/1.61 ! [X: $i] :
% 3.07/1.61 ( ( in @ X @ A )
% 3.07/1.61 => ( subset @ X @ A ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(transitivesetOp1_type,type,
% 3.07/1.61 transitivesetOp1: $o ).
% 3.07/1.61
% 3.07/1.61 thf(transitivesetOp1,definition,
% 3.07/1.61 ( transitivesetOp1
% 3.07/1.61 = ( ! [X: $i] :
% 3.07/1.61 ( ( transitiveset @ X )
% 3.07/1.61 => ! [A: $i] :
% 3.07/1.61 ( ( in @ A @ X )
% 3.07/1.61 => ( subset @ A @ X ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(binintTransitive_type,type,
% 3.07/1.61 binintTransitive: $o ).
% 3.07/1.61
% 3.07/1.61 thf(binintTransitive,definition,
% 3.07/1.61 ( binintTransitive
% 3.07/1.61 = ( ! [X: $i] :
% 3.07/1.61 ( ( transitiveset @ X )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( transitiveset @ Y )
% 3.07/1.61 => ( transitiveset @ ( binintersect @ X @ Y ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(transitivesetOp2_type,type,
% 3.07/1.61 transitivesetOp2: $o ).
% 3.07/1.61
% 3.07/1.61 thf(transitivesetOp2,definition,
% 3.07/1.61 ( transitivesetOp2
% 3.07/1.61 = ( ! [X: $i] :
% 3.07/1.61 ( ( transitiveset @ X )
% 3.07/1.61 => ! [A: $i,Xx: $i] :
% 3.07/1.61 ( ( in @ A @ X )
% 3.07/1.61 => ( ( in @ Xx @ A )
% 3.07/1.61 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(setunionTransitive_type,type,
% 3.07/1.61 setunionTransitive: $o ).
% 3.07/1.61
% 3.07/1.61 thf(setunionTransitive,definition,
% 3.07/1.61 ( setunionTransitive
% 3.07/1.61 = ( ! [X: $i] :
% 3.07/1.61 ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ X )
% 3.07/1.61 => ( transitiveset @ Xx ) )
% 3.07/1.61 => ( transitiveset @ ( setunion @ X ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(stricttotalorderedByIn_type,type,
% 3.07/1.61 stricttotalorderedByIn: $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(stricttotalorderedByIn,definition,
% 3.07/1.61 ( stricttotalorderedByIn
% 3.07/1.61 = ( ^ [A: $i] :
% 3.07/1.61 ( ! [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ A )
% 3.07/1.61 => ! [X: $i] :
% 3.07/1.61 ( ( in @ X @ A )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ A )
% 3.07/1.61 => ( ( ( in @ Xx @ X )
% 3.07/1.61 & ( in @ X @ Y ) )
% 3.07/1.61 => ( in @ Xx @ Y ) ) ) ) )
% 3.07/1.61 & ! [X: $i] :
% 3.07/1.61 ( ( in @ X @ A )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ A )
% 3.07/1.61 => ( ( X = Y )
% 3.07/1.61 | ( in @ X @ Y )
% 3.07/1.61 | ( in @ Y @ X ) ) ) )
% 3.07/1.61 & ! [X: $i] :
% 3.07/1.61 ( ( in @ X @ A )
% 3.07/1.61 => ~ ( in @ X @ X ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(wellorderedByIn_type,type,
% 3.07/1.61 wellorderedByIn: $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(wellorderedByIn,definition,
% 3.07/1.61 ( wellorderedByIn
% 3.07/1.61 = ( ^ [A: $i] :
% 3.07/1.61 ( ( stricttotalorderedByIn @ A )
% 3.07/1.61 & ! [X: $i] :
% 3.07/1.61 ( ( in @ X @ ( powerset @ A ) )
% 3.07/1.61 => ( ( nonempty @ X )
% 3.07/1.61 => ? [Xx: $i] :
% 3.07/1.61 ( ( in @ Xx @ X )
% 3.07/1.61 & ! [Y: $i] :
% 3.07/1.61 ( ( in @ Y @ X )
% 3.07/1.61 => ( ( Xx = Y )
% 3.07/1.61 | ( in @ Xx @ Y ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(ordinal_type,type,
% 3.07/1.61 ordinal: $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(ordinal,definition,
% 3.07/1.61 ( ordinal
% 3.07/1.61 = ( ^ [Xx: $i] :
% 3.07/1.61 ( ( transitiveset @ Xx )
% 3.07/1.61 & ( wellorderedByIn @ Xx ) ) ) ) ).
% 3.07/1.61
% 3.07/1.61 thf(limitOrdinal_type,type,
% 3.07/1.61 limitOrdinal: $i > $o ).
% 3.07/1.61
% 3.07/1.61 thf(ordinalMinLem1,conjecture,
% 3.07/1.61 ( setextAx
% 3.07/1.61 => ( emptysetAx
% 3.07/1.61 => ( setadjoinAx
% 3.07/1.61 => ( powersetAx
% 3.07/1.61 => ( setunionAx
% 3.07/1.61 => ( omega0Ax
% 3.07/1.61 => ( omegaSAx
% 3.07/1.61 => ( omegaIndAx
% 3.07/1.61 => ( replAx
% 3.07/1.61 => ( foundationAx
% 3.07/1.61 => ( wellorderingAx
% 3.07/1.61 => ( descrp
% 3.07/1.61 => ( dsetconstrI
% 3.07/1.61 => ( dsetconstrEL
% 3.07/1.61 => ( dsetconstrER
% 3.07/1.61 => ( exuE1
% 3.07/1.61 => ( prop2setE
% 3.07/1.61 => ( emptysetE
% 3.07/1.61 => ( emptysetimpfalse
% 3.07/1.61 => ( notinemptyset
% 3.07/1.61 => ( exuE3e
% 3.07/1.61 => ( setext
% 3.07/1.61 => ( emptyI
% 3.07/1.61 => ( noeltsimpempty
% 3.07/1.61 => ( setbeta
% 3.07/1.61 => ( nonemptyE1
% 3.07/1.61 => ( nonemptyI
% 3.07/1.61 => ( nonemptyI1
% 3.07/1.61 => ( setadjoinIL
% 3.07/1.61 => ( emptyinunitempty
% 3.07/1.61 => ( setadjoinIR
% 3.07/1.61 => ( setadjoinE
% 3.07/1.61 => ( setadjoinOr
% 3.07/1.61 => ( setoftrueEq
% 3.07/1.61 => ( powersetI
% 3.07/1.61 => ( emptyinPowerset
% 3.07/1.61 => ( emptyInPowerset
% 3.07/1.61 => ( powersetE
% 3.07/1.61 => ( setunionI
% 3.07/1.61 => ( setunionE
% 3.07/1.61 => ( subPowSU
% 3.07/1.61 => ( exuE2
% 3.07/1.61 => ( nonemptyImpWitness
% 3.07/1.61 => ( uniqinunit
% 3.07/1.61 => ( notinsingleton
% 3.07/1.61 => ( eqinunit
% 3.07/1.61 => ( singletonsswitch
% 3.07/1.61 => ( upairsetE
% 3.07/1.61 => ( upairsetIL
% 3.07/1.61 => ( upairsetIR
% 3.07/1.61 => ( emptyE1
% 3.07/1.61 => ( vacuousDall
% 3.07/1.61 => ( quantDeMorgan1
% 3.07/1.61 => ( quantDeMorgan2
% 3.07/1.61 => ( quantDeMorgan3
% 3.07/1.61 => ( quantDeMorgan4
% 3.07/1.61 => ( prop2setI
% 3.07/1.61 => ( prop2set2propI
% 3.07/1.61 => ( notdexE
% 3.07/1.61 => ( notdallE
% 3.07/1.61 => ( exuI1
% 3.07/1.61 => ( exuI3
% 3.07/1.61 => ( exuI2
% 3.07/1.61 => ( inCongP
% 3.07/1.61 => ( in__Cong
% 3.07/1.61 => ( exuE3u
% 3.07/1.61 => ( exu__Cong
% 3.07/1.61 => ( emptyset__Cong
% 3.07/1.61 => ( setadjoin__Cong
% 3.07/1.61 => ( powerset__Cong
% 3.07/1.61 => ( setunion__Cong
% 3.07/1.61 => ( omega__Cong
% 3.07/1.61 => ( exuEu
% 3.07/1.61 => ( descr__Cong
% 3.07/1.61 => ( dsetconstr__Cong
% 3.07/1.61 => ( subsetI1
% 3.07/1.61 => ( eqimpsubset2
% 3.07/1.61 => ( eqimpsubset1
% 3.07/1.61 => ( subsetI2
% 3.07/1.61 => ( emptysetsubset
% 3.07/1.61 => ( subsetE
% 3.07/1.61 => ( subsetE2
% 3.07/1.61 => ( notsubsetI
% 3.07/1.61 => ( notequalI1
% 3.07/1.61 => ( notequalI2
% 3.07/1.61 => ( subsetRefl
% 3.07/1.61 => ( subsetTrans
% 3.07/1.61 => ( setadjoinSub
% 3.07/1.61 => ( setadjoinSub2
% 3.07/1.61 => ( subset2powerset
% 3.07/1.61 => ( setextsub
% 3.07/1.61 => ( subsetemptysetimpeq
% 3.07/1.61 => ( powersetI1
% 3.07/1.61 => ( powersetE1
% 3.07/1.61 => ( inPowerset
% 3.07/1.61 => ( powersetsubset
% 3.07/1.61 => ( sepInPowerset
% 3.07/1.61 => ( sepSubset
% 3.07/1.61 => ( binunionIL
% 3.07/1.61 => ( upairset2IR
% 3.07/1.61 => ( binunionIR
% 3.07/1.61 => ( binunionEcases
% 3.07/1.61 => ( binunionE
% 3.07/1.61 => ( binunionLsub
% 3.07/1.61 => ( binunionRsub
% 3.07/1.61 => ( binintersectI
% 3.07/1.61 => ( binintersectSubset5
% 3.07/1.61 => ( binintersectEL
% 3.07/1.61 => ( binintersectLsub
% 3.07/1.61 => ( binintersectSubset2
% 3.07/1.61 => ( binintersectSubset3
% 3.07/1.61 => ( binintersectER
% 3.07/1.61 => ( disjointsetsI1
% 3.07/1.61 => ( binintersectRsub
% 3.07/1.61 => ( binintersectSubset4
% 3.07/1.61 => ( binintersectSubset1
% 3.07/1.61 => ( bs114d
% 3.07/1.61 => ( setminusI
% 3.07/1.61 => ( setminusEL
% 3.07/1.61 => ( setminusER
% 3.07/1.61 => ( setminusSubset2
% 3.07/1.61 => ( setminusERneg
% 3.07/1.61 => ( setminusELneg
% 3.07/1.61 => ( setminusILneg
% 3.07/1.61 => ( setminusIRneg
% 3.07/1.61 => ( setminusLsub
% 3.07/1.61 => ( setminusSubset1
% 3.07/1.61 => ( symdiffE
% 3.07/1.61 => ( symdiffI1
% 3.07/1.61 => ( symdiffI2
% 3.07/1.61 => ( symdiffIneg1
% 3.07/1.61 => ( symdiffIneg2
% 3.07/1.61 => ( secondinupair
% 3.07/1.61 => ( setukpairIL
% 3.07/1.61 => ( setukpairIR
% 3.07/1.61 => ( kpairiskpair
% 3.07/1.61 => ( kpairp
% 3.07/1.61 => ( singletonsubset
% 3.07/1.61 => ( singletoninpowerset
% 3.07/1.61 => ( singletoninpowunion
% 3.07/1.61 => ( upairset2E
% 3.07/1.61 => ( upairsubunion
% 3.07/1.61 => ( upairinpowunion
% 3.07/1.61 => ( ubforcartprodlem1
% 3.07/1.61 => ( ubforcartprodlem2
% 3.07/1.61 => ( ubforcartprodlem3
% 3.07/1.61 => ( cartprodpairin
% 3.07/1.61 => ( cartprodmempair1
% 3.07/1.61 => ( cartprodmempair
% 3.07/1.61 => ( setunionE2
% 3.07/1.61 => ( setunionsingleton1
% 3.07/1.61 => ( setunionsingleton2
% 3.07/1.61 => ( setunionsingleton
% 3.07/1.61 => ( singletonprop
% 3.07/1.61 => ( ex1E1
% 3.07/1.61 => ( ex1I
% 3.07/1.61 => ( ex1I2
% 3.07/1.61 => ( singletonsuniq
% 3.07/1.61 => ( setukpairinjL1
% 3.07/1.61 => ( kfstsingleton
% 3.07/1.61 => ( theprop
% 3.07/1.61 => ( kfstpairEq
% 3.07/1.61 => ( cartprodfstin
% 3.07/1.61 => ( setukpairinjL2
% 3.07/1.61 => ( setukpairinjL
% 3.07/1.61 => ( setukpairinjR11
% 3.07/1.61 => ( setukpairinjR12
% 3.07/1.61 => ( setukpairinjR1
% 3.07/1.61 => ( upairequniteq
% 3.07/1.61 => ( setukpairinjR2
% 3.07/1.61 => ( setukpairinjR
% 3.07/1.61 => ( ksndsingleton
% 3.07/1.61 => ( ksndpairEq
% 3.07/1.61 => ( kpairsurjEq
% 3.07/1.61 => ( cartprodsndin
% 3.07/1.61 => ( cartprodpairmemEL
% 3.07/1.61 => ( cartprodpairmemER
% 3.07/1.61 => ( cartprodmempaircEq
% 3.07/1.61 => ( cartprodfstpairEq
% 3.07/1.61 => ( cartprodsndpairEq
% 3.07/1.61 => ( cartprodpairsurjEq
% 3.07/1.61 => ( dpsetconstrI
% 3.07/1.61 => ( dpsetconstrSub
% 3.07/1.61 => ( setOfPairsIsBReln
% 3.07/1.61 => ( dpsetconstrERa
% 3.07/1.61 => ( dpsetconstrEL1
% 3.07/1.61 => ( dpsetconstrEL2
% 3.07/1.61 => ( dpsetconstrER
% 3.07/1.61 => ( funcImageSingleton
% 3.07/1.61 => ( apProp
% 3.07/1.61 => ( app
% 3.07/1.61 => ( infuncsetfunc
% 3.07/1.61 => ( ap2p
% 3.07/1.61 => ( funcinfuncset
% 3.07/1.61 => ( lamProp
% 3.07/1.61 => ( lamp
% 3.07/1.61 => ( lam2p
% 3.07/1.61 => ( brelnall1
% 3.07/1.61 => ( brelnall2
% 3.07/1.61 => ( ex1E2
% 3.07/1.61 => ( funcGraphProp1
% 3.07/1.61 => ( funcGraphProp3
% 3.07/1.61 => ( funcGraphProp2
% 3.07/1.61 => ( funcextLem
% 3.07/1.61 => ( funcGraphProp4
% 3.07/1.61 => ( subbreln
% 3.07/1.61 => ( eqbreln
% 3.07/1.61 => ( funcext
% 3.07/1.61 => ( funcext2
% 3.07/1.61 => ( ap2apEq1
% 3.07/1.61 => ( ap2apEq2
% 3.07/1.61 => ( beta1
% 3.07/1.61 => ( eta1
% 3.07/1.61 => ( lam2lamEq
% 3.07/1.61 => ( beta2
% 3.07/1.61 => ( eta2
% 3.07/1.61 => ( iffalseProp1
% 3.07/1.61 => ( iffalseProp2
% 3.07/1.61 => ( iftrueProp1
% 3.07/1.61 => ( iftrueProp2
% 3.07/1.61 => ( ifSingleton
% 3.07/1.61 => ( ifp
% 3.07/1.61 => ( theeq
% 3.07/1.61 => ( iftrue
% 3.07/1.61 => ( iffalse
% 3.07/1.61 => ( iftrueorfalse
% 3.07/1.61 => ( binintersectT_lem
% 3.07/1.61 => ( binunionT_lem
% 3.07/1.61 => ( powersetT_lem
% 3.07/1.61 => ( setminusT_lem
% 3.07/1.61 => ( complementT_lem
% 3.07/1.61 => ( setextT
% 3.07/1.61 => ( subsetTI
% 3.07/1.61 => ( powersetTI1
% 3.07/1.61 => ( powersetTE1
% 3.07/1.61 => ( complementTI1
% 3.07/1.61 => ( complementTE1
% 3.07/1.61 => ( binintersectTELcontra
% 3.07/1.61 => ( binintersectTERcontra
% 3.07/1.61 => ( contrasubsetT
% 3.07/1.61 => ( contrasubsetT1
% 3.07/1.61 => ( contrasubsetT2
% 3.07/1.61 => ( contrasubsetT3
% 3.07/1.61 => ( doubleComplementI1
% 3.07/1.61 => ( doubleComplementE1
% 3.07/1.61 => ( doubleComplementSub1
% 3.07/1.61 => ( doubleComplementSub2
% 3.07/1.61 => ( doubleComplementEq
% 3.07/1.61 => ( complementTnotintersectT
% 3.07/1.61 => ( complementImpComplementIntersect
% 3.07/1.61 => ( complementSubsetComplementIntersect
% 3.07/1.61 => ( complementInPowersetComplementIntersect
% 3.07/1.61 => ( contraSubsetComplement
% 3.07/1.61 => ( complementTcontraSubset
% 3.07/1.61 => ( binunionTILcontra
% 3.07/1.61 => ( binunionTIRcontra
% 3.07/1.61 => ( inIntersectImpInUnion
% 3.07/1.61 => ( inIntersectImpInUnion2
% 3.07/1.61 => ( inIntersectImpInIntersectUnions
% 3.07/1.61 => ( intersectInPowersetIntersectUnions
% 3.07/1.61 => ( inComplementUnionImpNotIn1
% 3.07/1.61 => ( inComplementUnionImpInComplement1
% 3.07/1.61 => ( binunionTE
% 3.07/1.61 => ( binunionTEcontra
% 3.07/1.61 => ( demorgan2a1
% 3.07/1.61 => ( complementUnionInPowersetComplement
% 3.07/1.61 => ( demorgan2a2
% 3.07/1.61 => ( demorgan1a
% 3.07/1.61 => ( demorgan1b
% 3.07/1.61 => ( demorgan1
% 3.07/1.61 => ( demorgan2a
% 3.07/1.61 => ( demorgan2b2
% 3.07/1.61 => ( demorgan2b
% 3.07/1.61 => ( demorgan2
% 3.07/1.61 => ( woz13rule0
% 3.07/1.61 => ( woz13rule1
% 3.07/1.61 => ( woz13rule2
% 3.07/1.61 => ( woz13rule3
% 3.07/1.61 => ( woz13rule4
% 3.07/1.61 => ( woz1_1
% 3.07/1.61 => ( woz1_2
% 3.07/1.61 => ( woz1_3
% 3.07/1.61 => ( woz1_4
% 3.07/1.61 => ( woz1_5
% 3.07/1.61 => ( breln1all2
% 3.07/1.61 => ( breln1SetBreln1
% 3.07/1.61 => ( choice2fnsingleton
% 3.07/1.61 => ( setOfPairsIsBReln1
% 3.07/1.61 => ( breln1all1
% 3.07/1.61 => ( subbreln1
% 3.07/1.61 => ( eqbreln1
% 3.07/1.61 => ( breln1invprop
% 3.07/1.61 => ( breln1invI
% 3.07/1.61 => ( breln1invE
% 3.07/1.61 => ( breln1compprop
% 3.07/1.61 => ( breln1compI
% 3.07/1.61 => ( breln1compE
% 3.07/1.61 => ( breln1compEex
% 3.07/1.61 => ( breln1unionprop
% 3.07/1.61 => ( breln1unionIL
% 3.07/1.61 => ( breln1unionIR
% 3.07/1.61 => ( breln1unionI
% 3.07/1.61 => ( breln1unionE
% 3.07/1.61 => ( breln1unionEcases
% 3.07/1.61 => ( breln1unionCommutes
% 3.07/1.61 => ( woz2Ex
% 3.07/1.61 => ( woz2W
% 3.07/1.61 => ( woz2A
% 3.07/1.61 => ( woz2B
% 3.07/1.61 => ( image1Ex
% 3.07/1.61 => ( image1Ex1
% 3.07/1.61 => ( image1Equiv
% 3.07/1.61 => ( image1E
% 3.07/1.61 => ( image1I
% 3.07/1.61 => ( injFuncInInjFuncSet
% 3.07/1.61 => ( injFuncSetFuncIn
% 3.07/1.61 => ( injFuncSetFuncInj
% 3.07/1.61 => ( surjFuncSetFuncIn
% 3.07/1.61 => ( surjFuncSetFuncSurj
% 3.07/1.61 => ( leftInvIsSurj
% 3.07/1.61 => ( surjCantorThm
% 3.07/1.61 => ( foundation2
% 3.07/1.61 => ( notinself
% 3.07/1.61 => ( notinself2
% 3.07/1.61 => ( omegaSp
% 3.07/1.61 => ( omegaSclos
% 3.07/1.61 => ( peano0notS
% 3.07/1.61 => ( peanoSinj
% 3.07/1.61 => ( transitivesetOp1
% 3.07/1.61 => ( binintTransitive
% 3.07/1.61 => ( transitivesetOp2
% 3.07/1.61 => ( setunionTransitive
% 3.07/1.61 => ! [X: $i] :
% 3.07/1.61 ( ( ordinal @ X )
% 3.07/1.61 => ! [Y: $i] :
% 3.07/1.61 ( ( ordinal @ Y )
% 3.07/1.61 => ( transitiveset @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.07/1.61 ------------------------
% 3.07/1.65 % (24648)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_24321 for (2999ds/2Mi)
% 3.07/1.65 % (24651)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_24321 for (2999ds/18Mi)
% 3.07/1.65 % (24646)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_24321 for (2999ds/4Mi)
% 3.07/1.65 % (24647)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_24321 for (2999ds/27Mi)
% 3.07/1.66 % (24648)Instruction limit reached!
