%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU597^1 : 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 : n022.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 09:35:30 AM UTC 2026
% Result : Theorem 15.26s 3.43s
% Output : Refutation 15.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 14
% Syntax : Number of formulae : 91 ( 20 unt; 0 typ; 9 def)
% Number of atoms : 2225 ( 563 equ; 0 cnn)
% Maximal formula atoms : 114 ( 24 avg)
% Number of connectives : 1444 ( 69 ~; 84 |; 339 &; 409 @)
% ( 11 <=>; 489 =>; 0 <=; 0 <~>)
% Maximal formula depth : 121 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 685 ( 681 usr; 128 con; 0-4 aty)
% ( 43 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 126 ( 51 ^; 69 !; 6 ?; 126 :)
% 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_155,type,
sK7: ( $i > $o ) > $i ).
thf(func_def_156,type,
sK8: ( $i > $o ) > $i ).
thf(func_def_157,type,
sK9: $i > $o ).
thf(func_def_173,type,
sK25: $i > ( $i > $o ) > $i ).
thf(func_def_175,type,
sK27: $i > $o ).
thf(func_def_182,type,
sK34: $i > $o ).
thf(func_def_184,type,
sK36: $i > $o ).
thf(func_def_191,type,
sK43: $i > $i > $i ).
thf(func_def_198,type,
sK50: ( $i > $o ) > $i ).
thf(func_def_199,type,
sK51: $i > $o ).
thf(func_def_200,type,
sK52: $i > $i ).
thf(func_def_201,type,
sK53: $i > $o ).
thf(func_def_206,type,
sK58: $i > $i ).
thf(func_def_209,type,
sK61: $i > $i ).
thf(func_def_219,type,
sK71: ( $i > $o ) > $i ).
thf(func_def_220,type,
sK72: $i > $o ).
thf(func_def_221,type,
sK73: $i > $i ).
thf(func_def_222,type,
sK74: ( $i > $o ) > $i ).
thf(func_def_223,type,
sK75: $i > $o ).
thf(func_def_224,type,
sK76: $i > $i > $i ).
thf(func_def_232,type,
sK84: ( $i > $o ) > $i > $i ).
thf(func_def_233,type,
sK85: $i > $o ).
thf(func_def_236,type,
sK88: $o > $i > $i > $i ).
thf(func_def_240,type,
sK92: $i > $i > $i ).
thf(func_def_247,type,
sK99: $i > $o ).
thf(func_def_251,type,
sK103: $i > $i > $i ).
thf(func_def_254,type,
sK106: $i > $o ).
thf(func_def_268,type,
sK120: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_269,type,
sK121: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_270,type,
sK122: $i > $o ).
thf(func_def_271,type,
sK123: $i > $o ).
thf(func_def_272,type,
sK124: $i > $i > $i ).
thf(func_def_273,type,
sK125: $i > $i > $i ).
thf(func_def_277,type,
sK129: $i > $o ).
thf(func_def_285,type,
sK137: $i > $i ).
thf(func_def_286,type,
sK138: $i > $i > $i > $i ).
thf(func_def_287,type,
sK139: $i > $i > $i ).
thf(func_def_288,type,
sK140: $i > $i > $i ).
thf(func_def_289,type,
sK141: $i > $i > $i ).
thf(func_def_290,type,
sK142: $i > $i > $i ).
thf(func_def_292,type,
sK144: $i > $i ).
thf(func_def_293,type,
sK145: $i > $i ).
thf(func_def_294,type,
sK146: $i > $i ).
thf(func_def_295,type,
sK147: $i > $i ).
thf(func_def_296,type,
sK148: $i > $i ).
thf(func_def_297,type,
sK149: $i > $i ).
thf(func_def_298,type,
sK150: $i > $i ).
thf(func_def_299,type,
sK151: $i > $i ).
thf(func_def_300,type,
sK152: $i > $i ).
thf(func_def_301,type,
sK153: $i > $i ).
thf(func_def_302,type,
sK154: $i > $i ).
thf(func_def_303,type,
sK155: $i > $i ).
thf(func_def_304,type,
sK156: $i > $i ).
thf(func_def_305,type,
sK157: $i > $i ).
thf(func_def_306,type,
sK158: $i > $i ).
thf(func_def_307,type,
sK159: $i > $i ).
thf(func_def_308,type,
sK160: $i > $i ).
thf(func_def_309,type,
sK161: $i > $i ).
thf(func_def_310,type,
sK162: $i > $i ).
thf(func_def_311,type,
sK163: $i > $i ).
thf(func_def_312,type,
sK164: $i > $i ).
thf(func_def_313,type,
sK165: $i > $i ).
thf(func_def_314,type,
sK166: $i > $i ).
thf(func_def_315,type,
sK167: $i > $i ).
thf(func_def_316,type,
sK168: $i > $i ).
thf(func_def_317,type,
sK169: $i > $i ).
thf(func_def_318,type,
sK170: $i > $i ).
thf(func_def_319,type,
sK171: $i > $i ).
thf(func_def_320,type,
sK172: $i > $i ).
thf(func_def_321,type,
sK173: $i > $i ).
thf(func_def_322,type,
sK174: $i > $i ).
thf(func_def_323,type,
sK175: $i > $i ).
thf(func_def_324,type,
sK176: $i > $i ).
thf(func_def_325,type,
sK177: $i > $i ).
thf(func_def_326,type,
sK178: $i > $i ).
thf(func_def_327,type,
sK179: $i > $i ).
thf(func_def_328,type,
sK180: $i > $i ).
thf(func_def_329,type,
sK181: $i > $i ).
thf(func_def_330,type,
sK182: $i > $i ).
thf(func_def_331,type,
sK183: $i > $i ).
thf(func_def_332,type,
sK184: $i > $i ).
thf(func_def_333,type,
sK185: $i > $i ).
thf(func_def_334,type,
sK186: $i > $i ).
thf(func_def_335,type,
sK187: $i > $i ).
thf(func_def_336,type,
sK188: $i > $i ).
thf(func_def_337,type,
sK189: $i > $i ).
thf(func_def_338,type,
sK190: $i > $i ).
thf(func_def_339,type,
sK191: $i > $i ).
thf(func_def_340,type,
sK192: $i > $i ).
thf(func_def_341,type,
sK193: $i > $i ).
thf(func_def_342,type,
sK194: $i > $i ).
thf(func_def_343,type,
sK195: $i > $i ).
thf(func_def_344,type,
sK196: $i > $i ).
thf(func_def_345,type,
sK197: $i > $i ).
thf(func_def_346,type,
sK198: $i > $i ).
thf(func_def_347,type,
sK199: $i > $i ).
thf(func_def_348,type,
sK200: $i > $i ).
thf(func_def_349,type,
sK201: $i > $i ).
thf(func_def_350,type,
sK202: $i > $i ).
thf(func_def_351,type,
sK203: $i > $i ).
thf(func_def_352,type,
sK204: $i > $i ).
thf(func_def_353,type,
sK205: $i > $i ).
thf(func_def_354,type,
sK206: $i > $i ).
thf(func_def_355,type,
sK207: $i > $i ).
thf(func_def_356,type,
sK208: $i > $i ).
thf(func_def_357,type,
sK209: $i > $i ).
thf(func_def_358,type,
sK210: $i > $i ).
thf(func_def_359,type,
sK211: $i > $i ).
thf(func_def_360,type,
sK212: $i > $i ).
thf(func_def_361,type,
sK213: $i > $i ).
thf(func_def_362,type,
sK214: $i > $i ).
thf(func_def_363,type,
sK215: $i > $i ).
thf(func_def_364,type,
sK216: $i > $i ).
thf(func_def_365,type,
sK217: $i > $i ).
thf(func_def_366,type,
sK218: $i > $i ).
thf(func_def_367,type,
sK219: $i > $i ).
thf(func_def_368,type,
sK220: $i > $i ).
thf(func_def_369,type,
sK221: $i > $i ).
thf(func_def_370,type,
sK222: $i > $i ).
thf(func_def_371,type,
sK223: $i > $i ).
thf(func_def_372,type,
sK224: $i > $i ).
thf(func_def_373,type,
sK225: $i > $i ).
thf(func_def_374,type,
sK226: $i > $i ).
thf(func_def_375,type,
sK227: $i > $i ).
thf(func_def_376,type,
sK228: $i > $i ).
thf(func_def_377,type,
sK229: $i > $i ).
thf(func_def_378,type,
sK230: $i > $i ).
thf(func_def_379,type,
sK231: $i > $i ).
thf(func_def_380,type,
sK232: $i > $i ).
thf(func_def_381,type,
sK233: $i > $i ).
thf(func_def_382,type,
sK234: $i > $i ).
thf(func_def_383,type,
sK235: $i > $i ).
thf(func_def_384,type,
sK236: $i > $i ).
thf(func_def_385,type,
sK237: $i > $i ).
thf(func_def_386,type,
sK238: $i > $i ).
thf(func_def_387,type,
sK239: $i > $i ).
thf(func_def_388,type,
sK240: $i > $i ).
thf(func_def_389,type,
sK241: $i > $i ).
thf(func_def_390,type,
sK242: $i > $i ).
thf(func_def_391,type,
sK243: $i > $i ).
thf(func_def_392,type,
sK244: $i > $i ).
thf(func_def_393,type,
sK245: $i > $i ).
thf(func_def_394,type,
sK246: $i > $i > $i ).
thf(func_def_395,type,
sK247: $i > $i > $i > $i ).
thf(func_def_396,type,
sK248: $i > $i > $i > $i ).
thf(func_def_397,type,
sK249: $i > $i > $i > $i ).
thf(func_def_398,type,
sK250: $i > $i > $i > $i ).
thf(func_def_399,type,
sK251: $i > $i > $i ).
thf(func_def_400,type,
sK252: $i > $i > $i ).
thf(func_def_401,type,
sK253: $i > $i > $i > $i ).
thf(func_def_402,type,
sK254: $i > $i > $i > $i ).
thf(func_def_403,type,
sK255: $i > $i ).
thf(func_def_404,type,
sK256: $i > $i > $i ).
thf(func_def_405,type,
sK257: $i > $i > $i > $i ).
thf(func_def_406,type,
sK258: $i > $i > $i > $i ).
thf(func_def_407,type,
sK259: $i > $i > $i > $i ).
thf(func_def_408,type,
sK260: $i > $i > $i > $i ).
thf(func_def_409,type,
sK261: $i > $i > $i ).
thf(func_def_410,type,
sK262: $i > $i > $i > $i ).
thf(func_def_411,type,
sK263: $i > $i > $i > $i ).
thf(func_def_412,type,
sK264: $i > $i > $i > $i ).
thf(func_def_413,type,
sK265: $i > $i > $i > $i ).
thf(func_def_414,type,
sK266: $i > $i > $i ).
thf(func_def_415,type,
sK267: $i > $i > $i ).
thf(func_def_416,type,
sK268: $i > $i > $i > $i ).
thf(func_def_417,type,
sK269: $i > $i > $i > $i ).
thf(func_def_418,type,
sK270: $i > $i > $i ).
thf(func_def_419,type,
sK271: $i > $i > $i > $i ).
thf(func_def_420,type,
sK272: $i > $i > $i > $i ).
thf(func_def_421,type,
sK273: $i > $i > $i > $i ).
thf(func_def_422,type,
sK274: $i > $i > $i > $i ).
thf(func_def_423,type,
sK275: $i > $i ).
thf(func_def_424,type,
sK276: $i > $i ).
thf(func_def_425,type,
sK277: $i > $i > $i ).
thf(func_def_426,type,
sK278: $i > $i > $i > $i ).
thf(func_def_427,type,
sK279: $i > $i > $i > $i ).
thf(func_def_428,type,
sK280: $i > $i > $i > $i ).
thf(func_def_429,type,
sK281: $i > $i > $i ).
thf(func_def_430,type,
sK282: $i > $i > $i > $i ).
thf(func_def_431,type,
sK283: $i > $i > $i > $i ).
thf(func_def_432,type,
sK284: $i > $i > $i > $i ).
thf(func_def_433,type,
sK285: $i > $i ).
thf(func_def_434,type,
sK286: $i > $i > $i ).
thf(func_def_435,type,
sK287: $i > $i > $i > $i ).
thf(func_def_436,type,
sK288: $i > $i > $i > $i ).
thf(func_def_437,type,
sK289: $i > $i > $i > $i ).
thf(func_def_438,type,
sK290: $i > $i > $i > $i ).
thf(func_def_439,type,
sK291: $i > $i > $i > $i ).
thf(func_def_440,type,
sK292: $i > $i > $i > $i ).
thf(func_def_441,type,
sK293: $i > $i > $i > $i ).
thf(func_def_442,type,
sK294: $i > $i > $i ).
thf(func_def_443,type,
sK295: $i > $i > $i > $i ).
thf(func_def_444,type,
sK296: $i > $i > $i > $i ).
thf(func_def_445,type,
sK297: $i > $i > $i > $i ).
thf(func_def_446,type,
sK298: $i > $i > $i ).
thf(func_def_447,type,
sK299: $i > $i > $i > $i ).
thf(func_def_448,type,
sK300: $i > $i > $i > $i ).
thf(func_def_449,type,
sK301: $i > $i > $i > $i ).
thf(func_def_450,type,
sK302: $i > $i > $i > $i ).
thf(func_def_451,type,
sK303: $i > $i ).
thf(func_def_452,type,
sK304: $i > $i > $i > $i ).
thf(func_def_453,type,
sK305: $i > $i ).
thf(func_def_454,type,
sK306: $i > $i > $i ).
thf(func_def_455,type,
sK307: $i > $i ).
thf(func_def_456,type,
sK308: $i > $i > $i ).
thf(func_def_457,type,
sK309: $i > $i > $i ).
thf(func_def_458,type,
sK310: $i > $i > $i > $i ).
thf(func_def_459,type,
sK311: $i > $i > $i ).
thf(func_def_460,type,
sK312: $i > $i > $i > $i ).
thf(func_def_461,type,
sK313: $i > $i > $i ).
thf(func_def_462,type,
sK314: $i > $i ).
thf(func_def_463,type,
sK315: $i > $i > $i > $i ).
thf(func_def_464,type,
sK316: $i > $i > $i ).
thf(func_def_465,type,
sK317: $i > $i ).
thf(func_def_466,type,
sK318: $i > $i ).
thf(func_def_467,type,
sK319: $i > $i > $i ).
thf(func_def_468,type,
sK320: $i > $i > $i > $i ).
thf(func_def_469,type,
sK321: $i > $i > $i ).
thf(func_def_470,type,
sK322: $i > $i > $i ).
thf(func_def_471,type,
sK323: $i > $i > $i ).
thf(func_def_472,type,
sK324: $i > $i > $i > $i ).
thf(func_def_473,type,
sK325: $i > $i > $i ).
thf(func_def_474,type,
sK326: $i > $i ).
thf(func_def_475,type,
sK327: $i > $i > $i ).
thf(func_def_476,type,
sK328: $i > $i > $i ).
thf(func_def_477,type,
sK329: $i > $i > $i ).
thf(func_def_478,type,
sK330: $i > $i ).
thf(func_def_479,type,
sK331: $i > $i ).
thf(func_def_480,type,
sK332: $i > $i > $i > $i ).
thf(func_def_481,type,
sK333: $i > $i > $i ).
thf(func_def_482,type,
sK334: $i > $i ).
thf(func_def_483,type,
sK335: $i > $i > $i ).
thf(func_def_484,type,
sK336: $i > $i > $i > $i ).
thf(func_def_485,type,
sK337: $i > $i > $i > $i ).
thf(func_def_486,type,
sK338: $i > $i > $i > $i ).
thf(func_def_487,type,
sK339: $i > $i > $i > $i ).
thf(func_def_488,type,
sK340: $i > $i ).
thf(func_def_489,type,
sK341: $i > $i > $i > $i ).
thf(func_def_490,type,
sK342: $i > $i > $i > $i ).
thf(func_def_491,type,
sK343: $i > $i > $i > $i ).
thf(func_def_492,type,
sK344: $i > $i > $i > $i ).
thf(func_def_493,type,
sK345: $i > $i > $i > $i ).
thf(func_def_494,type,
sK346: $i > $i > $i > $i ).
thf(func_def_495,type,
sK347: $i > $i > $i > $i ).
thf(func_def_496,type,
sK348: $i > $i > $i > $i ).
thf(func_def_497,type,
sK349: $i > $i ).
thf(func_def_498,type,
sK350: $i > $i > $i > $i ).
thf(func_def_499,type,
sK351: $i > $i > $i ).
thf(func_def_500,type,
sK352: $i > $i > $i ).
thf(func_def_501,type,
sK353: $i > $i > $i > $i ).
thf(func_def_502,type,
sK354: $i > $i ).
thf(func_def_503,type,
sK355: $i > $i > $i > $i ).
thf(func_def_504,type,
sK356: $i > $i > $i ).
thf(func_def_505,type,
sK357: $i > $i > $i ).
thf(func_def_506,type,
sK358: $i > $i > $i > $i ).
thf(func_def_507,type,
sK359: $i > $i > $i ).
thf(func_def_508,type,
sK360: $i > $i > $i ).
thf(func_def_509,type,
sK361: $i > $i > $i ).
thf(func_def_510,type,
sK362: $i > $i > $i > $i ).
thf(func_def_511,type,
sK363: $i > $i > $i > $i ).
thf(func_def_512,type,
sK364: $i > $i > $i > $i ).
thf(func_def_513,type,
sK365: $i > $i > $i > $i ).
thf(func_def_514,type,
sK366: $i > $i ).
thf(func_def_515,type,
sK367: $i > $i ).
thf(func_def_516,type,
sK368: $i > $i > $i ).
thf(func_def_517,type,
sK369: $i > $i > $i > $i ).
thf(func_def_518,type,
sK370: $i > $i > $i > $i ).
thf(func_def_519,type,
sK371: $i > $i > $i > $i ).
thf(func_def_520,type,
sK372: $i > $i > $i > $i ).
thf(func_def_521,type,
sK373: $i > $i > $i > $i ).
thf(func_def_522,type,
sK374: $i > $i > $i > $i ).
thf(func_def_523,type,
sK375: $i > $i > $i > $i ).
thf(func_def_524,type,
sK376: $i > $i ).
thf(func_def_525,type,
sK377: $i > $i ).
thf(func_def_526,type,
sK378: $i > $i > $i ).
thf(func_def_527,type,
sK379: $i > $i > $i > $i ).
thf(func_def_528,type,
sK380: $i > $i > $i > $i ).
thf(func_def_529,type,
sK381: $i > $i > $i > $i ).
thf(func_def_530,type,
sK382: $i > $i > $i > $i ).
thf(func_def_531,type,
sK383: $i > $i > $i ).
thf(func_def_532,type,
sK384: $i > $i > $i > $i ).
thf(func_def_533,type,
sK385: $i > $i > $i > $i ).
thf(func_def_534,type,
sK386: $i > $i > $i > $i ).
thf(func_def_535,type,
sK387: $i > $i > $i > $i ).
thf(func_def_536,type,
sK388: $i > $i > $i > $i ).
thf(func_def_537,type,
sK389: $i > $i > $i ).
thf(func_def_538,type,
sK390: $i > $i > $i ).
thf(func_def_539,type,
sK391: $i > $i > $i > $i ).
thf(func_def_540,type,
sK392: $i > $i > $i > $i ).
thf(func_def_541,type,
sK393: $i > $i > $i > $i ).
thf(func_def_542,type,
sK394: $i > $i > $i ).
thf(func_def_543,type,
sK395: $i > $i > $i ).
thf(func_def_544,type,
sK396: $i > $i > $i > $i ).
thf(func_def_545,type,
sK397: $i > $i ).
thf(func_def_546,type,
sK398: $i > $i > $i ).
thf(func_def_547,type,
sK399: $i > $i > $i > $i ).
thf(func_def_548,type,
sK400: $i > $i > $i > $i ).
thf(func_def_549,type,
sK401: $i > $i > $i > $i ).
thf(func_def_550,type,
sK402: $i > $i > $i > $i ).
thf(func_def_551,type,
sK403: $i > $i > $i ).
thf(func_def_552,type,
sK404: $i > $i > $i > $i ).
thf(func_def_553,type,
sK405: $i > $i > $i > $i ).
thf(func_def_554,type,
sK406: $i > $i > $i > $i ).
thf(func_def_555,type,
sK407: $i > $i > $i > $i ).
thf(func_def_556,type,
sK408: $i > $i ).
thf(func_def_557,type,
sK409: $i > $i > $i ).
thf(func_def_558,type,
sK410: $i > $i > $i > $i ).
thf(func_def_559,type,
sK411: $i > $i ).
thf(func_def_560,type,
sK412: $i > $i > $i > $i ).
thf(func_def_561,type,
sK413: $i > $i > $i > $i ).
thf(func_def_562,type,
sK414: $i > $i > $i > $i ).
thf(func_def_563,type,
sK415: $i > $i > $i > $i ).
thf(func_def_564,type,
sK416: $i > $i ).
thf(func_def_565,type,
sK417: $i > $i > $i ).
thf(func_def_566,type,
sK418: $i > $i > $i > $i ).
thf(func_def_567,type,
sK419: $i > $i > $i > $i ).
thf(func_def_568,type,
sK420: $i > $i > $i > $i ).
thf(func_def_569,type,
sK421: $i > $i > $i > $i ).
thf(func_def_570,type,
sK422: $i > $i > $i > $i ).
thf(func_def_571,type,
sK423: $i > $i > $i > $i ).
thf(func_def_572,type,
sK424: $i > $i > $i > $i ).
thf(func_def_573,type,
sK425: $i > $i > $i > $i ).
thf(func_def_574,type,
sK426: $i > $i ).
thf(func_def_575,type,
sK427: $i > $i > $i > $i ).
thf(func_def_576,type,
sK428: $i > $i > $i ).
thf(func_def_577,type,
sK429: $i > $i > $i > $i ).
thf(func_def_578,type,
sK430: $i > $i > $i > $i ).
thf(func_def_579,type,
sK431: $i > $i > $i > $i ).
thf(func_def_580,type,
sK432: $i > $i > $i ).
thf(func_def_581,type,
sK433: $i > $i > $i ).
thf(func_def_582,type,
sK434: $i > $i > $i > $i ).
thf(func_def_583,type,
sK435: $i > $i ).
thf(func_def_584,type,
sK436: $i > $i > $i ).
thf(func_def_585,type,
sK437: $i > $i > $i > $i ).
thf(func_def_586,type,
sK438: $i > $i > $i > $i ).
thf(func_def_587,type,
sK439: $i > $i > $i > $i ).
thf(func_def_588,type,
sK440: $i > $i > $i > $i ).
thf(func_def_589,type,
sK441: $i > $i > $i > $i ).
thf(func_def_590,type,
sK442: $i > $i > $i > $i ).
thf(func_def_591,type,
sK443: $i > $i > $i > $i ).
thf(func_def_592,type,
sK444: $i > $i > $i > $i ).
thf(func_def_593,type,
sK445: $i > $i > $i > $i ).
thf(func_def_594,type,
sK446: $i > $i > $i > $i ).
thf(func_def_595,type,
sK447: $i > $i > $i > $i ).
thf(func_def_596,type,
sK448: $i > $i > $i > $i ).
thf(func_def_597,type,
sK449: $i > $i > $i > $i ).
thf(func_def_598,type,
sK450: $i > $i > $i > $i ).
thf(func_def_599,type,
sK451: $i > $i > $i > $i ).
thf(func_def_600,type,
sK452: $i > $i > $i > $i ).
thf(func_def_601,type,
sK453: $i > $i ).
thf(func_def_602,type,
sK454: $i > $i > $i ).
thf(func_def_603,type,
sK455: $i > $i > $i > $i ).
thf(func_def_604,type,
sK456: $i > $i > $i > $i ).
thf(func_def_605,type,
sK457: $i > $i > $i > $i ).
thf(func_def_606,type,
sK458: $i > $i > $i ).
thf(func_def_607,type,
sK459: $i > $i > $i > $i ).
thf(func_def_608,type,
sK460: $i > $i > $i > $i ).
thf(func_def_609,type,
sK461: $i > $i > $i > $i ).
thf(func_def_610,type,
sK462: $i > $i ).
thf(func_def_611,type,
sK463: $i > $i ).
thf(func_def_612,type,
sK464: $i > $i > $i > $i ).
thf(func_def_613,type,
sK465: $i > $i > $i ).
thf(func_def_614,type,
sK466: $i > $i > $i ).
thf(func_def_615,type,
sK467: $i > $i > $i > $i ).
thf(func_def_616,type,
sK468: $i > $i > $i > $i ).
thf(func_def_617,type,
sK469: $i > $i > $i > $i ).
thf(func_def_618,type,
sK470: $i > $i > $i ).
thf(func_def_619,type,
sK471: $i > $i > $i ).
thf(func_def_620,type,
sK472: $i > $i > $i > $i ).
thf(func_def_621,type,
sK473: $i > $i > $i ).
thf(func_def_622,type,
sK474: $i > $i > $i ).
thf(func_def_623,type,
sK475: $i > $i > $i > $i ).
thf(func_def_624,type,
sK476: $i > $i > $i > $i ).
thf(func_def_625,type,
sK477: $i > $i > $i > $i ).
thf(func_def_626,type,
sK478: $i > $i > $i > $i ).
thf(func_def_627,type,
sK479: $i > $i > $i ).
thf(func_def_628,type,
sK480: $i > $i > $i ).
thf(func_def_629,type,
sK481: $i > $i > $i > $i ).
thf(func_def_630,type,
sK482: $i > $i > $i > $i ).
thf(func_def_631,type,
sK483: $i > $i ).
thf(func_def_632,type,
sK484: $i > $i > $i > $i ).
thf(func_def_633,type,
sK485: $i > $i > $i ).
thf(func_def_634,type,
sK486: $i > $i > $i ).
thf(func_def_635,type,
sK487: $i > $i > $i > $i ).
thf(func_def_636,type,
sK488: $i > $i > $i ).
thf(func_def_637,type,
sK489: $i > $i > $i > $i ).
thf(func_def_638,type,
sK490: $i > $i > $i > $i ).
thf(func_def_639,type,
sK491: $i > $i > $i > $i ).
thf(func_def_640,type,
sK492: $i > $i > $i > $i ).
thf(func_def_641,type,
sK493: $i > $i ).
thf(func_def_642,type,
sK494: $i > $i > $i ).
thf(func_def_643,type,
sK495: $i > $i > $i > $i ).
thf(func_def_644,type,
sK496: $i > $i > $i > $i ).
thf(func_def_645,type,
sK497: $i > $i > $i > $i ).
thf(func_def_646,type,
sK498: $i > $i > $i > $i ).
thf(func_def_647,type,
sK499: $i > $i > $i > $i ).
thf(func_def_648,type,
sK500: $i > $i > $i ).
thf(func_def_649,type,
sK501: $i > $i > $i ).
thf(func_def_650,type,
sK502: $i > $i > $i > $i ).
thf(func_def_651,type,
sK503: $i > $i > $i ).
thf(func_def_652,type,
sK504: $i > $i > $i ).
thf(func_def_653,type,
sK505: $i > $i > $i ).
thf(func_def_654,type,
sK506: $i > $i > $i > $i ).
thf(func_def_655,type,
sK507: $i > $i > $i > $i ).
thf(func_def_656,type,
sK508: $i > $i > $i > $i ).
thf(func_def_657,type,
sK509: $i > $i > $i > $i ).
thf(func_def_658,type,
sK510: $i > $i > $i > $i ).
thf(func_def_659,type,
sK511: $i > $i > $i ).
thf(func_def_660,type,
sK512: $i > $i > $i ).
thf(func_def_661,type,
sK513: $i > $i > $i ).
thf(func_def_662,type,
sK514: $i > $i > $i > $i ).
thf(func_def_663,type,
sK515: $i > $i > $i > $i ).
thf(func_def_664,type,
sK516: $i > $i ).
thf(func_def_665,type,
sK517: $i > $i > $i > $i ).
thf(func_def_666,type,
sK518: $i > $i > $i ).
thf(func_def_667,type,
sK519: $i > $i > $i ).
thf(func_def_668,type,
sK520: $i > $i > $i > $i ).
thf(func_def_669,type,
sK521: $i > $i > $i > $i ).
thf(func_def_670,type,
sK522: $i > $i > $i ).
thf(func_def_671,type,
sK523: $i > $i > $i ).
thf(func_def_672,type,
sK524: $i > $i > $i ).
thf(func_def_673,type,
sK525: $i > $i > $i > $i ).
thf(func_def_674,type,
sK526: $i > $i > $i ).
thf(func_def_675,type,
sK527: $i > $i ).
thf(func_def_676,type,
sK528: $i > $i > $i > $i ).
thf(func_def_677,type,
sK529: $i > $i > $i > $i ).
thf(func_def_678,type,
sK530: $i > $i > $i > $i ).
thf(func_def_679,type,
sK531: $i > $i > $i > $i ).
thf(func_def_680,type,
sK532: $i > $i > $i > $i ).
thf(func_def_681,type,
sK533: $i > $i > $i > $i ).
thf(func_def_682,type,
sK534: $i > $i > $i > $i ).
thf(func_def_683,type,
sK535: $i > $i ).
thf(func_def_684,type,
sK536: $i > $i ).
thf(func_def_685,type,
sK537: $i > $i > $i > $i ).
thf(func_def_686,type,
sK538: $i > $i > $i ).
thf(func_def_687,type,
sK539: $i > $i > $i ).
thf(func_def_688,type,
sK540: $i > $i > $i > $i ).
thf(func_def_689,type,
sK541: $i > $i > $i ).
thf(func_def_690,type,
sK542: $i > $i > $i > $i ).
thf(func_def_691,type,
sK543: $i > $i > $i ).
thf(func_def_692,type,
sK544: $i > $i > $i > $i ).
thf(func_def_693,type,
sK545: $i > $i > $i > $i ).
thf(func_def_694,type,
sK546: $i > $i ).
thf(func_def_695,type,
sK547: $i > $i > $i > $i ).
thf(func_def_696,type,
sK548: $i > $i > $i ).
thf(func_def_697,type,
sK549: $i > $i > $i > $i ).
thf(func_def_698,type,
sK550: $i > $i > $i > $i ).
thf(func_def_699,type,
sK551: $i > $i > $i ).
thf(func_def_700,type,
sK552: $i > $i > $i > $i ).
thf(func_def_701,type,
sK553: $i > $i > $i > $i ).
thf(func_def_702,type,
sK554: $i > $i > $i > $i ).
thf(func_def_703,type,
sK555: $i > $i > $i > $i ).
thf(func_def_704,type,
sK556: $i > $i ).
thf(func_def_705,type,
sK557: $i > $i > $i ).
thf(func_def_706,type,
sK558: $i > $i ).
thf(func_def_707,type,
sK559: $i > $i > $i > $i ).
thf(func_def_708,type,
sK560: $i > $i > $i > $i ).
thf(func_def_709,type,
sK561: $i > $i > $i > $i ).
thf(func_def_710,type,
sK562: $i > $i > $i > $i ).
thf(func_def_711,type,
sK563: $i > $i > $i > $i ).
thf(func_def_712,type,
sK564: $i > $i ).
thf(func_def_713,type,
sK565: $i > $i > $i ).
thf(func_def_714,type,
sK566: $i > $i > $i > $i ).
thf(func_def_715,type,
sK567: $i > $i > $i > $i ).
thf(func_def_716,type,
sK568: $i > $i > $i ).
thf(func_def_717,type,
sK569: $i > $i > $i ).
thf(func_def_718,type,
sK570: $i > $i > $i ).
thf(func_def_719,type,
sK571: $i > $i > $i > $i ).
thf(func_def_720,type,
sK572: $i > $i > $i > $i ).
thf(func_def_721,type,
sK573: $i > $i > $i ).
thf(func_def_722,type,
sK574: $i > $i ).
thf(func_def_723,type,
sK575: $i > $i ).
thf(func_def_724,type,
sK576: $i > $i > $i > $i ).
thf(func_def_725,type,
sK577: $i > $i > $i > $i ).
thf(func_def_726,type,
sK578: $i > $i > $i > $i ).
thf(func_def_727,type,
sK579: $i > $i > $i > $i ).
thf(func_def_728,type,
sK580: $i > $i > $i > $i ).
thf(func_def_729,type,
sK581: $i > $i > $i > $i ).
thf(func_def_730,type,
sK582: $i > $i > $i > $i ).
thf(func_def_731,type,
sK583: $i > $i > $i > $i ).
thf(func_def_732,type,
sK584: $i > $i > $i > $i ).
thf(func_def_733,type,
sK585: $i > $i > $i > $i ).
thf(func_def_734,type,
sK586: $i > $i > $i > $i ).
thf(func_def_735,type,
sK587: $i > $i > $i > $i ).
thf(func_def_736,type,
sK588: $i > $i > $i > $i ).
thf(func_def_737,type,
sK589: $i > $i > $i > $i ).
thf(func_def_738,type,
sK590: $i > $i > $i > $i ).
thf(func_def_742,type,
sK594: ( $i > $o ) > $i > $i ).
thf(func_def_743,type,
sK595: $i > $o ).
thf(func_def_746,type,
sK598: ( $i > $o ) > $i > ( $i > $o ) > $i > $i ).
thf(func_def_747,type,
sK599: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_750,type,
sK602: $i > $o ).
thf(func_def_751,type,
sK603: $i > $o ).
thf(func_def_754,type,
sK606: $i > $o ).
thf(func_def_760,type,
sK612: $i > $o ).
thf(func_def_761,type,
sK613: $i > ( $i > $o ) > $i ).
thf(func_def_763,type,
sK615: $i > $o ).
thf(func_def_768,type,
sK620: $i > $i ).
thf(func_def_780,type,
sK632: $i > $i > $i ).
thf(func_def_783,type,
sK635: $i > $o ).
thf(func_def_791,type,
sK643: ( $i > $o ) > $i > $i ).
thf(func_def_792,type,
sK644: $i > $o ).
thf(func_def_795,type,
sK647: $i > $i ).
thf(func_def_810,type,
sK662: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_811,type,
sK663: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_812,type,
sK664: $i > $o ).
thf(func_def_813,type,
sK665: $i > $o ).
thf(func_def_816,type,
sK668: $i > $i ).
thf(func_def_822,type,
sK674: $i > $i ).
thf(func_def_825,type,
sK677: $i > ( $i > $o ) > $i ).
thf(func_def_827,type,
sK679: $i > $o ).
thf(func_def_829,type,
sK681: ( $i > $o ) > $i > $i ).
thf(func_def_830,type,
sK682: $i > $o ).
thf(func_def_836,type,
sK688: $i > ( $i > $i > $o ) > $i ).
thf(func_def_837,type,
sK689: $i > ( $i > $i > $o ) > $i ).
thf(func_def_839,type,
sK691: $i > $i > $o ).
thf(func_def_840,type,
sK692: $i > $i ).
thf(func_def_846,type,
sK698: $i > $o ).
thf(func_def_854,type,
sK706: ( $i > $o ) > $i > $i ).
thf(func_def_855,type,
sK707: $i > $o ).
thf(func_def_861,type,
sK713: $i > $o ).
thf(func_def_863,type,
sK715: $i > $o ).
thf(func_def_883,type,
sK735: $i > $i ).
thf(func_def_885,type,
ph737:
!>[X0: $tType] : X0 ).
thf(func_def_886,type,
sK738: ( $i > $o ) > $i ).
thf(func_def_887,type,
sK739: ( $i > $o ) > $i > $i ).
thf(func_def_888,type,
sK740: $i > $i ).
thf(func_def_889,type,
sK741: $i > $i > $i ).
thf(func_def_890,type,
sK742: $i > $i > $i ).
thf(func_def_891,type,
sK743: $i > $i > $i ).
thf(func_def_892,type,
sK744: $i > $i ).
thf(func_def_893,type,
sK745: $i > $i ).
thf(func_def_894,type,
sK746: $i > $i > $i ).
thf(func_def_895,type,
sK747: $i > $i > $i ).
thf(func_def_896,type,
sK748: $i > $i > $i ).
thf(func_def_898,type,
sK750: $i > $i > $i ).
thf(func_def_899,type,
sK751: $i > $i > $i ).
thf(func_def_900,type,
sK752: $i > $i > $i ).
thf(func_def_901,type,
sK753: $i > $i > $i ).
thf(func_def_902,type,
sK754: $i > $i > $i ).
thf(func_def_903,type,
sK755: $i > $i > $i ).
thf(f12934,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f10310,f10332,f10785,f10952,f10954,f10963,f11034,f12655,f12757,f12933]) ).
thf(f12933,plain,
( ~ spl2_1296
| ~ spl2_1299 ),
inference(avatar_contradiction_clause,[status(thm)],[f12932]) ).
thf(f12932,plain,
( $false
| ~ spl2_1296
| ~ spl2_1299 ),
inference(trivial_inequality_removal,[status(thm)],[f12931]) ).
thf(f12931,plain,
( ( $false = $true )
| ~ spl2_1296
| ~ spl2_1299 ),
inference(forward_demodulation,[status(thm)],[f10771,f10784]) ).
thf(f10784,plain,
( ( powersetE1 = $false )
| ~ spl2_1299 ),
inference(avatar_component_clause,[status(thm)],[f10782]) ).
thf(f10782,definition,
( spl2_1299
<=> ( powersetE1 = $false ) ),
introduced(definition,[new_symbols(naming,[spl2_1299])],[avatar_definition]) ).
thf(f10771,plain,
( ( powersetE1 = $true )
| ~ spl2_1296 ),
inference(avatar_component_clause,[status(thm)],[f10769]) ).
thf(f10769,definition,
( spl2_1296
<=> ( powersetE1 = $true ) ),
introduced(definition,[new_symbols(naming,[spl2_1296])],[avatar_definition]) ).
thf(f12757,plain,
( ~ spl2_1195
| ~ spl2_1200
| ~ spl2_1298 ),
inference(avatar_contradiction_clause,[status(thm)],[f12756]) ).
thf(f12756,plain,
( $false
| ~ spl2_1195
| ~ spl2_1200
| ~ spl2_1298 ),
inference(trivial_inequality_removal,[status(thm)],[f12737]) ).
thf(f12737,plain,
( ( $false = $true )
| ~ spl2_1195
| ~ spl2_1200
| ~ spl2_1298 ),
inference(backward_demodulation,[status(thm)],[f12325,f12693]) ).
thf(f12693,plain,
( ! [X0: $i] :
( $false
= ( in @ sK749 @ ( binintersect @ X0 @ sK1 ) ) )
| ~ spl2_1195
| ~ spl2_1200
| ~ spl2_1298 ),
inference(trivial_inequality_removal,[status(thm)],[f12690]) ).
thf(f12690,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $false
= ( in @ sK749 @ ( binintersect @ X0 @ sK1 ) ) ) )
| ~ spl2_1195
| ~ spl2_1200
| ~ spl2_1298 ),
inference(superposition,[status(thm)],[f12324,f10331]) ).
thf(f10331,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ X3 )
= $true )
| ( $false
= ( in @ X2 @ ( binintersect @ X1 @ X3 ) ) ) )
| ~ spl2_1200 ),
inference(avatar_component_clause,[status(thm)],[f10330]) ).