% 3.07/1.66 % (24648)------------------------------
% 3.07/1.66 % (24648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.66 % (24648)Termination reason: Unknown
% 3.07/1.66 % (24648)Termination phase: shuffling
% 3.07/1.66
% 3.07/1.66 % (24648)Memory used [KB]: 1663
% 3.07/1.66 % (24648)Time elapsed: 0.002 s
% 3.07/1.66 % (24648)Instructions burned: 3 (million)
% 3.07/1.66 % (24648)------------------------------
% 3.07/1.66 % (24648)------------------------------
% 3.07/1.66 % (24646)Instruction limit reached!
% 3.07/1.66 % (24646)------------------------------
% 3.07/1.66 % (24646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.66 % (24646)Termination reason: Unknown
% 3.07/1.66 % (24646)Termination phase: shuffling
% 3.07/1.66
% 3.07/1.66 % (24646)Memory used [KB]: 1791
% 3.07/1.66 % (24646)Time elapsed: 0.003 s
% 3.07/1.66 % (24646)Instructions burned: 6 (million)
% 3.07/1.66 % (24646)------------------------------
% 3.07/1.66 % (24646)------------------------------
% 3.07/1.66 % (24651)Instruction limit reached!
% 3.07/1.66 % (24651)------------------------------
% 3.07/1.66 % (24651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.66 % (24651)Termination reason: Unknown
% 3.07/1.66 % (24651)Termination phase: shuffling
% 3.07/1.66
% 3.07/1.66 % (24651)Memory used [KB]: 1918
% 3.07/1.66 % (24651)Time elapsed: 0.008 s
% 3.07/1.66 % (24651)Instructions burned: 19 (million)
% 3.07/1.66 % (24651)------------------------------
% 3.07/1.66 % (24651)------------------------------
% 3.07/1.66 % (24645)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_24321 for (2999ds/183Mi)
% 3.07/1.66 % (24650)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_24321 for (2999ds/275Mi)
% 3.07/1.66 % (24649)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_24321 for (2999ds/2Mi)
% 3.07/1.66 % (24647)Instruction limit reached!
% 3.07/1.66 % (24647)------------------------------
% 3.07/1.66 % (24647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.66 % (24647)Termination reason: Unknown
% 3.07/1.66 % (24647)Termination phase: shuffling
% 3.07/1.66
% 3.07/1.66 % (24647)Memory used [KB]: 2174
% 3.07/1.66 % (24647)Time elapsed: 0.010 s
% 3.07/1.66 % (24647)Instructions burned: 27 (million)
% 3.07/1.66 % (24647)------------------------------
% 3.07/1.66 % (24647)------------------------------
% 3.07/1.66 % (24649)Instruction limit reached!
% 3.07/1.66 % (24649)------------------------------
% 3.07/1.66 % (24649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.66 % (24649)Termination reason: Unknown
% 3.07/1.66 % (24649)Termination phase: shuffling
% 3.07/1.66
% 3.07/1.66 % (24649)Memory used [KB]: 1663
% 3.07/1.66 % (24649)Time elapsed: 0.003 s
% 3.07/1.66 % (24649)Instructions burned: 2 (million)
% 3.07/1.66 % (24649)------------------------------
% 3.07/1.66 % (24649)------------------------------
% 3.07/1.67 % (24654)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_24321 for (2999ds/3Mi)
% 3.07/1.67 % (24656)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_24321 for (2999ds/37Mi)
% 3.07/1.67 % (24654)Instruction limit reached!
% 3.07/1.67 % (24654)------------------------------
% 3.07/1.67 % (24654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.67 % (24654)Termination reason: Unknown
% 3.07/1.67 % (24654)Termination phase: shuffling
% 3.07/1.67
% 3.07/1.67 % (24654)Memory used [KB]: 1663
% 3.07/1.67 % (24654)Time elapsed: 0.002 s
% 3.07/1.67 % (24654)Instructions burned: 3 (million)
% 3.07/1.67 % (24654)------------------------------
% 3.07/1.67 % (24654)------------------------------
% 3.07/1.67 % (24658)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_24321 for (2999ds/15Mi)
% 3.07/1.68 % (24659)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_24321 for (2999ds/3Mi)
% 3.07/1.68 % (24658)Instruction limit reached!
% 3.07/1.68 % (24658)------------------------------
% 3.07/1.68 % (24658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.68 % (24658)Termination reason: Unknown
% 3.07/1.68 % (24658)Termination phase: shuffling
% 3.07/1.68
% 3.07/1.68 % (24658)Memory used [KB]: 1918
% 3.07/1.68 % (24658)Time elapsed: 0.006 s
% 3.07/1.68 % (24658)Instructions burned: 16 (million)
% 3.07/1.68 % (24658)------------------------------
% 3.07/1.68 % (24658)------------------------------
% 3.07/1.68 % (24661)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_24321 for (2999ds/7Mi)
% 3.07/1.68 % (24656)Instruction limit reached!
% 3.07/1.68 % (24656)------------------------------
% 3.07/1.68 % (24656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.68 % (24656)Termination reason: Unknown
% 3.07/1.68 % (24656)Termination phase: shuffling
% 3.07/1.68
% 3.07/1.68 % (24656)Memory used [KB]: 2430
% 3.07/1.68 % (24656)Time elapsed: 0.011 s
% 3.07/1.68 % (24656)Instructions burned: 37 (million)
% 3.07/1.68 % (24656)------------------------------
% 3.07/1.68 % (24656)------------------------------
% 3.07/1.68 % (24659)Instruction limit reached!
% 3.07/1.68 % (24659)------------------------------
% 3.07/1.68 % (24659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.68 % (24659)Termination reason: Unknown
% 3.07/1.68 % (24659)Termination phase: shuffling
% 3.07/1.68
% 3.07/1.68 % (24659)Memory used [KB]: 1791
% 3.07/1.68 % (24659)Time elapsed: 0.003 s
% 3.07/1.68 % (24659)Instructions burned: 5 (million)
% 3.07/1.68 % (24659)------------------------------
% 3.07/1.68 % (24659)------------------------------
% 3.07/1.68 % (24661)Instruction limit reached!
% 3.07/1.68 % (24661)------------------------------
% 3.07/1.68 % (24661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.68 % (24661)Termination reason: Unknown
% 3.07/1.68 % (24661)Termination phase: shuffling
% 3.07/1.68
% 3.07/1.68 % (24661)Memory used [KB]: 1791
% 3.07/1.68 % (24661)Time elapsed: 0.003 s
% 3.07/1.68 % (24661)Instructions burned: 7 (million)
% 3.07/1.68 % (24661)------------------------------
% 3.07/1.68 % (24661)------------------------------
% 3.07/1.68 % (24660)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_24321 for (2999ds/1041Mi)
% 3.07/1.68 % (24662)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_24321 for (2999ds/16Mi)
% 3.07/1.69 % (24663)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_24321 for (2999ds/3Mi)
% 3.07/1.69 % (24663)Instruction limit reached!
% 3.07/1.69 % (24663)------------------------------
% 3.07/1.69 % (24663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.69 % (24663)Termination reason: Unknown
% 3.07/1.69 % (24663)Termination phase: shuffling
% 3.07/1.69
% 3.07/1.69 % (24663)Memory used [KB]: 1663
% 3.07/1.69 % (24663)Time elapsed: 0.002 s
% 3.07/1.69 % (24663)Instructions burned: 3 (million)
% 3.07/1.69 % (24663)------------------------------
% 3.07/1.69 % (24663)------------------------------
% 3.07/1.69 % (24665)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_24321 for (2999ds/7Mi)
% 3.07/1.69 % (24664)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_24321 for (2999ds/3Mi)
% 3.07/1.69 % (24664)Instruction limit reached!
% 3.07/1.69 % (24664)------------------------------
% 3.07/1.69 % (24664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.69 % (24664)Termination reason: Unknown
% 3.07/1.69 % (24664)Termination phase: shuffling
% 3.07/1.69
% 3.07/1.69 % (24664)Memory used [KB]: 1663
% 3.07/1.69 % (24664)Time elapsed: 0.003 s
% 3.07/1.69 % (24664)Instructions burned: 4 (million)
% 3.07/1.69 % (24664)------------------------------
% 3.07/1.69 % (24664)------------------------------
% 3.07/1.69 % (24662)Instruction limit reached!
% 3.07/1.69 % (24662)------------------------------
% 3.07/1.69 % (24662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.69 % (24662)Termination reason: Unknown
% 3.07/1.69 % (24662)Termination phase: shuffling
% 3.07/1.69
% 3.07/1.69 % (24662)Memory used [KB]: 1918
% 3.07/1.69 % (24662)Time elapsed: 0.006 s
% 3.07/1.69 % (24662)Instructions burned: 18 (million)
% 3.07/1.69 % (24662)------------------------------
% 3.07/1.69 % (24662)------------------------------
% 3.07/1.69 % (24665)Instruction limit reached!
% 3.07/1.69 % (24665)------------------------------
% 3.07/1.69 % (24665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.69 % (24665)Termination reason: Unknown
% 3.07/1.69 % (24665)Termination phase: shuffling
% 3.07/1.69
% 3.07/1.69 % (24665)Memory used [KB]: 1918
% 3.07/1.69 % (24665)Time elapsed: 0.004 s
% 3.07/1.69 % (24665)Instructions burned: 10 (million)
% 3.07/1.69 % (24665)------------------------------
% 3.07/1.69 % (24665)------------------------------
% 3.07/1.70 % (24666)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_24321 for (2999ds/3Mi)
% 3.14/1.70 % (24666)Instruction limit reached!
% 3.14/1.70 % (24666)------------------------------
% 3.14/1.70 % (24666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.70 % (24666)Termination reason: Unknown
% 3.14/1.70 % (24666)Termination phase: shuffling
% 3.14/1.70
% 3.14/1.70 % (24666)Memory used [KB]: 1663
% 3.14/1.70 % (24666)Time elapsed: 0.003 s
% 3.14/1.70 % (24666)Instructions burned: 6 (million)
% 3.14/1.70 % (24666)------------------------------
% 3.14/1.70 % (24666)------------------------------
% 3.14/1.70 % (24667)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_24321 for (2999ds/4Mi)
% 3.14/1.70 % (24668)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_24321 for (2999ds/18Mi)
% 3.14/1.70 % (24669)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_24321 for (2999ds/710Mi)
% 3.14/1.70 % (24667)Instruction limit reached!
% 3.14/1.70 % (24667)------------------------------
% 3.14/1.70 % (24667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.70 % (24667)Termination reason: Unknown
% 3.14/1.70 % (24667)Termination phase: shuffling
% 3.14/1.70
% 3.14/1.70 % (24667)Memory used [KB]: 1791
% 3.14/1.70 % (24667)Time elapsed: 0.003 s
% 3.14/1.70 % (24667)Instructions burned: 6 (million)
% 3.14/1.70 % (24667)------------------------------
% 3.14/1.70 % (24667)------------------------------
% 3.14/1.70 % (24668)Instruction limit reached!
% 3.14/1.70 % (24668)------------------------------
% 3.14/1.70 % (24668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.70 % (24668)Termination reason: Unknown
% 3.14/1.70 % (24668)Termination phase: shuffling
% 3.14/1.70
% 3.14/1.70 % (24668)Memory used [KB]: 2046
% 3.14/1.70 % (24668)Time elapsed: 0.007 s
% 3.14/1.70 % (24668)Instructions burned: 21 (million)
% 3.14/1.70 % (24668)------------------------------
% 3.14/1.70 % (24668)------------------------------
% 3.14/1.71 % (24670)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_24321 for (2999ds/6Mi)
% 3.14/1.71 % (24670)Instruction limit reached!
% 3.14/1.71 % (24670)------------------------------
% 3.14/1.71 % (24670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.71 % (24670)Termination reason: Unknown
% 3.14/1.71 % (24670)Termination phase: shuffling
% 3.14/1.71
% 3.14/1.71 % (24670)Memory used [KB]: 1791
% 3.14/1.71 % (24670)Time elapsed: 0.003 s
% 3.14/1.71 % (24670)Instructions burned: 6 (million)
% 3.14/1.71 % (24670)------------------------------
% 3.14/1.71 % (24670)------------------------------
% 3.14/1.71 % (24671)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_24321 for (2999ds/902Mi)
% 3.14/1.71 % (24672)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_24321 for (2999ds/21Mi)
% 3.14/1.72 % (24673)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_24321 for (2999ds/5Mi)
% 3.14/1.72 % (24673)Instruction limit reached!
% 3.14/1.72 % (24673)------------------------------
% 3.14/1.72 % (24673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.72 % (24673)Termination reason: Unknown
% 3.14/1.72 % (24673)Termination phase: shuffling
% 3.14/1.72
% 3.14/1.72 % (24673)Memory used [KB]: 1791
% 3.14/1.72 % (24673)Time elapsed: 0.003 s
% 3.14/1.72 % (24673)Instructions burned: 7 (million)
% 3.14/1.72 % (24673)------------------------------
% 3.14/1.72 % (24673)------------------------------
% 3.14/1.72 % (24672)Instruction limit reached!
% 3.14/1.72 % (24672)------------------------------
% 3.14/1.72 % (24672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.72 % (24672)Termination reason: Unknown
% 3.14/1.72 % (24672)Termination phase: shuffling
% 3.14/1.72
% 3.14/1.72 % (24672)Memory used [KB]: 2046
% 3.14/1.72 % (24672)Time elapsed: 0.007 s
% 3.14/1.72 % (24672)Instructions burned: 21 (million)
% 3.14/1.72 % (24672)------------------------------
% 3.14/1.72 % (24672)------------------------------
% 3.14/1.73 % (24674)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_24321 for (2999ds/6Mi)
% 3.14/1.73 % (24675)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_24321 for (2999ds/377Mi)
% 3.14/1.73 % (24674)Instruction limit reached!
% 3.14/1.73 % (24674)------------------------------
% 3.14/1.73 % (24674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.73 % (24674)Termination reason: Unknown
% 3.14/1.73 % (24674)Termination phase: shuffling
% 3.14/1.73
% 3.14/1.73 % (24674)Memory used [KB]: 1791
% 3.14/1.73 % (24674)Time elapsed: 0.003 s
% 3.14/1.73 % (24674)Instructions burned: 6 (million)
% 3.14/1.73 % (24674)------------------------------
% 3.14/1.73 % (24674)------------------------------
% 3.14/1.74 % (24676)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_24321 for (2998ds/779Mi)
% 3.14/1.75 % (24645)Instruction limit reached!
% 3.14/1.75 % (24645)------------------------------
% 3.14/1.75 % (24645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.75 % (24645)Termination reason: Unknown
% 3.14/1.75 % (24645)Termination phase: Property scanning
% 3.14/1.75
% 3.14/1.75 % (24645)Memory used [KB]: 3198
% 3.14/1.75 % (24645)Time elapsed: 0.085 s
% 3.14/1.75 % (24645)Instructions burned: 183 (million)
% 3.14/1.75 % (24645)------------------------------
% 3.14/1.75 % (24645)------------------------------
% 3.14/1.76 % (24677)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_24321 for (2998ds/19Mi)
% 3.14/1.76 % (24677)Instruction limit reached!
% 3.14/1.76 % (24677)------------------------------
% 3.14/1.76 % (24677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.76 % (24677)Termination reason: Unknown
% 3.14/1.76 % (24677)Termination phase: shuffling
% 3.14/1.76
% 3.14/1.76 % (24677)Memory used [KB]: 2046
% 3.14/1.76 % (24677)Time elapsed: 0.008 s
% 3.14/1.76 % (24677)Instructions burned: 22 (million)
% 3.14/1.76 % (24677)------------------------------
% 3.14/1.76 % (24677)------------------------------
% 3.14/1.77 % (24678)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_24321 for (2998ds/879Mi)
% 3.14/1.80 % (24650)Instruction limit reached!
% 3.14/1.80 % (24650)------------------------------
% 3.14/1.80 % (24650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.80 % (24650)Termination reason: Unknown
% 3.14/1.80 % (24650)Termination phase: Property scanning
% 3.14/1.80
% 3.14/1.80 % (24650)Memory used [KB]: 6012
% 3.14/1.80 % (24650)Time elapsed: 0.143 s
% 3.14/1.80 % (24650)Instructions burned: 276 (million)
% 3.14/1.80 % (24650)------------------------------
% 3.14/1.80 % (24650)------------------------------
% 3.14/1.82 % (24679)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_24321 for (2998ds/17Mi)
% 3.14/1.82 % (24679)Instruction limit reached!
% 3.14/1.82 % (24679)------------------------------
% 3.14/1.82 % (24679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.82 % (24679)Termination reason: Unknown
% 3.14/1.82 % (24679)Termination phase: shuffling
% 3.14/1.82
% 3.14/1.82 % (24679)Memory used [KB]: 2046
% 3.14/1.82 % (24679)Time elapsed: 0.007 s
% 3.14/1.82 % (24679)Instructions burned: 19 (million)
% 3.14/1.82 % (24679)------------------------------
% 3.14/1.82 % (24679)------------------------------
% 3.14/1.83 % (24675)Instruction limit reached!
% 3.14/1.83 % (24675)------------------------------
% 3.14/1.83 % (24675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.83 % (24675)Termination reason: Unknown
% 3.14/1.83 % (24675)Termination phase: Saturation
% 3.14/1.83
% 3.14/1.83 % (24675)Memory used [KB]: 9466
% 3.14/1.83 % (24675)Time elapsed: 0.101 s
% 3.14/1.83 % (24675)Instructions burned: 377 (million)
% 3.14/1.83 % (24675)------------------------------
% 3.14/1.83 % (24675)------------------------------
% 3.14/1.83 % (24680)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_24321 for (2998ds/3Mi)
% 3.14/1.83 % (24680)Instruction limit reached!
% 3.14/1.83 % (24680)------------------------------
% 3.14/1.83 % (24680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.83 % (24680)Termination reason: Unknown
% 3.14/1.83 % (24680)Termination phase: shuffling
% 3.14/1.83
% 3.14/1.83 % (24680)Memory used [KB]: 1663
% 3.14/1.83 % (24680)Time elapsed: 0.002 s
% 3.14/1.83 % (24680)Instructions burned: 3 (million)
% 3.14/1.83 % (24680)------------------------------
% 3.14/1.83 % (24680)------------------------------
% 3.14/1.84 % (24681)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_24321 for (2997ds/30Mi)
% 3.14/1.84 % (24682)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_24321 for (2997ds/127Mi)
% 3.14/1.85 % (24681)Instruction limit reached!
% 3.14/1.85 % (24681)------------------------------
% 3.14/1.85 % (24681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.85 % (24681)Termination reason: Unknown
% 3.14/1.85 % (24681)Termination phase: shuffling
% 3.14/1.85
% 3.14/1.85 % (24681)Memory used [KB]: 2302
% 3.14/1.85 % (24681)Time elapsed: 0.010 s
% 3.14/1.85 % (24681)Instructions burned: 31 (million)
% 3.14/1.85 % (24681)------------------------------
% 3.14/1.85 % (24681)------------------------------
% 3.14/1.86 % (24671)Refutation not found, incomplete strategy
% 3.14/1.86 % (24671)------------------------------
% 3.14/1.86 % (24671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.86 % (24671)Termination reason: Refutation not found, incomplete strategy
% 3.14/1.86
% 3.14/1.86
% 3.14/1.86 % (24671)Memory used [KB]: 11641
% 3.14/1.86 % (24671)Time elapsed: 0.147 s
% 3.14/1.86 % (24671)Instructions burned: 490 (million)
% 3.14/1.86 % (24671)------------------------------
% 3.14/1.86 % (24671)------------------------------
% 3.14/1.86 % (24683)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_24321 for (2997ds/100Mi)
% 3.14/1.87 % (24684)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_24321 for (2997ds/3Mi)
% 3.14/1.87 % (24684)Instruction limit reached!
% 3.14/1.87 % (24684)------------------------------
% 3.14/1.87 % (24684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.87 % (24684)Termination reason: Unknown
% 3.14/1.87 % (24684)Termination phase: shuffling
% 3.14/1.87
% 3.14/1.87 % (24684)Memory used [KB]: 1791
% 3.14/1.87 % (24684)Time elapsed: 0.003 s
% 3.14/1.87 % (24684)Instructions burned: 5 (million)
% 3.14/1.87 % (24684)------------------------------
% 3.14/1.87 % (24684)------------------------------
% 3.14/1.88 % (24685)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_24321 for (2997ds/20Mi)
% 3.14/1.88 % (24682)Instruction limit reached!