thf(f10330,definition,
( spl2_1200
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $false
= ( in @ X2 @ ( binintersect @ X1 @ X3 ) ) )
| ( ( in @ X2 @ X3 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl2_1200])],[avatar_definition]) ).
thf(f12324,plain,
( ( $false
= ( in @ sK749 @ sK1 ) )
| ~ spl2_1195
| ~ spl2_1298 ),
inference(binary_proxy_clausification,[status(thm)],[f12323]) ).
thf(f12323,plain,
( ( $false
= ( ( in @ sK749 @ ( binintersect @ sK0 @ sK1 ) )
=> ( in @ sK749 @ sK1 ) ) )
| ~ spl2_1195
| ~ spl2_1298 ),
inference(beta_eta_normalization,[status(thm)],[f12322]) ).
thf(f12322,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( binintersect @ sK0 @ sK1 ) )
=> ( in @ Y0 @ sK1 ) )
@ sK749 ) )
| ~ spl2_1195
| ~ spl2_1298 ),
inference(sigma_clausification,[status(thm)],[f12321]) ).
thf(f12321,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( binintersect @ sK0 @ sK1 ) )
=> ( in @ Y0 @ sK1 ) ) ) )
| ~ spl2_1195
| ~ spl2_1298 ),
inference(not_proxy_clausification,[status(thm)],[f12320]) ).
thf(f12320,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( binintersect @ sK0 @ sK1 ) )
=> ( in @ Y0 @ sK1 ) ) ) ) )
| ~ spl2_1195
| ~ spl2_1298 ),
inference(boolean_simplification,[status(thm)],[f12291]) ).
thf(f12291,plain,
( ( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( binintersect @ sK0 @ sK1 ) )
=> ( in @ Y0 @ sK1 ) ) ) )
= $true )
| ~ spl2_1195
| ~ spl2_1298 ),
inference(superposition,[status(thm)],[f10309,f11250]) ).
thf(f11250,plain,
( ( $false
= ( in @ ( binintersect @ sK0 @ sK1 ) @ ( powerset @ sK1 ) ) )
| ~ spl2_1298 ),
inference(trivial_inequality_removal,[status(thm)],[f11247]) ).
thf(f11247,plain,
( ( $true != $true )
| ( $false
= ( in @ ( binintersect @ sK0 @ sK1 ) @ ( powerset @ sK1 ) ) )
| ~ spl2_1298 ),
inference(superposition,[status(thm)],[f464,f10780]) ).
thf(f10780,plain,
( ! [X2: $i,X1: $i] :
( ( $true
= ( subset @ X2 @ X1 ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ~ spl2_1298 ),
inference(avatar_component_clause,[status(thm)],[f10779]) ).
thf(f10779,definition,
( spl2_1298
<=> ! [X2: $i,X1: $i] :
( ( $true
= ( subset @ X2 @ X1 ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_1298])],[avatar_definition]) ).
thf(f464,plain,
( ( subset @ ( binintersect @ sK0 @ sK1 ) @ sK1 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f348]) ).
thf(f348,plain,
( ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( sepSubset = $true )
& ( nonemptyE1 = $true )
& ( noeltsimpempty = $true )
& ( foundationAx = $true )
& ( vacuousDall = $true )
& ( powersetE = $true )
& ( notsubsetI = $true )
& ( setunionI = $true )
& ( setadjoinSub = $true )
& ( singletonsswitch = $true )
& ( binunionE = $true )
& ( dsetconstr__Cong = $true )
& ( subsetemptysetimpeq = $true )
& ( quantDeMorgan3 = $true )
& ( descr__Cong = $true )
& ( replAx = $true )
& ( setextsub = $true )
& ( sepInPowerset = $true )
& ( setadjoinSub2 = $true )
& ( emptyinPowerset = $true )
& ( binintersectSubset3 = $true )
& ( binunionLsub = $true )
& ( quantDeMorgan1 = $true )
& ( exuEu = $true )
& ( upairsetE = $true )
& ( dsetconstrEL = $true )
& ( subsetE = $true )
& ( binintersectSubset5 = $true )
& ( prop2setE = $true )
& ( prop2set2propI = $true )
& ( upairset2IR = $true )
& ( binintersectEL = $true )
& ( prop2setI = $true )
& ( setextAx = $true )
& ( setext = $true )
& ( exuE2 = $true )
& ( binintersectER = $true )
& ( notequalI1 = $true )
& ( notdexE = $true )
& ( powerset__Cong = $true )
& ( emptyE1 = $true )
& ( powersetI1 = $true )
& ( eqimpsubset2 = $true )
& ( binintersectLsub = $true )
& ( ( subset @ ( binintersect @ sK0 @ sK1 ) @ sK1 )
!= $true )
& ( emptyInPowerset = $true )
& ( in__Cong = $true )
& ( exuE3u = $true )
& ( binunionIL = $true )
& ( binunionIR = $true )
& ( setunionAx = $true )
& ( disjointsetsI1 = $true )
& ( emptyI = $true )
& ( descrp = $true )
& ( dsetconstrI = $true )
& ( binunionRsub = $true )
& ( wellorderingAx = $true )
& ( exuI3 = $true )
& ( powersetAx = $true )
& ( eqinunit = $true )
& ( setadjoinAx = $true )
& ( setbeta = $true )
& ( subPowSU = $true )
& ( emptysetsubset = $true )
& ( powersetE1 = $true )
& ( exuI2 = $true )
& ( exuE1 = $true )
& ( subsetTrans = $true )
& ( notinsingleton = $true )
& ( nonemptyImpWitness = $true )
& ( upairsetIR = $true )
& ( setadjoinIL = $true )
& ( omegaIndAx = $true )
& ( setoftrueEq = $true )
& ( emptysetimpfalse = $true )
& ( quantDeMorgan4 = $true )
& ( subsetI1 = $true )
& ( omega0Ax = $true )
& ( subsetRefl = $true )
& ( subset2powerset = $true )
& ( setadjoinIR = $true )
& ( setadjoin__Cong = $true )
& ( setadjoinE = $true )
& ( binunionEcases = $true )
& ( notequalI2 = $true )
& ( setadjoinOr = $true )
& ( uniqinunit = $true )
& ( emptysetAx = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( upairsetIL = $true )
& ( inPowerset = $true )
& ( binintersectI = $true )
& ( powersetsubset = $true )
& ( nonemptyI1 = $true )
& ( quantDeMorgan2 = $true )
& ( emptysetE = $true )
& ( subsetI2 = $true )
& ( dsetconstrER = $true )
& ( powersetI = $true )
& ( eqimpsubset1 = $true )
& ( exuE3e = $true )
& ( setunionE = $true )
& ( emptyinunitempty = $true )
& ( subsetE2 = $true )
& ( emptyset__Cong = $true )
& ( omegaSAx = $true )
& ( notinemptyset = $true )
& ( exu__Cong = $true )
& ( inCongP = $true )
& ( binintersectSubset2 = $true )
& ( nonemptyI = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f346,f347]) ).
thf(f347,plain,
( ? [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X1 )
!= $true )
=> ( ( subset @ ( binintersect @ sK0 @ sK1 ) @ sK1 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f346,plain,
( ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( sepSubset = $true )
& ( nonemptyE1 = $true )
& ( noeltsimpempty = $true )
& ( foundationAx = $true )
& ( vacuousDall = $true )
& ( powersetE = $true )
& ( notsubsetI = $true )
& ( setunionI = $true )
& ( setadjoinSub = $true )
& ( singletonsswitch = $true )
& ( binunionE = $true )
& ( dsetconstr__Cong = $true )
& ( subsetemptysetimpeq = $true )
& ( quantDeMorgan3 = $true )
& ( descr__Cong = $true )
& ( replAx = $true )
& ( setextsub = $true )
& ( sepInPowerset = $true )
& ( setadjoinSub2 = $true )
& ( emptyinPowerset = $true )
& ( binintersectSubset3 = $true )
& ( binunionLsub = $true )
& ( quantDeMorgan1 = $true )
& ( exuEu = $true )
& ( upairsetE = $true )
& ( dsetconstrEL = $true )
& ( subsetE = $true )
& ( binintersectSubset5 = $true )
& ( prop2setE = $true )
& ( prop2set2propI = $true )
& ( upairset2IR = $true )
& ( binintersectEL = $true )
& ( prop2setI = $true )
& ( setextAx = $true )
& ( setext = $true )
& ( exuE2 = $true )
& ( binintersectER = $true )
& ( notequalI1 = $true )
& ( notdexE = $true )
& ( powerset__Cong = $true )
& ( emptyE1 = $true )
& ( powersetI1 = $true )
& ( eqimpsubset2 = $true )
& ( binintersectLsub = $true )
& ? [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X1 )
!= $true )
& ( emptyInPowerset = $true )
& ( in__Cong = $true )
& ( exuE3u = $true )
& ( binunionIL = $true )
& ( binunionIR = $true )
& ( setunionAx = $true )
& ( disjointsetsI1 = $true )
& ( emptyI = $true )
& ( descrp = $true )
& ( dsetconstrI = $true )
& ( binunionRsub = $true )
& ( wellorderingAx = $true )
& ( exuI3 = $true )
& ( powersetAx = $true )
& ( eqinunit = $true )
& ( setadjoinAx = $true )
& ( setbeta = $true )
& ( subPowSU = $true )
& ( emptysetsubset = $true )
& ( powersetE1 = $true )
& ( exuI2 = $true )
& ( exuE1 = $true )
& ( subsetTrans = $true )
& ( notinsingleton = $true )
& ( nonemptyImpWitness = $true )
& ( upairsetIR = $true )
& ( setadjoinIL = $true )
& ( omegaIndAx = $true )
& ( setoftrueEq = $true )
& ( emptysetimpfalse = $true )
& ( quantDeMorgan4 = $true )
& ( subsetI1 = $true )
& ( omega0Ax = $true )
& ( subsetRefl = $true )
& ( subset2powerset = $true )
& ( setadjoinIR = $true )
& ( setadjoin__Cong = $true )
& ( setadjoinE = $true )
& ( binunionEcases = $true )
& ( notequalI2 = $true )
& ( setadjoinOr = $true )
& ( uniqinunit = $true )
& ( emptysetAx = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( upairsetIL = $true )
& ( inPowerset = $true )
& ( binintersectI = $true )
& ( powersetsubset = $true )
& ( nonemptyI1 = $true )
& ( quantDeMorgan2 = $true )
& ( emptysetE = $true )
& ( subsetI2 = $true )
& ( dsetconstrER = $true )
& ( powersetI = $true )
& ( eqimpsubset1 = $true )
& ( exuE3e = $true )
& ( setunionE = $true )
& ( emptyinunitempty = $true )
& ( subsetE2 = $true )
& ( emptyset__Cong = $true )
& ( omegaSAx = $true )
& ( notinemptyset = $true )
& ( exu__Cong = $true )
& ( inCongP = $true )
& ( binintersectSubset2 = $true )
& ( nonemptyI = $true ) ),
inference(flattening,[status(thm)],[f345]) ).
thf(f345,plain,
( ? [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X1 )
!= $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)],[f203]) ).
thf(f203,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 )
=> ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X1 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f202]) ).
thf(f202,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
=> ! [X0: $i,X1: $i] : ( subset @ ( binintersect @ X0 @ X1 ) @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f117]) ).
thf(f117,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
=> ! [X3: $i,X4: $i] : ( subset @ ( binintersect @ X3 @ X4 ) @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f116]) ).
thf(f116,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
=> ! [X3: $i,X4: $i] : ( subset @ ( binintersect @ X3 @ X4 ) @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.osm1bNkGRD/DTF2THF_7106.p',binintersectRsub) ).
thf(f10309,plain,
( ! [X2: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) ) )
= $true )
| ~ spl2_1195 ),
inference(avatar_component_clause,[status(thm)],[f10308]) ).
thf(f10308,definition,
( spl2_1195
<=> ! [X2: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_1195])],[avatar_definition]) ).
thf(f12325,plain,
( ( $true
= ( in @ sK749 @ ( binintersect @ sK0 @ sK1 ) ) )
| ~ spl2_1195
| ~ spl2_1298 ),
inference(binary_proxy_clausification,[status(thm)],[f12323]) ).
thf(f12655,plain,
( ~ spl2_1196
| ~ spl2_1199 ),
inference(avatar_contradiction_clause,[status(thm)],[f12654]) ).
thf(f12654,plain,
( $false
| ~ spl2_1196
| ~ spl2_1199 ),
inference(trivial_inequality_removal,[status(thm)],[f12653]) ).
thf(f12653,plain,
( ( $false = $true )
| ~ spl2_1196
| ~ spl2_1199 ),
inference(forward_demodulation,[status(thm)],[f10314,f10328]) ).
thf(f10328,plain,
( ( binintersectER = $false )
| ~ spl2_1199 ),
inference(avatar_component_clause,[status(thm)],[f10326]) ).
thf(f10326,definition,
( spl2_1199
<=> ( binintersectER = $false ) ),
introduced(definition,[new_symbols(naming,[spl2_1199])],[avatar_definition]) ).
thf(f10314,plain,
( ( binintersectER = $true )
| ~ spl2_1196 ),
inference(avatar_component_clause,[status(thm)],[f10312]) ).
thf(f10312,definition,
( spl2_1196
<=> ( binintersectER = $true ) ),
introduced(definition,[new_symbols(naming,[spl2_1196])],[avatar_definition]) ).
thf(f11034,plain,
( ~ spl2_1192
| ~ spl2_1194 ),
inference(avatar_contradiction_clause,[status(thm)],[f11033]) ).
thf(f11033,plain,
( $false
| ~ spl2_1192
| ~ spl2_1194 ),
inference(trivial_inequality_removal,[status(thm)],[f11032]) ).
thf(f11032,plain,
( ( $false = $true )
| ~ spl2_1192
| ~ spl2_1194 ),
inference(backward_demodulation,[status(thm)],[f10297,f10306]) ).
thf(f10306,plain,
( ( powersetAx = $false )
| ~ spl2_1194 ),
inference(avatar_component_clause,[status(thm)],[f10304]) ).
thf(f10304,definition,
( spl2_1194
<=> ( powersetAx = $false ) ),
introduced(definition,[new_symbols(naming,[spl2_1194])],[avatar_definition]) ).
thf(f10297,plain,
( ( powersetAx = $true )
| ~ spl2_1192 ),
inference(avatar_component_clause,[status(thm)],[f10295]) ).
thf(f10295,definition,
( spl2_1192
<=> ( powersetAx = $true ) ),
introduced(definition,[new_symbols(naming,[spl2_1192])],[avatar_definition]) ).
thf(f10963,plain,
spl2_1196,
inference(avatar_split_clause,[status(thm)],[f472,f10312]) ).
thf(f472,plain,
binintersectER = $true,
inference(cnf_transformation,[status(thm)],[f348]) ).
thf(f10954,plain,
spl2_1192,
inference(avatar_split_clause,[status(thm)],[f450,f10295]) ).
thf(f450,plain,
powersetAx = $true,
inference(cnf_transformation,[status(thm)],[f348]) ).
thf(f10952,plain,
spl2_1296,
inference(avatar_split_clause,[status(thm)],[f444,f10769]) ).
thf(f444,plain,
powersetE1 = $true,
inference(cnf_transformation,[status(thm)],[f348]) ).
thf(f10785,plain,
( spl2_1298
| spl2_1299 ),
inference(avatar_split_clause,[status(thm)],[f691,f10782,f10779]) ).
thf(f691,plain,
! [X2: $i,X1: $i] :
( ( powersetE1 = $false )
| ( $true
= ( subset @ X2 @ X1 ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f690]) ).
thf(f690,plain,
! [X2: $i,X1: $i] :
( ( ( ( in @ X2 @ ( powerset @ X1 ) )
=> ( subset @ X2 @ X1 ) )
= $true )
| ( powersetE1 = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f689]) ).
thf(f689,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( subset @ Y0 @ X1 ) )
@ X2 )
= $true )
| ( powersetE1 = $false ) ),
inference(pi_clausification,[status(thm)],[f688]) ).
thf(f688,plain,
! [X1: $i] :
( ( powersetE1 = $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( subset @ Y0 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f687]) ).
thf(f687,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( subset @ Y1 @ Y0 ) ) )
@ X1 )
= $true )
| ( powersetE1 = $false ) ),
inference(pi_clausification,[status(thm)],[f686]) ).
thf(f686,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( subset @ Y1 @ Y0 ) ) ) )
= $true )
| ( powersetE1 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f353]) ).
thf(f353,plain,
( powersetE1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f253]) ).
thf(f253,plain,
( powersetE1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f252]) ).
thf(f252,plain,
( powersetE1
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f96]) ).
thf(f96,axiom,
( powersetE1
= ( ! [X4: $i,X3: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ( subset @ X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.osm1bNkGRD/DTF2THF_7106.p',powersetE1) ).
thf(f10332,plain,
( spl2_1199
| spl2_1200 ),
inference(avatar_split_clause,[status(thm)],[f1031,f10330,f10326]) ).
thf(f1031,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( binintersectER = $false )
| ( $false
= ( in @ X2 @ ( binintersect @ X1 @ X3 ) ) )
| ( ( in @ X2 @ X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1030]) ).
thf(f1030,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( binintersectER = $false )
| ( ( ( in @ X2 @ ( binintersect @ X1 @ X3 ) )
=> ( in @ X2 @ X3 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1029]) ).
thf(f1029,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( binintersectER = $false )
| ( ( ^ [Y0: $i] :
( ( in @ X2 @ ( binintersect @ X1 @ Y0 ) )
=> ( in @ X2 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f1028]) ).
thf(f1028,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ ( binintersect @ X1 @ Y0 ) )
=> ( in @ X2 @ Y0 ) ) )
= $true )
| ( binintersectER = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1027]) ).
thf(f1027,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( binintersect @ X1 @ Y1 ) )
=> ( in @ Y0 @ Y1 ) ) )
@ X2 ) )
| ( binintersectER = $false ) ),
inference(pi_clausification,[status(thm)],[f1026]) ).
thf(f1026,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( binintersect @ X1 @ Y1 ) )
=> ( in @ Y0 @ Y1 ) ) ) ) )
| ( binintersectER = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1025]) ).
thf(f1025,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( binintersect @ Y0 @ Y2 ) )
=> ( in @ Y1 @ Y2 ) ) ) )
@ X1 )
= $true )
| ( binintersectER = $false ) ),
inference(pi_clausification,[status(thm)],[f1024]) ).
thf(f1024,plain,
( ( binintersectER = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( binintersect @ Y0 @ Y2 ) )
=> ( in @ Y1 @ Y2 ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f570]) ).
thf(f570,plain,
( binintersectER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( binintersect @ Y0 @ Y2 ) )
=> ( in @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f288]) ).
thf(f288,plain,
( binintersectER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( binintersect @ Y0 @ Y2 ) )
=> ( in @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f287]) ).
thf(f287,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( binintersect @ X2 @ X0 ) )
=> ( in @ X1 @ X0 ) )
= binintersectER ),
inference(rectify,[status(thm)],[f114]) ).
thf(f114,axiom,
! [X4: $i,X1: $i,X3: $i] :
( ( ( in @ X1 @ ( binintersect @ X3 @ X4 ) )
=> ( in @ X1 @ X4 ) )
= binintersectER ),
file('/export/starexec/sandbox/tmp/tmp.osm1bNkGRD/DTF2THF_7106.p',binintersectER) ).
thf(f10310,plain,
( spl2_1194
| spl2_1195 ),
inference(avatar_split_clause,[status(thm)],[f1045,f10308,f10304]) ).
thf(f1045,plain,
! [X2: $i,X1: $i] :
( ( ( ( in @ X2 @ ( powerset @ X1 ) )
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) ) )
= $true )
| ( powersetAx = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f1044]) ).
thf(f1044,plain,
! [X2: $i,X1: $i] :
( ( powersetAx = $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
= ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) ) )
@ X2 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f1043]) ).
thf(f1043,plain,
! [X1: $i] :
( ( powersetAx = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
= ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1042]) ).
thf(f1042,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
= ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) )
@ X1 )
= $true )
| ( powersetAx = $false ) ),
inference(pi_clausification,[status(thm)],[f1041]) ).
thf(f1041,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
= ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) )
| ( powersetAx = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f521]) ).
thf(f521,plain,
( powersetAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
= ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f169]) ).
thf(f169,plain,
( powersetAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
= ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f168]) ).
thf(f168,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
<=> ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= powersetAx ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
! [X4: $i,X3: $i] :
( ( ( in @ X4 @ ( powerset @ X3 ) )
<=> ! [X1: $i] :
( ( in @ X1 @ X4 )
=> ( in @ X1 @ X3 ) ) )
= powersetAx ),
file('/export/starexec/sandbox/tmp/tmp.osm1bNkGRD/DTF2THF_7106.p',powersetAx) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU597^1 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n022.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:28:06 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.45 ---- Original DTF file ---
% 0.28/0.45 thf(spec,logic,$$dhol).
% 0.28/0.45 %------------------------------------------------------------------------------
% 0.28/0.45 % File : SEU597^1 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.45 % Domain : Set Theory
% 0.28/0.45 % Problem : Preliminary Notions - Ops on Sets - Unions and Intersections
% 0.28/0.45 % Version : Especial.
% 0.28/0.45 % English : (! A:i.! B:i.subset (binintersect A B) B)
% 0.28/0.45
% 0.28/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.28/0.45 % Source : [Bro08]
% 0.28/0.45 % Names : ZFC099g [Bro08]
% 0.28/0.45
% 0.28/0.45 % Status : Theorem
% 0.28/0.45 % Rating : 0.22 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, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.3.0, 0.40 v5.2.0, 0.60 v5.1.0, 0.80 v5.0.0, 0.40 v4.1.0, 0.67 v4.0.1, 1.00 v3.7.0
% 0.28/0.45 % Syntax : Number of formulae : 246 ( 115 unt; 130 typ; 115 def)
% 0.28/0.45 % Number of atoms : 615 ( 167 equ; 0 cnn)
% 0.28/0.45 % Maximal formula atoms : 114 ( 5 avg)
% 0.28/0.45 % Number of connectives : 965 ( 30 ~; 6 |; 28 &; 613 @)
% 0.28/0.45 % ( 14 <=>; 274 =>; 0 <=; 0 <~>)
% 0.28/0.45 % Maximal formula depth : 120 ( 2 avg)
% 0.28/0.45 % Number of types : 2 ( 0 usr)
% 0.28/0.45 % Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% 0.28/0.45 % Number of symbols : 133 ( 130 usr; 117 con; 0-2 aty)
% 0.28/0.45 % Number of variables : 336 ( 30 ^; 277 !; 29 ?; 336 :)
% 0.28/0.45 % SPC : TH0_THM_EQU_NAR
% 0.28/0.45
% 0.28/0.45 % Comments : http://mathgate.info/detsetitem.php?id=293
% 0.28/0.45 %------------------------------------------------------------------------------
% 0.28/0.45 thf(in_type,type,
% 0.28/0.45 in: $i > $i > $o ).
% 0.28/0.45
% 0.28/0.45 thf(exu_type,type,
% 0.28/0.45 exu: ( $i > $o ) > $o ).
% 0.28/0.45
% 0.28/0.45 thf(exu,definition,
% 0.28/0.45 ( exu
% 0.28/0.45 = ( ^ [Xphi: $i > $o] :
% 0.28/0.45 ? [Xx: $i] :
% 0.28/0.45 ( ( Xphi @ Xx )
% 0.28/0.45 & ! [Xy: $i] :
% 0.28/0.45 ( ( Xphi @ Xy )
% 0.28/0.45 => ( Xx = Xy ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(setextAx_type,type,
% 0.28/0.45 setextAx: $o ).
% 0.28/0.45
% 0.28/0.45 thf(setextAx,definition,
% 0.28/0.45 ( setextAx
% 0.28/0.45 = ( ! [A: $i,B: $i] :
% 0.28/0.45 ( ! [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 <=> ( in @ Xx @ B ) )
% 0.28/0.45 => ( A = B ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(emptyset_type,type,
% 0.28/0.45 emptyset: $i ).
% 0.28/0.45
% 0.28/0.45 thf(emptysetAx_type,type,
% 0.28/0.45 emptysetAx: $o ).
% 0.28/0.45
% 0.28/0.45 thf(emptysetAx,definition,
% 0.28/0.45 ( emptysetAx
% 0.28/0.45 = ( ! [Xx: $i] :
% 0.28/0.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(setadjoin_type,type,
% 0.28/0.45 setadjoin: $i > $i > $i ).
% 0.28/0.45
% 0.28/0.45 thf(setadjoinAx_type,type,
% 0.28/0.45 setadjoinAx: $o ).
% 0.28/0.45
% 0.28/0.45 thf(setadjoinAx,definition,
% 0.28/0.45 ( setadjoinAx
% 0.28/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.45 <=> ( ( Xy = Xx )
% 0.28/0.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(powerset_type,type,
% 0.28/0.45 powerset: $i > $i ).
% 0.28/0.45
% 0.28/0.45 thf(powersetAx_type,type,
% 0.28/0.45 powersetAx: $o ).
% 0.28/0.45
% 0.28/0.45 thf(powersetAx,definition,
% 0.28/0.45 ( powersetAx
% 0.28/0.45 = ( ! [A: $i,B: $i] :
% 0.28/0.45 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.45 <=> ! [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ B )
% 0.28/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(setunion_type,type,
% 0.28/0.45 setunion: $i > $i ).
% 0.28/0.45
% 0.28/0.45 thf(setunionAx_type,type,
% 0.28/0.45 setunionAx: $o ).
% 0.28/0.45
% 0.28/0.45 thf(setunionAx,definition,
% 0.28/0.45 ( setunionAx
% 0.28/0.45 = ( ! [A: $i,Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.45 <=> ? [B: $i] :
% 0.28/0.45 ( ( in @ Xx @ B )
% 0.28/0.45 & ( in @ B @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(omega_type,type,
% 0.28/0.45 omega: $i ).
% 0.28/0.45
% 0.28/0.45 thf(omega0Ax_type,type,
% 0.28/0.45 omega0Ax: $o ).
% 0.28/0.45
% 0.28/0.45 thf(omega0Ax,definition,
% 0.28/0.45 ( omega0Ax
% 0.28/0.45 = ( in @ emptyset @ omega ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(omegaSAx_type,type,
% 0.28/0.45 omegaSAx: $o ).
% 0.28/0.45
% 0.28/0.45 thf(omegaSAx,definition,
% 0.28/0.45 ( omegaSAx
% 0.28/0.45 = ( ! [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ omega )
% 0.28/0.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(omegaIndAx_type,type,
% 0.28/0.45 omegaIndAx: $o ).
% 0.28/0.45
% 0.28/0.45 thf(omegaIndAx,definition,
% 0.28/0.45 ( omegaIndAx
% 0.28/0.45 = ( ! [A: $i] :
% 0.28/0.45 ( ( ( in @ emptyset @ A )
% 0.28/0.45 & ! [Xx: $i] :
% 0.28/0.45 ( ( ( in @ Xx @ omega )
% 0.28/0.45 & ( in @ Xx @ A ) )
% 0.28/0.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.28/0.45 => ! [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ omega )
% 0.28/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(replAx_type,type,
% 0.28/0.45 replAx: $o ).
% 0.28/0.45
% 0.28/0.45 thf(replAx,definition,
% 0.28/0.45 ( replAx
% 0.28/0.45 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.28/0.45 ( ! [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 => ( exu
% 0.28/0.45 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.28/0.45 => ? [B: $i] :
% 0.28/0.45 ! [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ B )
% 0.28/0.45 <=> ? [Xy: $i] :
% 0.28/0.45 ( ( in @ Xy @ A )
% 0.28/0.45 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(foundationAx_type,type,
% 0.28/0.45 foundationAx: $o ).
% 0.28/0.45
% 0.28/0.45 thf(foundationAx,definition,
% 0.28/0.45 ( foundationAx
% 0.28/0.45 = ( ! [A: $i] :
% 0.28/0.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.28/0.45 => ? [B: $i] :
% 0.28/0.45 ( ( in @ B @ A )
% 0.28/0.45 & ~ ? [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ B )
% 0.28/0.45 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(wellorderingAx_type,type,
% 0.28/0.45 wellorderingAx: $o ).
% 0.28/0.45
% 0.28/0.45 thf(wellorderingAx,definition,
% 0.28/0.45 ( wellorderingAx
% 0.28/0.45 = ( ! [A: $i] :
% 0.28/0.45 ? [B: $i] :
% 0.28/0.45 ( ! [C: $i] :
% 0.28/0.45 ( ( in @ C @ B )
% 0.28/0.45 => ! [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ C )
% 0.28/0.45 => ( in @ Xx @ A ) ) )
% 0.28/0.45 & ! [Xx: $i,Xy: $i] :
% 0.28/0.45 ( ( ( in @ Xx @ A )
% 0.28/0.45 & ( in @ Xy @ A ) )
% 0.28/0.45 => ( ! [C: $i] :
% 0.28/0.45 ( ( in @ C @ B )
% 0.28/0.45 => ( ( in @ Xx @ C )
% 0.28/0.45 <=> ( in @ Xy @ C ) ) )
% 0.28/0.45 => ( Xx = Xy ) ) )
% 0.28/0.45 & ! [C: $i,D: $i] :
% 0.28/0.45 ( ( ( in @ C @ B )
% 0.28/0.45 & ( in @ D @ B ) )
% 0.28/0.45 => ( ! [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ C )
% 0.28/0.45 => ( in @ Xx @ D ) )
% 0.28/0.45 | ! [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ D )
% 0.28/0.45 => ( in @ Xx @ C ) ) ) )
% 0.28/0.45 & ! [C: $i] :
% 0.28/0.45 ( ( ! [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ C )
% 0.28/0.45 => ( in @ Xx @ A ) )
% 0.28/0.45 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.28/0.45 => ? [D: $i,Xx: $i] :
% 0.28/0.45 ( ( in @ D @ B )
% 0.28/0.45 & ( in @ Xx @ C )
% 0.28/0.45 & ~ ? [Xy: $i] :
% 0.28/0.45 ( ( in @ Xy @ D )
% 0.28/0.45 & ( in @ Xy @ C ) )
% 0.28/0.45 & ! [E: $i] :
% 0.28/0.45 ( ( in @ E @ B )
% 0.28/0.45 => ( ! [Xy: $i] :
% 0.28/0.45 ( ( in @ Xy @ E )
% 0.28/0.45 => ( in @ Xy @ D ) )
% 0.28/0.45 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(descr_type,type,
% 0.28/0.45 descr: ( $i > $o ) > $i ).
% 0.28/0.45
% 0.28/0.45 thf(descrp_type,type,
% 0.28/0.45 descrp: $o ).
% 0.28/0.45
% 0.28/0.45 thf(descrp,definition,
% 0.28/0.45 ( descrp
% 0.28/0.45 = ( ! [Xphi: $i > $o] :
% 0.28/0.45 ( ( exu
% 0.28/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.45 => ( Xphi
% 0.28/0.45 @ ( descr
% 0.28/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(dsetconstr_type,type,
% 0.28/0.45 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.28/0.45
% 0.28/0.45 thf(dsetconstrI_type,type,
% 0.28/0.45 dsetconstrI: $o ).
% 0.28/0.45
% 0.28/0.45 thf(dsetconstrI,definition,
% 0.28/0.45 ( dsetconstrI
% 0.28/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 => ( ( Xphi @ Xx )
% 0.28/0.45 => ( in @ Xx
% 0.28/0.45 @ ( dsetconstr @ A
% 0.28/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(dsetconstrEL_type,type,
% 0.28/0.45 dsetconstrEL: $o ).
% 0.28/0.45
% 0.28/0.45 thf(dsetconstrEL,definition,
% 0.28/0.45 ( dsetconstrEL
% 0.28/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.45 ( ( in @ Xx
% 0.28/0.45 @ ( dsetconstr @ A
% 0.28/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.45 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(dsetconstrER_type,type,
% 0.28/0.45 dsetconstrER: $o ).
% 0.28/0.45
% 0.28/0.45 thf(dsetconstrER,definition,
% 0.28/0.45 ( dsetconstrER
% 0.28/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.45 ( ( in @ Xx
% 0.28/0.45 @ ( dsetconstr @ A
% 0.28/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.45 => ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(exuE1_type,type,
% 0.28/0.45 exuE1: $o ).
% 0.28/0.45
% 0.28/0.45 thf(exuE1,definition,
% 0.28/0.45 ( exuE1
% 0.28/0.45 = ( ! [Xphi: $i > $o] :
% 0.28/0.45 ( ( exu
% 0.28/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.45 => ? [Xx: $i] :
% 0.28/0.45 ( ( Xphi @ Xx )
% 0.28/0.45 & ! [Xy: $i] :
% 0.28/0.45 ( ( Xphi @ Xy )
% 0.28/0.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(prop2set_type,type,
% 0.28/0.45 prop2set: $o > $i ).
% 0.28/0.45
% 0.28/0.45 thf(prop2setE_type,type,
% 0.28/0.45 prop2setE: $o ).
% 0.28/0.45
% 0.28/0.45 thf(prop2setE,definition,
% 0.28/0.45 ( prop2setE
% 0.28/0.45 = ( ! [Xphi: $o,Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.28/0.45 => Xphi ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(emptysetE_type,type,
% 0.28/0.45 emptysetE: $o ).
% 0.28/0.45
% 0.28/0.45 thf(emptysetE,definition,
% 0.28/0.45 ( emptysetE
% 0.28/0.45 = ( ! [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ emptyset )
% 0.28/0.45 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(emptysetimpfalse_type,type,
% 0.28/0.45 emptysetimpfalse: $o ).
% 0.28/0.45
% 0.28/0.45 thf(emptysetimpfalse,definition,
% 0.28/0.45 ( emptysetimpfalse
% 0.28/0.45 = ( ! [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ emptyset )
% 0.28/0.45 => $false ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(notinemptyset_type,type,
% 0.28/0.45 notinemptyset: $o ).
% 0.28/0.45
% 0.28/0.45 thf(notinemptyset,definition,
% 0.28/0.45 ( notinemptyset
% 0.28/0.45 = ( ! [Xx: $i] :
% 0.28/0.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(exuE3e_type,type,
% 0.28/0.45 exuE3e: $o ).
% 0.28/0.45
% 0.28/0.45 thf(exuE3e,definition,
% 0.28/0.45 ( exuE3e
% 0.28/0.45 = ( ! [Xphi: $i > $o] :
% 0.28/0.45 ( ( exu
% 0.28/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.45 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(setext_type,type,
% 0.28/0.45 setext: $o ).
% 0.28/0.45
% 0.28/0.45 thf(setext,definition,
% 0.28/0.45 ( setext
% 0.28/0.45 = ( ! [A: $i,B: $i] :
% 0.28/0.45 ( ! [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 => ( in @ Xx @ B ) )
% 0.28/0.45 => ( ! [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ B )
% 0.28/0.45 => ( in @ Xx @ A ) )
% 0.28/0.45 => ( A = B ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(emptyI_type,type,
% 0.28/0.45 emptyI: $o ).
% 0.28/0.45
% 0.28/0.45 thf(emptyI,definition,
% 0.28/0.45 ( emptyI
% 0.28/0.45 = ( ! [A: $i] :
% 0.28/0.45 ( ! [Xx: $i] :
% 0.28/0.45 ~ ( in @ Xx @ A )
% 0.28/0.45 => ( A = emptyset ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(noeltsimpempty_type,type,
% 0.28/0.45 noeltsimpempty: $o ).
% 0.28/0.45
% 0.28/0.45 thf(noeltsimpempty,definition,
% 0.28/0.45 ( noeltsimpempty
% 0.28/0.45 = ( ! [A: $i] :
% 0.28/0.45 ( ! [Xx: $i] :
% 0.28/0.45 ~ ( in @ Xx @ A )
% 0.28/0.45 => ( A = emptyset ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(setbeta_type,type,
% 0.28/0.45 setbeta: $o ).
% 0.28/0.45
% 0.28/0.45 thf(setbeta,definition,
% 0.28/0.45 ( setbeta
% 0.28/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 => ( ( in @ Xx
% 0.28/0.45 @ ( dsetconstr @ A
% 0.28/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.45 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(nonempty_type,type,
% 0.28/0.45 nonempty: $i > $o ).
% 0.28/0.45
% 0.28/0.45 thf(nonempty,definition,
% 0.28/0.45 ( nonempty
% 0.28/0.45 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(nonemptyE1_type,type,
% 0.28/0.45 nonemptyE1: $o ).
% 0.28/0.45
% 0.28/0.45 thf(nonemptyE1,definition,
% 0.28/0.45 ( nonemptyE1
% 0.28/0.45 = ( ! [A: $i] :
% 0.28/0.45 ( ( nonempty @ A )
% 0.28/0.45 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(nonemptyI_type,type,
% 0.28/0.45 nonemptyI: $o ).
% 0.28/0.45
% 0.28/0.45 thf(nonemptyI,definition,
% 0.28/0.45 ( nonemptyI
% 0.28/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 => ( ( Xphi @ Xx )
% 0.28/0.45 => ( nonempty
% 0.28/0.45 @ ( dsetconstr @ A
% 0.28/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(nonemptyI1_type,type,
% 0.28/0.45 nonemptyI1: $o ).
% 0.28/0.45
% 0.28/0.45 thf(nonemptyI1,definition,
% 0.28/0.45 ( nonemptyI1
% 0.28/0.45 = ( ! [A: $i] :
% 0.28/0.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.28/0.45 => ( nonempty @ A ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(setadjoinIL_type,type,
% 0.28/0.45 setadjoinIL: $o ).
% 0.28/0.45
% 0.28/0.45 thf(setadjoinIL,definition,
% 0.28/0.45 ( setadjoinIL
% 0.28/0.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(emptyinunitempty_type,type,
% 0.28/0.45 emptyinunitempty: $o ).
% 0.28/0.45
% 0.28/0.45 thf(emptyinunitempty,definition,
% 0.28/0.45 ( emptyinunitempty
% 0.28/0.45 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(setadjoinIR_type,type,
% 0.28/0.45 setadjoinIR: $o ).
% 0.28/0.45
% 0.28/0.45 thf(setadjoinIR,definition,
% 0.28/0.45 ( setadjoinIR
% 0.28/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.45 ( ( in @ Xy @ A )
% 0.28/0.45 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(setadjoinE_type,type,
% 0.28/0.45 setadjoinE: $o ).
% 0.28/0.45
% 0.28/0.45 thf(setadjoinE,definition,
% 0.28/0.45 ( setadjoinE
% 0.28/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.45 => ! [Xphi: $o] :
% 0.28/0.45 ( ( ( Xy = Xx )
% 0.28/0.45 => Xphi )
% 0.28/0.45 => ( ( ( in @ Xy @ A )
% 0.28/0.45 => Xphi )
% 0.28/0.45 => Xphi ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(setadjoinOr_type,type,
% 0.28/0.45 setadjoinOr: $o ).
% 0.28/0.45
% 0.28/0.45 thf(setadjoinOr,definition,
% 0.28/0.45 ( setadjoinOr
% 0.28/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.45 => ( ( Xy = Xx )
% 0.28/0.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(setoftrueEq_type,type,
% 0.28/0.45 setoftrueEq: $o ).