% 3.14/1.88 % (24682)------------------------------
% 3.14/1.88 % (24682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.88 % (24682)Termination reason: Unknown
% 3.14/1.88 % (24682)Termination phase: shuffling
% 3.14/1.88
% 3.14/1.88 % (24682)Memory used [KB]: 2942
% 3.14/1.88 % (24682)Time elapsed: 0.036 s
% 3.14/1.88 % (24682)Instructions burned: 127 (million)
% 3.14/1.88 % (24682)------------------------------
% 3.14/1.88 % (24682)------------------------------
% 3.14/1.88 % (24683)Instruction limit reached!
% 3.14/1.88 % (24683)------------------------------
% 3.14/1.88 % (24683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.88 % (24683)Termination reason: Unknown
% 3.14/1.88 % (24683)Termination phase: Property scanning
% 3.14/1.88
% 3.14/1.88 % (24683)Memory used [KB]: 2814
% 3.14/1.88 % (24683)Time elapsed: 0.027 s
% 3.14/1.88 % (24683)Instructions burned: 101 (million)
% 3.14/1.88 % (24683)------------------------------
% 3.14/1.88 % (24683)------------------------------
% 3.14/1.88 % (24685)Instruction limit reached!
% 3.14/1.88 % (24685)------------------------------
% 3.14/1.88 % (24685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.88 % (24685)Termination reason: Unknown
% 3.14/1.88 % (24685)Termination phase: shuffling
% 3.14/1.88
% 3.14/1.88 % (24685)Memory used [KB]: 2046
% 3.14/1.88 % (24685)Time elapsed: 0.008 s
% 3.14/1.88 % (24685)Instructions burned: 22 (million)
% 3.14/1.88 % (24685)------------------------------
% 3.14/1.88 % (24685)------------------------------
% 3.14/1.89 % (24686)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_24321 for (2997ds/86Mi)
% 3.14/1.89 % (24687)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_24321 for (2997ds/107Mi)
% 3.14/1.89 % (24688)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_24321 for (2997ds/39Mi)
% 3.14/1.90 % (24688)Instruction limit reached!
% 3.14/1.90 % (24688)------------------------------
% 3.14/1.90 % (24688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.90 % (24688)Termination reason: Unknown
% 3.14/1.90 % (24688)Termination phase: shuffling
% 3.14/1.90
% 3.14/1.90 % (24688)Memory used [KB]: 2430
% 3.14/1.90 % (24688)Time elapsed: 0.012 s
% 3.14/1.90 % (24688)Instructions burned: 42 (million)
% 3.14/1.90 % (24688)------------------------------
% 3.14/1.90 % (24688)------------------------------
% 3.14/1.91 % (24686)Instruction limit reached!
% 3.14/1.91 % (24686)------------------------------
% 3.14/1.91 % (24686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.91 % (24686)Termination reason: Unknown
% 3.14/1.91 % (24686)Termination phase: Property scanning
% 3.14/1.91
% 3.14/1.91 % (24686)Memory used [KB]: 2814
% 3.14/1.91 % (24686)Time elapsed: 0.025 s
% 3.14/1.91 % (24686)Instructions burned: 86 (million)
% 3.14/1.91 % (24686)------------------------------
% 3.14/1.91 % (24686)------------------------------
% 3.14/1.91 % (24689)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_24321 for (2997ds/448Mi)
% 3.14/1.92 % (24669)Instruction limit reached!
% 3.14/1.92 % (24669)------------------------------
% 3.14/1.92 % (24669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.92 % (24669)Termination reason: Unknown
% 3.14/1.92 % (24669)Termination phase: Saturation
% 3.14/1.92
% 3.14/1.92 % (24669)Memory used [KB]: 12025
% 3.14/1.92 % (24669)Time elapsed: 0.220 s
% 3.14/1.92 % (24669)Instructions burned: 711 (million)
% 3.14/1.92 % (24669)------------------------------
% 3.14/1.92 % (24669)------------------------------
% 3.14/1.92 % (24687)Instruction limit reached!
% 3.14/1.92 % (24687)------------------------------
% 3.14/1.92 % (24687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.92 % (24687)Termination reason: Unknown
% 3.14/1.92 % (24687)Termination phase: SInE selection
% 3.14/1.92
% 3.14/1.92 % (24687)Memory used [KB]: 2942
% 3.14/1.92 % (24687)Time elapsed: 0.029 s
% 3.14/1.92 % (24687)Instructions burned: 108 (million)
% 3.14/1.92 % (24687)------------------------------
% 3.14/1.92 % (24687)------------------------------
% 3.14/1.92 % (24690)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_24321 for (2997ds/46Mi)
% 3.14/1.93 % (24691)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_24321 for (2997ds/98Mi)
% 3.14/1.93 % (24692)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_24321 for (2997ds/507Mi)
% 3.14/1.94 % (24690)Instruction limit reached!
% 3.14/1.94 % (24690)------------------------------
% 3.14/1.94 % (24690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.94 % (24690)Termination reason: Unknown
% 3.14/1.94 % (24690)Termination phase: shuffling
% 3.14/1.94
% 3.14/1.94 % (24690)Memory used [KB]: 2558
% 3.14/1.94 % (24690)Time elapsed: 0.015 s
% 3.14/1.94 % (24690)Instructions burned: 48 (million)
% 3.14/1.94 % (24690)------------------------------
% 3.14/1.94 % (24690)------------------------------
% 3.14/1.94 % (24676)Instruction limit reached!
% 3.14/1.94 % (24676)------------------------------
% 3.14/1.94 % (24676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.94 % (24676)Termination reason: Unknown
% 3.14/1.94 % (24676)Termination phase: Saturation
% 3.14/1.94
% 3.14/1.94 % (24676)Memory used [KB]: 8059
% 3.14/1.94 % (24676)Time elapsed: 0.198 s
% 3.14/1.94 % (24676)Instructions burned: 782 (million)
% 3.14/1.94 % (24676)------------------------------
% 3.14/1.94 % (24676)------------------------------
% 3.14/1.95 % (24694)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_24321 for (2996ds/39Mi)
% 3.14/1.95 % (24693)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_24321 for (2996ds/149Mi)
% 3.14/1.95 % (24691)Instruction limit reached!
% 3.14/1.95 % (24691)------------------------------
% 3.14/1.95 % (24691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.95 % (24691)Termination reason: Unknown
% 3.14/1.95 % (24691)Termination phase: Property scanning
% 3.14/1.95
% 3.14/1.95 % (24691)Memory used [KB]: 2942
% 3.14/1.95 % (24691)Time elapsed: 0.027 s
% 3.14/1.95 % (24691)Instructions burned: 99 (million)
% 3.14/1.95 % (24691)------------------------------
% 3.14/1.95 % (24691)------------------------------
% 3.14/1.96 % (24694)Instruction limit reached!
% 3.14/1.96 % (24694)------------------------------
% 3.14/1.96 % (24694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.96 % (24694)Termination reason: Unknown
% 3.14/1.96 % (24694)Termination phase: shuffling
% 3.14/1.96
% 3.14/1.96 % (24694)Memory used [KB]: 2430
% 3.14/1.96 % (24694)Time elapsed: 0.012 s
% 3.14/1.96 % (24694)Instructions burned: 40 (million)
% 3.14/1.96 % (24694)------------------------------
% 3.14/1.96 % (24694)------------------------------
% 3.14/1.96 % (24695)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_24321 for (2996ds/6Mi)
% 3.14/1.97 % (24695)Instruction limit reached!
% 3.14/1.97 % (24695)------------------------------
% 3.14/1.97 % (24695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.97 % (24695)Termination reason: Unknown
% 3.14/1.97 % (24695)Termination phase: shuffling
% 3.14/1.97
% 3.14/1.97 % (24695)Memory used [KB]: 1791
% 3.14/1.97 % (24695)Time elapsed: 0.003 s
% 3.14/1.97 % (24695)Instructions burned: 6 (million)
% 3.14/1.97 % (24695)------------------------------
% 3.14/1.97 % (24695)------------------------------
% 3.14/1.97 % (24696)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_24321 for (2996ds/1087Mi)
% 3.14/1.98 % (24697)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_24321 for (2996ds/47Mi)
% 3.14/1.99 % (24697)Instruction limit reached!
% 3.14/1.99 % (24697)------------------------------
% 3.14/1.99 % (24697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.99 % (24697)Termination reason: Unknown
% 3.14/1.99 % (24697)Termination phase: shuffling
% 3.14/1.99
% 3.14/1.99 % (24697)Memory used [KB]: 2558
% 3.14/1.99 % (24697)Time elapsed: 0.015 s
% 3.14/1.99 % (24697)Instructions burned: 50 (million)
% 3.14/1.99 % (24697)------------------------------
% 3.14/1.99 % (24697)------------------------------
% 3.14/1.99 % (24693)Instruction limit reached!
% 3.14/1.99 % (24693)------------------------------
% 3.14/1.99 % (24693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.99 % (24693)Termination reason: Unknown
% 3.14/1.99 % (24693)Termination phase: Function definition elimination
% 3.14/1.99
% 3.14/1.99 % (24693)Memory used [KB]: 3070
% 3.14/1.99 % (24693)Time elapsed: 0.043 s
% 3.14/1.99 % (24693)Instructions burned: 151 (million)
% 3.14/1.99 % (24693)------------------------------
% 3.14/1.99 % (24693)------------------------------
% 3.14/2.00 % (24660)Instruction limit reached!
% 3.14/2.00 % (24660)------------------------------
% 3.14/2.00 % (24660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/2.00 % (24660)Termination reason: Unknown
% 3.14/2.00 % (24660)Termination phase: Saturation
% 3.14/2.00
% 3.14/2.00 % (24660)Memory used [KB]: 18038
% 3.14/2.00 % (24660)Time elapsed: 0.317 s
% 3.14/2.00 % (24660)Instructions burned: 1041 (million)
% 3.14/2.00 % (24660)------------------------------
% 3.14/2.00 % (24660)------------------------------
% 3.14/2.00 % (24698)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_24321 for (2996ds/44Mi)
% 3.14/2.00 % (24699)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_24321 for (2996ds/432Mi)
% 3.14/2.01 % (24698)Instruction limit reached!
% 3.14/2.01 % (24698)------------------------------
% 3.14/2.01 % (24698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/2.01 % (24698)Termination reason: Unknown
% 3.14/2.01 % (24698)Termination phase: shuffling
% 3.14/2.01
% 3.14/2.01 % (24698)Memory used [KB]: 2558
% 3.14/2.01 % (24698)Time elapsed: 0.013 s
% 3.14/2.01 % (24698)Instructions burned: 44 (million)
% 3.14/2.01 % (24698)------------------------------
% 3.14/2.01 % (24698)------------------------------
% 5.67/2.02 % (24700)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_24321 for (2996ds/62Mi)
% 5.67/2.02 % (24701)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_24321 for (2996ds/31Mi)
% 5.67/2.03 % (24689)Instruction limit reached!
% 5.67/2.03 % (24689)------------------------------
% 5.67/2.03 % (24689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.67/2.03 % (24689)Termination reason: Unknown
% 5.67/2.03 % (24689)Termination phase: Saturation
% 5.67/2.03
% 5.67/2.03 % (24689)Memory used [KB]: 7931
% 5.67/2.03 % (24689)Time elapsed: 0.113 s
% 5.67/2.03 % (24689)Instructions burned: 450 (million)
% 5.67/2.03 % (24689)------------------------------
% 5.67/2.03 % (24689)------------------------------
% 5.67/2.03 % (24701)Instruction limit reached!
% 5.67/2.03 % (24701)------------------------------
% 5.67/2.03 % (24701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.67/2.03 % (24701)Termination reason: Unknown
% 5.67/2.03 % (24701)Termination phase: shuffling
% 5.67/2.03
% 5.67/2.03 % (24701)Memory used [KB]: 2302
% 5.67/2.03 % (24701)Time elapsed: 0.010 s
% 5.67/2.03 % (24701)Instructions burned: 31 (million)
% 5.67/2.03 % (24701)------------------------------
% 5.67/2.03 % (24701)------------------------------
% 5.67/2.04 % (24702)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_24321 for (2995ds/96Mi)
% 5.67/2.04 % (24703)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_24321 for (2995ds/453Mi)
% 5.67/2.05 % (24678)Instruction limit reached!
% 5.67/2.05 % (24678)------------------------------
% 5.67/2.05 % (24678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.67/2.05 % (24678)Termination reason: Unknown
% 5.67/2.05 % (24678)Termination phase: Saturation
% 5.67/2.05
% 5.67/2.05 % (24678)Memory used [KB]: 10874
% 5.67/2.05 % (24678)Time elapsed: 0.277 s
% 5.67/2.05 % (24678)Instructions burned: 881 (million)
% 5.67/2.05 % (24678)------------------------------
% 5.67/2.05 % (24678)------------------------------
% 5.67/2.05 % (24700)Instruction limit reached!
% 5.67/2.05 % (24700)------------------------------
% 5.67/2.05 % (24700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.67/2.05 % (24700)Termination reason: Unknown
% 5.67/2.05 % (24700)Termination phase: shuffling
% 5.67/2.05
% 5.67/2.05 % (24700)Memory used [KB]: 2814
% 5.67/2.05 % (24700)Time elapsed: 0.033 s
% 5.67/2.05 % (24700)Instructions burned: 63 (million)
% 5.67/2.05 % (24700)------------------------------
% 5.67/2.05 % (24700)------------------------------
% 5.67/2.06 % (24705)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_24321 for (2995ds/83Mi)
% 5.67/2.06 % (24702)Instruction limit reached!
% 5.67/2.06 % (24702)------------------------------
% 5.67/2.06 % (24702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.67/2.06 % (24702)Termination reason: Unknown
% 5.67/2.06 % (24702)Termination phase: Property scanning
% 5.67/2.06
% 5.67/2.06 % (24702)Memory used [KB]: 2814
% 5.67/2.06 % (24702)Time elapsed: 0.027 s
% 5.67/2.06 % (24702)Instructions burned: 99 (million)
% 5.67/2.06 % (24702)------------------------------
% 5.67/2.06 % (24702)------------------------------
% 5.67/2.07 % (24704)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_24321 for (2995ds/71Mi)
% 5.67/2.07 % (24706)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_24321 for (2995ds/11Mi)
% 5.67/2.07 % (24692)Instruction limit reached!
% 5.67/2.07 % (24692)------------------------------
% 5.67/2.07 % (24692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.67/2.07 % (24692)Termination reason: Unknown
% 5.67/2.07 % (24692)Termination phase: Saturation
% 5.67/2.07
% 5.67/2.07 % (24692)Memory used [KB]: 8443
% 5.67/2.07 % (24692)Time elapsed: 0.165 s
% 5.67/2.07 % (24692)Instructions burned: 507 (million)
% 5.67/2.07 % (24692)------------------------------
% 5.67/2.07 % (24692)------------------------------
% 5.67/2.08 % (24706)Instruction limit reached!
% 5.67/2.08 % (24706)------------------------------
% 5.67/2.08 % (24706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.67/2.08 % (24706)Termination reason: Unknown
% 5.67/2.08 % (24706)Termination phase: shuffling
% 5.67/2.08
% 5.67/2.08 % (24706)Memory used [KB]: 1918
% 5.67/2.08 % (24706)Time elapsed: 0.005 s
% 5.67/2.08 % (24706)Instructions burned: 14 (million)
% 5.67/2.08 % (24706)------------------------------
% 5.67/2.08 % (24706)------------------------------
% 5.67/2.08 % (24707)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_24321 for (2995ds/41Mi)
% 5.67/2.08 % (24708)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_24321 for (2995ds/6Mi)
% 5.67/2.08 % (24705)Instruction limit reached!
% 5.67/2.08 % (24705)------------------------------
% 5.67/2.08 % (24705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.67/2.08 % (24705)Termination reason: Unknown
% 5.67/2.08 % (24705)Termination phase: Property scanning
% 5.67/2.08
% 5.67/2.08 % (24705)Memory used [KB]: 2814
% 5.67/2.08 % (24705)Time elapsed: 0.025 s
% 5.67/2.08 % (24705)Instructions burned: 84 (million)
% 5.67/2.08 % (24705)------------------------------
% 5.67/2.08 % (24705)------------------------------
% 5.67/2.09 % (24708)Instruction limit reached!
% 5.67/2.09 % (24708)------------------------------
% 5.67/2.09 % (24708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.67/2.09 % (24708)Termination reason: Unknown
% 5.67/2.09 % (24708)Termination phase: shuffling
% 5.67/2.09
% 5.67/2.09 % (24708)Memory used [KB]: 1791
% 5.67/2.09 % (24708)Time elapsed: 0.003 s
% 5.67/2.09 % (24708)Instructions burned: 6 (million)
% 5.67/2.09 % (24708)------------------------------
% 5.67/2.09 % (24708)------------------------------
% 5.67/2.09 % (24707)Instruction limit reached!
% 5.67/2.09 % (24707)------------------------------
% 5.67/2.09 % (24707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.67/2.09 % (24707)Termination reason: Unknown
% 5.67/2.09 % (24707)Termination phase: shuffling
% 5.67/2.09
% 5.67/2.09 % (24707)Memory used [KB]: 2558
% 5.67/2.09 % (24707)Time elapsed: 0.013 s
% 5.67/2.09 % (24707)Instructions burned: 44 (million)
% 5.67/2.09 % (24707)------------------------------
% 5.67/2.09 % (24707)------------------------------
% 5.67/2.10 % (24709)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_24321 for (2995ds/150Mi)
% 5.67/2.10 % (24710)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_24321 for (2995ds/343Mi)
% 5.67/2.10 % (24704)Instruction limit reached!
% 5.67/2.10 % (24704)------------------------------
% 5.67/2.10 % (24704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.67/2.10 % (24704)Termination reason: Unknown
% 5.67/2.10 % (24704)Termination phase: Property scanning
% 5.67/2.10
% 5.67/2.10 % (24704)Memory used [KB]: 2814
% 5.67/2.10 % (24704)Time elapsed: 0.038 s
% 5.67/2.10 % (24704)Instructions burned: 71 (million)
% 5.67/2.10 % (24704)------------------------------
% 5.67/2.10 % (24704)------------------------------
% 5.67/2.10 % (24711)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_24321 for (2995ds/109Mi)
% 6.25/2.11 % (24712)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_24321 for (2995ds/253Mi)
% 6.25/2.12 % (24699)Instruction limit reached!
% 6.25/2.12 % (24699)------------------------------
% 6.25/2.12 % (24699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.25/2.12 % (24699)Termination reason: Unknown
% 6.25/2.12 % (24699)Termination phase: Saturation
% 6.25/2.12
% 6.25/2.12 % (24699)Memory used [KB]: 3454
% 6.25/2.12 % (24699)Time elapsed: 0.118 s
% 6.25/2.12 % (24699)Instructions burned: 434 (million)
% 6.25/2.12 % (24699)------------------------------
% 6.25/2.12 % (24699)------------------------------
% 6.25/2.13 % (24713)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_24321 for (2995ds/140Mi)
% 6.25/2.13 % (24711)Instruction limit reached!
% 6.25/2.13 % (24711)------------------------------
% 6.25/2.13 % (24711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.25/2.13 % (24711)Termination reason: Unknown
% 6.25/2.13 % (24711)Termination phase: SInE selection
% 6.25/2.13
% 6.25/2.13 % (24711)Memory used [KB]: 2942
% 6.25/2.13 % (24711)Time elapsed: 0.030 s
% 6.25/2.13 % (24711)Instructions burned: 112 (million)
% 6.25/2.13 % (24711)------------------------------
% 6.25/2.13 % (24711)------------------------------
% 6.25/2.14 % (24714)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_24321 for (2994ds/614Mi)
% 6.25/2.14 % (24709)Instruction limit reached!
% 6.25/2.14 % (24709)------------------------------
% 6.25/2.14 % (24709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.25/2.14 % (24709)Termination reason: Unknown
% 6.25/2.14 % (24709)Termination phase: Preprocessing 3
% 6.25/2.14
% 6.25/2.14 % (24709)Memory used [KB]: 5373
% 6.25/2.14 % (24709)Time elapsed: 0.050 s
% 6.25/2.14 % (24709)Instructions burned: 152 (million)
% 6.25/2.14 % (24709)------------------------------
% 6.25/2.14 % (24709)------------------------------
% 6.25/2.15 % (24703)Instruction limit reached!
% 6.25/2.15 % (24703)------------------------------
% 6.25/2.15 % (24703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.25/2.15 % (24703)Termination reason: Unknown
% 6.25/2.15 % (24703)Termination phase: Saturation
% 6.25/2.15
% 6.25/2.15 % (24703)Memory used [KB]: 7931
% 6.25/2.15 % (24703)Time elapsed: 0.113 s
% 6.25/2.15 % (24703)Instructions burned: 453 (million)
% 6.25/2.15 % (24703)------------------------------
% 6.25/2.15 % (24703)------------------------------
% 6.25/2.15 % (24715)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_24321 for (2994ds/202Mi)
% 6.25/2.16 % (24716)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_24321 for (2994ds/339Mi)
% 6.25/2.17 % (24713)Instruction limit reached!
% 6.25/2.17 % (24713)------------------------------
% 6.25/2.17 % (24713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.25/2.17 % (24713)Termination reason: Unknown
% 6.25/2.17 % (24713)Termination phase: Property scanning
% 6.25/2.17
% 6.25/2.17 % (24713)Memory used [KB]: 3198
% 6.25/2.17 % (24713)Time elapsed: 0.040 s
% 6.25/2.17 % (24713)Instructions burned: 141 (million)
% 6.25/2.17 % (24713)------------------------------
% 6.25/2.17 % (24713)------------------------------
% 6.25/2.18 % (24717)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_24321 for (2994ds/283Mi)
% 6.25/2.18 % (24710)Instruction limit reached!
% 6.25/2.18 % (24710)------------------------------
% 6.25/2.18 % (24710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.25/2.18 % (24710)Termination reason: Unknown
% 6.25/2.18 % (24710)Termination phase: Saturation
% 6.25/2.18
% 6.25/2.18 % (24710)Memory used [KB]: 8443
% 6.25/2.18 % (24710)Time elapsed: 0.089 s
% 6.25/2.18 % (24710)Instructions burned: 346 (million)
% 6.25/2.18 % (24710)------------------------------
% 6.25/2.18 % (24710)------------------------------
% 6.25/2.19 % (24712)Instruction limit reached!
% 6.25/2.19 % (24712)------------------------------
% 6.25/2.19 % (24712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.25/2.19 % (24712)Termination reason: Unknown
% 6.25/2.19 % (24712)Termination phase: Property scanning
% 6.25/2.19
% 6.25/2.19 % (24712)Memory used [KB]: 6012
% 6.25/2.19 % (24712)Time elapsed: 0.076 s
% 6.25/2.19 % (24712)Instructions burned: 255 (million)
% 6.25/2.19 % (24712)------------------------------
% 6.25/2.19 % (24712)------------------------------
% 6.25/2.19 % (24718)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_24321 for (2994ds/134Mi)
% 6.81/2.20 % (24719)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_24321 for (2994ds/298Mi)
% 6.81/2.21 % (24715)Instruction limit reached!
% 6.81/2.21 % (24715)------------------------------
% 6.81/2.21 % (24715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.21 % (24715)Termination reason: Unknown
% 6.81/2.21 % (24715)Termination phase: Property scanning
% 6.81/2.21
% 6.81/2.21 % (24715)Memory used [KB]: 5756
% 6.81/2.21 % (24715)Time elapsed: 0.059 s
% 6.81/2.21 % (24715)Instructions burned: 205 (million)
% 6.81/2.21 % (24715)------------------------------
% 6.81/2.21 % (24715)------------------------------
% 6.81/2.22 % (24720)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_24321 for (2994ds/192Mi)
% 6.81/2.23 % (24718)Instruction limit reached!
% 6.81/2.23 % (24718)------------------------------
% 6.81/2.23 % (24718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.23 % (24718)Termination reason: Unknown
% 6.81/2.23 % (24718)Termination phase: Property scanning
% 6.81/2.23
% 6.81/2.23 % (24718)Memory used [KB]: 3070
% 6.81/2.23 % (24718)Time elapsed: 0.036 s
% 6.81/2.23 % (24718)Instructions burned: 134 (million)
% 6.81/2.23 % (24718)------------------------------
% 6.81/2.23 % (24718)------------------------------
% 6.81/2.24 % (24721)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_24321 for (2993ds/258Mi)
% 6.81/2.25 % (24717)Instruction limit reached!
% 6.81/2.25 % (24717)------------------------------
% 6.81/2.25 % (24717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.25 % (24717)Termination reason: Unknown
% 6.81/2.25 % (24717)Termination phase: Saturation
% 6.81/2.25
% 6.81/2.25 % (24717)Memory used [KB]: 7931
% 6.81/2.25 % (24717)Time elapsed: 0.073 s
% 6.81/2.25 % (24717)Instructions burned: 283 (million)
% 6.81/2.25 % (24717)------------------------------
% 6.81/2.25 % (24717)------------------------------
% 6.81/2.25 % (24716)Instruction limit reached!
% 6.81/2.25 % (24716)------------------------------
% 6.81/2.25 % (24716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.25 % (24716)Termination reason: Unknown
% 6.81/2.25 % (24716)Termination phase: Saturation
% 6.81/2.25
% 6.81/2.25 % (24716)Memory used [KB]: 8315
% 6.81/2.25 % (24716)Time elapsed: 0.092 s
% 6.81/2.25 % (24716)Instructions burned: 341 (million)
% 6.81/2.25 % (24716)------------------------------
% 6.81/2.25 % (24716)------------------------------
% 6.81/2.26 % (24722)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_24321 for (2993ds/90Mi)
% 6.81/2.26 % (24723)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_24321 for (2993ds/231Mi)
% 6.81/2.27 % (24720)Instruction limit reached!
% 6.81/2.27 % (24720)------------------------------
% 6.81/2.27 % (24720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.27 % (24720)Termination reason: Unknown
% 6.81/2.27 % (24720)Termination phase: Property scanning
% 6.81/2.27
% 6.81/2.27 % (24720)Memory used [KB]: 3198
% 6.81/2.27 % (24720)Time elapsed: 0.050 s
% 6.81/2.27 % (24720)Instructions burned: 192 (million)
% 6.81/2.27 % (24720)------------------------------
% 6.81/2.27 % (24720)------------------------------
% 6.81/2.27 % (24719)Instruction limit reached!
% 6.81/2.27 % (24719)------------------------------
% 6.81/2.27 % (24719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.27 % (24719)Termination reason: Unknown
% 6.81/2.27 % (24719)Termination phase: Saturation
% 6.81/2.27
% 6.81/2.27 % (24719)Memory used [KB]: 7931
% 6.81/2.27 % (24719)Time elapsed: 0.076 s
% 6.81/2.27 % (24719)Instructions burned: 299 (million)
% 6.81/2.27 % (24719)------------------------------
% 6.81/2.27 % (24719)------------------------------
% 6.81/2.28 % (24724)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_24321 for (2993ds/458Mi)
% 6.81/2.28 % (24722)Instruction limit reached!
% 6.81/2.28 % (24722)------------------------------
% 6.81/2.28 % (24722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.28 % (24722)Termination reason: Unknown
% 6.81/2.28 % (24722)Termination phase: Property scanning
% 6.81/2.28
% 6.81/2.28 % (24722)Memory used [KB]: 2814
% 6.81/2.28 % (24722)Time elapsed: 0.025 s
% 6.81/2.28 % (24722)Instructions burned: 90 (million)
% 6.81/2.28 % (24722)------------------------------
% 6.81/2.28 % (24722)------------------------------
% 6.81/2.28 % (24725)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_24321 for (2993ds/31Mi)
% 6.81/2.29 % (24725)Instruction limit reached!
% 6.81/2.29 % (24725)------------------------------
% 6.81/2.29 % (24725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.29 % (24725)Termination reason: Unknown
% 6.81/2.29 % (24725)Termination phase: shuffling
% 6.81/2.29
% 6.81/2.29 % (24725)Memory used [KB]: 2302
% 6.81/2.29 % (24725)Time elapsed: 0.010 s
% 6.81/2.29 % (24725)Instructions burned: 32 (million)
% 6.81/2.29 % (24725)------------------------------
% 6.81/2.29 % (24725)------------------------------
% 6.81/2.29 % (24726)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_24321 for (2993ds/297Mi)
% 7.41/2.30 % (24727)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_24321 for (2993ds/987Mi)
% 7.41/2.30 % (24721)Instruction limit reached!
% 7.41/2.30 % (24721)------------------------------
% 7.41/2.30 % (24721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.30 % (24721)Termination reason: Unknown
% 7.41/2.30 % (24721)Termination phase: Saturation
% 7.41/2.30
% 7.41/2.30 % (24721)Memory used [KB]: 8059
% 7.41/2.30 % (24721)Time elapsed: 0.067 s
% 7.41/2.30 % (24721)Instructions burned: 258 (million)
% 7.41/2.30 % (24721)------------------------------
% 7.41/2.30 % (24721)------------------------------
% 7.41/2.31 % (24696)Instruction limit reached!
% 7.41/2.31 % (24696)------------------------------
% 7.41/2.31 % (24696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.31 % (24696)Termination reason: Unknown
% 7.41/2.31 % (24696)Termination phase: Saturation
% 7.41/2.31
% 7.41/2.31 % (24696)Memory used [KB]: 13304
% 7.41/2.31 % (24696)Time elapsed: 0.341 s
% 7.41/2.31 % (24696)Instructions burned: 1088 (million)
% 7.41/2.31 % (24696)------------------------------
% 7.41/2.31 % (24696)------------------------------
% 7.41/2.31 % (24728)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_24321 for (2993ds/182Mi)
% 7.41/2.31 % (24714)Instruction limit reached!
% 7.41/2.31 % (24714)------------------------------
% 7.41/2.31 % (24714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.31 % (24714)Termination reason: Unknown
% 7.41/2.31 % (24714)Termination phase: Saturation
% 7.41/2.31
% 7.41/2.31 % (24714)Memory used [KB]: 10490
% 7.41/2.31 % (24714)Time elapsed: 0.173 s
% 7.41/2.31 % (24714)Instructions burned: 617 (million)
% 7.41/2.31 % (24714)------------------------------
% 7.41/2.31 % (24714)------------------------------
% 7.41/2.32 % (24729)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_24321 for (2993ds/182Mi)
% 7.41/2.32 % (24723)Instruction limit reached!
% 7.41/2.32 % (24723)------------------------------
% 7.41/2.32 % (24723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.32 % (24723)Termination reason: Unknown
% 7.41/2.32 % (24723)Termination phase: Property scanning
% 7.41/2.32
% 7.41/2.32 % (24723)Memory used [KB]: 4477
% 7.41/2.32 % (24723)Time elapsed: 0.061 s
% 7.41/2.32 % (24723)Instructions burned: 234 (million)
% 7.41/2.32 % (24723)------------------------------
% 7.41/2.32 % (24723)------------------------------
% 7.41/2.32 % (24730)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_24321 for (2993ds/154Mi)
% 7.41/2.33 % (24731)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_24321 for (2993ds/79Mi)
% 7.41/2.35 % (24731)Instruction limit reached!
% 7.41/2.35 % (24731)------------------------------
% 7.41/2.35 % (24731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.35 % (24731)Termination reason: Unknown
% 7.41/2.35 % (24731)Termination phase: Property scanning
% 7.41/2.35
% 7.41/2.35 % (24731)Memory used [KB]: 2814
% 7.41/2.35 % (24731)Time elapsed: 0.022 s
% 7.41/2.35 % (24731)Instructions burned: 80 (million)
% 7.41/2.35 % (24731)------------------------------
% 7.41/2.35 % (24731)------------------------------
% 7.41/2.36 % (24728)Instruction limit reached!
% 7.41/2.36 % (24728)------------------------------
% 7.41/2.36 % (24728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.36 % (24728)Termination reason: Unknown
% 7.41/2.36 % (24728)Termination phase: Property scanning
% 7.41/2.36
% 7.41/2.36 % (24728)Memory used [KB]: 3198
% 7.41/2.36 % (24728)Time elapsed: 0.047 s
% 7.41/2.36 % (24728)Instructions burned: 182 (million)
% 7.41/2.36 % (24728)------------------------------
% 7.41/2.36 % (24728)------------------------------
% 7.41/2.36 % (24732)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_24321 for (2992ds/216Mi)
% 7.41/2.36 % (24730)Instruction limit reached!
% 7.41/2.36 % (24730)------------------------------
% 7.41/2.36 % (24730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.36 % (24730)Termination reason: Unknown
% 7.41/2.36 % (24730)Termination phase: Function definition elimination
% 7.41/2.36
% 7.41/2.36 % (24730)Memory used [KB]: 3198
% 7.41/2.36 % (24730)Time elapsed: 0.040 s
% 7.41/2.36 % (24730)Instructions burned: 155 (million)
% 7.41/2.36 % (24730)------------------------------
% 7.41/2.36 % (24730)------------------------------
% 7.41/2.37 % (24726)Instruction limit reached!
% 7.41/2.37 % (24726)------------------------------
% 7.41/2.37 % (24726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.37 % (24726)Termination reason: Unknown
% 7.41/2.37 % (24726)Termination phase: Saturation
% 7.41/2.37
% 7.41/2.37 % (24726)Memory used [KB]: 7931
% 7.41/2.37 % (24726)Time elapsed: 0.074 s
% 7.41/2.37 % (24726)Instructions burned: 299 (million)
% 7.41/2.37 % (24726)------------------------------
% 7.41/2.37 % (24726)------------------------------
% 7.41/2.37 % (24733)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_24321 for (2992ds/114Mi)
% 7.41/2.37 % (24729)Instruction limit reached!
% 7.41/2.37 % (24729)------------------------------
% 7.41/2.37 % (24729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.41/2.37 % (24729)Termination reason: Unknown
% 7.41/2.37 % (24729)Termination phase: Property scanning
% 7.41/2.37
% 7.41/2.37 % (24729)Memory used [KB]: 5756
% 7.41/2.37 % (24729)Time elapsed: 0.054 s
% 7.41/2.37 % (24729)Instructions burned: 183 (million)
% 7.41/2.37 % (24729)------------------------------
% 7.41/2.37 % (24729)------------------------------
% 7.41/2.37 % (24734)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_24321 for (2992ds/922Mi)
% 7.41/2.38 % (24735)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_24321 for (2992ds/182Mi)
% 7.41/2.38 % (24736)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_24321 for (2992ds/164Mi)
% 8.04/2.40 % (24733)Instruction limit reached!
% 8.04/2.40 % (24733)------------------------------
% 8.04/2.40 % (24733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.04/2.40 % (24733)Termination reason: Unknown
% 8.04/2.40 % (24733)Termination phase: Property scanning
% 8.04/2.40
% 8.04/2.40 % (24733)Memory used [KB]: 3070
% 8.04/2.40 % (24733)Time elapsed: 0.032 s
% 8.04/2.40 % (24733)Instructions burned: 115 (million)
% 8.04/2.40 % (24733)------------------------------
% 8.04/2.40 % (24733)------------------------------
% 8.04/2.40 % (24724)Instruction limit reached!
% 8.04/2.40 % (24724)------------------------------
% 8.04/2.40 % (24724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.04/2.40 % (24724)Termination reason: Unknown
% 8.04/2.40 % (24724)Termination phase: Saturation
% 8.04/2.40
% 8.04/2.40 % (24724)Memory used [KB]: 9722
% 8.04/2.40 % (24724)Time elapsed: 0.122 s
% 8.04/2.40 % (24724)Instructions burned: 461 (million)
% 8.04/2.40 % (24724)------------------------------
% 8.04/2.40 % (24724)------------------------------
% 8.04/2.41 % (24737)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_24321 for (2992ds/50Mi)
% 8.04/2.41 % (24738)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_24321 for (2992ds/368Mi)
% 8.04/2.42 % (24732)Instruction limit reached!
% 8.04/2.42 % (24732)------------------------------
% 8.04/2.42 % (24732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.04/2.42 % (24732)Termination reason: Unknown
% 8.04/2.42 % (24732)Termination phase: Function definition elimination
% 8.04/2.42
% 8.04/2.42 % (24732)Memory used [KB]: 3326
% 8.04/2.42 % (24732)Time elapsed: 0.055 s
% 8.04/2.42 % (24732)Instructions burned: 218 (million)
% 8.04/2.42 % (24732)------------------------------
% 8.04/2.42 % (24732)------------------------------
% 8.04/2.42 % (24735)Instruction limit reached!
% 8.04/2.42 % (24735)------------------------------
% 8.04/2.42 % (24735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.04/2.42 % (24735)Termination reason: Unknown
% 8.04/2.42 % (24735)Termination phase: Property scanning
% 8.04/2.42
% 8.04/2.42 % (24735)Memory used [KB]: 3198
% 8.04/2.42 % (24735)Time elapsed: 0.047 s
% 8.04/2.42 % (24735)Instructions burned: 182 (million)
% 8.04/2.42 % (24735)------------------------------
% 8.04/2.42 % (24735)------------------------------
% 8.04/2.42 % (24736)Instruction limit reached!
% 8.04/2.42 % (24736)------------------------------
% 8.04/2.42 % (24736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.04/2.42 % (24736)Termination reason: Unknown
% 8.04/2.42 % (24736)Termination phase: Property scanning
% 8.04/2.42
% 8.04/2.42 % (24736)Memory used [KB]: 3070
% 8.04/2.42 % (24736)Time elapsed: 0.043 s
% 8.04/2.42 % (24736)Instructions burned: 166 (million)
% 8.04/2.42 % (24736)------------------------------
% 8.04/2.42 % (24736)------------------------------
% 8.04/2.42 % (24737)Instruction limit reached!
% 8.04/2.42 % (24737)------------------------------
% 8.04/2.42 % (24737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.04/2.42 % (24737)Termination reason: Unknown
% 8.04/2.42 % (24737)Termination phase: shuffling
% 8.04/2.42
% 8.04/2.42 % (24737)Memory used [KB]: 2686
% 8.04/2.42 % (24737)Time elapsed: 0.015 s
% 8.04/2.42 % (24737)Instructions burned: 52 (million)
% 8.04/2.42 % (24737)------------------------------
% 8.04/2.42 % (24737)------------------------------
% 8.04/2.42 % (24739)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_24321 for (2991ds/1021Mi)
% 8.04/2.43 % (24740)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_24321 for (2991ds/267Mi)
% 8.04/2.43 % (24741)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_24321 for (2991ds/204Mi)
% 8.04/2.43 % (24742)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_24321 for (2991ds/26Mi)
% 8.04/2.44 % (24742)Instruction limit reached!
% 8.04/2.44 % (24742)------------------------------
% 8.04/2.44 % (24742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.04/2.44 % (24742)Termination reason: Unknown
% 8.04/2.44 % (24742)Termination phase: shuffling
% 8.04/2.44
% 8.04/2.44 % (24742)Memory used [KB]: 2302
% 8.04/2.44 % (24742)Time elapsed: 0.008 s
% 8.04/2.44 % (24742)Instructions burned: 26 (million)
% 8.04/2.44 % (24742)------------------------------
% 8.04/2.44 % (24742)------------------------------
% 8.04/2.45 % (24743)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_24321 for (2991ds/53Mi)
% 8.04/2.46 % (24743)Instruction limit reached!
% 8.04/2.46 % (24743)------------------------------
% 8.04/2.46 % (24743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.04/2.46 % (24743)Termination reason: Unknown
% 8.04/2.46 % (24743)Termination phase: shuffling
% 8.04/2.46
% 8.04/2.46 % (24743)Memory used [KB]: 2686
% 8.04/2.46 % (24743)Time elapsed: 0.016 s
% 8.04/2.46 % (24743)Instructions burned: 56 (million)
% 8.04/2.46 % (24743)------------------------------
% 8.04/2.46 % (24743)------------------------------
% 8.04/2.47 % (24744)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_24321 for (2991ds/4436Mi)
% 8.04/2.48 % (24741)Instruction limit reached!
% 8.04/2.48 % (24741)------------------------------
% 8.04/2.48 % (24741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.04/2.48 % (24741)Termination reason: Unknown
% 8.04/2.48 % (24741)Termination phase: Function definition elimination
% 8.04/2.48
% 8.04/2.48 % (24741)Memory used [KB]: 3198
% 8.04/2.48 % (24741)Time elapsed: 0.052 s
% 8.04/2.48 % (24741)Instructions burned: 207 (million)
% 8.04/2.48 % (24741)------------------------------
% 8.04/2.48 % (24741)------------------------------
% 8.04/2.49 % (24745)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_24321 for (2991ds/1539Mi)
% 8.51/2.50 % (24740)Instruction limit reached!
% 8.51/2.50 % (24740)------------------------------
% 8.51/2.50 % (24740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.51/2.50 % (24740)Termination reason: Unknown
% 8.51/2.50 % (24740)Termination phase: Saturation
% 8.51/2.50
% 8.51/2.50 % (24740)Memory used [KB]: 7803
% 8.51/2.50 % (24740)Time elapsed: 0.068 s
% 8.51/2.50 % (24740)Instructions burned: 271 (million)
% 8.51/2.50 % (24740)------------------------------
% 8.51/2.50 % (24740)------------------------------
% 8.51/2.51 % (24738)Instruction limit reached!
% 8.51/2.51 % (24738)------------------------------
% 8.51/2.51 % (24738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.51/2.51 % (24738)Termination reason: Unknown
% 8.51/2.51 % (24738)Termination phase: Saturation
% 8.51/2.51
% 8.51/2.51 % (24738)Memory used [KB]: 9466
% 8.51/2.51 % (24738)Time elapsed: 0.098 s
% 8.51/2.51 % (24738)Instructions burned: 369 (million)
% 8.51/2.51 % (24738)------------------------------
% 8.51/2.51 % (24738)------------------------------
% 8.51/2.51 % (24746)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_24321 for (2991ds/408Mi)
% 8.51/2.52 % (24747)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_24321 for (2991ds/5205Mi)
% 8.51/2.55 % (24727)Instruction limit reached!