% 0.28/0.45
% 0.28/0.45 thf(setoftrueEq,definition,
% 0.28/0.45 ( setoftrueEq
% 0.28/0.45 = ( ! [A: $i] :
% 0.28/0.45 ( ( dsetconstr @ A
% 0.28/0.45 @ ^ [Xx: $i] : $true )
% 0.28/0.45 = A ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(powersetI_type,type,
% 0.28/0.45 powersetI: $o ).
% 0.28/0.45
% 0.28/0.45 thf(powersetI,definition,
% 0.28/0.45 ( powersetI
% 0.28/0.45 = ( ! [A: $i,B: $i] :
% 0.28/0.45 ( ! [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ B )
% 0.28/0.45 => ( in @ Xx @ A ) )
% 0.28/0.45 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(emptyinPowerset_type,type,
% 0.28/0.45 emptyinPowerset: $o ).
% 0.28/0.45
% 0.28/0.45 thf(emptyinPowerset,definition,
% 0.28/0.45 ( emptyinPowerset
% 0.28/0.45 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(emptyInPowerset_type,type,
% 0.28/0.45 emptyInPowerset: $o ).
% 0.28/0.45
% 0.28/0.45 thf(emptyInPowerset,definition,
% 0.28/0.45 ( emptyInPowerset
% 0.28/0.45 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(powersetE_type,type,
% 0.28/0.45 powersetE: $o ).
% 0.28/0.45
% 0.28/0.45 thf(powersetE,definition,
% 0.28/0.45 ( powersetE
% 0.28/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.45 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.45 => ( ( in @ Xx @ B )
% 0.28/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(setunionI_type,type,
% 0.28/0.45 setunionI: $o ).
% 0.28/0.45
% 0.28/0.45 thf(setunionI,definition,
% 0.28/0.45 ( setunionI
% 0.28/0.45 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.28/0.45 ( ( in @ Xx @ B )
% 0.28/0.45 => ( ( in @ B @ A )
% 0.28/0.45 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(setunionE_type,type,
% 0.28/0.45 setunionE: $o ).
% 0.28/0.45
% 0.28/0.45 thf(setunionE,definition,
% 0.28/0.45 ( setunionE
% 0.28/0.45 = ( ! [A: $i,Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.45 => ! [Xphi: $o] :
% 0.28/0.45 ( ! [B: $i] :
% 0.28/0.45 ( ( in @ Xx @ B )
% 0.28/0.45 => ( ( in @ B @ A )
% 0.28/0.45 => Xphi ) )
% 0.28/0.45 => Xphi ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(subPowSU_type,type,
% 0.28/0.45 subPowSU: $o ).
% 0.28/0.45
% 0.28/0.45 thf(subPowSU,definition,
% 0.28/0.45 ( subPowSU
% 0.28/0.45 = ( ! [A: $i,Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(exuE2_type,type,
% 0.28/0.45 exuE2: $o ).
% 0.28/0.45
% 0.28/0.45 thf(exuE2,definition,
% 0.28/0.45 ( exuE2
% 0.28/0.45 = ( ! [Xphi: $i > $o] :
% 0.28/0.45 ( ( exu
% 0.28/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.45 => ? [Xx: $i] :
% 0.28/0.45 ! [Xy: $i] :
% 0.28/0.45 ( ( Xphi @ Xy )
% 0.28/0.45 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(nonemptyImpWitness_type,type,
% 0.28/0.45 nonemptyImpWitness: $o ).
% 0.28/0.45
% 0.28/0.45 thf(nonemptyImpWitness,definition,
% 0.28/0.45 ( nonemptyImpWitness
% 0.28/0.45 = ( ! [A: $i] :
% 0.28/0.45 ( ( nonempty @ A )
% 0.28/0.45 => ? [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 & $true ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(uniqinunit_type,type,
% 0.28/0.45 uniqinunit: $o ).
% 0.28/0.45
% 0.28/0.45 thf(uniqinunit,definition,
% 0.28/0.45 ( uniqinunit
% 0.28/0.45 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.45 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.45 => ( Xx = Xy ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(notinsingleton_type,type,
% 0.28/0.45 notinsingleton: $o ).
% 0.28/0.45
% 0.28/0.45 thf(notinsingleton,definition,
% 0.28/0.45 ( notinsingleton
% 0.28/0.45 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.45 ( ( Xx != Xy )
% 0.28/0.45 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(eqinunit_type,type,
% 0.28/0.45 eqinunit: $o ).
% 0.28/0.45
% 0.28/0.45 thf(eqinunit,definition,
% 0.28/0.45 ( eqinunit
% 0.28/0.45 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.45 ( ( Xx = Xy )
% 0.28/0.45 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(singletonsswitch_type,type,
% 0.28/0.45 singletonsswitch: $o ).
% 0.28/0.45
% 0.28/0.45 thf(singletonsswitch,definition,
% 0.28/0.45 ( singletonsswitch
% 0.28/0.45 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.45 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.45 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(upairsetE_type,type,
% 0.28/0.45 upairsetE: $o ).
% 0.28/0.45
% 0.28/0.45 thf(upairsetE,definition,
% 0.28/0.45 ( upairsetE
% 0.28/0.45 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.28/0.45 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.28/0.45 => ( ( Xz = Xx )
% 0.28/0.45 | ( Xz = Xy ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(upairsetIL_type,type,
% 0.28/0.45 upairsetIL: $o ).
% 0.28/0.45
% 0.28/0.45 thf(upairsetIL,definition,
% 0.28/0.45 ( upairsetIL
% 0.28/0.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(upairsetIR_type,type,
% 0.28/0.45 upairsetIR: $o ).
% 0.28/0.45
% 0.28/0.45 thf(upairsetIR,definition,
% 0.28/0.45 ( upairsetIR
% 0.28/0.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(emptyE1_type,type,
% 0.28/0.45 emptyE1: $o ).
% 0.28/0.45
% 0.28/0.45 thf(emptyE1,definition,
% 0.28/0.45 ( emptyE1
% 0.28/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.45 ( ? [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 & ( Xphi @ Xx ) )
% 0.28/0.45 => ( ( ( dsetconstr @ A
% 0.28/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.45 = emptyset )
% 0.28/0.45 => $false ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(vacuousDall_type,type,
% 0.28/0.45 vacuousDall: $o ).
% 0.28/0.45
% 0.28/0.45 thf(vacuousDall,definition,
% 0.28/0.45 ( vacuousDall
% 0.28/0.45 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ emptyset )
% 0.28/0.45 => ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(quantDeMorgan1_type,type,
% 0.28/0.45 quantDeMorgan1: $o ).
% 0.28/0.45
% 0.28/0.45 thf(quantDeMorgan1,definition,
% 0.28/0.45 ( quantDeMorgan1
% 0.28/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.45 ( ~ ! [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 => ( Xphi @ Xx ) )
% 0.28/0.45 => ? [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(quantDeMorgan2_type,type,
% 0.28/0.45 quantDeMorgan2: $o ).
% 0.28/0.45
% 0.28/0.45 thf(quantDeMorgan2,definition,
% 0.28/0.45 ( quantDeMorgan2
% 0.28/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.45 ( ! [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 => ~ ( Xphi @ Xx ) )
% 0.28/0.45 => ~ ? [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(quantDeMorgan3_type,type,
% 0.28/0.45 quantDeMorgan3: $o ).
% 0.28/0.45
% 0.28/0.45 thf(quantDeMorgan3,definition,
% 0.28/0.45 ( quantDeMorgan3
% 0.28/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.45 ( ~ ? [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 & ( Xphi @ Xx ) )
% 0.28/0.45 => ! [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(quantDeMorgan4_type,type,
% 0.28/0.45 quantDeMorgan4: $o ).
% 0.28/0.45
% 0.28/0.45 thf(quantDeMorgan4,definition,
% 0.28/0.45 ( quantDeMorgan4
% 0.28/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.45 ( ? [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 & ~ ( Xphi @ Xx ) )
% 0.28/0.45 => ~ ! [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(prop2setI_type,type,
% 0.28/0.45 prop2setI: $o ).
% 0.28/0.45
% 0.28/0.45 thf(prop2setI,definition,
% 0.28/0.45 ( prop2setI
% 0.28/0.45 = ( ! [Xphi: $o] :
% 0.28/0.45 ( Xphi
% 0.28/0.45 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(set2prop_type,type,
% 0.28/0.45 set2prop: $i > $o ).
% 0.28/0.45
% 0.28/0.45 thf(prop2set2propI_type,type,
% 0.28/0.45 prop2set2propI: $o ).
% 0.28/0.45
% 0.28/0.45 thf(prop2set2propI,definition,
% 0.28/0.45 ( prop2set2propI
% 0.28/0.45 = ( ! [Xphi: $o] :
% 0.28/0.45 ( Xphi
% 0.28/0.45 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(notdexE_type,type,
% 0.28/0.45 notdexE: $o ).
% 0.28/0.45
% 0.28/0.45 thf(notdexE,definition,
% 0.28/0.45 ( notdexE
% 0.28/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.45 ( ~ ? [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 & ( Xphi @ Xx ) )
% 0.28/0.45 => ! [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(notdallE_type,type,
% 0.28/0.45 notdallE: $o ).
% 0.28/0.45
% 0.28/0.45 thf(notdallE,definition,
% 0.28/0.45 ( notdallE
% 0.28/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.45 ( ~ ! [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 => ( Xphi @ Xx ) )
% 0.28/0.45 => ? [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(exuI1_type,type,
% 0.28/0.45 exuI1: $o ).
% 0.28/0.45
% 0.28/0.45 thf(exuI1,definition,
% 0.28/0.45 ( exuI1
% 0.28/0.45 = ( ! [Xphi: $i > $o] :
% 0.28/0.45 ( ? [Xx: $i] :
% 0.28/0.45 ( ( Xphi @ Xx )
% 0.28/0.45 & ! [Xy: $i] :
% 0.28/0.45 ( ( Xphi @ Xy )
% 0.28/0.45 => ( Xx = Xy ) ) )
% 0.28/0.45 => ( exu
% 0.28/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(exuI3_type,type,
% 0.28/0.45 exuI3: $o ).
% 0.28/0.45
% 0.28/0.45 thf(exuI3,definition,
% 0.28/0.45 ( exuI3
% 0.28/0.45 = ( ! [Xphi: $i > $o] :
% 0.28/0.45 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.28/0.45 => ( ! [Xx: $i,Xy: $i] :
% 0.28/0.45 ( ( Xphi @ Xx )
% 0.28/0.45 => ( ( Xphi @ Xy )
% 0.28/0.45 => ( Xx = Xy ) ) )
% 0.28/0.45 => ( exu
% 0.28/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(exuI2_type,type,
% 0.28/0.45 exuI2: $o ).
% 0.28/0.45
% 0.28/0.45 thf(exuI2,definition,
% 0.28/0.45 ( exuI2
% 0.28/0.45 = ( ! [Xphi: $i > $o] :
% 0.28/0.45 ( ? [Xx: $i] :
% 0.28/0.45 ! [Xy: $i] :
% 0.28/0.45 ( ( Xphi @ Xy )
% 0.28/0.45 <=> ( Xy = Xx ) )
% 0.28/0.45 => ( exu
% 0.28/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(inCongP_type,type,
% 0.28/0.45 inCongP: $o ).
% 0.28/0.45
% 0.28/0.45 thf(inCongP,definition,
% 0.28/0.45 ( inCongP
% 0.28/0.45 = ( ! [A: $i,B: $i] :
% 0.28/0.45 ( ( A = B )
% 0.28/0.45 => ! [Xx: $i,Xy: $i] :
% 0.28/0.45 ( ( Xx = Xy )
% 0.28/0.45 => ( ( in @ Xx @ A )
% 0.28/0.45 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(in__Cong_type,type,
% 0.28/0.45 in__Cong: $o ).
% 0.28/0.45
% 0.28/0.45 thf(in__Cong,definition,
% 0.28/0.45 ( in__Cong
% 0.28/0.45 = ( ! [A: $i,B: $i] :
% 0.28/0.45 ( ( A = B )
% 0.28/0.45 => ! [Xx: $i,Xy: $i] :
% 0.28/0.45 ( ( Xx = Xy )
% 0.28/0.45 => ( ( in @ Xx @ A )
% 0.28/0.45 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(exuE3u_type,type,
% 0.28/0.45 exuE3u: $o ).
% 0.28/0.45
% 0.28/0.45 thf(exuE3u,definition,
% 0.28/0.45 ( exuE3u
% 0.28/0.45 = ( ! [Xphi: $i > $o] :
% 0.28/0.45 ( ( exu
% 0.28/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.45 => ! [Xx: $i,Xy: $i] :
% 0.28/0.45 ( ( Xphi @ Xx )
% 0.28/0.45 => ( ( Xphi @ Xy )
% 0.28/0.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(exu__Cong_type,type,
% 0.28/0.45 exu__Cong: $o ).
% 0.28/0.45
% 0.28/0.45 thf(exu__Cong,definition,
% 0.28/0.45 ( exu__Cong
% 0.28/0.45 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.45 ( ! [Xx: $i,Xy: $i] :
% 0.28/0.45 ( ( Xx = Xy )
% 0.28/0.45 => ( ( Xphi @ Xx )
% 0.28/0.45 <=> ( Xpsi @ Xy ) ) )
% 0.28/0.45 => ( ( exu
% 0.28/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.45 <=> ( exu
% 0.28/0.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(emptyset__Cong_type,type,
% 0.28/0.45 emptyset__Cong: $o ).
% 0.28/0.45
% 0.28/0.45 thf(emptyset__Cong,definition,
% 0.28/0.45 ( emptyset__Cong
% 0.28/0.45 = ( emptyset = emptyset ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(setadjoin__Cong_type,type,
% 0.28/0.45 setadjoin__Cong: $o ).
% 0.28/0.45
% 0.28/0.45 thf(setadjoin__Cong,definition,
% 0.28/0.45 ( setadjoin__Cong
% 0.28/0.45 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.45 ( ( Xx = Xy )
% 0.28/0.45 => ! [Xz: $i,Xu: $i] :
% 0.28/0.45 ( ( Xz = Xu )
% 0.28/0.45 => ( ( setadjoin @ Xx @ Xz )
% 0.28/0.45 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(powerset__Cong_type,type,
% 0.28/0.45 powerset__Cong: $o ).
% 0.28/0.45
% 0.28/0.45 thf(powerset__Cong,definition,
% 0.28/0.45 ( powerset__Cong
% 0.28/0.45 = ( ! [A: $i,B: $i] :
% 0.28/0.45 ( ( A = B )
% 0.28/0.45 => ( ( powerset @ A )
% 0.28/0.45 = ( powerset @ B ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(setunion__Cong_type,type,
% 0.28/0.45 setunion__Cong: $o ).
% 0.28/0.45
% 0.28/0.45 thf(setunion__Cong,definition,
% 0.28/0.45 ( setunion__Cong
% 0.28/0.45 = ( ! [A: $i,B: $i] :
% 0.28/0.45 ( ( A = B )
% 0.28/0.45 => ( ( setunion @ A )
% 0.28/0.45 = ( setunion @ B ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(omega__Cong_type,type,
% 0.28/0.45 omega__Cong: $o ).
% 0.28/0.45
% 0.28/0.45 thf(omega__Cong,definition,
% 0.28/0.45 ( omega__Cong
% 0.28/0.45 = ( omega = omega ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(exuEu_type,type,
% 0.28/0.45 exuEu: $o ).
% 0.28/0.45
% 0.28/0.45 thf(exuEu,definition,
% 0.28/0.45 ( exuEu
% 0.28/0.45 = ( ! [Xphi: $i > $o] :
% 0.28/0.45 ( ( exu
% 0.28/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.45 => ! [Xx: $i,Xy: $i] :
% 0.28/0.45 ( ( Xphi @ Xx )
% 0.28/0.45 => ( ( Xphi @ Xy )
% 0.28/0.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(descr__Cong_type,type,
% 0.28/0.45 descr__Cong: $o ).
% 0.28/0.45
% 0.28/0.45 thf(descr__Cong,definition,
% 0.28/0.45 ( descr__Cong
% 0.28/0.45 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.45 ( ! [Xx: $i,Xy: $i] :
% 0.28/0.45 ( ( Xx = Xy )
% 0.28/0.45 => ( ( Xphi @ Xx )
% 0.28/0.45 <=> ( Xpsi @ Xy ) ) )
% 0.28/0.45 => ( ( exu
% 0.28/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.45 => ( ( exu
% 0.28/0.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.28/0.45 => ( ( descr
% 0.28/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.45 = ( descr
% 0.28/0.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(dsetconstr__Cong_type,type,
% 0.28/0.45 dsetconstr__Cong: $o ).
% 0.28/0.45
% 0.28/0.45 thf(dsetconstr__Cong,definition,
% 0.28/0.45 ( dsetconstr__Cong
% 0.28/0.45 = ( ! [A: $i,B: $i] :
% 0.28/0.45 ( ( A = B )
% 0.28/0.45 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.45 ( ! [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 => ! [Xy: $i] :
% 0.28/0.45 ( ( in @ Xy @ B )
% 0.28/0.45 => ( ( Xx = Xy )
% 0.28/0.45 => ( ( Xphi @ Xx )
% 0.28/0.45 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.28/0.45 => ( ( dsetconstr @ A
% 0.28/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.45 = ( dsetconstr @ B
% 0.28/0.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(subset_type,type,
% 0.28/0.45 subset: $i > $i > $o ).
% 0.28/0.45
% 0.28/0.45 thf(disjoint_type,type,
% 0.28/0.45 disjoint: $i > $i > $o ).
% 0.28/0.45
% 0.28/0.45 thf(setsmeet_type,type,
% 0.28/0.45 setsmeet: $i > $i > $o ).
% 0.28/0.45
% 0.28/0.45 thf(subsetI1_type,type,
% 0.28/0.45 subsetI1: $o ).
% 0.28/0.45
% 0.28/0.45 thf(subsetI1,definition,
% 0.28/0.45 ( subsetI1
% 0.28/0.45 = ( ! [A: $i,B: $i] :
% 0.28/0.45 ( ! [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 => ( in @ Xx @ B ) )
% 0.28/0.45 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(eqimpsubset2_type,type,
% 0.28/0.45 eqimpsubset2: $o ).
% 0.28/0.45
% 0.28/0.45 thf(eqimpsubset2,definition,
% 0.28/0.45 ( eqimpsubset2
% 0.28/0.45 = ( ! [A: $i,B: $i] :
% 0.28/0.45 ( ( A = B )
% 0.28/0.45 => ( subset @ B @ A ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(eqimpsubset1_type,type,
% 0.28/0.45 eqimpsubset1: $o ).
% 0.28/0.45
% 0.28/0.45 thf(eqimpsubset1,definition,
% 0.28/0.45 ( eqimpsubset1
% 0.28/0.45 = ( ! [A: $i,B: $i] :
% 0.28/0.45 ( ( A = B )
% 0.28/0.45 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(subsetI2_type,type,
% 0.28/0.45 subsetI2: $o ).
% 0.28/0.45
% 0.28/0.45 thf(subsetI2,definition,
% 0.28/0.45 ( subsetI2
% 0.28/0.45 = ( ! [A: $i,B: $i] :
% 0.28/0.45 ( ! [Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 => ( in @ Xx @ B ) )
% 0.28/0.45 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(emptysetsubset_type,type,
% 0.28/0.45 emptysetsubset: $o ).
% 0.28/0.45
% 0.28/0.45 thf(emptysetsubset,definition,
% 0.28/0.45 ( emptysetsubset
% 0.28/0.45 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(subsetE_type,type,
% 0.28/0.45 subsetE: $o ).
% 0.28/0.45
% 0.28/0.45 thf(subsetE,definition,
% 0.28/0.45 ( subsetE
% 0.28/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.45 ( ( subset @ A @ B )
% 0.28/0.45 => ( ( in @ Xx @ A )
% 0.28/0.45 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(subsetE2_type,type,
% 0.28/0.45 subsetE2: $o ).
% 0.28/0.45
% 0.28/0.45 thf(subsetE2,definition,
% 0.28/0.45 ( subsetE2
% 0.28/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.45 ( ( subset @ A @ B )
% 0.28/0.45 => ( ~ ( in @ Xx @ B )
% 0.28/0.45 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(notsubsetI_type,type,
% 0.28/0.45 notsubsetI: $o ).
% 0.28/0.45
% 0.28/0.45 thf(notsubsetI,definition,
% 0.28/0.45 ( notsubsetI
% 0.28/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 => ( ~ ( in @ Xx @ B )
% 0.28/0.45 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(notequalI1_type,type,
% 0.28/0.45 notequalI1: $o ).
% 0.28/0.45
% 0.28/0.45 thf(notequalI1,definition,
% 0.28/0.45 ( notequalI1
% 0.28/0.45 = ( ! [A: $i,B: $i] :
% 0.28/0.45 ( ~ ( subset @ A @ B )
% 0.28/0.45 => ( A != B ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(notequalI2_type,type,
% 0.28/0.45 notequalI2: $o ).
% 0.28/0.45
% 0.28/0.45 thf(notequalI2,definition,
% 0.28/0.45 ( notequalI2
% 0.28/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 => ( ~ ( in @ Xx @ B )
% 0.28/0.45 => ( A != B ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(subsetRefl_type,type,
% 0.28/0.45 subsetRefl: $o ).
% 0.28/0.45
% 0.28/0.45 thf(subsetRefl,definition,
% 0.28/0.45 ( subsetRefl
% 0.28/0.45 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(subsetTrans_type,type,
% 0.28/0.45 subsetTrans: $o ).
% 0.28/0.45
% 0.28/0.45 thf(subsetTrans,definition,
% 0.28/0.45 ( subsetTrans
% 0.28/0.45 = ( ! [A: $i,B: $i,C: $i] :
% 0.28/0.45 ( ( subset @ A @ B )
% 0.28/0.45 => ( ( subset @ B @ C )
% 0.28/0.45 => ( subset @ A @ C ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(setadjoinSub_type,type,
% 0.28/0.45 setadjoinSub: $o ).
% 0.28/0.45
% 0.28/0.45 thf(setadjoinSub,definition,
% 0.28/0.45 ( setadjoinSub
% 0.28/0.45 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(setadjoinSub2_type,type,
% 0.28/0.45 setadjoinSub2: $o ).
% 0.28/0.45
% 0.28/0.45 thf(setadjoinSub2,definition,
% 0.28/0.45 ( setadjoinSub2
% 0.28/0.45 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.28/0.45 ( ( subset @ A @ B )
% 0.28/0.45 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(subset2powerset_type,type,
% 0.28/0.45 subset2powerset: $o ).
% 0.28/0.45
% 0.28/0.45 thf(subset2powerset,definition,
% 0.28/0.45 ( subset2powerset
% 0.28/0.45 = ( ! [A: $i,B: $i] :
% 0.28/0.45 ( ( subset @ A @ B )
% 0.28/0.45 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(setextsub_type,type,
% 0.28/0.45 setextsub: $o ).
% 0.28/0.45
% 0.28/0.45 thf(setextsub,definition,
% 0.28/0.45 ( setextsub
% 0.28/0.45 = ( ! [A: $i,B: $i] :
% 0.28/0.45 ( ( subset @ A @ B )
% 0.28/0.45 => ( ( subset @ B @ A )
% 0.28/0.45 => ( A = B ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(subsetemptysetimpeq_type,type,
% 0.28/0.45 subsetemptysetimpeq: $o ).
% 0.28/0.45
% 0.28/0.45 thf(subsetemptysetimpeq,definition,
% 0.28/0.45 ( subsetemptysetimpeq
% 0.28/0.45 = ( ! [A: $i] :
% 0.28/0.45 ( ( subset @ A @ emptyset )
% 0.28/0.45 => ( A = emptyset ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(powersetI1_type,type,
% 0.28/0.45 powersetI1: $o ).
% 0.28/0.45
% 0.28/0.45 thf(powersetI1,definition,
% 0.28/0.45 ( powersetI1
% 0.28/0.45 = ( ! [A: $i,B: $i] :
% 0.28/0.45 ( ( subset @ B @ A )
% 0.28/0.45 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(powersetE1_type,type,
% 0.28/0.45 powersetE1: $o ).
% 0.28/0.45
% 0.28/0.45 thf(powersetE1,definition,
% 0.28/0.45 ( powersetE1
% 0.28/0.45 = ( ! [A: $i,B: $i] :
% 0.28/0.45 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.45 => ( subset @ B @ A ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(inPowerset_type,type,
% 0.28/0.45 inPowerset: $o ).
% 0.28/0.45
% 0.28/0.45 thf(inPowerset,definition,
% 0.28/0.45 ( inPowerset
% 0.28/0.45 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(powersetsubset_type,type,
% 0.28/0.45 powersetsubset: $o ).
% 0.28/0.45
% 0.28/0.45 thf(powersetsubset,definition,
% 0.28/0.45 ( powersetsubset
% 0.28/0.45 = ( ! [A: $i,B: $i] :
% 0.28/0.45 ( ( subset @ A @ B )
% 0.28/0.45 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(sepInPowerset_type,type,
% 0.28/0.45 sepInPowerset: $o ).
% 0.28/0.45
% 0.28/0.45 thf(sepInPowerset,definition,
% 0.28/0.45 ( sepInPowerset
% 0.28/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.45 ( in
% 0.28/0.45 @ ( dsetconstr @ A
% 0.28/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.45 @ ( powerset @ A ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(sepSubset_type,type,
% 0.28/0.45 sepSubset: $o ).
% 0.28/0.45
% 0.28/0.45 thf(sepSubset,definition,
% 0.28/0.45 ( sepSubset
% 0.28/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.45 ( subset
% 0.28/0.45 @ ( dsetconstr @ A
% 0.28/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.45 @ A ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(binunion_type,type,
% 0.28/0.45 binunion: $i > $i > $i ).
% 0.28/0.45
% 0.28/0.45 thf(binunionIL_type,type,
% 0.28/0.45 binunionIL: $o ).
% 0.28/0.45
% 0.28/0.45 thf(binunionIL,definition,
% 0.28/0.45 ( binunionIL
% 0.28/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(upairset2IR_type,type,
% 0.28/0.45 upairset2IR: $o ).
% 0.28/0.45
% 0.28/0.45 thf(upairset2IR,definition,
% 0.28/0.45 ( upairset2IR
% 0.28/0.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(binunionIR_type,type,
% 0.28/0.45 binunionIR: $o ).
% 0.28/0.45
% 0.28/0.45 thf(binunionIR,definition,
% 0.28/0.45 ( binunionIR
% 0.28/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ B )
% 0.28/0.45 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(binunionEcases_type,type,
% 0.28/0.45 binunionEcases: $o ).
% 0.28/0.45
% 0.28/0.45 thf(binunionEcases,definition,
% 0.28/0.45 ( binunionEcases
% 0.28/0.45 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.28/0.45 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.28/0.45 => ( ( ( in @ Xx @ A )
% 0.28/0.45 => Xphi )
% 0.28/0.45 => ( ( ( in @ Xx @ B )
% 0.28/0.45 => Xphi )
% 0.28/0.45 => Xphi ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(binunionE_type,type,
% 0.28/0.45 binunionE: $o ).
% 0.28/0.45
% 0.28/0.45 thf(binunionE,definition,
% 0.28/0.45 ( binunionE
% 0.28/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.28/0.45 => ( ( in @ Xx @ A )
% 0.28/0.45 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(binunionLsub_type,type,
% 0.28/0.45 binunionLsub: $o ).
% 0.28/0.45
% 0.28/0.45 thf(binunionLsub,definition,
% 0.28/0.45 ( binunionLsub
% 0.28/0.45 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(binunionRsub_type,type,
% 0.28/0.45 binunionRsub: $o ).
% 0.28/0.45
% 0.28/0.45 thf(binunionRsub,definition,
% 0.28/0.45 ( binunionRsub
% 0.28/0.45 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 thf(binintersect_type,type,
% 0.28/0.45 binintersect: $i > $i > $i ).
% 0.28/0.45
% 0.28/0.45 thf(binintersectI_type,type,
% 0.28/0.45 binintersectI: $o ).
% 0.28/0.45
% 0.28/0.45 thf(binintersectI,definition,
% 0.28/0.45 ( binintersectI
% 0.28/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.45 ( ( in @ Xx @ A )
% 0.28/0.45 => ( ( in @ Xx @ B )
% 0.28/0.45 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(binintersectSubset5_type,type,
% 0.28/0.46 binintersectSubset5: $o ).
% 0.28/0.46
% 0.28/0.46 thf(binintersectSubset5,definition,
% 0.28/0.46 ( binintersectSubset5
% 0.28/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.28/0.46 ( ( subset @ C @ A )
% 0.28/0.46 => ( ( subset @ C @ B )
% 0.28/0.46 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(binintersectEL_type,type,
% 0.28/0.46 binintersectEL: $o ).
% 0.28/0.46
% 0.28/0.46 thf(binintersectEL,definition,
% 0.28/0.46 ( binintersectEL
% 0.28/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.28/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(binintersectLsub_type,type,
% 0.28/0.46 binintersectLsub: $o ).
% 0.28/0.46
% 0.28/0.46 thf(binintersectLsub,definition,
% 0.28/0.46 ( binintersectLsub
% 0.28/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(binintersectSubset2_type,type,
% 0.28/0.46 binintersectSubset2: $o ).
% 0.28/0.46
% 0.28/0.46 thf(binintersectSubset2,definition,
% 0.28/0.46 ( binintersectSubset2
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ( subset @ A @ B )
% 0.28/0.46 => ( ( binintersect @ A @ B )
% 0.28/0.46 = A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(binintersectSubset3_type,type,
% 0.28/0.46 binintersectSubset3: $o ).
% 0.28/0.46
% 0.28/0.46 thf(binintersectSubset3,definition,
% 0.28/0.46 ( binintersectSubset3
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ( ( binintersect @ A @ B )
% 0.28/0.46 = B )
% 0.28/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(binintersectER_type,type,
% 0.28/0.46 binintersectER: $o ).
% 0.28/0.46
% 0.28/0.46 thf(binintersectER,definition,
% 0.28/0.46 ( binintersectER
% 0.28/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.28/0.46 => ( in @ Xx @ B ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(disjointsetsI1_type,type,
% 0.28/0.46 disjointsetsI1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(disjointsetsI1,definition,
% 0.28/0.46 ( disjointsetsI1
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ~ ? [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 & ( in @ Xx @ B ) )
% 0.28/0.46 => ( ( binintersect @ A @ B )
% 0.28/0.46 = emptyset ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(binintersectRsub,conjecture,
% 0.28/0.46 ( setextAx
% 0.28/0.46 => ( emptysetAx
% 0.28/0.46 => ( setadjoinAx
% 0.28/0.46 => ( powersetAx
% 0.28/0.46 => ( setunionAx
% 0.28/0.46 => ( omega0Ax
% 0.28/0.46 => ( omegaSAx
% 0.28/0.46 => ( omegaIndAx
% 0.28/0.46 => ( replAx
% 0.28/0.46 => ( foundationAx
% 0.28/0.46 => ( wellorderingAx
% 0.28/0.46 => ( descrp
% 0.28/0.46 => ( dsetconstrI
% 0.28/0.46 => ( dsetconstrEL
% 0.28/0.46 => ( dsetconstrER
% 0.28/0.46 => ( exuE1
% 0.28/0.46 => ( prop2setE
% 0.28/0.46 => ( emptysetE
% 0.28/0.46 => ( emptysetimpfalse
% 0.28/0.46 => ( notinemptyset
% 0.28/0.46 => ( exuE3e
% 0.28/0.46 => ( setext
% 0.28/0.46 => ( emptyI
% 0.28/0.46 => ( noeltsimpempty
% 0.28/0.46 => ( setbeta
% 0.28/0.46 => ( nonemptyE1
% 0.28/0.46 => ( nonemptyI
% 0.28/0.46 => ( nonemptyI1
% 0.28/0.46 => ( setadjoinIL
% 0.28/0.46 => ( emptyinunitempty
% 0.28/0.46 => ( setadjoinIR
% 0.28/0.46 => ( setadjoinE
% 0.28/0.46 => ( setadjoinOr
% 0.28/0.46 => ( setoftrueEq
% 0.28/0.46 => ( powersetI
% 0.28/0.46 => ( emptyinPowerset
% 0.28/0.46 => ( emptyInPowerset
% 0.28/0.46 => ( powersetE
% 0.28/0.46 => ( setunionI
% 0.28/0.46 => ( setunionE
% 0.28/0.46 => ( subPowSU
% 0.28/0.46 => ( exuE2
% 0.28/0.46 => ( nonemptyImpWitness
% 0.28/0.46 => ( uniqinunit
% 0.28/0.46 => ( notinsingleton
% 0.28/0.46 => ( eqinunit
% 0.28/0.46 => ( singletonsswitch
% 0.28/0.46 => ( upairsetE
% 0.28/0.46 => ( upairsetIL
% 0.28/0.46 => ( upairsetIR
% 0.28/0.46 => ( emptyE1
% 0.28/0.46 => ( vacuousDall
% 0.28/0.46 => ( quantDeMorgan1
% 0.28/0.46 => ( quantDeMorgan2
% 0.28/0.46 => ( quantDeMorgan3
% 0.28/0.46 => ( quantDeMorgan4
% 0.28/0.46 => ( prop2setI
% 0.28/0.46 => ( prop2set2propI
% 0.28/0.46 => ( notdexE
% 0.28/0.46 => ( notdallE
% 0.28/0.46 => ( exuI1
% 0.28/0.46 => ( exuI3
% 0.28/0.46 => ( exuI2
% 0.28/0.46 => ( inCongP
% 0.28/0.46 => ( in__Cong
% 0.28/0.46 => ( exuE3u
% 0.28/0.46 => ( exu__Cong
% 0.28/0.46 => ( emptyset__Cong
% 0.28/0.46 => ( setadjoin__Cong
% 0.28/0.46 => ( powerset__Cong
% 0.28/0.46 => ( setunion__Cong
% 0.28/0.46 => ( omega__Cong
% 0.28/0.46 => ( exuEu
% 0.28/0.46 => ( descr__Cong
% 0.28/0.46 => ( dsetconstr__Cong
% 0.28/0.46 => ( subsetI1
% 0.28/0.46 => ( eqimpsubset2
% 0.28/0.46 => ( eqimpsubset1
% 0.28/0.46 => ( subsetI2
% 0.28/0.46 => ( emptysetsubset
% 0.28/0.46 => ( subsetE
% 0.28/0.46 => ( subsetE2
% 0.28/0.46 => ( notsubsetI
% 0.28/0.46 => ( notequalI1
% 0.28/0.46 => ( notequalI2
% 0.28/0.46 => ( subsetRefl
% 0.28/0.46 => ( subsetTrans
% 0.28/0.46 => ( setadjoinSub
% 0.28/0.46 => ( setadjoinSub2
% 0.28/0.46 => ( subset2powerset
% 0.28/0.46 => ( setextsub
% 0.28/0.46 => ( subsetemptysetimpeq
% 0.28/0.46 => ( powersetI1
% 0.28/0.46 => ( powersetE1
% 0.28/0.46 => ( inPowerset
% 0.28/0.46 => ( powersetsubset
% 0.28/0.46 => ( sepInPowerset
% 0.28/0.46 => ( sepSubset
% 0.28/0.46 => ( binunionIL
% 0.28/0.46 => ( upairset2IR
% 0.28/0.46 => ( binunionIR
% 0.28/0.46 => ( binunionEcases
% 0.28/0.46 => ( binunionE
% 0.28/0.46 => ( binunionLsub
% 0.28/0.46 => ( binunionRsub
% 0.28/0.46 => ( binintersectI
% 0.28/0.46 => ( binintersectSubset5
% 0.28/0.46 => ( binintersectEL
% 0.28/0.46 => ( binintersectLsub
% 0.28/0.46 => ( binintersectSubset2
% 0.28/0.46 => ( binintersectSubset3
% 0.28/0.46 => ( binintersectER
% 0.28/0.46 => ( disjointsetsI1
% 0.28/0.46 => ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 2.30/1.42 ---- Embedded in THF ---
% 2.30/1.42 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.30/1.42 %%% Generated on Tue Feb 24 12:28:07 EST 2026
% 2.30/1.42 %%% using '$$dhol' embedding, version 1.3.0.
% 2.30/1.42 %%% Logic specification used:
% 2.30/1.42 %%% thf(spec, logic, $$dhol).
% 2.30/1.42
% 2.30/1.42 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.osm1bNkGRD/DTF2DTF7106.p
% See solution above
% 2.30/1.42 ------------------------
% 2.30/1.45 ---- Cleaned THF ---
% 2.30/1.45 thf(in_type,type,
% 2.30/1.45 in: $i > $i > $o ).
% 2.30/1.45
% 2.30/1.45 thf(exu_type,type,
% 2.30/1.45 exu: ( $i > $o ) > $o ).
% 2.30/1.45
% 2.30/1.45 thf(exu,definition,
% 2.30/1.45 ( exu
% 2.30/1.45 = ( ^ [Xphi: $i > $o] :
% 2.30/1.45 ? [Xx: $i] :
% 2.30/1.45 ( ( Xphi @ Xx )
% 2.30/1.45 & ! [Xy: $i] :
% 2.30/1.45 ( ( Xphi @ Xy )
% 2.30/1.45 => ( Xx = Xy ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(setextAx_type,type,
% 2.30/1.45 setextAx: $o ).
% 2.30/1.45
% 2.30/1.45 thf(setextAx,definition,
% 2.30/1.45 ( setextAx
% 2.30/1.45 = ( ! [A: $i,B: $i] :
% 2.30/1.45 ( ! [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ A )
% 2.30/1.45 <=> ( in @ Xx @ B ) )
% 2.30/1.45 => ( A = B ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(emptyset_type,type,
% 2.30/1.45 emptyset: $i ).
% 2.30/1.45
% 2.30/1.45 thf(emptysetAx_type,type,
% 2.30/1.45 emptysetAx: $o ).
% 2.30/1.45
% 2.30/1.45 thf(emptysetAx,definition,
% 2.30/1.45 ( emptysetAx
% 2.30/1.45 = ( ! [Xx: $i] :
% 2.30/1.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(setadjoin_type,type,
% 2.30/1.45 setadjoin: $i > $i > $i ).
% 2.30/1.45
% 2.30/1.45 thf(setadjoinAx_type,type,
% 2.30/1.45 setadjoinAx: $o ).
% 2.30/1.45
% 2.30/1.45 thf(setadjoinAx,definition,
% 2.30/1.45 ( setadjoinAx
% 2.30/1.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.30/1.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.30/1.45 <=> ( ( Xy = Xx )
% 2.30/1.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(powerset_type,type,
% 2.30/1.45 powerset: $i > $i ).
% 2.30/1.45
% 2.30/1.45 thf(powersetAx_type,type,
% 2.30/1.45 powersetAx: $o ).
% 2.30/1.45
% 2.30/1.45 thf(powersetAx,definition,
% 2.30/1.45 ( powersetAx
% 2.30/1.45 = ( ! [A: $i,B: $i] :
% 2.30/1.45 ( ( in @ B @ ( powerset @ A ) )
% 2.30/1.45 <=> ! [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ B )
% 2.30/1.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(setunion_type,type,
% 2.30/1.45 setunion: $i > $i ).
% 2.30/1.45
% 2.30/1.45 thf(setunionAx_type,type,
% 2.30/1.45 setunionAx: $o ).
% 2.30/1.45
% 2.30/1.45 thf(setunionAx,definition,
% 2.30/1.45 ( setunionAx
% 2.30/1.45 = ( ! [A: $i,Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ ( setunion @ A ) )
% 2.30/1.45 <=> ? [B: $i] :
% 2.30/1.45 ( ( in @ Xx @ B )
% 2.30/1.45 & ( in @ B @ A ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(omega_type,type,
% 2.30/1.45 omega: $i ).
% 2.30/1.45
% 2.30/1.45 thf(omega0Ax_type,type,
% 2.30/1.45 omega0Ax: $o ).
% 2.30/1.45
% 2.30/1.45 thf(omega0Ax,definition,
% 2.30/1.45 ( omega0Ax
% 2.30/1.45 = ( in @ emptyset @ omega ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(omegaSAx_type,type,
% 2.30/1.45 omegaSAx: $o ).
% 2.30/1.45
% 2.30/1.45 thf(omegaSAx,definition,
% 2.30/1.45 ( omegaSAx
% 2.30/1.45 = ( ! [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ omega )
% 2.30/1.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(omegaIndAx_type,type,
% 2.30/1.45 omegaIndAx: $o ).
% 2.30/1.45
% 2.30/1.45 thf(omegaIndAx,definition,
% 2.30/1.45 ( omegaIndAx
% 2.30/1.45 = ( ! [A: $i] :
% 2.30/1.45 ( ( ( in @ emptyset @ A )
% 2.30/1.45 & ! [Xx: $i] :
% 2.30/1.45 ( ( ( in @ Xx @ omega )
% 2.30/1.45 & ( in @ Xx @ A ) )
% 2.30/1.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.30/1.45 => ! [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ omega )
% 2.30/1.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(replAx_type,type,
% 2.30/1.45 replAx: $o ).
% 2.30/1.45
% 2.30/1.45 thf(replAx,definition,
% 2.30/1.45 ( replAx
% 2.30/1.45 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.30/1.45 ( ! [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ A )
% 2.30/1.45 => ( exu
% 2.30/1.45 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.30/1.45 => ? [B: $i] :
% 2.30/1.45 ! [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ B )
% 2.30/1.45 <=> ? [Xy: $i] :
% 2.30/1.45 ( ( in @ Xy @ A )
% 2.30/1.45 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(foundationAx_type,type,
% 2.30/1.45 foundationAx: $o ).
% 2.30/1.45
% 2.30/1.45 thf(foundationAx,definition,
% 2.30/1.45 ( foundationAx
% 2.30/1.45 = ( ! [A: $i] :
% 2.30/1.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.30/1.45 => ? [B: $i] :
% 2.30/1.45 ( ( in @ B @ A )
% 2.30/1.45 & ~ ? [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ B )
% 2.30/1.45 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(wellorderingAx_type,type,
% 2.30/1.45 wellorderingAx: $o ).
% 2.30/1.45
% 2.30/1.45 thf(wellorderingAx,definition,
% 2.30/1.45 ( wellorderingAx
% 2.30/1.45 = ( ! [A: $i] :
% 2.30/1.45 ? [B: $i] :
% 2.30/1.45 ( ! [C: $i] :
% 2.30/1.45 ( ( in @ C @ B )
% 2.30/1.45 => ! [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ C )
% 2.30/1.45 => ( in @ Xx @ A ) ) )
% 2.30/1.45 & ! [Xx: $i,Xy: $i] :
% 2.30/1.45 ( ( ( in @ Xx @ A )
% 2.30/1.45 & ( in @ Xy @ A ) )
% 2.30/1.45 => ( ! [C: $i] :
% 2.30/1.45 ( ( in @ C @ B )
% 2.30/1.45 => ( ( in @ Xx @ C )
% 2.30/1.45 <=> ( in @ Xy @ C ) ) )
% 2.30/1.45 => ( Xx = Xy ) ) )
% 2.30/1.45 & ! [C: $i,D: $i] :
% 2.30/1.45 ( ( ( in @ C @ B )
% 2.30/1.45 & ( in @ D @ B ) )
% 2.30/1.45 => ( ! [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ C )
% 2.30/1.45 => ( in @ Xx @ D ) )
% 2.30/1.45 | ! [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ D )
% 2.30/1.45 => ( in @ Xx @ C ) ) ) )
% 2.30/1.45 & ! [C: $i] :
% 2.30/1.45 ( ( ! [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ C )
% 2.30/1.45 => ( in @ Xx @ A ) )
% 2.30/1.45 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.30/1.45 => ? [D: $i,Xx: $i] :
% 2.30/1.45 ( ( in @ D @ B )
% 2.30/1.45 & ( in @ Xx @ C )
% 2.30/1.45 & ~ ? [Xy: $i] :
% 2.30/1.45 ( ( in @ Xy @ D )
% 2.30/1.45 & ( in @ Xy @ C ) )
% 2.30/1.45 & ! [E: $i] :
% 2.30/1.45 ( ( in @ E @ B )
% 2.30/1.45 => ( ! [Xy: $i] :
% 2.30/1.45 ( ( in @ Xy @ E )
% 2.30/1.45 => ( in @ Xy @ D ) )
% 2.30/1.45 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(descr_type,type,
% 2.30/1.45 descr: ( $i > $o ) > $i ).
% 2.30/1.45
% 2.30/1.45 thf(descrp_type,type,
% 2.30/1.45 descrp: $o ).
% 2.30/1.45
% 2.30/1.45 thf(descrp,definition,
% 2.30/1.45 ( descrp
% 2.30/1.45 = ( ! [Xphi: $i > $o] :
% 2.30/1.45 ( ( exu
% 2.30/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.30/1.45 => ( Xphi
% 2.30/1.45 @ ( descr
% 2.30/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(dsetconstr_type,type,
% 2.30/1.45 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.30/1.45
% 2.30/1.45 thf(dsetconstrI_type,type,
% 2.30/1.45 dsetconstrI: $o ).
% 2.30/1.45
% 2.30/1.45 thf(dsetconstrI,definition,
% 2.30/1.45 ( dsetconstrI
% 2.30/1.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ A )
% 2.30/1.45 => ( ( Xphi @ Xx )
% 2.30/1.45 => ( in @ Xx
% 2.30/1.45 @ ( dsetconstr @ A
% 2.30/1.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(dsetconstrEL_type,type,
% 2.30/1.45 dsetconstrEL: $o ).
% 2.30/1.45
% 2.30/1.45 thf(dsetconstrEL,definition,
% 2.30/1.45 ( dsetconstrEL
% 2.30/1.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.30/1.45 ( ( in @ Xx
% 2.30/1.45 @ ( dsetconstr @ A
% 2.30/1.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.30/1.45 => ( in @ Xx @ A ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(dsetconstrER_type,type,
% 2.30/1.45 dsetconstrER: $o ).
% 2.30/1.45
% 2.30/1.45 thf(dsetconstrER,definition,
% 2.30/1.45 ( dsetconstrER
% 2.30/1.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.30/1.45 ( ( in @ Xx
% 2.30/1.45 @ ( dsetconstr @ A
% 2.30/1.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.30/1.45 => ( Xphi @ Xx ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(exuE1_type,type,
% 2.30/1.45 exuE1: $o ).
% 2.30/1.45
% 2.30/1.45 thf(exuE1,definition,
% 2.30/1.45 ( exuE1
% 2.30/1.45 = ( ! [Xphi: $i > $o] :
% 2.30/1.45 ( ( exu
% 2.30/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.30/1.45 => ? [Xx: $i] :
% 2.30/1.45 ( ( Xphi @ Xx )
% 2.30/1.45 & ! [Xy: $i] :
% 2.30/1.45 ( ( Xphi @ Xy )
% 2.30/1.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(prop2set_type,type,
% 2.30/1.45 prop2set: $o > $i ).
% 2.30/1.45
% 2.30/1.45 thf(prop2setE_type,type,
% 2.30/1.45 prop2setE: $o ).
% 2.30/1.45
% 2.30/1.45 thf(prop2setE,definition,
% 2.30/1.45 ( prop2setE
% 2.30/1.45 = ( ! [Xphi: $o,Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.30/1.45 => Xphi ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(emptysetE_type,type,
% 2.30/1.45 emptysetE: $o ).
% 2.30/1.45
% 2.30/1.45 thf(emptysetE,definition,
% 2.30/1.45 ( emptysetE
% 2.30/1.45 = ( ! [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ emptyset )
% 2.30/1.45 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(emptysetimpfalse_type,type,
% 2.30/1.45 emptysetimpfalse: $o ).
% 2.30/1.45
% 2.30/1.45 thf(emptysetimpfalse,definition,
% 2.30/1.45 ( emptysetimpfalse
% 2.30/1.45 = ( ! [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ emptyset )
% 2.30/1.45 => $false ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(notinemptyset_type,type,
% 2.30/1.45 notinemptyset: $o ).
% 2.30/1.45
% 2.30/1.45 thf(notinemptyset,definition,
% 2.30/1.45 ( notinemptyset
% 2.30/1.45 = ( ! [Xx: $i] :
% 2.30/1.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(exuE3e_type,type,
% 2.30/1.45 exuE3e: $o ).
% 2.30/1.45
% 2.30/1.45 thf(exuE3e,definition,
% 2.30/1.45 ( exuE3e
% 2.30/1.45 = ( ! [Xphi: $i > $o] :
% 2.30/1.45 ( ( exu
% 2.30/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.30/1.45 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(setext_type,type,
% 2.30/1.45 setext: $o ).
% 2.30/1.45
% 2.30/1.45 thf(setext,definition,
% 2.30/1.45 ( setext
% 2.30/1.45 = ( ! [A: $i,B: $i] :
% 2.30/1.45 ( ! [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ A )
% 2.30/1.45 => ( in @ Xx @ B ) )
% 2.30/1.45 => ( ! [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ B )
% 2.30/1.45 => ( in @ Xx @ A ) )
% 2.30/1.45 => ( A = B ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(emptyI_type,type,
% 2.30/1.45 emptyI: $o ).
% 2.30/1.45
% 2.30/1.45 thf(emptyI,definition,
% 2.30/1.45 ( emptyI
% 2.30/1.45 = ( ! [A: $i] :
% 2.30/1.45 ( ! [Xx: $i] :
% 2.30/1.45 ~ ( in @ Xx @ A )
% 2.30/1.45 => ( A = emptyset ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(noeltsimpempty_type,type,
% 2.30/1.45 noeltsimpempty: $o ).
% 2.30/1.45
% 2.30/1.45 thf(noeltsimpempty,definition,
% 2.30/1.45 ( noeltsimpempty
% 2.30/1.45 = ( ! [A: $i] :
% 2.30/1.45 ( ! [Xx: $i] :
% 2.30/1.45 ~ ( in @ Xx @ A )
% 2.30/1.45 => ( A = emptyset ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(setbeta_type,type,
% 2.30/1.45 setbeta: $o ).
% 2.30/1.45
% 2.30/1.45 thf(setbeta,definition,
% 2.30/1.45 ( setbeta
% 2.30/1.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ A )
% 2.30/1.45 => ( ( in @ Xx
% 2.30/1.45 @ ( dsetconstr @ A
% 2.30/1.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.30/1.45 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(nonempty_type,type,
% 2.30/1.45 nonempty: $i > $o ).
% 2.30/1.45
% 2.30/1.45 thf(nonempty,definition,
% 2.30/1.45 ( nonempty
% 2.30/1.45 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(nonemptyE1_type,type,
% 2.30/1.45 nonemptyE1: $o ).
% 2.30/1.45
% 2.30/1.45 thf(nonemptyE1,definition,
% 2.30/1.45 ( nonemptyE1
% 2.30/1.45 = ( ! [A: $i] :
% 2.30/1.45 ( ( nonempty @ A )
% 2.30/1.45 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(nonemptyI_type,type,
% 2.30/1.45 nonemptyI: $o ).
% 2.30/1.45
% 2.30/1.45 thf(nonemptyI,definition,
% 2.30/1.45 ( nonemptyI
% 2.30/1.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ A )
% 2.30/1.45 => ( ( Xphi @ Xx )
% 2.30/1.45 => ( nonempty
% 2.30/1.45 @ ( dsetconstr @ A
% 2.30/1.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(nonemptyI1_type,type,
% 2.30/1.45 nonemptyI1: $o ).
% 2.30/1.45
% 2.30/1.45 thf(nonemptyI1,definition,
% 2.30/1.45 ( nonemptyI1
% 2.30/1.45 = ( ! [A: $i] :
% 2.30/1.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.30/1.45 => ( nonempty @ A ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(setadjoinIL_type,type,
% 2.30/1.45 setadjoinIL: $o ).
% 2.30/1.45
% 2.30/1.45 thf(setadjoinIL,definition,
% 2.30/1.45 ( setadjoinIL
% 2.30/1.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(emptyinunitempty_type,type,
% 2.30/1.45 emptyinunitempty: $o ).
% 2.30/1.45
% 2.30/1.45 thf(emptyinunitempty,definition,
% 2.30/1.45 ( emptyinunitempty
% 2.30/1.45 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(setadjoinIR_type,type,
% 2.30/1.45 setadjoinIR: $o ).
% 2.30/1.45
% 2.30/1.45 thf(setadjoinIR,definition,
% 2.30/1.45 ( setadjoinIR
% 2.30/1.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.30/1.45 ( ( in @ Xy @ A )
% 2.30/1.45 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(setadjoinE_type,type,
% 2.30/1.45 setadjoinE: $o ).
% 2.30/1.45
% 2.30/1.45 thf(setadjoinE,definition,
% 2.30/1.45 ( setadjoinE
% 2.30/1.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.30/1.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.30/1.45 => ! [Xphi: $o] :
% 2.30/1.45 ( ( ( Xy = Xx )
% 2.30/1.45 => Xphi )
% 2.30/1.45 => ( ( ( in @ Xy @ A )
% 2.30/1.45 => Xphi )
% 2.30/1.45 => Xphi ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(setadjoinOr_type,type,
% 2.30/1.45 setadjoinOr: $o ).
% 2.30/1.45
% 2.30/1.45 thf(setadjoinOr,definition,
% 2.30/1.45 ( setadjoinOr
% 2.30/1.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.30/1.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.30/1.45 => ( ( Xy = Xx )
% 2.30/1.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(setoftrueEq_type,type,
% 2.30/1.45 setoftrueEq: $o ).
% 2.30/1.45
% 2.30/1.45 thf(setoftrueEq,definition,
% 2.30/1.45 ( setoftrueEq
% 2.30/1.45 = ( ! [A: $i] :
% 2.30/1.45 ( ( dsetconstr @ A
% 2.30/1.45 @ ^ [Xx: $i] : $true )
% 2.30/1.45 = A ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(powersetI_type,type,
% 2.30/1.45 powersetI: $o ).
% 2.30/1.45
% 2.30/1.45 thf(powersetI,definition,
% 2.30/1.45 ( powersetI
% 2.30/1.45 = ( ! [A: $i,B: $i] :
% 2.30/1.45 ( ! [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ B )
% 2.30/1.45 => ( in @ Xx @ A ) )
% 2.30/1.45 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(emptyinPowerset_type,type,
% 2.30/1.45 emptyinPowerset: $o ).
% 2.30/1.45
% 2.30/1.45 thf(emptyinPowerset,definition,
% 2.30/1.45 ( emptyinPowerset
% 2.30/1.45 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(emptyInPowerset_type,type,
% 2.30/1.45 emptyInPowerset: $o ).
% 2.30/1.45
% 2.30/1.45 thf(emptyInPowerset,definition,
% 2.30/1.45 ( emptyInPowerset
% 2.30/1.45 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(powersetE_type,type,
% 2.30/1.45 powersetE: $o ).
% 2.30/1.45
% 2.30/1.45 thf(powersetE,definition,
% 2.30/1.45 ( powersetE
% 2.30/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.45 ( ( in @ B @ ( powerset @ A ) )
% 2.30/1.45 => ( ( in @ Xx @ B )
% 2.30/1.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(setunionI_type,type,
% 2.30/1.45 setunionI: $o ).
% 2.30/1.45
% 2.30/1.45 thf(setunionI,definition,
% 2.30/1.45 ( setunionI
% 2.30/1.45 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.30/1.45 ( ( in @ Xx @ B )
% 2.30/1.45 => ( ( in @ B @ A )
% 2.30/1.45 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(setunionE_type,type,
% 2.30/1.45 setunionE: $o ).
% 2.30/1.45
% 2.30/1.45 thf(setunionE,definition,
% 2.30/1.45 ( setunionE
% 2.30/1.45 = ( ! [A: $i,Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ ( setunion @ A ) )
% 2.30/1.45 => ! [Xphi: $o] :
% 2.30/1.45 ( ! [B: $i] :
% 2.30/1.45 ( ( in @ Xx @ B )
% 2.30/1.45 => ( ( in @ B @ A )
% 2.30/1.45 => Xphi ) )
% 2.30/1.45 => Xphi ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(subPowSU_type,type,
% 2.30/1.45 subPowSU: $o ).
% 2.30/1.45
% 2.30/1.45 thf(subPowSU,definition,
% 2.30/1.45 ( subPowSU
% 2.30/1.45 = ( ! [A: $i,Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ A )
% 2.30/1.45 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(exuE2_type,type,
% 2.30/1.45 exuE2: $o ).
% 2.30/1.45
% 2.30/1.45 thf(exuE2,definition,
% 2.30/1.45 ( exuE2
% 2.30/1.45 = ( ! [Xphi: $i > $o] :
% 2.30/1.45 ( ( exu
% 2.30/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.30/1.45 => ? [Xx: $i] :
% 2.30/1.45 ! [Xy: $i] :
% 2.30/1.45 ( ( Xphi @ Xy )
% 2.30/1.45 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(nonemptyImpWitness_type,type,
% 2.30/1.45 nonemptyImpWitness: $o ).
% 2.30/1.45
% 2.30/1.45 thf(nonemptyImpWitness,definition,
% 2.30/1.45 ( nonemptyImpWitness
% 2.30/1.45 = ( ! [A: $i] :
% 2.30/1.45 ( ( nonempty @ A )
% 2.30/1.45 => ? [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ A )
% 2.30/1.45 & $true ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(uniqinunit_type,type,
% 2.30/1.45 uniqinunit: $o ).
% 2.30/1.45
% 2.30/1.45 thf(uniqinunit,definition,
% 2.30/1.45 ( uniqinunit
% 2.30/1.45 = ( ! [Xx: $i,Xy: $i] :
% 2.30/1.45 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.30/1.45 => ( Xx = Xy ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(notinsingleton_type,type,
% 2.30/1.45 notinsingleton: $o ).
% 2.30/1.45
% 2.30/1.45 thf(notinsingleton,definition,
% 2.30/1.45 ( notinsingleton
% 2.30/1.45 = ( ! [Xx: $i,Xy: $i] :
% 2.30/1.45 ( ( Xx != Xy )
% 2.30/1.45 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(eqinunit_type,type,
% 2.30/1.45 eqinunit: $o ).
% 2.30/1.45
% 2.30/1.45 thf(eqinunit,definition,
% 2.30/1.45 ( eqinunit
% 2.30/1.45 = ( ! [Xx: $i,Xy: $i] :
% 2.30/1.45 ( ( Xx = Xy )
% 2.30/1.45 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(singletonsswitch_type,type,
% 2.30/1.45 singletonsswitch: $o ).
% 2.30/1.45
% 2.30/1.45 thf(singletonsswitch,definition,
% 2.30/1.45 ( singletonsswitch
% 2.30/1.45 = ( ! [Xx: $i,Xy: $i] :
% 2.30/1.45 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.30/1.45 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(upairsetE_type,type,
% 2.30/1.45 upairsetE: $o ).
% 2.30/1.45
% 2.30/1.45 thf(upairsetE,definition,
% 2.30/1.45 ( upairsetE
% 2.30/1.45 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.30/1.45 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.30/1.45 => ( ( Xz = Xx )
% 2.30/1.45 | ( Xz = Xy ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(upairsetIL_type,type,
% 2.30/1.45 upairsetIL: $o ).
% 2.30/1.45
% 2.30/1.45 thf(upairsetIL,definition,
% 2.30/1.45 ( upairsetIL
% 2.30/1.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(upairsetIR_type,type,
% 2.30/1.45 upairsetIR: $o ).
% 2.30/1.45
% 2.30/1.45 thf(upairsetIR,definition,
% 2.30/1.45 ( upairsetIR
% 2.30/1.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(emptyE1_type,type,
% 2.30/1.45 emptyE1: $o ).
% 2.30/1.45
% 2.30/1.45 thf(emptyE1,definition,
% 2.30/1.45 ( emptyE1
% 2.30/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.30/1.45 ( ? [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ A )
% 2.30/1.45 & ( Xphi @ Xx ) )
% 2.30/1.45 => ( ( ( dsetconstr @ A
% 2.30/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.30/1.45 = emptyset )
% 2.30/1.45 => $false ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(vacuousDall_type,type,
% 2.30/1.45 vacuousDall: $o ).
% 2.30/1.45
% 2.30/1.45 thf(vacuousDall,definition,
% 2.30/1.45 ( vacuousDall
% 2.30/1.45 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ emptyset )
% 2.30/1.45 => ( Xphi @ Xx ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(quantDeMorgan1_type,type,
% 2.30/1.45 quantDeMorgan1: $o ).
% 2.30/1.45
% 2.30/1.45 thf(quantDeMorgan1,definition,
% 2.30/1.45 ( quantDeMorgan1
% 2.30/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.30/1.45 ( ~ ! [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ A )
% 2.30/1.45 => ( Xphi @ Xx ) )
% 2.30/1.45 => ? [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ A )
% 2.30/1.45 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(quantDeMorgan2_type,type,
% 2.30/1.45 quantDeMorgan2: $o ).
% 2.30/1.45
% 2.30/1.45 thf(quantDeMorgan2,definition,
% 2.30/1.45 ( quantDeMorgan2
% 2.30/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.30/1.45 ( ! [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ A )
% 2.30/1.45 => ~ ( Xphi @ Xx ) )
% 2.30/1.45 => ~ ? [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ A )
% 2.30/1.45 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(quantDeMorgan3_type,type,
% 2.30/1.45 quantDeMorgan3: $o ).
% 2.30/1.45
% 2.30/1.45 thf(quantDeMorgan3,definition,
% 2.30/1.45 ( quantDeMorgan3
% 2.30/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.30/1.45 ( ~ ? [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ A )
% 2.30/1.45 & ( Xphi @ Xx ) )
% 2.30/1.45 => ! [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ A )
% 2.30/1.45 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(quantDeMorgan4_type,type,
% 2.30/1.45 quantDeMorgan4: $o ).
% 2.30/1.45
% 2.30/1.45 thf(quantDeMorgan4,definition,
% 2.30/1.45 ( quantDeMorgan4
% 2.30/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.30/1.45 ( ? [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ A )
% 2.30/1.45 & ~ ( Xphi @ Xx ) )
% 2.30/1.45 => ~ ! [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ A )
% 2.30/1.45 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(prop2setI_type,type,
% 2.30/1.45 prop2setI: $o ).
% 2.30/1.45
% 2.30/1.45 thf(prop2setI,definition,
% 2.30/1.45 ( prop2setI
% 2.30/1.45 = ( ! [Xphi: $o] :
% 2.30/1.45 ( Xphi
% 2.30/1.45 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(set2prop_type,type,
% 2.30/1.45 set2prop: $i > $o ).
% 2.30/1.45
% 2.30/1.45 thf(prop2set2propI_type,type,
% 2.30/1.45 prop2set2propI: $o ).
% 2.30/1.45
% 2.30/1.45 thf(prop2set2propI,definition,
% 2.30/1.45 ( prop2set2propI
% 2.30/1.45 = ( ! [Xphi: $o] :
% 2.30/1.45 ( Xphi
% 2.30/1.45 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(notdexE_type,type,
% 2.30/1.45 notdexE: $o ).
% 2.30/1.45
% 2.30/1.45 thf(notdexE,definition,
% 2.30/1.45 ( notdexE
% 2.30/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.30/1.45 ( ~ ? [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ A )
% 2.30/1.45 & ( Xphi @ Xx ) )
% 2.30/1.45 => ! [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ A )
% 2.30/1.45 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(notdallE_type,type,
% 2.30/1.45 notdallE: $o ).
% 2.30/1.45
% 2.30/1.45 thf(notdallE,definition,
% 2.30/1.45 ( notdallE
% 2.30/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.30/1.45 ( ~ ! [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ A )
% 2.30/1.45 => ( Xphi @ Xx ) )
% 2.30/1.45 => ? [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ A )
% 2.30/1.45 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(exuI1_type,type,
% 2.30/1.45 exuI1: $o ).
% 2.30/1.45
% 2.30/1.45 thf(exuI1,definition,
% 2.30/1.45 ( exuI1
% 2.30/1.45 = ( ! [Xphi: $i > $o] :
% 2.30/1.45 ( ? [Xx: $i] :
% 2.30/1.45 ( ( Xphi @ Xx )
% 2.30/1.45 & ! [Xy: $i] :
% 2.30/1.45 ( ( Xphi @ Xy )
% 2.30/1.45 => ( Xx = Xy ) ) )
% 2.30/1.45 => ( exu
% 2.30/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(exuI3_type,type,
% 2.30/1.45 exuI3: $o ).
% 2.30/1.45
% 2.30/1.45 thf(exuI3,definition,
% 2.30/1.45 ( exuI3
% 2.30/1.45 = ( ! [Xphi: $i > $o] :
% 2.30/1.45 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.30/1.45 => ( ! [Xx: $i,Xy: $i] :
% 2.30/1.45 ( ( Xphi @ Xx )
% 2.30/1.45 => ( ( Xphi @ Xy )
% 2.30/1.45 => ( Xx = Xy ) ) )
% 2.30/1.45 => ( exu
% 2.30/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(exuI2_type,type,
% 2.30/1.45 exuI2: $o ).
% 2.30/1.45
% 2.30/1.45 thf(exuI2,definition,
% 2.30/1.45 ( exuI2
% 2.30/1.45 = ( ! [Xphi: $i > $o] :
% 2.30/1.45 ( ? [Xx: $i] :
% 2.30/1.45 ! [Xy: $i] :
% 2.30/1.45 ( ( Xphi @ Xy )
% 2.30/1.45 <=> ( Xy = Xx ) )
% 2.30/1.45 => ( exu
% 2.30/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(inCongP_type,type,
% 2.30/1.45 inCongP: $o ).
% 2.30/1.45
% 2.30/1.45 thf(inCongP,definition,
% 2.30/1.45 ( inCongP
% 2.30/1.45 = ( ! [A: $i,B: $i] :
% 2.30/1.45 ( ( A = B )
% 2.30/1.45 => ! [Xx: $i,Xy: $i] :
% 2.30/1.45 ( ( Xx = Xy )
% 2.30/1.45 => ( ( in @ Xx @ A )
% 2.30/1.45 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(in__Cong_type,type,
% 2.30/1.45 in__Cong: $o ).
% 2.30/1.45
% 2.30/1.45 thf(in__Cong,definition,
% 2.30/1.45 ( in__Cong
% 2.30/1.45 = ( ! [A: $i,B: $i] :
% 2.30/1.45 ( ( A = B )
% 2.30/1.45 => ! [Xx: $i,Xy: $i] :
% 2.30/1.45 ( ( Xx = Xy )
% 2.30/1.45 => ( ( in @ Xx @ A )
% 2.30/1.45 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(exuE3u_type,type,
% 2.30/1.45 exuE3u: $o ).
% 2.30/1.45
% 2.30/1.45 thf(exuE3u,definition,
% 2.30/1.45 ( exuE3u
% 2.30/1.45 = ( ! [Xphi: $i > $o] :
% 2.30/1.45 ( ( exu
% 2.30/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.30/1.45 => ! [Xx: $i,Xy: $i] :
% 2.30/1.45 ( ( Xphi @ Xx )
% 2.30/1.45 => ( ( Xphi @ Xy )
% 2.30/1.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(exu__Cong_type,type,
% 2.30/1.45 exu__Cong: $o ).
% 2.30/1.45
% 2.30/1.45 thf(exu__Cong,definition,
% 2.30/1.45 ( exu__Cong
% 2.30/1.45 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.30/1.45 ( ! [Xx: $i,Xy: $i] :
% 2.30/1.45 ( ( Xx = Xy )
% 2.30/1.45 => ( ( Xphi @ Xx )
% 2.30/1.45 <=> ( Xpsi @ Xy ) ) )
% 2.30/1.45 => ( ( exu
% 2.30/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.30/1.45 <=> ( exu
% 2.30/1.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(emptyset__Cong_type,type,
% 2.30/1.45 emptyset__Cong: $o ).
% 2.30/1.45
% 2.30/1.45 thf(emptyset__Cong,definition,
% 2.30/1.45 ( emptyset__Cong
% 2.30/1.45 = ( emptyset = emptyset ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(setadjoin__Cong_type,type,
% 2.30/1.45 setadjoin__Cong: $o ).
% 2.30/1.45
% 2.30/1.45 thf(setadjoin__Cong,definition,
% 2.30/1.45 ( setadjoin__Cong
% 2.30/1.45 = ( ! [Xx: $i,Xy: $i] :
% 2.30/1.45 ( ( Xx = Xy )
% 2.30/1.45 => ! [Xz: $i,Xu: $i] :
% 2.30/1.45 ( ( Xz = Xu )
% 2.30/1.45 => ( ( setadjoin @ Xx @ Xz )
% 2.30/1.45 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(powerset__Cong_type,type,
% 2.30/1.45 powerset__Cong: $o ).
% 2.30/1.45
% 2.30/1.45 thf(powerset__Cong,definition,
% 2.30/1.45 ( powerset__Cong
% 2.30/1.45 = ( ! [A: $i,B: $i] :
% 2.30/1.45 ( ( A = B )
% 2.30/1.45 => ( ( powerset @ A )
% 2.30/1.45 = ( powerset @ B ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(setunion__Cong_type,type,
% 2.30/1.45 setunion__Cong: $o ).
% 2.30/1.45
% 2.30/1.45 thf(setunion__Cong,definition,
% 2.30/1.45 ( setunion__Cong
% 2.30/1.45 = ( ! [A: $i,B: $i] :
% 2.30/1.45 ( ( A = B )
% 2.30/1.45 => ( ( setunion @ A )
% 2.30/1.45 = ( setunion @ B ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(omega__Cong_type,type,
% 2.30/1.45 omega__Cong: $o ).
% 2.30/1.45
% 2.30/1.45 thf(omega__Cong,definition,
% 2.30/1.45 ( omega__Cong
% 2.30/1.45 = ( omega = omega ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(exuEu_type,type,
% 2.30/1.45 exuEu: $o ).
% 2.30/1.45
% 2.30/1.45 thf(exuEu,definition,
% 2.30/1.45 ( exuEu
% 2.30/1.45 = ( ! [Xphi: $i > $o] :
% 2.30/1.45 ( ( exu
% 2.30/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.30/1.45 => ! [Xx: $i,Xy: $i] :
% 2.30/1.45 ( ( Xphi @ Xx )
% 2.30/1.45 => ( ( Xphi @ Xy )
% 2.30/1.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(descr__Cong_type,type,
% 2.30/1.45 descr__Cong: $o ).
% 2.30/1.45
% 2.30/1.45 thf(descr__Cong,definition,
% 2.30/1.45 ( descr__Cong
% 2.30/1.45 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.30/1.45 ( ! [Xx: $i,Xy: $i] :
% 2.30/1.45 ( ( Xx = Xy )
% 2.30/1.45 => ( ( Xphi @ Xx )
% 2.30/1.45 <=> ( Xpsi @ Xy ) ) )
% 2.30/1.45 => ( ( exu
% 2.30/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.30/1.45 => ( ( exu
% 2.30/1.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.30/1.45 => ( ( descr
% 2.30/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.30/1.45 = ( descr
% 2.30/1.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(dsetconstr__Cong_type,type,
% 2.30/1.45 dsetconstr__Cong: $o ).
% 2.30/1.45
% 2.30/1.45 thf(dsetconstr__Cong,definition,
% 2.30/1.45 ( dsetconstr__Cong
% 2.30/1.45 = ( ! [A: $i,B: $i] :
% 2.30/1.45 ( ( A = B )
% 2.30/1.45 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.30/1.45 ( ! [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ A )
% 2.30/1.45 => ! [Xy: $i] :
% 2.30/1.45 ( ( in @ Xy @ B )
% 2.30/1.45 => ( ( Xx = Xy )
% 2.30/1.45 => ( ( Xphi @ Xx )
% 2.30/1.45 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.30/1.45 => ( ( dsetconstr @ A
% 2.30/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.30/1.45 = ( dsetconstr @ B
% 2.30/1.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(subset_type,type,
% 2.30/1.45 subset: $i > $i > $o ).
% 2.30/1.45
% 2.30/1.45 thf(disjoint_type,type,
% 2.30/1.45 disjoint: $i > $i > $o ).
% 2.30/1.45
% 2.30/1.45 thf(setsmeet_type,type,
% 2.30/1.45 setsmeet: $i > $i > $o ).
% 2.30/1.45
% 2.30/1.45 thf(subsetI1_type,type,
% 2.30/1.45 subsetI1: $o ).
% 2.30/1.45
% 2.30/1.45 thf(subsetI1,definition,
% 2.30/1.45 ( subsetI1
% 2.30/1.45 = ( ! [A: $i,B: $i] :
% 2.30/1.45 ( ! [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ A )
% 2.30/1.45 => ( in @ Xx @ B ) )
% 2.30/1.45 => ( subset @ A @ B ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(eqimpsubset2_type,type,
% 2.30/1.45 eqimpsubset2: $o ).
% 2.30/1.45
% 2.30/1.45 thf(eqimpsubset2,definition,
% 2.30/1.45 ( eqimpsubset2
% 2.30/1.45 = ( ! [A: $i,B: $i] :
% 2.30/1.45 ( ( A = B )
% 2.30/1.45 => ( subset @ B @ A ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(eqimpsubset1_type,type,
% 2.30/1.45 eqimpsubset1: $o ).
% 2.30/1.45
% 2.30/1.45 thf(eqimpsubset1,definition,
% 2.30/1.45 ( eqimpsubset1
% 2.30/1.45 = ( ! [A: $i,B: $i] :
% 2.30/1.45 ( ( A = B )
% 2.30/1.45 => ( subset @ A @ B ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(subsetI2_type,type,
% 2.30/1.45 subsetI2: $o ).
% 2.30/1.45
% 2.30/1.45 thf(subsetI2,definition,
% 2.30/1.45 ( subsetI2
% 2.30/1.45 = ( ! [A: $i,B: $i] :
% 2.30/1.45 ( ! [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ A )
% 2.30/1.45 => ( in @ Xx @ B ) )
% 2.30/1.45 => ( subset @ A @ B ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(emptysetsubset_type,type,
% 2.30/1.45 emptysetsubset: $o ).
% 2.30/1.45
% 2.30/1.45 thf(emptysetsubset,definition,
% 2.30/1.45 ( emptysetsubset
% 2.30/1.45 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(subsetE_type,type,
% 2.30/1.45 subsetE: $o ).
% 2.30/1.45
% 2.30/1.45 thf(subsetE,definition,
% 2.30/1.45 ( subsetE
% 2.30/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.45 ( ( subset @ A @ B )
% 2.30/1.45 => ( ( in @ Xx @ A )
% 2.30/1.45 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(subsetE2_type,type,
% 2.30/1.45 subsetE2: $o ).
% 2.30/1.45
% 2.30/1.45 thf(subsetE2,definition,
% 2.30/1.45 ( subsetE2
% 2.30/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.45 ( ( subset @ A @ B )
% 2.30/1.45 => ( ~ ( in @ Xx @ B )
% 2.30/1.45 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(notsubsetI_type,type,
% 2.30/1.45 notsubsetI: $o ).
% 2.30/1.45
% 2.30/1.45 thf(notsubsetI,definition,
% 2.30/1.45 ( notsubsetI
% 2.30/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ A )
% 2.30/1.45 => ( ~ ( in @ Xx @ B )
% 2.30/1.45 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(notequalI1_type,type,
% 2.30/1.45 notequalI1: $o ).
% 2.30/1.45
% 2.30/1.45 thf(notequalI1,definition,
% 2.30/1.45 ( notequalI1
% 2.30/1.45 = ( ! [A: $i,B: $i] :
% 2.30/1.45 ( ~ ( subset @ A @ B )
% 2.30/1.45 => ( A != B ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(notequalI2_type,type,
% 2.30/1.45 notequalI2: $o ).
% 2.30/1.45
% 2.30/1.45 thf(notequalI2,definition,
% 2.30/1.45 ( notequalI2
% 2.30/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ A )
% 2.30/1.45 => ( ~ ( in @ Xx @ B )
% 2.30/1.45 => ( A != B ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(subsetRefl_type,type,
% 2.30/1.45 subsetRefl: $o ).
% 2.30/1.45
% 2.30/1.45 thf(subsetRefl,definition,
% 2.30/1.45 ( subsetRefl
% 2.30/1.45 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(subsetTrans_type,type,
% 2.30/1.45 subsetTrans: $o ).
% 2.30/1.45
% 2.30/1.45 thf(subsetTrans,definition,
% 2.30/1.45 ( subsetTrans
% 2.30/1.45 = ( ! [A: $i,B: $i,C: $i] :
% 2.30/1.45 ( ( subset @ A @ B )
% 2.30/1.45 => ( ( subset @ B @ C )
% 2.30/1.45 => ( subset @ A @ C ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(setadjoinSub_type,type,
% 2.30/1.45 setadjoinSub: $o ).
% 2.30/1.45
% 2.30/1.45 thf(setadjoinSub,definition,
% 2.30/1.45 ( setadjoinSub
% 2.30/1.45 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(setadjoinSub2_type,type,
% 2.30/1.45 setadjoinSub2: $o ).
% 2.30/1.45
% 2.30/1.45 thf(setadjoinSub2,definition,
% 2.30/1.45 ( setadjoinSub2
% 2.30/1.45 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.30/1.45 ( ( subset @ A @ B )
% 2.30/1.45 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(subset2powerset_type,type,
% 2.30/1.45 subset2powerset: $o ).
% 2.30/1.45
% 2.30/1.45 thf(subset2powerset,definition,
% 2.30/1.45 ( subset2powerset
% 2.30/1.45 = ( ! [A: $i,B: $i] :
% 2.30/1.45 ( ( subset @ A @ B )
% 2.30/1.45 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(setextsub_type,type,
% 2.30/1.45 setextsub: $o ).
% 2.30/1.45
% 2.30/1.45 thf(setextsub,definition,
% 2.30/1.45 ( setextsub
% 2.30/1.45 = ( ! [A: $i,B: $i] :
% 2.30/1.45 ( ( subset @ A @ B )
% 2.30/1.45 => ( ( subset @ B @ A )
% 2.30/1.45 => ( A = B ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(subsetemptysetimpeq_type,type,
% 2.30/1.45 subsetemptysetimpeq: $o ).