% 8.51/2.55 % (24727)------------------------------
% 8.51/2.55 % (24727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.51/2.55 % (24727)Termination reason: Unknown
% 8.51/2.55 % (24727)Termination phase: Saturation
% 8.51/2.55
% 8.51/2.55 % (24727)Memory used [KB]: 13560
% 8.51/2.55 % (24727)Time elapsed: 0.252 s
% 8.51/2.55 % (24727)Instructions burned: 990 (million)
% 8.51/2.55 % (24727)------------------------------
% 8.51/2.55 % (24727)------------------------------
% 8.51/2.56 % (24748)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_24321 for (2990ds/1913Mi)
% 8.95/2.63 % (24746)Instruction limit reached!
% 8.95/2.63 % (24746)------------------------------
% 8.95/2.63 % (24746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.95/2.63 % (24746)Termination reason: Unknown
% 8.95/2.63 % (24746)Termination phase: Saturation
% 8.95/2.63
% 8.95/2.63 % (24746)Memory used [KB]: 11897
% 8.95/2.63 % (24746)Time elapsed: 0.119 s
% 8.95/2.63 % (24746)Instructions burned: 409 (million)
% 8.95/2.63 % (24746)------------------------------
% 8.95/2.63 % (24746)------------------------------
% 8.95/2.64 % (24749)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_24321 for (2989ds/4350Mi)
% 8.95/2.65 % (24734)Instruction limit reached!
% 8.95/2.65 % (24734)------------------------------
% 8.95/2.65 % (24734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.95/2.65 % (24734)Termination reason: Unknown
% 8.95/2.65 % (24734)Termination phase: Saturation
% 8.95/2.65
% 8.95/2.65 % (24734)Memory used [KB]: 13176
% 8.95/2.65 % (24734)Time elapsed: 0.283 s
% 8.95/2.65 % (24734)Instructions burned: 922 (million)
% 8.95/2.65 % (24734)------------------------------
% 8.95/2.65 % (24734)------------------------------
% 8.95/2.67 % (24750)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_24321 for (2989ds/68Mi)
% 8.95/2.68 % (24750)Instruction limit reached!
% 8.95/2.68 % (24750)------------------------------
% 8.95/2.68 % (24750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.95/2.68 % (24750)Termination reason: Unknown
% 8.95/2.68 % (24750)Termination phase: Property scanning
% 8.95/2.68
% 8.95/2.68 % (24750)Memory used [KB]: 2814
% 8.95/2.68 % (24750)Time elapsed: 0.020 s
% 8.95/2.68 % (24750)Instructions burned: 70 (million)
% 8.95/2.68 % (24750)------------------------------
% 8.95/2.68 % (24750)------------------------------
% 8.95/2.69 % (24751)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_24321 for (2989ds/358Mi)
% 9.40/2.74 % (24739)Instruction limit reached!
% 9.40/2.74 % (24739)------------------------------
% 9.40/2.74 % (24739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.40/2.74 % (24739)Termination reason: Unknown
% 9.40/2.74 % (24739)Termination phase: Saturation
% 9.40/2.74
% 9.40/2.74 % (24739)Memory used [KB]: 13560
% 9.40/2.74 % (24739)Time elapsed: 0.314 s
% 9.40/2.74 % (24739)Instructions burned: 1023 (million)
% 9.40/2.74 % (24739)------------------------------
% 9.40/2.74 % (24739)------------------------------
% 9.40/2.75 % (24752)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_24321 for (2988ds/31Mi)
% 9.40/2.76 % (24752)Instruction limit reached!
% 9.40/2.76 % (24752)------------------------------
% 9.40/2.76 % (24752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.40/2.76 % (24752)Termination reason: Unknown
% 9.40/2.76 % (24752)Termination phase: shuffling
% 9.40/2.76
% 9.40/2.76 % (24752)Memory used [KB]: 2430
% 9.40/2.76 % (24752)Time elapsed: 0.011 s
% 9.40/2.76 % (24752)Instructions burned: 32 (million)
% 9.40/2.76 % (24752)------------------------------
% 9.40/2.76 % (24752)------------------------------
% 9.40/2.77 % (24753)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_24321 for (2988ds/279Mi)
% 9.40/2.78 % (24751)Instruction limit reached!
% 9.40/2.78 % (24751)------------------------------
% 9.40/2.78 % (24751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.40/2.78 % (24751)Termination reason: Unknown
% 9.40/2.78 % (24751)Termination phase: Saturation
% 9.40/2.78
% 9.40/2.78 % (24751)Memory used [KB]: 8443
% 9.40/2.78 % (24751)Time elapsed: 0.092 s
% 9.40/2.78 % (24751)Instructions burned: 359 (million)
% 9.40/2.78 % (24751)------------------------------
% 9.40/2.78 % (24751)------------------------------
% 9.40/2.79 % (24754)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_24321 for (2988ds/258Mi)
% 9.84/2.82 % (24744)First to succeed.
% 9.84/2.82 % (24744)Refutation found. Thanks to Tanya!
% 9.84/2.82 % SZS status Theorem for DTF2THF_24321
% 9.84/2.82 % SZS output start Proof for DTF2THF_24321
% 9.84/2.82 thf(func_def_0, type, in: $i > $i > $o).
% 9.84/2.82 thf(func_def_1, type, exu: ($i > $o) > $o).
% 9.84/2.82 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 9.84/2.82 thf(func_def_8, type, powerset: $i > $i).
% 9.84/2.82 thf(func_def_10, type, setunion: $i > $i).
% 9.84/2.82 thf(func_def_19, type, descr: ($i > $o) > $i).
% 9.84/2.82 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 9.84/2.82 thf(func_def_26, type, prop2set: $o > $i).
% 9.84/2.82 thf(func_def_36, type, nonempty: $i > $o).
% 9.84/2.82 thf(func_def_69, type, set2prop: $i > $o).
% 9.84/2.82 thf(func_def_88, type, subset: $i > $i > $o).
% 9.84/2.82 thf(func_def_89, type, disjoint: $i > $i > $o).
% 9.84/2.82 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 9.84/2.82 thf(func_def_114, type, binunion: $i > $i > $i).
% 9.84/2.82 thf(func_def_122, type, binintersect: $i > $i > $i).
% 9.84/2.82 thf(func_def_135, type, regular: $i > $o).
% 9.84/2.82 thf(func_def_136, type, setminus: $i > $i > $i).
% 9.84/2.82 thf(func_def_147, type, symdiff: $i > $i > $i).
% 9.84/2.82 thf(func_def_153, type, iskpair: $i > $o).
% 9.84/2.82 thf(func_def_158, type, kpair: $i > $i > $i).
% 9.84/2.82 thf(func_def_160, type, cartprod: $i > $i > $i).
% 9.84/2.82 thf(func_def_177, type, singleton: $i > $o).
% 9.84/2.82 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 9.84/2.82 thf(func_def_184, type, atmost1p: $i > $o).
% 9.84/2.82 thf(func_def_185, type, atleast2p: $i > $o).
% 9.84/2.82 thf(func_def_186, type, atmost2p: $i > $o).
% 9.84/2.82 thf(func_def_187, type, upairsetp: $i > $o).
% 9.84/2.82 thf(func_def_191, type, kfst: $i > $i).
% 9.84/2.82 thf(func_def_203, type, ksnd: $i > $i).
% 9.84/2.82 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 9.84/2.82 thf(func_def_222, type, func: $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_223, type, funcSet: $i > $i > $i).
% 9.84/2.82 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 9.84/2.82 thf(func_def_259, type, if: $i > $o > $i > $i > $i).
% 9.84/2.82 thf(func_def_323, type, breln1: $i > $i > $o).
% 9.84/2.82 thf(func_def_325, type, breln1Set: $i > $i).
% 9.84/2.82 thf(func_def_327, type, transitive: $i > $i > $o).
% 9.84/2.82 thf(func_def_328, type, antisymmetric: $i > $i > $o).
% 9.84/2.82 thf(func_def_329, type, reflexive: $i > $i > $o).
% 9.84/2.82 thf(func_def_330, type, refltransitive: $i > $i > $o).
% 9.84/2.82 thf(func_def_331, type, refllinearorder: $i > $i > $o).
% 9.84/2.82 thf(func_def_332, type, reflwellordering: $i > $i > $o).
% 9.84/2.82 thf(func_def_338, type, breln1invset: $i > $i > $i).
% 9.84/2.82 thf(func_def_342, type, breln1compset: $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_360, type, image1: $i > ($i > $i) > $i).
% 9.84/2.82 thf(func_def_364, type, injective: $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_365, type, injFuncSet: $i > $i > $i).
% 9.84/2.82 thf(func_def_369, type, surjective: $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_370, type, surjFuncSet: $i > $i > $i).
% 9.84/2.82 thf(func_def_378, type, omegaS: $i > $i).
% 9.84/2.82 thf(func_def_382, type, peano3: $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_383, type, peano4: $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_384, type, peano5: $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_386, type, peano: $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_387, type, transitiveset: $i > $o).
% 9.84/2.82 thf(func_def_392, type, stricttotalorderedByIn: $i > $o).
% 9.84/2.82 thf(func_def_393, type, wellorderedByIn: $i > $o).
% 9.84/2.82 thf(func_def_394, type, ordinal: $i > $o).
% 9.84/2.82 thf(func_def_395, type, limitOrdinal: $i > $o).
% 9.84/2.82 thf(func_def_411, type, sP0: $i > $o).
% 9.84/2.82 thf(func_def_412, type, sP1: $i > ($i > $o) > $o).
% 9.84/2.82 thf(func_def_413, type, sP2: $i > $i > ($i > $o) > $i > $o).
% 9.84/2.82 thf(func_def_414, type, sP3: ($i > $o) > $i > $o).
% 9.84/2.82 thf(func_def_415, type, sP4: ($i > $o) > $i > $o).
% 9.84/2.82 thf(func_def_416, type, sP5: $i > ($i > $o) > $o).
% 9.84/2.82 thf(func_def_419, type, sP8: $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_420, type, sP9: $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_421, type, sP10: ($i > $o) > $o).
% 9.84/2.82 thf(func_def_422, type, sP11: $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_423, type, sP12: $i > ($i > $i > $o) > $i > $o).
% 9.84/2.82 thf(func_def_424, type, sP13: $i > ($i > $i > $o) > $i > $o).
% 9.84/2.82 thf(func_def_426, type, sP15: $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_428, type, sP17: $i > $i > $o).
% 9.84/2.82 thf(func_def_430, type, sP19: $i > $i > $o > $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_431, type, sP20: $i > ($i > $o) > $o).
% 9.84/2.82 thf(func_def_433, type, sP22: $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_434, type, sP23: ($i > $o) > $i > $o).
% 9.84/2.82 thf(func_def_435, type, sP24: $i > ($i > $o) > $i > $i > $o).
% 9.84/2.82 thf(func_def_436, type, sP25: $i > ($i > $o) > $i > $o).
% 9.84/2.82 thf(func_def_438, type, sP27: ($i > $o) > $o).
% 9.84/2.82 thf(func_def_439, type, sP28: $i > $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_440, type, sP29: $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_441, type, sP30: $i > $i > $o).
% 9.84/2.82 thf(func_def_444, type, sP33: $i > ($i > $o) > $o).
% 9.84/2.82 thf(func_def_446, type, sP35: $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_448, type, sP37: ($i > $o) > $i > $o).
% 9.84/2.82 thf(func_def_449, type, sP38: $i > ($i > $o) > $i > $o).
% 9.84/2.82 thf(func_def_450, type, sP39: $i > $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_451, type, sP40: $i > $i > ($i > $i) > $o).
% 9.84/2.82 thf(func_def_453, type, sP42: $i > $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_454, type, sP43: $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_456, type, sP45: $i > $i > $o).
% 9.84/2.82 thf(func_def_458, type, sP47: ($i > $o) > $o).
% 9.84/2.82 thf(func_def_459, type, sP48: $i > ($i > $i) > $i > $o).
% 9.84/2.82 thf(func_def_463, type, sP52: $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_464, type, sP53: $i > $i > $o).
% 9.84/2.82 thf(func_def_465, type, sP54: $i > $o).
% 9.84/2.82 thf(func_def_466, type, sP55: $i > $i > $o).
% 9.84/2.82 thf(func_def_467, type, sP56: $i > $i > $o).
% 9.84/2.82 thf(func_def_468, type, sP57: $i > $i > $o).
% 9.84/2.82 thf(func_def_469, type, sP58: $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_470, type, sP59: ($i > $o) > $i > $o).
% 9.84/2.82 thf(func_def_473, type, sP62: $i > $i > $o > $o).
% 9.84/2.82 thf(func_def_475, type, sP64: $i > $o).
% 9.84/2.82 thf(func_def_476, type, sP65: $i > $o).
% 9.84/2.82 thf(func_def_477, type, sP66: $i > ($i > $o) > ($i > $o) > $i > $o).
% 9.84/2.82 thf(func_def_478, type, sP67: $i > $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_479, type, sP68: $i > $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_480, type, sP69: $i > ($i > $i) > $i > $o).
% 9.84/2.82 thf(func_def_482, type, sP71: ($i > $o) > $i > $o).
% 9.84/2.82 thf(func_def_484, type, sP73: $i > $i > ($i > $i) > $o).
% 9.84/2.82 thf(func_def_487, type, sP76: $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_488, type, sP77: $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_489, type, sP78: $o > $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_490, type, sP79: $o > $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_491, type, sP80: $i > ($i > $i > $o) > $i > $o).
% 9.84/2.82 thf(func_def_492, type, sP81: $i > ($i > $i > $o) > $o).
% 9.84/2.82 thf(func_def_494, type, sP83: ($i > $o) > $o).
% 9.84/2.82 thf(func_def_495, type, sP84: $i > $i > $o > $o).
% 9.84/2.82 thf(func_def_498, type, sP87: $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_499, type, sP88: $o > $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_500, type, sP89: $i > $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_501, type, sP90: ($i > $o) > $o).
% 9.84/2.82 thf(func_def_503, type, sP92: $i > $i > $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_504, type, sP93: $i > ($i > $o) > $o).
% 9.84/2.82 thf(func_def_506, type, sP95: ($i > $i) > $i > $i > $o).
% 9.84/2.82 thf(func_def_509, type, sP98: $i > $i > $o > $o).
% 9.84/2.82 thf(func_def_510, type, sP99: $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_511, type, sP100: $i > $i > $o > $o).
% 9.84/2.82 thf(func_def_512, type, sP101: $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_513, type, sP102: ($i > $o) > $i > $o).
% 9.84/2.82 thf(func_def_514, type, sP103: $i > ($i > $o) > $i > $o).
% 9.84/2.82 thf(func_def_515, type, sP104: $i > ($i > $o) > $o).
% 9.84/2.82 thf(func_def_516, type, sP105: ($i > $o) > $i > $o).
% 9.84/2.82 thf(func_def_528, type, sK117: $i > $o).
% 9.84/2.82 thf(func_def_540, type, sK129: $i > $i > $i).
% 9.84/2.82 thf(func_def_541, type, sK130: $i > $i).
% 9.84/2.82 thf(func_def_544, type, sK133: $i > $i > ($i > $o) > $i > $i).
% 9.84/2.82 thf(func_def_545, type, sK134: $i > $i > ($i > $o) > $i > $i).
% 9.84/2.82 thf(func_def_546, type, sK135: $i > ($i > $o) > $i).
% 9.84/2.82 thf(func_def_550, type, sK139: $i > $o).
% 9.84/2.82 thf(func_def_579, type, sK168: $i > $o).
% 9.84/2.82 thf(func_def_592, type, sK181: $i > $o).
% 9.84/2.82 thf(func_def_637, type, sK226: ($i > $o) > $i > $i).
% 9.84/2.82 thf(func_def_638, type, sK227: ($i > $o) > $i > $i).
% 9.84/2.82 thf(func_def_639, type, sK228: ($i > $o) > $i > $i).
% 9.84/2.82 thf(func_def_640, type, sK229: $i > $o).
% 9.84/2.82 thf(func_def_681, type, sK270: $i > $i > $o).
% 9.84/2.82 thf(func_def_685, type, sK274: $i > $o).
% 9.84/2.82 thf(func_def_686, type, sK275: ($i > $o) > $i > $i).
% 9.84/2.82 thf(func_def_687, type, sK276: $i > ($i > $o) > $i).
% 9.84/2.82 thf(func_def_692, type, sK281: $i > $i).
% 9.84/2.82 thf(func_def_693, type, sK282: ($i > $i) > $i > $i > $i).
% 9.84/2.82 thf(func_def_721, type, sK310: $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_722, type, sK311: $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_723, type, sK312: $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_724, type, sK313: $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_734, type, sK323: ($i > $o) > $i).
% 9.84/2.82 thf(func_def_735, type, sK324: $i > $o).
% 9.84/2.82 thf(func_def_736, type, sK325: $i > ($i > $o) > $i).
% 9.84/2.82 thf(func_def_737, type, sK326: ($i > $o) > $i).
% 9.84/2.82 thf(func_def_738, type, sK327: $i > $o).
% 9.84/2.82 thf(func_def_739, type, sK328: $i > $i > $o).
% 9.84/2.82 thf(func_def_741, type, sK330: $i > $o).
% 9.84/2.82 thf(func_def_766, type, sK355: $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_767, type, sK356: $i > $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_771, type, sK360: $i > $i > ($i > $i > $o) > $i).
% 9.84/2.82 thf(func_def_772, type, sK361: $i > ($i > $i > $o) > $i > $i).
% 9.84/2.82 thf(func_def_773, type, sK362: $i > ($i > $i > $o) > $i > $i).
% 9.84/2.82 thf(func_def_774, type, sK363: $i > ($i > $i > $o) > $i > $i).
% 9.84/2.82 thf(func_def_777, type, sK366: $i > $i > $o).
% 9.84/2.82 thf(func_def_783, type, sK372: $i > $i).
% 9.84/2.82 thf(func_def_790, type, sK379: $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_791, type, sK380: $i > $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_797, type, sK386: $i > $i > $i).
% 9.84/2.82 thf(func_def_800, type, sK389: $i > $i > $i).
% 9.84/2.82 thf(func_def_801, type, sK390: $i > $i > $o > $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_808, type, sK397: $i > $o).
% 9.84/2.82 thf(func_def_810, type, sK399: $i > ($i > $o) > $i).
% 9.84/2.82 thf(func_def_811, type, sK400: $i > ($i > $o) > $i).
% 9.84/2.82 thf(func_def_822, type, sK411: $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_826, type, sK415: $i > $o).
% 9.84/2.82 thf(func_def_827, type, sK416: $i > ($i > $o) > $i > $i > $i).
% 9.84/2.82 thf(func_def_828, type, sK417: $i > ($i > $o) > $i > $i > $i).
% 9.84/2.82 thf(func_def_829, type, sK418: ($i > $o) > $i > $i).
% 9.84/2.82 thf(func_def_833, type, sK422: $i > $o).
% 9.84/2.82 thf(func_def_834, type, sK423: $i > $o).
% 9.84/2.82 thf(func_def_845, type, sK434: $i > $i).
% 9.84/2.82 thf(func_def_862, type, sK451: $i > ($i > $o) > $i > $i).
% 9.84/2.82 thf(func_def_863, type, sK452: $i > $o).
% 9.84/2.82 thf(func_def_884, type, sK473: $i > $o).
% 9.84/2.82 thf(func_def_888, type, sK477: $i > $i).
% 9.84/2.82 thf(func_def_890, type, sK479: $i > ($i > $i) > $i > $i).
% 9.84/2.82 thf(func_def_892, type, sK481: $i > $o).
% 9.84/2.82 thf(func_def_894, type, sK483: ($i > $o) > $i).
% 9.84/2.82 thf(func_def_895, type, sK484: $i > ($i > $o) > $i).
% 9.84/2.82 thf(func_def_896, type, sK485: $i > $o).
% 9.84/2.82 thf(func_def_901, type, sK490: $i > $i).
% 9.84/2.82 thf(func_def_911, type, sK500: $i > $i > $o).
% 9.84/2.82 thf(func_def_914, type, sK503: $i > $o).
% 9.84/2.82 thf(func_def_918, type, sK507: $i > $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_919, type, sK508: $i > $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_929, type, sK518: $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_930, type, sK519: $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_940, type, sK529: $i > $i > $i).
% 9.84/2.82 thf(func_def_941, type, sK530: $i > $i > $i).
% 9.84/2.82 thf(func_def_942, type, sK531: $i > $o).
% 9.84/2.82 thf(func_def_943, type, sK532: $i > $o).
% 9.84/2.82 thf(func_def_944, type, sK533: ($i > $o) > ($i > $o) > $i).
% 9.84/2.82 thf(func_def_945, type, sK534: ($i > $o) > ($i > $o) > $i).
% 9.84/2.82 thf(func_def_954, type, sK543: $i > $o).