% 2.30/1.45
% 2.30/1.45 thf(subsetemptysetimpeq,definition,
% 2.30/1.45 ( subsetemptysetimpeq
% 2.30/1.45 = ( ! [A: $i] :
% 2.30/1.45 ( ( subset @ A @ emptyset )
% 2.30/1.45 => ( A = emptyset ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(powersetI1_type,type,
% 2.30/1.45 powersetI1: $o ).
% 2.30/1.45
% 2.30/1.45 thf(powersetI1,definition,
% 2.30/1.45 ( powersetI1
% 2.30/1.45 = ( ! [A: $i,B: $i] :
% 2.30/1.45 ( ( subset @ B @ A )
% 2.30/1.45 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(powersetE1_type,type,
% 2.30/1.45 powersetE1: $o ).
% 2.30/1.45
% 2.30/1.45 thf(powersetE1,definition,
% 2.30/1.45 ( powersetE1
% 2.30/1.45 = ( ! [A: $i,B: $i] :
% 2.30/1.45 ( ( in @ B @ ( powerset @ A ) )
% 2.30/1.45 => ( subset @ B @ A ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(inPowerset_type,type,
% 2.30/1.45 inPowerset: $o ).
% 2.30/1.45
% 2.30/1.45 thf(inPowerset,definition,
% 2.30/1.45 ( inPowerset
% 2.30/1.45 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(powersetsubset_type,type,
% 2.30/1.45 powersetsubset: $o ).
% 2.30/1.45
% 2.30/1.45 thf(powersetsubset,definition,
% 2.30/1.45 ( powersetsubset
% 2.30/1.45 = ( ! [A: $i,B: $i] :
% 2.30/1.45 ( ( subset @ A @ B )
% 2.30/1.45 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(sepInPowerset_type,type,
% 2.30/1.45 sepInPowerset: $o ).
% 2.30/1.45
% 2.30/1.45 thf(sepInPowerset,definition,
% 2.30/1.45 ( sepInPowerset
% 2.30/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.30/1.45 ( in
% 2.30/1.45 @ ( dsetconstr @ A
% 2.30/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.30/1.45 @ ( powerset @ A ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(sepSubset_type,type,
% 2.30/1.45 sepSubset: $o ).
% 2.30/1.45
% 2.30/1.45 thf(sepSubset,definition,
% 2.30/1.45 ( sepSubset
% 2.30/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.30/1.45 ( subset
% 2.30/1.45 @ ( dsetconstr @ A
% 2.30/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.30/1.45 @ A ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(binunion_type,type,
% 2.30/1.45 binunion: $i > $i > $i ).
% 2.30/1.45
% 2.30/1.45 thf(binunionIL_type,type,
% 2.30/1.45 binunionIL: $o ).
% 2.30/1.45
% 2.30/1.45 thf(binunionIL,definition,
% 2.30/1.45 ( binunionIL
% 2.30/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ A )
% 2.30/1.45 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(upairset2IR_type,type,
% 2.30/1.45 upairset2IR: $o ).
% 2.30/1.45
% 2.30/1.45 thf(upairset2IR,definition,
% 2.30/1.45 ( upairset2IR
% 2.30/1.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(binunionIR_type,type,
% 2.30/1.45 binunionIR: $o ).
% 2.30/1.45
% 2.30/1.45 thf(binunionIR,definition,
% 2.30/1.45 ( binunionIR
% 2.30/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ B )
% 2.30/1.45 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(binunionEcases_type,type,
% 2.30/1.45 binunionEcases: $o ).
% 2.30/1.45
% 2.30/1.45 thf(binunionEcases,definition,
% 2.30/1.45 ( binunionEcases
% 2.30/1.45 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.30/1.45 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.30/1.45 => ( ( ( in @ Xx @ A )
% 2.30/1.45 => Xphi )
% 2.30/1.45 => ( ( ( in @ Xx @ B )
% 2.30/1.45 => Xphi )
% 2.30/1.45 => Xphi ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(binunionE_type,type,
% 2.30/1.45 binunionE: $o ).
% 2.30/1.45
% 2.30/1.45 thf(binunionE,definition,
% 2.30/1.45 ( binunionE
% 2.30/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.30/1.45 => ( ( in @ Xx @ A )
% 2.30/1.45 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(binunionLsub_type,type,
% 2.30/1.45 binunionLsub: $o ).
% 2.30/1.45
% 2.30/1.45 thf(binunionLsub,definition,
% 2.30/1.45 ( binunionLsub
% 2.30/1.45 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(binunionRsub_type,type,
% 2.30/1.45 binunionRsub: $o ).
% 2.30/1.45
% 2.30/1.45 thf(binunionRsub,definition,
% 2.30/1.45 ( binunionRsub
% 2.30/1.45 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(binintersect_type,type,
% 2.30/1.45 binintersect: $i > $i > $i ).
% 2.30/1.45
% 2.30/1.45 thf(binintersectI_type,type,
% 2.30/1.45 binintersectI: $o ).
% 2.30/1.45
% 2.30/1.45 thf(binintersectI,definition,
% 2.30/1.45 ( binintersectI
% 2.30/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ A )
% 2.30/1.45 => ( ( in @ Xx @ B )
% 2.30/1.45 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(binintersectSubset5_type,type,
% 2.30/1.45 binintersectSubset5: $o ).
% 2.30/1.45
% 2.30/1.45 thf(binintersectSubset5,definition,
% 2.30/1.45 ( binintersectSubset5
% 2.30/1.45 = ( ! [A: $i,B: $i,C: $i] :
% 2.30/1.45 ( ( subset @ C @ A )
% 2.30/1.45 => ( ( subset @ C @ B )
% 2.30/1.45 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(binintersectEL_type,type,
% 2.30/1.45 binintersectEL: $o ).
% 2.30/1.45
% 2.30/1.45 thf(binintersectEL,definition,
% 2.30/1.45 ( binintersectEL
% 2.30/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.30/1.45 => ( in @ Xx @ A ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(binintersectLsub_type,type,
% 2.30/1.45 binintersectLsub: $o ).
% 2.30/1.45
% 2.30/1.45 thf(binintersectLsub,definition,
% 2.30/1.45 ( binintersectLsub
% 2.30/1.45 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(binintersectSubset2_type,type,
% 2.30/1.45 binintersectSubset2: $o ).
% 2.30/1.45
% 2.30/1.45 thf(binintersectSubset2,definition,
% 2.30/1.45 ( binintersectSubset2
% 2.30/1.45 = ( ! [A: $i,B: $i] :
% 2.30/1.45 ( ( subset @ A @ B )
% 2.30/1.45 => ( ( binintersect @ A @ B )
% 2.30/1.45 = A ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(binintersectSubset3_type,type,
% 2.30/1.45 binintersectSubset3: $o ).
% 2.30/1.45
% 2.30/1.45 thf(binintersectSubset3,definition,
% 2.30/1.45 ( binintersectSubset3
% 2.30/1.45 = ( ! [A: $i,B: $i] :
% 2.30/1.45 ( ( ( binintersect @ A @ B )
% 2.30/1.45 = B )
% 2.30/1.45 => ( subset @ B @ A ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(binintersectER_type,type,
% 2.30/1.45 binintersectER: $o ).
% 2.30/1.45
% 2.30/1.45 thf(binintersectER,definition,
% 2.30/1.45 ( binintersectER
% 2.30/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.30/1.45 => ( in @ Xx @ B ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(disjointsetsI1_type,type,
% 2.30/1.45 disjointsetsI1: $o ).
% 2.30/1.45
% 2.30/1.45 thf(disjointsetsI1,definition,
% 2.30/1.45 ( disjointsetsI1
% 2.30/1.45 = ( ! [A: $i,B: $i] :
% 2.30/1.45 ( ~ ? [Xx: $i] :
% 2.30/1.45 ( ( in @ Xx @ A )
% 2.30/1.45 & ( in @ Xx @ B ) )
% 2.30/1.45 => ( ( binintersect @ A @ B )
% 2.30/1.45 = emptyset ) ) ) ) ).
% 2.30/1.45
% 2.30/1.45 thf(binintersectRsub,conjecture,
% 2.30/1.45 ( setextAx
% 2.30/1.45 => ( emptysetAx
% 2.30/1.45 => ( setadjoinAx
% 2.30/1.45 => ( powersetAx
% 2.30/1.45 => ( setunionAx
% 2.30/1.45 => ( omega0Ax
% 2.30/1.45 => ( omegaSAx
% 2.30/1.45 => ( omegaIndAx
% 2.30/1.45 => ( replAx
% 2.30/1.45 => ( foundationAx
% 2.30/1.45 => ( wellorderingAx
% 2.30/1.45 => ( descrp
% 2.30/1.45 => ( dsetconstrI
% 2.30/1.45 => ( dsetconstrEL
% 2.30/1.45 => ( dsetconstrER
% 2.30/1.45 => ( exuE1
% 2.30/1.45 => ( prop2setE
% 2.30/1.45 => ( emptysetE
% 2.30/1.45 => ( emptysetimpfalse
% 2.30/1.45 => ( notinemptyset
% 2.30/1.45 => ( exuE3e
% 2.30/1.45 => ( setext
% 2.30/1.45 => ( emptyI
% 2.30/1.45 => ( noeltsimpempty
% 2.30/1.45 => ( setbeta
% 2.30/1.45 => ( nonemptyE1
% 2.30/1.45 => ( nonemptyI
% 2.30/1.45 => ( nonemptyI1
% 2.30/1.45 => ( setadjoinIL
% 2.30/1.45 => ( emptyinunitempty
% 2.30/1.45 => ( setadjoinIR
% 2.30/1.45 => ( setadjoinE
% 2.30/1.45 => ( setadjoinOr
% 2.30/1.45 => ( setoftrueEq
% 2.30/1.45 => ( powersetI
% 2.30/1.45 => ( emptyinPowerset
% 2.30/1.45 => ( emptyInPowerset
% 2.30/1.45 => ( powersetE
% 2.30/1.45 => ( setunionI
% 2.30/1.45 => ( setunionE
% 2.30/1.45 => ( subPowSU
% 2.30/1.45 => ( exuE2
% 2.30/1.45 => ( nonemptyImpWitness
% 2.30/1.45 => ( uniqinunit
% 2.30/1.45 => ( notinsingleton
% 2.30/1.45 => ( eqinunit
% 2.30/1.45 => ( singletonsswitch
% 2.30/1.45 => ( upairsetE
% 2.30/1.45 => ( upairsetIL
% 2.30/1.45 => ( upairsetIR
% 2.30/1.45 => ( emptyE1
% 2.30/1.45 => ( vacuousDall
% 2.30/1.45 => ( quantDeMorgan1
% 2.30/1.45 => ( quantDeMorgan2
% 2.30/1.45 => ( quantDeMorgan3
% 2.30/1.45 => ( quantDeMorgan4
% 2.30/1.45 => ( prop2setI
% 2.30/1.45 => ( prop2set2propI
% 2.30/1.45 => ( notdexE
% 2.30/1.45 => ( notdallE
% 2.30/1.45 => ( exuI1
% 2.30/1.45 => ( exuI3
% 2.30/1.45 => ( exuI2
% 2.30/1.45 => ( inCongP
% 2.30/1.45 => ( in__Cong
% 2.30/1.45 => ( exuE3u
% 2.30/1.45 => ( exu__Cong
% 2.30/1.45 => ( emptyset__Cong
% 2.30/1.45 => ( setadjoin__Cong
% 2.30/1.45 => ( powerset__Cong
% 2.30/1.45 => ( setunion__Cong
% 2.30/1.45 => ( omega__Cong
% 2.30/1.45 => ( exuEu
% 2.30/1.45 => ( descr__Cong
% 2.30/1.45 => ( dsetconstr__Cong
% 2.30/1.45 => ( subsetI1
% 2.30/1.45 => ( eqimpsubset2
% 2.30/1.45 => ( eqimpsubset1
% 2.30/1.45 => ( subsetI2
% 2.30/1.45 => ( emptysetsubset
% 2.30/1.45 => ( subsetE
% 2.30/1.45 => ( subsetE2
% 2.30/1.45 => ( notsubsetI
% 2.30/1.45 => ( notequalI1
% 2.30/1.45 => ( notequalI2
% 2.30/1.45 => ( subsetRefl
% 2.30/1.45 => ( subsetTrans
% 2.30/1.45 => ( setadjoinSub
% 2.30/1.45 => ( setadjoinSub2
% 2.30/1.45 => ( subset2powerset
% 2.30/1.45 => ( setextsub
% 2.30/1.45 => ( subsetemptysetimpeq
% 2.30/1.45 => ( powersetI1
% 2.30/1.45 => ( powersetE1
% 2.30/1.45 => ( inPowerset
% 2.30/1.45 => ( powersetsubset
% 2.30/1.45 => ( sepInPowerset
% 2.30/1.45 => ( sepSubset
% 2.30/1.45 => ( binunionIL
% 2.30/1.45 => ( upairset2IR
% 2.30/1.45 => ( binunionIR
% 2.30/1.45 => ( binunionEcases
% 2.30/1.45 => ( binunionE
% 2.30/1.45 => ( binunionLsub
% 2.30/1.45 => ( binunionRsub
% 2.30/1.45 => ( binintersectI
% 2.30/1.45 => ( binintersectSubset5
% 2.30/1.45 => ( binintersectEL
% 2.30/1.45 => ( binintersectLsub
% 2.30/1.45 => ( binintersectSubset2
% 2.30/1.45 => ( binintersectSubset3
% 2.30/1.45 => ( binintersectER
% 2.30/1.45 => ( disjointsetsI1
% 2.30/1.45 => ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.30/1.45 ------------------------
% 2.30/1.47 % (7382)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_7106 for (2999ds/27Mi)
% 2.30/1.47 % (7383)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7106 for (2999ds/2Mi)
% 2.30/1.47 % (7386)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7106 for (2999ds/18Mi)
% 2.30/1.47 % (7383)Instruction limit reached!
% 2.30/1.47 % (7383)------------------------------
% 2.30/1.47 % (7383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.47 % (7383)Termination reason: Unknown
% 2.30/1.47 % (7383)Termination phase: shuffling
% 2.30/1.47
% 2.30/1.47 % (7383)Memory used [KB]: 1151
% 2.30/1.47 % (7383)Time elapsed: 0.002 s
% 2.30/1.47 % (7383)Instructions burned: 3 (million)
% 2.30/1.47 % (7383)------------------------------
% 2.30/1.47 % (7383)------------------------------
% 2.30/1.48 % (7386)Instruction limit reached!
% 2.30/1.48 % (7386)------------------------------
% 2.30/1.48 % (7386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.48 % (7386)Termination reason: Unknown
% 2.30/1.48 % (7386)Termination phase: Preprocessing 3
% 2.30/1.48
% 2.30/1.48 % (7386)Memory used [KB]: 1535
% 2.30/1.48 % (7386)Time elapsed: 0.007 s
% 2.30/1.48 % (7386)Instructions burned: 18 (million)
% 2.30/1.48 % (7386)------------------------------
% 2.30/1.48 % (7386)------------------------------
% 2.30/1.48 % (7380)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7106 for (2999ds/183Mi)
% 2.30/1.48 % (7381)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_7106 for (2999ds/4Mi)
% 2.30/1.48 % (7384)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_7106 for (2999ds/2Mi)
% 2.30/1.48 % (7385)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_7106 for (2999ds/275Mi)
% 2.30/1.48 % (7382)Instruction limit reached!
% 2.30/1.48 % (7382)------------------------------
% 2.30/1.48 % (7382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.48 % (7382)Termination reason: Unknown
% 2.30/1.48 % (7382)Termination phase: Clausification
% 2.30/1.48
% 2.30/1.48 % (7382)Memory used [KB]: 1535
% 2.30/1.48 % (7382)Time elapsed: 0.009 s
% 2.30/1.48 % (7382)Instructions burned: 27 (million)
% 2.30/1.48 % (7382)------------------------------
% 2.30/1.48 % (7382)------------------------------
% 2.30/1.48 % (7384)Instruction limit reached!
% 2.30/1.48 % (7384)------------------------------
% 2.30/1.48 % (7384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.48 % (7384)Termination reason: Unknown
% 2.30/1.48 % (7384)Termination phase: shuffling
% 2.30/1.48
% 2.30/1.48 % (7384)Memory used [KB]: 1151
% 2.30/1.48 % (7384)Time elapsed: 0.003 s
% 2.30/1.48 % (7384)Instructions burned: 2 (million)
% 2.30/1.48 % (7384)------------------------------
% 2.30/1.48 % (7384)------------------------------
% 2.30/1.48 % (7381)Instruction limit reached!
% 2.30/1.48 % (7381)------------------------------
% 2.30/1.48 % (7381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.48 % (7381)Termination reason: Unknown
% 2.30/1.48 % (7381)Termination phase: shuffling
% 2.30/1.48
% 2.30/1.48 % (7381)Memory used [KB]: 1151
% 2.30/1.48 % (7381)Time elapsed: 0.004 s
% 2.30/1.48 % (7381)Instructions burned: 4 (million)
% 2.30/1.48 % (7381)------------------------------
% 2.30/1.48 % (7381)------------------------------
% 2.30/1.48 % (7387)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7106 for (2999ds/3Mi)
% 2.30/1.48 % (7387)Instruction limit reached!
% 2.30/1.48 % (7387)------------------------------
% 2.30/1.48 % (7387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.30/1.48 % (7387)Termination reason: Unknown
% 2.30/1.48 % (7387)Termination phase: shuffling
% 2.30/1.48
% 2.30/1.48 % (7387)Memory used [KB]: 1279
% 2.30/1.48 % (7387)Time elapsed: 0.003 s
% 2.30/1.48 % (7387)Instructions burned: 4 (million)
% 2.30/1.48 % (7387)------------------------------
% 2.30/1.48 % (7387)------------------------------
% 2.30/1.49 % (7388)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_7106 for (2999ds/37Mi)
% 2.30/1.49 % (7392)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_7106 for (2999ds/7Mi)
% 2.40/1.50 % (7392)Instruction limit reached!
% 2.40/1.50 % (7392)------------------------------
% 2.40/1.50 % (7392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.50 % (7392)Termination reason: Unknown
% 2.40/1.50 % (7392)Termination phase: shuffling
% 2.40/1.50
% 2.40/1.50 % (7392)Memory used [KB]: 1279
% 2.40/1.50 % (7392)Time elapsed: 0.004 s
% 2.40/1.50 % (7392)Instructions burned: 7 (million)
% 2.40/1.50 % (7392)------------------------------
% 2.40/1.50 % (7392)------------------------------
% 2.40/1.50 % (7389)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_7106 for (2999ds/15Mi)
% 2.40/1.50 % (7390)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_7106 for (2999ds/3Mi)
% 2.40/1.50 % (7391)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_7106 for (2999ds/1041Mi)
% 2.40/1.50 % (7390)Instruction limit reached!
% 2.40/1.50 % (7390)------------------------------
% 2.40/1.50 % (7390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.50 % (7390)Termination reason: Unknown
% 2.40/1.50 % (7390)Termination phase: shuffling
% 2.40/1.50
% 2.40/1.50 % (7390)Memory used [KB]: 1151
% 2.40/1.50 % (7390)Time elapsed: 0.004 s
% 2.40/1.50 % (7390)Instructions burned: 4 (million)
% 2.40/1.50 % (7390)------------------------------
% 2.40/1.50 % (7390)------------------------------
% 2.40/1.50 % (7388)Instruction limit reached!
% 2.40/1.50 % (7388)------------------------------
% 2.40/1.50 % (7388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.50 % (7388)Termination reason: Unknown
% 2.40/1.50 % (7388)Termination phase: Function definition elimination
% 2.40/1.50
% 2.40/1.50 % (7388)Memory used [KB]: 1663
% 2.40/1.50 % (7388)Time elapsed: 0.013 s
% 2.40/1.50 % (7388)Instructions burned: 40 (million)
% 2.40/1.50 % (7388)------------------------------
% 2.40/1.50 % (7388)------------------------------
% 2.40/1.51 % (7389)Instruction limit reached!
% 2.40/1.51 % (7389)------------------------------
% 2.40/1.51 % (7389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.51 % (7389)Termination reason: Unknown
% 2.40/1.51 % (7389)Termination phase: Naming
% 2.40/1.51
% 2.40/1.51 % (7389)Memory used [KB]: 1407
% 2.40/1.51 % (7389)Time elapsed: 0.011 s
% 2.40/1.51 % (7389)Instructions burned: 16 (million)
% 2.40/1.51 % (7389)------------------------------
% 2.40/1.51 % (7389)------------------------------
% 2.40/1.51 % (7393)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_7106 for (2999ds/16Mi)
% 2.40/1.51 % (7395)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_7106 for (2999ds/3Mi)
% 2.40/1.51 % (7395)Instruction limit reached!
% 2.40/1.51 % (7395)------------------------------
% 2.40/1.51 % (7395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.51 % (7395)Termination reason: Unknown
% 2.40/1.51 % (7395)Termination phase: shuffling
% 2.40/1.51
% 2.40/1.51 % (7395)Memory used [KB]: 1279
% 2.40/1.51 % (7395)Time elapsed: 0.003 s
% 2.40/1.51 % (7395)Instructions burned: 4 (million)
% 2.40/1.51 % (7395)------------------------------
% 2.40/1.51 % (7395)------------------------------
% 2.40/1.51 % (7393)Instruction limit reached!
% 2.40/1.51 % (7393)------------------------------
% 2.40/1.51 % (7393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.51 % (7393)Termination reason: Unknown
% 2.40/1.51 % (7393)Termination phase: Property scanning
% 2.40/1.51
% 2.40/1.51 % (7393)Memory used [KB]: 1535
% 2.40/1.51 % (7393)Time elapsed: 0.007 s
% 2.40/1.51 % (7393)Instructions burned: 18 (million)
% 2.40/1.51 % (7393)------------------------------
% 2.40/1.51 % (7393)------------------------------
% 2.40/1.52 % (7394)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_7106 for (2999ds/3Mi)
% 2.40/1.52 % (7394)Instruction limit reached!
% 2.40/1.52 % (7394)------------------------------
% 2.40/1.52 % (7394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.52 % (7394)Termination reason: Unknown
% 2.40/1.52 % (7394)Termination phase: shuffling
% 2.40/1.52
% 2.40/1.52 % (7394)Memory used [KB]: 1151
% 2.40/1.52 % (7394)Time elapsed: 0.003 s
% 2.40/1.52 % (7394)Instructions burned: 3 (million)
% 2.40/1.52 % (7394)------------------------------
% 2.40/1.52 % (7394)------------------------------
% 2.40/1.52 % (7397)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_7106 for (2999ds/3Mi)
% 2.40/1.52 % (7398)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_7106 for (2999ds/4Mi)
% 2.40/1.52 % (7397)Instruction limit reached!
% 2.40/1.52 % (7397)------------------------------
% 2.40/1.52 % (7397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.52 % (7397)Termination reason: Unknown
% 2.40/1.52 % (7397)Termination phase: shuffling
% 2.40/1.52
% 2.40/1.52 % (7397)Memory used [KB]: 1279
% 2.40/1.52 % (7397)Time elapsed: 0.003 s
% 2.40/1.52 % (7397)Instructions burned: 5 (million)
% 2.40/1.52 % (7397)------------------------------
% 2.40/1.52 % (7397)------------------------------
% 2.40/1.52 % (7398)Instruction limit reached!
% 2.40/1.52 % (7398)------------------------------
% 2.40/1.52 % (7398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.52 % (7398)Termination reason: Unknown
% 2.40/1.52 % (7398)Termination phase: shuffling
% 2.40/1.52
% 2.40/1.52 % (7398)Memory used [KB]: 1279
% 2.40/1.52 % (7398)Time elapsed: 0.003 s
% 2.40/1.52 % (7398)Instructions burned: 5 (million)
% 2.40/1.52 % (7398)------------------------------
% 2.40/1.52 % (7398)------------------------------
% 2.40/1.52 % (7396)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_7106 for (2999ds/7Mi)
% 2.40/1.53 % (7396)Instruction limit reached!
% 2.40/1.53 % (7396)------------------------------
% 2.40/1.53 % (7396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.53 % (7396)Termination reason: Unknown
% 2.40/1.53 % (7396)Termination phase: shuffling
% 2.40/1.53
% 2.40/1.53 % (7396)Memory used [KB]: 1279
% 2.40/1.53 % (7396)Time elapsed: 0.006 s
% 2.40/1.53 % (7396)Instructions burned: 8 (million)
% 2.40/1.53 % (7396)------------------------------
% 2.40/1.53 % (7396)------------------------------
% 2.40/1.53 % (7399)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_7106 for (2999ds/18Mi)
% 2.40/1.53 % (7400)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_7106 for (2999ds/710Mi)
% 2.40/1.53 % (7399)Instruction limit reached!
% 2.40/1.53 % (7399)------------------------------
% 2.40/1.53 % (7399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.53 % (7399)Termination reason: Unknown
% 2.40/1.53 % (7399)Termination phase: Property scanning
% 2.40/1.53
% 2.40/1.53 % (7399)Memory used [KB]: 1535
% 2.40/1.53 % (7399)Time elapsed: 0.006 s
% 2.40/1.53 % (7399)Instructions burned: 19 (million)
% 2.40/1.53 % (7399)------------------------------
% 2.40/1.53 % (7399)------------------------------
% 2.40/1.53 % (7401)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7106 for (2999ds/6Mi)
% 2.40/1.54 % (7401)Instruction limit reached!
% 2.40/1.54 % (7401)------------------------------
% 2.40/1.54 % (7401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.54 % (7401)Termination reason: Unknown
% 2.40/1.54 % (7401)Termination phase: shuffling
% 2.40/1.54
% 2.40/1.54 % (7401)Memory used [KB]: 1279
% 2.40/1.54 % (7401)Time elapsed: 0.004 s
% 2.40/1.54 % (7401)Instructions burned: 8 (million)
% 2.40/1.54 % (7401)------------------------------
% 2.40/1.54 % (7401)------------------------------
% 2.40/1.54 % (7403)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_7106 for (2999ds/21Mi)
% 2.40/1.55 % (7402)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_7106 for (2999ds/902Mi)
% 2.40/1.55 % (7404)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_7106 for (2999ds/5Mi)
% 2.40/1.55 % (7404)Instruction limit reached!
% 2.40/1.55 % (7404)------------------------------
% 2.40/1.55 % (7404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.55 % (7404)Termination reason: Unknown
% 2.40/1.55 % (7404)Termination phase: shuffling
% 2.40/1.55
% 2.40/1.55 % (7404)Memory used [KB]: 1279
% 2.40/1.55 % (7404)Time elapsed: 0.004 s
% 2.40/1.55 % (7404)Instructions burned: 8 (million)
% 2.40/1.55 % (7404)------------------------------
% 2.40/1.55 % (7404)------------------------------
% 2.40/1.55 % (7403)Instruction limit reached!
% 2.40/1.55 % (7403)------------------------------
% 2.40/1.55 % (7403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.55 % (7403)Termination reason: Unknown
% 2.40/1.55 % (7403)Termination phase: Property scanning
% 2.40/1.55
% 2.40/1.55 % (7403)Memory used [KB]: 1535
% 2.40/1.55 % (7403)Time elapsed: 0.007 s
% 2.40/1.55 % (7403)Instructions burned: 22 (million)
% 2.40/1.55 % (7403)------------------------------
% 2.40/1.55 % (7403)------------------------------
% 2.40/1.56 % (7406)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_7106 for (2999ds/377Mi)
% 2.40/1.56 % (7405)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_7106 for (2999ds/6Mi)
% 2.40/1.56 % (7405)Instruction limit reached!
% 2.40/1.56 % (7405)------------------------------
% 2.40/1.56 % (7405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.56 % (7405)Termination reason: Unknown
% 2.40/1.56 % (7405)Termination phase: shuffling
% 2.40/1.56
% 2.40/1.56 % (7405)Memory used [KB]: 1279
% 2.40/1.56 % (7405)Time elapsed: 0.004 s
% 2.40/1.56 % (7405)Instructions burned: 8 (million)
% 2.40/1.56 % (7405)------------------------------
% 2.40/1.56 % (7405)------------------------------
% 2.40/1.57 % (7407)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_7106 for (2999ds/779Mi)
% 2.40/1.58 % (7380)Instruction limit reached!
% 2.40/1.58 % (7380)------------------------------
% 2.40/1.58 % (7380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.58 % (7380)Termination reason: Unknown
% 2.40/1.58 % (7380)Termination phase: Saturation
% 2.40/1.58
% 2.40/1.58 % (7380)Memory used [KB]: 6908
% 2.40/1.58 % (7380)Time elapsed: 0.100 s
% 2.40/1.58 % (7380)Instructions burned: 183 (million)
% 2.40/1.58 % (7380)------------------------------
% 2.40/1.58 % (7380)------------------------------
% 2.40/1.59 % (7408)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_7106 for (2998ds/19Mi)
% 2.40/1.60 % (7408)Instruction limit reached!
% 2.40/1.60 % (7408)------------------------------
% 2.40/1.60 % (7408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.60 % (7408)Termination reason: Unknown
% 2.40/1.60 % (7408)Termination phase: Property scanning
% 2.40/1.60
% 2.40/1.60 % (7408)Memory used [KB]: 1535
% 2.40/1.60 % (7408)Time elapsed: 0.011 s
% 2.40/1.60 % (7408)Instructions burned: 20 (million)
% 2.40/1.60 % (7408)------------------------------
% 2.40/1.60 % (7408)------------------------------
% 2.40/1.62 % (7409)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_7106 for (2998ds/879Mi)
% 2.40/1.63 % (7385)Instruction limit reached!
% 2.40/1.63 % (7385)------------------------------
% 2.40/1.63 % (7385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.63 % (7385)Termination reason: Unknown
% 2.40/1.63 % (7385)Termination phase: Saturation
% 2.40/1.63
% 2.40/1.63 % (7385)Memory used [KB]: 7675
% 2.40/1.63 % (7385)Time elapsed: 0.153 s
% 2.40/1.63 % (7385)Instructions burned: 275 (million)
% 2.40/1.63 % (7385)------------------------------
% 2.40/1.63 % (7385)------------------------------
% 2.40/1.64 % (7410)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_7106 for (2998ds/17Mi)
% 2.40/1.65 % (7410)Instruction limit reached!
% 2.40/1.65 % (7410)------------------------------
% 2.40/1.65 % (7410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.65 % (7410)Termination reason: Unknown
% 2.40/1.65 % (7410)Termination phase: Property scanning
% 2.40/1.65
% 2.40/1.65 % (7410)Memory used [KB]: 1535
% 2.40/1.65 % (7410)Time elapsed: 0.007 s
% 2.40/1.65 % (7410)Instructions burned: 18 (million)
% 2.40/1.65 % (7410)------------------------------
% 2.40/1.65 % (7410)------------------------------
% 2.40/1.66 % (7411)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_7106 for (2998ds/3Mi)
% 2.40/1.66 % (7411)Instruction limit reached!
% 2.40/1.66 % (7411)------------------------------
% 2.40/1.66 % (7411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.66 % (7411)Termination reason: Unknown
% 2.40/1.66 % (7411)Termination phase: shuffling
% 2.40/1.66
% 2.40/1.66 % (7411)Memory used [KB]: 1279
% 2.40/1.66 % (7411)Time elapsed: 0.003 s
% 2.40/1.66 % (7411)Instructions burned: 5 (million)
% 2.40/1.66 % (7411)------------------------------
% 2.40/1.66 % (7411)------------------------------
% 2.40/1.67 % (7412)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_7106 for (2997ds/30Mi)
% 2.40/1.67 % (7406)Instruction limit reached!
% 2.40/1.67 % (7406)------------------------------
% 2.40/1.67 % (7406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.67 % (7406)Termination reason: Unknown
% 2.40/1.67 % (7406)Termination phase: Saturation
% 2.40/1.67
% 2.40/1.67 % (7406)Memory used [KB]: 7291
% 2.40/1.67 % (7406)Time elapsed: 0.116 s
% 2.40/1.67 % (7406)Instructions burned: 377 (million)
% 2.40/1.67 % (7406)------------------------------
% 2.40/1.67 % (7406)------------------------------
% 2.40/1.68 % (7412)Instruction limit reached!
% 2.40/1.68 % (7412)------------------------------
% 2.40/1.68 % (7412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.68 % (7412)Termination reason: Unknown
% 2.40/1.68 % (7412)Termination phase: Property scanning
% 2.40/1.68
% 2.40/1.68 % (7412)Memory used [KB]: 1535
% 2.40/1.68 % (7412)Time elapsed: 0.011 s
% 2.40/1.68 % (7412)Instructions burned: 33 (million)
% 2.40/1.68 % (7412)------------------------------
% 2.40/1.68 % (7412)------------------------------
% 2.40/1.68 % (7413)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_7106 for (2997ds/127Mi)
% 2.40/1.69 % (7414)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_7106 for (2997ds/100Mi)
% 2.40/1.72 % (7414)Instruction limit reached!
% 2.40/1.72 % (7414)------------------------------
% 2.40/1.72 % (7414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.72 % (7414)Termination reason: Unknown
% 2.40/1.72 % (7414)Termination phase: Saturation
% 2.40/1.72
% 2.40/1.72 % (7414)Memory used [KB]: 6396
% 2.40/1.72 % (7414)Time elapsed: 0.032 s
% 2.40/1.72 % (7414)Instructions burned: 101 (million)
% 2.40/1.72 % (7414)------------------------------
% 2.40/1.72 % (7414)------------------------------
% 2.40/1.72 % (7413)Instruction limit reached!
% 2.40/1.72 % (7413)------------------------------
% 2.40/1.72 % (7413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.72 % (7413)Termination reason: Unknown
% 2.40/1.72 % (7413)Termination phase: Saturation
% 2.40/1.72
% 2.40/1.72 % (7413)Memory used [KB]: 6780
% 2.40/1.72 % (7413)Time elapsed: 0.037 s
% 2.40/1.72 % (7413)Instructions burned: 127 (million)
% 2.40/1.72 % (7413)------------------------------
% 2.40/1.72 % (7413)------------------------------
% 2.40/1.73 % (7415)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_7106 for (2997ds/3Mi)
% 2.40/1.73 % (7416)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_7106 for (2997ds/20Mi)
% 2.40/1.73 % (7415)Instruction limit reached!
% 2.40/1.73 % (7415)------------------------------
% 2.40/1.73 % (7415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.73 % (7415)Termination reason: Unknown
% 2.40/1.73 % (7415)Termination phase: shuffling
% 2.40/1.73
% 2.40/1.73 % (7415)Memory used [KB]: 1279
% 2.40/1.73 % (7415)Time elapsed: 0.003 s
% 2.40/1.73 % (7415)Instructions burned: 5 (million)
% 2.40/1.73 % (7415)------------------------------
% 2.40/1.73 % (7415)------------------------------
% 2.40/1.73 % (7416)Instruction limit reached!
% 2.40/1.73 % (7416)------------------------------
% 2.40/1.73 % (7416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.73 % (7416)Termination reason: Unknown
% 2.40/1.73 % (7416)Termination phase: Unused predicate definition removal
% 2.40/1.73
% 2.40/1.73 % (7416)Memory used [KB]: 1407
% 2.40/1.73 % (7416)Time elapsed: 0.007 s
% 2.40/1.73 % (7416)Instructions burned: 21 (million)
% 2.40/1.73 % (7416)------------------------------
% 2.40/1.73 % (7416)------------------------------
% 2.40/1.74 % (7417)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_7106 for (2997ds/86Mi)
% 2.40/1.74 % (7418)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_7106 for (2997ds/107Mi)
% 2.40/1.75 % (7407)Instruction limit reached!
% 2.40/1.75 % (7407)------------------------------
% 2.40/1.75 % (7407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.75 % (7407)Termination reason: Unknown
% 2.40/1.75 % (7407)Termination phase: Saturation
% 2.40/1.75
% 2.40/1.75 % (7407)Memory used [KB]: 6524
% 2.40/1.75 % (7407)Time elapsed: 0.184 s
% 2.40/1.75 % (7407)Instructions burned: 780 (million)
% 2.40/1.75 % (7407)------------------------------
% 2.40/1.75 % (7407)------------------------------
% 2.40/1.76 % (7419)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_7106 for (2996ds/39Mi)
% 2.40/1.76 % (7417)Instruction limit reached!
% 2.40/1.76 % (7417)------------------------------
% 2.40/1.76 % (7417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.76 % (7417)Termination reason: Unknown
% 2.40/1.76 % (7417)Termination phase: Saturation
% 2.40/1.76
% 2.40/1.76 % (7417)Memory used [KB]: 6396
% 2.40/1.76 % (7417)Time elapsed: 0.026 s
% 2.40/1.76 % (7417)Instructions burned: 86 (million)
% 2.40/1.76 % (7417)------------------------------
% 2.40/1.76 % (7417)------------------------------
% 2.40/1.77 % (7418)Instruction limit reached!
% 2.40/1.77 % (7418)------------------------------
% 2.40/1.77 % (7418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.77 % (7418)Termination reason: Unknown
% 2.40/1.77 % (7418)Termination phase: Saturation
% 2.40/1.77
% 2.40/1.77 % (7418)Memory used [KB]: 6524
% 2.40/1.77 % (7418)Time elapsed: 0.029 s
% 2.40/1.77 % (7418)Instructions burned: 107 (million)
% 2.40/1.77 % (7418)------------------------------
% 2.40/1.77 % (7418)------------------------------
% 2.40/1.77 % (7419)Instruction limit reached!
% 2.40/1.77 % (7419)------------------------------
% 2.40/1.77 % (7419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.77 % (7419)Termination reason: Unknown
% 2.40/1.77 % (7419)Termination phase: Function definition elimination
% 2.40/1.77
% 2.40/1.77 % (7419)Memory used [KB]: 1663
% 2.40/1.77 % (7419)Time elapsed: 0.011 s
% 2.40/1.77 % (7419)Instructions burned: 40 (million)
% 2.40/1.77 % (7419)------------------------------
% 2.40/1.77 % (7419)------------------------------
% 2.40/1.77 % (7420)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_7106 for (2996ds/448Mi)
% 2.40/1.77 % (7391)Instruction limit reached!
% 2.40/1.77 % (7391)------------------------------
% 2.40/1.77 % (7391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.77 % (7391)Termination reason: Unknown
% 2.40/1.77 % (7391)Termination phase: Saturation
% 2.40/1.77
% 2.40/1.77 % (7391)Memory used [KB]: 8059
% 2.40/1.77 % (7391)Time elapsed: 0.277 s
% 2.40/1.77 % (7391)Instructions burned: 1044 (million)
% 2.40/1.77 % (7391)------------------------------
% 2.40/1.77 % (7391)------------------------------
% 2.40/1.77 % (7400)Instruction limit reached!
% 2.40/1.77 % (7400)------------------------------
% 2.40/1.77 % (7400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.77 % (7400)Termination reason: Unknown
% 2.40/1.77 % (7400)Termination phase: Saturation
% 2.40/1.77
% 2.40/1.77 % (7400)Memory used [KB]: 8571
% 2.40/1.77 % (7400)Time elapsed: 0.243 s
% 2.40/1.77 % (7400)Instructions burned: 712 (million)
% 2.40/1.77 % (7400)------------------------------
% 2.40/1.77 % (7400)------------------------------
% 2.40/1.78 % (7421)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_7106 for (2996ds/46Mi)
% 2.40/1.78 % (7422)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_7106 for (2996ds/98Mi)
% 2.40/1.78 % (7423)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_7106 for (2996ds/507Mi)
% 2.40/1.78 % (7424)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_7106 for (2996ds/149Mi)
% 2.40/1.79 % (7421)Instruction limit reached!
% 2.40/1.79 % (7421)------------------------------
% 2.40/1.79 % (7421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.79 % (7421)Termination reason: Unknown
% 2.40/1.79 % (7421)Termination phase: Twee Goal Transformation
% 2.40/1.79
% 2.40/1.79 % (7421)Memory used [KB]: 1535
% 2.40/1.79 % (7421)Time elapsed: 0.013 s
% 2.40/1.79 % (7421)Instructions burned: 48 (million)
% 2.40/1.79 % (7421)------------------------------
% 2.40/1.79 % (7421)------------------------------
% 2.40/1.80 % (7425)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_7106 for (2996ds/39Mi)
% 2.40/1.81 % (7422)Instruction limit reached!
% 2.40/1.81 % (7422)------------------------------
% 2.40/1.81 % (7422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.81 % (7422)Termination reason: Unknown
% 2.40/1.81 % (7422)Termination phase: Saturation
% 2.40/1.81
% 2.40/1.81 % (7422)Memory used [KB]: 1663
% 2.40/1.81 % (7422)Time elapsed: 0.026 s
% 2.40/1.81 % (7422)Instructions burned: 101 (million)
% 2.40/1.81 % (7422)------------------------------
% 2.40/1.81 % (7422)------------------------------
% 2.40/1.81 % (7425)Instruction limit reached!
% 2.40/1.81 % (7425)------------------------------
% 2.40/1.81 % (7425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.81 % (7425)Termination reason: Unknown
% 2.40/1.81 % (7425)Termination phase: Function definition elimination
% 2.40/1.81
% 2.40/1.81 % (7425)Memory used [KB]: 1535
% 2.40/1.81 % (7425)Time elapsed: 0.011 s
% 2.40/1.81 % (7425)Instructions burned: 39 (million)
% 2.40/1.81 % (7425)------------------------------
% 2.40/1.81 % (7425)------------------------------
% 2.40/1.82 % (7426)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_7106 for (2996ds/6Mi)
% 2.40/1.82 % (7426)Instruction limit reached!
% 2.40/1.82 % (7426)------------------------------
% 2.40/1.82 % (7426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.82 % (7426)Termination reason: Unknown
% 2.40/1.82 % (7426)Termination phase: shuffling
% 2.40/1.82
% 2.40/1.82 % (7426)Memory used [KB]: 1279
% 2.40/1.82 % (7426)Time elapsed: 0.003 s
% 2.40/1.82 % (7426)Instructions burned: 8 (million)
% 2.40/1.82 % (7426)------------------------------
% 2.40/1.82 % (7426)------------------------------
% 2.40/1.82 % (7427)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_7106 for (2996ds/1087Mi)
% 2.40/1.83 % (7428)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_7106 for (2996ds/47Mi)
% 2.40/1.83 % (7424)Instruction limit reached!
% 2.40/1.83 % (7424)------------------------------
% 2.40/1.83 % (7424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.83 % (7424)Termination reason: Unknown
% 2.40/1.83 % (7424)Termination phase: Saturation
% 2.40/1.83
% 2.40/1.83 % (7424)Memory used [KB]: 6780
% 2.40/1.83 % (7424)Time elapsed: 0.048 s
% 2.40/1.83 % (7424)Instructions burned: 152 (million)
% 2.40/1.83 % (7424)------------------------------
% 2.40/1.83 % (7424)------------------------------
% 2.40/1.84 % (7428)Instruction limit reached!
% 2.40/1.84 % (7428)------------------------------
% 2.40/1.84 % (7428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.84 % (7428)Termination reason: Unknown
% 2.40/1.84 % (7428)Termination phase: Property scanning
% 2.40/1.84
% 2.40/1.84 % (7428)Memory used [KB]: 1535
% 2.40/1.84 % (7428)Time elapsed: 0.013 s
% 2.40/1.84 % (7428)Instructions burned: 47 (million)
% 2.40/1.84 % (7428)------------------------------
% 2.40/1.84 % (7428)------------------------------
% 2.40/1.84 % (7429)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_7106 for (2996ds/44Mi)
% 2.40/1.85 % (7430)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_7106 for (2996ds/432Mi)
% 2.40/1.85 % (7429)Instruction limit reached!
% 2.40/1.85 % (7429)------------------------------
% 2.40/1.85 % (7429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.85 % (7429)Termination reason: Unknown
% 2.40/1.85 % (7429)Termination phase: Function definition elimination
% 2.40/1.85
% 2.40/1.85 % (7429)Memory used [KB]: 1663
% 2.40/1.85 % (7429)Time elapsed: 0.013 s
% 2.40/1.85 % (7429)Instructions burned: 48 (million)
% 2.40/1.85 % (7429)------------------------------
% 2.40/1.85 % (7429)------------------------------
% 2.40/1.86 % (7431)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_7106 for (2996ds/62Mi)
% 2.40/1.88 % (7431)Instruction limit reached!
% 2.40/1.88 % (7431)------------------------------
% 2.40/1.88 % (7431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.88 % (7431)Termination reason: Unknown
% 2.40/1.88 % (7431)Termination phase: Saturation
% 2.40/1.88
% 2.40/1.88 % (7431)Memory used [KB]: 6140
% 2.40/1.88 % (7431)Time elapsed: 0.017 s
% 2.40/1.88 % (7431)Instructions burned: 65 (million)
% 2.40/1.88 % (7431)------------------------------
% 2.40/1.88 % (7431)------------------------------
% 2.40/1.88 % (7402)Instruction limit reached!
% 2.40/1.88 % (7402)------------------------------
% 2.40/1.88 % (7402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.88 % (7402)Termination reason: Unknown
% 2.40/1.88 % (7402)Termination phase: Saturation
% 2.40/1.88
% 2.40/1.88 % (7402)Memory used [KB]: 10618
% 2.40/1.88 % (7402)Time elapsed: 0.336 s
% 2.40/1.88 % (7402)Instructions burned: 902 (million)
% 2.40/1.88 % (7402)------------------------------
% 2.40/1.88 % (7402)------------------------------
% 2.40/1.89 % (7420)Instruction limit reached!
% 2.40/1.89 % (7420)------------------------------
% 2.40/1.89 % (7420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.89 % (7420)Termination reason: Unknown
% 2.40/1.89 % (7420)Termination phase: Saturation
% 2.40/1.89
% 2.40/1.89 % (7420)Memory used [KB]: 6524
% 2.40/1.89 % (7420)Time elapsed: 0.115 s
% 2.40/1.89 % (7420)Instructions burned: 449 (million)
% 2.40/1.89 % (7420)------------------------------
% 2.40/1.89 % (7420)------------------------------
% 2.40/1.89 % (7432)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_7106 for (2995ds/31Mi)
% 2.40/1.89 % (7433)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_7106 for (2995ds/96Mi)
% 2.40/1.89 % (7432)Instruction limit reached!
% 2.40/1.89 % (7432)------------------------------
% 2.40/1.89 % (7432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.89 % (7432)Termination reason: Unknown
% 2.40/1.89 % (7432)Termination phase: Property scanning
% 2.40/1.89
% 2.40/1.89 % (7432)Memory used [KB]: 1535
% 2.40/1.89 % (7432)Time elapsed: 0.009 s
% 2.40/1.89 % (7432)Instructions burned: 31 (million)
% 2.40/1.89 % (7432)------------------------------
% 2.40/1.89 % (7432)------------------------------
% 2.40/1.90 % (7434)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_7106 for (2995ds/453Mi)
% 2.40/1.90 % (7435)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_7106 for (2995ds/71Mi)
% 2.40/1.91 % (7409)Instruction limit reached!
% 2.40/1.91 % (7409)------------------------------
% 2.40/1.91 % (7409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.91 % (7409)Termination reason: Unknown
% 2.40/1.91 % (7409)Termination phase: Saturation
% 2.40/1.91
% 2.40/1.91 % (7409)Memory used [KB]: 7419
% 2.40/1.91 % (7409)Time elapsed: 0.320 s
% 2.40/1.91 % (7409)Instructions burned: 881 (million)
% 2.40/1.91 % (7409)------------------------------
% 2.40/1.91 % (7409)------------------------------
% 2.40/1.92 % (7433)Instruction limit reached!
% 2.40/1.92 % (7433)------------------------------
% 2.40/1.92 % (7433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.92 % (7433)Termination reason: Unknown
% 2.40/1.92 % (7433)Termination phase: Saturation
% 2.40/1.92
% 2.40/1.92 % (7433)Memory used [KB]: 6524
% 2.40/1.92 % (7433)Time elapsed: 0.030 s
% 2.40/1.92 % (7433)Instructions burned: 99 (million)
% 2.40/1.92 % (7433)------------------------------
% 2.40/1.92 % (7433)------------------------------
% 2.40/1.92 % (7435)Instruction limit reached!
% 2.40/1.92 % (7435)------------------------------
% 2.40/1.92 % (7435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.92 % (7435)Termination reason: Unknown
% 2.40/1.92 % (7435)Termination phase: Saturation
% 2.40/1.92
% 2.40/1.92 % (7435)Memory used [KB]: 6268
% 2.40/1.92 % (7435)Time elapsed: 0.021 s
% 2.40/1.92 % (7435)Instructions burned: 72 (million)
% 2.40/1.92 % (7435)------------------------------
% 2.40/1.92 % (7435)------------------------------
% 2.40/1.92 % (7436)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_7106 for (2995ds/83Mi)
% 2.40/1.93 % (7437)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_7106 for (2995ds/11Mi)
% 2.40/1.93 % (7437)Instruction limit reached!
% 2.40/1.93 % (7437)------------------------------
% 2.40/1.93 % (7437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.93 % (7437)Termination reason: Unknown
% 2.40/1.93 % (7437)Termination phase: shuffling
% 2.40/1.93
% 2.40/1.93 % (7437)Memory used [KB]: 1407
% 2.40/1.93 % (7437)Time elapsed: 0.005 s
% 2.40/1.93 % (7437)Instructions burned: 12 (million)
% 2.40/1.93 % (7437)------------------------------
% 2.40/1.93 % (7437)------------------------------
% 2.40/1.93 % (7438)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_7106 for (2995ds/41Mi)
% 2.40/1.94 % (7423)Instruction limit reached!
% 2.40/1.94 % (7423)------------------------------
% 2.40/1.94 % (7423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.94 % (7423)Termination reason: Unknown
% 2.40/1.94 % (7423)Termination phase: Saturation
% 2.40/1.94
% 2.40/1.94 % (7423)Memory used [KB]: 7164
% 2.40/1.94 % (7423)Time elapsed: 0.154 s
% 2.40/1.94 % (7423)Instructions burned: 508 (million)
% 2.40/1.94 % (7423)------------------------------
% 2.40/1.94 % (7423)------------------------------
% 2.40/1.94 % (7439)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7106 for (2995ds/6Mi)
% 2.40/1.94 % (7438)Instruction limit reached!
% 2.40/1.94 % (7438)------------------------------
% 2.40/1.94 % (7438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.94 % (7438)Termination reason: Unknown
% 2.40/1.94 % (7438)Termination phase: Function definition elimination
% 2.40/1.94
% 2.40/1.94 % (7438)Memory used [KB]: 1663
% 2.40/1.94 % (7438)Time elapsed: 0.011 s
% 2.40/1.94 % (7438)Instructions burned: 41 (million)
% 2.40/1.94 % (7438)------------------------------
% 2.40/1.94 % (7438)------------------------------
% 2.40/1.94 % (7439)Instruction limit reached!
% 2.40/1.94 % (7439)------------------------------
% 2.40/1.94 % (7439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.94 % (7439)Termination reason: Unknown
% 2.40/1.94 % (7439)Termination phase: shuffling
% 2.40/1.94
% 2.40/1.94 % (7439)Memory used [KB]: 1279
% 2.40/1.94 % (7439)Time elapsed: 0.004 s
% 2.40/1.94 % (7439)Instructions burned: 8 (million)
% 2.40/1.94 % (7439)------------------------------
% 2.40/1.94 % (7439)------------------------------
% 2.40/1.95 % (7440)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_7106 for (2995ds/150Mi)
% 2.40/1.95 % (7436)Instruction limit reached!
% 2.40/1.95 % (7436)------------------------------
% 2.40/1.95 % (7436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.95 % (7436)Termination reason: Unknown
% 2.40/1.95 % (7436)Termination phase: Saturation
% 2.40/1.95
% 2.40/1.95 % (7436)Memory used [KB]: 6268
% 2.40/1.95 % (7436)Time elapsed: 0.023 s
% 2.40/1.95 % (7436)Instructions burned: 83 (million)
% 2.40/1.95 % (7436)------------------------------
% 2.40/1.95 % (7436)------------------------------
% 2.40/1.95 % (7441)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_7106 for (2995ds/343Mi)
% 2.40/1.95 % (7442)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_7106 for (2995ds/109Mi)
% 2.40/1.96 % (7443)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_7106 for (2995ds/253Mi)
% 2.40/1.96 % (7430)Instruction limit reached!
% 2.40/1.96 % (7430)------------------------------
% 2.40/1.96 % (7430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.96 % (7430)Termination reason: Unknown
% 2.40/1.96 % (7430)Termination phase: Saturation
% 2.40/1.96
% 2.40/1.96 % (7430)Memory used [KB]: 2430
% 2.40/1.96 % (7430)Time elapsed: 0.108 s
% 2.40/1.96 % (7430)Instructions burned: 432 (million)
% 2.40/1.96 % (7430)------------------------------
% 2.40/1.96 % (7430)------------------------------
% 2.40/1.97 % (7444)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_7106 for (2995ds/140Mi)
% 2.40/1.98 % (7442)Instruction limit reached!
% 2.40/1.98 % (7442)------------------------------
% 2.40/1.98 % (7442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.98 % (7442)Termination reason: Unknown
% 2.40/1.98 % (7442)Termination phase: Saturation
% 2.40/1.98
% 2.40/1.98 % (7442)Memory used [KB]: 6652
% 2.40/1.98 % (7442)Time elapsed: 0.031 s
% 2.40/1.98 % (7442)Instructions burned: 111 (million)
% 2.40/1.98 % (7442)------------------------------
% 2.40/1.98 % (7442)------------------------------
% 2.40/1.99 % (7440)Instruction limit reached!
% 2.40/1.99 % (7440)------------------------------
% 2.40/1.99 % (7440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/1.99 % (7440)Termination reason: Unknown
% 2.40/1.99 % (7440)Termination phase: Saturation
% 2.40/1.99
% 2.40/1.99 % (7440)Memory used [KB]: 7419
% 2.40/1.99 % (7440)Time elapsed: 0.046 s
% 2.40/1.99 % (7440)Instructions burned: 150 (million)
% 2.40/1.99 % (7440)------------------------------
% 2.40/1.99 % (7440)------------------------------
% 2.40/1.99 % (7445)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_7106 for (2994ds/614Mi)
% 2.40/2.00 % (7446)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_7106 for (2994ds/202Mi)
% 2.40/2.00 % (7444)Instruction limit reached!
% 2.40/2.00 % (7444)------------------------------
% 2.40/2.00 % (7444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/2.00 % (7444)Termination reason: Unknown
% 2.40/2.00 % (7444)Termination phase: Saturation
% 2.40/2.00
% 2.40/2.00 % (7444)Memory used [KB]: 6268
% 2.40/2.00 % (7444)Time elapsed: 0.062 s
% 2.40/2.00 % (7444)Instructions burned: 141 (million)
% 2.40/2.00 % (7444)------------------------------
% 2.40/2.00 % (7444)------------------------------
% 2.40/2.01 % (7434)Instruction limit reached!
% 2.40/2.01 % (7434)------------------------------
% 2.40/2.01 % (7434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.40/2.01 % (7434)Termination reason: Unknown
% 2.40/2.01 % (7434)Termination phase: Saturation
% 2.40/2.01
% 2.40/2.01 % (7434)Memory used [KB]: 6268
% 2.40/2.01 % (7434)Time elapsed: 0.114 s
% 2.40/2.01 % (7434)Instructions burned: 454 (million)
% 2.40/2.01 % (7434)------------------------------
% 2.40/2.01 % (7434)------------------------------
% 6.07/2.01 % (7447)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_7106 for (2994ds/339Mi)
% 6.07/2.02 % (7448)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_7106 for (2994ds/283Mi)
% 6.07/2.03 % (7443)Instruction limit reached!
% 6.07/2.03 % (7443)------------------------------
% 6.07/2.03 % (7443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.07/2.03 % (7443)Termination reason: Unknown
% 6.07/2.03 % (7443)Termination phase: Saturation
% 6.07/2.03
% 6.07/2.03 % (7443)Memory used [KB]: 7803
% 6.07/2.03 % (7443)Time elapsed: 0.103 s
% 6.07/2.03 % (7443)Instructions burned: 253 (million)
% 6.07/2.03 % (7443)------------------------------
% 6.07/2.03 % (7443)------------------------------
% 6.07/2.04 % (7449)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_7106 for (2994ds/134Mi)
% 6.07/2.06 % (7446)Instruction limit reached!
% 6.07/2.06 % (7446)------------------------------
% 6.07/2.06 % (7446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.07/2.06 % (7446)Termination reason: Unknown
% 6.07/2.06 % (7446)Termination phase: Saturation
% 6.07/2.06
% 6.07/2.06 % (7446)Memory used [KB]: 7675
% 6.07/2.06 % (7446)Time elapsed: 0.064 s
% 6.07/2.06 % (7446)Instructions burned: 204 (million)
% 6.07/2.06 % (7446)------------------------------
% 6.07/2.06 % (7446)------------------------------
% 6.07/2.07 % (7450)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_7106 for (2993ds/298Mi)
% 6.07/2.08 % (7449)Instruction limit reached!
% 6.07/2.08 % (7449)------------------------------
% 6.07/2.08 % (7449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.07/2.08 % (7449)Termination reason: Unknown
% 6.07/2.08 % (7449)Termination phase: Saturation
% 6.07/2.08
% 6.07/2.08 % (7449)Memory used [KB]: 6908
% 6.07/2.08 % (7449)Time elapsed: 0.038 s
% 6.07/2.08 % (7449)Instructions burned: 135 (million)
% 6.07/2.08 % (7449)------------------------------
% 6.07/2.08 % (7449)------------------------------
% 6.07/2.09 % (7448)Instruction limit reached!
% 6.07/2.09 % (7448)------------------------------
% 6.07/2.09 % (7448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.07/2.09 % (7448)Termination reason: Unknown
% 6.07/2.09 % (7448)Termination phase: Saturation
% 6.07/2.09
% 6.07/2.09 % (7448)Memory used [KB]: 8187
% 6.07/2.09 % (7448)Time elapsed: 0.072 s
% 6.07/2.09 % (7448)Instructions burned: 283 (million)
% 6.07/2.09 % (7448)------------------------------
% 6.07/2.09 % (7448)------------------------------
% 6.07/2.09 % (7451)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_7106 for (2993ds/192Mi)
% 6.07/2.10 % (7452)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_7106 for (2993ds/258Mi)
% 6.07/2.11 % (7441)Instruction limit reached!
% 6.07/2.11 % (7441)------------------------------
% 6.07/2.11 % (7441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.07/2.11 % (7441)Termination reason: Unknown
% 6.07/2.11 % (7441)Termination phase: Saturation
% 6.07/2.11
% 6.07/2.11 % (7441)Memory used [KB]: 7164
% 6.07/2.11 % (7441)Time elapsed: 0.178 s
% 6.07/2.11 % (7441)Instructions burned: 344 (million)
% 6.07/2.11 % (7441)------------------------------
% 6.07/2.11 % (7441)------------------------------
% 6.07/2.11 % (7447)Instruction limit reached!
% 6.07/2.11 % (7447)------------------------------
% 6.07/2.11 % (7447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.07/2.11 % (7447)Termination reason: Unknown
% 6.07/2.11 % (7447)Termination phase: Saturation
% 6.07/2.11
% 6.07/2.11 % (7447)Memory used [KB]: 7931
% 6.07/2.11 % (7447)Time elapsed: 0.100 s
% 6.07/2.11 % (7447)Instructions burned: 339 (million)
% 6.07/2.11 % (7447)------------------------------
% 6.07/2.11 % (7447)------------------------------
% 6.72/2.12 % (7453)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_7106 for (2993ds/90Mi)
% 6.72/2.12 % (7454)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_7106 for (2993ds/231Mi)
% 6.72/2.15 % (7451)Instruction limit reached!
% 6.72/2.15 % (7451)------------------------------
% 6.72/2.15 % (7451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.15 % (7451)Termination reason: Unknown
% 6.72/2.15 % (7451)Termination phase: Saturation
% 6.72/2.15
% 6.72/2.15 % (7451)Memory used [KB]: 7036
% 6.72/2.15 % (7451)Time elapsed: 0.056 s
% 6.72/2.15 % (7451)Instructions burned: 194 (million)
% 6.72/2.15 % (7451)------------------------------
% 6.72/2.15 % (7451)------------------------------
% 6.72/2.15 % (7453)Instruction limit reached!
% 6.72/2.15 % (7453)------------------------------
% 6.72/2.15 % (7453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.15 % (7453)Termination reason: Unknown
% 6.72/2.15 % (7453)Termination phase: Saturation
% 6.72/2.15
% 6.72/2.15 % (7453)Memory used [KB]: 6652
% 6.72/2.15 % (7453)Time elapsed: 0.028 s
% 6.72/2.15 % (7453)Instructions burned: 90 (million)
% 6.72/2.15 % (7453)------------------------------
% 6.72/2.15 % (7453)------------------------------
% 6.72/2.15 % (7450)Instruction limit reached!
% 6.72/2.15 % (7450)------------------------------
% 6.72/2.15 % (7450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.15 % (7450)Termination reason: Unknown
% 6.72/2.15 % (7450)Termination phase: Saturation
% 6.72/2.15
% 6.72/2.15 % (7450)Memory used [KB]: 6524
% 6.72/2.15 % (7450)Time elapsed: 0.076 s
% 6.72/2.15 % (7450)Instructions burned: 299 (million)
% 6.72/2.15 % (7450)------------------------------
% 6.72/2.15 % (7450)------------------------------
% 6.72/2.16 % (7455)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_7106 for (2993ds/458Mi)
% 6.72/2.16 % (7457)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_7106 for (2993ds/297Mi)
% 6.72/2.16 % (7456)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_7106 for (2993ds/31Mi)
% 6.72/2.16 % (7427)Instruction limit reached!
% 6.72/2.16 % (7427)------------------------------
% 6.72/2.16 % (7427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.16 % (7427)Termination reason: Unknown
% 6.72/2.16 % (7427)Termination phase: Saturation
% 6.72/2.16
% 6.72/2.16 % (7427)Memory used [KB]: 9978
% 6.72/2.16 % (7427)Time elapsed: 0.344 s
% 6.72/2.16 % (7427)Instructions burned: 1087 (million)
% 6.72/2.16 % (7427)------------------------------
% 6.72/2.16 % (7427)------------------------------
% 6.72/2.17 % (7456)Instruction limit reached!
% 6.72/2.17 % (7456)------------------------------
% 6.72/2.17 % (7456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.17 % (7456)Termination reason: Unknown
% 6.72/2.17 % (7456)Termination phase: Property scanning
% 6.72/2.17
% 6.72/2.17 % (7456)Memory used [KB]: 1535
% 6.72/2.17 % (7456)Time elapsed: 0.011 s
% 6.72/2.17 % (7456)Instructions burned: 33 (million)
% 6.72/2.17 % (7456)------------------------------
% 6.72/2.17 % (7456)------------------------------
% 6.72/2.17 % (7458)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_7106 for (2992ds/987Mi)
% 6.72/2.18 % (7452)Instruction limit reached!
% 6.72/2.18 % (7452)------------------------------
% 6.72/2.18 % (7452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.18 % (7452)Termination reason: Unknown
% 6.72/2.18 % (7452)Termination phase: Saturation
% 6.72/2.18
% 6.72/2.18 % (7452)Memory used [KB]: 7036
% 6.72/2.18 % (7452)Time elapsed: 0.078 s
% 6.72/2.18 % (7452)Instructions burned: 260 (million)
% 6.72/2.18 % (7452)------------------------------
% 6.72/2.18 % (7452)------------------------------
% 6.72/2.18 % (7459)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_7106 for (2992ds/182Mi)
% 6.72/2.18 % (7445)Instruction limit reached!
% 6.72/2.18 % (7445)------------------------------
% 6.72/2.18 % (7445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.18 % (7445)Termination reason: Unknown
% 6.72/2.18 % (7445)Termination phase: Saturation
% 6.72/2.18
% 6.72/2.18 % (7445)Memory used [KB]: 8059
% 6.72/2.18 % (7445)Time elapsed: 0.211 s
% 6.72/2.18 % (7445)Instructions burned: 614 (million)
% 6.72/2.18 % (7445)------------------------------
% 6.72/2.18 % (7445)------------------------------
% 6.72/2.19 % (7460)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_7106 for (2992ds/182Mi)
% 6.72/2.19 % (7454)Instruction limit reached!
% 6.72/2.19 % (7454)------------------------------
% 6.72/2.19 % (7454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.19 % (7454)Termination reason: Unknown
% 6.72/2.19 % (7454)Termination phase: Saturation
% 6.72/2.19
% 6.72/2.19 % (7454)Memory used [KB]: 9722
% 6.72/2.19 % (7454)Time elapsed: 0.068 s
% 6.72/2.19 % (7454)Instructions burned: 231 (million)
% 6.72/2.19 % (7454)------------------------------
% 6.72/2.19 % (7454)------------------------------
% 6.72/2.19 % (7461)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_7106 for (2992ds/154Mi)
% 7.34/2.20 % (7462)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_7106 for (2992ds/79Mi)
% 7.34/2.22 % (7462)Instruction limit reached!
% 7.34/2.22 % (7462)------------------------------
% 7.34/2.22 % (7462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.34/2.22 % (7462)Termination reason: Unknown
% 7.34/2.22 % (7462)Termination phase: Saturation
% 7.34/2.22
% 7.34/2.22 % (7462)Memory used [KB]: 6268
% 7.34/2.22 % (7462)Time elapsed: 0.023 s
% 7.34/2.22 % (7462)Instructions burned: 79 (million)
% 7.34/2.22 % (7462)------------------------------
% 7.34/2.22 % (7462)------------------------------
% 7.34/2.23 % (7463)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_7106 for (2992ds/216Mi)
% 7.34/2.23 % (7461)Instruction limit reached!
% 7.34/2.23 % (7461)------------------------------
% 7.34/2.23 % (7461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.34/2.23 % (7461)Termination reason: Unknown
% 7.34/2.23 % (7461)Termination phase: Saturation
% 7.34/2.23
% 7.34/2.23 % (7461)Memory used [KB]: 6268
% 7.34/2.23 % (7461)Time elapsed: 0.040 s
% 7.34/2.23 % (7461)Instructions burned: 155 (million)
% 7.34/2.23 % (7461)------------------------------
% 7.34/2.23 % (7461)------------------------------
% 7.34/2.23 % (7457)Instruction limit reached!
% 7.34/2.23 % (7457)------------------------------
% 7.34/2.23 % (7457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.34/2.23 % (7457)Termination reason: Unknown
% 7.34/2.23 % (7457)Termination phase: Saturation
% 7.34/2.23
% 7.34/2.23 % (7457)Memory used [KB]: 7291
% 7.34/2.23 % (7457)Time elapsed: 0.075 s
% 7.34/2.23 % (7457)Instructions burned: 298 (million)
% 7.34/2.23 % (7457)------------------------------
% 7.34/2.23 % (7457)------------------------------
% 7.34/2.23 % (7459)Instruction limit reached!
% 7.34/2.23 % (7459)------------------------------
% 7.34/2.23 % (7459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.34/2.23 % (7459)Termination reason: Unknown
% 7.34/2.23 % (7459)Termination phase: Saturation
% 7.34/2.23
% 7.34/2.23 % (7459)Memory used [KB]: 6908
% 7.34/2.23 % (7459)Time elapsed: 0.058 s
% 7.34/2.23 % (7459)Instructions burned: 182 (million)
% 7.34/2.23 % (7459)------------------------------
% 7.34/2.23 % (7459)------------------------------
% 7.34/2.24 % (7464)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_7106 for (2992ds/114Mi)
% 7.34/2.24 % (7465)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_7106 for (2992ds/922Mi)
% 7.34/2.24 % (7460)Instruction limit reached!
% 7.34/2.24 % (7460)------------------------------
% 7.34/2.24 % (7460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.34/2.24 % (7460)Termination reason: Unknown
% 7.34/2.24 % (7460)Termination phase: Saturation
% 7.34/2.24
% 7.34/2.24 % (7460)Memory used [KB]: 8699
% 7.34/2.24 % (7460)Time elapsed: 0.059 s
% 7.34/2.24 % (7460)Instructions burned: 183 (million)
% 7.34/2.24 % (7460)------------------------------
% 7.34/2.24 % (7460)------------------------------
% 7.34/2.24 % (7466)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_7106 for (2992ds/182Mi)
% 7.34/2.25 % (7467)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_7106 for (2992ds/164Mi)
% 7.34/2.27 % (7464)Instruction limit reached!
% 7.34/2.27 % (7464)------------------------------
% 7.34/2.27 % (7464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.34/2.27 % (7464)Termination reason: Unknown
% 7.34/2.27 % (7464)Termination phase: Saturation
% 7.34/2.27
% 7.34/2.27 % (7464)Memory used [KB]: 6652
% 7.34/2.27 % (7464)Time elapsed: 0.032 s
% 7.34/2.27 % (7464)Instructions burned: 116 (million)
% 7.34/2.27 % (7464)------------------------------
% 7.34/2.27 % (7464)------------------------------
% 7.34/2.28 % (7468)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_7106 for (2991ds/50Mi)
% 7.34/2.28 % (7463)Instruction limit reached!
% 7.34/2.28 % (7463)------------------------------
% 7.34/2.28 % (7463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.34/2.28 % (7463)Termination reason: Unknown
% 7.34/2.28 % (7463)Termination phase: Saturation
% 7.34/2.28
% 7.34/2.28 % (7463)Memory used [KB]: 6908
% 7.34/2.28 % (7463)Time elapsed: 0.054 s
% 7.34/2.28 % (7463)Instructions burned: 219 (million)
% 7.34/2.28 % (7463)------------------------------
% 7.34/2.28 % (7463)------------------------------
% 7.34/2.29 % (7466)Instruction limit reached!
% 7.34/2.29 % (7466)------------------------------
% 7.34/2.29 % (7466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.34/2.29 % (7466)Termination reason: Unknown
% 7.34/2.29 % (7466)Termination phase: Saturation
% 7.34/2.29
% 7.34/2.29 % (7466)Memory used [KB]: 6268
% 7.34/2.29 % (7466)Time elapsed: 0.050 s
% 7.34/2.29 % (7466)Instructions burned: 183 (million)
% 7.34/2.29 % (7466)------------------------------
% 7.34/2.29 % (7466)------------------------------
% 7.34/2.29 % (7469)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_7106 for (2991ds/368Mi)
% 7.34/2.29 % (7468)Instruction limit reached!
% 7.34/2.29 % (7468)------------------------------
% 7.34/2.29 % (7468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.34/2.29 % (7468)Termination reason: Unknown
% 7.34/2.29 % (7468)Termination phase: Property scanning
% 7.34/2.29
% 7.34/2.29 % (7468)Memory used [KB]: 1663
% 7.34/2.29 % (7468)Time elapsed: 0.014 s
% 7.34/2.29 % (7468)Instructions burned: 53 (million)
% 7.34/2.29 % (7468)------------------------------
% 7.34/2.29 % (7468)------------------------------
% 7.82/2.30 % (7455)Instruction limit reached!
% 7.82/2.30 % (7455)------------------------------
% 7.82/2.30 % (7455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.82/2.30 % (7455)Termination reason: Unknown
% 7.82/2.30 % (7455)Termination phase: Saturation
% 7.82/2.30
% 7.82/2.30 % (7455)Memory used [KB]: 7291
% 7.82/2.30 % (7455)Time elapsed: 0.142 s
% 7.82/2.30 % (7455)Instructions burned: 459 (million)
% 7.82/2.30 % (7455)------------------------------
% 7.82/2.30 % (7455)------------------------------
% 7.82/2.30 % (7467)Instruction limit reached!
% 7.82/2.30 % (7467)------------------------------
% 7.82/2.30 % (7467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.82/2.30 % (7467)Termination reason: Unknown
% 7.82/2.30 % (7467)Termination phase: Saturation
% 7.82/2.30
% 7.82/2.30 % (7467)Memory used [KB]: 2046
% 7.82/2.30 % (7467)Time elapsed: 0.047 s
% 7.82/2.30 % (7467)Instructions burned: 164 (million)
% 7.82/2.30 % (7467)------------------------------
% 7.82/2.30 % (7467)------------------------------
% 7.82/2.30 % (7470)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_7106 for (2991ds/1021Mi)
% 7.82/2.30 % (7471)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_7106 for (2991ds/267Mi)
% 7.82/2.31 % (7472)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_7106 for (2991ds/204Mi)
% 7.82/2.31 % (7473)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_7106 for (2991ds/26Mi)
% 7.82/2.31 % (7473)Instruction limit reached!
% 7.82/2.31 % (7473)------------------------------
% 7.82/2.31 % (7473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.82/2.31 % (7473)Termination reason: Unknown
% 7.82/2.31 % (7473)Termination phase: Property scanning
% 7.82/2.31
% 7.82/2.31 % (7473)Memory used [KB]: 1535
% 7.82/2.31 % (7473)Time elapsed: 0.008 s
% 7.82/2.31 % (7473)Instructions burned: 27 (million)
% 7.82/2.31 % (7473)------------------------------
% 7.82/2.31 % (7473)------------------------------
% 7.82/2.32 % (7474)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_7106 for (2991ds/53Mi)
% 7.82/2.34 % (7474)Instruction limit reached!
% 7.82/2.34 % (7474)------------------------------
% 7.82/2.34 % (7474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.82/2.34 % (7474)Termination reason: Unknown
% 7.82/2.34 % (7474)Termination phase: Property scanning
% 7.82/2.34
% 7.82/2.34 % (7474)Memory used [KB]: 1663
% 7.82/2.34 % (7474)Time elapsed: 0.014 s
% 7.82/2.34 % (7474)Instructions burned: 54 (million)
% 7.82/2.34 % (7474)------------------------------
% 7.82/2.34 % (7474)------------------------------
% 7.82/2.35 % (7475)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_7106 for (2991ds/4436Mi)
% 7.82/2.37 % (7472)Instruction limit reached!
% 7.82/2.37 % (7472)------------------------------
% 7.82/2.37 % (7472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.82/2.37 % (7472)Termination reason: Unknown
% 7.82/2.37 % (7472)Termination phase: Saturation
% 7.82/2.37
% 7.82/2.37 % (7472)Memory used [KB]: 6908
% 7.82/2.37 % (7472)Time elapsed: 0.061 s
% 7.82/2.37 % (7472)Instructions burned: 205 (million)
% 7.82/2.37 % (7472)------------------------------
% 7.82/2.37 % (7472)------------------------------
% 7.82/2.37 % (7471)Instruction limit reached!
% 7.82/2.37 % (7471)------------------------------
% 7.82/2.37 % (7471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.82/2.37 % (7471)Termination reason: Unknown
% 7.82/2.37 % (7471)Termination phase: Saturation
% 7.82/2.37
% 7.82/2.37 % (7471)Memory used [KB]: 8059
% 7.82/2.37 % (7471)Time elapsed: 0.068 s
% 7.82/2.37 % (7471)Instructions burned: 267 (million)
% 7.82/2.37 % (7471)------------------------------
% 7.82/2.37 % (7471)------------------------------
% 7.82/2.38 % (7476)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_7106 for (2990ds/1539Mi)
% 7.82/2.38 % (7477)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_7106 for (2990ds/408Mi)
% 8.21/2.40 % (7469)Instruction limit reached!
% 8.21/2.40 % (7469)------------------------------
% 8.21/2.40 % (7469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.21/2.40 % (7469)Termination reason: Unknown
% 8.21/2.40 % (7469)Termination phase: Saturation
% 8.21/2.40
% 8.21/2.40 % (7469)Memory used [KB]: 7291
% 8.21/2.40 % (7469)Time elapsed: 0.114 s
% 8.21/2.40 % (7469)Instructions burned: 370 (million)
% 8.21/2.40 % (7469)------------------------------
% 8.21/2.40 % (7469)------------------------------
% 8.21/2.41 % (7458)Instruction limit reached!
% 8.21/2.41 % (7458)------------------------------
% 8.21/2.41 % (7458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.21/2.41 % (7458)Termination reason: Unknown
% 8.21/2.41 % (7458)Termination phase: Saturation
% 8.21/2.41
% 8.21/2.41 % (7458)Memory used [KB]: 8187
% 8.21/2.41 % (7458)Time elapsed: 0.237 s
% 8.21/2.41 % (7458)Instructions burned: 988 (million)
% 8.21/2.41 % (7458)------------------------------
% 8.21/2.41 % (7458)------------------------------
% 8.21/2.41 % (7478)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_7106 for (2990ds/5205Mi)
% 8.21/2.42 % (7479)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_7106 for (2990ds/1913Mi)
% 8.58/2.51 % (7477)Instruction limit reached!
% 8.58/2.51 % (7477)------------------------------
% 8.58/2.51 % (7477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.58/2.51 % (7477)Termination reason: Unknown
% 8.58/2.51 % (7477)Termination phase: Saturation
% 8.58/2.51
% 8.58/2.51 % (7477)Memory used [KB]: 9083
% 8.58/2.51 % (7477)Time elapsed: 0.134 s
% 8.58/2.51 % (7477)Instructions burned: 410 (million)
% 8.58/2.51 % (7477)------------------------------
% 8.58/2.51 % (7477)------------------------------
% 8.58/2.52 % (7480)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_7106 for (2989ds/4350Mi)
% 8.58/2.53 % (7465)Instruction limit reached!
% 8.58/2.53 % (7465)------------------------------
% 8.58/2.53 % (7465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.58/2.53 % (7465)Termination reason: Unknown
% 8.58/2.53 % (7465)Termination phase: Saturation
% 8.58/2.53
% 8.58/2.53 % (7465)Memory used [KB]: 9083
% 8.58/2.53 % (7465)Time elapsed: 0.294 s
% 8.58/2.53 % (7465)Instructions burned: 922 (million)
% 8.58/2.53 % (7465)------------------------------
% 8.58/2.53 % (7465)------------------------------
% 8.58/2.54 % (7481)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_7106 for (2989ds/68Mi)
% 8.58/2.56 % (7481)Instruction limit reached!