% 9.84/2.82 thf(func_def_956, type, sK545: $i > ($i > $o) > $i).
% 9.84/2.82 thf(func_def_957, type, sK546: $i > ($i > $o) > $i).
% 9.84/2.82 thf(func_def_964, type, sK553: $i > ($i > $o) > $i > $i).
% 9.84/2.82 thf(func_def_965, type, sK554: $i > ($i > $o) > $i > $i).
% 9.84/2.82 thf(func_def_966, type, sK555: ($i > $o) > $i > $i).
% 9.84/2.82 thf(func_def_969, type, sK558: $i > $o).
% 9.84/2.82 thf(func_def_977, type, sK566: $i > $i > $o).
% 9.84/2.82 thf(func_def_979, type, sK568: $i > $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_985, type, sK574: $i > $i).
% 9.84/2.82 thf(func_def_987, type, sK576: $i > ($i > $i) > $i > $i).
% 9.84/2.82 thf(func_def_988, type, sK577: $i > $i > ($i > $i) > $i).
% 9.84/2.82 thf(func_def_1013, type, sK602: $i > $i > $o).
% 9.84/2.82 thf(func_def_1028, type, sK617: $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_1029, type, sK618: $i > $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_1030, type, sK619: $i > $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_1031, type, sK620: $i > $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_1040, type, sK629: $i > $i > $i).
% 9.84/2.82 thf(func_def_1059, type, sK648: $i > $i > $i).
% 9.84/2.82 thf(func_def_1067, type, sK656: ($i > $o) > $i).
% 9.84/2.82 thf(func_def_1068, type, sK657: $i > ($i > $o) > $i).
% 9.84/2.82 thf(func_def_1069, type, sK658: $i > $o).
% 9.84/2.82 thf(func_def_1076, type, sK665: $i > $i).
% 9.84/2.82 thf(func_def_1077, type, sK666: $i > ($i > $i) > $i > $i).
% 9.84/2.82 thf(func_def_1082, type, sK671: $i > $o).
% 9.84/2.82 thf(func_def_1103, type, sK692: $i > $o).
% 9.84/2.82 thf(func_def_1104, type, sK693: ($i > $o) > $i > $i).
% 9.84/2.82 thf(func_def_1118, type, sK707: $i > $i).
% 9.84/2.82 thf(func_def_1120, type, sK709: $i > ($i > $i) > $i > $i).
% 9.84/2.82 thf(func_def_1135, type, sK724: $i > $i > $i).
% 9.84/2.82 thf(func_def_1136, type, sK725: $i > $i > $i).
% 9.84/2.82 thf(func_def_1137, type, sK726: $i > $i > $i).
% 9.84/2.82 thf(func_def_1138, type, sK727: $i > $i > $i).
% 9.84/2.82 thf(func_def_1139, type, sK728: $i > $i > $i).
% 9.84/2.82 thf(func_def_1140, type, sK729: $i > $i > $i).
% 9.84/2.82 thf(func_def_1141, type, sK730: $i > $i > $i).
% 9.84/2.82 thf(func_def_1142, type, sK731: $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_1143, type, sK732: $i > $i).
% 9.84/2.82 thf(func_def_1144, type, sK733: $i > $i).
% 9.84/2.82 thf(func_def_1145, type, sK734: $i > $i).
% 9.84/2.82 thf(func_def_1146, type, sK735: $i > $i).
% 9.84/2.82 thf(func_def_1147, type, sK736: $i > $i > $i).
% 9.84/2.82 thf(func_def_1148, type, sK737: $i > $i > $i).
% 9.84/2.82 thf(func_def_1149, type, sK738: $i > $i > $i).
% 9.84/2.82 thf(func_def_1150, type, sK739: $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_1151, type, sK740: $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_1153, type, sK742: $i > $i).
% 9.84/2.82 thf(func_def_1154, type, sK743: $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_1160, type, sK749: $i > $o).
% 9.84/2.82 thf(func_def_1162, type, sK751: $i > ($i > $o) > $i).
% 9.84/2.82 thf(func_def_1163, type, sK752: ($i > $o) > $i > $i).
% 9.84/2.82 thf(func_def_1170, type, sK759: $i > $i).
% 9.84/2.82 thf(func_def_1172, type, sK761: $i > $i).
% 9.84/2.82 thf(func_def_1174, type, sK763: $i > ($i > $i) > $i > $i).
% 9.84/2.82 thf(func_def_1180, type, sK769: $i > $i > $o > $i).
% 9.84/2.82 thf(func_def_1193, type, sK782: $i > $i > $i).
% 9.84/2.82 thf(func_def_1194, type, sK783: $i > $i).
% 9.84/2.82 thf(func_def_1195, type, sK784: $i > $i).
% 9.84/2.82 thf(func_def_1217, type, sK806: $i > ($i > $o) > ($i > $o) > $i > $i).
% 9.84/2.82 thf(func_def_1218, type, sK807: $i > ($i > $o) > ($i > $o) > $i > $i).
% 9.84/2.82 thf(func_def_1221, type, sK810: $i > $o).
% 9.84/2.82 thf(func_def_1222, type, sK811: $i > $o).
% 9.84/2.82 thf(func_def_1228, type, sK817: $i > $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_1229, type, sK818: $i > $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_1230, type, sK819: $i > $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_1231, type, sK820: $i > $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_1250, type, sK839: $i > $i).
% 9.84/2.82 thf(func_def_1251, type, sK840: $i > $i).
% 9.84/2.82 thf(func_def_1252, type, sK841: ($i > $i) > $i > $i).
% 9.84/2.82 thf(func_def_1253, type, sK842: $i > ($i > $i) > $i > $i).
% 9.84/2.82 thf(func_def_1257, type, sK846: $i > $o).
% 9.84/2.82 thf(func_def_1258, type, sK847: ($i > $o) > $i > $i).
% 9.84/2.82 thf(func_def_1259, type, sK848: ($i > $o) > $i > $i).
% 9.84/2.82 thf(func_def_1273, type, sK862: $i > $i).
% 9.84/2.82 thf(func_def_1274, type, sK863: ($i > $i) > $i > $i > $i).
% 9.84/2.82 thf(func_def_1275, type, sK864: $i > $i > ($i > $i) > $i).
% 9.84/2.82 thf(func_def_1278, type, sK867: $i > $i > $i).
% 9.84/2.82 thf(func_def_1285, type, sK874: $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_1286, type, sK875: $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_1295, type, sK884: $i > $i > $o).
% 9.84/2.82 thf(func_def_1296, type, sK885: ($i > $i > $o) > $i > $i).
% 9.84/2.82 thf(func_def_1297, type, sK886: $i > $i > ($i > $i > $o) > $i).
% 9.84/2.82 thf(func_def_1298, type, sK887: $i > ($i > $i > $o) > $i).
% 9.84/2.82 thf(func_def_1299, type, sK888: $i > ($i > $i > $o) > $i > $i).
% 9.84/2.82 thf(func_def_1300, type, sK889: ($i > $o) > $i).
% 9.84/2.82 thf(func_def_1301, type, sK890: ($i > $o) > $i).
% 9.84/2.82 thf(func_def_1302, type, sK891: $i > $o).
% 9.84/2.82 thf(func_def_1318, type, sK907: $i > $i).
% 9.84/2.82 thf(func_def_1320, type, sK909: $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_1321, type, sK910: $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_1332, type, sK921: $i > $i).
% 9.84/2.82 thf(func_def_1345, type, sK934: $i > $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_1367, type, sK956: $i > ($i > $o) > $i).
% 9.84/2.82 thf(func_def_1368, type, sK957: ($i > $o) > $i).
% 9.84/2.82 thf(func_def_1369, type, sK958: $i > $o).
% 9.84/2.82 thf(func_def_1377, type, sK966: $i > $i > $i).
% 9.84/2.82 thf(func_def_1394, type, sK983: $i > $i > $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_1401, type, sK990: $i > $o).
% 9.84/2.82 thf(func_def_1402, type, sK991: ($i > $o) > $i > $i).
% 9.84/2.82 thf(func_def_1403, type, sK992: $i > ($i > $o) > $i).
% 9.84/2.82 thf(func_def_1404, type, sK993: $i > $i).
% 9.84/2.82 thf(func_def_1407, type, sK996: $i > $i > ($i > $i) > $i).
% 9.84/2.82 thf(func_def_1408, type, sK997: ($i > $i) > $i > $i > $i).
% 9.84/2.82 thf(func_def_1409, type, sK998: $i > ($i > $i) > $i > $i > $i).
% 9.84/2.82 thf(func_def_1428, type, sK1017: $i > $i > $o).
% 9.84/2.82 thf(func_def_1469, type, sK1058: $i > $o).
% 9.84/2.82 thf(func_def_1470, type, sK1059: $i > $o).
% 9.84/2.82 thf(func_def_1471, type, sK1060: ($i > $o) > ($i > $o) > $i).
% 9.84/2.82 thf(func_def_1472, type, sK1061: ($i > $o) > ($i > $o) > $i).
% 9.84/2.82 thf(func_def_1489, type, sK1078: $i > $i > $o).
% 9.84/2.82 thf(func_def_1492, type, sK1081: $i > $o).
% 9.84/2.82 thf(func_def_1494, type, sK1083: $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_1506, type, sK1095: $i > $i).
% 9.84/2.82 thf(func_def_1508, type, sK1097: $i > $i).
% 9.84/2.82 thf(func_def_1511, type, sK1100: $i > $i > $o).
% 9.84/2.82 thf(func_def_1542, type, sK1131: $i > $i > $i).
% 9.84/2.82 thf(func_def_1550, type, sK1139: $i > $o).
% 9.84/2.82 thf(func_def_1567, type, sK1156: $i > $o).
% 9.84/2.82 thf(func_def_1571, type, sK1160: $i > $i > $i > $o).
% 9.84/2.82 thf(func_def_1572, type, sK1161: $i > $i > $i > $i).
% 9.84/2.82 thf(func_def_1578, type, sK1167: $i > ($i > $o) > $i > $i).
% 9.84/2.82 thf(func_def_1579, type, sK1168: $i > ($i > $o) > $i > $i).
% 9.84/2.82 thf(func_def_1580, type, sK1169: ($i > $o) > $i > $i).
% 9.84/2.82 thf(func_def_1583, type, sK1172: $i > $o).
% 9.84/2.82 thf(func_def_1589, type, sK1178: ($i > $o) > $i > $i).
% 9.84/2.82 thf(func_def_1590, type, sK1179: ($i > $o) > $i > $i).
% 9.84/2.82 thf(func_def_1591, type, sK1180: $i > ($i > $o) > $i).
% 9.84/2.82 thf(func_def_1593, type, sK1182: $i > $o).
% 9.84/2.82 thf(func_def_1594, type, sK1183: $i > $i).
% 9.84/2.82 thf(func_def_1597, type, sK1186: $i > $i > ($i > $i) > $i).
% 9.84/2.82 thf(func_def_1602, type, sK1191: $i > $i).
% 9.84/2.82 thf(func_def_1603, type, sK1192: $i > $i).
% 9.84/2.82 thf(func_def_1605, type, sK1194: $i > $i).
% 9.84/2.82 thf(func_def_1606, type, sK1195: $i > $i).
% 9.84/2.82 thf(func_def_1607, type, sK1196: $i > $i).
% 9.84/2.82 thf(func_def_1608, type, ph1197: !>[X0: $tType]:(X0)).
% 9.84/2.82 thf(f10494,plain,(
% 9.84/2.82 $false),
% 9.84/2.82 inference(avatar_sat_refutation,[status(thm)],[f9788,f10357,f10493])).
% 9.84/2.82 thf(f10493,plain,(
% 9.84/2.82 spl1189_219),
% 9.84/2.82 inference(avatar_contradiction_clause,[status(thm)],[f10492])).
% 9.84/2.82 thf(f10492,plain,(
% 9.84/2.82 $false | spl1189_219),
% 9.84/2.82 inference(trivial_inequality_removal,[status(thm)],[f10482])).
% 9.84/2.82 thf(f10482,plain,(
% 9.84/2.82 ($false = $true) | spl1189_219),
% 9.84/2.82 inference(backward_demodulation,[status(thm)],[f8933,f10428])).
% 9.84/2.82 thf(f10428,plain,(
% 9.84/2.82 ((in @ sK1190 @ sK980) = $false) | spl1189_219),
% 9.84/2.82 inference(trivial_inequality_removal,[status(thm)],[f10419])).
% 9.84/2.82 thf(f10419,plain,(
% 9.84/2.82 ((in @ sK1190 @ sK980) = $false) | ($true != $true) | spl1189_219),
% 9.84/2.82 inference(superposition,[status(thm)],[f9786,f7083])).
% 9.84/2.82 thf(f7083,plain,(
% 9.84/2.82 ( ! [X1 : $i] : (($true = (subset @ X1 @ sK980)) | ((in @ X1 @ sK980) = $false)) )),
% 9.84/2.82 inference(binary_proxy_clausification,[status(thm)],[f7082])).
% 9.84/2.82 thf(f7082,plain,(
% 9.84/2.82 ( ! [X1 : $i] : ((((in @ X1 @ sK980) => (subset @ X1 @ sK980)) = $true)) )),
% 9.84/2.82 inference(beta_eta_normalization,[status(thm)],[f7081])).
% 9.84/2.82 thf(f7081,plain,(
% 9.84/2.82 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ sK980) => (subset @ Y0 @ sK980))) @ X1))) )),
% 9.84/2.82 inference(pi_clausification,[status(thm)],[f7079])).
% 9.84/2.82 thf(f7079,plain,(
% 9.84/2.82 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK980) => (subset @ Y0 @ sK980)))) = $true)),
% 9.84/2.82 inference(binary_proxy_clausification,[status(thm)],[f7078])).
% 9.84/2.82 thf(f7078,plain,(
% 9.84/2.82 ($true = ((wellorderedByIn @ sK980) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK980) => (subset @ Y0 @ sK980))))))),
% 9.84/2.82 inference(beta_eta_normalization,[status(thm)],[f6528])).
% 9.84/2.82 thf(f6528,plain,(
% 9.84/2.82 ($true = ((^[Y0 : $i]: ((wellorderedByIn @ Y0) & ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (subset @ Y2 @ Y1))))) @ Y0))) @ sK980))),
% 9.84/2.82 inference(definition_unfolding,[status(thm)],[f5201,f5551])).
% 9.84/2.82 thf(f5551,plain,(
% 9.84/2.82 (ordinal = (^[Y0 : $i]: ((wellorderedByIn @ Y0) & ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (subset @ Y2 @ Y1))))) @ Y0))))),
% 9.84/2.82 inference(definition_unfolding,[status(thm)],[f4899,f5320])).
% 9.84/2.82 thf(f5320,plain,(
% 9.84/2.82 (transitiveset = (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))))),
% 9.84/2.82 inference(cnf_transformation,[status(thm)],[f343])).
% 9.84/2.82 thf(f343,plain,(
% 9.84/2.82 (transitiveset = (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))))),
% 9.84/2.82 inference(fool_elimination,[status(thm)],[f342])).
% 9.84/2.82 thf(f342,plain,(
% 9.84/2.82 ((^[X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (subset @ X1 @ X0)))) = transitiveset)),
% 9.84/2.82 inference(rectify,[status(thm)],[f331])).
% 9.84/2.82 thf(f331,axiom,(
% 9.84/2.82 ((^[X3 : $i] : (! [X11 : $i] : ((in @ X11 @ X3) => (subset @ X11 @ X3)))) = transitiveset)),
% 9.84/2.82 file('/export/starexec/sandbox/tmp/tmp.SkoTPvEhFx/DTF2THF_24321.p',transitiveset)).
% 9.84/2.82 thf(f4899,plain,(
% 9.84/2.82 (ordinal = (^[Y0 : $i]: ((wellorderedByIn @ Y0) & (transitiveset @ Y0))))),
% 9.84/2.82 inference(cnf_transformation,[status(thm)],[f639])).
% 9.84/2.82 thf(f639,plain,(
% 9.84/2.82 (ordinal = (^[Y0 : $i]: ((wellorderedByIn @ Y0) & (transitiveset @ Y0))))),
% 9.84/2.82 inference(fool_elimination,[status(thm)],[f638])).
% 9.84/2.82 thf(f638,plain,(
% 9.84/2.82 ((^[X0 : $i] : ((transitiveset @ X0) & (wellorderedByIn @ X0))) = ordinal)),
% 9.84/2.82 inference(rectify,[status(thm)],[f338])).
% 9.84/2.82 thf(f338,axiom,(
% 9.84/2.82 ((^[X1 : $i] : ((transitiveset @ X1) & (wellorderedByIn @ X1))) = ordinal)),
% 9.84/2.82 file('/export/starexec/sandbox/tmp/tmp.SkoTPvEhFx/DTF2THF_24321.p',ordinal)).
% 9.84/2.82 thf(f5201,plain,(
% 9.84/2.82 ((ordinal @ sK980) = $true)),
% 9.84/2.82 inference(cnf_transformation,[status(thm)],[f3188])).
% 9.84/2.82 thf(f3188,plain,(
% 9.84/2.82 (ex1I2 = $true) & (omega__Cong = $true) & (singletoninpowerset = $true) & (ksndsingleton = $true) & (woz13rule3 = $true) & (setminusILneg = $true) & (kfstpairEq = $true) & (woz1_1 = $true) & (exuEu = $true) & (subsetRefl = $true) & (peanoSinj = $true) & (image1I = $true) & (cartprodpairsurjEq = $true) & (binintersectSubset4 = $true) & (exuI3 = $true) & (secondinupair = $true) & (funcGraphProp1 = $true) & (binintersectSubset3 = $true) & (eqbreln = $true) & (sepInPowerset = $true) & (nonemptyE1 = $true) & (subsetI1 = $true) & (inIntersectImpInUnion2 = $true) & (transitivesetOp1 = $true) & (apProp = $true) & (upairsetE = $true) & (setunionAx = $true) & (breln1unionI = $true) & (complementInPowersetComplementIntersect = $true) & (dsetconstrER = $true) & (dsetconstrEL = $true) & (foundationAx = $true) & (funcextLem = $true) & (setunionsingleton1 = $true) & (binunionTEcontra = $true) & (setadjoinIL = $true) & (binintersectSubset1 = $true) & (cartprodfstpairEq = $true) & (complementTE1 = $true) & (((ordinal @ sK980) = $true) & (((transitiveset @ (binintersect @ sK980 @ sK981)) != $true) & ((ordinal @ sK981) = $true))) & (upairsetIR = $true) & (breln1compI = $true) & (exuE3u = $true) & (notdallE = $true) & (setukpairIR = $true) & (doubleComplementSub2 = $true) & (woz2A = $true) & (omegaSAx = $true) & (doubleComplementE1 = $true) & (dpsetconstrERa = $true) & (sepSubset = $true) & (contrasubsetT1 = $true) & (woz2Ex = $true) & (lam2lamEq = $true) & (cartprodpairin = $true) & (lamp = $true) & (cartprodsndpairEq = $true) & (ap2apEq2 = $true) & (singletonprop = $true) & (breln1unionE = $true) & (setextT = $true) & (omega0Ax = $true) & (doubleComplementI1 = $true) & (quantDeMorgan4 = $true) & (breln1unionEcases = $true) & (notdexE = $true) & (eqimpsubset2 = $true) & (setextAx = $true) & (image1Equiv = $true) & (ubforcartprodlem2 = $true) & (vacuousDall = $true) & (setminusIRneg = $true) & (breln1all2 = $true) & (replAx = $true) & (setminusSubset1 = $true) & (binunionIL = $true) & (setext = $true) & (contrasubsetT3 = $true) & (binunionLsub = $true) & (contrasubsetT = $true) & (setukpairinjL = $true) & (exuE2 = $true) & (iftrue = $true) & (setminusERneg = $true) & (woz2B = $true) & (setukpairinjR11 = $true) & (inComplementUnionImpInComplement1 = $true) & (setminusSubset2 = $true) & (cartprodmempaircEq = $true) & (binintersectLsub = $true) & (funcImageSingleton = $true) & (bs114d = $true) & (binintersectER = $true) & (inIntersectImpInIntersectUnions = $true) & (dpsetconstrSub = $true) & (kpairsurjEq = $true) & (breln1invE = $true) & (eqinunit = $true) & (injFuncSetFuncInj = $true) & (demorgan2b = $true) & (cartprodfstin = $true) & (funcGraphProp4 = $true) & (ex1I = $true) & (ap2p = $true) & (inComplementUnionImpNotIn1 = $true) & (image1Ex = $true) & (exuI2 = $true) & (notinself = $true) & (emptyset__Cong = $true) & (binunionEcases = $true) & (dpsetconstrEL2 = $true) & (cartprodpairmemER = $true) & (lam2p = $true) & (inCongP = $true) & (setukpairinjR1 = $true) & (prop2setE = $true) & (binunionRsub = $true) & (ifSingleton = $true) & (inPowerset = $true) & (woz2W = $true) & (iffalseProp1 = $true) & (ex1E1 = $true) & (setunionE2 = $true) & (funcext = $true) & (singletonsubset = $true) & (uniqinunit = $true) & (woz13rule2 = $true) & (notinsingleton = $true) & (woz1_4 = $true) & (setminusI = $true) & (powersetsubset = $true) & (complementSubsetComplementIntersect = $true) & (powerset__Cong = $true) & (dpsetconstrI = $true) & (inIntersectImpInUnion = $true) & (woz1_2 = $true) & (surjFuncSetFuncSurj = $true) & (subsetE = $true) & (quantDeMorgan1 = $true) & (iftrueorfalse = $true) & (theeq = $true) & (cartprodmempair1 = $true) & (wellorderingAx = $true) & (quantDeMorgan2 = $true) & (demorgan2 = $true) & (powersetI = $true) & (funcGraphProp2 = $true) & (setukpairinjR12 = $true) & (symdiffI2 = $true) & (setukpairinjR2 = $true) & (subsetI2 = $true) & (subsetemptysetimpeq = $true) & (emptyI = $true) & (setukpairinjL2 = $true) & (beta1 = $true) & (surjCantorThm = $true) & (setminusEL = $true) & (demorgan2b2 = $true) & (notinemptyset = $true) & (powersetAx = $true) & (notinself2 = $true) & (powersetTI1 = $true) & (binintersectRsub = $true) & (subbreln = $true) & (upairsetIL = $true) & (subsetE2 = $true) & (kpairp = $true) & (doubleComplementSub1 = $true) & (notsubsetI = $true) & (binintersectEL = $true) & (setOfPairsIsBReln = $true) & (doubleComplementEq = $true) & (iffalse = $true) & (notequalI2 = $true) & (emptysetsubset = $true) & (upairequniteq = $true) & (dsetconstrI = $true) & (setunionE = $true) & (nonemptyImpWitness = $true) & (powersetE1 = $true) & (binunionIR = $true) & (binunionTIRcontra = $true) & (setadjoinIR = $true) & (demorgan2a1 = $true) & (noeltsimpempty = $true) & (funcext2 = $true) & (ifp = $true) & (breln1all1 = $true) & (nonemptyI1 = $true) & (surjFuncSetFuncIn = $true) & (injFuncInInjFuncSet = $true) & (setadjoinAx = $true) & (ap2apEq1 = $true) & (symdiffE = $true) & (binintersectSubset5 = $true) & (powersetTE1 = $true) & (woz1_3 = $true) & (funcGraphProp3 = $true) & (symdiffI1 = $true) & (kfstsingleton = $true) & (setminusLsub = $true) & (iftrueProp2 = $true) & (breln1compE = $true) & (setminusER = $true) & (ex1E2 = $true) & (beta2 = $true) & (eta2 = $true) & (upairsubunion = $true) & (exuE1 = $true) & (ubforcartprodlem3 = $true) & (theprop = $true) & (binunionE = $true) & (emptysetimpfalse = $true) & (complementTcontraSubset = $true) & (brelnall1 = $true) & (upairset2IR = $true) & (binintTransitive = $true) & (prop2setI = $true) & (funcinfuncset = $true) & (infuncsetfunc = $true) & (breln1compprop = $true) & (setunionTransitive = $true) & (woz13rule4 = $true) & (nonemptyI = $true) & (descrp = $true) & (ksndpairEq = $true) & (woz13rule0 = $true) & (setextsub = $true) & (breln1invprop = $true) & (symdiffIneg1 = $true) & (powersetI1 = $true) & (setukpairinjL1 = $true) & (setunionsingleton2 = $true) & (exuI1 = $true) & (omegaSclos = $true) & (breln1unionCommutes = $true) & (singletonsuniq = $true) & (iftrueProp1 = $true) & (powersetE = $true) & (subsetTrans = $true) & (setoftrueEq = $true) & (woz1_5 = $true) & (image1E = $true) & (emptyinPowerset = $true) & (breln1unionIR = $true) & (exu__Cong = $true) & (upairinpowunion = $true) & (emptyinunitempty = $true) & (contraSubsetComplement = $true) & (foundation2 = $true) & (emptyE1 = $true) & (dsetconstr__Cong = $true) & (singletoninpowunion = $true) & (intersectInPowersetIntersectUnions = $true) & (setunionI = $true) & (setadjoinSub2 = $true) & (setOfPairsIsBReln1 = $true) & (setukpairIL = $true) & (setbeta = $true) & (brelnall2 = $true) & (subset2powerset = $true) & (contrasubsetT2 = $true) & (setadjoinOr = $true) & (breln1SetBreln1 = $true) & (cartprodmempair = $true) & (lamProp = $true) & (subPowSU = $true) & (setadjoinSub = $true) & (binintersectT_lem = $true) & (setadjoin__Cong = $true) & (binintersectTELcontra = $true) & (emptysetAx = $true) & (transitivesetOp2 = $true) & (complementUnionInPowersetComplement = $true) & (iffalseProp2 = $true) & (descr__Cong = $true) & (symdiffIneg2 = $true) & (demorgan1a = $true) & (breln1invI = $true) & (binintersectI = $true) & (demorgan1 = $true) & (leftInvIsSurj = $true) & (notequalI1 = $true) & (setminusT_lem = $true) & (peano0notS = $true) & (binunionT_lem = $true) & (complementImpComplementIntersect = $true) & (emptyInPowerset = $true) & (setunionsingleton = $true) & (demorgan2a = $true) & (eta1 = $true) & (eqimpsubset1 = $true) & (disjointsetsI1 = $true) & (binunionTILcontra = $true) & (subsetTI = $true) & (breln1unionIL = $true) & (singletonsswitch = $true) & (eqbreln1 = $true) & (quantDeMorgan3 = $true) & (dpsetconstrER = $true) & (setukpairinjR = $true) & (kpairiskpair = $true) & (emptysetE = $true) & (cartprodsndin = $true) & (setunion__Cong = $true) & (exuE3e = $true) & (setadjoinE = $true) & (complementTI1 = $true) & (omegaIndAx = $true) & (breln1compEex = $true) & (injFuncSetFuncIn = $true) & (prop2set2propI = $true) & (binintersectTERcontra = $true) & (complementTnotintersectT = $true) & (dpsetconstrEL1 = $true) & (subbreln1 = $true) & (image1Ex1 = $true) & (breln1unionprop = $true) & (complementT_lem = $true) & (app = $true) & (omegaSp = $true) & (upairset2E = $true) & (demorgan1b = $true) & (choice2fnsingleton = $true) & (ubforcartprodlem1 = $true) & (binunionTE = $true) & (powersetT_lem = $true) & (woz13rule1 = $true) & (demorgan2a2 = $true) & (binintersectSubset2 = $true) & (setminusELneg = $true) & (cartprodpairmemEL = $true) & (in__Cong = $true)),
% 9.84/2.82 inference(skolemisation,[status(esa),new_symbols(skolem,[sK980,sK981])],[f1360,f3187,f3186])).
% 9.84/2.82 thf(f3186,plain,(
% 9.84/2.82 ? [X0 : $i] : (($true = (ordinal @ X0)) & ? [X1 : $i] : (($true != (transitiveset @ (binintersect @ X0 @ X1))) & ($true = (ordinal @ X1)))) => (((ordinal @ sK980) = $true) & ? [X1 : $i] : (((transitiveset @ (binintersect @ sK980 @ X1)) != $true) & ($true = (ordinal @ X1))))),
% 9.84/2.82 introduced(definition,[],[choice_axiom])).
% 9.84/2.82 thf(f3187,plain,(
% 9.84/2.82 ? [X1 : $i] : (((transitiveset @ (binintersect @ sK980 @ X1)) != $true) & ($true = (ordinal @ X1))) => (((transitiveset @ (binintersect @ sK980 @ sK981)) != $true) & ((ordinal @ sK981) = $true))),
% 9.84/2.82 introduced(definition,[],[choice_axiom])).
% 9.84/2.82 thf(f1360,plain,(
% 9.84/2.82 (ex1I2 = $true) & (omega__Cong = $true) & (singletoninpowerset = $true) & (ksndsingleton = $true) & (woz13rule3 = $true) & (setminusILneg = $true) & (kfstpairEq = $true) & (woz1_1 = $true) & (exuEu = $true) & (subsetRefl = $true) & (peanoSinj = $true) & (image1I = $true) & (cartprodpairsurjEq = $true) & (binintersectSubset4 = $true) & (exuI3 = $true) & (secondinupair = $true) & (funcGraphProp1 = $true) & (binintersectSubset3 = $true) & (eqbreln = $true) & (sepInPowerset = $true) & (nonemptyE1 = $true) & (subsetI1 = $true) & (inIntersectImpInUnion2 = $true) & (transitivesetOp1 = $true) & (apProp = $true) & (upairsetE = $true) & (setunionAx = $true) & (breln1unionI = $true) & (complementInPowersetComplementIntersect = $true) & (dsetconstrER = $true) & (dsetconstrEL = $true) & (foundationAx = $true) & (funcextLem = $true) & (setunionsingleton1 = $true) & (binunionTEcontra = $true) & (setadjoinIL = $true) & (binintersectSubset1 = $true) & (cartprodfstpairEq = $true) & (complementTE1 = $true) & ? [X0 : $i] : (($true = (ordinal @ X0)) & ? [X1 : $i] : (($true != (transitiveset @ (binintersect @ X0 @ X1))) & ($true = (ordinal @ X1)))) & (upairsetIR = $true) & (breln1compI = $true) & (exuE3u = $true) & (notdallE = $true) & (setukpairIR = $true) & (doubleComplementSub2 = $true) & (woz2A = $true) & (omegaSAx = $true) & (doubleComplementE1 = $true) & (dpsetconstrERa = $true) & (sepSubset = $true) & (contrasubsetT1 = $true) & (woz2Ex = $true) & (lam2lamEq = $true) & (cartprodpairin = $true) & (lamp = $true) & (cartprodsndpairEq = $true) & (ap2apEq2 = $true) & (singletonprop = $true) & (breln1unionE = $true) & (setextT = $true) & (omega0Ax = $true) & (doubleComplementI1 = $true) & (quantDeMorgan4 = $true) & (breln1unionEcases = $true) & (notdexE = $true) & (eqimpsubset2 = $true) & (setextAx = $true) & (image1Equiv = $true) & (ubforcartprodlem2 = $true) & (vacuousDall = $true) & (setminusIRneg = $true) & (breln1all2 = $true) & (replAx = $true) & (setminusSubset1 = $true) & (binunionIL = $true) & (setext = $true) & (contrasubsetT3 = $true) & (binunionLsub = $true) & (contrasubsetT = $true) & (setukpairinjL = $true) & (exuE2 = $true) & (iftrue = $true) & (setminusERneg = $true) & (woz2B = $true) & (setukpairinjR11 = $true) & (inComplementUnionImpInComplement1 = $true) & (setminusSubset2 = $true) & (cartprodmempaircEq = $true) & (binintersectLsub = $true) & (funcImageSingleton = $true) & (bs114d = $true) & (binintersectER = $true) & (inIntersectImpInIntersectUnions = $true) & (dpsetconstrSub = $true) & (kpairsurjEq = $true) & (breln1invE = $true) & (eqinunit = $true) & (injFuncSetFuncInj = $true) & (demorgan2b = $true) & (cartprodfstin = $true) & (funcGraphProp4 = $true) & (ex1I = $true) & (ap2p = $true) & (inComplementUnionImpNotIn1 = $true) & (image1Ex = $true) & (exuI2 = $true) & (notinself = $true) & (emptyset__Cong = $true) & (binunionEcases = $true) & (dpsetconstrEL2 = $true) & (cartprodpairmemER = $true) & (lam2p = $true) & (inCongP = $true) & (setukpairinjR1 = $true) & (prop2setE = $true) & (binunionRsub = $true) & (ifSingleton = $true) & (inPowerset = $true) & (woz2W = $true) & (iffalseProp1 = $true) & (ex1E1 = $true) & (setunionE2 = $true) & (funcext = $true) & (singletonsubset = $true) & (uniqinunit = $true) & (woz13rule2 = $true) & (notinsingleton = $true) & (woz1_4 = $true) & (setminusI = $true) & (powersetsubset = $true) & (complementSubsetComplementIntersect = $true) & (powerset__Cong = $true) & (dpsetconstrI = $true) & (inIntersectImpInUnion = $true) & (woz1_2 = $true) & (surjFuncSetFuncSurj = $true) & (subsetE = $true) & (quantDeMorgan1 = $true) & (iftrueorfalse = $true) & (theeq = $true) & (cartprodmempair1 = $true) & (wellorderingAx = $true) & (quantDeMorgan2 = $true) & (demorgan2 = $true) & (powersetI = $true) & (funcGraphProp2 = $true) & (setukpairinjR12 = $true) & (symdiffI2 = $true) & (setukpairinjR2 = $true) & (subsetI2 = $true) & (subsetemptysetimpeq = $true) & (emptyI = $true) & (setukpairinjL2 = $true) & (beta1 = $true) & (surjCantorThm = $true) & (setminusEL = $true) & (demorgan2b2 = $true) & (notinemptyset = $true) & (powersetAx = $true) & (notinself2 = $true) & (powersetTI1 = $true) & (binintersectRsub = $true) & (subbreln = $true) & (upairsetIL = $true) & (subsetE2 = $true) & (kpairp = $true) & (doubleComplementSub1 = $true) & (notsubsetI = $true) & (binintersectEL = $true) & (setOfPairsIsBReln = $true) & (doubleComplementEq = $true) & (iffalse = $true) & (notequalI2 = $true) & (emptysetsubset = $true) & (upairequniteq = $true) & (dsetconstrI = $true) & (setunionE = $true) & (nonemptyImpWitness = $true) & (powersetE1 = $true) & (binunionIR = $true) & (binunionTIRcontra = $true) & (setadjoinIR = $true) & (demorgan2a1 = $true) & (noeltsimpempty = $true) & (funcext2 = $true) & (ifp = $true) & (breln1all1 = $true) & (nonemptyI1 = $true) & (surjFuncSetFuncIn = $true) & (injFuncInInjFuncSet = $true) & (setadjoinAx = $true) & (ap2apEq1 = $true) & (symdiffE = $true) & (binintersectSubset5 = $true) & (powersetTE1 = $true) & (woz1_3 = $true) & (funcGraphProp3 = $true) & (symdiffI1 = $true) & (kfstsingleton = $true) & (setminusLsub = $true) & (iftrueProp2 = $true) & (breln1compE = $true) & (setminusER = $true) & (ex1E2 = $true) & (beta2 = $true) & (eta2 = $true) & (upairsubunion = $true) & (exuE1 = $true) & (ubforcartprodlem3 = $true) & (theprop = $true) & (binunionE = $true) & (emptysetimpfalse = $true) & (complementTcontraSubset = $true) & (brelnall1 = $true) & (upairset2IR = $true) & (binintTransitive = $true) & (prop2setI = $true) & (funcinfuncset = $true) & (infuncsetfunc = $true) & (breln1compprop = $true) & (setunionTransitive = $true) & (woz13rule4 = $true) & (nonemptyI = $true) & (descrp = $true) & (ksndpairEq = $true) & (woz13rule0 = $true) & (setextsub = $true) & (breln1invprop = $true) & (symdiffIneg1 = $true) & (powersetI1 = $true) & (setukpairinjL1 = $true) & (setunionsingleton2 = $true) & (exuI1 = $true) & (omegaSclos = $true) & (breln1unionCommutes = $true) & (singletonsuniq = $true) & (iftrueProp1 = $true) & (powersetE = $true) & (subsetTrans = $true) & (setoftrueEq = $true) & (woz1_5 = $true) & (image1E = $true) & (emptyinPowerset = $true) & (breln1unionIR = $true) & (exu__Cong = $true) & (upairinpowunion = $true) & (emptyinunitempty = $true) & (contraSubsetComplement = $true) & (foundation2 = $true) & (emptyE1 = $true) & (dsetconstr__Cong = $true) & (singletoninpowunion = $true) & (intersectInPowersetIntersectUnions = $true) & (setunionI = $true) & (setadjoinSub2 = $true) & (setOfPairsIsBReln1 = $true) & (setukpairIL = $true) & (setbeta = $true) & (brelnall2 = $true) & (subset2powerset = $true) & (contrasubsetT2 = $true) & (setadjoinOr = $true) & (breln1SetBreln1 = $true) & (cartprodmempair = $true) & (lamProp = $true) & (subPowSU = $true) & (setadjoinSub = $true) & (binintersectT_lem = $true) & (setadjoin__Cong = $true) & (binintersectTELcontra = $true) & (emptysetAx = $true) & (transitivesetOp2 = $true) & (complementUnionInPowersetComplement = $true) & (iffalseProp2 = $true) & (descr__Cong = $true) & (symdiffIneg2 = $true) & (demorgan1a = $true) & (breln1invI = $true) & (binintersectI = $true) & (demorgan1 = $true) & (leftInvIsSurj = $true) & (notequalI1 = $true) & (setminusT_lem = $true) & (peano0notS = $true) & (binunionT_lem = $true) & (complementImpComplementIntersect = $true) & (emptyInPowerset = $true) & (setunionsingleton = $true) & (demorgan2a = $true) & (eta1 = $true) & (eqimpsubset1 = $true) & (disjointsetsI1 = $true) & (binunionTILcontra = $true) & (subsetTI = $true) & (breln1unionIL = $true) & (singletonsswitch = $true) & (eqbreln1 = $true) & (quantDeMorgan3 = $true) & (dpsetconstrER = $true) & (setukpairinjR = $true) & (kpairiskpair = $true) & (emptysetE = $true) & (cartprodsndin = $true) & (setunion__Cong = $true) & (exuE3e = $true) & (setadjoinE = $true) & (complementTI1 = $true) & (omegaIndAx = $true) & (breln1compEex = $true) & (injFuncSetFuncIn = $true) & (prop2set2propI = $true) & (binintersectTERcontra = $true) & (complementTnotintersectT = $true) & (dpsetconstrEL1 = $true) & (subbreln1 = $true) & (image1Ex1 = $true) & (breln1unionprop = $true) & (complementT_lem = $true) & (app = $true) & (omegaSp = $true) & (upairset2E = $true) & (demorgan1b = $true) & (choice2fnsingleton = $true) & (ubforcartprodlem1 = $true) & (binunionTE = $true) & (powersetT_lem = $true) & (woz13rule1 = $true) & (demorgan2a2 = $true) & (binintersectSubset2 = $true) & (setminusELneg = $true) & (cartprodpairmemEL = $true) & (in__Cong = $true)),
% 9.84/2.82 inference(flattening,[status(thm)],[f1359])).
% 9.84/2.82 thf(f1359,plain,(
% 9.84/2.82 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i] : (($true = (ordinal @ X0)) & ? [X1 : $i] : (($true != (transitiveset @ (binintersect @ X0 @ X1))) & ($true = (ordinal @ X1)))) & (setunionTransitive = $true)) & (transitivesetOp2 = $true)) & (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)),
% 9.84/2.82 inference(ennf_transformation,[status(thm)],[f971])).
% 9.84/2.82 thf(f971,plain,(
% 9.84/2.82 ~((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) => ((transitivesetOp2 = $true) => ((setunionTransitive = $true) => ! [X0 : $i] : (($true = (ordinal @ X0)) => ! [X1 : $i] : (($true = (ordinal @ X1)) => ($true = (transitiveset @ (binintersect @ X0 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 9.84/2.82 inference(fool_elimination,[status(thm)],[f970])).
% 9.84/2.82 thf(f970,plain,(
% 9.84/2.82 ~(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 => (transitivesetOp2 => (setunionTransitive => ! [X0 : $i] : ((ordinal @ X0) => ! [X1 : $i] : ((ordinal @ X1) => (transitiveset @ (binintersect @ X0 @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 9.84/2.82 inference(rectify,[status(thm)],[f340])).
% 9.84/2.82 thf(f340,negated_conjecture,(
% 9.84/2.82 ~(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 => (transitivesetOp2 => (setunionTransitive => ! [X11 : $i] : ((ordinal @ X11) => ! [X16 : $i] : ((ordinal @ X16) => (transitiveset @ (binintersect @ X11 @ X16))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 9.84/2.82 inference(negated_conjecture,[status(cth)],[f339])).
% 9.84/2.82 thf(f339,conjecture,(
% 9.84/2.82 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 => (transitivesetOp2 => (setunionTransitive => ! [X11 : $i] : ((ordinal @ X11) => ! [X16 : $i] : ((ordinal @ X16) => (transitiveset @ (binintersect @ X11 @ X16)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 9.84/2.82 file('/export/starexec/sandbox/tmp/tmp.SkoTPvEhFx/DTF2THF_24321.p',ordinalMinLem1)).
% 9.84/2.82 thf(f9786,plain,(
% 9.84/2.82 ((subset @ sK1190 @ sK980) != $true) | spl1189_219),
% 9.84/2.82 inference(avatar_component_clause,[status(thm)],[f9785])).
% 9.84/2.82 thf(f9785,definition,(
% 9.84/2.82 spl1189_219 <=> ((subset @ sK1190 @ sK980) = $true)),
% 9.84/2.82 introduced(definition,[new_symbols(naming,[spl1189_219])],[avatar_definition])).