% 8.58/2.56 % (7481)------------------------------
% 8.58/2.56 % (7481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.58/2.56 % (7481)Termination reason: Unknown
% 8.58/2.56 % (7481)Termination phase: Saturation
% 8.58/2.56
% 8.58/2.56 % (7481)Memory used [KB]: 6268
% 8.58/2.56 % (7481)Time elapsed: 0.019 s
% 8.58/2.56 % (7481)Instructions burned: 70 (million)
% 8.58/2.56 % (7481)------------------------------
% 8.58/2.56 % (7481)------------------------------
% 8.58/2.57 % (7482)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_7106 for (2988ds/358Mi)
% 9.06/2.63 % (7470)Instruction limit reached!
% 9.06/2.63 % (7470)------------------------------
% 9.06/2.63 % (7470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.06/2.63 % (7470)Termination reason: Unknown
% 9.06/2.63 % (7470)Termination phase: Saturation
% 9.06/2.63
% 9.06/2.63 % (7470)Memory used [KB]: 9466
% 9.06/2.63 % (7470)Time elapsed: 0.331 s
% 9.06/2.63 % (7470)Instructions burned: 1023 (million)
% 9.06/2.63 % (7470)------------------------------
% 9.06/2.63 % (7470)------------------------------
% 9.06/2.64 % (7483)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_7106 for (2988ds/31Mi)
% 9.06/2.65 % (7483)Instruction limit reached!
% 9.06/2.65 % (7483)------------------------------
% 9.06/2.65 % (7483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.06/2.65 % (7483)Termination reason: Unknown
% 9.06/2.65 % (7483)Termination phase: Property scanning
% 9.06/2.65
% 9.06/2.65 % (7483)Memory used [KB]: 1535
% 9.06/2.65 % (7483)Time elapsed: 0.010 s
% 9.06/2.65 % (7483)Instructions burned: 34 (million)
% 9.06/2.65 % (7483)------------------------------
% 9.06/2.65 % (7483)------------------------------
% 9.06/2.66 % (7484)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_7106 for (2988ds/279Mi)
% 9.06/2.68 % (7482)Instruction limit reached!
% 9.06/2.68 % (7482)------------------------------
% 9.06/2.68 % (7482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.06/2.68 % (7482)Termination reason: Unknown
% 9.06/2.68 % (7482)Termination phase: Saturation
% 9.06/2.68
% 9.06/2.68 % (7482)Memory used [KB]: 7164
% 9.06/2.68 % (7482)Time elapsed: 0.107 s
% 9.06/2.68 % (7482)Instructions burned: 358 (million)
% 9.06/2.68 % (7482)------------------------------
% 9.06/2.68 % (7482)------------------------------
% 9.06/2.69 % (7485)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_7106 for (2987ds/258Mi)
% 9.54/2.73 % (7484)Instruction limit reached!
% 9.54/2.73 % (7484)------------------------------
% 9.54/2.73 % (7484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.54/2.73 % (7484)Termination reason: Unknown
% 9.54/2.73 % (7484)Termination phase: Saturation
% 9.54/2.73
% 9.54/2.73 % (7484)Memory used [KB]: 6268
% 9.54/2.73 % (7484)Time elapsed: 0.070 s
% 9.54/2.73 % (7484)Instructions burned: 279 (million)
% 9.54/2.73 % (7484)------------------------------
% 9.54/2.73 % (7484)------------------------------
% 9.54/2.74 % (7486)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_7106 for (2987ds/26Mi)
% 9.54/2.74 % (7486)Instruction limit reached!
% 9.54/2.74 % (7486)------------------------------
% 9.54/2.74 % (7486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.54/2.74 % (7486)Termination reason: Unknown
% 9.54/2.74 % (7486)Termination phase: Preprocessing 3
% 9.54/2.74
% 9.54/2.74 % (7486)Memory used [KB]: 1535
% 9.54/2.74 % (7486)Time elapsed: 0.008 s
% 9.54/2.74 % (7486)Instructions burned: 28 (million)
% 9.54/2.74 % (7486)------------------------------
% 9.54/2.74 % (7486)------------------------------
% 9.54/2.75 % (7487)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_7106 for (2987ds/995Mi)
% 9.54/2.76 % (7485)Instruction limit reached!
% 9.54/2.76 % (7485)------------------------------
% 9.54/2.76 % (7485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.54/2.76 % (7485)Termination reason: Unknown
% 9.54/2.76 % (7485)Termination phase: Saturation
% 9.54/2.76
% 9.54/2.76 % (7485)Memory used [KB]: 7547
% 9.54/2.76 % (7485)Time elapsed: 0.073 s
% 9.54/2.76 % (7485)Instructions burned: 259 (million)
% 9.54/2.76 % (7485)------------------------------
% 9.54/2.76 % (7485)------------------------------
% 9.54/2.77 % (7488)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_7106 for (2986ds/373Mi)
% 9.72/2.85 % (7476)Instruction limit reached!
% 9.72/2.85 % (7476)------------------------------
% 9.72/2.85 % (7476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.72/2.85 % (7476)Termination reason: Unknown
% 9.72/2.85 % (7476)Termination phase: Saturation
% 9.72/2.85
% 9.72/2.85 % (7476)Memory used [KB]: 8443
% 9.72/2.85 % (7476)Time elapsed: 0.479 s
% 9.72/2.85 % (7476)Instructions burned: 1540 (million)
% 9.72/2.85 % (7476)------------------------------
% 9.72/2.85 % (7476)------------------------------
% 9.72/2.86 % (7489)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_7106 for (2985ds/253Mi)
% 9.72/2.88 % (7488)Instruction limit reached!
% 9.72/2.88 % (7488)------------------------------
% 9.72/2.88 % (7488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.72/2.88 % (7488)Termination reason: Unknown
% 9.72/2.88 % (7488)Termination phase: Saturation
% 9.72/2.88
% 9.72/2.88 % (7488)Memory used [KB]: 7164
% 9.72/2.88 % (7488)Time elapsed: 0.115 s
% 9.72/2.88 % (7488)Instructions burned: 375 (million)
% 9.72/2.88 % (7488)------------------------------
% 9.72/2.88 % (7488)------------------------------
% 9.72/2.89 % (7490)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_7106 for (2985ds/832Mi)
% 10.33/2.93 % (7489)Instruction limit reached!
% 10.33/2.93 % (7489)------------------------------
% 10.33/2.93 % (7489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.33/2.93 % (7489)Termination reason: Unknown
% 10.33/2.93 % (7489)Termination phase: Saturation
% 10.33/2.93
% 10.33/2.93 % (7489)Memory used [KB]: 6268
% 10.33/2.93 % (7489)Time elapsed: 0.063 s
% 10.33/2.93 % (7489)Instructions burned: 255 (million)
% 10.33/2.93 % (7489)------------------------------
% 10.33/2.93 % (7489)------------------------------
% 10.33/2.93 % (7491)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_7106 for (2985ds/668Mi)
% 10.33/2.99 % (7479)Instruction limit reached!
% 10.33/2.99 % (7479)------------------------------
% 10.33/2.99 % (7479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.33/2.99 % (7479)Termination reason: Unknown
% 10.33/2.99 % (7479)Termination phase: Saturation
% 10.33/2.99
% 10.33/2.99 % (7479)Memory used [KB]: 3582
% 10.33/2.99 % (7479)Time elapsed: 0.576 s
% 10.33/2.99 % (7479)Instructions burned: 1915 (million)
% 10.33/2.99 % (7479)------------------------------
% 10.33/2.99 % (7479)------------------------------
% 10.33/3.00 % (7487)Instruction limit reached!
% 10.33/3.00 % (7487)------------------------------
% 10.33/3.00 % (7487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.33/3.00 % (7487)Termination reason: Unknown
% 10.33/3.00 % (7487)Termination phase: Saturation
% 10.33/3.00
% 10.33/3.00 % (7487)Memory used [KB]: 8187
% 10.33/3.00 % (7487)Time elapsed: 0.245 s
% 10.33/3.00 % (7487)Instructions burned: 997 (million)
% 10.33/3.00 % (7487)------------------------------
% 10.33/3.00 % (7487)------------------------------
% 10.33/3.00 % (7492)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_7106 for (2984ds/40Mi)
% 10.33/3.01 % (7493)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_7106 for (2984ds/294Mi)
% 13.20/3.01 % (7492)Instruction limit reached!
% 13.20/3.01 % (7492)------------------------------
% 13.20/3.01 % (7492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.20/3.01 % (7492)Termination reason: Unknown
% 13.20/3.01 % (7492)Termination phase: Function definition elimination
% 13.20/3.01
% 13.20/3.01 % (7492)Memory used [KB]: 1663
% 13.20/3.01 % (7492)Time elapsed: 0.011 s
% 13.20/3.01 % (7492)Instructions burned: 40 (million)
% 13.20/3.01 % (7492)------------------------------
% 13.20/3.01 % (7492)------------------------------
% 13.20/3.02 % (7494)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_7106 for (2984ds/187Mi)
% 13.20/3.08 % (7494)Instruction limit reached!
% 13.20/3.08 % (7494)------------------------------
% 13.20/3.08 % (7494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.20/3.08 % (7494)Termination reason: Unknown
% 13.20/3.08 % (7494)Termination phase: Saturation
% 13.20/3.08
% 13.20/3.08 % (7494)Memory used [KB]: 7036
% 13.20/3.08 % (7494)Time elapsed: 0.058 s
% 13.20/3.08 % (7494)Instructions burned: 188 (million)
% 13.20/3.08 % (7494)------------------------------
% 13.20/3.08 % (7494)------------------------------
% 13.20/3.08 % (7493)Instruction limit reached!
% 13.20/3.08 % (7493)------------------------------
% 13.20/3.08 % (7493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.20/3.08 % (7493)Termination reason: Unknown
% 13.20/3.08 % (7493)Termination phase: Saturation
% 13.20/3.08
% 13.20/3.08 % (7493)Memory used [KB]: 6268
% 13.20/3.08 % (7493)Time elapsed: 0.077 s
% 13.20/3.08 % (7493)Instructions burned: 295 (million)
% 13.20/3.08 % (7493)------------------------------
% 13.20/3.08 % (7493)------------------------------
% 13.20/3.09 % (7495)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_7106 for (2983ds/371Mi)
% 13.20/3.09 % (7496)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_7106 for (2983ds/1827Mi)
% 13.20/3.10 % (7491)Instruction limit reached!
% 13.20/3.10 % (7491)------------------------------
% 13.20/3.10 % (7491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.20/3.10 % (7491)Termination reason: Unknown
% 13.20/3.10 % (7491)Termination phase: Saturation
% 13.20/3.10
% 13.20/3.10 % (7491)Memory used [KB]: 12537
% 13.20/3.10 % (7491)Time elapsed: 0.166 s
% 13.20/3.10 % (7491)Instructions burned: 668 (million)
% 13.20/3.10 % (7491)------------------------------
% 13.20/3.10 % (7491)------------------------------
% 13.20/3.11 % (7497)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_7106 for (2983ds/70Mi)
% 13.85/3.13 % (7497)Instruction limit reached!
% 13.85/3.13 % (7497)------------------------------
% 13.85/3.13 % (7497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.85/3.13 % (7497)Termination reason: Unknown
% 13.85/3.13 % (7497)Termination phase: Saturation
% 13.85/3.13
% 13.85/3.13 % (7497)Memory used [KB]: 1663
% 13.85/3.13 % (7497)Time elapsed: 0.019 s
% 13.85/3.13 % (7497)Instructions burned: 72 (million)
% 13.85/3.13 % (7497)------------------------------
% 13.85/3.13 % (7497)------------------------------
% 13.85/3.14 % (7498)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_7106 for (2983ds/316Mi)
% 13.85/3.15 % (7490)Instruction limit reached!
% 13.85/3.15 % (7490)------------------------------
% 13.85/3.15 % (7490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.85/3.15 % (7490)Termination reason: Unknown
% 13.85/3.15 % (7490)Termination phase: Saturation
% 13.85/3.15
% 13.85/3.15 % (7490)Memory used [KB]: 8827
% 13.85/3.15 % (7490)Time elapsed: 0.262 s
% 13.85/3.15 % (7490)Instructions burned: 833 (million)
% 13.85/3.15 % (7490)------------------------------
% 13.85/3.15 % (7490)------------------------------
% 13.85/3.16 % (7499)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_7106 for (2983ds/932Mi)
% 14.21/3.20 % (7495)Instruction limit reached!
% 14.21/3.20 % (7495)------------------------------
% 14.21/3.20 % (7495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.21/3.20 % (7495)Termination reason: Unknown
% 14.21/3.20 % (7495)Termination phase: Saturation
% 14.21/3.20
% 14.21/3.20 % (7495)Memory used [KB]: 7164
% 14.21/3.20 % (7495)Time elapsed: 0.113 s
% 14.21/3.20 % (7495)Instructions burned: 372 (million)
% 14.21/3.20 % (7495)------------------------------
% 14.21/3.20 % (7495)------------------------------
% 14.21/3.21 % (7500)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_7106 for (2982ds/4714Mi)
% 14.21/3.21 % (7498)Instruction limit reached!
% 14.21/3.21 % (7498)------------------------------
% 14.21/3.21 % (7498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.21/3.21 % (7498)Termination reason: Unknown
% 14.21/3.21 % (7498)Termination phase: Saturation
% 14.21/3.21
% 14.21/3.21 % (7498)Memory used [KB]: 6652
% 14.21/3.21 % (7498)Time elapsed: 0.079 s
% 14.21/3.21 % (7498)Instructions burned: 316 (million)
% 14.21/3.21 % (7498)------------------------------
% 14.21/3.21 % (7498)------------------------------
% 14.21/3.22 % (7501)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_7106 for (2982ds/8250Mi)
% 14.72/3.40 % (7499)Instruction limit reached!
% 14.72/3.40 % (7499)------------------------------
% 14.72/3.40 % (7499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.72/3.40 % (7499)Termination reason: Unknown
% 14.72/3.40 % (7499)Termination phase: Saturation
% 14.72/3.40
% 14.72/3.40 % (7499)Memory used [KB]: 8443
% 14.72/3.40 % (7499)Time elapsed: 0.235 s
% 14.72/3.40 % (7499)Instructions burned: 933 (million)
% 14.72/3.40 % (7499)------------------------------
% 14.72/3.40 % (7499)------------------------------
% 15.26/3.41 % (7502)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_7106 for (2980ds/770Mi)
% 15.26/3.42 % (7496)First to succeed.
% 15.26/3.43 % (7496)Refutation found. Thanks to Tanya!
% 15.26/3.43 % SZS status Theorem for DTF2THF_7106
% 15.26/3.43 % SZS output start Proof for DTF2THF_7106
% 15.26/3.43 thf(func_def_0, type, in: $i > $i > $o).
% 15.26/3.43 thf(func_def_1, type, exu: ($i > $o) > $o).
% 15.26/3.43 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 15.26/3.43 thf(func_def_8, type, powerset: $i > $i).
% 15.26/3.43 thf(func_def_10, type, setunion: $i > $i).
% 15.26/3.43 thf(func_def_19, type, descr: ($i > $o) > $i).
% 15.26/3.43 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 15.26/3.43 thf(func_def_26, type, prop2set: $o > $i).
% 15.26/3.43 thf(func_def_36, type, nonempty: $i > $o).
% 15.26/3.43 thf(func_def_69, type, set2prop: $i > $o).
% 15.26/3.43 thf(func_def_88, type, subset: $i > $i > $o).
% 15.26/3.43 thf(func_def_89, type, disjoint: $i > $i > $o).
% 15.26/3.43 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 15.26/3.43 thf(func_def_114, type, binunion: $i > $i > $i).
% 15.26/3.43 thf(func_def_122, type, binintersect: $i > $i > $i).
% 15.26/3.43 thf(func_def_155, type, sK7: ($i > $o) > $i).
% 15.26/3.43 thf(func_def_156, type, sK8: ($i > $o) > $i).
% 15.26/3.43 thf(func_def_157, type, sK9: $i > $o).
% 15.26/3.43 thf(func_def_173, type, sK25: $i > ($i > $o) > $i).
% 15.26/3.43 thf(func_def_175, type, sK27: $i > $o).
% 15.26/3.43 thf(func_def_182, type, sK34: $i > $o).
% 15.26/3.43 thf(func_def_184, type, sK36: $i > $o).
% 15.26/3.43 thf(func_def_191, type, sK43: $i > $i > $i).
% 15.26/3.43 thf(func_def_198, type, sK50: ($i > $o) > $i).
% 15.26/3.43 thf(func_def_199, type, sK51: $i > $o).
% 15.26/3.43 thf(func_def_200, type, sK52: $i > $i).
% 15.26/3.43 thf(func_def_201, type, sK53: $i > $o).
% 15.26/3.43 thf(func_def_206, type, sK58: $i > $i).
% 15.26/3.43 thf(func_def_209, type, sK61: $i > $i).
% 15.26/3.43 thf(func_def_219, type, sK71: ($i > $o) > $i).
% 15.26/3.43 thf(func_def_220, type, sK72: $i > $o).
% 15.26/3.43 thf(func_def_221, type, sK73: $i > $i).
% 15.26/3.43 thf(func_def_222, type, sK74: ($i > $o) > $i).
% 15.26/3.43 thf(func_def_223, type, sK75: $i > $o).
% 15.26/3.43 thf(func_def_224, type, sK76: $i > $i > $i).
% 15.26/3.43 thf(func_def_232, type, sK84: ($i > $o) > $i > $i).
% 15.26/3.43 thf(func_def_233, type, sK85: $i > $o).
% 15.26/3.43 thf(func_def_236, type, sK88: $o > $i > $i > $i).
% 15.26/3.43 thf(func_def_240, type, sK92: $i > $i > $i).
% 15.26/3.43 thf(func_def_247, type, sK99: $i > $o).
% 15.26/3.43 thf(func_def_251, type, sK103: $i > $i > $i).
% 15.26/3.43 thf(func_def_254, type, sK106: $i > $o).
% 15.26/3.43 thf(func_def_268, type, sK120: ($i > $o) > ($i > $o) > $i).
% 15.26/3.43 thf(func_def_269, type, sK121: ($i > $o) > ($i > $o) > $i).
% 15.26/3.43 thf(func_def_270, type, sK122: $i > $o).
% 15.26/3.43 thf(func_def_271, type, sK123: $i > $o).
% 15.26/3.43 thf(func_def_272, type, sK124: $i > $i > $i).
% 15.26/3.43 thf(func_def_273, type, sK125: $i > $i > $i).
% 15.26/3.43 thf(func_def_277, type, sK129: $i > $o).
% 15.26/3.43 thf(func_def_285, type, sK137: $i > $i).
% 15.26/3.43 thf(func_def_286, type, sK138: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_287, type, sK139: $i > $i > $i).
% 15.26/3.43 thf(func_def_288, type, sK140: $i > $i > $i).
% 15.26/3.43 thf(func_def_289, type, sK141: $i > $i > $i).
% 15.26/3.43 thf(func_def_290, type, sK142: $i > $i > $i).
% 15.26/3.43 thf(func_def_292, type, sK144: $i > $i).
% 15.26/3.43 thf(func_def_293, type, sK145: $i > $i).
% 15.26/3.43 thf(func_def_294, type, sK146: $i > $i).
% 15.26/3.43 thf(func_def_295, type, sK147: $i > $i).
% 15.26/3.43 thf(func_def_296, type, sK148: $i > $i).
% 15.26/3.43 thf(func_def_297, type, sK149: $i > $i).
% 15.26/3.43 thf(func_def_298, type, sK150: $i > $i).
% 15.26/3.43 thf(func_def_299, type, sK151: $i > $i).
% 15.26/3.43 thf(func_def_300, type, sK152: $i > $i).
% 15.26/3.43 thf(func_def_301, type, sK153: $i > $i).
% 15.26/3.43 thf(func_def_302, type, sK154: $i > $i).
% 15.26/3.43 thf(func_def_303, type, sK155: $i > $i).
% 15.26/3.43 thf(func_def_304, type, sK156: $i > $i).
% 15.26/3.43 thf(func_def_305, type, sK157: $i > $i).
% 15.26/3.43 thf(func_def_306, type, sK158: $i > $i).
% 15.26/3.43 thf(func_def_307, type, sK159: $i > $i).
% 15.26/3.43 thf(func_def_308, type, sK160: $i > $i).
% 15.26/3.43 thf(func_def_309, type, sK161: $i > $i).
% 15.26/3.43 thf(func_def_310, type, sK162: $i > $i).
% 15.26/3.43 thf(func_def_311, type, sK163: $i > $i).
% 15.26/3.43 thf(func_def_312, type, sK164: $i > $i).
% 15.26/3.43 thf(func_def_313, type, sK165: $i > $i).
% 15.26/3.43 thf(func_def_314, type, sK166: $i > $i).
% 15.26/3.43 thf(func_def_315, type, sK167: $i > $i).
% 15.26/3.43 thf(func_def_316, type, sK168: $i > $i).
% 15.26/3.43 thf(func_def_317, type, sK169: $i > $i).
% 15.26/3.43 thf(func_def_318, type, sK170: $i > $i).
% 15.26/3.43 thf(func_def_319, type, sK171: $i > $i).
% 15.26/3.43 thf(func_def_320, type, sK172: $i > $i).
% 15.26/3.43 thf(func_def_321, type, sK173: $i > $i).
% 15.26/3.43 thf(func_def_322, type, sK174: $i > $i).
% 15.26/3.43 thf(func_def_323, type, sK175: $i > $i).
% 15.26/3.43 thf(func_def_324, type, sK176: $i > $i).
% 15.26/3.43 thf(func_def_325, type, sK177: $i > $i).
% 15.26/3.43 thf(func_def_326, type, sK178: $i > $i).
% 15.26/3.43 thf(func_def_327, type, sK179: $i > $i).
% 15.26/3.43 thf(func_def_328, type, sK180: $i > $i).
% 15.26/3.43 thf(func_def_329, type, sK181: $i > $i).
% 15.26/3.43 thf(func_def_330, type, sK182: $i > $i).
% 15.26/3.43 thf(func_def_331, type, sK183: $i > $i).
% 15.26/3.43 thf(func_def_332, type, sK184: $i > $i).
% 15.26/3.43 thf(func_def_333, type, sK185: $i > $i).
% 15.26/3.43 thf(func_def_334, type, sK186: $i > $i).
% 15.26/3.43 thf(func_def_335, type, sK187: $i > $i).
% 15.26/3.43 thf(func_def_336, type, sK188: $i > $i).
% 15.26/3.43 thf(func_def_337, type, sK189: $i > $i).
% 15.26/3.43 thf(func_def_338, type, sK190: $i > $i).
% 15.26/3.43 thf(func_def_339, type, sK191: $i > $i).
% 15.26/3.43 thf(func_def_340, type, sK192: $i > $i).
% 15.26/3.43 thf(func_def_341, type, sK193: $i > $i).
% 15.26/3.43 thf(func_def_342, type, sK194: $i > $i).
% 15.26/3.43 thf(func_def_343, type, sK195: $i > $i).
% 15.26/3.43 thf(func_def_344, type, sK196: $i > $i).
% 15.26/3.43 thf(func_def_345, type, sK197: $i > $i).
% 15.26/3.43 thf(func_def_346, type, sK198: $i > $i).
% 15.26/3.43 thf(func_def_347, type, sK199: $i > $i).
% 15.26/3.43 thf(func_def_348, type, sK200: $i > $i).
% 15.26/3.43 thf(func_def_349, type, sK201: $i > $i).
% 15.26/3.43 thf(func_def_350, type, sK202: $i > $i).
% 15.26/3.43 thf(func_def_351, type, sK203: $i > $i).
% 15.26/3.43 thf(func_def_352, type, sK204: $i > $i).
% 15.26/3.43 thf(func_def_353, type, sK205: $i > $i).
% 15.26/3.43 thf(func_def_354, type, sK206: $i > $i).
% 15.26/3.43 thf(func_def_355, type, sK207: $i > $i).
% 15.26/3.43 thf(func_def_356, type, sK208: $i > $i).
% 15.26/3.43 thf(func_def_357, type, sK209: $i > $i).
% 15.26/3.43 thf(func_def_358, type, sK210: $i > $i).
% 15.26/3.43 thf(func_def_359, type, sK211: $i > $i).
% 15.26/3.43 thf(func_def_360, type, sK212: $i > $i).
% 15.26/3.43 thf(func_def_361, type, sK213: $i > $i).
% 15.26/3.43 thf(func_def_362, type, sK214: $i > $i).
% 15.26/3.43 thf(func_def_363, type, sK215: $i > $i).
% 15.26/3.43 thf(func_def_364, type, sK216: $i > $i).
% 15.26/3.43 thf(func_def_365, type, sK217: $i > $i).
% 15.26/3.43 thf(func_def_366, type, sK218: $i > $i).
% 15.26/3.43 thf(func_def_367, type, sK219: $i > $i).
% 15.26/3.43 thf(func_def_368, type, sK220: $i > $i).
% 15.26/3.43 thf(func_def_369, type, sK221: $i > $i).
% 15.26/3.43 thf(func_def_370, type, sK222: $i > $i).
% 15.26/3.43 thf(func_def_371, type, sK223: $i > $i).
% 15.26/3.43 thf(func_def_372, type, sK224: $i > $i).
% 15.26/3.43 thf(func_def_373, type, sK225: $i > $i).
% 15.26/3.43 thf(func_def_374, type, sK226: $i > $i).
% 15.26/3.43 thf(func_def_375, type, sK227: $i > $i).
% 15.26/3.43 thf(func_def_376, type, sK228: $i > $i).
% 15.26/3.43 thf(func_def_377, type, sK229: $i > $i).
% 15.26/3.43 thf(func_def_378, type, sK230: $i > $i).
% 15.26/3.43 thf(func_def_379, type, sK231: $i > $i).
% 15.26/3.43 thf(func_def_380, type, sK232: $i > $i).
% 15.26/3.43 thf(func_def_381, type, sK233: $i > $i).
% 15.26/3.43 thf(func_def_382, type, sK234: $i > $i).
% 15.26/3.43 thf(func_def_383, type, sK235: $i > $i).
% 15.26/3.43 thf(func_def_384, type, sK236: $i > $i).
% 15.26/3.43 thf(func_def_385, type, sK237: $i > $i).
% 15.26/3.43 thf(func_def_386, type, sK238: $i > $i).
% 15.26/3.43 thf(func_def_387, type, sK239: $i > $i).
% 15.26/3.43 thf(func_def_388, type, sK240: $i > $i).
% 15.26/3.43 thf(func_def_389, type, sK241: $i > $i).
% 15.26/3.43 thf(func_def_390, type, sK242: $i > $i).
% 15.26/3.43 thf(func_def_391, type, sK243: $i > $i).
% 15.26/3.43 thf(func_def_392, type, sK244: $i > $i).
% 15.26/3.43 thf(func_def_393, type, sK245: $i > $i).
% 15.26/3.43 thf(func_def_394, type, sK246: $i > $i > $i).
% 15.26/3.43 thf(func_def_395, type, sK247: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_396, type, sK248: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_397, type, sK249: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_398, type, sK250: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_399, type, sK251: $i > $i > $i).
% 15.26/3.43 thf(func_def_400, type, sK252: $i > $i > $i).
% 15.26/3.43 thf(func_def_401, type, sK253: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_402, type, sK254: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_403, type, sK255: $i > $i).
% 15.26/3.43 thf(func_def_404, type, sK256: $i > $i > $i).
% 15.26/3.43 thf(func_def_405, type, sK257: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_406, type, sK258: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_407, type, sK259: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_408, type, sK260: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_409, type, sK261: $i > $i > $i).
% 15.26/3.43 thf(func_def_410, type, sK262: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_411, type, sK263: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_412, type, sK264: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_413, type, sK265: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_414, type, sK266: $i > $i > $i).
% 15.26/3.43 thf(func_def_415, type, sK267: $i > $i > $i).
% 15.26/3.43 thf(func_def_416, type, sK268: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_417, type, sK269: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_418, type, sK270: $i > $i > $i).
% 15.26/3.43 thf(func_def_419, type, sK271: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_420, type, sK272: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_421, type, sK273: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_422, type, sK274: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_423, type, sK275: $i > $i).
% 15.26/3.43 thf(func_def_424, type, sK276: $i > $i).
% 15.26/3.43 thf(func_def_425, type, sK277: $i > $i > $i).
% 15.26/3.43 thf(func_def_426, type, sK278: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_427, type, sK279: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_428, type, sK280: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_429, type, sK281: $i > $i > $i).
% 15.26/3.43 thf(func_def_430, type, sK282: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_431, type, sK283: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_432, type, sK284: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_433, type, sK285: $i > $i).
% 15.26/3.43 thf(func_def_434, type, sK286: $i > $i > $i).
% 15.26/3.43 thf(func_def_435, type, sK287: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_436, type, sK288: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_437, type, sK289: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_438, type, sK290: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_439, type, sK291: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_440, type, sK292: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_441, type, sK293: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_442, type, sK294: $i > $i > $i).
% 15.26/3.43 thf(func_def_443, type, sK295: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_444, type, sK296: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_445, type, sK297: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_446, type, sK298: $i > $i > $i).
% 15.26/3.43 thf(func_def_447, type, sK299: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_448, type, sK300: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_449, type, sK301: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_450, type, sK302: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_451, type, sK303: $i > $i).
% 15.26/3.43 thf(func_def_452, type, sK304: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_453, type, sK305: $i > $i).
% 15.26/3.43 thf(func_def_454, type, sK306: $i > $i > $i).
% 15.26/3.43 thf(func_def_455, type, sK307: $i > $i).
% 15.26/3.43 thf(func_def_456, type, sK308: $i > $i > $i).
% 15.26/3.43 thf(func_def_457, type, sK309: $i > $i > $i).
% 15.26/3.43 thf(func_def_458, type, sK310: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_459, type, sK311: $i > $i > $i).
% 15.26/3.43 thf(func_def_460, type, sK312: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_461, type, sK313: $i > $i > $i).
% 15.26/3.43 thf(func_def_462, type, sK314: $i > $i).
% 15.26/3.43 thf(func_def_463, type, sK315: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_464, type, sK316: $i > $i > $i).
% 15.26/3.43 thf(func_def_465, type, sK317: $i > $i).
% 15.26/3.43 thf(func_def_466, type, sK318: $i > $i).
% 15.26/3.43 thf(func_def_467, type, sK319: $i > $i > $i).
% 15.26/3.43 thf(func_def_468, type, sK320: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_469, type, sK321: $i > $i > $i).
% 15.26/3.43 thf(func_def_470, type, sK322: $i > $i > $i).
% 15.26/3.43 thf(func_def_471, type, sK323: $i > $i > $i).
% 15.26/3.43 thf(func_def_472, type, sK324: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_473, type, sK325: $i > $i > $i).
% 15.26/3.43 thf(func_def_474, type, sK326: $i > $i).
% 15.26/3.43 thf(func_def_475, type, sK327: $i > $i > $i).
% 15.26/3.43 thf(func_def_476, type, sK328: $i > $i > $i).
% 15.26/3.43 thf(func_def_477, type, sK329: $i > $i > $i).
% 15.26/3.43 thf(func_def_478, type, sK330: $i > $i).
% 15.26/3.43 thf(func_def_479, type, sK331: $i > $i).
% 15.26/3.43 thf(func_def_480, type, sK332: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_481, type, sK333: $i > $i > $i).
% 15.26/3.43 thf(func_def_482, type, sK334: $i > $i).
% 15.26/3.43 thf(func_def_483, type, sK335: $i > $i > $i).
% 15.26/3.43 thf(func_def_484, type, sK336: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_485, type, sK337: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_486, type, sK338: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_487, type, sK339: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_488, type, sK340: $i > $i).
% 15.26/3.43 thf(func_def_489, type, sK341: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_490, type, sK342: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_491, type, sK343: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_492, type, sK344: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_493, type, sK345: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_494, type, sK346: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_495, type, sK347: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_496, type, sK348: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_497, type, sK349: $i > $i).
% 15.26/3.43 thf(func_def_498, type, sK350: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_499, type, sK351: $i > $i > $i).
% 15.26/3.43 thf(func_def_500, type, sK352: $i > $i > $i).
% 15.26/3.43 thf(func_def_501, type, sK353: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_502, type, sK354: $i > $i).
% 15.26/3.43 thf(func_def_503, type, sK355: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_504, type, sK356: $i > $i > $i).
% 15.26/3.43 thf(func_def_505, type, sK357: $i > $i > $i).
% 15.26/3.43 thf(func_def_506, type, sK358: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_507, type, sK359: $i > $i > $i).
% 15.26/3.43 thf(func_def_508, type, sK360: $i > $i > $i).
% 15.26/3.43 thf(func_def_509, type, sK361: $i > $i > $i).
% 15.26/3.43 thf(func_def_510, type, sK362: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_511, type, sK363: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_512, type, sK364: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_513, type, sK365: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_514, type, sK366: $i > $i).
% 15.26/3.43 thf(func_def_515, type, sK367: $i > $i).
% 15.26/3.43 thf(func_def_516, type, sK368: $i > $i > $i).
% 15.26/3.43 thf(func_def_517, type, sK369: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_518, type, sK370: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_519, type, sK371: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_520, type, sK372: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_521, type, sK373: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_522, type, sK374: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_523, type, sK375: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_524, type, sK376: $i > $i).
% 15.26/3.43 thf(func_def_525, type, sK377: $i > $i).
% 15.26/3.43 thf(func_def_526, type, sK378: $i > $i > $i).
% 15.26/3.43 thf(func_def_527, type, sK379: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_528, type, sK380: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_529, type, sK381: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_530, type, sK382: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_531, type, sK383: $i > $i > $i).
% 15.26/3.43 thf(func_def_532, type, sK384: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_533, type, sK385: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_534, type, sK386: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_535, type, sK387: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_536, type, sK388: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_537, type, sK389: $i > $i > $i).
% 15.26/3.43 thf(func_def_538, type, sK390: $i > $i > $i).
% 15.26/3.43 thf(func_def_539, type, sK391: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_540, type, sK392: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_541, type, sK393: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_542, type, sK394: $i > $i > $i).
% 15.26/3.43 thf(func_def_543, type, sK395: $i > $i > $i).
% 15.26/3.43 thf(func_def_544, type, sK396: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_545, type, sK397: $i > $i).
% 15.26/3.43 thf(func_def_546, type, sK398: $i > $i > $i).
% 15.26/3.43 thf(func_def_547, type, sK399: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_548, type, sK400: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_549, type, sK401: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_550, type, sK402: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_551, type, sK403: $i > $i > $i).
% 15.26/3.43 thf(func_def_552, type, sK404: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_553, type, sK405: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_554, type, sK406: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_555, type, sK407: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_556, type, sK408: $i > $i).
% 15.26/3.43 thf(func_def_557, type, sK409: $i > $i > $i).
% 15.26/3.43 thf(func_def_558, type, sK410: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_559, type, sK411: $i > $i).
% 15.26/3.43 thf(func_def_560, type, sK412: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_561, type, sK413: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_562, type, sK414: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_563, type, sK415: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_564, type, sK416: $i > $i).
% 15.26/3.43 thf(func_def_565, type, sK417: $i > $i > $i).
% 15.26/3.43 thf(func_def_566, type, sK418: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_567, type, sK419: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_568, type, sK420: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_569, type, sK421: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_570, type, sK422: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_571, type, sK423: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_572, type, sK424: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_573, type, sK425: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_574, type, sK426: $i > $i).
% 15.26/3.43 thf(func_def_575, type, sK427: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_576, type, sK428: $i > $i > $i).
% 15.26/3.43 thf(func_def_577, type, sK429: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_578, type, sK430: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_579, type, sK431: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_580, type, sK432: $i > $i > $i).
% 15.26/3.43 thf(func_def_581, type, sK433: $i > $i > $i).
% 15.26/3.43 thf(func_def_582, type, sK434: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_583, type, sK435: $i > $i).
% 15.26/3.43 thf(func_def_584, type, sK436: $i > $i > $i).
% 15.26/3.43 thf(func_def_585, type, sK437: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_586, type, sK438: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_587, type, sK439: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_588, type, sK440: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_589, type, sK441: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_590, type, sK442: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_591, type, sK443: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_592, type, sK444: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_593, type, sK445: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_594, type, sK446: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_595, type, sK447: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_596, type, sK448: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_597, type, sK449: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_598, type, sK450: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_599, type, sK451: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_600, type, sK452: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_601, type, sK453: $i > $i).
% 15.26/3.43 thf(func_def_602, type, sK454: $i > $i > $i).
% 15.26/3.43 thf(func_def_603, type, sK455: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_604, type, sK456: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_605, type, sK457: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_606, type, sK458: $i > $i > $i).
% 15.26/3.43 thf(func_def_607, type, sK459: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_608, type, sK460: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_609, type, sK461: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_610, type, sK462: $i > $i).
% 15.26/3.43 thf(func_def_611, type, sK463: $i > $i).
% 15.26/3.43 thf(func_def_612, type, sK464: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_613, type, sK465: $i > $i > $i).
% 15.26/3.43 thf(func_def_614, type, sK466: $i > $i > $i).
% 15.26/3.43 thf(func_def_615, type, sK467: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_616, type, sK468: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_617, type, sK469: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_618, type, sK470: $i > $i > $i).
% 15.26/3.43 thf(func_def_619, type, sK471: $i > $i > $i).
% 15.26/3.43 thf(func_def_620, type, sK472: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_621, type, sK473: $i > $i > $i).
% 15.26/3.43 thf(func_def_622, type, sK474: $i > $i > $i).
% 15.26/3.43 thf(func_def_623, type, sK475: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_624, type, sK476: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_625, type, sK477: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_626, type, sK478: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_627, type, sK479: $i > $i > $i).
% 15.26/3.43 thf(func_def_628, type, sK480: $i > $i > $i).
% 15.26/3.43 thf(func_def_629, type, sK481: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_630, type, sK482: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_631, type, sK483: $i > $i).
% 15.26/3.43 thf(func_def_632, type, sK484: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_633, type, sK485: $i > $i > $i).
% 15.26/3.43 thf(func_def_634, type, sK486: $i > $i > $i).
% 15.26/3.43 thf(func_def_635, type, sK487: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_636, type, sK488: $i > $i > $i).
% 15.26/3.43 thf(func_def_637, type, sK489: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_638, type, sK490: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_639, type, sK491: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_640, type, sK492: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_641, type, sK493: $i > $i).
% 15.26/3.43 thf(func_def_642, type, sK494: $i > $i > $i).
% 15.26/3.43 thf(func_def_643, type, sK495: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_644, type, sK496: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_645, type, sK497: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_646, type, sK498: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_647, type, sK499: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_648, type, sK500: $i > $i > $i).
% 15.26/3.43 thf(func_def_649, type, sK501: $i > $i > $i).
% 15.26/3.43 thf(func_def_650, type, sK502: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_651, type, sK503: $i > $i > $i).
% 15.26/3.43 thf(func_def_652, type, sK504: $i > $i > $i).
% 15.26/3.43 thf(func_def_653, type, sK505: $i > $i > $i).
% 15.26/3.43 thf(func_def_654, type, sK506: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_655, type, sK507: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_656, type, sK508: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_657, type, sK509: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_658, type, sK510: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_659, type, sK511: $i > $i > $i).
% 15.26/3.43 thf(func_def_660, type, sK512: $i > $i > $i).
% 15.26/3.43 thf(func_def_661, type, sK513: $i > $i > $i).
% 15.26/3.43 thf(func_def_662, type, sK514: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_663, type, sK515: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_664, type, sK516: $i > $i).