% 9.84/2.82 thf(f8933,plain,(
% 9.84/2.82 ((in @ sK1190 @ sK980) = $true)),
% 9.84/2.82 inference(trivial_inequality_removal,[status(thm)],[f8925])).
% 9.84/2.82 thf(f8925,plain,(
% 9.84/2.82 ((in @ sK1190 @ sK980) = $true) | ($true != $true)),
% 9.84/2.82 inference(superposition,[status(thm)],[f7304,f6846])).
% 9.84/2.82 thf(f6846,plain,(
% 9.84/2.82 ($true = (in @ sK1190 @ (binintersect @ sK980 @ sK981)))),
% 9.84/2.82 inference(binary_proxy_clausification,[status(thm)],[f6844])).
% 9.84/2.82 thf(f6844,plain,(
% 9.84/2.82 ($false = ((in @ sK1190 @ (binintersect @ sK980 @ sK981)) => (subset @ sK1190 @ (binintersect @ sK980 @ sK981))))),
% 9.84/2.82 inference(beta_eta_normalization,[status(thm)],[f6843])).
% 9.84/2.82 thf(f6843,plain,(
% 9.84/2.82 ($false = ((^[Y0 : $i]: ((in @ Y0 @ (binintersect @ sK980 @ sK981)) => (subset @ Y0 @ (binintersect @ sK980 @ sK981)))) @ sK1190))),
% 9.84/2.82 inference(sigma_clausification,[status(thm)],[f6842])).
% 9.84/2.82 thf(f6842,plain,(
% 9.84/2.82 ($true != (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (binintersect @ sK980 @ sK981)) => (subset @ Y0 @ (binintersect @ sK980 @ sK981))))))),
% 9.84/2.82 inference(beta_eta_normalization,[status(thm)],[f6529])).
% 9.84/2.82 thf(f6529,plain,(
% 9.84/2.82 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))) @ (binintersect @ sK980 @ sK981)) != $true)),
% 9.84/2.82 inference(definition_unfolding,[status(thm)],[f5200,f5320])).
% 9.84/2.82 thf(f5200,plain,(
% 9.84/2.82 ((transitiveset @ (binintersect @ sK980 @ sK981)) != $true)),
% 9.84/2.82 inference(cnf_transformation,[status(thm)],[f3188])).
% 9.84/2.82 thf(f7304,plain,(
% 9.84/2.82 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X3 @ (binintersect @ X5 @ X4))) | ($true = (in @ X3 @ X5))) )),
% 9.84/2.82 inference(trivial_inequality_removal,[status(thm)],[f5774])).
% 9.84/2.82 thf(f5774,plain,(
% 9.84/2.82 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X3 @ (binintersect @ X5 @ X4))) | ($true != $true) | ($true = (in @ X3 @ X5))) )),
% 9.84/2.82 inference(definition_unfolding,[status(thm)],[f3803,f5069])).
% 9.84/2.82 thf(f5069,plain,(
% 9.84/2.82 (binintersectEL = $true)),
% 9.84/2.82 inference(cnf_transformation,[status(thm)],[f3188])).
% 9.84/2.82 thf(f3803,plain,(
% 9.84/2.82 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X3 @ (binintersect @ X5 @ X4))) | ($true = (in @ X3 @ X5)) | (binintersectEL != $true)) )),
% 9.84/2.82 inference(cnf_transformation,[status(thm)],[f1960])).
% 9.84/2.82 thf(f1960,plain,(
% 9.84/2.82 ((binintersectEL = $true) | (($true = (in @ sK288 @ (binintersect @ sK290 @ sK289))) & ($true != (in @ sK288 @ sK290)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X3 @ (binintersect @ X5 @ X4))) | ($true = (in @ X3 @ X5))) | (binintersectEL != $true))),
% 9.84/2.82 inference(skolemisation,[status(esa),new_symbols(skolem,[sK288,sK289,sK290])],[f1958,f1959])).
% 9.84/2.82 thf(f1959,plain,(
% 9.84/2.82 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (binintersect @ X2 @ X1))) & ($true != (in @ X0 @ X2))) => (($true = (in @ sK288 @ (binintersect @ sK290 @ sK289))) & ($true != (in @ sK288 @ sK290)))),
% 9.84/2.82 introduced(definition,[],[choice_axiom])).
% 9.84/2.82 thf(f1958,plain,(
% 9.84/2.82 ((binintersectEL = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (binintersect @ X2 @ X1))) & ($true != (in @ X0 @ X2)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X3 @ (binintersect @ X5 @ X4))) | ($true = (in @ X3 @ X5))) | (binintersectEL != $true))),
% 9.84/2.82 inference(rectify,[status(thm)],[f1957])).
% 9.84/2.82 thf(f1957,plain,(
% 9.84/2.82 ((binintersectEL = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (binintersect @ X2 @ X1))) & ($true != (in @ X0 @ X2)))) & (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ (binintersect @ X2 @ X1))) | ($true = (in @ X0 @ X2))) | (binintersectEL != $true))),
% 9.84/2.82 inference(nnf_transformation,[status(thm)],[f1277])).
% 9.84/2.82 thf(f1277,plain,(
% 9.84/2.82 (binintersectEL = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ (binintersect @ X2 @ X1))) | ($true = (in @ X0 @ X2)))),
% 9.84/2.82 inference(ennf_transformation,[status(thm)],[f789])).
% 9.84/2.82 thf(f789,plain,(
% 9.84/2.82 (binintersectEL = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (binintersect @ X2 @ X1))) => ($true = (in @ X0 @ X2)))),
% 9.84/2.82 inference(fool_elimination,[status(thm)],[f788])).
% 9.84/2.82 thf(f788,plain,(
% 9.84/2.82 (binintersectEL = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (binintersect @ X2 @ X1)) => (in @ X0 @ X2)))),
% 9.84/2.82 inference(rectify,[status(thm)],[f110])).
% 9.84/2.82 thf(f110,axiom,(
% 9.84/2.82 (binintersectEL = ! [X1 : $i,X4 : $i,X3 : $i] : ((in @ X1 @ (binintersect @ X3 @ X4)) => (in @ X1 @ X3)))),
% 9.84/2.82 file('/export/starexec/sandbox/tmp/tmp.SkoTPvEhFx/DTF2THF_24321.p',binintersectEL)).
% 9.84/2.82 thf(f10357,plain,(
% 9.84/2.82 spl1189_218),
% 9.84/2.82 inference(avatar_contradiction_clause,[status(thm)],[f10356])).
% 9.84/2.82 thf(f10356,plain,(
% 9.84/2.82 $false | spl1189_218),
% 9.84/2.82 inference(trivial_inequality_removal,[status(thm)],[f10346])).
% 9.84/2.82 thf(f10346,plain,(
% 9.84/2.82 ($false = $true) | spl1189_218),
% 9.84/2.82 inference(backward_demodulation,[status(thm)],[f8876,f10323])).
% 9.84/2.82 thf(f10323,plain,(
% 9.84/2.82 ((in @ sK1190 @ sK981) = $false) | spl1189_218),
% 9.84/2.82 inference(trivial_inequality_removal,[status(thm)],[f10317])).
% 9.84/2.82 thf(f10317,plain,(
% 9.84/2.82 ((in @ sK1190 @ sK981) = $false) | ($true != $true) | spl1189_218),
% 9.84/2.82 inference(superposition,[status(thm)],[f9783,f7141])).
% 9.84/2.82 thf(f7141,plain,(
% 9.84/2.82 ( ! [X1 : $i] : (($true = (subset @ X1 @ sK981)) | ($false = (in @ X1 @ sK981))) )),
% 9.84/2.82 inference(binary_proxy_clausification,[status(thm)],[f7140])).
% 9.84/2.82 thf(f7140,plain,(
% 9.84/2.82 ( ! [X1 : $i] : (($true = ((in @ X1 @ sK981) => (subset @ X1 @ sK981)))) )),
% 9.84/2.82 inference(beta_eta_normalization,[status(thm)],[f7139])).
% 9.84/2.82 thf(f7139,plain,(
% 9.84/2.82 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ sK981) => (subset @ Y0 @ sK981))) @ X1))) )),
% 9.84/2.82 inference(pi_clausification,[status(thm)],[f7137])).
% 9.84/2.82 thf(f7137,plain,(
% 9.84/2.82 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK981) => (subset @ Y0 @ sK981)))))),
% 9.84/2.82 inference(binary_proxy_clausification,[status(thm)],[f7136])).
% 9.84/2.82 thf(f7136,plain,(
% 9.84/2.82 (((wellorderedByIn @ sK981) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK981) => (subset @ Y0 @ sK981))))) = $true)),
% 9.84/2.82 inference(beta_eta_normalization,[status(thm)],[f6530])).
% 9.84/2.82 thf(f6530,plain,(
% 9.84/2.82 (((^[Y0 : $i]: ((wellorderedByIn @ Y0) & ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (subset @ Y2 @ Y1))))) @ Y0))) @ sK981) = $true)),
% 9.84/2.82 inference(definition_unfolding,[status(thm)],[f5199,f5551])).
% 9.84/2.82 thf(f5199,plain,(
% 9.84/2.82 ((ordinal @ sK981) = $true)),
% 9.84/2.82 inference(cnf_transformation,[status(thm)],[f3188])).
% 9.84/2.82 thf(f9783,plain,(
% 9.84/2.82 ($true != (subset @ sK1190 @ sK981)) | spl1189_218),
% 9.84/2.82 inference(avatar_component_clause,[status(thm)],[f9782])).
% 9.84/2.82 thf(f9782,definition,(
% 9.84/2.82 spl1189_218 <=> ($true = (subset @ sK1190 @ sK981))),
% 9.84/2.82 introduced(definition,[new_symbols(naming,[spl1189_218])],[avatar_definition])).
% 9.84/2.82 thf(f8876,plain,(
% 9.84/2.82 ((in @ sK1190 @ sK981) = $true)),
% 9.84/2.82 inference(trivial_inequality_removal,[status(thm)],[f8870])).
% 9.84/2.82 thf(f8870,plain,(
% 9.84/2.82 ((in @ sK1190 @ sK981) = $true) | ($true != $true)),
% 9.84/2.82 inference(superposition,[status(thm)],[f7072,f6846])).
% 9.84/2.82 thf(f7072,plain,(
% 9.84/2.82 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (binintersect @ X3 @ X4)) != $true) | ((in @ X5 @ X4) = $true)) )),
% 9.84/2.82 inference(trivial_inequality_removal,[status(thm)],[f6218])).
% 9.84/2.82 thf(f6218,plain,(
% 9.84/2.82 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != $true) | ((in @ X5 @ (binintersect @ X3 @ X4)) != $true) | ((in @ X5 @ X4) = $true)) )),
% 9.84/2.82 inference(definition_unfolding,[status(thm)],[f4426,f5146])).
% 9.84/2.82 thf(f5146,plain,(
% 9.84/2.82 (binintersectER = $true)),
% 9.84/2.82 inference(cnf_transformation,[status(thm)],[f3188])).
% 9.84/2.82 thf(f4426,plain,(
% 9.84/2.82 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X4) = $true) | ((in @ X5 @ (binintersect @ X3 @ X4)) != $true) | (binintersectER != $true)) )),
% 9.84/2.82 inference(cnf_transformation,[status(thm)],[f2660])).
% 9.84/2.82 thf(f2660,plain,(
% 9.84/2.82 ((binintersectER = $true) | (((in @ sK696 @ sK695) != $true) & ($true = (in @ sK696 @ (binintersect @ sK694 @ sK695))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X4) = $true) | ((in @ X5 @ (binintersect @ X3 @ X4)) != $true)) | (binintersectER != $true))),
% 9.84/2.82 inference(skolemisation,[status(esa),new_symbols(skolem,[sK694,sK695,sK696])],[f2658,f2659])).
% 9.84/2.82 thf(f2659,plain,(
% 9.84/2.82 ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X2 @ X1)) & ((in @ X2 @ (binintersect @ X0 @ X1)) = $true)) => (((in @ sK696 @ sK695) != $true) & ($true = (in @ sK696 @ (binintersect @ sK694 @ sK695))))),
% 9.84/2.82 introduced(definition,[],[choice_axiom])).
% 9.84/2.82 thf(f2658,plain,(
% 9.84/2.82 ((binintersectER = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X2 @ X1)) & ((in @ X2 @ (binintersect @ X0 @ X1)) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X4) = $true) | ((in @ X5 @ (binintersect @ X3 @ X4)) != $true)) | (binintersectER != $true))),
% 9.84/2.82 inference(rectify,[status(thm)],[f2657])).
% 9.84/2.82 thf(f2657,plain,(
% 9.84/2.82 ((binintersectER = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X2 @ X1)) & ((in @ X2 @ (binintersect @ X0 @ X1)) = $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ X1)) | ((in @ X2 @ (binintersect @ X0 @ X1)) != $true)) | (binintersectER != $true))),
% 9.84/2.82 inference(nnf_transformation,[status(thm)],[f1204])).
% 9.84/2.82 thf(f1204,plain,(
% 9.84/2.82 (binintersectER = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ X1)) | ((in @ X2 @ (binintersect @ X0 @ X1)) != $true))),
% 9.84/2.82 inference(ennf_transformation,[status(thm)],[f903])).
% 9.84/2.82 thf(f903,plain,(
% 9.84/2.82 (binintersectER = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (binintersect @ X0 @ X1)) = $true) => ($true = (in @ X2 @ X1)))),
% 9.84/2.82 inference(fool_elimination,[status(thm)],[f902])).
% 9.84/2.82 thf(f902,plain,(
% 9.84/2.82 (binintersectER = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X1)))),
% 9.84/2.82 inference(rectify,[status(thm)],[f114])).
% 9.84/2.82 thf(f114,axiom,(
% 9.84/2.82 (binintersectER = ! [X3 : $i,X4 : $i,X1 : $i] : ((in @ X1 @ (binintersect @ X3 @ X4)) => (in @ X1 @ X4)))),
% 9.84/2.82 file('/export/starexec/sandbox/tmp/tmp.SkoTPvEhFx/DTF2THF_24321.p',binintersectER)).
% 9.84/2.82 thf(f9788,plain,(
% 9.84/2.82 ~spl1189_218 | ~spl1189_219),
% 9.84/2.82 inference(avatar_split_clause,[status(thm)],[f9777,f9785,f9782])).
% 9.84/2.82 thf(f9777,plain,(
% 9.84/2.82 ($true != (subset @ sK1190 @ sK981)) | ((subset @ sK1190 @ sK980) != $true)),
% 9.84/2.82 inference(trivial_inequality_removal,[status(thm)],[f9772])).
% 9.84/2.82 thf(f9772,plain,(
% 9.84/2.82 ($true != (subset @ sK1190 @ sK981)) | ((subset @ sK1190 @ sK980) != $true) | ($false = $true)),
% 9.84/2.82 inference(superposition,[status(thm)],[f6845,f6933])).
% 9.84/2.82 thf(f6933,plain,(
% 9.84/2.82 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (subset @ X1 @ (binintersect @ X0 @ X2))) | ($true != (subset @ X1 @ X0)) | ((subset @ X1 @ X2) != $true)) )),
% 9.84/2.82 inference(trivial_inequality_removal,[status(thm)],[f5765])).
% 9.84/2.82 thf(f5765,plain,(
% 9.84/2.82 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (subset @ X1 @ (binintersect @ X0 @ X2))) | ((subset @ X1 @ X2) != $true) | ($true != (subset @ X1 @ X0)) | ($true != $true)) )),
% 9.84/2.82 inference(definition_unfolding,[status(thm)],[f3799,f5044])).
% 9.84/2.82 thf(f5044,plain,(
% 9.84/2.82 (binintersectSubset5 = $true)),
% 9.84/2.82 inference(cnf_transformation,[status(thm)],[f3188])).
% 9.84/2.82 thf(f3799,plain,(
% 9.84/2.82 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ X1 @ X2) != $true) | ($true = (subset @ X1 @ (binintersect @ X0 @ X2))) | ($true != (subset @ X1 @ X0)) | (binintersectSubset5 != $true)) )),
% 9.84/2.82 inference(cnf_transformation,[status(thm)],[f1952])).
% 9.84/2.82 thf(f1952,plain,(
% 9.84/2.82 (! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ X2) != $true) | ($true = (subset @ X1 @ (binintersect @ X0 @ X2))) | ($true != (subset @ X1 @ X0))) | (binintersectSubset5 != $true)) & ((binintersectSubset5 = $true) | (($true = (subset @ sK284 @ sK285)) & ($true != (subset @ sK284 @ (binintersect @ sK283 @ sK285))) & ($true = (subset @ sK284 @ sK283))))),
% 9.84/2.82 inference(skolemisation,[status(esa),new_symbols(skolem,[sK283,sK284,sK285])],[f1950,f1951])).
% 9.84/2.82 thf(f1951,plain,(
% 9.84/2.82 ? [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X4 @ X5) = $true) & ((subset @ X4 @ (binintersect @ X3 @ X5)) != $true) & ((subset @ X4 @ X3) = $true)) => (($true = (subset @ sK284 @ sK285)) & ($true != (subset @ sK284 @ (binintersect @ sK283 @ sK285))) & ($true = (subset @ sK284 @ sK283)))),
% 9.84/2.82 introduced(definition,[],[choice_axiom])).
% 9.84/2.82 thf(f1950,plain,(
% 9.84/2.82 (! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ X2) != $true) | ($true = (subset @ X1 @ (binintersect @ X0 @ X2))) | ($true != (subset @ X1 @ X0))) | (binintersectSubset5 != $true)) & ((binintersectSubset5 = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X4 @ X5) = $true) & ((subset @ X4 @ (binintersect @ X3 @ X5)) != $true) & ((subset @ X4 @ X3) = $true)))),
% 9.84/2.82 inference(rectify,[status(thm)],[f1949])).
% 9.84/2.82 thf(f1949,plain,(
% 9.84/2.82 (! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ X2) != $true) | ($true = (subset @ X1 @ (binintersect @ X0 @ X2))) | ($true != (subset @ X1 @ X0))) | (binintersectSubset5 != $true)) & ((binintersectSubset5 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ X2) = $true) & ($true != (subset @ X1 @ (binintersect @ X0 @ X2))) & ($true = (subset @ X1 @ X0))))),
% 9.84/2.82 inference(nnf_transformation,[status(thm)],[f1102])).
% 9.84/2.82 thf(f1102,plain,(
% 9.84/2.82 ! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ X2) != $true) | ($true = (subset @ X1 @ (binintersect @ X0 @ X2))) | ($true != (subset @ X1 @ X0))) <=> (binintersectSubset5 = $true)),
% 9.84/2.82 inference(flattening,[status(thm)],[f1101])).
% 9.84/2.82 thf(f1101,plain,(
% 9.84/2.82 ! [X0 : $i,X1 : $i,X2 : $i] : ((($true = (subset @ X1 @ (binintersect @ X0 @ X2))) | ((subset @ X1 @ X2) != $true)) | ($true != (subset @ X1 @ X0))) <=> (binintersectSubset5 = $true)),
% 9.84/2.82 inference(ennf_transformation,[status(thm)],[f551])).
% 9.84/2.82 thf(f551,plain,(
% 9.84/2.82 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (subset @ X1 @ X0)) => (((subset @ X1 @ X2) = $true) => ($true = (subset @ X1 @ (binintersect @ X0 @ X2))))) <=> (binintersectSubset5 = $true)),
% 9.84/2.82 inference(fool_elimination,[status(thm)],[f550])).
% 9.84/2.82 thf(f550,plain,(
% 9.84/2.82 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X0) => ((subset @ X1 @ X2) => (subset @ X1 @ (binintersect @ X0 @ X2)))) = binintersectSubset5)),
% 9.84/2.82 inference(rectify,[status(thm)],[f109])).
% 9.84/2.82 thf(f109,axiom,(
% 9.84/2.82 (! [X3 : $i,X5 : $i,X4 : $i] : ((subset @ X5 @ X3) => ((subset @ X5 @ X4) => (subset @ X5 @ (binintersect @ X3 @ X4)))) = binintersectSubset5)),
% 9.84/2.82 file('/export/starexec/sandbox/tmp/tmp.SkoTPvEhFx/DTF2THF_24321.p',binintersectSubset5)).
% 9.84/2.82 thf(f6845,plain,(
% 9.84/2.82 ((subset @ sK1190 @ (binintersect @ sK980 @ sK981)) = $false)),
% 9.84/2.82 inference(binary_proxy_clausification,[status(thm)],[f6844])).
% 9.84/2.82 % SZS output end Proof for DTF2THF_24321
% 9.84/2.82 % (24744)------------------------------
% 9.84/2.82 % (24744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.84/2.82 % (24744)Termination reason: Refutation
% 9.84/2.82
% 9.84/2.82 % (24744)Memory used [KB]: 13560
% 9.84/2.82 % (24744)Time elapsed: 0.346 s
% 9.84/2.82 % (24744)Instructions burned: 1096 (million)
% 9.84/2.82 % (24744)------------------------------
% 9.84/2.82 % (24744)------------------------------
% 9.84/2.82 % (24622)Success in time 1.197 s
%------------------------------------------------------------------------------