% 15.26/3.43 thf(func_def_665, type, sK517: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_666, type, sK518: $i > $i > $i).
% 15.26/3.43 thf(func_def_667, type, sK519: $i > $i > $i).
% 15.26/3.43 thf(func_def_668, type, sK520: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_669, type, sK521: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_670, type, sK522: $i > $i > $i).
% 15.26/3.43 thf(func_def_671, type, sK523: $i > $i > $i).
% 15.26/3.43 thf(func_def_672, type, sK524: $i > $i > $i).
% 15.26/3.43 thf(func_def_673, type, sK525: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_674, type, sK526: $i > $i > $i).
% 15.26/3.43 thf(func_def_675, type, sK527: $i > $i).
% 15.26/3.43 thf(func_def_676, type, sK528: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_677, type, sK529: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_678, type, sK530: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_679, type, sK531: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_680, type, sK532: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_681, type, sK533: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_682, type, sK534: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_683, type, sK535: $i > $i).
% 15.26/3.43 thf(func_def_684, type, sK536: $i > $i).
% 15.26/3.43 thf(func_def_685, type, sK537: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_686, type, sK538: $i > $i > $i).
% 15.26/3.43 thf(func_def_687, type, sK539: $i > $i > $i).
% 15.26/3.43 thf(func_def_688, type, sK540: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_689, type, sK541: $i > $i > $i).
% 15.26/3.43 thf(func_def_690, type, sK542: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_691, type, sK543: $i > $i > $i).
% 15.26/3.43 thf(func_def_692, type, sK544: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_693, type, sK545: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_694, type, sK546: $i > $i).
% 15.26/3.43 thf(func_def_695, type, sK547: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_696, type, sK548: $i > $i > $i).
% 15.26/3.43 thf(func_def_697, type, sK549: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_698, type, sK550: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_699, type, sK551: $i > $i > $i).
% 15.26/3.43 thf(func_def_700, type, sK552: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_701, type, sK553: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_702, type, sK554: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_703, type, sK555: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_704, type, sK556: $i > $i).
% 15.26/3.43 thf(func_def_705, type, sK557: $i > $i > $i).
% 15.26/3.43 thf(func_def_706, type, sK558: $i > $i).
% 15.26/3.43 thf(func_def_707, type, sK559: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_708, type, sK560: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_709, type, sK561: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_710, type, sK562: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_711, type, sK563: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_712, type, sK564: $i > $i).
% 15.26/3.43 thf(func_def_713, type, sK565: $i > $i > $i).
% 15.26/3.43 thf(func_def_714, type, sK566: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_715, type, sK567: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_716, type, sK568: $i > $i > $i).
% 15.26/3.43 thf(func_def_717, type, sK569: $i > $i > $i).
% 15.26/3.43 thf(func_def_718, type, sK570: $i > $i > $i).
% 15.26/3.43 thf(func_def_719, type, sK571: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_720, type, sK572: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_721, type, sK573: $i > $i > $i).
% 15.26/3.43 thf(func_def_722, type, sK574: $i > $i).
% 15.26/3.43 thf(func_def_723, type, sK575: $i > $i).
% 15.26/3.43 thf(func_def_724, type, sK576: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_725, type, sK577: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_726, type, sK578: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_727, type, sK579: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_728, type, sK580: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_729, type, sK581: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_730, type, sK582: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_731, type, sK583: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_732, type, sK584: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_733, type, sK585: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_734, type, sK586: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_735, type, sK587: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_736, type, sK588: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_737, type, sK589: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_738, type, sK590: $i > $i > $i > $i).
% 15.26/3.43 thf(func_def_742, type, sK594: ($i > $o) > $i > $i).
% 15.26/3.43 thf(func_def_743, type, sK595: $i > $o).
% 15.26/3.43 thf(func_def_746, type, sK598: ($i > $o) > $i > ($i > $o) > $i > $i).
% 15.26/3.43 thf(func_def_747, type, sK599: $i > $i > ($i > $o) > ($i > $o) > $i).
% 15.26/3.43 thf(func_def_750, type, sK602: $i > $o).
% 15.26/3.43 thf(func_def_751, type, sK603: $i > $o).
% 15.26/3.43 thf(func_def_754, type, sK606: $i > $o).
% 15.26/3.43 thf(func_def_760, type, sK612: $i > $o).
% 15.26/3.43 thf(func_def_761, type, sK613: $i > ($i > $o) > $i).
% 15.26/3.43 thf(func_def_763, type, sK615: $i > $o).
% 15.26/3.43 thf(func_def_768, type, sK620: $i > $i).
% 15.26/3.43 thf(func_def_780, type, sK632: $i > $i > $i).
% 15.26/3.43 thf(func_def_783, type, sK635: $i > $o).
% 15.26/3.43 thf(func_def_791, type, sK643: ($i > $o) > $i > $i).
% 15.26/3.43 thf(func_def_792, type, sK644: $i > $o).
% 15.26/3.43 thf(func_def_795, type, sK647: $i > $i).
% 15.26/3.43 thf(func_def_810, type, sK662: ($i > $o) > ($i > $o) > $i).
% 15.26/3.43 thf(func_def_811, type, sK663: ($i > $o) > ($i > $o) > $i).
% 15.26/3.43 thf(func_def_812, type, sK664: $i > $o).
% 15.26/3.43 thf(func_def_813, type, sK665: $i > $o).
% 15.26/3.43 thf(func_def_816, type, sK668: $i > $i).
% 15.26/3.43 thf(func_def_822, type, sK674: $i > $i).
% 15.26/3.43 thf(func_def_825, type, sK677: $i > ($i > $o) > $i).
% 15.26/3.43 thf(func_def_827, type, sK679: $i > $o).
% 15.26/3.43 thf(func_def_829, type, sK681: ($i > $o) > $i > $i).
% 15.26/3.43 thf(func_def_830, type, sK682: $i > $o).
% 15.26/3.43 thf(func_def_836, type, sK688: $i > ($i > $i > $o) > $i).
% 15.26/3.43 thf(func_def_837, type, sK689: $i > ($i > $i > $o) > $i).
% 15.26/3.43 thf(func_def_839, type, sK691: $i > $i > $o).
% 15.26/3.43 thf(func_def_840, type, sK692: $i > $i).
% 15.26/3.43 thf(func_def_846, type, sK698: $i > $o).
% 15.26/3.43 thf(func_def_854, type, sK706: ($i > $o) > $i > $i).
% 15.26/3.43 thf(func_def_855, type, sK707: $i > $o).
% 15.26/3.43 thf(func_def_861, type, sK713: $i > $o).
% 15.26/3.43 thf(func_def_863, type, sK715: $i > $o).
% 15.26/3.43 thf(func_def_883, type, sK735: $i > $i).
% 15.26/3.43 thf(func_def_885, type, ph737: !>[X0: $tType]:(X0)).
% 15.26/3.43 thf(func_def_886, type, sK738: ($i > $o) > $i).
% 15.26/3.43 thf(func_def_887, type, sK739: ($i > $o) > $i > $i).
% 15.26/3.43 thf(func_def_888, type, sK740: $i > $i).
% 15.26/3.43 thf(func_def_889, type, sK741: $i > $i > $i).
% 15.26/3.43 thf(func_def_890, type, sK742: $i > $i > $i).
% 15.26/3.43 thf(func_def_891, type, sK743: $i > $i > $i).
% 15.26/3.43 thf(func_def_892, type, sK744: $i > $i).
% 15.26/3.43 thf(func_def_893, type, sK745: $i > $i).
% 15.26/3.43 thf(func_def_894, type, sK746: $i > $i > $i).
% 15.26/3.43 thf(func_def_895, type, sK747: $i > $i > $i).
% 15.26/3.43 thf(func_def_896, type, sK748: $i > $i > $i).
% 15.26/3.43 thf(func_def_898, type, sK750: $i > $i > $i).
% 15.26/3.43 thf(func_def_899, type, sK751: $i > $i > $i).
% 15.26/3.43 thf(func_def_900, type, sK752: $i > $i > $i).
% 15.26/3.43 thf(func_def_901, type, sK753: $i > $i > $i).
% 15.26/3.43 thf(func_def_902, type, sK754: $i > $i > $i).
% 15.26/3.43 thf(func_def_903, type, sK755: $i > $i > $i).
% 15.26/3.43 thf(f12934,plain,(
% 15.26/3.43 $false),
% 15.26/3.43 inference(avatar_sat_refutation,[status(thm)],[f10310,f10332,f10785,f10952,f10954,f10963,f11034,f12655,f12757,f12933])).
% 15.26/3.43 thf(f12933,plain,(
% 15.26/3.43 ~spl2_1296 | ~spl2_1299),
% 15.26/3.43 inference(avatar_contradiction_clause,[status(thm)],[f12932])).
% 15.26/3.43 thf(f12932,plain,(
% 15.26/3.43 $false | (~spl2_1296 | ~spl2_1299)),
% 15.26/3.43 inference(trivial_inequality_removal,[status(thm)],[f12931])).
% 15.26/3.43 thf(f12931,plain,(
% 15.26/3.43 ($false = $true) | (~spl2_1296 | ~spl2_1299)),
% 15.26/3.43 inference(forward_demodulation,[status(thm)],[f10771,f10784])).
% 15.26/3.43 thf(f10784,plain,(
% 15.26/3.43 (powersetE1 = $false) | ~spl2_1299),
% 15.26/3.43 inference(avatar_component_clause,[status(thm)],[f10782])).
% 15.26/3.43 thf(f10782,definition,(
% 15.26/3.43 spl2_1299 <=> (powersetE1 = $false)),
% 15.26/3.43 introduced(definition,[new_symbols(naming,[spl2_1299])],[avatar_definition])).
% 15.26/3.43 thf(f10771,plain,(
% 15.26/3.43 (powersetE1 = $true) | ~spl2_1296),
% 15.26/3.43 inference(avatar_component_clause,[status(thm)],[f10769])).
% 15.26/3.43 thf(f10769,definition,(
% 15.26/3.43 spl2_1296 <=> (powersetE1 = $true)),
% 15.26/3.43 introduced(definition,[new_symbols(naming,[spl2_1296])],[avatar_definition])).
% 15.26/3.43 thf(f12757,plain,(
% 15.26/3.43 ~spl2_1195 | ~spl2_1200 | ~spl2_1298),
% 15.26/3.43 inference(avatar_contradiction_clause,[status(thm)],[f12756])).
% 15.26/3.43 thf(f12756,plain,(
% 15.26/3.43 $false | (~spl2_1195 | ~spl2_1200 | ~spl2_1298)),
% 15.26/3.43 inference(trivial_inequality_removal,[status(thm)],[f12737])).
% 15.26/3.43 thf(f12737,plain,(
% 15.26/3.43 ($false = $true) | (~spl2_1195 | ~spl2_1200 | ~spl2_1298)),
% 15.26/3.43 inference(backward_demodulation,[status(thm)],[f12325,f12693])).
% 15.26/3.43 thf(f12693,plain,(
% 15.26/3.43 ( ! [X0 : $i] : (($false = (in @ sK749 @ (binintersect @ X0 @ sK1)))) ) | (~spl2_1195 | ~spl2_1200 | ~spl2_1298)),
% 15.26/3.43 inference(trivial_inequality_removal,[status(thm)],[f12690])).
% 15.26/3.43 thf(f12690,plain,(
% 15.26/3.43 ( ! [X0 : $i] : (($false = $true) | ($false = (in @ sK749 @ (binintersect @ X0 @ sK1)))) ) | (~spl2_1195 | ~spl2_1200 | ~spl2_1298)),
% 15.26/3.43 inference(superposition,[status(thm)],[f12324,f10331])).
% 15.26/3.43 thf(f10331,plain,(
% 15.26/3.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X2 @ X3) = $true) | ($false = (in @ X2 @ (binintersect @ X1 @ X3)))) ) | ~spl2_1200),
% 15.26/3.43 inference(avatar_component_clause,[status(thm)],[f10330])).
% 15.26/3.43 thf(f10330,definition,(
% 15.26/3.43 spl2_1200 <=> ! [X2 : $i,X1 : $i,X3 : $i] : (($false = (in @ X2 @ (binintersect @ X1 @ X3))) | ((in @ X2 @ X3) = $true))),
% 15.26/3.43 introduced(definition,[new_symbols(naming,[spl2_1200])],[avatar_definition])).
% 15.26/3.43 thf(f12324,plain,(
% 15.26/3.43 ($false = (in @ sK749 @ sK1)) | (~spl2_1195 | ~spl2_1298)),
% 15.26/3.43 inference(binary_proxy_clausification,[status(thm)],[f12323])).
% 15.26/3.43 thf(f12323,plain,(
% 15.26/3.43 ($false = ((in @ sK749 @ (binintersect @ sK0 @ sK1)) => (in @ sK749 @ sK1))) | (~spl2_1195 | ~spl2_1298)),
% 15.26/3.43 inference(beta_eta_normalization,[status(thm)],[f12322])).
% 15.26/3.43 thf(f12322,plain,(
% 15.26/3.43 ($false = ((^[Y0 : $i]: ((in @ Y0 @ (binintersect @ sK0 @ sK1)) => (in @ Y0 @ sK1))) @ sK749)) | (~spl2_1195 | ~spl2_1298)),
% 15.26/3.43 inference(sigma_clausification,[status(thm)],[f12321])).
% 15.26/3.43 thf(f12321,plain,(
% 15.26/3.43 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (binintersect @ sK0 @ sK1)) => (in @ Y0 @ sK1))))) | (~spl2_1195 | ~spl2_1298)),
% 15.26/3.43 inference(not_proxy_clausification,[status(thm)],[f12320])).
% 15.26/3.43 thf(f12320,plain,(
% 15.26/3.43 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (binintersect @ sK0 @ sK1)) => (in @ Y0 @ sK1)))))) | (~spl2_1195 | ~spl2_1298)),
% 15.26/3.43 inference(boolean_simplification,[status(thm)],[f12291])).
% 15.26/3.43 thf(f12291,plain,(
% 15.26/3.43 (($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (binintersect @ sK0 @ sK1)) => (in @ Y0 @ sK1))))) = $true) | (~spl2_1195 | ~spl2_1298)),
% 15.26/3.43 inference(superposition,[status(thm)],[f10309,f11250])).
% 15.26/3.43 thf(f11250,plain,(
% 15.26/3.43 ($false = (in @ (binintersect @ sK0 @ sK1) @ (powerset @ sK1))) | ~spl2_1298),
% 15.26/3.43 inference(trivial_inequality_removal,[status(thm)],[f11247])).
% 15.26/3.43 thf(f11247,plain,(
% 15.26/3.43 ($true != $true) | ($false = (in @ (binintersect @ sK0 @ sK1) @ (powerset @ sK1))) | ~spl2_1298),
% 15.26/3.43 inference(superposition,[status(thm)],[f464,f10780])).
% 15.26/3.43 thf(f10780,plain,(
% 15.26/3.43 ( ! [X2 : $i,X1 : $i] : (($true = (subset @ X2 @ X1)) | ($false = (in @ X2 @ (powerset @ X1)))) ) | ~spl2_1298),
% 15.26/3.43 inference(avatar_component_clause,[status(thm)],[f10779])).
% 15.26/3.43 thf(f10779,definition,(
% 15.26/3.43 spl2_1298 <=> ! [X2 : $i,X1 : $i] : (($true = (subset @ X2 @ X1)) | ($false = (in @ X2 @ (powerset @ X1))))),
% 15.26/3.43 introduced(definition,[new_symbols(naming,[spl2_1298])],[avatar_definition])).
% 15.26/3.43 thf(f464,plain,(
% 15.26/3.43 ((subset @ (binintersect @ sK0 @ sK1) @ sK1) != $true)),
% 15.26/3.43 inference(cnf_transformation,[status(thm)],[f348])).
% 15.26/3.43 thf(f348,plain,(
% 15.26/3.43 (omega__Cong = $true) & (setunion__Cong = $true) & (sepSubset = $true) & (nonemptyE1 = $true) & (noeltsimpempty = $true) & (foundationAx = $true) & (vacuousDall = $true) & (powersetE = $true) & (notsubsetI = $true) & (setunionI = $true) & (setadjoinSub = $true) & (singletonsswitch = $true) & (binunionE = $true) & (dsetconstr__Cong = $true) & (subsetemptysetimpeq = $true) & (quantDeMorgan3 = $true) & (descr__Cong = $true) & (replAx = $true) & (setextsub = $true) & (sepInPowerset = $true) & (setadjoinSub2 = $true) & (emptyinPowerset = $true) & (binintersectSubset3 = $true) & (binunionLsub = $true) & (quantDeMorgan1 = $true) & (exuEu = $true) & (upairsetE = $true) & (dsetconstrEL = $true) & (subsetE = $true) & (binintersectSubset5 = $true) & (prop2setE = $true) & (prop2set2propI = $true) & (upairset2IR = $true) & (binintersectEL = $true) & (prop2setI = $true) & (setextAx = $true) & (setext = $true) & (exuE2 = $true) & (binintersectER = $true) & (notequalI1 = $true) & (notdexE = $true) & (powerset__Cong = $true) & (emptyE1 = $true) & (powersetI1 = $true) & (eqimpsubset2 = $true) & (binintersectLsub = $true) & ((subset @ (binintersect @ sK0 @ sK1) @ sK1) != $true) & (emptyInPowerset = $true) & (in__Cong = $true) & (exuE3u = $true) & (binunionIL = $true) & (binunionIR = $true) & (setunionAx = $true) & (disjointsetsI1 = $true) & (emptyI = $true) & (descrp = $true) & (dsetconstrI = $true) & (binunionRsub = $true) & (wellorderingAx = $true) & (exuI3 = $true) & (powersetAx = $true) & (eqinunit = $true) & (setadjoinAx = $true) & (setbeta = $true) & (subPowSU = $true) & (emptysetsubset = $true) & (powersetE1 = $true) & (exuI2 = $true) & (exuE1 = $true) & (subsetTrans = $true) & (notinsingleton = $true) & (nonemptyImpWitness = $true) & (upairsetIR = $true) & (setadjoinIL = $true) & (omegaIndAx = $true) & (setoftrueEq = $true) & (emptysetimpfalse = $true) & (quantDeMorgan4 = $true) & (subsetI1 = $true) & (omega0Ax = $true) & (subsetRefl = $true) & (subset2powerset = $true) & (setadjoinIR = $true) & (setadjoin__Cong = $true) & (setadjoinE = $true) & (binunionEcases = $true) & (notequalI2 = $true) & (setadjoinOr = $true) & (uniqinunit = $true) & (emptysetAx = $true) & (exuI1 = $true) & (notdallE = $true) & (upairsetIL = $true) & (inPowerset = $true) & (binintersectI = $true) & (powersetsubset = $true) & (nonemptyI1 = $true) & (quantDeMorgan2 = $true) & (emptysetE = $true) & (subsetI2 = $true) & (dsetconstrER = $true) & (powersetI = $true) & (eqimpsubset1 = $true) & (exuE3e = $true) & (setunionE = $true) & (emptyinunitempty = $true) & (subsetE2 = $true) & (emptyset__Cong = $true) & (omegaSAx = $true) & (notinemptyset = $true) & (exu__Cong = $true) & (inCongP = $true) & (binintersectSubset2 = $true) & (nonemptyI = $true)),
% 15.26/3.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f346,f347])).
% 15.26/3.43 thf(f347,plain,(
% 15.26/3.43 ? [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X0 @ X1) @ X1) != $true) => ((subset @ (binintersect @ sK0 @ sK1) @ sK1) != $true)),
% 15.26/3.43 introduced(definition,[],[choice_axiom])).
% 15.26/3.43 thf(f346,plain,(
% 15.26/3.43 (omega__Cong = $true) & (setunion__Cong = $true) & (sepSubset = $true) & (nonemptyE1 = $true) & (noeltsimpempty = $true) & (foundationAx = $true) & (vacuousDall = $true) & (powersetE = $true) & (notsubsetI = $true) & (setunionI = $true) & (setadjoinSub = $true) & (singletonsswitch = $true) & (binunionE = $true) & (dsetconstr__Cong = $true) & (subsetemptysetimpeq = $true) & (quantDeMorgan3 = $true) & (descr__Cong = $true) & (replAx = $true) & (setextsub = $true) & (sepInPowerset = $true) & (setadjoinSub2 = $true) & (emptyinPowerset = $true) & (binintersectSubset3 = $true) & (binunionLsub = $true) & (quantDeMorgan1 = $true) & (exuEu = $true) & (upairsetE = $true) & (dsetconstrEL = $true) & (subsetE = $true) & (binintersectSubset5 = $true) & (prop2setE = $true) & (prop2set2propI = $true) & (upairset2IR = $true) & (binintersectEL = $true) & (prop2setI = $true) & (setextAx = $true) & (setext = $true) & (exuE2 = $true) & (binintersectER = $true) & (notequalI1 = $true) & (notdexE = $true) & (powerset__Cong = $true) & (emptyE1 = $true) & (powersetI1 = $true) & (eqimpsubset2 = $true) & (binintersectLsub = $true) & ? [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X0 @ X1) @ X1) != $true) & (emptyInPowerset = $true) & (in__Cong = $true) & (exuE3u = $true) & (binunionIL = $true) & (binunionIR = $true) & (setunionAx = $true) & (disjointsetsI1 = $true) & (emptyI = $true) & (descrp = $true) & (dsetconstrI = $true) & (binunionRsub = $true) & (wellorderingAx = $true) & (exuI3 = $true) & (powersetAx = $true) & (eqinunit = $true) & (setadjoinAx = $true) & (setbeta = $true) & (subPowSU = $true) & (emptysetsubset = $true) & (powersetE1 = $true) & (exuI2 = $true) & (exuE1 = $true) & (subsetTrans = $true) & (notinsingleton = $true) & (nonemptyImpWitness = $true) & (upairsetIR = $true) & (setadjoinIL = $true) & (omegaIndAx = $true) & (setoftrueEq = $true) & (emptysetimpfalse = $true) & (quantDeMorgan4 = $true) & (subsetI1 = $true) & (omega0Ax = $true) & (subsetRefl = $true) & (subset2powerset = $true) & (setadjoinIR = $true) & (setadjoin__Cong = $true) & (setadjoinE = $true) & (binunionEcases = $true) & (notequalI2 = $true) & (setadjoinOr = $true) & (uniqinunit = $true) & (emptysetAx = $true) & (exuI1 = $true) & (notdallE = $true) & (upairsetIL = $true) & (inPowerset = $true) & (binintersectI = $true) & (powersetsubset = $true) & (nonemptyI1 = $true) & (quantDeMorgan2 = $true) & (emptysetE = $true) & (subsetI2 = $true) & (dsetconstrER = $true) & (powersetI = $true) & (eqimpsubset1 = $true) & (exuE3e = $true) & (setunionE = $true) & (emptyinunitempty = $true) & (subsetE2 = $true) & (emptyset__Cong = $true) & (omegaSAx = $true) & (notinemptyset = $true) & (exu__Cong = $true) & (inCongP = $true) & (binintersectSubset2 = $true) & (nonemptyI = $true)),
% 15.26/3.43 inference(flattening,[status(thm)],[f345])).
% 15.26/3.43 thf(f345,plain,(
% 15.26/3.43 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X0 @ X1) @ X1) != $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)),
% 15.26/3.43 inference(ennf_transformation,[status(thm)],[f203])).
% 15.26/3.43 thf(f203,plain,(
% 15.26/3.43 ~((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) => ! [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X0 @ X1) @ X1) = $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 15.26/3.43 inference(fool_elimination,[status(thm)],[f202])).
% 15.26/3.43 thf(f202,plain,(
% 15.26/3.43 ~(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 => ! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X0 @ X1) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 15.26/3.43 inference(rectify,[status(thm)],[f117])).
% 15.26/3.43 thf(f117,negated_conjecture,(
% 15.26/3.43 ~(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 => ! [X3 : $i,X4 : $i] : (subset @ (binintersect @ X3 @ X4) @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 15.26/3.43 inference(negated_conjecture,[status(cth)],[f116])).
% 15.26/3.43 thf(f116,conjecture,(
% 15.26/3.43 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 => ! [X3 : $i,X4 : $i] : (subset @ (binintersect @ X3 @ X4) @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 15.26/3.43 file('/export/starexec/sandbox/tmp/tmp.osm1bNkGRD/DTF2THF_7106.p',binintersectRsub)).
% 15.26/3.43 thf(f10309,plain,(
% 15.26/3.43 ( ! [X2 : $i,X1 : $i] : ((((in @ X2 @ (powerset @ X1)) = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1))))) = $true)) ) | ~spl2_1195),
% 15.26/3.43 inference(avatar_component_clause,[status(thm)],[f10308])).
% 15.26/3.43 thf(f10308,definition,(
% 15.26/3.43 spl2_1195 <=> ! [X2 : $i,X1 : $i] : (((in @ X2 @ (powerset @ X1)) = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1))))) = $true)),
% 15.26/3.43 introduced(definition,[new_symbols(naming,[spl2_1195])],[avatar_definition])).
% 15.26/3.43 thf(f12325,plain,(
% 15.26/3.43 ($true = (in @ sK749 @ (binintersect @ sK0 @ sK1))) | (~spl2_1195 | ~spl2_1298)),
% 15.26/3.43 inference(binary_proxy_clausification,[status(thm)],[f12323])).
% 15.26/3.43 thf(f12655,plain,(
% 15.26/3.43 ~spl2_1196 | ~spl2_1199),
% 15.26/3.43 inference(avatar_contradiction_clause,[status(thm)],[f12654])).
% 15.26/3.43 thf(f12654,plain,(
% 15.26/3.43 $false | (~spl2_1196 | ~spl2_1199)),
% 15.26/3.43 inference(trivial_inequality_removal,[status(thm)],[f12653])).
% 15.26/3.43 thf(f12653,plain,(
% 15.26/3.43 ($false = $true) | (~spl2_1196 | ~spl2_1199)),
% 15.26/3.43 inference(forward_demodulation,[status(thm)],[f10314,f10328])).
% 15.26/3.43 thf(f10328,plain,(
% 15.26/3.43 (binintersectER = $false) | ~spl2_1199),
% 15.26/3.43 inference(avatar_component_clause,[status(thm)],[f10326])).
% 15.26/3.43 thf(f10326,definition,(
% 15.26/3.43 spl2_1199 <=> (binintersectER = $false)),
% 15.26/3.43 introduced(definition,[new_symbols(naming,[spl2_1199])],[avatar_definition])).
% 15.26/3.43 thf(f10314,plain,(
% 15.26/3.43 (binintersectER = $true) | ~spl2_1196),
% 15.26/3.43 inference(avatar_component_clause,[status(thm)],[f10312])).
% 15.26/3.43 thf(f10312,definition,(
% 15.26/3.43 spl2_1196 <=> (binintersectER = $true)),
% 15.26/3.43 introduced(definition,[new_symbols(naming,[spl2_1196])],[avatar_definition])).
% 15.26/3.43 thf(f11034,plain,(
% 15.26/3.43 ~spl2_1192 | ~spl2_1194),
% 15.26/3.43 inference(avatar_contradiction_clause,[status(thm)],[f11033])).
% 15.26/3.43 thf(f11033,plain,(
% 15.26/3.43 $false | (~spl2_1192 | ~spl2_1194)),
% 15.26/3.43 inference(trivial_inequality_removal,[status(thm)],[f11032])).
% 15.26/3.43 thf(f11032,plain,(
% 15.26/3.43 ($false = $true) | (~spl2_1192 | ~spl2_1194)),
% 15.26/3.43 inference(backward_demodulation,[status(thm)],[f10297,f10306])).
% 15.26/3.43 thf(f10306,plain,(
% 15.26/3.43 (powersetAx = $false) | ~spl2_1194),
% 15.26/3.43 inference(avatar_component_clause,[status(thm)],[f10304])).
% 15.26/3.43 thf(f10304,definition,(
% 15.26/3.43 spl2_1194 <=> (powersetAx = $false)),
% 15.26/3.43 introduced(definition,[new_symbols(naming,[spl2_1194])],[avatar_definition])).
% 15.26/3.43 thf(f10297,plain,(
% 15.26/3.43 (powersetAx = $true) | ~spl2_1192),
% 15.26/3.43 inference(avatar_component_clause,[status(thm)],[f10295])).
% 15.26/3.43 thf(f10295,definition,(
% 15.26/3.43 spl2_1192 <=> (powersetAx = $true)),
% 15.26/3.43 introduced(definition,[new_symbols(naming,[spl2_1192])],[avatar_definition])).
% 15.26/3.43 thf(f10963,plain,(
% 15.26/3.43 spl2_1196),
% 15.26/3.43 inference(avatar_split_clause,[status(thm)],[f472,f10312])).
% 15.26/3.43 thf(f472,plain,(
% 15.26/3.43 (binintersectER = $true)),
% 15.26/3.43 inference(cnf_transformation,[status(thm)],[f348])).
% 15.26/3.43 thf(f10954,plain,(
% 15.26/3.43 spl2_1192),
% 15.26/3.43 inference(avatar_split_clause,[status(thm)],[f450,f10295])).
% 15.26/3.43 thf(f450,plain,(
% 15.26/3.43 (powersetAx = $true)),
% 15.26/3.43 inference(cnf_transformation,[status(thm)],[f348])).
% 15.26/3.43 thf(f10952,plain,(
% 15.26/3.43 spl2_1296),
% 15.26/3.43 inference(avatar_split_clause,[status(thm)],[f444,f10769])).
% 15.26/3.43 thf(f444,plain,(
% 15.26/3.43 (powersetE1 = $true)),
% 15.26/3.43 inference(cnf_transformation,[status(thm)],[f348])).
% 15.26/3.43 thf(f10785,plain,(
% 15.26/3.43 spl2_1298 | spl2_1299),
% 15.26/3.43 inference(avatar_split_clause,[status(thm)],[f691,f10782,f10779])).
% 15.26/3.43 thf(f691,plain,(
% 15.26/3.43 ( ! [X2 : $i,X1 : $i] : ((powersetE1 = $false) | ($true = (subset @ X2 @ X1)) | ($false = (in @ X2 @ (powerset @ X1)))) )),
% 15.26/3.43 inference(binary_proxy_clausification,[status(thm)],[f690])).
% 15.26/3.43 thf(f690,plain,(
% 15.26/3.43 ( ! [X2 : $i,X1 : $i] : ((((in @ X2 @ (powerset @ X1)) => (subset @ X2 @ X1)) = $true) | (powersetE1 = $false)) )),
% 15.26/3.43 inference(beta_eta_normalization,[status(thm)],[f689])).
% 15.26/3.43 thf(f689,plain,(
% 15.26/3.43 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (subset @ Y0 @ X1))) @ X2) = $true) | (powersetE1 = $false)) )),
% 15.26/3.43 inference(pi_clausification,[status(thm)],[f688])).
% 15.26/3.43 thf(f688,plain,(
% 15.26/3.43 ( ! [X1 : $i] : ((powersetE1 = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (subset @ Y0 @ X1)))))) )),
% 15.26/3.43 inference(beta_eta_normalization,[status(thm)],[f687])).
% 15.26/3.43 thf(f687,plain,(
% 15.26/3.43 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0))))) @ X1) = $true) | (powersetE1 = $false)) )),
% 15.26/3.43 inference(pi_clausification,[status(thm)],[f686])).
% 15.26/3.43 thf(f686,plain,(
% 15.26/3.43 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) = $true) | (powersetE1 = $false)),
% 15.26/3.43 inference(binary_proxy_clausification,[status(thm)],[f353])).
% 15.26/3.43 thf(f353,plain,(
% 15.26/3.43 (powersetE1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))))),
% 15.26/3.43 inference(cnf_transformation,[status(thm)],[f253])).
% 15.26/3.43 thf(f253,plain,(
% 15.26/3.43 (powersetE1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))))),
% 15.26/3.43 inference(fool_elimination,[status(thm)],[f252])).
% 15.26/3.43 thf(f252,plain,(
% 15.26/3.43 (powersetE1 = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => (subset @ X0 @ X1)))),
% 15.26/3.43 inference(rectify,[status(thm)],[f96])).
% 15.26/3.43 thf(f96,axiom,(
% 15.26/3.43 (powersetE1 = ! [X4 : $i,X3 : $i] : ((in @ X4 @ (powerset @ X3)) => (subset @ X4 @ X3)))),
% 15.26/3.43 file('/export/starexec/sandbox/tmp/tmp.osm1bNkGRD/DTF2THF_7106.p',powersetE1)).
% 15.26/3.43 thf(f10332,plain,(
% 15.26/3.43 spl2_1199 | spl2_1200),
% 15.26/3.43 inference(avatar_split_clause,[status(thm)],[f1031,f10330,f10326])).
% 15.26/3.43 thf(f1031,plain,(
% 15.26/3.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((binintersectER = $false) | ($false = (in @ X2 @ (binintersect @ X1 @ X3))) | ((in @ X2 @ X3) = $true)) )),
% 15.26/3.43 inference(binary_proxy_clausification,[status(thm)],[f1030])).
% 15.26/3.43 thf(f1030,plain,(
% 15.26/3.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((binintersectER = $false) | (((in @ X2 @ (binintersect @ X1 @ X3)) => (in @ X2 @ X3)) = $true)) )),
% 15.26/3.43 inference(beta_eta_normalization,[status(thm)],[f1029])).
% 15.26/3.43 thf(f1029,plain,(
% 15.26/3.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((binintersectER = $false) | (((^[Y0 : $i]: ((in @ X2 @ (binintersect @ X1 @ Y0)) => (in @ X2 @ Y0))) @ X3) = $true)) )),
% 15.26/3.43 inference(pi_clausification,[status(thm)],[f1028])).
% 15.26/3.43 thf(f1028,plain,(
% 15.26/3.43 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ (binintersect @ X1 @ Y0)) => (in @ X2 @ Y0)))) = $true) | (binintersectER = $false)) )),
% 15.26/3.43 inference(beta_eta_normalization,[status(thm)],[f1027])).
% 15.26/3.43 thf(f1027,plain,(
% 15.26/3.43 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (binintersect @ X1 @ Y1)) => (in @ Y0 @ Y1))))) @ X2)) | (binintersectER = $false)) )),
% 15.26/3.43 inference(pi_clausification,[status(thm)],[f1026])).
% 15.26/3.43 thf(f1026,plain,(
% 15.26/3.43 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (binintersect @ X1 @ Y1)) => (in @ Y0 @ Y1))))))) | (binintersectER = $false)) )),
% 15.26/3.43 inference(beta_eta_normalization,[status(thm)],[f1025])).
% 15.26/3.43 thf(f1025,plain,(
% 15.26/3.43 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y2))))))) @ X1) = $true) | (binintersectER = $false)) )),
% 15.26/3.43 inference(pi_clausification,[status(thm)],[f1024])).
% 15.26/3.43 thf(f1024,plain,(
% 15.26/3.43 (binintersectER = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y2)))))))) = $true)),
% 15.26/3.43 inference(binary_proxy_clausification,[status(thm)],[f570])).
% 15.26/3.43 thf(f570,plain,(
% 15.26/3.43 (binintersectER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y2)))))))))),
% 15.26/3.43 inference(cnf_transformation,[status(thm)],[f288])).
% 15.26/3.43 thf(f288,plain,(
% 15.26/3.43 (binintersectER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y2)))))))))),
% 15.26/3.43 inference(fool_elimination,[status(thm)],[f287])).
% 15.26/3.43 thf(f287,plain,(
% 15.26/3.43 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (binintersect @ X2 @ X0)) => (in @ X1 @ X0)) = binintersectER)),
% 15.26/3.43 inference(rectify,[status(thm)],[f114])).
% 15.26/3.43 thf(f114,axiom,(
% 15.26/3.43 (! [X4 : $i,X1 : $i,X3 : $i] : ((in @ X1 @ (binintersect @ X3 @ X4)) => (in @ X1 @ X4)) = binintersectER)),
% 15.26/3.43 file('/export/starexec/sandbox/tmp/tmp.osm1bNkGRD/DTF2THF_7106.p',binintersectER)).
% 15.26/3.43 thf(f10310,plain,(
% 15.26/3.43 spl2_1194 | spl2_1195),
% 15.26/3.43 inference(avatar_split_clause,[status(thm)],[f1045,f10308,f10304])).
% 15.26/3.43 thf(f1045,plain,(
% 15.26/3.43 ( ! [X2 : $i,X1 : $i] : ((((in @ X2 @ (powerset @ X1)) = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1))))) = $true) | (powersetAx = $false)) )),
% 15.26/3.43 inference(beta_eta_normalization,[status(thm)],[f1044])).
% 15.26/3.43 thf(f1044,plain,(
% 15.26/3.43 ( ! [X2 : $i,X1 : $i] : ((powersetAx = $false) | (((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) = (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))))) @ X2) = $true)) )),
% 15.26/3.43 inference(pi_clausification,[status(thm)],[f1043])).
% 15.26/3.43 thf(f1043,plain,(
% 15.26/3.43 ( ! [X1 : $i] : ((powersetAx = $false) | ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) = (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1))))))) = $true)) )),
% 15.26/3.43 inference(beta_eta_normalization,[status(thm)],[f1042])).
% 15.26/3.43 thf(f1042,plain,(
% 15.26/3.43 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))))))) @ X1) = $true) | (powersetAx = $false)) )),
% 15.26/3.43 inference(pi_clausification,[status(thm)],[f1041])).
% 15.26/3.43 thf(f1041,plain,(
% 15.26/3.43 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))))))))) | (powersetAx = $false)),
% 15.26/3.43 inference(binary_proxy_clausification,[status(thm)],[f521])).
% 15.26/3.43 thf(f521,plain,(
% 15.26/3.43 (powersetAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))))),
% 15.26/3.43 inference(cnf_transformation,[status(thm)],[f169])).
% 15.26/3.43 thf(f169,plain,(
% 15.26/3.43 (powersetAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))))),
% 15.26/3.43 inference(fool_elimination,[status(thm)],[f168])).
% 15.26/3.43 thf(f168,plain,(
% 15.26/3.43 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) <=> ! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1))) = powersetAx)),
% 15.26/3.43 inference(rectify,[status(thm)],[f5])).
% 15.26/3.43 thf(f5,axiom,(
% 15.26/3.43 (! [X4 : $i,X3 : $i] : ((in @ X4 @ (powerset @ X3)) <=> ! [X1 : $i] : ((in @ X1 @ X4) => (in @ X1 @ X3))) = powersetAx)),
% 15.26/3.43 file('/export/starexec/sandbox/tmp/tmp.osm1bNkGRD/DTF2THF_7106.p',powersetAx)).
% 15.26/3.43 % SZS output end Proof for DTF2THF_7106
% 15.26/3.43 % (7496)------------------------------
% 15.26/3.43 % (7496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.26/3.43 % (7496)Termination reason: Refutation
% 15.26/3.43
% 15.26/3.43 % (7496)Memory used [KB]: 13688
% 15.26/3.43 % (7496)Time elapsed: 0.336 s
% 15.26/3.43 % (7496)Instructions burned: 1087 (million)
% 15.26/3.43 % (7496)------------------------------
% 15.26/3.43 % (7496)------------------------------
% 15.26/3.43 % (7379)Success in time 1.968 s
%------------------------------------------------------------------------------